Subgroups — #14244144

Order 1792.

1660 conjugacy classes of subgroups.

The subgroup lattice has 1586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11743667	C₂	1	1	yes	maximal, characteristic
2	#11743570	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3242	C₂	1	1	yes	maximal, characteristic, complemented
4	#11740926	C₂	1	1	yes	maximal, characteristic, complemented
5	#11740892	C₂	1	1	yes	maximal, characteristic
6	#11739414	C₂	1	1	yes	maximal, characteristic, complemented
7	#11739411	C₂	1	1	yes	maximal, characteristic, complemented
8	#11739375	C₂	1	1	yes	maximal, characteristic, complemented
9	#11739358	C₂	1	1	yes	maximal, characteristic, complemented
10	#11739177	C₂	1	1	yes	maximal, characteristic, complemented
11	#11739177	C₂	1	1	yes	maximal, characteristic, complemented
12	#11739068	C₂	1	1	yes	maximal, characteristic, complemented
13	#11739065	C₂	1	1	yes	maximal, characteristic, complemented
14	#11738947	C₂	1	1	yes	maximal, characteristic, complemented
15	#11738945	C₂	1	1	yes	maximal, characteristic, complemented
16	#11738943	C₂	1	1	yes	maximal, characteristic
17	#11738943	C₂	1	1	yes	maximal, characteristic
18	#11738905	C₂	1	1	yes	maximal, characteristic, complemented
19	#11738899	C₂	1	1	yes	maximal, characteristic
20	#11738867	C₂	1	1	yes	maximal, characteristic, complemented
21	#11738857	C₂	1	1	yes	maximal, characteristic
22	#11738711	C₂	1	1	yes	maximal, characteristic, complemented
23	#11738666	C₂	1	1	yes	maximal, characteristic, complemented
24	#11738664	C₂	1	1	yes	maximal, characteristic, complemented
25	#11738664	C₂	1	1	yes	maximal, characteristic, complemented
26	#11738580	C₂	1	1	yes	maximal, characteristic, complemented
27	#11738548	C₂	1	1	yes	maximal, characteristic, complemented
28	#11738482	C₂	1	1	yes	maximal, characteristic, complemented
29	#11738453	C₂	1	1	yes	maximal, characteristic, complemented
30	#11736832	C₂	1	1	yes	maximal, characteristic
31	#11736804	C₂	1	1	yes	maximal, characteristic, complemented
32	C₇×#544	C₂²	1	1	yes	characteristic
33	C₇×#541	C₂²	1	1	yes	characteristic
34	#90421	—	2	1	no	—
35	#90421	C₂²	1	1	yes	characteristic
36	#90421	C₂²	1	1	yes	characteristic
37	#90418	—	2	1	no	—
38	#90418	C₂²	1	1	yes	characteristic
39	#90418	C₂²	1	1	yes	characteristic
40	#90412	C₂²	1	1	yes	characteristic, complemented
41	#90412	C₂²	1	1	yes	characteristic, complemented
42	#90392	—	2	1	no	—
43	#90392	—	2	1	no	—
44	#90392	—	2	1	no	—
45	#90392	—	2	1	no	—
46	#90381	—	2	1	no	—
47	#90381	—	2	1	no	—
48	#90381	C₂²	1	1	yes	characteristic
49	#90381	C₂²	1	1	yes	characteristic
50	#90381	C₂²	1	1	yes	characteristic
51	#90381	C₂²	1	1	yes	characteristic
52	C₇⋊#564	—	2	1	no	—
53	C₇⋊#564	—	2	1	no	—
54	#90376	—	2	1	no	—
55	#90376	—	2	1	no	—
56	#90376	C₂²	1	1	yes	characteristic, complemented
57	#90376	C₂²	1	1	yes	characteristic, complemented
58	#90325	—	2	1	no	—
59	#90325	—	2	1	no	—
60	D₇×C₂²⋊Q₈	—	2	1	no	—
61	D₇×C₂²⋊Q₈	—	2	1	no	—
62	#90316	C₂²	1	1	yes	characteristic
63	#90316	C₂²	1	1	yes	characteristic
64	#90313	C₂²	1	1	yes	characteristic
65	#90313	C₂²	1	1	yes	characteristic
66	#90260	C₂²	1	1	yes	characteristic, complemented
67	#90260	C₂²	1	1	yes	characteristic, complemented
68	#90258	C₂²	1	1	yes	characteristic, complemented
69	#90258	C₂²	1	1	yes	characteristic, complemented
70	#90212	C₂²	1	1	yes	characteristic
71	#90212	C₂²	1	1	yes	characteristic
72	#90209	C₂²	1	1	yes	characteristic
73	#90208	C₂²	1	1	yes	characteristic
74	#90208	C₂²	1	1	yes	characteristic
75	C₂×#6456	C₂²	1	1	yes	characteristic
76	#90191	C₂²	1	1	yes	characteristic
77	C₇×#501	C₂²	1	1	yes	characteristic, complemented
78	C₇×#499	C₂²	1	1	yes	characteristic, complemented
79	C₇×#491	C₂²	1	1	yes	characteristic, complemented
80	C₇×#487	C₂²	1	1	yes	characteristic, complemented
81	C₇×#485	C₂²	1	1	yes	characteristic
82	C₇×#485	C₂²	1	1	yes	characteristic
83	C₇×#484	C₂²	1	1	yes	characteristic
84	C₇×#483	C₂²	1	1	yes	characteristic
85	C₇×#479	C₂²	1	1	yes	characteristic, complemented
86	C₇×#479	C₂²	1	1	yes	characteristic, complemented
87	C₇×#477	C₂²	1	1	yes	characteristic, complemented
88	C₇×#475	C₂²	1	1	yes	characteristic, complemented
89	C₇×#433	C₂²	1	1	yes	characteristic
90	#89866	C₂²	1	1	yes	characteristic, complemented
91	#89865	C₂²	1	1	yes	characteristic, complemented
92	#89863	C₂²	1	1	yes	characteristic, complemented
93	#89855	C₂²	1	1	yes	characteristic
94	#89855	C₂²	1	1	yes	characteristic
95	#89852	C₂²	1	1	yes	characteristic, complemented
96	#89841	C₂²	1	1	yes	characteristic, complemented
97	#89838	C₂²	1	1	yes	characteristic
98	#89838	C₂²	1	1	yes	characteristic
99	#89836	C₂²	1	1	yes	characteristic, complemented
100	#89835	C₂²	1	1	yes	characteristic, complemented
101	#89835	C₂²	1	1	yes	characteristic, complemented
102	#89818	C₂²	1	1	yes	characteristic
103	#89818	C₂²	1	1	yes	characteristic
104	#89817	C₂²	1	1	yes	characteristic
105	#89817	C₂²	1	1	yes	characteristic
106	#89798	C₂²	1	1	yes	characteristic
107	#89798	C₂²	1	1	yes	characteristic
108	C₄×#1143	C₂²	1	1	yes	characteristic
109	C₄×#1143	C₂²	1	1	yes	characteristic
110	#89772	C₂²	1	1	yes	characteristic
111	#89768	C₂²	1	1	yes	characteristic
112	#89768	C₂²	1	1	yes	characteristic
113	#89743	C₂²	1	1	yes	characteristic
114	#89742	C₂²	1	1	yes	characteristic
115	#89663	C₂²	1	1	yes	characteristic
116	#89663	C₂²	1	1	yes	characteristic
117	#89662	C₂²	1	1	yes	characteristic
118	#89662	C₂²	1	1	yes	characteristic
119	#89661	C₂²	1	1	yes	characteristic
120	#89661	C₂²	1	1	yes	characteristic
121	#89661	C₂²	1	1	yes	characteristic
122	#89661	C₂²	1	1	yes	characteristic
123	#89650	C₂²	1	1	yes	characteristic, complemented
124	#89649	C₂²	1	1	yes	characteristic, complemented
125	#89649	C₂²	1	1	yes	characteristic, complemented
126	#89648	C₂²	1	1	yes	characteristic, complemented
127	#89648	C₂²	1	1	yes	characteristic, complemented
128	#89647	C₂²	1	1	yes	characteristic, complemented
129	#89647	C₂²	1	1	yes	characteristic, complemented
130	#89646	C₂²	1	1	yes	characteristic, complemented
131	#89643	C₂²	1	1	yes	characteristic
132	#89643	C₂²	1	1	yes	characteristic
133	#89642	C₂²	1	1	yes	characteristic
134	#89642	C₂²	1	1	yes	characteristic
135	#89630	C₂²	1	1	yes	characteristic, complemented
136	#89629	C₂²	1	1	yes	characteristic, complemented
137	#89629	C₂²	1	1	yes	characteristic, complemented
138	#89628	C₂²	1	1	yes	characteristic, complemented
139	#89628	C₂²	1	1	yes	characteristic, complemented
140	#89627	C₂²	1	1	yes	characteristic, complemented
141	#89626	C₂²	1	1	yes	characteristic, complemented
142	#89626	C₂²	1	1	yes	characteristic, complemented
143	#89624	C₂²	1	1	yes	characteristic
144	#89624	C₂²	1	1	yes	characteristic
145	#89624	C₂²	1	1	yes	characteristic
146	#89624	C₂²	1	1	yes	characteristic
147	#89619	C₂²	1	1	yes	characteristic
148	#89619	C₂²	1	1	yes	characteristic
149	#89613	C₂²	1	1	yes	characteristic
150	#89613	C₂²	1	1	yes	characteristic
151	#89603	C₂²	1	1	yes	characteristic, complemented
152	#89602	C₂²	1	1	yes	characteristic, complemented
153	#89600	C₂²	1	1	yes	characteristic, complemented
154	#89600	C₂²	1	1	yes	characteristic, complemented
155	#89590	C₂²	1	1	yes	characteristic
156	#89590	C₂²	1	1	yes	characteristic
157	#89590	C₂²	1	1	yes	characteristic
158	#89590	C₂²	1	1	yes	characteristic
159	#89590	C₂²	1	1	yes	characteristic
160	#89590	C₂²	1	1	yes	characteristic
161	#89590	C₂²	1	1	yes	characteristic
162	#89590	C₂²	1	1	yes	characteristic
163	#89589	C₂²	1	1	yes	characteristic
164	#89589	C₂²	1	1	yes	characteristic
165	#89589	C₂²	1	1	yes	characteristic
166	#89589	C₂²	1	1	yes	characteristic
167	#89571	C₂²	1	1	yes	characteristic, complemented
168	#89571	C₂²	1	1	yes	characteristic, complemented
169	#89569	C₂²	1	1	yes	characteristic, complemented
170	#89569	C₂²	1	1	yes	characteristic, complemented
171	#89569	C₂²	1	1	yes	characteristic, complemented
172	#89569	C₂²	1	1	yes	characteristic, complemented
173	#89568	C₂²	1	1	yes	characteristic, complemented
174	#89568	C₂²	1	1	yes	characteristic, complemented
175	#89566	C₂²	1	1	yes	characteristic, complemented
176	#89566	C₂²	1	1	yes	characteristic, complemented
177	#89564	C₂²	1	1	yes	characteristic, complemented
178	#89564	C₂²	1	1	yes	characteristic, complemented
179	#89564	C₂²	1	1	yes	characteristic, complemented
180	#89564	C₂²	1	1	yes	characteristic, complemented
181	#89563	C₂²	1	1	yes	characteristic, complemented
182	#89563	C₂²	1	1	yes	characteristic, complemented
183	#89560	C₂²	1	1	yes	characteristic
184	#89560	C₂²	1	1	yes	characteristic
185	#89560	C₂²	1	1	yes	characteristic
186	#89560	C₂²	1	1	yes	characteristic
187	#89503	C₂²	1	1	yes	characteristic
188	#89503	C₂²	1	1	yes	characteristic
189	#89495	C₂²	1	1	yes	characteristic
190	#89495	C₂²	1	1	yes	characteristic
191	#89492	C₂²	1	1	yes	characteristic
192	#89492	C₂²	1	1	yes	characteristic
193	#89491	C₂²	1	1	yes	characteristic
194	#89490	C₂²	1	1	yes	characteristic
195	#89482	C₂²	1	1	yes	characteristic
196	#89482	C₂²	1	1	yes	characteristic
197	#89473	C₂²	1	1	yes	characteristic, complemented
198	#89473	C₂²	1	1	yes	characteristic, complemented
199	C₄×#1132	C₂²	1	1	yes	characteristic
200	C₄×#1132	C₂²	1	1	yes	characteristic
201	#89451	C₂²	1	1	yes	characteristic, complemented
202	C₈×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
203	#61848	—	7	1	no	maximal, Sylow
204	C₂×Q₈×D₇	—	2	1	no	—
205	C₂×Q₈×D₇	—	2	1	no	—
206	C₂²×D₂₈	C₂³	1	1	yes	characteristic
207	C₂²×C₄×D₇	—	2	1	no	—
208	C₇×C₄⋊Q₈	—	2	1	no	—
209	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
211	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
212	C₇×#126	—	2	1	no	—
213	C₇×#126	—	2	1	no	—
214	C₇×#125	—	2	1	no	—
215	C₇×#125	—	2	1	no	—
216	C₇×#125	—	2	1	no	—
217	C₇×#125	C₂³	1	1	yes	characteristic
218	C₇×#125	C₂³	1	1	yes	characteristic
219	C₇×#125	C₂³	1	1	yes	characteristic
220	C₇×C₂²⋊Q₈	—	2	1	no	—
221	C₇×C₂²⋊Q₈	—	2	1	no	—
222	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
225	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
226	C₇×#117	C₂³	1	1	yes	characteristic
227	C₇×#117	C₂³	1	1	yes	characteristic
228	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	#6509	—	2	1	no	—
230	#6509	—	2	1	no	—
231	#6509	—	2	1	no	—
232	#6509	—	2	1	no	—
233	#6509	—	2	1	no	—
234	#6509	—	2	1	no	—
235	Q₈×Dic₇	C₂³	1	1	yes	characteristic
236	Q₈×Dic₇	C₂³	1	1	yes	characteristic
237	Q₈×Dic₇	C₂³	1	1	yes	characteristic
238	Q₈×Dic₇	C₂³	1	1	yes	characteristic
239	#6507	C₂³	1	1	yes	characteristic
240	#6507	C₂³	1	1	yes	characteristic
241	#6507	C₂³	1	1	yes	characteristic
242	#6507	C₂³	1	1	yes	characteristic
243	C₂×#1143	C₂³	1	1	yes	characteristic
244	C₂×#1143	C₂³	1	1	yes	characteristic
245	C₂×#1143	C₂³	1	1	yes	characteristic
246	C₂×#1143	C₂³	1	1	yes	characteristic
247	C₂×(C₂×D₇)⋊C₄	—	2	1	no	—
248	#6489	C₂³	1	1	yes	characteristic
249	#6489	C₂³	1	1	yes	characteristic
250	#6487	—	2	1	no	—
251	#6487	—	2	1	no	—
252	#6487	C₂³	1	1	yes	characteristic
253	#6487	C₂³	1	1	yes	characteristic
254	C₂×C₄×Dic₇	C₂³	1	1	yes	characteristic
255	C₂×#1132	C₂³	1	1	yes	characteristic
256	C₂×#1132	C₂³	1	1	yes	characteristic
257	C₂×#1132	C₂³	1	1	yes	characteristic
258	C₂×#1132	C₂³	1	1	yes	characteristic
259	#6460	—	2	1	no	—
260	#6460	—	2	1	no	—
261	#6460	—	2	1	no	—
262	#6460	—	2	1	no	—
263	#6460	—	2	1	no	—
264	#6460	—	2	1	no	—
265	#6459	—	2	1	no	—
266	#6459	—	2	1	no	—
267	#6459	—	2	1	no	—
268	#6459	—	2	1	no	—
269	#6459	—	2	1	no	—
270	#6459	—	2	1	no	—
271	#6459	—	2	1	no	—
272	#6459	—	2	1	no	—
273	#6459	—	2	1	no	—
274	#6459	—	2	1	no	—
275	#6459	—	2	1	no	—
276	#6459	—	2	1	no	—
277	#6456	—	2	1	no	—
278	#6456	—	2	1	no	—
279	#6456	—	2	1	no	—
280	#6456	—	2	1	no	—
281	#6456	C₂³	1	1	yes	characteristic
282	#6456	C₂³	1	1	yes	characteristic
283	#6456	C₂³	1	1	yes	characteristic
284	#6456	C₂³	1	1	yes	characteristic
285	#6456	C₂³	1	1	yes	characteristic
286	#6456	C₂³	1	1	yes	characteristic
287	#6456	C₂³	1	1	yes	characteristic
288	#6456	C₂³	1	1	yes	characteristic
289	D₇×C₄⋊C₄	—	2	1	no	—
290	D₇×C₄⋊C₄	—	2	1	no	—
291	D₇×C₄⋊C₄	—	2	1	no	—
292	D₇×C₄⋊C₄	—	2	1	no	—
293	D₇×C₄⋊C₄	—	2	1	no	—
294	D₇×C₄⋊C₄	—	2	1	no	—
295	#6453	—	2	1	no	—
296	#6453	—	2	1	no	—
297	#6453	—	2	1	no	—
298	#6453	—	2	1	no	—
299	#6453	—	2	1	no	—
300	#6453	—	2	1	no	—
301	#6453	—	2	1	no	—
302	#6453	D₄	1	1	yes	characteristic
303	#6453	D₄	1	1	yes	characteristic
304	#6453	C₂³	1	1	yes	characteristic
305	#6453	C₂³	1	1	yes	characteristic
306	#6453	C₂³	1	1	yes	characteristic
307	#6453	C₂³	1	1	yes	characteristic
308	#6453	C₂³	1	1	yes	characteristic
309	#6453	C₂³	1	1	yes	characteristic
310	#6452	—	2	1	no	—
311	#6452	—	2	1	no	—
312	#6452	—	2	1	no	—
313	#6452	—	2	1	no	—
314	#6452	—	2	1	no	—
315	#6452	—	2	1	no	—
316	#6452	—	2	1	no	—
317	#6452	—	2	1	no	—
318	#6452	—	2	1	no	—
319	#6452	—	2	1	no	—
320	#6452	—	2	1	no	—
321	#6452	—	2	1	no	—
322	#6452	—	2	1	no	—
323	#6452	—	2	1	no	—
324	#6452	—	2	1	no	—
325	#6452	—	2	1	no	—
326	#6452	—	2	1	no	—
327	#6452	—	2	1	no	—
328	#6451	—	2	1	no	—
329	#6451	—	2	1	no	—
330	#6451	—	2	1	no	—
331	#6451	—	2	1	no	—
332	#6451	—	2	1	no	—
333	#6451	D₄	1	1	yes	characteristic
334	#6451	D₄	1	1	yes	characteristic
335	#6451	C₂³	1	1	yes	characteristic
336	#6451	C₂³	1	1	yes	characteristic
337	#6451	C₂³	1	1	yes	characteristic
338	#6451	C₂³	1	1	yes	characteristic
339	#6451	C₂³	1	1	yes	characteristic
340	#6451	C₂³	1	1	yes	characteristic
341	#6450	—	2	1	no	—
342	#6450	—	2	1	no	—
343	#6450	—	2	1	no	—
344	#6450	—	2	1	no	—
345	#6450	—	2	1	no	—
346	#6450	—	2	1	no	—
347	#6450	C₂³	1	1	yes	characteristic
348	#6450	C₂³	1	1	yes	characteristic
349	#6450	C₂³	1	1	yes	characteristic
350	#6450	C₂³	1	1	yes	characteristic
351	D₇×C₂²⋊C₄	—	2	1	no	—
352	D₇×C₂²⋊C₄	—	2	1	no	—
353	D₇×C₂²⋊C₄	—	2	1	no	—
354	D₇×C₂²⋊C₄	—	2	1	no	—
355	#6442	—	2	1	no	—
356	#6442	—	2	1	no	—
357	#6442	—	2	1	no	—
358	#6442	—	2	1	no	—
359	#6442	—	2	1	no	—
360	#6442	—	2	1	no	—
361	#6441	—	2	1	no	—
362	#6441	—	2	1	no	—
363	#6441	—	2	1	no	—
364	#6441	—	2	1	no	—
365	#6441	D₄	1	1	yes	characteristic
366	#6441	D₄	1	1	yes	characteristic
367	#6441	D₄	1	1	yes	characteristic
368	#6441	D₄	1	1	yes	characteristic
369	#6440	—	2	1	no	—
370	#6440	—	2	1	no	—
371	C₄×D₂₈	—	2	1	no	—
372	C₄×D₂₈	—	2	1	no	—
373	C₄×D₂₈	C₂³	1	1	yes	characteristic
374	C₄×D₂₈	C₂³	1	1	yes	characteristic
375	C₄×D₂₈	C₂³	1	1	yes	characteristic
376	C₄×D₂₈	C₂³	1	1	yes	characteristic
377	#6433	—	2	1	no	—
378	#6433	—	2	1	no	—
379	#6433	—	2	1	no	—
380	#6433	—	2	1	no	—
381	#6433	C₂³	1	1	yes	characteristic
382	#6432	C₂³	1	1	yes	characteristic
383	C₄×Dic₁₄	—	2	1	no	—
384	C₄×Dic₁₄	—	2	1	no	—
385	C₄×Dic₁₄	—	2	1	no	—
386	C₄×Dic₁₄	—	2	1	no	—
387	C₄×Dic₁₄	—	2	1	no	—
388	C₄×Dic₁₄	—	2	1	no	—
389	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
390	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
391	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
392	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
393	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
394	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
395	C₇×#107	C₂³	1	1	yes	characteristic
396	C₇×#107	C₂³	1	1	yes	characteristic
397	C₇×#107	C₂³	1	1	yes	characteristic
398	C₇×#107	C₂³	1	1	yes	characteristic
399	C₇×#106	C₂³	1	1	yes	characteristic
400	C₇×#106	C₂³	1	1	yes	characteristic
401	C₇×#106	C₂³	1	1	yes	characteristic
402	C₇×#106	C₂³	1	1	yes	characteristic
403	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
404	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
405	C₇×#103	C₂³	1	1	yes	characteristic
406	C₇×#103	C₂³	1	1	yes	characteristic
407	C₇×#103	C₂³	1	1	yes	characteristic
408	C₇×#103	C₂³	1	1	yes	characteristic
409	C₇×#103	C₂³	1	1	yes	characteristic
410	C₇×#103	C₂³	1	1	yes	characteristic
411	C₇×#103	C₂³	1	1	yes	characteristic
412	C₇×#103	C₂³	1	1	yes	characteristic
413	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
414	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
415	C₇×#97	C₂³	1	1	yes	characteristic
416	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
417	#6409	C₂³	1	1	yes	characteristic
418	#6409	C₂³	1	1	yes	characteristic
419	#6409	C₂³	1	1	yes	characteristic
420	#6409	C₂³	1	1	yes	characteristic
421	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
422	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
423	#6395	C₂³	1	1	yes	characteristic
424	#6395	C₂³	1	1	yes	characteristic
425	#6395	C₂³	1	1	yes	characteristic
426	#6395	C₂³	1	1	yes	characteristic
427	#6392	C₂³	1	1	yes	characteristic
428	#6392	C₂³	1	1	yes	characteristic
429	#6391	C₂³	1	1	yes	characteristic
430	#6391	C₂³	1	1	yes	characteristic
431	#6390	C₂³	1	1	yes	characteristic
432	#6390	C₂³	1	1	yes	characteristic
433	#6390	C₂³	1	1	yes	characteristic
434	#6390	C₂³	1	1	yes	characteristic
435	#6389	C₂³	1	1	yes	characteristic
436	#6389	C₂³	1	1	yes	characteristic
437	#6389	C₂³	1	1	yes	characteristic
438	#6389	C₂³	1	1	yes	characteristic
439	Dic₇⋊C₈	C₂³	1	1	yes	characteristic
440	Dic₇⋊C₈	C₂³	1	1	yes	characteristic
441	Dic₇⋊C₈	C₂³	1	1	yes	characteristic
442	Dic₇⋊C₈	C₂³	1	1	yes	characteristic
443	Dic₇⋊C₈	C₂³	1	1	yes	characteristic
444	Dic₇⋊C₈	C₂³	1	1	yes	characteristic
445	Dic₇⋊C₈	C₂³	1	1	yes	characteristic
446	Dic₇⋊C₈	C₂³	1	1	yes	characteristic
447	C₈×Dic₇	C₂³	1	1	yes	characteristic
448	C₈×Dic₇	C₂³	1	1	yes	characteristic
449	C₈×Dic₇	C₂³	1	1	yes	characteristic
450	C₈×Dic₇	C₂³	1	1	yes	characteristic
451	#6384	C₂³	1	1	yes	characteristic
452	#6384	C₂³	1	1	yes	characteristic
453	#6384	C₂³	1	1	yes	characteristic
454	#6384	C₂³	1	1	yes	characteristic
455	#6384	C₂³	1	1	yes	characteristic
456	#6384	C₂³	1	1	yes	characteristic
457	#6384	C₂³	1	1	yes	characteristic
458	#6384	C₂³	1	1	yes	characteristic
459	#6383	C₂³	1	1	yes	characteristic
460	#6383	C₂³	1	1	yes	characteristic
461	#6383	C₂³	1	1	yes	characteristic
462	#6383	C₂³	1	1	yes	characteristic
463	#6382	C₂³	1	1	yes	characteristic
464	#6382	C₂³	1	1	yes	characteristic
465	#6382	C₂³	1	1	yes	characteristic
466	#6382	C₂³	1	1	yes	characteristic
467	#6382	C₂³	1	1	yes	characteristic
468	#6382	C₂³	1	1	yes	characteristic
469	#6381	C₂³	1	1	yes	characteristic
470	#6381	C₂³	1	1	yes	characteristic
471	#6381	C₂³	1	1	yes	characteristic
472	#6381	C₂³	1	1	yes	characteristic
473	#6381	C₂³	1	1	yes	characteristic
474	#6381	C₂³	1	1	yes	characteristic
475	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
476	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
477	#6377	C₂³	1	1	yes	characteristic
478	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
479	#3556	—	7	1	no	—
480	#3501	—	7	1	no	—
481	#3388	—	7	1	no	—
482	#3388	—	7	1	no	—
483	#3388	—	7	1	no	—
484	#3388	—	7	1	no	—
485	#3386	—	7	1	no	—
486	#3386	—	7	1	no	—
487	#3381	—	7	1	no	—
488	#3381	—	7	1	no	—
489	#3372	—	7	1	no	—
490	#3372	—	7	1	no	—
491	#3372	—	7	1	no	—
492	#3372	—	7	1	no	—
493	#3372	—	7	1	no	—
494	#3372	—	7	1	no	—
495	#3359	—	7	1	no	—
496	#3359	—	7	1	no	—
497	#3242	—	7	1	no	—
498	#3242	—	7	1	no	—
499	#3242	—	7	1	no	—
500	#3242	D₇	1	1	yes	characteristic, complemented
501	#3237	—	7	1	no	—
502	#3231	—	7	1	no	—
503	#3123	—	7	1	no	—
504	#3123	—	7	1	no	—
505	#3123	—	7	1	no	—
506	#3123	—	7	1	no	—
507	#3110	—	7	1	no	—
508	#3101	—	7	1	no	—
509	#2985	—	7	1	no	—
510	C₂³×D₇	—	2	1	no	—
511	C₂×C₇×Q₈	—	2	1	no	—
512	C₂×C₇×Q₈	—	2	1	no	—
513	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
514	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
515	C₂²×C₄×C₇	—	2	1	no	—
516	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
517	C₂²×Dic₇	C₂×D₄	1	1	yes	characteristic
518	C₂²×Dic₇	C₂×D₄	1	1	yes	characteristic
519	Q₈×D₇	—	8	2	no	—
520	Q₈×D₇	—	8	2	no	—
521	C₂×D₂₈	—	2	1	no	—
522	C₂×D₂₈	—	2	2	no	—
523	C₂×D₂₈	—	2	2	no	—
524	C₂×D₂₈	C₂⁴	1	1	yes	characteristic
525	C₂×D₂₈	C₂⁴	1	1	yes	characteristic
526	C₂×C₄×D₇	—	2	1	no	—
527	C₂×C₄×D₇	—	2	1	no	—
528	C₂×C₄×D₇	—	2	1	no	—
529	C₂×C₄×D₇	—	2	1	no	—
530	C₂×C₄×D₇	—	2	1	no	—
531	C₂×C₄×D₇	—	2	1	no	—
532	C₂×C₄×D₇	—	2	1	no	—
533	C₂×C₄×D₇	—	2	1	no	—
534	C₂×C₄×D₇	—	2	1	no	—
535	C₂×C₄×D₇	—	2	1	no	—
536	C₂×C₄×D₇	—	2	1	no	—
537	C₂×C₄×D₇	—	2	1	no	—
538	C₂×C₄×D₇	—	8	2	no	—
539	C₂×Dic₁₄	—	2	1	no	—
540	C₂×Dic₁₄	—	2	1	no	—
541	C₂×Dic₁₄	—	2	1	no	—
542	C₂×Dic₁₄	—	2	1	no	—
543	C₂×Dic₁₄	—	2	1	no	—
544	C₂×Dic₁₄	—	2	1	no	—
545	C₂×Dic₁₄	C₂×D₄	1	1	yes	characteristic
546	C₂×Dic₁₄	C₂×D₄	1	1	yes	characteristic
547	C₂×Dic₁₄	C₂×D₄	1	1	yes	characteristic
548	C₂×Dic₁₄	C₂×D₄	1	1	yes	characteristic
549	C₂×Dic₁₄	C₂⁴	1	1	yes	characteristic
550	C₂×Dic₁₄	C₂⁴	1	1	yes	characteristic
551	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
552	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
553	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
554	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
555	C₇×C₄⋊C₄	—	2	1	no	—
556	C₇×C₄⋊C₄	—	2	1	no	—
557	C₇×C₄⋊C₄	—	2	1	no	—
558	C₇×C₄⋊C₄	—	2	1	no	—
559	C₇×C₄⋊C₄	—	2	1	no	—
560	C₇×C₄⋊C₄	—	2	1	no	—
561	C₇×C₄⋊C₄	—	2	1	no	—
562	C₇×C₄⋊C₄	—	2	1	no	—
563	C₇×C₄⋊C₄	—	2	1	no	—
564	C₇×C₄⋊C₄	—	2	1	no	—
565	C₇×C₄⋊C₄	—	2	1	no	—
566	C₇×C₄⋊C₄	—	2	1	no	—
567	C₇×C₄⋊C₄	—	2	1	no	—
568	C₇×C₄⋊C₄	—	2	1	no	—
569	C₇×C₄⋊C₄	—	2	1	no	—
570	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
571	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
572	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
573	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
574	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
575	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
576	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
577	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
578	C₇×C₂²⋊C₄	—	2	1	no	—
579	C₇×C₂²⋊C₄	—	2	1	no	—
580	C₇×C₂²⋊C₄	—	2	1	no	—
581	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
582	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
583	C₄²×C₇	—	2	1	no	—
584	C₄²×C₇	—	2	1	no	—
585	C₄²×C₇	—	2	1	no	—
586	C₄²×C₇	C₂⁴	1	1	yes	characteristic
587	C₄²×C₇	C₂⁴	1	1	yes	characteristic
588	C₂²⋊Dic₇	—	2	1	no	—
589	C₂²⋊Dic₇	—	2	1	no	—
590	C₂²⋊Dic₇	—	2	1	no	—
591	C₂²⋊Dic₇	C₂×D₄	1	1	yes	characteristic
592	C₂²⋊Dic₇	C₂×D₄	1	1	yes	characteristic
593	#1143	—	2	2	no	—
594	#1143	—	2	2	no	—
595	#1143	—	2	2	no	—
596	#1143	—	2	2	no	—
597	(C₂×D₇)⋊C₄	—	2	1	no	—
598	(C₂×D₇)⋊C₄	—	2	1	no	—
599	(C₂×D₇)⋊C₄	—	2	1	no	—
600	(C₂×D₇)⋊C₄	—	2	1	no	—
601	(C₂×D₇)⋊C₄	—	2	1	no	—
602	(C₂×D₇)⋊C₄	—	2	1	no	—
603	(C₂×D₇)⋊C₄	—	2	1	no	—
604	(C₂×D₇)⋊C₄	—	2	1	no	—
605	(C₂×D₇)⋊C₄	—	2	1	no	—
606	(C₂×D₇)⋊C₄	—	2	1	no	—
607	(C₂×D₇)⋊C₄	—	2	1	no	—
608	(C₂×D₇)⋊C₄	—	2	1	no	—
609	C₄⋊Dic₇	—	2	1	no	—
610	C₄⋊Dic₇	—	2	1	no	—
611	C₄⋊Dic₇	—	2	1	no	—
612	C₄⋊Dic₇	—	2	1	no	—
613	C₄⋊Dic₇	—	2	1	no	—
614	C₄⋊Dic₇	—	2	1	no	—
615	C₄⋊Dic₇	—	2	1	no	—
616	C₄⋊Dic₇	—	2	1	no	—
617	C₄⋊Dic₇	—	2	1	no	—
618	C₄⋊Dic₇	—	2	1	no	—
619	C₄⋊Dic₇	—	2	1	no	—
620	C₄⋊Dic₇	—	2	1	no	—
621	C₄⋊Dic₇	C₂×D₄	1	1	yes	characteristic
622	C₄⋊Dic₇	C₂×D₄	1	1	yes	characteristic
623	C₄⋊Dic₇	C₂×D₄	1	1	yes	characteristic
624	C₄⋊Dic₇	C₂×D₄	1	1	yes	characteristic
625	C₄⋊Dic₇	C₂×D₄	1	1	yes	characteristic
626	C₄⋊Dic₇	C₂×D₄	1	1	yes	characteristic
627	C₄⋊Dic₇	C₂⁴	1	1	yes	characteristic
628	C₄⋊Dic₇	C₂⁴	1	1	yes	characteristic
629	C₄⋊Dic₇	C₂⁴	1	1	yes	characteristic
630	C₄⋊Dic₇	C₂⁴	1	1	yes	characteristic
631	Dic₇⋊C₄	—	2	1	no	—
632	Dic₇⋊C₄	—	2	1	no	—
633	Dic₇⋊C₄	—	2	1	no	—
634	Dic₇⋊C₄	—	2	1	no	—
635	Dic₇⋊C₄	—	2	1	no	—
636	Dic₇⋊C₄	—	2	1	no	—
637	Dic₇⋊C₄	—	2	1	no	—
638	Dic₇⋊C₄	—	2	1	no	—
639	Dic₇⋊C₄	—	2	1	no	—
640	Dic₇⋊C₄	—	2	1	no	—
641	Dic₇⋊C₄	—	2	1	no	—
642	Dic₇⋊C₄	—	2	1	no	—
643	Dic₇⋊C₄	—	2	1	no	—
644	Dic₇⋊C₄	—	2	1	no	—
645	Dic₇⋊C₄	—	2	1	no	—
646	Dic₇⋊C₄	—	2	1	no	—
647	Dic₇⋊C₄	—	2	1	no	—
648	Dic₇⋊C₄	—	2	1	no	—
649	Dic₇⋊C₄	—	2	1	no	—
650	Dic₇⋊C₄	—	2	1	no	—
651	Dic₇⋊C₄	—	2	1	no	—
652	Dic₇⋊C₄	—	2	1	no	—
653	Dic₇⋊C₄	—	2	1	no	—
654	Dic₇⋊C₄	—	2	1	no	—
655	Dic₇⋊C₄	—	2	1	no	—
656	Dic₇⋊C₄	—	2	1	no	—
657	Dic₇⋊C₄	—	2	1	no	—
658	Dic₇⋊C₄	—	2	1	no	—
659	Dic₇⋊C₄	—	2	1	no	—
660	Dic₇⋊C₄	—	2	1	no	—
661	Dic₇⋊C₄	C₂×D₄	1	1	yes	characteristic
662	Dic₇⋊C₄	C₂×D₄	1	1	yes	characteristic
663	Dic₇⋊C₄	C₂×D₄	1	1	yes	characteristic
664	Dic₇⋊C₄	C₂×D₄	1	1	yes	characteristic
665	Dic₇⋊C₄	C₂×D₄	1	1	yes	characteristic
666	Dic₇⋊C₄	C₂×D₄	1	1	yes	characteristic
667	Dic₇⋊C₄	C₂×D₄	1	1	yes	characteristic
668	Dic₇⋊C₄	C₂×D₄	1	1	yes	characteristic
669	C₄×Dic₇	—	2	1	no	—
670	C₄×Dic₇	—	2	1	no	—
671	C₄×Dic₇	—	2	1	no	—
672	C₄×Dic₇	—	2	1	no	—
673	C₄×Dic₇	—	2	1	no	—
674	C₄×Dic₇	—	2	1	no	—
675	C₄×Dic₇	—	2	1	no	—
676	C₄×Dic₇	—	2	1	no	—
677	C₄×Dic₇	—	2	1	no	—
678	C₄×Dic₇	—	2	1	no	—
679	C₄×Dic₇	—	2	1	no	—
680	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
681	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
682	C₄×Dic₇	C₂⁴	1	1	yes	characteristic
683	C₄×Dic₇	C₂⁴	1	1	yes	characteristic
684	C₄×Dic₇	C₂⁴	1	1	yes	characteristic
685	C₄×Dic₇	C₂⁴	1	1	yes	characteristic
686	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
687	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
688	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
689	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
690	#1132	—	2	2	no	—
691	#1132	—	2	2	no	—
692	#1132	—	2	2	no	—
693	#1132	—	2	2	no	—
694	#564	—	14	1	no	—
695	#564	—	14	1	no	—
696	#557	—	7	1	no	—
697	#557	—	7	1	no	—
698	#557	—	7	1	no	—
699	#557	—	7	1	no	—
700	#557	—	7	1	no	—
701	#557	—	7	1	no	—
702	#557	—	7	1	no	—
703	#557	—	7	1	no	—
704	#557	—	14	1	no	—
705	#557	—	14	1	no	—
706	#554	—	7	1	no	—
707	#554	—	7	1	no	—
708	#554	—	7	1	no	—
709	#554	—	7	1	no	—
710	#554	—	7	1	no	—
711	#554	—	7	1	no	—
712	#554	—	14	1	no	—
713	#554	—	14	1	no	—
714	#554	—	14	1	no	—
715	D₄×Q₈	—	7	1	no	—
716	D₄×Q₈	—	7	1	no	—
717	D₄×Q₈	—	14	1	no	—
718	#544	—	7	1	no	—
719	#544	C₂×D₇	1	1	yes	characteristic
720	#543	—	14	1	no	—
721	#543	—	14	1	no	—
722	#541	—	7	1	no	—
723	#541	—	7	1	no	—
724	#541	—	7	1	no	—
725	#541	—	14	1	no	—
726	#541	—	14	1	no	—
727	#541	—	14	1	no	—
728	#541	—	14	1	no	—
729	#541	C₂×D₇	1	1	yes	characteristic
730	#533	—	7	1	no	—
731	#533	—	7	1	no	—
732	#533	—	7	1	no	—
733	#533	—	7	1	no	—
734	C₂×C₂²⋊Q₈	—	14	1	no	—
735	C₂×C₂²⋊Q₈	—	14	1	no	—
736	#518	—	7	1	no	—
737	#518	—	7	1	no	—
738	C₂×C₄×D₄	—	7	1	no	—
739	#501	—	7	1	no	—
740	#501	—	7	1	no	—
741	#501	—	7	1	no	—
742	#501	—	7	1	no	—
743	#501	—	7	1	no	—
744	#501	C₂×D₇	1	1	yes	characteristic, complemented
745	#500	—	7	1	no	—
746	#499	—	7	1	no	—
747	#499	—	7	1	no	—
748	#499	—	7	1	no	—
749	#499	C₂×D₇	1	1	yes	characteristic, complemented
750	#498	—	7	1	no	—
751	#491	—	7	1	no	—
752	#491	—	7	1	no	—
753	#491	—	7	1	no	—
754	#491	—	7	1	no	—
755	#491	—	7	1	no	—
756	#491	C₂×D₇	1	1	yes	characteristic, complemented
757	#487	—	7	1	no	—
758	#487	—	7	1	no	—
759	#487	—	7	1	no	—
760	#487	—	7	1	no	—
761	#487	—	7	1	no	—
762	#487	C₂×D₇	1	1	yes	characteristic, complemented
763	#485	—	7	1	no	—
764	#485	—	7	1	no	—
765	#485	—	7	1	no	—
766	#485	—	7	1	no	—
767	#485	—	7	1	no	—
768	#485	—	7	1	no	—
769	#485	C₂×D₇	1	1	yes	characteristic
770	#485	C₂×D₇	1	1	yes	characteristic
771	#484	—	7	1	no	—
772	#484	C₂×D₇	1	1	yes	characteristic
773	#483	—	7	1	no	—
774	#483	C₂×D₇	1	1	yes	characteristic
775	#479	—	7	1	no	—
776	#479	—	7	1	no	—
777	#479	—	7	1	no	—
778	#479	—	7	1	no	—
779	#479	—	7	1	no	—
780	#479	—	7	1	no	—
781	#479	—	7	1	no	—
782	#479	—	7	1	no	—
783	#479	—	7	1	no	—
784	#479	—	7	1	no	—
785	#479	C₂×D₇	1	1	yes	characteristic, complemented
786	#479	C₂×D₇	1	1	yes	characteristic, complemented
787	#478	—	7	1	no	—
788	#478	—	7	1	no	—
789	#478	—	7	1	no	—
790	#478	—	7	1	no	—
791	#478	—	7	1	no	—
792	#478	—	7	1	no	—
793	#478	—	7	1	no	—
794	#478	—	7	1	no	—
795	#477	—	7	1	no	—
796	#477	—	7	1	no	—
797	#477	—	7	1	no	—
798	#477	—	7	1	no	—
799	#477	—	7	1	no	—
800	#477	C₂×D₇	1	1	yes	characteristic, complemented
801	#476	—	7	1	no	—
802	#476	—	7	1	no	—
803	#475	—	7	1	no	—
804	#475	—	7	1	no	—
805	#475	—	7	1	no	—
806	#475	—	7	1	no	—
807	#475	—	7	1	no	—
808	#475	C₂×D₇	1	1	yes	characteristic, complemented
809	#474	—	7	1	no	—
810	#474	—	7	1	no	—
811	#461	—	7	1	no	—
812	#461	—	7	1	no	—
813	#461	—	7	1	no	—
814	#461	—	7	1	no	—
815	#461	—	7	1	no	—
816	#461	—	7	1	no	—
817	#461	—	7	1	no	—
818	#461	—	7	1	no	—
819	#461	—	7	1	no	—
820	#461	—	7	1	no	—
821	#461	—	7	1	no	—
822	#461	—	7	1	no	—
823	#450	—	7	1	no	—
824	#450	—	7	1	no	—
825	#450	—	7	1	no	—
826	#450	—	7	1	no	—
827	#446	—	7	1	no	—
828	#446	—	7	1	no	—
829	#446	—	7	1	no	—
830	#446	—	7	1	no	—
831	#446	—	7	1	no	—
832	#446	—	7	1	no	—
833	C₈×Q₈	—	7	1	no	—
834	C₈×Q₈	—	7	1	no	—
835	#440	—	7	1	no	—
836	#440	—	7	1	no	—
837	#440	—	7	1	no	—
838	#440	—	7	1	no	—
839	#440	—	7	1	no	—
840	#440	—	7	1	no	—
841	#440	—	7	1	no	—
842	#440	—	7	1	no	—
843	#440	—	7	1	no	—
844	#440	—	7	1	no	—
845	#440	—	7	1	no	—
846	#440	—	7	1	no	—
847	C₄×SD₁₆	—	7	1	no	—
848	C₄×SD₁₆	—	7	1	no	—
849	C₄×SD₁₆	—	7	1	no	—
850	C₄×SD₁₆	—	7	1	no	—
851	C₄×SD₁₆	—	7	1	no	—
852	C₄×SD₁₆	—	7	1	no	—
853	C₄×SD₁₆	—	7	1	no	—
854	C₄×SD₁₆	—	7	1	no	—
855	C₄×SD₁₆	—	7	1	no	—
856	C₄×SD₁₆	—	7	1	no	—
857	C₄×SD₁₆	—	7	1	no	—
858	C₄×SD₁₆	—	7	1	no	—
859	#433	—	7	1	no	—
860	#433	—	7	1	no	—
861	#433	—	7	1	no	—
862	#433	C₂×D₇	1	1	yes	characteristic
863	#432	—	7	1	no	—
864	#431	—	7	1	no	—
865	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
866	C₂²×D₇	—	2	1	no	—
867	C₂²×D₇	—	2	1	no	—
868	C₂²×D₇	—	2	4	no	—
869	C₂²×D₇	—	8	1	no	—
870	C₂²×D₇	—	8	1	no	—
871	C₇×Q₈	—	2	1	no	—
872	C₇×Q₈	—	2	1	no	—
873	C₇×Q₈	—	2	1	no	—
874	C₇×Q₈	—	2	1	no	—
875	C₇×Q₈	—	8	1	no	—
876	C₇×Q₈	—	8	1	no	—
877	C₂×C₄×C₇	—	2	1	no	—
878	C₂×C₄×C₇	—	2	1	no	—
879	C₂×C₄×C₇	—	2	1	no	—
880	C₂×C₄×C₇	—	2	1	no	—
881	C₂×C₄×C₇	—	2	1	no	—
882	C₂×C₄×C₇	—	2	1	no	—
883	C₂×C₄×C₇	—	2	1	no	—
884	C₂×C₄×C₇	—	2	1	no	—
885	C₂×C₄×C₇	—	2	1	no	—
886	C₂×C₄×C₇	—	2	1	no	—
887	C₂×C₄×C₇	—	8	1	no	—
888	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
889	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
890	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
891	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
892	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
893	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
894	C₂×Dic₇	—	2	2	no	—
895	C₂×Dic₇	—	2	1	no	—
896	C₂×Dic₇	—	2	1	no	—
897	C₂×Dic₇	—	2	1	no	—
898	C₂×Dic₇	—	2	1	no	—
899	C₂×Dic₇	—	2	1	no	—
900	C₂×Dic₇	—	2	1	no	—
901	C₂×Dic₇	—	4	1	no	—
902	C₂×Dic₇	C₂²×D₄	1	1	yes	characteristic
903	C₂×Dic₇	C₂²×D₄	1	1	yes	characteristic
904	C₂×Dic₇	C₂²×D₄	1	1	yes	characteristic
905	C₂×Dic₇	C₂²×D₄	1	1	yes	characteristic
906	C₂×Dic₇	C₂²×D₄	1	1	yes	characteristic
907	C₂×Dic₇	C₂²×D₄	1	1	yes	characteristic
908	C₂×Dic₇	C₂²×D₄	1	1	yes	characteristic
909	C₂×Dic₇	C₂²×D₄	1	1	yes	characteristic
910	D₂₈	—	2	4	no	—
911	D₂₈	—	2	1	no	—
912	D₂₈	—	2	1	no	—
913	D₂₈	2₋¹⁺⁴	1	2	yes	—
914	D₂₈	2₋¹⁺⁴	1	2	yes	—
915	C₄×D₇	—	4	2	no	—
916	C₄×D₇	—	4	2	no	—
917	C₄×D₇	—	8	1	no	—
918	C₄×D₇	—	8	1	no	—
919	C₄×D₇	—	8	1	no	—
920	C₄×D₇	—	8	1	no	—
921	C₄×D₇	—	8	1	no	—
922	C₄×D₇	—	8	1	no	—
923	C₄×D₇	—	8	1	no	—
924	C₄×D₇	—	8	1	no	—
925	C₄×D₇	—	8	1	no	—
926	C₄×D₇	—	8	1	no	—
927	Dic₁₄	—	2	2	no	—
928	Dic₁₄	—	2	2	no	—
929	Dic₁₄	—	2	1	no	—
930	Dic₁₄	—	2	1	no	—
931	Dic₁₄	—	2	1	no	—
932	Dic₁₄	—	2	1	no	—
933	Dic₁₄	—	4	1	no	—
934	Dic₁₄	—	4	1	no	—
935	Dic₁₄	—	4	2	no	—
936	Dic₁₄	—	4	2	no	—
937	Dic₁₄	—	4	2	no	—
938	Dic₁₄	—	8	1	no	—
939	Dic₁₄	—	8	1	no	—
940	Dic₁₄	—	8	1	no	—
941	C₇×C₈	—	2	1	no	—
942	C₇×C₈	—	2	1	no	—
943	C₇×C₈	—	2	1	no	—
944	C₇×C₈	—	2	1	no	—
945	C₇⋊C₈	—	2	1	no	—
946	C₇⋊C₈	—	2	1	no	—
947	C₇⋊C₈	—	2	1	no	—
948	C₇⋊C₈	—	2	1	no	—
949	C₂²×Q₈	—	14	1	no	—
950	C₂²×Q₈	—	14	1	no	—
951	C₂²×D₄	—	7	1	no	—
952	C₂³×C₄	—	14	1	no	—
953	C₂×SD₁₆	—	7	1	no	—
954	C₂×SD₁₆	—	7	1	no	—
955	C₂×SD₁₆	—	7	1	no	—
956	C₂×SD₁₆	—	7	1	no	—
957	C₂×SD₁₆	—	7	1	no	—
958	C₂×SD₁₆	—	7	1	no	—
959	C₂×SD₁₆	—	7	1	no	—
960	C₂×SD₁₆	—	7	1	no	—
961	C₄⋊Q₈	—	2	1	no	—
962	C₄⋊Q₈	—	7	1	no	—
963	C₄⋊Q₈	—	7	1	no	—
964	C₄⋊Q₈	—	7	1	no	—
965	C₄⋊Q₈	—	7	1	no	—
966	C₄⋊Q₈	—	7	1	no	—
967	C₄⋊Q₈	—	7	1	no	—
968	C₄⋊Q₈	—	7	1	no	—
969	C₄⋊Q₈	—	7	1	no	—
970	C₄⋊Q₈	—	7	1	no	—
971	C₄⋊Q₈	—	7	1	no	—
972	C₄⋊Q₈	—	7	1	no	—
973	C₄⋊Q₈	—	7	1	no	—
974	C₄⋊Q₈	—	7	1	no	—
975	C₄⋊Q₈	—	14	1	no	—
976	C₄⋊Q₈	—	14	1	no	—
977	C₄⋊Q₈	—	14	1	no	—
978	C₄⋊Q₈	—	14	1	no	—
979	C₄⋊Q₈	—	14	1	no	—
980	C₄⋊Q₈	C₂²×D₇	1	1	yes	characteristic
981	C₄⋊Q₈	C₂²×D₇	1	1	yes	characteristic
982	C₄⋊Q₈	C₂²×D₇	1	1	yes	characteristic
983	#126	—	2	1	no	—
984	#126	—	2	1	no	—
985	#126	—	14	1	no	—
986	#126	—	14	1	no	—
987	#126	—	14	1	no	—
988	#126	—	14	1	no	—
989	#126	—	14	1	no	—
990	#126	—	14	1	no	—
991	#125	—	2	1	no	—
992	#125	—	2	1	no	—
993	#125	—	2	1	no	—
994	#125	—	7	1	no	—
995	#125	—	7	1	no	—
996	#125	—	7	1	no	—
997	#125	—	7	1	no	—
998	#125	—	7	1	no	—
999	#125	—	7	1	no	—
1000	#125	—	7	1	no	—
1001	#125	—	7	1	no	—
1002	#125	—	7	1	no	—
1003	#125	—	14	1	no	—
1004	#125	—	14	1	no	—
1005	#125	—	14	1	no	—
1006	#125	—	14	1	no	—
1007	#125	—	14	1	no	—
1008	#125	—	14	1	no	—
1009	#125	—	14	1	no	—
1010	#125	—	14	1	no	—
1011	#125	—	14	1	no	—
1012	#125	—	14	1	no	—
1013	#125	—	14	1	no	—
1014	#125	—	14	1	no	—
1015	#125	—	14	1	no	—
1016	#125	—	14	1	no	—
1017	#125	—	14	1	no	—
1018	#125	—	14	1	no	—
1019	#125	—	14	1	no	—
1020	#125	—	14	1	no	—
1021	#125	—	14	1	no	—
1022	#125	—	14	1	no	—
1023	#125	—	14	1	no	—
1024	#125	—	14	1	no	—
1025	#125	—	14	1	no	—
1026	#125	—	14	1	no	—
1027	#125	—	14	1	no	—
1028	#125	—	14	1	no	—
1029	#125	—	14	1	no	—
1030	#125	—	14	1	no	—
1031	#125	—	14	1	no	—
1032	#125	C₂²×D₇	1	1	yes	characteristic
1033	#125	C₂²×D₇	1	1	yes	characteristic
1034	#125	C₂²×D₇	1	1	yes	characteristic
1035	C₂²⋊Q₈	—	2	1	no	—
1036	C₂²⋊Q₈	—	2	1	no	—
1037	C₂²⋊Q₈	—	7	1	no	—
1038	C₂²⋊Q₈	—	7	1	no	—
1039	C₂²⋊Q₈	—	7	1	no	—
1040	C₂²⋊Q₈	—	7	1	no	—
1041	C₂²⋊Q₈	—	7	1	no	—
1042	C₂²⋊Q₈	—	7	1	no	—
1043	C₂²⋊Q₈	—	14	1	no	—
1044	C₂²⋊Q₈	—	14	1	no	—
1045	C₂²⋊Q₈	—	14	1	no	—
1046	C₂²⋊Q₈	—	14	1	no	—
1047	C₂²⋊Q₈	—	14	1	no	—
1048	C₂²⋊Q₈	—	14	1	no	—
1049	C₂²⋊Q₈	—	14	1	no	—
1050	C₂²⋊Q₈	—	14	1	no	—
1051	C₂²⋊Q₈	—	14	1	no	—
1052	C₂²⋊Q₈	—	14	1	no	—
1053	C₂²⋊Q₈	—	14	1	no	—
1054	C₂²⋊Q₈	—	14	1	no	—
1055	C₂²⋊Q₈	—	14	1	no	—
1056	C₂²⋊Q₈	—	14	1	no	—
1057	C₂²⋊Q₈	—	14	1	no	—
1058	C₂²⋊Q₈	—	14	1	no	—
1059	C₂²⋊Q₈	—	14	1	no	—
1060	C₂²⋊Q₈	—	14	1	no	—
1061	C₂²⋊Q₈	—	14	1	no	—
1062	C₂²⋊Q₈	—	14	1	no	—
1063	C₂²⋊Q₈	—	14	1	no	—
1064	C₂²⋊Q₈	—	14	1	no	—
1065	C₂²⋊Q₈	—	14	1	no	—
1066	C₂²⋊Q₈	—	14	1	no	—
1067	C₂²⋊Q₈	—	14	1	no	—
1068	C₂²⋊Q₈	—	14	1	no	—
1069	C₂²⋊Q₈	—	14	1	no	—
1070	C₂²⋊Q₈	—	14	1	no	—
1071	C₂²⋊Q₈	—	14	1	no	—
1072	C₂²⋊Q₈	—	14	1	no	—
1073	C₂²⋊Q₈	C₂²×D₇	1	1	yes	characteristic
1074	C₂²⋊Q₈	C₂²×D₇	1	1	yes	characteristic
1075	C₄×Q₈	—	7	1	no	—
1076	C₄×Q₈	—	7	1	no	—
1077	C₄×Q₈	—	7	1	no	—
1078	C₄×Q₈	—	7	1	no	—
1079	C₄×Q₈	—	7	1	no	—
1080	C₄×Q₈	—	7	1	no	—
1081	C₄×Q₈	—	7	1	no	—
1082	C₄×Q₈	—	7	1	no	—
1083	C₄×Q₈	—	7	1	no	—
1084	C₄×Q₈	—	7	1	no	—
1085	C₄×Q₈	—	7	1	no	—
1086	C₄×Q₈	—	7	1	no	—
1087	C₄×Q₈	—	7	1	no	—
1088	C₄×Q₈	—	7	1	no	—
1089	C₄×Q₈	—	14	1	no	—
1090	C₄×Q₈	—	14	1	no	—
1091	C₄×Q₈	—	14	1	no	—
1092	C₄×Q₈	—	14	1	no	—
1093	C₄×Q₈	—	14	1	no	—
1094	C₄×Q₈	—	14	1	no	—
1095	C₄×Q₈	—	14	1	no	—
1096	C₄×Q₈	—	14	1	no	—
1097	C₄×Q₈	—	14	1	no	—
1098	C₄×Q₈	—	14	1	no	—
1099	C₄×Q₈	—	14	1	no	—
1100	C₄×Q₈	—	14	1	no	—
1101	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
1102	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
1103	C₄×D₄	—	7	1	no	—
1104	C₄×D₄	—	7	1	no	—
1105	C₄×D₄	—	7	1	no	—
1106	C₄×D₄	—	7	1	no	—
1107	C₄×D₄	—	7	1	no	—
1108	C₄×D₄	—	7	1	no	—
1109	C₄×D₄	—	7	1	no	—
1110	C₄×D₄	—	7	1	no	—
1111	C₄×D₄	—	7	1	no	—
1112	C₄×D₄	—	7	1	no	—
1113	C₄×D₄	—	7	1	no	—
1114	C₄×D₄	—	7	1	no	—
1115	C₄×D₄	—	14	1	no	—
1116	C₄×D₄	—	14	1	no	—
1117	C₄×D₄	—	14	1	no	—
1118	C₄×D₄	—	14	1	no	—
1119	C₄×D₄	—	14	1	no	—
1120	C₄×D₄	—	14	1	no	—
1121	#117	—	7	1	no	—
1122	#117	—	7	1	no	—
1123	#117	—	14	1	no	—
1124	#117	—	14	1	no	—
1125	#117	C₂²×D₇	1	1	yes	characteristic
1126	#117	C₂²×D₇	1	1	yes	characteristic
1127	C₂×C₄⋊C₄	—	14	1	no	—
1128	C₂×C₄⋊C₄	—	14	1	no	—
1129	C₂×C₄⋊C₄	—	14	1	no	—
1130	C₂×C₄⋊C₄	—	14	1	no	—
1131	C₂×C₄⋊C₄	—	14	1	no	—
1132	C₂×C₄⋊C₄	—	14	1	no	—
1133	C₂×C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
1134	C₂×C₂²⋊C₄	—	14	1	no	—
1135	C₂×C₂²⋊C₄	—	14	1	no	—
1136	C₂×C₂²⋊C₄	—	14	1	no	—
1137	C₂×C₂²⋊C₄	—	14	1	no	—
1138	C₂×C₂²⋊C₄	—	14	1	no	—
1139	C₂×C₄²	—	7	1	no	—
1140	#107	—	7	1	no	—
1141	#107	—	7	1	no	—
1142	#107	—	7	1	no	—
1143	#107	—	7	1	no	—
1144	#107	—	7	1	no	—
1145	#107	—	7	1	no	—
1146	#107	—	7	1	no	—
1147	#107	—	7	1	no	—
1148	#107	C₂²×D₇	1	1	yes	characteristic
1149	#107	C₂²×D₇	1	1	yes	characteristic
1150	#107	C₂²×D₇	1	1	yes	characteristic
1151	#107	C₂²×D₇	1	1	yes	characteristic
1152	#106	—	7	1	no	—
1153	#106	—	7	1	no	—
1154	#106	—	7	1	no	—
1155	#106	—	7	1	no	—
1156	#106	—	7	1	no	—
1157	#106	—	7	1	no	—
1158	#106	—	7	1	no	—
1159	#106	—	7	1	no	—
1160	#106	C₂²×D₇	1	1	yes	characteristic
1161	#106	C₂²×D₇	1	1	yes	characteristic
1162	#106	C₂²×D₇	1	1	yes	characteristic
1163	#106	C₂²×D₇	1	1	yes	characteristic
1164	C₄⋊C₈	—	7	1	no	—
1165	C₄⋊C₈	—	7	1	no	—
1166	C₄⋊C₈	—	7	1	no	—
1167	C₄⋊C₈	—	7	1	no	—
1168	C₄⋊C₈	—	7	1	no	—
1169	C₄⋊C₈	—	7	1	no	—
1170	C₄⋊C₈	—	7	1	no	—
1171	C₄⋊C₈	—	7	1	no	—
1172	C₄⋊C₈	—	7	1	no	—
1173	C₄⋊C₈	—	7	1	no	—
1174	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
1175	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
1176	#103	—	7	1	no	—
1177	#103	—	7	1	no	—
1178	#103	—	7	1	no	—
1179	#103	—	7	1	no	—
1180	#103	—	7	1	no	—
1181	#103	—	7	1	no	—
1182	#103	—	7	1	no	—
1183	#103	—	7	1	no	—
1184	#103	—	7	1	no	—
1185	#103	—	7	1	no	—
1186	#103	—	7	1	no	—
1187	#103	—	7	1	no	—
1188	#103	—	7	1	no	—
1189	#103	—	7	1	no	—
1190	#103	—	7	1	no	—
1191	#103	—	7	1	no	—
1192	#103	C₂²×D₇	1	1	yes	characteristic
1193	#103	C₂²×D₇	1	1	yes	characteristic
1194	#103	C₂²×D₇	1	1	yes	characteristic
1195	#103	C₂²×D₇	1	1	yes	characteristic
1196	#103	C₂²×D₇	1	1	yes	characteristic
1197	#103	C₂²×D₇	1	1	yes	characteristic
1198	#103	C₂²×D₇	1	1	yes	characteristic
1199	#103	C₂²×D₇	1	1	yes	characteristic
1200	#102	—	7	1	no	—
1201	#102	—	7	1	no	—
1202	#102	—	7	1	no	—
1203	#102	—	7	1	no	—
1204	#102	—	7	1	no	—
1205	#102	—	7	1	no	—
1206	#102	—	7	1	no	—
1207	#102	—	7	1	no	—
1208	C₂²⋊C₈	—	7	1	no	—
1209	C₂²⋊C₈	—	7	1	no	—
1210	C₂²⋊C₈	C₂²×D₇	1	1	yes	characteristic
1211	C₂²⋊C₈	C₂²×D₇	1	1	yes	characteristic
1212	#97	—	7	1	no	—
1213	#97	—	7	1	no	—
1214	#97	—	7	1	no	—
1215	#97	—	7	1	no	—
1216	#97	—	7	1	no	—
1217	#97	C₂²×D₇	1	1	yes	characteristic
1218	C₄×C₈	—	7	1	no	—
1219	C₄×C₈	—	7	1	no	—
1220	C₄×C₈	—	7	1	no	—
1221	C₄×C₈	—	7	1	no	—
1222	C₄×C₈	—	7	1	no	—
1223	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
1224	C₂²×C₇	—	2	1	no	—
1225	C₂²×C₇	—	2	1	no	—
1226	C₂²×C₇	—	2	1	no	—
1227	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
1228	C₂×D₇	—	2	2	no	—
1229	C₂×D₇	—	2	2	no	—
1230	C₂×D₇	—	4	1	no	—
1231	C₂×D₇	—	4	1	no	—
1232	C₂×D₇	—	4	1	no	—
1233	C₂×D₇	—	4	1	no	—
1234	C₂×D₇	—	8	4	no	—
1235	C₄×C₇	—	2	1	no	—
1236	C₄×C₇	—	2	1	no	—
1237	C₄×C₇	—	2	1	no	—
1238	C₄×C₇	—	2	1	no	—
1239	C₄×C₇	—	2	1	no	—
1240	C₄×C₇	—	4	1	no	—
1241	C₄×C₇	—	4	1	no	—
1242	C₄×C₇	—	4	1	no	—
1243	C₄×C₇	—	4	1	no	—
1244	C₄×C₇	—	4	1	no	—
1245	C₄×C₇	—	4	1	no	—
1246	C₄×C₇	—	4	1	no	—
1247	C₄×C₇	—	4	1	no	—
1248	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1249	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1250	Dic₇	—	2	1	no	—
1251	Dic₇	—	2	1	no	—
1252	Dic₇	—	2	1	no	—
1253	Dic₇	—	2	1	no	—
1254	Dic₇	—	2	1	no	—
1255	Dic₇	—	2	1	no	—
1256	Dic₇	—	2	1	no	—
1257	Dic₇	—	4	1	no	—
1258	Dic₇	—	4	1	no	—
1259	Dic₇	—	4	1	no	—
1260	Dic₇	—	4	1	no	—
1261	Dic₇	—	4	1	no	—
1262	Dic₇	—	4	1	no	—
1263	Dic₇	#577	1	2	yes	—
1264	C₂⁴	—	14	1	no	—
1265	C₂×Q₈	—	2	1	no	—
1266	C₂×Q₈	—	2	1	no	—
1267	C₂×Q₈	—	7	1	no	—
1268	C₂×Q₈	—	7	1	no	—
1269	C₂×Q₈	—	7	1	no	—
1270	C₂×Q₈	—	7	1	no	—
1271	C₂×Q₈	—	7	1	no	—
1272	C₂×Q₈	—	7	1	no	—
1273	C₂×Q₈	—	14	1	no	—
1274	C₂×Q₈	—	14	1	no	—
1275	C₂×Q₈	—	14	1	no	—
1276	C₂×Q₈	—	14	1	no	—
1277	C₂×Q₈	—	14	1	no	—
1278	C₂×Q₈	—	14	1	no	—
1279	C₂×Q₈	—	56	2	no	—
1280	C₂×Q₈	—	56	2	no	—
1281	C₂×Q₈	C₂³×D₇	1	1	yes	characteristic
1282	C₂×Q₈	C₂³×D₇	1	1	yes	characteristic
1283	C₂×D₄	—	7	1	no	—
1284	C₂×D₄	—	7	1	no	—
1285	C₂×D₄	—	14	2	no	—
1286	C₂×D₄	—	14	2	no	—
1287	C₂×D₄	—	14	1	no	—
1288	C₂²×C₄	—	2	1	no	—
1289	C₂²×C₄	—	7	1	no	—
1290	C₂²×C₄	—	7	1	no	—
1291	C₂²×C₄	—	14	1	no	—
1292	C₂²×C₄	—	14	1	no	—
1293	C₂²×C₄	—	14	1	no	—
1294	C₂²×C₄	—	14	1	no	—
1295	C₂²×C₄	—	14	1	no	—
1296	C₂²×C₄	—	14	1	no	—
1297	C₂²×C₄	—	14	1	no	—
1298	C₂²×C₄	—	14	1	no	—
1299	C₂²×C₄	—	14	1	no	—
1300	C₂²×C₄	—	14	1	no	—
1301	C₂²×C₄	—	14	1	no	—
1302	C₂²×C₄	—	14	1	no	—
1303	C₂²×C₄	—	56	2	no	—
1304	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
1305	SD₁₆	—	14	2	no	—
1306	SD₁₆	—	14	2	no	—
1307	SD₁₆	—	14	2	no	—
1308	SD₁₆	—	14	2	no	—
1309	SD₁₆	—	14	2	no	—
1310	SD₁₆	—	14	2	no	—
1311	SD₁₆	—	14	2	no	—
1312	SD₁₆	—	14	2	no	—
1313	C₂×C₈	—	7	1	no	—
1314	C₂×C₈	—	7	1	no	—
1315	C₂×C₈	—	7	1	no	—
1316	C₂×C₈	—	7	1	no	—
1317	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
1318	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
1319	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
1320	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
1321	C₄⋊C₄	—	2	1	no	—
1322	C₄⋊C₄	—	2	1	no	—
1323	C₄⋊C₄	—	2	1	no	—
1324	C₄⋊C₄	—	2	1	no	—
1325	C₄⋊C₄	—	2	1	no	—
1326	C₄⋊C₄	—	2	1	no	—
1327	C₄⋊C₄	—	2	1	no	—
1328	C₄⋊C₄	—	2	1	no	—
1329	C₄⋊C₄	—	2	1	no	—
1330	C₄⋊C₄	—	2	1	no	—
1331	C₄⋊C₄	—	2	1	no	—
1332	C₄⋊C₄	—	2	1	no	—
1333	C₄⋊C₄	—	2	1	no	—
1334	C₄⋊C₄	—	2	1	no	—
1335	C₄⋊C₄	—	2	1	no	—
1336	C₄⋊C₄	—	7	1	no	—
1337	C₄⋊C₄	—	7	1	no	—
1338	C₄⋊C₄	—	7	1	no	—
1339	C₄⋊C₄	—	7	1	no	—
1340	C₄⋊C₄	—	7	1	no	—
1341	C₄⋊C₄	—	7	1	no	—
1342	C₄⋊C₄	—	7	1	no	—
1343	C₄⋊C₄	—	7	1	no	—
1344	C₄⋊C₄	—	7	1	no	—
1345	C₄⋊C₄	—	7	1	no	—
1346	C₄⋊C₄	—	7	1	no	—
1347	C₄⋊C₄	—	7	1	no	—
1348	C₄⋊C₄	—	7	1	no	—
1349	C₄⋊C₄	—	7	1	no	—
1350	C₄⋊C₄	—	7	1	no	—
1351	C₄⋊C₄	—	7	1	no	—
1352	C₄⋊C₄	—	7	1	no	—
1353	C₄⋊C₄	—	7	1	no	—
1354	C₄⋊C₄	—	14	1	no	—
1355	C₄⋊C₄	—	14	1	no	—
1356	C₄⋊C₄	—	14	1	no	—
1357	C₄⋊C₄	—	14	1	no	—
1358	C₄⋊C₄	—	14	1	no	—
1359	C₄⋊C₄	—	14	1	no	—
1360	C₄⋊C₄	—	14	1	no	—
1361	C₄⋊C₄	—	14	1	no	—
1362	C₄⋊C₄	—	14	1	no	—
1363	C₄⋊C₄	—	14	1	no	—
1364	C₄⋊C₄	—	14	1	no	—
1365	C₄⋊C₄	—	14	1	no	—
1366	C₄⋊C₄	—	14	1	no	—
1367	C₄⋊C₄	—	14	1	no	—
1368	C₄⋊C₄	—	14	1	no	—
1369	C₄⋊C₄	—	14	1	no	—
1370	C₄⋊C₄	—	14	1	no	—
1371	C₄⋊C₄	—	14	1	no	—
1372	C₄⋊C₄	—	14	1	no	—
1373	C₄⋊C₄	—	14	1	no	—
1374	C₄⋊C₄	—	14	1	no	—
1375	C₄⋊C₄	—	14	1	no	—
1376	C₄⋊C₄	—	14	1	no	—
1377	C₄⋊C₄	—	14	1	no	—
1378	C₄⋊C₄	—	14	1	no	—
1379	C₄⋊C₄	—	14	1	no	—
1380	C₄⋊C₄	—	14	1	no	—
1381	C₄⋊C₄	—	14	1	no	—
1382	C₄⋊C₄	—	14	1	no	—
1383	C₄⋊C₄	—	14	1	no	—
1384	C₄⋊C₄	—	14	1	no	—
1385	C₄⋊C₄	—	14	1	no	—
1386	C₄⋊C₄	—	14	1	no	—
1387	C₄⋊C₄	—	14	1	no	—
1388	C₄⋊C₄	—	14	1	no	—
1389	C₄⋊C₄	—	14	1	no	—
1390	C₄⋊C₄	—	14	1	no	—
1391	C₄⋊C₄	—	14	1	no	—
1392	C₄⋊C₄	—	14	1	no	—
1393	C₄⋊C₄	—	14	1	no	—
1394	C₄⋊C₄	—	14	1	no	—
1395	C₄⋊C₄	—	14	1	no	—
1396	C₄⋊C₄	D₄×D₇	1	1	yes	characteristic
1397	C₄⋊C₄	D₄×D₇	1	1	yes	characteristic
1398	C₄⋊C₄	C₂³×D₇	1	1	yes	characteristic
1399	C₄⋊C₄	C₂³×D₇	1	1	yes	characteristic
1400	C₄⋊C₄	C₂³×D₇	1	1	yes	characteristic
1401	C₄⋊C₄	C₂³×D₇	1	1	yes	characteristic
1402	C₄⋊C₄	C₂³×D₇	1	1	yes	characteristic
1403	C₄⋊C₄	C₂³×D₇	1	1	yes	characteristic
1404	C₂²⋊C₄	—	2	1	no	—
1405	C₂²⋊C₄	—	2	1	no	—
1406	C₂²⋊C₄	—	2	1	no	—
1407	C₂²⋊C₄	—	7	1	no	—
1408	C₂²⋊C₄	—	7	1	no	—
1409	C₂²⋊C₄	—	14	1	no	—
1410	C₂²⋊C₄	—	14	1	no	—
1411	C₂²⋊C₄	—	14	1	no	—
1412	C₂²⋊C₄	—	14	1	no	—
1413	C₂²⋊C₄	—	14	1	no	—
1414	C₂²⋊C₄	—	14	1	no	—
1415	C₂²⋊C₄	—	14	1	no	—
1416	C₂²⋊C₄	—	14	1	no	—
1417	C₂²⋊C₄	—	14	1	no	—
1418	C₂²⋊C₄	—	14	1	no	—
1419	C₂²⋊C₄	—	14	1	no	—
1420	C₂²⋊C₄	—	14	1	no	—
1421	C₂²⋊C₄	—	14	1	no	—
1422	C₂²⋊C₄	—	14	1	no	—
1423	C₂²⋊C₄	—	14	1	no	—
1424	C₂²⋊C₄	D₄×D₇	1	1	yes	characteristic
1425	C₂²⋊C₄	D₄×D₇	1	1	yes	characteristic
1426	C₄²	—	2	1	no	—
1427	C₄²	—	2	1	no	—
1428	C₄²	—	2	1	no	—
1429	C₄²	—	7	1	no	—
1430	C₄²	—	7	1	no	—
1431	C₄²	—	7	1	no	—
1432	C₄²	—	7	1	no	—
1433	C₄²	—	7	1	no	—
1434	C₄²	—	7	1	no	—
1435	C₄²	—	14	1	no	—
1436	C₄²	—	14	1	no	—
1437	C₄²	—	14	1	no	—
1438	C₄²	—	14	1	no	—
1439	C₄²	—	14	1	no	—
1440	C₄²	—	14	1	no	—
1441	C₄²	—	14	1	no	—
1442	C₄²	—	14	1	no	—
1443	C₄²	—	14	1	no	—
1444	C₄²	—	14	1	no	—
1445	C₄²	—	14	1	no	—
1446	C₄²	C₂³×D₇	1	1	yes	characteristic
1447	C₄²	C₂³×D₇	1	1	yes	characteristic
1448	C₂×C₇	—	4	1	no	—
1449	C₂×C₇	#3486	1	1	yes	characteristic
1450	C₂×C₇	C₂×#577	1	1	yes	characteristic
1451	C₂×C₇	#3586	1	1	yes	characteristic
1452	D₇	—	4	2	no	—
1453	D₇	—	4	2	no	—
1454	C₂³	—	14	4	no	—
1455	C₂³	—	14	1	no	—
1456	C₂³	—	14	1	no	—
1457	C₂³	—	56	1	no	—
1458	C₂³	—	56	1	no	—
1459	C₂³	C₂×D₄×D₇	1	1	yes	characteristic
1460	Q₈	—	2	1	no	—
1461	Q₈	—	2	1	no	—
1462	Q₈	—	2	1	no	—
1463	Q₈	—	2	1	no	—
1464	Q₈	—	8	1	no	—
1465	Q₈	—	8	1	no	—
1466	Q₈	—	14	2	no	—
1467	Q₈	—	14	2	no	—
1468	Q₈	—	14	1	no	—
1469	Q₈	—	14	1	no	—
1470	Q₈	—	14	1	no	—
1471	Q₈	—	14	1	no	—
1472	Q₈	—	28	1	no	—
1473	Q₈	—	28	1	no	—
1474	Q₈	—	28	2	no	—
1475	Q₈	—	28	2	no	—
1476	Q₈	—	28	2	no	—
1477	Q₈	—	56	1	no	—
1478	Q₈	—	56	1	no	—
1479	Q₈	—	56	1	no	—
1480	D₄	—	7	2	no	—
1481	D₄	—	7	2	no	—
1482	D₄	—	14	4	no	—
1483	D₄	—	14	1	no	—
1484	D₄	—	14	1	no	—
1485	C₂×C₄	—	2	1	no	—
1486	C₂×C₄	—	2	1	no	—
1487	C₂×C₄	—	2	1	no	—
1488	C₂×C₄	—	2	1	no	—
1489	C₂×C₄	—	2	1	no	—
1490	C₂×C₄	—	2	1	no	—
1491	C₂×C₄	—	2	1	no	—
1492	C₂×C₄	—	2	1	no	—
1493	C₂×C₄	—	2	1	no	—
1494	C₂×C₄	—	2	1	no	—
1495	C₂×C₄	—	7	1	no	—
1496	C₂×C₄	—	7	1	no	—
1497	C₂×C₄	—	7	1	no	—
1498	C₂×C₄	—	7	1	no	—
1499	C₂×C₄	—	7	1	no	—
1500	C₂×C₄	—	7	1	no	—
1501	C₂×C₄	—	7	1	no	—
1502	C₂×C₄	—	7	1	no	—
1503	C₂×C₄	—	8	1	no	—
1504	C₂×C₄	—	14	2	no	—
1505	C₂×C₄	—	14	1	no	—
1506	C₂×C₄	—	14	1	no	—
1507	C₂×C₄	—	14	1	no	—
1508	C₂×C₄	—	14	1	no	—
1509	C₂×C₄	—	14	1	no	—
1510	C₂×C₄	—	14	1	no	—
1511	C₂×C₄	—	28	2	no	—
1512	C₂×C₄	—	28	2	no	—
1513	C₂×C₄	—	28	1	no	—
1514	C₂×C₄	—	56	1	no	—
1515	C₂×C₄	—	56	1	no	—
1516	C₂×C₄	—	56	1	no	—
1517	C₂×C₄	—	56	1	no	—
1518	C₂×C₄	—	56	1	no	—
1519	C₂×C₄	—	56	1	no	—
1520	C₂×C₄	—	56	1	no	—
1521	C₂×C₄	—	56	1	no	—
1522	C₂×C₄	—	56	1	no	—
1523	C₂×C₄	—	56	1	no	—
1524	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
1525	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
1526	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
1527	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
1528	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
1529	C₂×C₄	C₂⁴×D₇	1	1	yes	characteristic
1530	C₈	—	2	1	no	—
1531	C₈	—	2	1	no	—
1532	C₈	—	2	1	no	—
1533	C₈	—	2	1	no	—
1534	C₈	—	14	1	no	—
1535	C₈	—	14	1	no	—
1536	C₈	—	14	1	no	—
1537	C₈	—	14	1	no	—
1538	C₇	#61848	1	1	yes	characteristic, complemented, Sylow
1539	C₂²	—	2	1	no	—
1540	C₂²	—	2	1	no	—
1541	C₂²	—	2	1	no	—
1542	C₂²	—	14	2	no	—
1543	C₂²	—	14	2	no	—
1544	C₂²	—	28	1	no	—
1545	C₂²	—	28	1	no	—
1546	C₂²	—	28	1	no	—
1547	C₂²	—	28	1	no	—
1548	C₂²	—	56	4	no	—
1549	C₂²	C₂²×D₄×D₇	1	1	yes	characteristic
1550	C₄	—	2	1	no	—
1551	C₄	—	2	1	no	—
1552	C₄	—	2	1	no	—
1553	C₄	—	2	1	no	—
1554	C₄	—	2	1	no	—
1555	C₄	—	4	1	no	—
1556	C₄	—	4	1	no	—
1557	C₄	—	4	1	no	—
1558	C₄	—	4	1	no	—
1559	C₄	—	4	1	no	—
1560	C₄	—	4	1	no	—
1561	C₄	—	4	1	no	—
1562	C₄	—	4	1	no	—
1563	C₄	—	7	2	no	—
1564	C₄	—	14	1	no	—
1565	C₄	—	14	1	no	—
1566	C₄	—	14	1	no	—
1567	C₄	—	14	1	no	—
1568	C₄	—	14	1	no	—
1569	C₄	—	14	1	no	—
1570	C₄	—	14	1	no	—
1571	C₄	—	28	1	no	—
1572	C₄	—	28	1	no	—
1573	C₄	—	28	1	no	—
1574	C₄	—	28	1	no	—
1575	C₄	—	28	1	no	—
1576	C₄	—	28	1	no	—
1577	C₄	D₇×2₋¹⁺⁴	1	1	yes	characteristic
1578	C₄	D₇×2₋¹⁺⁴	1	1	yes	characteristic
1579	C₂	—	4	1	no	—
1580	C₂	—	28	2	no	—
1581	C₂	—	28	2	no	—
1582	C₂	#11743423	1	1	yes	characteristic
1583	C₂	D₇×#577	1	1	yes	characteristic
1584	C₂	#11744279	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇
commutator, cosocle	C₂×C₄×C₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇
Fitting	C₇×#3242	C₂
socle	C₂²×C₇	C₂³×D₄
prime radical	C₂²×D₂₈	C₂³
hypercenter	#3242	D₇
hypocenter	C₇	#61848
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3242

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #11743570	C₂	semidirect
3. C₇×#3242	C₂	semidirect
4. #11740926	C₂	semidirect
6. #11739414	C₂	semidirect
7. #11739411	C₂	semidirect
8. #11739375	C₂	semidirect
9. #11739358	C₂	semidirect
10. #11739177	C₂	semidirect
11. #11739177	C₂	semidirect
12. #11739068	C₂	semidirect
13. #11739065	C₂	semidirect
14. #11738947	C₂	semidirect
15. #11738945	C₂	semidirect
18. #11738905	C₂	semidirect
20. #11738867	C₂	semidirect
22. #11738711	C₂	semidirect
23. #11738666	C₂	semidirect
24. #11738664	C₂	semidirect
25. #11738664	C₂	semidirect
26. #11738580	C₂	semidirect
27. #11738548	C₂	semidirect
28. #11738482	C₂	semidirect
29. #11738453	C₂	semidirect
31. #11736804	C₂	semidirect
40. #90412	C₂²	semidirect
41. #90412	C₂²	semidirect
56. #90376	C₂²	semidirect
57. #90376	C₂²	semidirect
66. #90260	C₂²	semidirect
67. #90260	C₂²	semidirect
68. #90258	C₂²	semidirect
69. #90258	C₂²	semidirect
77. C₇×#501	C₂²	semidirect
78. C₇×#499	C₂²	semidirect
79. C₇×#491	C₂²	semidirect
80. C₇×#487	C₂²	semidirect
85. C₇×#479	C₂²	semidirect
86. C₇×#479	C₂²	semidirect
87. C₇×#477	C₂²	semidirect
88. C₇×#475	C₂²	semidirect
90. #89866	C₂²	semidirect
91. #89865	C₂²	semidirect
92. #89863	C₂²	semidirect
95. #89852	C₂²	semidirect
96. #89841	C₂²	semidirect
99. #89836	C₂²	semidirect
100. #89835	C₂²	semidirect
101. #89835	C₂²	semidirect
123. #89650	C₂²	semidirect
124. #89649	C₂²	semidirect
125. #89649	C₂²	semidirect
126. #89648	C₂²	semidirect
127. #89648	C₂²	semidirect
128. #89647	C₂²	semidirect
129. #89647	C₂²	semidirect
130. #89646	C₂²	semidirect
135. #89630	C₂²	semidirect
136. #89629	C₂²	semidirect
137. #89629	C₂²	semidirect
138. #89628	C₂²	semidirect
139. #89628	C₂²	semidirect
140. #89627	C₂²	semidirect
141. #89626	C₂²	semidirect
142. #89626	C₂²	semidirect
151. #89603	C₂²	semidirect
152. #89602	C₂²	semidirect
153. #89600	C₂²	semidirect
154. #89600	C₂²	semidirect
167. #89571	C₂²	semidirect
168. #89571	C₂²	semidirect
169. #89569	C₂²	semidirect
170. #89569	C₂²	semidirect
171. #89569	C₂²	semidirect
172. #89569	C₂²	semidirect
173. #89568	C₂²	semidirect
174. #89568	C₂²	semidirect
175. #89566	C₂²	semidirect
176. #89566	C₂²	semidirect
177. #89564	C₂²	semidirect
178. #89564	C₂²	semidirect
179. #89564	C₂²	semidirect
180. #89564	C₂²	semidirect
181. #89563	C₂²	semidirect
182. #89563	C₂²	semidirect
197. #89473	C₂²	semidirect
198. #89473	C₂²	semidirect
201. #89451	C₂²	semidirect
202. C₈×Dic₁₄	C₂²	semidirect
500. #3242	D₇	semidirect
744. #501	C₂×D₇	semidirect
749. #499	C₂×D₇	semidirect
756. #491	C₂×D₇	semidirect
762. #487	C₂×D₇	semidirect
785. #479	C₂×D₇	semidirect
786. #479	C₂×D₇	semidirect
800. #477	C₂×D₇	semidirect
808. #475	C₂×D₇	semidirect
1538. C₇	#61848	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11743667	2
#11743570	2
C₇×#3242	2
#11740926	2
#11740892	2
#11739414	2
#11739411	2
#11739375	2
#11739358	2
#11739177	2
#11739068	2
#11739065	2
#11738947	2
#11738945	2
#11738943	2
#11738905	2
#11738899	2
#11738867	2
#11738857	2
#11738711	2
#11738666	2
#11738664	2
#11738580	2
#11738548	2
#11738482	2
#11738453	2
#11736832	2
#11736804	2
#61848	7