Subgroups — C₇×#61467 #13238683

Order 1792.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3383	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3351	C₂	1	2	yes	maximal, complemented
9	C₇×#3332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3327	C₂	1	2	yes	maximal, complemented
12	C₇×#3326	C₂	1	2	yes	maximal, complemented
13	C₇×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3277	C₂	1	2	yes	maximal, complemented
15	C₇×#3183	C₂	1	2	yes	maximal, complemented
16	C₇×#3182	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3117	C₂	1	2	yes	maximal, complemented
18	C₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3111	C₂	1	2	yes	maximal, complemented
21	C₇×#2971	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₇×#137	C₂	1	2	yes	maximal, complemented
24	C₂×C₇×#137	C₂²	1	1	yes	characteristic
25	C₂×C₇×#137	C₂²	1	2	yes	—
26	C₇×#559	—	2	1	no	—
27	C₇×#559	C₂²	1	1	yes	characteristic
28	C₇×#557	C₂²	1	1	yes	characteristic
29	C₇×#557	C₂²	1	1	yes	characteristic
30	C₇×#556	—	2	1	no	—
31	C₇×#556	—	2	1	no	—
32	C₇×#556	C₂²	1	1	yes	characteristic
33	C₇×#556	C₂²	1	1	yes	characteristic
34	C₇×#553	—	2	2	no	—
35	C₇×#553	C₂²	1	2	yes	—
36	C₇×#552	—	2	2	no	—
37	C₇×#552	C₂²	1	2	yes	—
38	C₇×#550	C₂²	1	1	yes	characteristic
39	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
40	C₇×#548	C₂²	1	2	yes	—
41	C₇×#548	C₂²	1	2	yes	—
42	C₇×#547	—	2	1	no	—
43	C₇×#547	C₂²	1	1	yes	characteristic
44	C₇×#533	—	2	1	no	—
45	C₇×#533	C₂²	1	1	yes	characteristic
46	C₇×#532	—	2	1	no	—
47	C₇×#532	C₂²	1	1	yes	characteristic
48	C₇×#529	—	2	2	no	—
49	C₇×#529	—	2	2	no	—
50	C₇×#529	C₂²	1	2	yes	—
51	C₇×#529	C₂²	1	2	yes	—
52	C₄×C₇×#41	—	2	1	no	—
53	C₄×C₇×#41	—	2	1	no	—
54	C₄×C₇×#41	C₂²	1	2	yes	—
55	C₄×C₇×#41	C₂²	1	1	yes	characteristic
56	C₄×C₇×#41	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
59	C₇×#500	C₂²	1	1	yes	characteristic
60	C₇×#499	C₂²	1	2	yes	—
61	C₇×#495	C₂²	1	2	yes	—
62	C₇×#492	C₂²	1	1	yes	characteristic
63	C₇×#488	C₂²	1	2	yes	—
64	C₇×#488	C₂²	1	2	yes	—
65	C₇×#487	C₂²	1	1	yes	characteristic
66	C₇×#486	C₂²	1	1	yes	characteristic
67	C₇×#485	C₂²	1	2	yes	—
68	C₇×#484	C₂²	1	2	yes	—
69	C₇×#483	C₂²	1	2	yes	—
70	C₇×#482	C₂²	1	2	yes	—
71	C₇×#482	C₂²	1	2	yes	—
72	C₇×#481	C₂²	1	2	yes	—
73	C₇×#479	C₂²	1	2	yes	—
74	C₇×#479	C₂²	1	2	yes	—
75	C₇×#479	C₂²	1	2	yes	—
76	C₇×#478	C₂²	1	2	yes	—
77	C₇×#475	C₂²	1	1	yes	characteristic
78	C₇×#475	C₂²	1	1	yes	characteristic
79	C₇×#475	C₂²	1	1	yes	characteristic
80	C₇×#474	C₂²	1	1	yes	characteristic
81	C₇×#470	C₂²	1	2	yes	—
82	C₇×#469	C₂²	1	2	yes	—
83	C₇×#468	C₂²	1	2	yes	—
84	C₇×#468	C₂²	1	2	yes	—
85	C₇×#468	C₂²	1	2	yes	—
86	C₇×#468	C₂²	1	2	yes	—
87	C₇×#464	C₂²	1	2	yes	—
88	C₇×#464	C₂²	1	2	yes	—
89	C₇×#464	C₂²	1	2	yes	—
90	C₇×#463	C₂²	1	2	yes	—
91	C₇×#462	C₂²	1	1	yes	characteristic
92	C₇×#462	C₂²	1	1	yes	characteristic
93	C₇×#460	C₂²	1	1	yes	characteristic
94	C₇×#459	C₂²	1	1	yes	characteristic
95	C₇×#452	C₂²	1	2	yes	—
96	C₇×#451	C₂²	1	2	yes	—
97	C₇×#451	C₂²	1	2	yes	—
98	C₇×#449	C₂²	1	2	yes	—
99	C₇×#449	C₂²	1	2	yes	—
100	C₇×#448	C₂²	1	2	yes	—
101	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
102	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
103	C₇×#442	C₂²	1	2	yes	—
104	C₇×#441	C₂²	1	2	yes	—
105	C₇×#441	C₂²	1	1	yes	characteristic
106	C₇×#441	C₂²	1	2	yes	—
107	C₇×#441	C₂²	1	1	yes	characteristic
108	C₇×#440	C₂²	1	2	yes	—
109	C₇×#440	C₂²	1	2	yes	—
110	C₇×#440	C₂²	1	1	yes	characteristic
111	C₇×#440	C₂²	1	1	yes	characteristic
112	C₇×#440	C₂²	1	2	yes	—
113	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
114	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
115	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
116	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
117	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
118	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
120	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
121	C₇×#436	C₂²	1	2	yes	—
122	C₇×#436	C₂²	1	1	yes	characteristic
123	C₇×#436	C₂²	1	2	yes	—
124	C₇×#436	C₂²	1	1	yes	characteristic
125	C₇×#432	C₂²	1	2	yes	—
126	C₇×#432	C₂²	1	1	yes	characteristic
127	C₇×#428	C₂²	1	1	yes	characteristic
128	C₇×#428	C₂²	1	2	yes	—
129	C₇×#419	C₂²	1	2	yes	—
130	C₇×#419	C₂²	1	1	yes	characteristic
131	C₇×#417	C₂²	1	1	yes	characteristic
132	C₇×#417	C₂²	1	2	yes	—
133	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
134	C₄×C₇×M₁₆	C₂²	1	2	yes	—
135	#61467	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	—	2	1	no	—
138	C₂×C₇×#41	D₄	1	1	yes	characteristic
139	C₂×C₇×#41	C₂³	1	1	yes	characteristic
140	C₂×C₇×#41	C₂³	1	2	yes	—
141	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
142	C₂²×C₇×Q₈	C₂³	1	2	yes	—
143	C₇×#137	—	2	4	no	—
144	C₇×#137	—	2	8	no	—
145	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×D₈	C₂³	1	2	yes	—
155	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₇×M₁₆	C₂³	1	2	yes	—
157	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₇×M₁₆	C₂³	1	2	yes	—
159	C₇×C₄⋊Q₈	—	2	1	no	—
160	C₇×C₄⋊Q₈	—	2	1	no	—
161	C₇×C₄⋊Q₈	—	2	1	no	—
162	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₇×#127	—	2	1	no	—
166	C₇×#127	C₂³	1	1	yes	characteristic
167	C₇×#126	—	2	2	no	—
168	C₇×#126	—	2	2	no	—
169	C₇×#126	—	2	2	no	—
170	C₇×#126	—	2	2	no	—
171	C₇×#126	—	2	2	no	—
172	C₇×#126	—	2	2	no	—
173	C₇×#125	—	2	2	no	—
174	C₇×#125	—	2	2	no	—
175	C₇×#125	—	2	2	no	—
176	C₇×#125	—	2	1	no	—
177	C₇×#125	C₂³	1	2	yes	—
178	C₇×#125	C₂³	1	2	yes	—
179	C₇×#124	—	2	1	no	—
180	C₇×#124	—	2	1	no	—
181	C₇×#124	—	2	2	no	—
182	C₇×#124	—	2	2	no	—
183	C₇×#124	—	2	1	no	—
184	C₇×#124	C₂³	1	2	yes	—
185	C₇×#124	C₂³	1	2	yes	—
186	C₇×#123	—	2	2	no	—
187	C₇×#123	—	2	2	no	—
188	C₇×#123	—	2	2	no	—
189	C₇×#123	—	2	2	no	—
190	C₇×#123	—	2	2	no	—
191	C₇×#123	—	2	2	no	—
192	C₇×C₂²⋊Q₈	—	2	1	no	—
193	C₇×C₂²⋊Q₈	—	2	1	no	—
194	C₇×C₂²⋊Q₈	—	2	2	no	—
195	C₇×C₂²⋊Q₈	—	2	1	no	—
196	C₇×C₂²⋊Q₈	—	2	2	no	—
197	C₇×C₂²⋊Q₈	—	2	2	no	—
198	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₇×#121	—	2	2	no	—
202	C₇×#121	—	2	2	no	—
203	C₇×#121	—	2	2	no	—
204	C₇×#121	—	2	1	no	—
205	C₇×#121	—	2	2	no	—
206	C₇×#121	C₂³	1	2	yes	—
207	C₇×#121	C₂³	1	2	yes	—
208	C₇×#121	C₂³	1	2	yes	—
209	C₄×C₇×Q₈	—	2	1	no	—
210	C₄×C₇×Q₈	—	2	1	no	—
211	C₄×C₇×Q₈	—	2	1	no	—
212	C₄×C₇×Q₈	—	2	1	no	—
213	C₄×C₇×Q₈	—	2	2	no	—
214	C₄×C₇×Q₈	—	2	2	no	—
215	C₄×C₇×Q₈	—	2	1	no	—
216	C₄×C₇×Q₈	—	2	1	no	—
217	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
218	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
219	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
220	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
221	C₄×C₇×Q₈	C₂³	1	2	yes	—
222	C₄×C₇×Q₈	C₂³	1	2	yes	—
223	C₄×C₇×Q₈	C₂³	1	2	yes	—
224	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
225	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
226	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
227	C₄×C₇×Q₈	C₂³	1	2	yes	—
228	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
229	C₄×C₇×D₄	—	2	1	no	—
230	C₄×C₇×D₄	—	2	2	no	—
231	C₄×C₇×D₄	—	2	1	no	—
232	C₄×C₇×D₄	—	2	2	no	—
233	C₄×C₇×D₄	—	2	1	no	—
234	C₄×C₇×D₄	—	2	2	no	—
235	C₄×C₇×D₄	—	2	2	no	—
236	C₄×C₇×D₄	—	2	1	no	—
237	C₄×C₇×D₄	—	2	1	no	—
238	C₄×C₇×D₄	—	2	2	no	—
239	C₄×C₇×D₄	—	2	2	no	—
240	C₄×C₇×D₄	—	2	2	no	—
241	C₄×C₇×D₄	—	2	1	no	—
242	C₄×C₇×D₄	D₄	1	1	yes	characteristic
243	C₄×C₇×D₄	D₄	1	2	yes	—
244	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
245	C₄×C₇×D₄	C₂³	1	2	yes	—
246	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
247	C₄×C₇×D₄	C₂³	1	2	yes	—
248	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
249	C₄×C₇×D₄	C₂³	1	2	yes	—
250	C₇×#117	—	2	1	no	—
251	C₇×#117	—	2	1	no	—
252	C₇×#117	—	2	2	no	—
253	C₇×#117	—	2	2	no	—
254	C₇×#117	—	2	1	no	—
255	C₇×#117	—	2	2	no	—
256	C₇×#117	—	2	2	no	—
257	C₇×#117	D₄	1	1	yes	characteristic
258	C₇×#117	D₄	1	2	yes	—
259	C₇×#117	C₂³	1	1	yes	characteristic
260	C₇×#117	C₂³	1	2	yes	—
261	C₂×C₇×C₄⋊C₄	—	2	2	no	—
262	C₂×C₇×C₄⋊C₄	—	2	1	no	—
263	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₄²×C₇	—	2	2	no	—
266	C₂×C₄²×C₇	—	2	1	no	—
267	C₂×C₄²×C₇	—	2	2	no	—
268	C₂×C₄²×C₇	—	2	1	no	—
269	C₂×C₄²×C₇	C₂³	1	2	yes	—
270	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
271	C₇×#107	C₂³	1	1	yes	characteristic
272	C₇×#107	C₂³	1	2	yes	—
273	C₇×#107	C₂³	1	2	yes	—
274	C₇×#107	C₂³	1	2	yes	—
275	C₇×#107	C₂³	1	1	yes	characteristic
276	C₇×#106	C₂³	1	2	yes	—
277	C₇×#106	C₂³	1	2	yes	—
278	C₇×#106	C₂³	1	2	yes	—
279	C₇×#106	C₂³	1	1	yes	characteristic
280	C₇×#106	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	2	yes	—
284	C₇×C₄⋊C₈	C₂³	1	2	yes	—
285	C₇×#103	C₂³	1	2	yes	—
286	C₇×#103	C₂³	1	2	yes	—
287	C₇×#103	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	1	yes	characteristic
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	1	yes	characteristic
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#102	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₇×#97	C₂³	1	1	yes	characteristic
309	C₇×#97	C₂³	1	1	yes	characteristic
310	C₇×#97	C₂³	1	2	yes	—
311	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₇×C₈	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	2	yes	—
315	#3482	C₂×C₇	1	1	yes	characteristic, complemented
316	#3480	C₂×C₇	1	1	yes	characteristic, complemented
317	#3394	C₂×C₇	1	1	yes	characteristic, complemented
318	#3383	C₂×C₇	1	1	yes	characteristic, complemented
319	#3365	C₂×C₇	1	1	yes	characteristic, complemented
320	#3364	C₂×C₇	1	1	yes	characteristic, complemented
321	#3353	C₂×C₇	1	1	yes	characteristic, complemented
322	#3351	C₂×C₇	1	2	yes	complemented
323	#3332	C₂×C₇	1	1	yes	characteristic, complemented
324	#3328	C₂×C₇	1	1	yes	characteristic, complemented
325	#3327	C₂×C₇	1	2	yes	complemented
326	#3326	C₂×C₇	1	2	yes	complemented
327	#3278	C₂×C₇	1	1	yes	characteristic, complemented
328	#3277	C₂×C₇	1	2	yes	complemented
329	#3183	C₂×C₇	1	2	yes	complemented
330	#3182	C₂×C₇	1	1	yes	characteristic, complemented
331	#3117	C₂×C₇	1	2	yes	complemented
332	#3115	C₂×C₇	1	1	yes	characteristic, complemented
333	#3113	C₂×C₇	1	1	yes	characteristic, complemented
334	#3111	C₂×C₇	1	2	yes	complemented
335	#2971	C₂×C₇	1	1	yes	characteristic, complemented
336	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
337	C₄×#137	C₂×C₇	1	2	yes	complemented
338	C₇×#41	—	2	2	no	—
339	C₇×#41	—	2	4	no	—
340	C₇×#41	—	4	2	no	—
341	C₇×#41	—	4	1	no	—
342	C₇×#41	—	4	2	no	—
343	C₇×#41	—	4	4	no	—
344	C₇×#41	—	4	4	no	—
345	C₂×C₇×Q₈	—	2	1	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	—	2	1	no	—
348	C₂×C₇×Q₈	—	2	1	no	—
349	C₂×C₇×Q₈	—	2	4	no	—
350	C₂×C₇×Q₈	—	2	2	no	—
351	C₂×C₇×Q₈	—	4	2	no	—
352	C₂×C₇×Q₈	—	4	1	no	—
353	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
354	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
355	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
356	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
357	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₇×D₄	—	2	2	no	—
359	C₂×C₇×D₄	—	2	1	no	—
360	C₂×C₇×D₄	—	2	2	no	—
361	C₂×C₇×D₄	—	2	2	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	—	2	1	no	—
364	C₂×C₇×D₄	—	2	1	no	—
365	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
366	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
367	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
368	C₂×C₇×D₄	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₇	—	2	2	no	—
370	C₂²×C₄×C₇	—	2	1	no	—
371	C₂²×C₄×C₇	—	2	2	no	—
372	C₂²×C₄×C₇	—	2	1	no	—
373	C₂²×C₄×C₇	—	2	1	no	—
374	C₂²×C₄×C₇	—	2	2	no	—
375	C₂²×C₄×C₇	—	2	2	no	—
376	C₂²×C₄×C₇	—	2	1	no	—
377	C₂²×C₄×C₇	—	2	1	no	—
378	C₂²×C₄×C₇	—	2	2	no	—
379	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
381	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
383	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
385	C₇×Q₁₆	—	2	2	no	—
386	C₇×Q₁₆	—	2	4	no	—
387	C₇×Q₁₆	—	4	2	no	—
388	C₇×Q₁₆	#41	1	4	yes	complemented
389	C₇×SD₁₆	—	2	4	no	—
390	C₇×SD₁₆	—	2	2	no	—
391	C₇×SD₁₆	—	2	4	no	—
392	C₇×SD₁₆	—	2	2	no	—
393	C₇×SD₁₆	—	4	2	no	—
394	C₇×D₈	—	4	2	no	—
395	C₇×M₁₆	—	2	2	no	—
396	C₇×M₁₆	—	2	4	no	—
397	C₇×M₁₆	—	4	2	no	—
398	C₇×M₁₆	—	4	1	no	—
399	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
400	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
401	C₂×C₇×C₈	C₂⁴	1	2	yes	—
402	C₂×C₇×C₈	C₂⁴	1	2	yes	—
403	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
404	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
405	C₇×C₄⋊C₄	—	2	1	no	—
406	C₇×C₄⋊C₄	—	2	1	no	—
407	C₇×C₄⋊C₄	—	2	1	no	—
408	C₇×C₄⋊C₄	—	2	2	no	—
409	C₇×C₄⋊C₄	—	2	2	no	—
410	C₇×C₄⋊C₄	—	2	2	no	—
411	C₇×C₄⋊C₄	—	2	1	no	—
412	C₇×C₄⋊C₄	—	2	1	no	—
413	C₇×C₄⋊C₄	—	2	2	no	—
414	C₇×C₄⋊C₄	—	2	1	no	—
415	C₇×C₄⋊C₄	—	2	1	no	—
416	C₇×C₄⋊C₄	—	2	2	no	—
417	C₇×C₄⋊C₄	—	2	2	no	—
418	C₇×C₄⋊C₄	—	2	2	no	—
419	C₇×C₄⋊C₄	—	2	2	no	—
420	C₇×C₄⋊C₄	—	2	2	no	—
421	C₇×C₄⋊C₄	—	2	1	no	—
422	C₇×C₄⋊C₄	—	2	1	no	—
423	C₇×C₄⋊C₄	—	2	2	no	—
424	C₇×C₄⋊C₄	—	2	1	no	—
425	C₇×C₄⋊C₄	—	2	2	no	—
426	C₇×C₄⋊C₄	—	2	1	no	—
427	C₇×C₄⋊C₄	—	2	2	no	—
428	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
429	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
430	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
431	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
432	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
433	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
434	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
435	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
436	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
437	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
438	C₇×C₂²⋊C₄	—	2	2	no	—
439	C₇×C₂²⋊C₄	—	2	2	no	—
440	C₇×C₂²⋊C₄	—	2	2	no	—
441	C₇×C₂²⋊C₄	—	2	1	no	—
442	C₇×C₂²⋊C₄	—	2	2	no	—
443	C₇×C₂²⋊C₄	—	2	2	no	—
444	C₇×C₂²⋊C₄	—	2	2	no	—
445	C₇×C₂²⋊C₄	—	2	2	no	—
446	C₇×C₂²⋊C₄	—	2	2	no	—
447	C₇×C₂²⋊C₄	—	2	2	no	—
448	C₇×C₂²⋊C₄	—	2	1	no	—
449	C₇×C₂²⋊C₄	—	2	1	no	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	—	2	2	no	—
453	C₇×C₂²⋊C₄	—	2	2	no	—
454	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
455	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
456	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
457	C₄²×C₇	—	2	1	no	—
458	C₄²×C₇	—	2	1	no	—
459	C₄²×C₇	—	2	1	no	—
460	C₄²×C₇	—	2	1	no	—
461	C₄²×C₇	—	2	2	no	—
462	C₄²×C₇	—	2	2	no	—
463	C₄²×C₇	—	2	2	no	—
464	C₄²×C₇	—	2	2	no	—
465	C₄²×C₇	—	2	1	no	—
466	C₄²×C₇	—	2	1	no	—
467	C₄²×C₇	—	2	2	no	—
468	C₄²×C₇	—	2	1	no	—
469	C₄²×C₇	C₂×D₄	1	2	yes	—
470	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₇	C₂×D₄	1	2	yes	—
472	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₇	C₂⁴	1	2	yes	—
474	C₄²×C₇	C₂⁴	1	1	yes	characteristic
475	C₄²×C₇	C₂⁴	1	1	yes	characteristic
476	C₂×#137	C₂²×C₇	1	1	yes	characteristic
477	C₂×#137	C₂²×C₇	1	2	yes	—
478	#559	—	2	1	no	—
479	#559	C₂²×C₇	1	1	yes	characteristic
480	#557	C₂²×C₇	1	1	yes	characteristic
481	#557	C₂²×C₇	1	1	yes	characteristic
482	#556	—	2	1	no	—
483	#556	—	2	1	no	—
484	#556	C₂²×C₇	1	1	yes	characteristic
485	#556	C₂²×C₇	1	1	yes	characteristic
486	#553	—	2	2	no	—
487	#553	C₂²×C₇	1	2	yes	—
488	#552	—	2	2	no	—
489	#552	C₂²×C₇	1	2	yes	—
490	#550	C₂²×C₇	1	1	yes	characteristic
491	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
492	#548	C₂²×C₇	1	2	yes	—
493	#548	C₂²×C₇	1	2	yes	—
494	#547	—	2	1	no	—
495	#547	C₂²×C₇	1	1	yes	characteristic
496	#533	—	2	1	no	—
497	#533	C₂²×C₇	1	1	yes	characteristic
498	#532	—	2	1	no	—
499	#532	C₂²×C₇	1	1	yes	characteristic
500	#529	—	2	2	no	—
501	#529	—	2	2	no	—
502	#529	C₂²×C₇	1	2	yes	—
503	#529	C₂²×C₇	1	2	yes	—
504	C₄×#41	—	2	1	no	—
505	C₄×#41	—	2	1	no	—
506	C₄×#41	C₂²×C₇	1	2	yes	—
507	C₄×#41	C₂²×C₇	1	1	yes	characteristic
508	C₄×#41	C₂²×C₇	1	1	yes	characteristic
509	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
510	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
511	#500	C₂²×C₇	1	1	yes	characteristic
512	#499	C₂²×C₇	1	2	yes	—
513	#495	C₂²×C₇	1	2	yes	—
514	#492	C₂²×C₇	1	1	yes	characteristic
515	#488	C₂²×C₇	1	2	yes	—
516	#488	C₂²×C₇	1	2	yes	—
517	#487	C₂²×C₇	1	1	yes	characteristic
518	#486	C₂²×C₇	1	1	yes	characteristic
519	#485	C₂²×C₇	1	2	yes	—
520	#484	C₂²×C₇	1	2	yes	—
521	#483	C₂²×C₇	1	2	yes	—
522	#482	C₂²×C₇	1	2	yes	—
523	#482	C₂²×C₇	1	2	yes	—
524	#481	C₂²×C₇	1	2	yes	—
525	#479	C₂²×C₇	1	2	yes	—
526	#479	C₂²×C₇	1	2	yes	—
527	#479	C₂²×C₇	1	2	yes	—
528	#478	C₂²×C₇	1	2	yes	—
529	#475	C₂²×C₇	1	1	yes	characteristic
530	#475	C₂²×C₇	1	1	yes	characteristic
531	#475	C₂²×C₇	1	1	yes	characteristic
532	#474	C₂²×C₇	1	1	yes	characteristic
533	#470	C₂²×C₇	1	2	yes	—
534	#469	C₂²×C₇	1	2	yes	—
535	#468	C₂²×C₇	1	2	yes	—
536	#468	C₂²×C₇	1	2	yes	—
537	#468	C₂²×C₇	1	2	yes	—
538	#468	C₂²×C₇	1	2	yes	—
539	#464	C₂²×C₇	1	2	yes	—
540	#464	C₂²×C₇	1	2	yes	—
541	#464	C₂²×C₇	1	2	yes	—
542	#463	C₂²×C₇	1	2	yes	—
543	#462	C₂²×C₇	1	1	yes	characteristic
544	#462	C₂²×C₇	1	1	yes	characteristic
545	#460	C₂²×C₇	1	1	yes	characteristic
546	#459	C₂²×C₇	1	1	yes	characteristic
547	#452	C₂²×C₇	1	2	yes	—
548	#451	C₂²×C₇	1	2	yes	—
549	#451	C₂²×C₇	1	2	yes	—
550	#449	C₂²×C₇	1	2	yes	—
551	#449	C₂²×C₇	1	2	yes	—
552	#448	C₂²×C₇	1	2	yes	—
553	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
554	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
555	#442	C₂²×C₇	1	2	yes	—
556	#441	C₂²×C₇	1	2	yes	—
557	#441	C₂²×C₇	1	2	yes	—
558	#441	C₂²×C₇	1	1	yes	characteristic
559	#441	C₂²×C₇	1	1	yes	characteristic
560	#440	C₂²×C₇	1	1	yes	characteristic
561	#440	C₂²×C₇	1	2	yes	—
562	#440	C₂²×C₇	1	2	yes	—
563	#440	C₂²×C₇	1	2	yes	—
564	#440	C₂²×C₇	1	1	yes	characteristic
565	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
566	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
567	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
568	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
569	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
570	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
571	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
572	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
573	#436	C₂²×C₇	1	1	yes	characteristic
574	#436	C₂²×C₇	1	2	yes	—
575	#436	C₂²×C₇	1	1	yes	characteristic
576	#436	C₂²×C₇	1	2	yes	—
577	#432	C₂²×C₇	1	2	yes	—
578	#432	C₂²×C₇	1	1	yes	characteristic
579	#428	C₂²×C₇	1	1	yes	characteristic
580	#428	C₂²×C₇	1	2	yes	—
581	#419	C₂²×C₇	1	2	yes	—
582	#419	C₂²×C₇	1	1	yes	characteristic
583	#417	C₂²×C₇	1	2	yes	—
584	#417	C₂²×C₇	1	1	yes	characteristic
585	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
586	C₄×M₁₆	C₂²×C₇	1	2	yes	—
587	C₂³×C₇	—	2	1	no	—
588	C₂³×C₇	—	2	2	no	—
589	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
590	C₂³×C₇	C₂²×D₄	1	2	yes	—
591	C₇×Q₈	—	2	2	no	—
592	C₇×Q₈	—	2	1	no	—
593	C₇×Q₈	—	2	1	no	—
594	C₇×Q₈	—	2	1	no	—
595	C₇×Q₈	—	2	2	no	—
596	C₇×Q₈	—	2	2	no	—
597	C₇×Q₈	—	2	1	no	—
598	C₇×Q₈	—	4	2	no	—
599	C₇×Q₈	—	4	4	no	—
600	C₇×Q₈	—	4	2	no	—
601	C₇×Q₈	—	4	2	no	—
602	C₇×Q₈	C₂×#41	1	2	yes	—
603	C₇×Q₈	C₂×#41	1	2	yes	—
604	C₇×D₄	—	2	2	no	—
605	C₇×D₄	—	2	1	no	—
606	C₇×D₄	—	2	2	no	—
607	C₇×D₄	—	2	1	no	—
608	C₇×D₄	—	2	2	no	—
609	C₇×D₄	—	4	2	no	—
610	C₇×D₄	—	4	4	no	—
611	C₇×D₄	—	4	2	no	—
612	C₇×D₄	—	4	4	no	—
613	C₇×D₄	—	4	4	no	—
614	C₇×D₄	—	4	2	no	—
615	C₇×D₄	—	8	1	no	—
616	C₇×D₄	—	8	2	no	—
617	C₂×C₄×C₇	—	2	1	no	—
618	C₂×C₄×C₇	—	2	1	no	—
619	C₂×C₄×C₇	—	2	2	no	—
620	C₂×C₄×C₇	—	2	2	no	—
621	C₂×C₄×C₇	—	2	1	no	—
622	C₂×C₄×C₇	—	2	2	no	—
623	C₂×C₄×C₇	—	2	1	no	—
624	C₂×C₄×C₇	—	2	1	no	—
625	C₂×C₄×C₇	—	2	1	no	—
626	C₂×C₄×C₇	—	2	1	no	—
627	C₂×C₄×C₇	—	2	1	no	—
628	C₂×C₄×C₇	—	2	2	no	—
629	C₂×C₄×C₇	—	2	2	no	—
630	C₂×C₄×C₇	—	2	1	no	—
631	C₂×C₄×C₇	—	2	2	no	—
632	C₂×C₄×C₇	—	4	2	no	—
633	C₂×C₄×C₇	—	4	1	no	—
634	C₂×C₄×C₇	—	4	2	no	—
635	C₂×C₄×C₇	—	4	4	no	—
636	C₂×C₄×C₇	—	4	2	no	—
637	C₂×C₄×C₇	—	4	2	no	—
638	C₂×C₄×C₇	—	4	4	no	—
639	C₂×C₄×C₇	—	4	2	no	—
640	C₂×C₄×C₇	—	4	4	no	—
641	C₂×C₄×C₇	—	4	4	no	—
642	C₂×C₄×C₇	—	4	2	no	—
643	C₂×C₄×C₇	—	8	2	no	—
644	C₂×C₄×C₇	—	8	1	no	—
645	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
647	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
648	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
649	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
650	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
651	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
652	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
653	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
654	C₇×C₈	—	2	1	no	—
655	C₇×C₈	—	2	2	no	—
656	C₇×C₈	—	2	1	no	—
657	C₇×C₈	—	2	2	no	—
658	C₇×C₈	—	2	1	no	—
659	C₇×C₈	C₂×#41	1	2	yes	—
660	C₂×#41	—	2	1	no	—
661	C₂×#41	—	2	1	no	—
662	C₂×#41	C₇×D₄	1	1	yes	characteristic
663	C₂×#41	C₂³×C₇	1	1	yes	characteristic
664	C₂×#41	C₂³×C₇	1	2	yes	—
665	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
666	C₂²×Q₈	C₂³×C₇	1	2	yes	—
667	#137	—	2	4	no	—
668	#137	—	2	8	no	—
669	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
670	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
671	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
672	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
673	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
674	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
675	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
677	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
678	C₂×D₈	C₂³×C₇	1	2	yes	—
679	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
680	C₂×M₁₆	C₂³×C₇	1	2	yes	—
681	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
682	C₂×M₁₆	C₂³×C₇	1	2	yes	—
683	C₄⋊Q₈	—	2	1	no	—
684	C₄⋊Q₈	—	2	1	no	—
685	C₄⋊Q₈	—	2	1	no	—
686	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
687	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
688	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
689	#127	—	2	1	no	—
690	#127	C₂³×C₇	1	1	yes	characteristic
691	#126	—	2	2	no	—
692	#126	—	2	2	no	—
693	#126	—	2	2	no	—
694	#126	—	2	2	no	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	—	2	2	no	—
700	#125	—	2	1	no	—
701	#125	C₂³×C₇	1	2	yes	—
702	#125	C₂³×C₇	1	2	yes	—
703	#124	—	2	1	no	—
704	#124	—	2	1	no	—
705	#124	—	2	2	no	—
706	#124	—	2	2	no	—
707	#124	—	2	1	no	—
708	#124	C₂³×C₇	1	2	yes	—
709	#124	C₂³×C₇	1	2	yes	—
710	#123	—	2	2	no	—
711	#123	—	2	2	no	—
712	#123	—	2	2	no	—
713	#123	—	2	2	no	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	2	1	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	1	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
723	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
724	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	—	2	2	no	—
728	#121	—	2	1	no	—
729	#121	—	2	2	no	—
730	#121	C₂³×C₇	1	2	yes	—
731	#121	C₂³×C₇	1	2	yes	—
732	#121	C₂³×C₇	1	2	yes	—
733	C₄×Q₈	—	2	1	no	—
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	2	no	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
742	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
743	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
744	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
745	C₄×Q₈	C₂³×C₇	1	2	yes	—
746	C₄×Q₈	C₂³×C₇	1	2	yes	—
747	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
748	C₄×Q₈	C₂³×C₇	1	2	yes	—
749	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
750	C₄×Q₈	C₂³×C₇	1	2	yes	—
751	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
752	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
753	C₄×D₄	—	2	1	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	1	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	1	no	—
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	2	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	1	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	1	no	—
766	C₄×D₄	C₇×D₄	1	1	yes	characteristic
767	C₄×D₄	C₇×D₄	1	2	yes	—
768	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
769	C₄×D₄	C₂³×C₇	1	2	yes	—
770	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₇	1	2	yes	—
772	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
773	C₄×D₄	C₂³×C₇	1	2	yes	—
774	#117	—	2	1	no	—
775	#117	—	2	1	no	—
776	#117	—	2	2	no	—
777	#117	—	2	2	no	—
778	#117	—	2	1	no	—
779	#117	—	2	2	no	—
780	#117	—	2	2	no	—
781	#117	C₇×D₄	1	1	yes	characteristic
782	#117	C₇×D₄	1	2	yes	—
783	#117	C₂³×C₇	1	1	yes	characteristic
784	#117	C₂³×C₇	1	2	yes	—
785	C₂×C₄⋊C₄	—	2	2	no	—
786	C₂×C₄⋊C₄	—	2	1	no	—
787	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
788	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
789	C₂×C₄²	—	2	2	no	—
790	C₂×C₄²	—	2	1	no	—
791	C₂×C₄²	—	2	2	no	—
792	C₂×C₄²	—	2	1	no	—
793	C₂×C₄²	C₂³×C₇	1	2	yes	—
794	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
795	#107	C₂³×C₇	1	1	yes	characteristic
796	#107	C₂³×C₇	1	2	yes	—
797	#107	C₂³×C₇	1	2	yes	—
798	#107	C₂³×C₇	1	1	yes	characteristic
799	#107	C₂³×C₇	1	2	yes	—
800	#106	C₂³×C₇	1	1	yes	characteristic
801	#106	C₂³×C₇	1	2	yes	—
802	#106	C₂³×C₇	1	1	yes	characteristic
803	#106	C₂³×C₇	1	2	yes	—
804	#106	C₂³×C₇	1	2	yes	—
805	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
806	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
807	C₄⋊C₈	C₂³×C₇	1	2	yes	—
808	C₄⋊C₈	C₂³×C₇	1	2	yes	—
809	#103	C₂³×C₇	1	1	yes	characteristic
810	#103	C₂³×C₇	1	1	yes	characteristic
811	#103	C₂³×C₇	1	1	yes	characteristic
812	#103	C₂³×C₇	1	2	yes	—
813	#103	C₂³×C₇	1	2	yes	—
814	#103	C₂³×C₇	1	1	yes	characteristic
815	#103	C₂³×C₇	1	2	yes	—
816	#103	C₂³×C₇	1	1	yes	characteristic
817	#103	C₂³×C₇	1	2	yes	—
818	#103	C₂³×C₇	1	1	yes	characteristic
819	#103	C₂³×C₇	1	2	yes	—
820	#103	C₂³×C₇	1	2	yes	—
821	#103	C₂³×C₇	1	2	yes	—
822	#102	C₂³×C₇	1	2	yes	—
823	#102	C₂³×C₇	1	1	yes	characteristic
824	#102	C₂³×C₇	1	2	yes	—
825	#102	C₂³×C₇	1	1	yes	characteristic
826	#102	C₂³×C₇	1	2	yes	—
827	#102	C₂³×C₇	1	2	yes	—
828	#102	C₂³×C₇	1	2	yes	—
829	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
830	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
832	#97	C₂³×C₇	1	1	yes	characteristic
833	#97	C₂³×C₇	1	1	yes	characteristic
834	#97	C₂³×C₇	1	2	yes	—
835	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
836	C₄×C₈	C₂³×C₇	1	2	yes	—
837	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
838	C₄×C₈	C₂³×C₇	1	2	yes	—
839	C₂²×C₇	—	2	1	no	—
840	C₂²×C₇	—	2	2	no	—
841	C₂²×C₇	—	2	1	no	—
842	C₂²×C₇	—	2	2	no	—
843	C₂²×C₇	—	2	1	no	—
844	C₂²×C₇	—	2	2	no	—
845	C₂²×C₇	—	4	1	no	—
846	C₂²×C₇	—	4	2	no	—
847	C₂²×C₇	—	4	1	no	—
848	C₂²×C₇	—	4	2	no	—
849	C₂²×C₇	—	4	2	no	—
850	C₂²×C₇	—	4	1	no	—
851	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
852	C₄×C₇	—	2	1	no	—
853	C₄×C₇	—	2	2	no	—
854	C₄×C₇	—	2	1	no	—
855	C₄×C₇	—	2	2	no	—
856	C₄×C₇	—	2	1	no	—
857	C₄×C₇	—	2	2	no	—
858	C₄×C₇	—	2	2	no	—
859	C₄×C₇	—	2	1	no	—
860	C₄×C₇	—	2	2	no	—
861	C₄×C₇	—	4	1	no	—
862	C₄×C₇	—	4	1	no	—
863	C₄×C₇	—	4	1	no	—
864	C₄×C₇	—	4	1	no	—
865	C₄×C₇	—	4	2	no	—
866	C₄×C₇	—	4	1	no	—
867	C₄×C₇	—	4	2	no	—
868	C₄×C₇	—	4	2	no	—
869	C₄×C₇	#575	1	2	yes	—
870	C₄×C₇	C₂²×#41	1	1	yes	characteristic
871	C₄×C₇	#585	1	1	yes	characteristic
872	#41	—	2	2	no	—
873	#41	—	2	4	no	—
874	#41	—	4	2	no	—
875	#41	—	4	1	no	—
876	#41	—	4	2	no	—
877	#41	—	4	4	no	—
878	#41	—	4	4	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	4	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	4	2	no	—
886	C₂×Q₈	—	4	1	no	—
887	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
890	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
900	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
901	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₇	1	2	yes	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
914	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
915	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
916	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
917	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
919	Q₁₆	—	2	2	no	—
920	Q₁₆	—	2	4	no	—
921	Q₁₆	—	4	2	no	—
922	Q₁₆	C₇×#41	1	4	yes	complemented
923	SD₁₆	—	2	4	no	—
924	SD₁₆	—	2	2	no	—
925	SD₁₆	—	2	4	no	—
926	SD₁₆	—	2	2	no	—
927	SD₁₆	—	4	2	no	—
928	D₈	—	4	2	no	—
929	M₁₆	—	2	2	no	—
930	M₁₆	—	2	4	no	—
931	M₁₆	—	4	2	no	—
932	M₁₆	—	4	1	no	—
933	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₇	1	2	yes	—
936	C₂×C₈	C₂⁴×C₇	1	2	yes	—
937	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
963	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
964	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
965	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
969	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
989	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
990	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	C₂×C₇×D₄	1	2	yes	—
1004	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1005	C₄²	C₂×C₇×D₄	1	2	yes	—
1006	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₇	1	2	yes	—
1008	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1010	C₂×C₇	—	4	1	no	—
1011	C₂×C₇	—	4	2	no	—
1012	C₂×C₇	—	8	1	no	—
1013	C₂×C₇	—	8	2	no	—
1014	C₂×C₇	D₄×#41	1	1	yes	characteristic
1015	C₂×C₇	C₂×#575	1	1	yes	characteristic
1016	C₂×C₇	#3586	1	1	yes	characteristic
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1020	C₂³	C₂²×C₇×D₄	1	2	yes	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	4	2	no	—
1029	Q₈	—	4	4	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	4	2	no	—
1032	Q₈	C₂×C₇×#41	1	2	yes	—
1033	Q₈	C₂×C₇×#41	1	2	yes	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	4	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	4	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	8	1	no	—
1046	D₄	—	8	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	4	1	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	4	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	4	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	—	8	1	no	—
1075	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1076	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1077	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1078	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1079	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1080	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1081	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1082	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1083	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1084	C₈	—	2	1	no	—
1085	C₈	—	2	2	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	2	no	—
1088	C₈	—	2	1	no	—
1089	C₈	C₂×C₇×#41	1	2	yes	—
1090	C₇	#61467	1	1	yes	characteristic, direct product factor, Sylow
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1104	C₄	—	2	1	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	C₇×#575	1	2	yes	—
1122	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1123	C₄	C₇×#585	1	1	yes	characteristic
1124	C₂	—	4	1	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	8	1	no	—
1127	C₂	—	8	2	no	—
1128	C₂	C₇×D₄×#41	1	1	yes	characteristic
1129	C₂	C₂×C₇×#575	1	1	yes	characteristic
1130	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3482	C₂	semidirect
2. C₇×#3480	C₂	semidirect
3. C₇×#3394	C₂	semidirect
4. C₇×#3383	C₂	semidirect
5. C₇×#3365	C₂	semidirect
6. C₇×#3364	C₂	semidirect
7. C₇×#3353	C₂	semidirect
8. C₇×#3351	C₂	semidirect
9. C₇×#3332	C₂	semidirect
10. C₇×#3328	C₂	semidirect
11. C₇×#3327	C₂	semidirect
12. C₇×#3326	C₂	semidirect
13. C₇×#3278	C₂	semidirect
14. C₇×#3277	C₂	semidirect
15. C₇×#3183	C₂	semidirect
16. C₇×#3182	C₂	semidirect
17. C₇×#3117	C₂	semidirect
18. C₇×#3115	C₂	semidirect
19. C₇×#3113	C₂	semidirect
20. C₇×#3111	C₂	semidirect
21. C₇×#2971	C₂	semidirect
22. C₄×C₇×#137	C₂	semidirect
23. C₄×C₇×#137	C₂	semidirect
135. #61467	C₇	direct (N × H)
315. #3482	C₂×C₇	semidirect
316. #3480	C₂×C₇	semidirect
317. #3394	C₂×C₇	semidirect
318. #3383	C₂×C₇	semidirect
319. #3365	C₂×C₇	semidirect
320. #3364	C₂×C₇	semidirect
321. #3353	C₂×C₇	semidirect
322. #3351	C₂×C₇	semidirect
323. #3332	C₂×C₇	semidirect
324. #3328	C₂×C₇	semidirect
325. #3327	C₂×C₇	semidirect
326. #3326	C₂×C₇	semidirect
327. #3278	C₂×C₇	semidirect
328. #3277	C₂×C₇	semidirect
329. #3183	C₂×C₇	semidirect
330. #3182	C₂×C₇	semidirect
331. #3117	C₂×C₇	semidirect
332. #3115	C₂×C₇	semidirect
333. #3113	C₂×C₇	semidirect
334. #3111	C₂×C₇	semidirect
335. #2971	C₂×C₇	semidirect
336. C₄×#137	C₂×C₇	semidirect
337. C₄×#137	C₂×C₇	semidirect
388. C₇×Q₁₆	#41	semidirect
922. Q₁₆	C₇×#41	semidirect
1090. C₇	#61467	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3482	2
C₇×#3480	2
C₇×#3394	2
C₇×#3383	2
C₇×#3365	2
C₇×#3364	2
C₇×#3353	2
C₇×#3351	2
C₇×#3332	2
C₇×#3328	2
C₇×#3327	2
C₇×#3326	2
C₇×#3278	2
C₇×#3277	2
C₇×#3183	2
C₇×#3182	2
C₇×#3117	2
C₇×#3115	2
C₇×#3113	2
C₇×#3111	2
C₇×#2971	2
C₄×C₇×#137	2
#61467	7

Subgroups — C7×#61467 #13238683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61467 #13238683