Subgroups — C₇×#61294 #13238510

Order 1792.

1802 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3350	C₂	1	2	yes	maximal, complemented
4	C₇×#3349	C₂	1	2	yes	maximal, complemented
5	C₇×#3348	C₂	1	2	yes	maximal, complemented
6	C₇×#3347	C₂	1	2	yes	maximal, complemented
7	C₇×#3346	C₂	1	2	yes	maximal, complemented
8	C₇×#3345	C₂	1	2	yes	maximal, complemented
9	C₇×#3344	C₂	1	2	yes	maximal, complemented
10	C₇×#3343	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#501	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3099	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2912	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#135	C₂²	1	1	yes	characteristic
25	C₂×C₇×#131	C₂²	1	1	yes	characteristic
26	C₂×C₇×#131	C₂²	1	1	yes	characteristic
27	C₇×#556	C₂²	1	2	yes	—
28	C₇×#555	C₂²	1	2	yes	—
29	C₇×#554	C₂²	1	2	yes	—
30	C₇×#553	—	2	2	no	—
31	C₇×#553	—	2	2	no	—
32	C₇×#553	—	2	2	no	—
33	C₇×#553	C₂²	1	2	yes	—
34	C₇×#553	C₂²	1	2	yes	—
35	C₇×#552	C₂²	1	2	yes	—
36	C₇×#552	C₂²	1	2	yes	—
37	C₇×#548	—	2	2	no	—
38	C₇×#547	C₂²	1	2	yes	—
39	C₇×#542	—	2	1	no	—
40	C₇×#542	—	2	1	no	—
41	C₇×#541	—	2	1	no	—
42	C₇×#540	—	2	1	no	—
43	C₇×#537	C₂²	1	1	yes	characteristic
44	C₇×#537	C₂²	1	1	yes	characteristic
45	C₇×#537	C₂²	1	1	yes	characteristic
46	C₇×#537	C₂²	1	1	yes	characteristic
47	C₇×#533	—	2	1	no	—
48	C₇×#532	—	2	1	no	—
49	C₇×#532	C₂²	1	1	yes	characteristic
50	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
51	C₇×#529	—	2	1	no	—
52	C₇×#529	—	2	1	no	—
53	C₂×C₇×#125	C₂²	1	1	yes	characteristic
54	C₇×#520	C₂²	1	1	yes	characteristic
55	C₇×#520	C₂²	1	1	yes	characteristic
56	C₇×#520	C₂²	1	1	yes	characteristic
57	C₇×#520	C₂²	1	1	yes	characteristic
58	C₄×C₇×#41	C₂²	1	1	yes	characteristic
59	C₄×C₇×#41	C₂²	1	1	yes	characteristic
60	C₇×#501	C₂²	1	2	yes	—
61	C₇×#501	C₂²	1	2	yes	—
62	C₇×#501	C₂²	1	2	yes	—
63	C₇×#501	C₂²	1	2	yes	—
64	C₇×#485	C₂²	1	2	yes	—
65	C₇×#485	C₂²	1	2	yes	—
66	C₇×#485	C₂²	1	2	yes	—
67	C₇×#485	C₂²	1	2	yes	—
68	C₇×#484	C₂²	1	2	yes	—
69	C₇×#484	C₂²	1	2	yes	—
70	C₇×#483	C₂²	1	2	yes	—
71	C₇×#483	C₂²	1	2	yes	—
72	C₇×#482	C₂²	1	2	yes	—
73	C₇×#482	C₂²	1	2	yes	—
74	C₇×#482	C₂²	1	2	yes	—
75	C₇×#482	C₂²	1	2	yes	—
76	C₇×#481	C₂²	1	2	yes	—
77	C₇×#481	C₂²	1	2	yes	—
78	C₇×#480	C₂²	1	2	yes	—
79	C₇×#480	C₂²	1	2	yes	—
80	C₇×#479	C₂²	1	2	yes	—
81	C₇×#479	C₂²	1	2	yes	—
82	C₇×#478	C₂²	1	2	yes	—
83	C₇×#478	C₂²	1	2	yes	—
84	C₇×#477	C₂²	1	2	yes	—
85	C₇×#476	C₂²	1	2	yes	—
86	C₇×#475	C₂²	1	2	yes	—
87	C₇×#474	C₂²	1	2	yes	—
88	C₇×#470	C₂²	1	2	yes	—
89	C₇×#469	C₂²	1	2	yes	—
90	C₇×#468	C₂²	1	2	yes	—
91	C₇×#468	C₂²	1	2	yes	—
92	C₇×#467	C₂²	1	2	yes	—
93	C₇×#466	C₂²	1	2	yes	—
94	C₇×#465	C₂²	1	2	yes	—
95	C₇×#465	C₂²	1	2	yes	—
96	C₇×#442	C₂²	1	1	yes	characteristic
97	C₇×#442	C₂²	1	1	yes	characteristic
98	C₇×#441	C₂²	1	1	yes	characteristic
99	C₇×#441	C₂²	1	1	yes	characteristic
100	C₇×#440	C₂²	1	1	yes	characteristic
101	C₇×#440	C₂²	1	1	yes	characteristic
102	C₇×#440	C₂²	1	1	yes	characteristic
103	C₇×#440	C₂²	1	1	yes	characteristic
104	C₇×#435	C₂²	1	2	yes	—
105	C₇×#435	C₂²	1	2	yes	—
106	C₇×#435	C₂²	1	2	yes	—
107	C₇×#435	C₂²	1	2	yes	—
108	C₇×#428	C₂²	1	1	yes	characteristic
109	C₇×#428	C₂²	1	1	yes	characteristic
110	C₇×#428	C₂²	1	2	yes	—
111	C₇×#428	C₂²	1	2	yes	—
112	C₇×#428	C₂²	1	1	yes	characteristic
113	C₇×#428	C₂²	1	1	yes	characteristic
114	C₇×#428	C₂²	1	2	yes	—
115	C₇×#428	C₂²	1	2	yes	—
116	C₇×#427	C₂²	1	1	yes	characteristic
117	C₇×#427	C₂²	1	2	yes	—
118	C₇×#427	C₂²	1	2	yes	—
119	C₂×C₇×#107	C₂²	1	1	yes	characteristic
120	C₂×C₇×#107	C₂²	1	1	yes	characteristic
121	C₂×C₇×#107	C₂²	1	2	yes	—
122	C₂×C₇×#106	C₂²	1	1	yes	characteristic
123	C₂×C₇×#106	C₂²	1	1	yes	characteristic
124	C₂×C₇×#106	C₂²	1	2	yes	—
125	C₇×#423	C₂²	1	1	yes	characteristic
126	C₇×#417	C₂²	1	1	yes	characteristic
127	C₇×#417	C₂²	1	1	yes	characteristic
128	C₇×#417	C₂²	1	1	yes	characteristic
129	C₇×#417	C₂²	1	1	yes	characteristic
130	C₇×#416	C₂²	1	1	yes	characteristic
131	C₇×#416	C₂²	1	1	yes	characteristic
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₇×#408	C₂²	1	1	yes	characteristic
134	C₂×C₇×#97	C₂²	1	1	yes	characteristic
135	#61294	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	2	no	—
137	C₂×C₇×#41	C₂³	1	1	yes	characteristic
138	C₂×C₇×#41	C₂³	1	1	yes	characteristic
139	C₂×C₇×#41	C₂³	1	1	yes	characteristic
140	C₂×C₇×#41	C₂³	1	1	yes	characteristic
141	C₂²×C₇×Q₈	—	2	1	no	—
142	C₇×#135	—	2	4	no	—
143	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
147	C₇×#131	—	2	4	no	—
148	C₇×#131	—	2	4	no	—
149	C₂×C₇×M₁₆	C₂³	1	2	yes	—
150	C₂×C₇×M₁₆	C₂³	1	2	yes	—
151	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
153	C₂²×C₇×C₈	C₂³	1	2	yes	—
154	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
155	C₂²×C₇×C₈	C₂³	1	2	yes	—
156	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
157	C₇×C₄⋊Q₈	—	2	1	no	—
158	C₇×C₄⋊Q₈	—	2	1	no	—
159	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
160	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₇×#127	D₄	1	1	yes	characteristic
163	C₇×#126	—	2	2	no	—
164	C₇×#126	—	2	2	no	—
165	C₇×#126	—	2	2	no	—
166	C₇×#126	—	2	2	no	—
167	C₇×#126	—	2	2	no	—
168	C₇×#126	—	2	2	no	—
169	C₇×#125	—	2	2	no	—
170	C₇×#125	—	2	2	no	—
171	C₇×#125	—	2	2	no	—
172	C₇×#125	—	2	1	no	—
173	C₇×#125	—	2	1	no	—
174	C₇×#125	C₂³	1	2	yes	—
175	C₇×#125	C₂³	1	2	yes	—
176	C₇×#124	—	2	2	no	—
177	C₇×#124	—	2	2	no	—
178	C₇×#124	—	2	2	no	—
179	C₇×#124	D₄	1	1	yes	characteristic
180	C₇×#124	D₄	1	1	yes	characteristic
181	C₇×#123	—	2	2	no	—
182	C₇×#123	—	2	2	no	—
183	C₇×#123	—	2	2	no	—
184	C₇×#123	—	2	2	no	—
185	C₇×#123	—	2	2	no	—
186	C₇×#123	—	2	2	no	—
187	C₇×C₂²⋊Q₈	—	2	1	no	—
188	C₇×C₂²⋊Q₈	—	2	1	no	—
189	C₇×C₂²⋊Q₈	—	2	1	no	—
190	C₇×C₂²⋊Q₈	—	2	1	no	—
191	C₇×C₂²⋊Q₈	—	2	2	no	—
192	C₇×C₂²⋊Q₈	—	2	2	no	—
193	C₇×C₂²⋊Q₈	—	2	2	no	—
194	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₇×#121	—	2	1	no	—
199	C₇×#121	—	2	1	no	—
200	C₇×#121	—	2	1	no	—
201	C₇×#121	—	2	1	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	—	2	2	no	—
207	C₇×#121	—	2	2	no	—
208	C₇×#121	—	2	2	no	—
209	C₇×#121	D₄	1	2	yes	—
210	C₇×#121	D₄	1	2	yes	—
211	C₇×#121	C₂³	1	2	yes	—
212	C₇×#121	C₂³	1	2	yes	—
213	C₇×#121	C₂³	1	2	yes	—
214	C₇×#121	C₂³	1	2	yes	—
215	C₄×C₇×Q₈	—	2	1	no	—
216	C₄×C₇×Q₈	—	2	1	no	—
217	C₄×C₇×Q₈	—	2	1	no	—
218	C₄×C₇×Q₈	—	2	1	no	—
219	C₄×C₇×Q₈	—	2	2	no	—
220	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
221	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
222	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
223	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
224	C₄×C₇×D₄	—	2	1	no	—
225	C₄×C₇×D₄	—	2	1	no	—
226	C₄×C₇×D₄	—	2	1	no	—
227	C₄×C₇×D₄	—	2	1	no	—
228	C₄×C₇×D₄	—	2	2	no	—
229	C₄×C₇×D₄	—	2	2	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	1	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	C₂³	1	1	yes	characteristic
240	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
241	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
242	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
243	C₄×C₇×D₄	C₂³	1	2	yes	—
244	C₄×C₇×D₄	C₂³	1	2	yes	—
245	C₇×#117	—	2	2	no	—
246	C₇×#117	—	2	2	no	—
247	C₇×#117	—	2	2	no	—
248	C₇×#117	—	2	1	no	—
249	C₇×#117	—	2	1	no	—
250	C₇×#117	C₂³	1	2	yes	—
251	C₇×#117	C₂³	1	2	yes	—
252	C₇×#117	C₂³	1	2	yes	—
253	C₇×#117	C₂³	1	2	yes	—
254	C₇×#117	C₂³	1	1	yes	characteristic
255	C₇×#117	C₂³	1	1	yes	characteristic
256	C₂×C₇×C₄⋊C₄	—	2	1	no	—
257	C₂×C₇×C₄⋊C₄	—	2	1	no	—
258	C₂×C₇×C₄⋊C₄	—	2	1	no	—
259	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₄²×C₇	—	2	1	no	—
268	C₂×C₄²×C₇	—	2	1	no	—
269	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
270	C₇×#107	C₂³	1	2	yes	—
271	C₇×#107	C₂³	1	2	yes	—
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	2	yes	—
276	C₇×#107	C₂³	1	2	yes	—
277	C₇×#107	C₂³	1	2	yes	—
278	C₇×#107	C₂³	1	1	yes	characteristic
279	C₇×#107	C₂³	1	1	yes	characteristic
280	C₇×#106	C₂³	1	2	yes	—
281	C₇×#106	C₂³	1	2	yes	—
282	C₇×#106	C₂³	1	2	yes	—
283	C₇×#106	C₂³	1	2	yes	—
284	C₇×#106	C₂³	1	2	yes	—
285	C₇×#106	C₂³	1	2	yes	—
286	C₇×#106	C₂³	1	2	yes	—
287	C₇×#106	C₂³	1	2	yes	—
288	C₇×#106	C₂³	1	1	yes	characteristic
289	C₇×#106	C₂³	1	1	yes	characteristic
290	C₇×C₄⋊C₈	C₂³	1	2	yes	—
291	C₇×C₄⋊C₈	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#103	C₂³	1	1	yes	characteristic
299	C₇×#103	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	1	yes	characteristic
306	C₇×#102	C₂³	1	1	yes	characteristic
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	1	yes	characteristic
313	C₇×#97	C₂³	1	1	yes	characteristic
314	C₇×#97	C₂³	1	1	yes	characteristic
315	C₇×#97	C₂³	1	1	yes	characteristic
316	#3512	C₂×C₇	1	1	yes	characteristic, complemented
317	#3511	C₂×C₇	1	1	yes	characteristic, complemented
318	#3350	C₂×C₇	1	2	yes	complemented
319	#3349	C₂×C₇	1	2	yes	complemented
320	#3348	C₂×C₇	1	2	yes	complemented
321	#3347	C₂×C₇	1	2	yes	complemented
322	#3346	C₂×C₇	1	2	yes	complemented
323	#3345	C₂×C₇	1	2	yes	complemented
324	#3344	C₂×C₇	1	2	yes	complemented
325	#3343	C₂×C₇	1	2	yes	complemented
326	C₂×#501	C₂×C₇	1	1	yes	characteristic, complemented
327	#3099	C₂×C₇	1	1	yes	characteristic, complemented
328	#3099	C₂×C₇	1	1	yes	characteristic, complemented
329	#3098	C₂×C₇	1	1	yes	characteristic, complemented
330	#3098	C₂×C₇	1	1	yes	characteristic, complemented
331	#3080	C₂×C₇	1	1	yes	characteristic, complemented
332	#3079	C₂×C₇	1	1	yes	characteristic, complemented
333	#3061	C₂×C₇	1	1	yes	characteristic, complemented
334	#3060	C₂×C₇	1	1	yes	characteristic, complemented
335	#2943	C₂×C₇	1	1	yes	characteristic, complemented
336	#2932	C₂×C₇	1	1	yes	characteristic, complemented
337	#2913	C₂×C₇	1	1	yes	characteristic, complemented
338	#2912	C₂×C₇	1	1	yes	characteristic, complemented
339	C₇×#41	—	2	2	no	—
340	C₇×#41	—	2	2	no	—
341	C₇×#41	—	2	2	no	—
342	C₇×#41	—	2	2	no	—
343	C₇×#41	—	2	2	no	—
344	C₇×#41	—	2	2	no	—
345	C₇×#41	—	2	2	no	—
346	C₇×#41	—	2	2	no	—
347	C₇×#41	—	8	4	no	—
348	C₂×C₇×Q₈	—	2	2	no	—
349	C₂×C₇×Q₈	—	2	2	no	—
350	C₂×C₇×Q₈	—	8	2	no	—
351	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
352	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
353	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
354	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
355	C₂×C₇×D₄	—	2	1	no	—
356	C₂×C₇×D₄	—	2	1	no	—
357	C₂×C₇×D₄	—	2	2	no	—
358	C₂×C₇×D₄	—	2	2	no	—
359	C₂×C₇×D₄	—	2	2	no	—
360	C₂×C₇×D₄	—	2	2	no	—
361	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
362	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
363	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
364	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
365	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
366	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
367	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
368	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₇	—	2	1	no	—
370	C₂²×C₄×C₇	—	2	1	no	—
371	C₂²×C₄×C₇	—	2	1	no	—
372	C₂²×C₄×C₇	—	2	1	no	—
373	C₂²×C₄×C₇	—	2	2	no	—
374	C₂²×C₄×C₇	—	2	2	no	—
375	C₂²×C₄×C₇	—	2	2	no	—
376	C₂²×C₄×C₇	—	2	2	no	—
377	C₂²×C₄×C₇	—	2	1	no	—
378	C₂²×C₄×C₇	—	2	1	no	—
379	C₂²×C₄×C₇	—	2	1	no	—
380	C₂²×C₄×C₇	—	2	1	no	—
381	C₂²×C₄×C₇	—	2	1	no	—
382	C₂²×C₄×C₇	—	2	1	no	—
383	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
388	C₇×Q₁₆	—	2	2	no	—
389	C₇×SD₁₆	—	2	2	no	—
390	C₇×SD₁₆	—	2	2	no	—
391	C₇×D₈	—	2	2	no	—
392	C₇×M₁₆	—	2	2	no	—
393	C₇×M₁₆	—	2	2	no	—
394	C₇×M₁₆	—	2	4	no	—
395	C₇×M₁₆	—	2	4	no	—
396	C₂×C₇×C₈	—	2	2	no	—
397	C₂×C₇×C₈	—	2	4	no	—
398	C₂×C₇×C₈	—	2	4	no	—
399	C₂×C₇×C₈	#41	1	4	yes	complemented
400	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
401	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
402	C₂×C₇×C₈	C₂⁴	1	2	yes	—
403	C₂×C₇×C₈	C₂⁴	1	2	yes	—
404	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
405	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
406	C₇×C₄⋊C₄	—	2	2	no	—
407	C₇×C₄⋊C₄	—	2	2	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	2	no	—
412	C₇×C₄⋊C₄	—	2	1	no	—
413	C₇×C₄⋊C₄	—	2	1	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	1	no	—
421	C₇×C₄⋊C₄	—	2	1	no	—
422	C₇×C₄⋊C₄	—	2	1	no	—
423	C₇×C₄⋊C₄	—	2	1	no	—
424	C₇×C₄⋊C₄	—	2	2	no	—
425	C₇×C₄⋊C₄	—	2	2	no	—
426	C₇×C₄⋊C₄	—	2	2	no	—
427	C₇×C₄⋊C₄	—	2	2	no	—
428	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
429	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
430	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
431	C₇×C₄⋊C₄	C₂⁴	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	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	2	yes	—
438	C₇×C₂²⋊C₄	—	2	2	no	—
439	C₇×C₂²⋊C₄	—	2	2	no	—
440	C₇×C₂²⋊C₄	—	2	1	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	1	no	—
451	C₇×C₂²⋊C₄	—	2	1	no	—
452	C₇×C₂²⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
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	1	no	—
463	C₄²×C₇	—	2	1	no	—
464	C₄²×C₇	—	2	1	no	—
465	C₄²×C₇	—	2	1	no	—
466	C₄²×C₇	—	2	2	no	—
467	C₄²×C₇	—	2	2	no	—
468	C₄²×C₇	—	2	2	no	—
469	C₄²×C₇	—	2	2	no	—
470	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₇	C₂⁴	1	1	yes	characteristic
473	C₄²×C₇	C₂⁴	1	1	yes	characteristic
474	C₂×#135	C₂²×C₇	1	1	yes	characteristic
475	C₂×#131	C₂²×C₇	1	1	yes	characteristic
476	C₂×#131	C₂²×C₇	1	1	yes	characteristic
477	#556	C₂²×C₇	1	2	yes	—
478	#555	C₂²×C₇	1	2	yes	—
479	#554	C₂²×C₇	1	2	yes	—
480	#553	—	2	2	no	—
481	#553	—	2	2	no	—
482	#553	—	2	2	no	—
483	#553	C₂²×C₇	1	2	yes	—
484	#553	C₂²×C₇	1	2	yes	—
485	#552	C₂²×C₇	1	2	yes	—
486	#552	C₂²×C₇	1	2	yes	—
487	#548	—	2	2	no	—
488	#547	C₂²×C₇	1	2	yes	—
489	#542	—	2	1	no	—
490	#542	—	2	1	no	—
491	#541	—	2	1	no	—
492	#540	—	2	1	no	—
493	#537	C₂²×C₇	1	1	yes	characteristic
494	#537	C₂²×C₇	1	1	yes	characteristic
495	#537	C₂²×C₇	1	1	yes	characteristic
496	#537	C₂²×C₇	1	1	yes	characteristic
497	#533	—	2	1	no	—
498	#532	—	2	1	no	—
499	#532	C₂²×C₇	1	1	yes	characteristic
500	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
501	#529	—	2	1	no	—
502	#529	—	2	1	no	—
503	C₂×#125	C₂²×C₇	1	1	yes	characteristic
504	#520	C₂²×C₇	1	1	yes	characteristic
505	#520	C₂²×C₇	1	1	yes	characteristic
506	#520	C₂²×C₇	1	1	yes	characteristic
507	#520	C₂²×C₇	1	1	yes	characteristic
508	C₄×#41	C₂²×C₇	1	1	yes	characteristic
509	C₄×#41	C₂²×C₇	1	1	yes	characteristic
510	#501	C₂²×C₇	1	2	yes	—
511	#501	C₂²×C₇	1	2	yes	—
512	#501	C₂²×C₇	1	2	yes	—
513	#501	C₂²×C₇	1	2	yes	—
514	#485	C₂²×C₇	1	2	yes	—
515	#485	C₂²×C₇	1	2	yes	—
516	#485	C₂²×C₇	1	2	yes	—
517	#485	C₂²×C₇	1	2	yes	—
518	#484	C₂²×C₇	1	2	yes	—
519	#484	C₂²×C₇	1	2	yes	—
520	#483	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	#482	C₂²×C₇	1	2	yes	—
525	#482	C₂²×C₇	1	2	yes	—
526	#481	C₂²×C₇	1	2	yes	—
527	#481	C₂²×C₇	1	2	yes	—
528	#480	C₂²×C₇	1	2	yes	—
529	#480	C₂²×C₇	1	2	yes	—
530	#479	C₂²×C₇	1	2	yes	—
531	#479	C₂²×C₇	1	2	yes	—
532	#478	C₂²×C₇	1	2	yes	—
533	#478	C₂²×C₇	1	2	yes	—
534	#477	C₂²×C₇	1	2	yes	—
535	#476	C₂²×C₇	1	2	yes	—
536	#475	C₂²×C₇	1	2	yes	—
537	#474	C₂²×C₇	1	2	yes	—
538	#470	C₂²×C₇	1	2	yes	—
539	#469	C₂²×C₇	1	2	yes	—
540	#468	C₂²×C₇	1	2	yes	—
541	#468	C₂²×C₇	1	2	yes	—
542	#467	C₂²×C₇	1	2	yes	—
543	#466	C₂²×C₇	1	2	yes	—
544	#465	C₂²×C₇	1	2	yes	—
545	#465	C₂²×C₇	1	2	yes	—
546	#442	C₂²×C₇	1	1	yes	characteristic
547	#442	C₂²×C₇	1	1	yes	characteristic
548	#441	C₂²×C₇	1	1	yes	characteristic
549	#441	C₂²×C₇	1	1	yes	characteristic
550	#440	C₂²×C₇	1	1	yes	characteristic
551	#440	C₂²×C₇	1	1	yes	characteristic
552	#440	C₂²×C₇	1	1	yes	characteristic
553	#440	C₂²×C₇	1	1	yes	characteristic
554	#435	C₂²×C₇	1	2	yes	—
555	#435	C₂²×C₇	1	2	yes	—
556	#435	C₂²×C₇	1	2	yes	—
557	#435	C₂²×C₇	1	2	yes	—
558	#428	C₂²×C₇	1	1	yes	characteristic
559	#428	C₂²×C₇	1	1	yes	characteristic
560	#428	C₂²×C₇	1	1	yes	characteristic
561	#428	C₂²×C₇	1	1	yes	characteristic
562	#428	C₂²×C₇	1	2	yes	—
563	#428	C₂²×C₇	1	2	yes	—
564	#428	C₂²×C₇	1	2	yes	—
565	#428	C₂²×C₇	1	2	yes	—
566	#427	C₂²×C₇	1	2	yes	—
567	#427	C₂²×C₇	1	2	yes	—
568	#427	C₂²×C₇	1	1	yes	characteristic
569	C₂×#107	C₂²×C₇	1	2	yes	—
570	C₂×#107	C₂²×C₇	1	1	yes	characteristic
571	C₂×#107	C₂²×C₇	1	1	yes	characteristic
572	C₂×#106	C₂²×C₇	1	2	yes	—
573	C₂×#106	C₂²×C₇	1	1	yes	characteristic
574	C₂×#106	C₂²×C₇	1	1	yes	characteristic
575	#423	C₂²×C₇	1	1	yes	characteristic
576	#417	C₂²×C₇	1	1	yes	characteristic
577	#417	C₂²×C₇	1	1	yes	characteristic
578	#417	C₂²×C₇	1	1	yes	characteristic
579	#417	C₂²×C₇	1	1	yes	characteristic
580	#416	C₂²×C₇	1	1	yes	characteristic
581	#416	C₂²×C₇	1	1	yes	characteristic
582	#408	C₂²×C₇	1	1	yes	characteristic
583	#408	C₂²×C₇	1	1	yes	characteristic
584	C₂×#97	C₂²×C₇	1	1	yes	characteristic
585	C₂³×C₇	—	2	1	no	—
586	C₂³×C₇	—	2	1	no	—
587	C₂³×C₇	C₂²×D₄	1	2	yes	—
588	C₂³×C₇	C₂²×D₄	1	2	yes	—
589	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
590	C₇×Q₈	—	2	2	no	—
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	1	no	—
596	C₇×Q₈	—	4	4	no	—
597	C₇×Q₈	—	8	2	no	—
598	C₇×D₄	—	2	4	no	—
599	C₇×D₄	—	2	4	no	—
600	C₇×D₄	—	2	2	no	—
601	C₇×D₄	—	2	2	no	—
602	C₇×D₄	—	2	1	no	—
603	C₇×D₄	—	2	1	no	—
604	C₇×D₄	—	2	1	no	—
605	C₇×D₄	—	2	1	no	—
606	C₇×D₄	—	4	2	no	—
607	C₇×D₄	—	4	2	no	—
608	C₇×D₄	—	4	2	no	—
609	C₇×D₄	—	4	2	no	—
610	C₇×D₄	—	8	2	no	—
611	C₇×D₄	—	8	2	no	—
612	C₇×D₄	—	8	2	no	—
613	C₇×D₄	—	8	2	no	—
614	C₂×C₄×C₇	—	2	2	no	—
615	C₂×C₄×C₇	—	2	2	no	—
616	C₂×C₄×C₇	—	2	2	no	—
617	C₂×C₄×C₇	—	2	2	no	—
618	C₂×C₄×C₇	—	2	1	no	—
619	C₂×C₄×C₇	—	2	1	no	—
620	C₂×C₄×C₇	—	2	1	no	—
621	C₂×C₄×C₇	—	2	1	no	—
622	C₂×C₄×C₇	—	2	1	no	—
623	C₂×C₄×C₇	—	2	1	no	—
624	C₂×C₄×C₇	—	2	2	no	—
625	C₂×C₄×C₇	—	2	2	no	—
626	C₂×C₄×C₇	—	2	2	no	—
627	C₂×C₄×C₇	—	2	2	no	—
628	C₂×C₄×C₇	—	4	1	no	—
629	C₂×C₄×C₇	—	4	1	no	—
630	C₂×C₄×C₇	—	4	2	no	—
631	C₂×C₄×C₇	—	4	2	no	—
632	C₂×C₄×C₇	—	4	2	no	—
633	C₂×C₄×C₇	—	4	2	no	—
634	C₂×C₄×C₇	—	8	1	no	—
635	C₂×C₄×C₇	—	8	1	no	—
636	C₂×C₄×C₇	—	8	2	no	—
637	C₂×C₄×C₇	—	8	1	no	—
638	C₂×C₄×C₇	—	8	2	no	—
639	C₂×C₄×C₇	—	8	1	no	—
640	C₂×C₄×C₇	—	8	1	no	—
641	C₂×C₄×C₇	—	8	1	no	—
642	C₂×C₄×C₇	—	8	2	no	—
643	C₂×C₄×C₇	—	8	2	no	—
644	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
645	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
646	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
650	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
651	C₂×C₄×C₇	C₂×#41	1	2	yes	—
652	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
653	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
654	C₇×C₈	—	2	2	no	—
655	C₇×C₈	—	2	2	no	—
656	C₇×C₈	—	2	1	no	—
657	C₇×C₈	—	2	1	no	—
658	C₇×C₈	C₂×#41	1	2	yes	—
659	C₇×C₈	C₂×#41	1	2	yes	—
660	C₂×#41	—	2	2	no	—
661	C₂×#41	C₂³×C₇	1	1	yes	characteristic
662	C₂×#41	C₂³×C₇	1	1	yes	characteristic
663	C₂×#41	C₂³×C₇	1	1	yes	characteristic
664	C₂×#41	C₂³×C₇	1	1	yes	characteristic
665	C₂²×Q₈	—	2	1	no	—
666	#135	—	2	4	no	—
667	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
668	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
669	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
670	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
671	#131	—	2	4	no	—
672	#131	—	2	4	no	—
673	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
674	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
675	C₂×M₁₆	C₂³×C₇	1	2	yes	—
676	C₂×M₁₆	C₂³×C₇	1	2	yes	—
677	C₂²×C₈	C₂³×C₇	1	2	yes	—
678	C₂²×C₈	C₂³×C₇	1	2	yes	—
679	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
680	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
681	C₄⋊Q₈	—	2	1	no	—
682	C₄⋊Q₈	—	2	1	no	—
683	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
684	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
685	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
686	#127	C₇×D₄	1	1	yes	characteristic
687	#126	—	2	2	no	—
688	#126	—	2	2	no	—
689	#126	—	2	2	no	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#126	—	2	2	no	—
693	#125	—	2	2	no	—
694	#125	—	2	2	no	—
695	#125	—	2	2	no	—
696	#125	—	2	1	no	—
697	#125	—	2	1	no	—
698	#125	C₂³×C₇	1	2	yes	—
699	#125	C₂³×C₇	1	2	yes	—
700	#124	—	2	2	no	—
701	#124	—	2	2	no	—
702	#124	—	2	2	no	—
703	#124	C₇×D₄	1	1	yes	characteristic
704	#124	C₇×D₄	1	1	yes	characteristic
705	#123	—	2	2	no	—
706	#123	—	2	2	no	—
707	#123	—	2	2	no	—
708	#123	—	2	2	no	—
709	#123	—	2	2	no	—
710	#123	—	2	2	no	—
711	C₂²⋊Q₈	—	2	1	no	—
712	C₂²⋊Q₈	—	2	1	no	—
713	C₂²⋊Q₈	—	2	1	no	—
714	C₂²⋊Q₈	—	2	1	no	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	2	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
719	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
720	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
721	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
722	#121	—	2	1	no	—
723	#121	—	2	1	no	—
724	#121	—	2	1	no	—
725	#121	—	2	1	no	—
726	#121	—	2	2	no	—
727	#121	—	2	2	no	—
728	#121	—	2	2	no	—
729	#121	—	2	2	no	—
730	#121	—	2	2	no	—
731	#121	—	2	2	no	—
732	#121	—	2	2	no	—
733	#121	C₇×D₄	1	2	yes	—
734	#121	C₇×D₄	1	2	yes	—
735	#121	C₂³×C₇	1	2	yes	—
736	#121	C₂³×C₇	1	2	yes	—
737	#121	C₂³×C₇	1	2	yes	—
738	#121	C₂³×C₇	1	2	yes	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	—	2	1	no	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	2	no	—
744	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
745	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
746	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
747	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
748	C₄×D₄	—	2	1	no	—
749	C₄×D₄	—	2	1	no	—
750	C₄×D₄	—	2	1	no	—
751	C₄×D₄	—	2	1	no	—
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	1	no	—
758	C₄×D₄	—	2	1	no	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
764	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
765	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
766	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
767	C₄×D₄	C₂³×C₇	1	2	yes	—
768	C₄×D₄	C₂³×C₇	1	2	yes	—
769	#117	—	2	2	no	—
770	#117	—	2	2	no	—
771	#117	—	2	2	no	—
772	#117	—	2	1	no	—
773	#117	—	2	1	no	—
774	#117	C₂³×C₇	1	1	yes	characteristic
775	#117	C₂³×C₇	1	1	yes	characteristic
776	#117	C₂³×C₇	1	2	yes	—
777	#117	C₂³×C₇	1	2	yes	—
778	#117	C₂³×C₇	1	2	yes	—
779	#117	C₂³×C₇	1	2	yes	—
780	C₂×C₄⋊C₄	—	2	1	no	—
781	C₂×C₄⋊C₄	—	2	1	no	—
782	C₂×C₄⋊C₄	—	2	1	no	—
783	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
784	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
788	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
789	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
790	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
791	C₂×C₄²	—	2	1	no	—
792	C₂×C₄²	—	2	1	no	—
793	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
794	#107	C₂³×C₇	1	1	yes	characteristic
795	#107	C₂³×C₇	1	2	yes	—
796	#107	C₂³×C₇	1	2	yes	—
797	#107	C₂³×C₇	1	2	yes	—
798	#107	C₂³×C₇	1	2	yes	—
799	#107	C₂³×C₇	1	2	yes	—
800	#107	C₂³×C₇	1	2	yes	—
801	#107	C₂³×C₇	1	1	yes	characteristic
802	#107	C₂³×C₇	1	2	yes	—
803	#107	C₂³×C₇	1	2	yes	—
804	#106	C₂³×C₇	1	1	yes	characteristic
805	#106	C₂³×C₇	1	2	yes	—
806	#106	C₂³×C₇	1	2	yes	—
807	#106	C₂³×C₇	1	2	yes	—
808	#106	C₂³×C₇	1	2	yes	—
809	#106	C₂³×C₇	1	2	yes	—
810	#106	C₂³×C₇	1	2	yes	—
811	#106	C₂³×C₇	1	1	yes	characteristic
812	#106	C₂³×C₇	1	2	yes	—
813	#106	C₂³×C₇	1	2	yes	—
814	C₄⋊C₈	C₂³×C₇	1	2	yes	—
815	C₄⋊C₈	C₂³×C₇	1	2	yes	—
816	#103	C₂³×C₇	1	1	yes	characteristic
817	#103	C₂³×C₇	1	1	yes	characteristic
818	#103	C₂³×C₇	1	1	yes	characteristic
819	#103	C₂³×C₇	1	1	yes	characteristic
820	#103	C₂³×C₇	1	2	yes	—
821	#103	C₂³×C₇	1	2	yes	—
822	#103	C₂³×C₇	1	2	yes	—
823	#103	C₂³×C₇	1	2	yes	—
824	#102	C₂³×C₇	1	1	yes	characteristic
825	#102	C₂³×C₇	1	1	yes	characteristic
826	#102	C₂³×C₇	1	1	yes	characteristic
827	#102	C₂³×C₇	1	1	yes	characteristic
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	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
833	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
834	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
835	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
836	#97	C₂³×C₇	1	1	yes	characteristic
837	#97	C₂³×C₇	1	1	yes	characteristic
838	#97	C₂³×C₇	1	1	yes	characteristic
839	#97	C₂³×C₇	1	1	yes	characteristic
840	C₂²×C₇	—	2	1	no	—
841	C₂²×C₇	—	2	1	no	—
842	C₂²×C₇	—	2	2	no	—
843	C₂²×C₇	—	2	2	no	—
844	C₂²×C₇	—	2	2	no	—
845	C₂²×C₇	—	2	2	no	—
846	C₂²×C₇	—	2	2	no	—
847	C₂²×C₇	—	2	2	no	—
848	C₂²×C₇	—	4	1	no	—
849	C₂²×C₇	—	4	1	no	—
850	C₂²×C₇	—	4	1	no	—
851	C₂²×C₇	—	4	1	no	—
852	C₂²×C₇	—	4	1	no	—
853	C₂²×C₇	—	4	1	no	—
854	C₂²×C₇	#547	1	2	yes	—
855	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
856	C₄×C₇	—	2	1	no	—
857	C₄×C₇	—	2	1	no	—
858	C₄×C₇	—	2	1	no	—
859	C₄×C₇	—	2	1	no	—
860	C₄×C₇	—	2	2	no	—
861	C₄×C₇	—	2	2	no	—
862	C₄×C₇	—	4	1	no	—
863	C₄×C₇	—	4	1	no	—
864	C₄×C₇	—	4	2	no	—
865	C₄×C₇	—	4	2	no	—
866	C₄×C₇	—	4	2	no	—
867	C₄×C₇	—	4	1	no	—
868	C₄×C₇	—	4	1	no	—
869	C₄×C₇	—	4	2	no	—
870	C₄×C₇	—	4	1	no	—
871	C₄×C₇	—	4	1	no	—
872	C₄×C₇	#547	1	2	yes	—
873	C₄×C₇	C₂²×#41	1	1	yes	characteristic
874	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
875	#41	—	2	2	no	—
876	#41	—	2	2	no	—
877	#41	—	2	2	no	—
878	#41	—	2	2	no	—
879	#41	—	2	2	no	—
880	#41	—	2	2	no	—
881	#41	—	2	2	no	—
882	#41	—	2	2	no	—
883	#41	—	8	4	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	8	2	no	—
887	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
888	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
898	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
899	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
900	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
901	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
902	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
903	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
904	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
920	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
921	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
922	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
923	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
924	Q₁₆	—	2	2	no	—
925	SD₁₆	—	2	2	no	—
926	SD₁₆	—	2	2	no	—
927	D₈	—	2	2	no	—
928	M₁₆	—	2	2	no	—
929	M₁₆	—	2	2	no	—
930	M₁₆	—	2	4	no	—
931	M₁₆	—	2	4	no	—
932	C₂×C₈	—	2	2	no	—
933	C₂×C₈	—	2	4	no	—
934	C₂×C₈	—	2	4	no	—
935	C₂×C₈	C₇×#41	1	4	yes	complemented
936	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₇	1	2	yes	—
939	C₂×C₈	C₂⁴×C₇	1	2	yes	—
940	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
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	2	yes	—
970	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	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	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	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	C₂×C₇×D₄	1	2	yes	—
993	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
994	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
995	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1007	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1010	C₂×C₇	—	2	2	no	—
1011	C₂×C₇	—	4	2	no	—
1012	C₂×C₇	—	4	2	no	—
1013	C₂×C₇	—	8	1	no	—
1014	C₂×C₇	—	8	1	no	—
1015	C₂×C₇	C₂×#547	1	1	yes	characteristic
1016	C₂×C₇	#3585	1	1	yes	characteristic
1017	C₂×C₇	#3586	1	1	yes	characteristic
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	C₂²×C₇×D₄	1	2	yes	—
1021	C₂³	C₂²×C₇×D₄	1	2	yes	—
1022	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	2	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	4	4	no	—
1030	Q₈	—	8	2	no	—
1031	D₄	—	2	4	no	—
1032	D₄	—	2	4	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	4	1	no	—
1062	C₂×C₄	—	4	1	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	2	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	8	1	no	—
1068	C₂×C₄	—	8	1	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	—	8	1	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	1	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	1	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1078	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1079	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1080	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1081	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1082	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1083	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1084	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1085	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1086	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1087	C₈	—	2	2	no	—
1088	C₈	—	2	2	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	1	no	—
1091	C₈	C₂×C₇×#41	1	2	yes	—
1092	C₈	C₂×C₇×#41	1	2	yes	—
1093	C₇	#61294	1	1	yes	characteristic, direct product factor, Sylow
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	C₇×#547	1	2	yes	—
1109	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	2	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	C₇×#547	1	2	yes	—
1127	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1128	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1129	C₂	—	2	2	no	—
1130	C₂	—	4	2	no	—
1131	C₂	—	4	2	no	—
1132	C₂	—	8	1	no	—
1133	C₂	—	8	1	no	—
1134	C₂	C₂×C₇×#547	1	1	yes	characteristic
1135	C₂	C₇×#3585	1	1	yes	characteristic
1136	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 ◁ C₇×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3512	C₂	semidirect
2. C₇×#3511	C₂	semidirect
3. C₇×#3350	C₂	semidirect
4. C₇×#3349	C₂	semidirect
5. C₇×#3348	C₂	semidirect
6. C₇×#3347	C₂	semidirect
7. C₇×#3346	C₂	semidirect
8. C₇×#3345	C₂	semidirect
9. C₇×#3344	C₂	semidirect
10. C₇×#3343	C₂	semidirect
11. C₂×C₇×#501	C₂	semidirect
12. C₇×#3099	C₂	semidirect
13. C₇×#3099	C₂	semidirect
14. C₇×#3098	C₂	semidirect
15. C₇×#3098	C₂	semidirect
16. C₇×#3080	C₂	semidirect
17. C₇×#3079	C₂	semidirect
18. C₇×#3061	C₂	semidirect
19. C₇×#3060	C₂	semidirect
20. C₇×#2943	C₂	semidirect
21. C₇×#2932	C₂	semidirect
22. C₇×#2913	C₂	semidirect
23. C₇×#2912	C₂	semidirect
135. #61294	C₇	direct (N × H)
316. #3512	C₂×C₇	semidirect
317. #3511	C₂×C₇	semidirect
318. #3350	C₂×C₇	semidirect
319. #3349	C₂×C₇	semidirect
320. #3348	C₂×C₇	semidirect
321. #3347	C₂×C₇	semidirect
322. #3346	C₂×C₇	semidirect
323. #3345	C₂×C₇	semidirect
324. #3344	C₂×C₇	semidirect
325. #3343	C₂×C₇	semidirect
326. C₂×#501	C₂×C₇	semidirect
327. #3099	C₂×C₇	semidirect
328. #3099	C₂×C₇	semidirect
329. #3098	C₂×C₇	semidirect
330. #3098	C₂×C₇	semidirect
331. #3080	C₂×C₇	semidirect
332. #3079	C₂×C₇	semidirect
333. #3061	C₂×C₇	semidirect
334. #3060	C₂×C₇	semidirect
335. #2943	C₂×C₇	semidirect
336. #2932	C₂×C₇	semidirect
337. #2913	C₂×C₇	semidirect
338. #2912	C₂×C₇	semidirect
399. C₂×C₇×C₈	#41	semidirect
935. C₂×C₈	C₇×#41	semidirect
1093. C₇	#61294	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×#3512	2
C₇×#3511	2
C₇×#3350	2
C₇×#3349	2
C₇×#3348	2
C₇×#3347	2
C₇×#3346	2
C₇×#3345	2
C₇×#3344	2
C₇×#3343	2
C₂×C₇×#501	2
C₇×#3099	2
C₇×#3098	2
C₇×#3080	2
C₇×#3079	2
C₇×#3061	2
C₇×#3060	2
C₇×#2943	2
C₇×#2932	2
C₇×#2913	2
C₇×#2912	2
#61294	7

Subgroups — C7×#61294 #13238510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61294 #13238510