Subgroups — C₇×#61462 #13238678

Order 1792.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3347	C₂	1	2	yes	maximal, complemented
8	C₇×#3340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3321	C₂	1	2	yes	maximal, complemented
10	C₇×#3309	C₂	1	2	yes	maximal, complemented
11	C₇×#3305	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3304	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3287	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3271	C₂	1	2	yes	maximal, complemented
15	C₇×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3180	C₂	1	2	yes	maximal, complemented
17	C₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3115	C₂	1	2	yes	maximal, complemented
19	C₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3111	C₂	1	2	yes	maximal, complemented
21	C₇×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2943	C₂	1	2	yes	maximal, complemented
24	C₂×C₇×#137	C₂²	1	1	yes	characteristic
25	C₂×C₇×#135	C₂²	1	2	yes	—
26	C₇×#559	—	2	1	no	—
27	C₇×#559	C₂²	1	1	yes	characteristic
28	C₇×Q₈²	C₂²	1	1	yes	characteristic
29	C₇×#557	C₂²	1	1	yes	characteristic
30	C₇×#556	—	2	1	no	—
31	C₇×#556	C₂²	1	1	yes	characteristic
32	C₇×#555	—	2	1	no	—
33	C₇×#555	—	2	2	no	—
34	C₇×#555	C₂²	1	1	yes	characteristic
35	C₇×#555	C₂²	1	2	yes	—
36	C₇×#553	—	2	2	no	—
37	C₇×#553	C₂²	1	2	yes	—
38	C₇×#550	—	2	1	no	—
39	C₇×#550	C₂²	1	2	yes	—
40	C₇×#550	C₂²	1	1	yes	characteristic
41	C₇×#550	C₂²	1	1	yes	characteristic
42	C₇×#550	C₂²	1	1	yes	characteristic
43	C₇×#548	C₂²	1	2	yes	—
44	C₇×#532	—	2	1	no	—
45	C₇×#532	—	2	2	no	—
46	C₇×#532	—	2	1	no	—
47	C₇×#532	C₂²	1	2	yes	—
48	C₇×#532	C₂²	1	1	yes	characteristic
49	C₇×#532	C₂²	1	1	yes	characteristic
50	C₇×#529	—	2	2	no	—
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	2	yes	—
56	C₄×C₇×#41	C₂²	1	1	yes	characteristic
57	C₄×C₇×#41	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
59	C₇×#501	C₂²	1	2	yes	—
60	C₇×#498	C₂²	1	1	yes	characteristic
61	C₇×#496	C₂²	1	2	yes	—
62	C₇×#493	C₂²	1	1	yes	characteristic
63	C₇×#490	C₂²	1	2	yes	—
64	C₇×#489	C₂²	1	2	yes	—
65	C₇×#486	C₂²	1	1	yes	characteristic
66	C₇×#486	C₂²	1	1	yes	characteristic
67	C₇×#485	C₂²	1	2	yes	—
68	C₇×#482	C₂²	1	2	yes	—
69	C₇×#482	C₂²	1	2	yes	—
70	C₇×#482	C₂²	1	2	yes	—
71	C₇×#482	C₂²	1	2	yes	—
72	C₇×#480	C₂²	1	2	yes	—
73	C₇×#479	C₂²	1	2	yes	—
74	C₇×#478	C₂²	1	2	yes	—
75	C₇×#477	C₂²	1	1	yes	characteristic
76	C₇×#477	C₂²	1	1	yes	characteristic
77	C₇×#475	C₂²	1	1	yes	characteristic
78	C₇×#475	C₂²	1	2	yes	—
79	C₇×#474	C₂²	1	1	yes	characteristic
80	C₇×#474	C₂²	1	2	yes	—
81	C₇×#469	C₂²	1	2	yes	—
82	C₇×#469	C₂²	1	2	yes	—
83	C₇×#466	C₂²	1	2	yes	—
84	C₇×#466	C₂²	1	2	yes	—
85	C₇×#465	C₂²	1	2	yes	—
86	C₇×#465	C₂²	1	2	yes	—
87	C₇×#464	C₂²	1	2	yes	—
88	C₇×#463	C₂²	1	2	yes	—
89	C₇×#460	C₂²	1	2	yes	—
90	C₇×#460	C₂²	1	1	yes	characteristic
91	C₇×#460	C₂²	1	1	yes	characteristic
92	C₇×#460	C₂²	1	1	yes	characteristic
93	C₇×#459	C₂²	1	1	yes	characteristic
94	C₇×#459	C₂²	1	2	yes	—
95	C₇×#452	C₂²	1	2	yes	—
96	C₇×#449	C₂²	1	2	yes	—
97	C₇×#449	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×#446	C₂²	1	1	yes	characteristic
102	C₇×#446	C₂²	1	1	yes	characteristic
103	C₇×#442	C₂²	1	2	yes	—
104	C₇×#442	C₂²	1	2	yes	—
105	C₇×#442	C₂²	1	2	yes	—
106	C₇×#442	C₂²	1	2	yes	—
107	C₇×#441	C₂²	1	1	yes	characteristic
108	C₇×#441	C₂²	1	2	yes	—
109	C₇×#441	C₂²	1	1	yes	characteristic
110	C₇×#440	C₂²	1	1	yes	characteristic
111	C₇×#440	C₂²	1	2	yes	—
112	C₇×#440	C₂²	1	2	yes	—
113	C₇×#440	C₂²	1	2	yes	—
114	C₇×#440	C₂²	1	2	yes	—
115	C₇×#440	C₂²	1	2	yes	—
116	C₇×#440	C₂²	1	1	yes	characteristic
117	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
118	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
121	C₇×#435	C₂²	1	2	yes	—
122	C₇×#435	C₂²	1	2	yes	—
123	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
124	C₇×C₈×D₄	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×#427	C₂²	1	2	yes	—
129	C₇×#419	C₂²	1	1	yes	characteristic
130	C₇×#417	C₂²	1	1	yes	characteristic
131	C₇×#416	C₂²	1	2	yes	—
132	C₇×#416	C₂²	1	2	yes	—
133	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
134	C₂×C₇×#97	C₂²	1	2	yes	—
135	#61462	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	—	2	1	no	—
139	C₂×C₇×#41	—	2	2	no	—
140	C₂×C₇×#41	D₄	1	1	yes	characteristic
141	C₂×C₇×#41	C₂³	1	2	yes	—
142	C₂×C₇×#41	C₂³	1	2	yes	—
143	C₂×C₇×#41	C₂³	1	1	yes	characteristic
144	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
145	C₇×#137	—	2	4	no	—
146	C₇×#135	—	2	8	no	—
147	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
150	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
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×D₈	C₂³	1	2	yes	—
156	C₂×C₇×D₈	C₂³	1	2	yes	—
157	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
159	C₂²×C₇×C₈	C₂³	1	2	yes	—
160	C₂²×C₇×C₈	C₂³	1	2	yes	—
161	C₇×C₄⋊Q₈	—	2	1	no	—
162	C₇×C₄⋊Q₈	—	2	1	no	—
163	C₇×C₄⋊Q₈	—	2	2	no	—
164	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₇×#127	—	2	1	no	—
168	C₇×#127	—	2	2	no	—
169	C₇×#127	—	2	1	no	—
170	C₇×#127	C₂³	1	1	yes	characteristic
171	C₇×#127	C₂³	1	1	yes	characteristic
172	C₇×#127	C₂³	1	2	yes	—
173	C₇×#126	—	2	2	no	—
174	C₇×#126	—	2	2	no	—
175	C₇×#126	—	2	2	no	—
176	C₇×#125	—	2	2	no	—
177	C₇×#125	C₂³	1	2	yes	—
178	C₇×#124	—	2	1	no	—
179	C₇×#124	—	2	1	no	—
180	C₇×#124	—	2	2	no	—
181	C₇×#124	—	2	2	no	—
182	C₇×#124	—	2	2	no	—
183	C₇×#124	—	2	2	no	—
184	C₇×#124	—	2	2	no	—
185	C₇×#124	—	2	1	no	—
186	C₇×#124	—	2	1	no	—
187	C₇×#124	C₂³	1	2	yes	—
188	C₇×#123	—	2	2	no	—
189	C₇×#123	—	2	2	no	—
190	C₇×#123	—	2	2	no	—
191	C₇×C₂²⋊Q₈	—	2	2	no	—
192	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₇×#121	—	2	2	no	—
194	C₇×#121	—	2	1	no	—
195	C₇×#121	—	2	2	no	—
196	C₇×#121	—	2	2	no	—
197	C₇×#121	—	2	1	no	—
198	C₇×#121	—	2	2	no	—
199	C₇×#121	—	2	1	no	—
200	C₇×#121	—	2	1	no	—
201	C₇×#121	—	2	2	no	—
202	C₇×#121	—	2	2	no	—
203	C₇×#121	—	2	2	no	—
204	C₇×#121	—	2	2	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	C₇×#121	C₂³	1	2	yes	—
210	C₇×#121	C₂³	1	2	yes	—
211	C₄×C₇×Q₈	—	2	1	no	—
212	C₄×C₇×Q₈	—	2	1	no	—
213	C₄×C₇×Q₈	—	2	1	no	—
214	C₄×C₇×Q₈	—	2	1	no	—
215	C₄×C₇×Q₈	—	2	1	no	—
216	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
217	C₄×C₇×Q₈	C₂³	1	2	yes	—
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	1	yes	characteristic
223	C₄×C₇×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	C₄×C₇×D₄	—	2	2	no	—
227	C₄×C₇×D₄	—	2	1	no	—
228	C₄×C₇×D₄	—	2	2	no	—
229	C₄×C₇×D₄	—	2	1	no	—
230	C₄×C₇×D₄	—	2	2	no	—
231	C₄×C₇×D₄	—	2	2	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	1	no	—
236	C₄×C₇×D₄	—	2	1	no	—
237	C₄×C₇×D₄	—	2	2	no	—
238	C₄×C₇×D₄	—	2	2	no	—
239	C₄×C₇×D₄	—	2	2	no	—
240	C₄×C₇×D₄	—	2	1	no	—
241	C₄×C₇×D₄	—	2	1	no	—
242	C₄×C₇×D₄	D₄	1	2	yes	—
243	C₄×C₇×D₄	D₄	1	1	yes	characteristic
244	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
245	C₄×C₇×D₄	C₂³	1	2	yes	—
246	C₄×C₇×D₄	C₂³	1	2	yes	—
247	C₄×C₇×D₄	C₂³	1	2	yes	—
248	C₄×C₇×D₄	C₂³	1	2	yes	—
249	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
250	C₄×C₇×D₄	C₂³	1	2	yes	—
251	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
252	C₇×#117	—	2	1	no	—
253	C₇×#117	—	2	2	no	—
254	C₇×#117	—	2	2	no	—
255	C₇×#117	—	2	2	no	—
256	C₇×#117	—	2	2	no	—
257	C₇×#117	—	2	1	no	—
258	C₇×#117	D₄	1	1	yes	characteristic
259	C₇×#117	D₄	1	2	yes	—
260	C₇×#117	C₂³	1	2	yes	—
261	C₇×#117	C₂³	1	1	yes	characteristic
262	C₇×#117	C₂³	1	2	yes	—
263	C₂×C₇×C₄⋊C₄	—	2	1	no	—
264	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₄²×C₇	—	2	1	no	—
266	C₂×C₄²×C₇	—	2	2	no	—
267	C₂×C₄²×C₇	—	2	2	no	—
268	C₂×C₄²×C₇	—	2	1	no	—
269	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₇	C₂³	1	2	yes	—
271	C₇×#107	C₂³	1	1	yes	characteristic
272	C₇×#107	C₂³	1	2	yes	—
273	C₇×#107	C₂³	1	1	yes	characteristic
274	C₇×#107	C₂³	1	2	yes	—
275	C₇×#107	C₂³	1	2	yes	—
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	2	yes	—
283	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₇×C₄⋊C₈	C₂³	1	2	yes	—
285	C₇×#103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
291	C₇×#103	C₂³	1	1	yes	characteristic
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	1	yes	characteristic
294	C₇×#102	C₂³	1	1	yes	characteristic
295	C₇×#102	C₂³	1	2	yes	—
296	C₇×#102	C₂³	1	2	yes	—
297	C₇×#102	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
309	C₇×#97	C₂³	1	2	yes	—
310	C₇×#97	C₂³	1	1	yes	characteristic
311	C₇×#97	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	1	yes	characteristic
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	#3483	C₂×C₇	1	1	yes	characteristic, complemented
316	#3480	C₂×C₇	1	1	yes	characteristic, complemented
317	#3399	C₂×C₇	1	1	yes	characteristic, complemented
318	#3387	C₂×C₇	1	1	yes	characteristic, complemented
319	#3375	C₂×C₇	1	1	yes	characteristic, complemented
320	#3368	C₂×C₇	1	1	yes	characteristic, complemented
321	#3347	C₂×C₇	1	2	yes	complemented
322	#3340	C₂×C₇	1	1	yes	characteristic, complemented
323	#3321	C₂×C₇	1	2	yes	complemented
324	#3309	C₂×C₇	1	2	yes	complemented
325	#3305	C₂×C₇	1	1	yes	characteristic, complemented
326	#3304	C₂×C₇	1	1	yes	characteristic, complemented
327	#3287	C₂×C₇	1	1	yes	characteristic, complemented
328	#3271	C₂×C₇	1	2	yes	complemented
329	#3184	C₂×C₇	1	1	yes	characteristic, complemented
330	#3180	C₂×C₇	1	2	yes	complemented
331	#3115	C₂×C₇	1	2	yes	complemented
332	#3115	C₂×C₇	1	1	yes	characteristic, complemented
333	#3112	C₂×C₇	1	1	yes	characteristic, complemented
334	#3111	C₂×C₇	1	2	yes	complemented
335	#2970	C₂×C₇	1	1	yes	characteristic, complemented
336	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
337	#2943	C₂×C₇	1	2	yes	complemented
338	C₇×#41	—	2	4	no	—
339	C₇×#41	—	2	4	no	—
340	C₇×#41	—	2	2	no	—
341	C₇×#41	—	4	2	no	—
342	C₇×#41	—	4	2	no	—
343	C₇×#41	—	4	2	no	—
344	C₇×#41	—	4	1	no	—
345	C₇×#41	—	4	4	no	—
346	C₇×#41	—	4	4	no	—
347	C₇×#41	—	8	4	no	—
348	C₇×#41	—	8	2	no	—
349	C₂×C₇×Q₈	—	2	1	no	—
350	C₂×C₇×Q₈	—	2	1	no	—
351	C₂×C₇×Q₈	—	2	2	no	—
352	C₂×C₇×Q₈	—	2	1	no	—
353	C₂×C₇×Q₈	—	2	2	no	—
354	C₂×C₇×Q₈	—	4	1	no	—
355	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
356	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
357	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₇×D₄	—	2	2	no	—
360	C₂×C₇×D₄	—	2	2	no	—
361	C₂×C₇×D₄	—	2	2	no	—
362	C₂×C₇×D₄	—	2	1	no	—
363	C₂×C₇×D₄	—	2	2	no	—
364	C₂×C₇×D₄	—	2	2	no	—
365	C₂×C₇×D₄	—	2	2	no	—
366	C₂×C₇×D₄	—	2	2	no	—
367	C₂×C₇×D₄	—	2	2	no	—
368	C₂×C₇×D₄	—	2	1	no	—
369	C₂×C₇×D₄	—	2	1	no	—
370	C₂×C₇×D₄	—	2	1	no	—
371	C₂×C₇×D₄	—	2	2	no	—
372	C₂×C₇×D₄	—	2	1	no	—
373	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
374	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
375	C₂×C₇×D₄	C₂⁴	1	2	yes	—
376	C₂×C₇×D₄	C₂⁴	1	2	yes	—
377	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₇	—	2	1	no	—
379	C₂²×C₄×C₇	—	2	1	no	—
380	C₂²×C₄×C₇	—	2	2	no	—
381	C₂²×C₄×C₇	—	2	2	no	—
382	C₂²×C₄×C₇	—	2	1	no	—
383	C₂²×C₄×C₇	—	2	2	no	—
384	C₂²×C₄×C₇	—	2	2	no	—
385	C₂²×C₄×C₇	—	2	1	no	—
386	C₂²×C₄×C₇	—	2	2	no	—
387	C₂²×C₄×C₇	—	2	1	no	—
388	C₂²×C₄×C₇	—	2	2	no	—
389	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
392	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
393	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
395	C₇×Q₁₆	—	2	2	no	—
396	C₇×Q₁₆	#41	1	4	yes	complemented
397	C₇×SD₁₆	—	2	4	no	—
398	C₇×SD₁₆	—	2	4	no	—
399	C₇×SD₁₆	—	2	2	no	—
400	C₇×SD₁₆	—	2	2	no	—
401	C₇×SD₁₆	—	4	2	no	—
402	C₇×D₈	—	2	4	no	—
403	C₇×D₈	—	4	2	no	—
404	C₇×D₈	—	4	2	no	—
405	C₇×M₁₆	—	2	2	no	—
406	C₇×M₁₆	—	4	1	no	—
407	C₂×C₇×C₈	—	2	4	no	—
408	C₂×C₇×C₈	—	4	2	no	—
409	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
410	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
411	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
412	C₂×C₇×C₈	C₂⁴	1	2	yes	—
413	C₂×C₇×C₈	C₂⁴	1	2	yes	—
414	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
415	C₇×C₄⋊C₄	—	2	1	no	—
416	C₇×C₄⋊C₄	—	2	1	no	—
417	C₇×C₄⋊C₄	—	2	1	no	—
418	C₇×C₄⋊C₄	—	2	1	no	—
419	C₇×C₄⋊C₄	—	2	1	no	—
420	C₇×C₄⋊C₄	—	2	1	no	—
421	C₇×C₄⋊C₄	—	2	2	no	—
422	C₇×C₄⋊C₄	—	2	1	no	—
423	C₇×C₄⋊C₄	—	2	2	no	—
424	C₇×C₄⋊C₄	—	2	2	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	—	2	1	no	—
429	C₇×C₄⋊C₄	—	2	2	no	—
430	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
431	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
432	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
433	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
434	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
435	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
436	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
437	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
438	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
439	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	2	no	—
449	C₇×C₂²⋊C₄	—	2	2	no	—
450	C₇×C₂²⋊C₄	—	2	1	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	—	2	1	no	—
453	C₇×C₂²⋊C₄	—	2	2	no	—
454	C₇×C₂²⋊C₄	—	2	2	no	—
455	C₇×C₂²⋊C₄	—	2	2	no	—
456	C₇×C₂²⋊C₄	—	2	2	no	—
457	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
458	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
459	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
460	C₄²×C₇	—	2	1	no	—
461	C₄²×C₇	—	2	1	no	—
462	C₄²×C₇	—	2	2	no	—
463	C₄²×C₇	—	2	1	no	—
464	C₄²×C₇	—	2	1	no	—
465	C₄²×C₇	—	2	2	no	—
466	C₄²×C₇	—	2	2	no	—
467	C₄²×C₇	—	2	2	no	—
468	C₄²×C₇	—	2	1	no	—
469	C₄²×C₇	—	2	1	no	—
470	C₄²×C₇	—	2	1	no	—
471	C₄²×C₇	C₂×D₄	1	2	yes	—
472	C₄²×C₇	C₂×D₄	1	2	yes	—
473	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
474	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₇	C₂⁴	1	1	yes	characteristic
476	C₄²×C₇	C₂⁴	1	1	yes	characteristic
477	C₄²×C₇	C₂⁴	1	2	yes	—
478	C₂×#137	C₂²×C₇	1	1	yes	characteristic
479	C₂×#135	C₂²×C₇	1	2	yes	—
480	#559	—	2	1	no	—
481	#559	C₂²×C₇	1	1	yes	characteristic
482	Q₈²	C₂²×C₇	1	1	yes	characteristic
483	#557	C₂²×C₇	1	1	yes	characteristic
484	#556	—	2	1	no	—
485	#556	C₂²×C₇	1	1	yes	characteristic
486	#555	—	2	1	no	—
487	#555	—	2	2	no	—
488	#555	C₂²×C₇	1	1	yes	characteristic
489	#555	C₂²×C₇	1	2	yes	—
490	#553	—	2	2	no	—
491	#553	C₂²×C₇	1	2	yes	—
492	#550	—	2	1	no	—
493	#550	C₂²×C₇	1	1	yes	characteristic
494	#550	C₂²×C₇	1	2	yes	—
495	#550	C₂²×C₇	1	1	yes	characteristic
496	#550	C₂²×C₇	1	1	yes	characteristic
497	#548	C₂²×C₇	1	2	yes	—
498	#532	—	2	1	no	—
499	#532	—	2	2	no	—
500	#532	—	2	1	no	—
501	#532	C₂²×C₇	1	1	yes	characteristic
502	#532	C₂²×C₇	1	2	yes	—
503	#532	C₂²×C₇	1	1	yes	characteristic
504	#529	—	2	2	no	—
505	#529	C₂²×C₇	1	2	yes	—
506	C₄×#41	—	2	1	no	—
507	C₄×#41	—	2	1	no	—
508	C₄×#41	C₂²×C₇	1	2	yes	—
509	C₄×#41	C₂²×C₇	1	2	yes	—
510	C₄×#41	C₂²×C₇	1	1	yes	characteristic
511	C₄×#41	C₂²×C₇	1	1	yes	characteristic
512	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
513	#501	C₂²×C₇	1	2	yes	—
514	#498	C₂²×C₇	1	1	yes	characteristic
515	#496	C₂²×C₇	1	2	yes	—
516	#493	C₂²×C₇	1	1	yes	characteristic
517	#490	C₂²×C₇	1	2	yes	—
518	#489	C₂²×C₇	1	2	yes	—
519	#486	C₂²×C₇	1	1	yes	characteristic
520	#486	C₂²×C₇	1	1	yes	characteristic
521	#485	C₂²×C₇	1	2	yes	—
522	#482	C₂²×C₇	1	2	yes	—
523	#482	C₂²×C₇	1	2	yes	—
524	#482	C₂²×C₇	1	2	yes	—
525	#482	C₂²×C₇	1	2	yes	—
526	#480	C₂²×C₇	1	2	yes	—
527	#479	C₂²×C₇	1	2	yes	—
528	#478	C₂²×C₇	1	2	yes	—
529	#477	C₂²×C₇	1	1	yes	characteristic
530	#477	C₂²×C₇	1	1	yes	characteristic
531	#475	C₂²×C₇	1	1	yes	characteristic
532	#475	C₂²×C₇	1	2	yes	—
533	#474	C₂²×C₇	1	1	yes	characteristic
534	#474	C₂²×C₇	1	2	yes	—
535	#469	C₂²×C₇	1	2	yes	—
536	#469	C₂²×C₇	1	2	yes	—
537	#466	C₂²×C₇	1	2	yes	—
538	#466	C₂²×C₇	1	2	yes	—
539	#465	C₂²×C₇	1	2	yes	—
540	#465	C₂²×C₇	1	2	yes	—
541	#464	C₂²×C₇	1	2	yes	—
542	#463	C₂²×C₇	1	2	yes	—
543	#460	C₂²×C₇	1	1	yes	characteristic
544	#460	C₂²×C₇	1	1	yes	characteristic
545	#460	C₂²×C₇	1	2	yes	—
546	#460	C₂²×C₇	1	1	yes	characteristic
547	#459	C₂²×C₇	1	1	yes	characteristic
548	#459	C₂²×C₇	1	2	yes	—
549	#452	C₂²×C₇	1	2	yes	—
550	#449	C₂²×C₇	1	2	yes	—
551	#449	C₂²×C₇	1	2	yes	—
552	#449	C₂²×C₇	1	2	yes	—
553	#449	C₂²×C₇	1	2	yes	—
554	#448	C₂²×C₇	1	2	yes	—
555	#446	C₂²×C₇	1	1	yes	characteristic
556	#446	C₂²×C₇	1	1	yes	characteristic
557	#442	C₂²×C₇	1	2	yes	—
558	#442	C₂²×C₇	1	2	yes	—
559	#442	C₂²×C₇	1	2	yes	—
560	#442	C₂²×C₇	1	2	yes	—
561	#441	C₂²×C₇	1	1	yes	characteristic
562	#441	C₂²×C₇	1	2	yes	—
563	#441	C₂²×C₇	1	1	yes	characteristic
564	#440	C₂²×C₇	1	2	yes	—
565	#440	C₂²×C₇	1	2	yes	—
566	#440	C₂²×C₇	1	2	yes	—
567	#440	C₂²×C₇	1	2	yes	—
568	#440	C₂²×C₇	1	1	yes	characteristic
569	#440	C₂²×C₇	1	2	yes	—
570	#440	C₂²×C₇	1	1	yes	characteristic
571	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
572	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
573	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
574	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
575	#435	C₂²×C₇	1	2	yes	—
576	#435	C₂²×C₇	1	2	yes	—
577	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
578	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
579	#432	C₂²×C₇	1	2	yes	—
580	#432	C₂²×C₇	1	1	yes	characteristic
581	#428	C₂²×C₇	1	1	yes	characteristic
582	#427	C₂²×C₇	1	2	yes	—
583	#419	C₂²×C₇	1	1	yes	characteristic
584	#417	C₂²×C₇	1	1	yes	characteristic
585	#416	C₂²×C₇	1	2	yes	—
586	#416	C₂²×C₇	1	2	yes	—
587	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
588	C₂×#97	C₂²×C₇	1	2	yes	—
589	C₂³×C₇	—	2	2	no	—
590	C₂³×C₇	—	2	2	no	—
591	C₂³×C₇	—	2	1	no	—
592	C₂³×C₇	C₂²×D₄	1	2	yes	—
593	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
594	C₇×Q₈	—	2	2	no	—
595	C₇×Q₈	—	2	1	no	—
596	C₇×Q₈	—	2	1	no	—
597	C₇×Q₈	—	2	1	no	—
598	C₇×Q₈	—	2	1	no	—
599	C₇×Q₈	—	4	2	no	—
600	C₇×Q₈	—	4	2	no	—
601	C₇×Q₈	—	8	2	no	—
602	C₇×Q₈	—	8	1	no	—
603	C₇×Q₈	C₂×#41	1	2	yes	—
604	C₇×Q₈	C₂×#41	1	2	yes	—
605	C₇×D₄	—	2	2	no	—
606	C₇×D₄	—	2	2	no	—
607	C₇×D₄	—	2	2	no	—
608	C₇×D₄	—	2	1	no	—
609	C₇×D₄	—	2	2	no	—
610	C₇×D₄	—	2	1	no	—
611	C₇×D₄	—	2	2	no	—
612	C₇×D₄	—	4	2	no	—
613	C₇×D₄	—	4	2	no	—
614	C₇×D₄	—	4	4	no	—
615	C₇×D₄	—	4	4	no	—
616	C₇×D₄	—	4	4	no	—
617	C₇×D₄	—	4	4	no	—
618	C₇×D₄	—	4	2	no	—
619	C₇×D₄	—	4	2	no	—
620	C₇×D₄	—	8	1	no	—
621	C₇×D₄	—	8	2	no	—
622	C₇×D₄	—	8	1	no	—
623	C₇×D₄	—	8	2	no	—
624	C₇×D₄	—	8	2	no	—
625	C₇×D₄	—	8	2	no	—
626	C₇×D₄	—	8	2	no	—
627	C₂×C₄×C₇	—	2	1	no	—
628	C₂×C₄×C₇	—	2	1	no	—
629	C₂×C₄×C₇	—	2	2	no	—
630	C₂×C₄×C₇	—	2	2	no	—
631	C₂×C₄×C₇	—	2	1	no	—
632	C₂×C₄×C₇	—	2	2	no	—
633	C₂×C₄×C₇	—	2	1	no	—
634	C₂×C₄×C₇	—	2	1	no	—
635	C₂×C₄×C₇	—	2	1	no	—
636	C₂×C₄×C₇	—	2	1	no	—
637	C₂×C₄×C₇	—	2	2	no	—
638	C₂×C₄×C₇	—	2	2	no	—
639	C₂×C₄×C₇	—	2	1	no	—
640	C₂×C₄×C₇	—	2	1	no	—
641	C₂×C₄×C₇	—	4	2	no	—
642	C₂×C₄×C₇	—	4	2	no	—
643	C₂×C₄×C₇	—	4	1	no	—
644	C₂×C₄×C₇	—	4	4	no	—
645	C₂×C₄×C₇	—	4	4	no	—
646	C₂×C₄×C₇	—	4	2	no	—
647	C₂×C₄×C₇	—	4	2	no	—
648	C₂×C₄×C₇	—	4	4	no	—
649	C₂×C₄×C₇	—	4	4	no	—
650	C₂×C₄×C₇	—	4	4	no	—
651	C₂×C₄×C₇	—	4	2	no	—
652	C₂×C₄×C₇	—	4	2	no	—
653	C₂×C₄×C₇	—	8	2	no	—
654	C₂×C₄×C₇	—	8	1	no	—
655	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
656	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
657	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
658	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
659	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
660	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
661	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
662	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
663	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
664	C₇×C₈	—	2	2	no	—
665	C₇×C₈	—	2	1	no	—
666	C₇×C₈	—	2	1	no	—
667	C₇×C₈	—	2	2	no	—
668	C₇×C₈	—	2	1	no	—
669	C₇×C₈	C₂×#41	1	2	yes	—
670	C₂×#41	—	2	1	no	—
671	C₂×#41	—	2	1	no	—
672	C₂×#41	—	2	1	no	—
673	C₂×#41	—	2	2	no	—
674	C₂×#41	C₇×D₄	1	1	yes	characteristic
675	C₂×#41	C₂³×C₇	1	2	yes	—
676	C₂×#41	C₂³×C₇	1	2	yes	—
677	C₂×#41	C₂³×C₇	1	1	yes	characteristic
678	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
679	#137	—	2	4	no	—
680	#135	—	2	8	no	—
681	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
682	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
683	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
686	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
687	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
688	C₂×D₈	C₂³×C₇	1	2	yes	—
689	C₂×D₈	C₂³×C₇	1	2	yes	—
690	C₂×D₈	C₂³×C₇	1	2	yes	—
691	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
692	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
693	C₂²×C₈	C₂³×C₇	1	2	yes	—
694	C₂²×C₈	C₂³×C₇	1	2	yes	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	1	no	—
697	C₄⋊Q₈	—	2	2	no	—
698	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
699	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
701	#127	—	2	1	no	—
702	#127	—	2	2	no	—
703	#127	—	2	1	no	—
704	#127	C₂³×C₇	1	2	yes	—
705	#127	C₂³×C₇	1	1	yes	characteristic
706	#127	C₂³×C₇	1	1	yes	characteristic
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	C₂³×C₇	1	2	yes	—
712	#124	—	2	1	no	—
713	#124	—	2	1	no	—
714	#124	—	2	2	no	—
715	#124	—	2	2	no	—
716	#124	—	2	2	no	—
717	#124	—	2	2	no	—
718	#124	—	2	2	no	—
719	#124	—	2	1	no	—
720	#124	—	2	1	no	—
721	#124	C₂³×C₇	1	2	yes	—
722	#123	—	2	2	no	—
723	#123	—	2	2	no	—
724	#123	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
727	#121	—	2	2	no	—
728	#121	—	2	1	no	—
729	#121	—	2	2	no	—
730	#121	—	2	2	no	—
731	#121	—	2	1	no	—
732	#121	—	2	2	no	—
733	#121	—	2	1	no	—
734	#121	—	2	1	no	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	—	2	2	no	—
739	#121	—	2	2	no	—
740	#121	C₂³×C₇	1	2	yes	—
741	#121	C₂³×C₇	1	2	yes	—
742	#121	C₂³×C₇	1	2	yes	—
743	#121	C₂³×C₇	1	2	yes	—
744	#121	C₂³×C₇	1	2	yes	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
751	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
752	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
753	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
754	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₇	1	2	yes	—
757	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
758	C₄×Q₈	C₂³×C₇	1	2	yes	—
759	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
760	C₄×D₄	—	2	2	no	—
761	C₄×D₄	—	2	1	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	1	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	C₇×D₄	1	2	yes	—
777	C₄×D₄	C₇×D₄	1	1	yes	characteristic
778	C₄×D₄	C₂³×C₇	1	2	yes	—
779	C₄×D₄	C₂³×C₇	1	2	yes	—
780	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
781	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
782	C₄×D₄	C₂³×C₇	1	2	yes	—
783	C₄×D₄	C₂³×C₇	1	2	yes	—
784	C₄×D₄	C₂³×C₇	1	2	yes	—
785	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
786	#117	—	2	1	no	—
787	#117	—	2	2	no	—
788	#117	—	2	2	no	—
789	#117	—	2	2	no	—
790	#117	—	2	2	no	—
791	#117	—	2	1	no	—
792	#117	C₇×D₄	1	1	yes	characteristic
793	#117	C₇×D₄	1	2	yes	—
794	#117	C₂³×C₇	1	2	yes	—
795	#117	C₂³×C₇	1	2	yes	—
796	#117	C₂³×C₇	1	1	yes	characteristic
797	C₂×C₄⋊C₄	—	2	1	no	—
798	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
799	C₂×C₄²	—	2	1	no	—
800	C₂×C₄²	—	2	2	no	—
801	C₂×C₄²	—	2	2	no	—
802	C₂×C₄²	—	2	1	no	—
803	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
804	C₂×C₄²	C₂³×C₇	1	2	yes	—
805	#107	C₂³×C₇	1	2	yes	—
806	#107	C₂³×C₇	1	2	yes	—
807	#107	C₂³×C₇	1	1	yes	characteristic
808	#107	C₂³×C₇	1	1	yes	characteristic
809	#107	C₂³×C₇	1	2	yes	—
810	#106	C₂³×C₇	1	1	yes	characteristic
811	#106	C₂³×C₇	1	2	yes	—
812	#106	C₂³×C₇	1	1	yes	characteristic
813	#106	C₂³×C₇	1	2	yes	—
814	#106	C₂³×C₇	1	2	yes	—
815	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₇	1	2	yes	—
818	C₄⋊C₈	C₂³×C₇	1	2	yes	—
819	#103	C₂³×C₇	1	1	yes	characteristic
820	#103	C₂³×C₇	1	1	yes	characteristic
821	#103	C₂³×C₇	1	2	yes	—
822	#103	C₂³×C₇	1	2	yes	—
823	#103	C₂³×C₇	1	1	yes	characteristic
824	#103	C₂³×C₇	1	1	yes	characteristic
825	#103	C₂³×C₇	1	1	yes	characteristic
826	#103	C₂³×C₇	1	1	yes	characteristic
827	#103	C₂³×C₇	1	2	yes	—
828	#102	C₂³×C₇	1	2	yes	—
829	#102	C₂³×C₇	1	2	yes	—
830	#102	C₂³×C₇	1	2	yes	—
831	#102	C₂³×C₇	1	2	yes	—
832	#102	C₂³×C₇	1	1	yes	characteristic
833	#102	C₂³×C₇	1	1	yes	characteristic
834	#102	C₂³×C₇	1	2	yes	—
835	#102	C₂³×C₇	1	2	yes	—
836	#102	C₂³×C₇	1	2	yes	—
837	#102	C₂³×C₇	1	2	yes	—
838	#102	C₂³×C₇	1	2	yes	—
839	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
840	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
842	#97	C₂³×C₇	1	1	yes	characteristic
843	#97	C₂³×C₇	1	2	yes	—
844	#97	C₂³×C₇	1	2	yes	—
845	#97	C₂³×C₇	1	2	yes	—
846	#97	C₂³×C₇	1	1	yes	characteristic
847	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
848	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
849	C₂²×C₇	—	2	1	no	—
850	C₂²×C₇	—	2	2	no	—
851	C₂²×C₇	—	2	1	no	—
852	C₂²×C₇	—	2	2	no	—
853	C₂²×C₇	—	2	1	no	—
854	C₂²×C₇	—	2	2	no	—
855	C₂²×C₇	—	4	1	no	—
856	C₂²×C₇	—	4	2	no	—
857	C₂²×C₇	—	4	2	no	—
858	C₂²×C₇	—	4	2	no	—
859	C₂²×C₇	—	4	2	no	—
860	C₂²×C₇	—	4	1	no	—
861	C₂²×C₇	—	4	2	no	—
862	C₂²×C₇	—	4	2	no	—
863	C₂²×C₇	—	4	1	no	—
864	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
865	C₄×C₇	—	2	1	no	—
866	C₄×C₇	—	2	2	no	—
867	C₄×C₇	—	2	1	no	—
868	C₄×C₇	—	2	2	no	—
869	C₄×C₇	—	2	1	no	—
870	C₄×C₇	—	2	2	no	—
871	C₄×C₇	—	2	2	no	—
872	C₄×C₇	—	2	1	no	—
873	C₄×C₇	—	2	2	no	—
874	C₄×C₇	—	4	2	no	—
875	C₄×C₇	—	4	1	no	—
876	C₄×C₇	—	4	1	no	—
877	C₄×C₇	—	4	1	no	—
878	C₄×C₇	—	4	1	no	—
879	C₄×C₇	—	4	1	no	—
880	C₄×C₇	—	4	2	no	—
881	C₄×C₇	#575	1	2	yes	—
882	C₄×C₇	C₂²×#41	1	1	yes	characteristic
883	C₄×C₇	#585	1	1	yes	characteristic
884	#41	—	2	4	no	—
885	#41	—	2	4	no	—
886	#41	—	2	2	no	—
887	#41	—	4	2	no	—
888	#41	—	4	2	no	—
889	#41	—	4	2	no	—
890	#41	—	4	1	no	—
891	#41	—	4	4	no	—
892	#41	—	4	4	no	—
893	#41	—	8	4	no	—
894	#41	—	8	2	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	2	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	4	1	no	—
901	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
920	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
921	C₂×D₄	C₂⁴×C₇	1	2	yes	—
922	C₂×D₄	C₂⁴×C₇	1	2	yes	—
923	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
936	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
937	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
938	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
939	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
941	Q₁₆	—	2	2	no	—
942	Q₁₆	C₇×#41	1	4	yes	complemented
943	SD₁₆	—	2	4	no	—
944	SD₁₆	—	2	4	no	—
945	SD₁₆	—	2	2	no	—
946	SD₁₆	—	2	2	no	—
947	SD₁₆	—	4	2	no	—
948	D₈	—	2	4	no	—
949	D₈	—	4	2	no	—
950	D₈	—	4	2	no	—
951	M₁₆	—	2	2	no	—
952	M₁₆	—	4	1	no	—
953	C₂×C₈	—	2	4	no	—
954	C₂×C₈	—	4	2	no	—
955	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
956	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
957	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₇	1	2	yes	—
959	C₂×C₈	C₂⁴×C₇	1	2	yes	—
960	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
977	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
978	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
979	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
985	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1004	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1005	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	C₂×C₇×D₄	1	2	yes	—
1018	C₄²	C₂×C₇×D₄	1	2	yes	—
1019	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1020	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1021	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₇	1	2	yes	—
1024	C₂×C₇	—	4	1	no	—
1025	C₂×C₇	—	4	2	no	—
1026	C₂×C₇	—	8	2	no	—
1027	C₂×C₇	—	8	1	no	—
1028	C₂×C₇	—	8	2	no	—
1029	C₂×C₇	D₄×#41	1	1	yes	characteristic
1030	C₂×C₇	C₂×#575	1	1	yes	characteristic
1031	C₂×C₇	#3585	1	1	yes	characteristic
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	C₂²×C₇×D₄	1	2	yes	—
1036	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	4	2	no	—
1043	Q₈	—	4	2	no	—
1044	Q₈	—	8	2	no	—
1045	Q₈	—	8	1	no	—
1046	Q₈	C₂×C₇×#41	1	2	yes	—
1047	Q₈	C₂×C₇×#41	1	2	yes	—
1048	D₄	—	2	2	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	4	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	4	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	4	2	no	—
1063	D₄	—	8	1	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	1	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	4	no	—
1088	C₂×C₄	—	4	4	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	4	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	1	no	—
1098	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1099	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1100	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1102	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1103	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1104	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1105	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1106	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1107	C₈	—	2	2	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	2	no	—
1111	C₈	—	2	1	no	—
1112	C₈	C₂×C₇×#41	1	2	yes	—
1113	C₇	#61462	1	1	yes	characteristic, direct product factor, Sylow
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	4	2	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	C₇×#575	1	2	yes	—
1147	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1148	C₄	C₇×#585	1	1	yes	characteristic
1149	C₂	—	4	1	no	—
1150	C₂	—	4	2	no	—
1151	C₂	—	8	2	no	—
1152	C₂	—	8	1	no	—
1153	C₂	—	8	2	no	—
1154	C₂	C₇×D₄×#41	1	1	yes	characteristic
1155	C₂	C₂×C₇×#575	1	1	yes	characteristic
1156	C₂	C₇×#3585	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×#3483	C₂	semidirect
2. C₇×#3480	C₂	semidirect
3. C₇×#3399	C₂	semidirect
4. C₇×#3387	C₂	semidirect
5. C₇×#3375	C₂	semidirect
6. C₇×#3368	C₂	semidirect
7. C₇×#3347	C₂	semidirect
8. C₇×#3340	C₂	semidirect
9. C₇×#3321	C₂	semidirect
10. C₇×#3309	C₂	semidirect
11. C₇×#3305	C₂	semidirect
12. C₇×#3304	C₂	semidirect
13. C₇×#3287	C₂	semidirect
14. C₇×#3271	C₂	semidirect
15. C₇×#3184	C₂	semidirect
16. C₇×#3180	C₂	semidirect
17. C₇×#3115	C₂	semidirect
18. C₇×#3115	C₂	semidirect
19. C₇×#3112	C₂	semidirect
20. C₇×#3111	C₂	semidirect
21. C₇×#2970	C₂	semidirect
22. C₄×C₇×#137	C₂	semidirect
23. C₇×#2943	C₂	semidirect
135. #61462	C₇	direct (N × H)
315. #3483	C₂×C₇	semidirect
316. #3480	C₂×C₇	semidirect
317. #3399	C₂×C₇	semidirect
318. #3387	C₂×C₇	semidirect
319. #3375	C₂×C₇	semidirect
320. #3368	C₂×C₇	semidirect
321. #3347	C₂×C₇	semidirect
322. #3340	C₂×C₇	semidirect
323. #3321	C₂×C₇	semidirect
324. #3309	C₂×C₇	semidirect
325. #3305	C₂×C₇	semidirect
326. #3304	C₂×C₇	semidirect
327. #3287	C₂×C₇	semidirect
328. #3271	C₂×C₇	semidirect
329. #3184	C₂×C₇	semidirect
330. #3180	C₂×C₇	semidirect
331. #3115	C₂×C₇	semidirect
332. #3115	C₂×C₇	semidirect
333. #3112	C₂×C₇	semidirect
334. #3111	C₂×C₇	semidirect
335. #2970	C₂×C₇	semidirect
336. C₄×#137	C₂×C₇	semidirect
337. #2943	C₂×C₇	semidirect
396. C₇×Q₁₆	#41	semidirect
942. Q₁₆	C₇×#41	semidirect
1113. C₇	#61462	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×#3483	2
C₇×#3480	2
C₇×#3399	2
C₇×#3387	2
C₇×#3375	2
C₇×#3368	2
C₇×#3347	2
C₇×#3340	2
C₇×#3321	2
C₇×#3309	2
C₇×#3305	2
C₇×#3304	2
C₇×#3287	2
C₇×#3271	2
C₇×#3184	2
C₇×#3180	2
C₇×#3115	2
C₇×#3112	2
C₇×#3111	2
C₇×#2970	2
C₄×C₇×#137	2
C₇×#2943	2
#61462	7

Subgroups — C7×#61462 #13238678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61462 #13238678