Subgroups — C₇×#61476 #13238692

Order 1792.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3337	C₂	1	2	yes	maximal, complemented
8	C₇×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3330	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3317	C₂	1	2	yes	maximal, complemented
12	C₇×#3307	C₂	1	2	yes	maximal, complemented
13	C₇×#3284	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3284	C₂	1	2	yes	maximal, complemented
15	C₇×#3174	C₂	1	2	yes	maximal, complemented
16	C₇×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3120	C₂	1	2	yes	maximal, complemented
18	C₇×#3119	C₂	1	2	yes	maximal, complemented
19	C₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2952	C₂	1	2	yes	maximal, complemented
23	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#135	C₂²	1	1	yes	characteristic
25	C₂×C₇×#135	C₂²	1	2	yes	—
26	C₇×#557	C₂²	1	1	yes	characteristic
27	C₇×#557	C₂²	1	1	yes	characteristic
28	C₇×#554	C₂²	1	1	yes	characteristic
29	C₇×#554	C₂²	1	1	yes	characteristic
30	C₇×#553	—	2	2	no	—
31	C₇×#553	—	2	1	no	—
32	C₇×#553	C₂²	1	2	yes	—
33	C₇×#552	—	2	2	no	—
34	C₇×#552	—	2	1	no	—
35	C₇×#552	C₂²	1	2	yes	—
36	C₇×#550	—	2	1	no	—
37	C₇×#550	C₂²	1	2	yes	—
38	C₇×#550	C₂²	1	1	yes	characteristic
39	C₇×#550	C₂²	1	1	yes	characteristic
40	C₇×#547	—	2	1	no	—
41	C₇×#547	C₂²	1	2	yes	—
42	C₇×#547	C₂²	1	1	yes	characteristic
43	C₇×#547	C₂²	1	1	yes	characteristic
44	C₇×#541	C₂²	1	2	yes	—
45	C₇×#540	—	2	2	no	—
46	C₇×#540	C₂²	1	2	yes	—
47	C₇×#539	—	2	2	no	—
48	C₇×#533	C₂²	1	1	yes	characteristic
49	C₇×#532	—	2	1	no	—
50	C₇×#532	C₂²	1	1	yes	characteristic
51	C₇×#529	—	2	1	no	—
52	C₇×#529	—	2	1	no	—
53	C₇×#529	C₂²	1	1	yes	characteristic
54	C₂×C₇×#125	—	2	1	no	—
55	C₇×#520	C₂²	1	2	yes	—
56	C₇×#520	C₂²	1	2	yes	—
57	C₄×C₇×#41	C₂²	1	1	yes	characteristic
58	C₄×C₇×#41	C₂²	1	1	yes	characteristic
59	C₇×#499	C₂²	1	2	yes	—
60	C₇×#498	C₂²	1	1	yes	characteristic
61	C₇×#492	C₂²	1	1	yes	characteristic
62	C₇×#492	C₂²	1	2	yes	—
63	C₇×#491	C₂²	1	2	yes	—
64	C₇×#490	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×#481	C₂²	1	2	yes	—
72	C₇×#480	C₂²	1	2	yes	—
73	C₇×#479	C₂²	1	2	yes	—
74	C₇×#479	C₂²	1	2	yes	—
75	C₇×#478	C₂²	1	2	yes	—
76	C₇×#478	C₂²	1	2	yes	—
77	C₇×#477	C₂²	1	1	yes	characteristic
78	C₇×#476	C₂²	1	1	yes	characteristic
79	C₇×#475	C₂²	1	1	yes	characteristic
80	C₇×#474	C₂²	1	1	yes	characteristic
81	C₇×#468	C₂²	1	2	yes	—
82	C₇×#468	C₂²	1	2	yes	—
83	C₇×#465	C₂²	1	2	yes	—
84	C₇×#465	C₂²	1	2	yes	—
85	C₇×#465	C₂²	1	2	yes	—
86	C₇×#465	C₂²	1	2	yes	—
87	C₇×#462	C₂²	1	1	yes	characteristic
88	C₇×#462	C₂²	1	2	yes	—
89	C₇×#461	C₂²	1	2	yes	—
90	C₇×#461	C₂²	1	1	yes	characteristic
91	C₇×#460	C₂²	1	2	yes	—
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×#452	C₂²	1	2	yes	—
97	C₇×#452	C₂²	1	2	yes	—
98	C₇×#449	C₂²	1	2	yes	—
99	C₇×#449	C₂²	1	2	yes	—
100	C₇×#449	C₂²	1	2	yes	—
101	C₇×#446	C₂²	1	1	yes	characteristic
102	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
103	C₇×#442	C₂²	1	2	yes	—
104	C₇×#442	C₂²	1	2	yes	—
105	C₇×#441	C₂²	1	2	yes	—
106	C₇×#441	C₂²	1	2	yes	—
107	C₇×#440	C₂²	1	2	yes	—
108	C₇×#440	C₂²	1	2	yes	—
109	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
110	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
111	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
112	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
114	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
115	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
116	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
117	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
118	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
119	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
120	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
121	C₇×#436	C₂²	1	1	yes	characteristic
122	C₇×#435	C₂²	1	2	yes	—
123	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
124	C₇×C₈×D₄	C₂²	1	2	yes	—
125	C₇×#433	C₂²	1	2	yes	—
126	C₇×#432	C₂²	1	1	yes	characteristic
127	C₇×#427	C₂²	1	1	yes	characteristic
128	C₂×C₇×#106	C₂²	1	2	yes	—
129	C₇×#417	C₂²	1	2	yes	—
130	C₇×#417	C₂²	1	2	yes	—
131	C₇×#416	C₂²	1	1	yes	characteristic
132	C₇×#416	C₂²	1	1	yes	characteristic
133	C₇×#405	C₂²	1	2	yes	—
134	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
135	#61476	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	C₂³	1	1	yes	characteristic
140	C₂×C₇×#41	C₂³	1	1	yes	characteristic
141	C₂×C₇×#41	C₂³	1	2	yes	—
142	C₂×C₇×#41	C₂³	1	2	yes	—
143	C₇×#135	—	2	4	no	—
144	C₇×#135	—	2	8	no	—
145	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
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×D₈	C₂³	1	1	yes	characteristic
154	C₂×C₇×D₈	C₂³	1	2	yes	—
155	C₂×C₇×M₁₆	C₂³	1	2	yes	—
156	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
157	C₂²×C₇×C₈	C₂³	1	2	yes	—
158	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
159	C₇×C₄⋊Q₈	—	2	1	no	—
160	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₇×#127	—	2	1	no	—
165	C₇×#127	—	2	2	no	—
166	C₇×#127	C₂³	1	1	yes	characteristic
167	C₇×#127	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
173	C₇×#125	—	2	2	no	—
174	C₇×#125	—	2	2	no	—
175	C₇×#125	—	2	1	no	—
176	C₇×#125	—	2	1	no	—
177	C₇×#125	—	2	2	no	—
178	C₇×#125	—	2	2	no	—
179	C₇×#125	—	2	2	no	—
180	C₇×#125	—	2	1	no	—
181	C₇×#125	D₄	1	1	yes	characteristic
182	C₇×#125	C₂³	1	2	yes	—
183	C₇×#125	C₂³	1	2	yes	—
184	C₇×#124	—	2	1	no	—
185	C₇×#124	D₄	1	1	yes	characteristic
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×#123	—	2	2	no	—
193	C₇×#123	—	2	2	no	—
194	C₇×#123	D₄	1	2	yes	—
195	C₇×C₂²⋊Q₈	—	2	1	no	—
196	C₇×C₂²⋊Q₈	—	2	1	no	—
197	C₇×C₂²⋊Q₈	—	2	1	no	—
198	C₇×C₂²⋊Q₈	—	2	2	no	—
199	C₇×C₂²⋊Q₈	—	2	2	no	—
200	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
201	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₇×#121	—	2	1	no	—
205	C₇×#121	—	2	2	no	—
206	C₇×#121	—	2	2	no	—
207	C₇×#121	—	2	1	no	—
208	C₇×#121	—	2	1	no	—
209	C₇×#121	—	2	2	no	—
210	C₇×#121	—	2	2	no	—
211	C₇×#121	—	2	2	no	—
212	C₇×#121	—	2	2	no	—
213	C₇×#121	—	2	2	no	—
214	C₇×#121	—	2	2	no	—
215	C₇×#121	D₄	1	1	yes	characteristic
216	C₇×#121	C₂³	1	2	yes	—
217	C₇×#121	C₂³	1	2	yes	—
218	C₇×#121	C₂³	1	2	yes	—
219	C₄×C₇×Q₈	—	2	1	no	—
220	C₄×C₇×Q₈	—	2	1	no	—
221	C₄×C₇×Q₈	—	2	1	no	—
222	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
223	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
224	C₄×C₇×Q₈	C₂³	1	2	yes	—
225	C₄×C₇×Q₈	C₂³	1	2	yes	—
226	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
227	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
228	C₄×C₇×Q₈	C₂³	1	2	yes	—
229	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
230	C₄×C₇×D₄	—	2	1	no	—
231	C₄×C₇×D₄	—	2	1	no	—
232	C₄×C₇×D₄	—	2	1	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	2	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	2	no	—
241	C₄×C₇×D₄	—	2	2	no	—
242	C₄×C₇×D₄	—	2	1	no	—
243	C₄×C₇×D₄	C₂³	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	1	yes	characteristic
248	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
249	C₄×C₇×D₄	C₂³	1	2	yes	—
250	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
251	C₄×C₇×D₄	C₂³	1	2	yes	—
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	1	no	—
257	C₇×#117	—	2	1	no	—
258	C₇×#117	C₂³	1	1	yes	characteristic
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	2	no	—
263	C₂×C₇×C₄⋊C₄	—	2	1	no	—
264	C₂×C₇×C₄⋊C₄	—	2	2	no	—
265	C₂×C₇×C₄⋊C₄	—	2	1	no	—
266	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
267	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
268	C₂×C₄²×C₇	—	2	1	no	—
269	C₂×C₄²×C₇	—	2	1	no	—
270	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
271	C₇×#107	C₂³	1	2	yes	—
272	C₇×#107	C₂³	1	2	yes	—
273	C₇×#107	C₂³	1	1	yes	characteristic
274	C₇×#107	C₂³	1	1	yes	characteristic
275	C₇×#106	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	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	2	yes	—
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	2	yes	—
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	1	yes	characteristic
295	C₇×#102	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
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	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
315	#3517	C₂×C₇	1	1	yes	characteristic, complemented
316	#3515	C₂×C₇	1	1	yes	characteristic, complemented
317	#3392	C₂×C₇	1	1	yes	characteristic, complemented
318	#3381	C₂×C₇	1	1	yes	characteristic, complemented
319	#3374	C₂×C₇	1	1	yes	characteristic, complemented
320	#3366	C₂×C₇	1	1	yes	characteristic, complemented
321	#3337	C₂×C₇	1	2	yes	complemented
322	#3335	C₂×C₇	1	1	yes	characteristic, complemented
323	#3333	C₂×C₇	1	1	yes	characteristic, complemented
324	#3330	C₂×C₇	1	1	yes	characteristic, complemented
325	#3317	C₂×C₇	1	2	yes	complemented
326	#3307	C₂×C₇	1	2	yes	complemented
327	#3284	C₂×C₇	1	1	yes	characteristic, complemented
328	#3284	C₂×C₇	1	2	yes	complemented
329	#3174	C₂×C₇	1	2	yes	complemented
330	#3167	C₂×C₇	1	1	yes	characteristic, complemented
331	#3120	C₂×C₇	1	2	yes	complemented
332	#3119	C₂×C₇	1	2	yes	complemented
333	#3116	C₂×C₇	1	1	yes	characteristic, complemented
334	#3115	C₂×C₇	1	1	yes	characteristic, complemented
335	#2966	C₂×C₇	1	1	yes	characteristic, complemented
336	#2952	C₂×C₇	1	2	yes	complemented
337	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
338	C₇×#41	—	2	2	no	—
339	C₇×#41	—	2	4	no	—
340	C₇×#41	—	2	2	no	—
341	C₇×#41	—	2	4	no	—
342	C₇×#41	—	4	1	no	—
343	C₇×#41	—	4	1	no	—
344	C₇×#41	—	4	2	no	—
345	C₇×#41	—	4	2	no	—
346	C₇×#41	—	8	2	no	—
347	C₇×#41	—	8	2	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	C₂×D₄	1	1	yes	characteristic
352	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
353	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
354	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
355	C₂×C₇×D₄	—	2	1	no	—
356	C₂×C₇×D₄	—	2	2	no	—
357	C₂×C₇×D₄	—	2	1	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	—	2	2	no	—
362	C₂×C₇×D₄	—	2	1	no	—
363	C₂×C₇×D₄	—	2	1	no	—
364	C₂×C₇×D₄	—	2	2	no	—
365	C₂×C₇×D₄	—	2	2	no	—
366	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
367	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
368	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
369	C₂×C₇×D₄	C₂⁴	1	2	yes	—
370	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₇	—	2	2	no	—
372	C₂²×C₄×C₇	—	2	2	no	—
373	C₂²×C₄×C₇	—	2	1	no	—
374	C₂²×C₄×C₇	—	2	1	no	—
375	C₂²×C₄×C₇	—	2	1	no	—
376	C₂²×C₄×C₇	—	2	1	no	—
377	C₂²×C₄×C₇	—	2	2	no	—
378	C₂²×C₄×C₇	—	2	2	no	—
379	C₂²×C₄×C₇	—	2	1	no	—
380	C₂²×C₄×C₇	—	2	1	no	—
381	C₂²×C₄×C₇	—	2	2	no	—
382	C₂²×C₄×C₇	—	2	2	no	—
383	C₂²×C₄×C₇	—	2	2	no	—
384	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
388	C₇×Q₁₆	—	2	2	no	—
389	C₇×Q₁₆	—	2	4	no	—
390	C₇×SD₁₆	—	2	4	no	—
391	C₇×SD₁₆	—	2	2	no	—
392	C₇×SD₁₆	—	4	2	no	—
393	C₇×SD₁₆	—	4	2	no	—
394	C₇×SD₁₆	—	4	2	no	—
395	C₇×SD₁₆	#41	1	4	yes	complemented
396	C₇×D₈	—	2	2	no	—
397	C₇×D₈	—	2	4	no	—
398	C₇×M₁₆	—	4	2	no	—
399	C₂×C₇×C₈	—	2	2	no	—
400	C₂×C₇×C₈	—	2	4	no	—
401	C₂×C₇×C₈	—	4	1	no	—
402	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
403	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
404	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
405	C₂×C₇×C₈	C₂⁴	1	2	yes	—
406	C₂×C₇×C₈	C₂⁴	1	2	yes	—
407	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
408	C₇×C₄⋊C₄	—	2	1	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	2	no	—
415	C₇×C₄⋊C₄	—	2	2	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	1	no	—
424	C₇×C₄⋊C₄	—	2	2	no	—
425	C₇×C₄⋊C₄	—	2	1	no	—
426	C₇×C₄⋊C₄	—	2	2	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	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
435	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
436	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
437	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
438	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
439	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
440	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
441	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
442	C₇×C₂²⋊C₄	—	2	2	no	—
443	C₇×C₂²⋊C₄	—	2	2	no	—
444	C₇×C₂²⋊C₄	—	2	1	no	—
445	C₇×C₂²⋊C₄	—	2	1	no	—
446	C₇×C₂²⋊C₄	—	2	2	no	—
447	C₇×C₂²⋊C₄	—	2	1	no	—
448	C₇×C₂²⋊C₄	—	2	2	no	—
449	C₇×C₂²⋊C₄	—	2	1	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	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
461	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	1	no	—
467	C₄²×C₇	—	2	1	no	—
468	C₄²×C₇	—	2	2	no	—
469	C₄²×C₇	—	2	2	no	—
470	C₄²×C₇	—	2	2	no	—
471	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₇	C₂⁴	1	1	yes	characteristic
474	C₄²×C₇	C₂⁴	1	1	yes	characteristic
475	C₄²×C₇	C₂⁴	1	2	yes	—
476	C₂×#135	C₂²×C₇	1	1	yes	characteristic
477	C₂×#135	C₂²×C₇	1	2	yes	—
478	#557	C₂²×C₇	1	1	yes	characteristic
479	#557	C₂²×C₇	1	1	yes	characteristic
480	#554	C₂²×C₇	1	1	yes	characteristic
481	#554	C₂²×C₇	1	1	yes	characteristic
482	#553	—	2	2	no	—
483	#553	—	2	1	no	—
484	#553	C₂²×C₇	1	2	yes	—
485	#552	—	2	2	no	—
486	#552	—	2	1	no	—
487	#552	C₂²×C₇	1	2	yes	—
488	#550	—	2	1	no	—
489	#550	C₂²×C₇	1	1	yes	characteristic
490	#550	C₂²×C₇	1	2	yes	—
491	#550	C₂²×C₇	1	1	yes	characteristic
492	#547	—	2	1	no	—
493	#547	C₂²×C₇	1	1	yes	characteristic
494	#547	C₂²×C₇	1	2	yes	—
495	#547	C₂²×C₇	1	1	yes	characteristic
496	#541	C₂²×C₇	1	2	yes	—
497	#540	—	2	2	no	—
498	#540	C₂²×C₇	1	2	yes	—
499	#539	—	2	2	no	—
500	#533	C₂²×C₇	1	1	yes	characteristic
501	#532	—	2	1	no	—
502	#532	C₂²×C₇	1	1	yes	characteristic
503	#529	—	2	1	no	—
504	#529	—	2	1	no	—
505	#529	C₂²×C₇	1	1	yes	characteristic
506	C₂×#125	—	2	1	no	—
507	#520	C₂²×C₇	1	2	yes	—
508	#520	C₂²×C₇	1	2	yes	—
509	C₄×#41	C₂²×C₇	1	1	yes	characteristic
510	C₄×#41	C₂²×C₇	1	1	yes	characteristic
511	#499	C₂²×C₇	1	2	yes	—
512	#498	C₂²×C₇	1	1	yes	characteristic
513	#492	C₂²×C₇	1	1	yes	characteristic
514	#492	C₂²×C₇	1	2	yes	—
515	#491	C₂²×C₇	1	2	yes	—
516	#490	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	#481	C₂²×C₇	1	2	yes	—
524	#480	C₂²×C₇	1	2	yes	—
525	#479	C₂²×C₇	1	2	yes	—
526	#479	C₂²×C₇	1	2	yes	—
527	#478	C₂²×C₇	1	2	yes	—
528	#478	C₂²×C₇	1	2	yes	—
529	#477	C₂²×C₇	1	1	yes	characteristic
530	#476	C₂²×C₇	1	1	yes	characteristic
531	#475	C₂²×C₇	1	1	yes	characteristic
532	#474	C₂²×C₇	1	1	yes	characteristic
533	#468	C₂²×C₇	1	2	yes	—
534	#468	C₂²×C₇	1	2	yes	—
535	#465	C₂²×C₇	1	2	yes	—
536	#465	C₂²×C₇	1	2	yes	—
537	#465	C₂²×C₇	1	2	yes	—
538	#465	C₂²×C₇	1	2	yes	—
539	#462	C₂²×C₇	1	1	yes	characteristic
540	#462	C₂²×C₇	1	2	yes	—
541	#461	C₂²×C₇	1	1	yes	characteristic
542	#461	C₂²×C₇	1	2	yes	—
543	#460	C₂²×C₇	1	1	yes	characteristic
544	#460	C₂²×C₇	1	2	yes	—
545	#459	C₂²×C₇	1	1	yes	characteristic
546	#459	C₂²×C₇	1	2	yes	—
547	#452	C₂²×C₇	1	2	yes	—
548	#452	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	#446	C₂²×C₇	1	1	yes	characteristic
554	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
555	#442	C₂²×C₇	1	2	yes	—
556	#442	C₂²×C₇	1	2	yes	—
557	#441	C₂²×C₇	1	2	yes	—
558	#441	C₂²×C₇	1	2	yes	—
559	#440	C₂²×C₇	1	2	yes	—
560	#440	C₂²×C₇	1	2	yes	—
561	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
562	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
563	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
564	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
565	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
566	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
567	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
568	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
569	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
570	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
571	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
572	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
573	#436	C₂²×C₇	1	1	yes	characteristic
574	#435	C₂²×C₇	1	2	yes	—
575	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
576	C₈×D₄	C₂²×C₇	1	2	yes	—
577	#433	C₂²×C₇	1	2	yes	—
578	#432	C₂²×C₇	1	1	yes	characteristic
579	#427	C₂²×C₇	1	1	yes	characteristic
580	C₂×#106	C₂²×C₇	1	2	yes	—
581	#417	C₂²×C₇	1	2	yes	—
582	#417	C₂²×C₇	1	2	yes	—
583	#416	C₂²×C₇	1	1	yes	characteristic
584	#416	C₂²×C₇	1	1	yes	characteristic
585	#405	C₂²×C₇	1	2	yes	—
586	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
587	C₂³×C₇	—	2	1	no	—
588	C₂³×C₇	—	2	1	no	—
589	C₂³×C₇	—	2	2	no	—
590	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
591	C₂³×C₇	C₂²×D₄	1	2	yes	—
592	C₇×Q₈	—	2	2	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	—	8	1	no	—
600	C₇×Q₈	C₂×#41	1	2	yes	—
601	C₇×D₄	—	2	2	no	—
602	C₇×D₄	—	2	1	no	—
603	C₇×D₄	—	2	2	no	—
604	C₇×D₄	—	2	1	no	—
605	C₇×D₄	—	2	2	no	—
606	C₇×D₄	—	2	1	no	—
607	C₇×D₄	—	4	2	no	—
608	C₇×D₄	—	4	2	no	—
609	C₇×D₄	—	4	4	no	—
610	C₇×D₄	—	4	2	no	—
611	C₇×D₄	—	4	4	no	—
612	C₇×D₄	—	4	2	no	—
613	C₇×D₄	—	8	1	no	—
614	C₇×D₄	—	8	2	no	—
615	C₇×D₄	—	8	2	no	—
616	C₇×D₄	—	8	2	no	—
617	C₇×D₄	—	8	2	no	—
618	C₇×D₄	—	8	2	no	—
619	C₇×D₄	C₂×#41	1	2	yes	—
620	C₂×C₄×C₇	—	2	1	no	—
621	C₂×C₄×C₇	—	2	2	no	—
622	C₂×C₄×C₇	—	2	1	no	—
623	C₂×C₄×C₇	—	2	2	no	—
624	C₂×C₄×C₇	—	2	1	no	—
625	C₂×C₄×C₇	—	2	2	no	—
626	C₂×C₄×C₇	—	2	1	no	—
627	C₂×C₄×C₇	—	2	1	no	—
628	C₂×C₄×C₇	—	2	1	no	—
629	C₂×C₄×C₇	—	2	1	no	—
630	C₂×C₄×C₇	—	2	1	no	—
631	C₂×C₄×C₇	—	2	2	no	—
632	C₂×C₄×C₇	—	2	2	no	—
633	C₂×C₄×C₇	—	2	2	no	—
634	C₂×C₄×C₇	—	4	1	no	—
635	C₂×C₄×C₇	—	4	2	no	—
636	C₂×C₄×C₇	—	4	4	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	2	no	—
641	C₂×C₄×C₇	—	8	1	no	—
642	C₂×C₄×C₇	—	8	1	no	—
643	C₂×C₄×C₇	—	8	2	no	—
644	C₂×C₄×C₇	—	8	2	no	—
645	C₂×C₄×C₇	—	8	2	no	—
646	C₂×C₄×C₇	—	8	2	no	—
647	C₂×C₄×C₇	—	8	2	no	—
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	C₂²×D₄	1	2	yes	—
652	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
653	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
654	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
655	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
656	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
657	C₇×C₈	—	2	1	no	—
658	C₇×C₈	—	2	2	no	—
659	C₇×C₈	—	2	1	no	—
660	C₇×C₈	—	2	1	no	—
661	C₇×C₈	—	2	2	no	—
662	C₇×C₈	C₂×#41	1	2	yes	—
663	C₂×#41	—	2	1	no	—
664	C₂×#41	—	2	1	no	—
665	C₂×#41	—	2	1	no	—
666	C₂×#41	C₂³×C₇	1	1	yes	characteristic
667	C₂×#41	C₂³×C₇	1	1	yes	characteristic
668	C₂×#41	C₂³×C₇	1	2	yes	—
669	C₂×#41	C₂³×C₇	1	2	yes	—
670	#135	—	2	4	no	—
671	#135	—	2	8	no	—
672	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
673	C₂×Q₁₆	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	2	yes	—
677	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
680	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
681	C₂×D₈	C₂³×C₇	1	2	yes	—
682	C₂×M₁₆	C₂³×C₇	1	2	yes	—
683	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
684	C₂²×C₈	C₂³×C₇	1	2	yes	—
685	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
686	C₄⋊Q₈	—	2	1	no	—
687	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
688	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
689	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
690	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
691	#127	—	2	1	no	—
692	#127	—	2	2	no	—
693	#127	C₂³×C₇	1	1	yes	characteristic
694	#127	C₂³×C₇	1	2	yes	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	C₇×D₄	1	2	yes	—
700	#125	—	2	2	no	—
701	#125	—	2	2	no	—
702	#125	—	2	1	no	—
703	#125	—	2	1	no	—
704	#125	—	2	2	no	—
705	#125	—	2	2	no	—
706	#125	—	2	2	no	—
707	#125	—	2	1	no	—
708	#125	C₇×D₄	1	1	yes	characteristic
709	#125	C₂³×C₇	1	2	yes	—
710	#125	C₂³×C₇	1	2	yes	—
711	#124	—	2	1	no	—
712	#124	C₇×D₄	1	1	yes	characteristic
713	#123	—	2	2	no	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	C₇×D₄	1	2	yes	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
728	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
729	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
730	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
731	#121	—	2	1	no	—
732	#121	—	2	2	no	—
733	#121	—	2	2	no	—
734	#121	—	2	1	no	—
735	#121	—	2	1	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	—	2	2	no	—
739	#121	—	2	2	no	—
740	#121	—	2	2	no	—
741	#121	—	2	2	no	—
742	#121	C₇×D₄	1	1	yes	characteristic
743	#121	C₂³×C₇	1	2	yes	—
744	#121	C₂³×C₇	1	2	yes	—
745	#121	C₂³×C₇	1	2	yes	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
750	C₄×Q₈	C₂³×C₇	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	2	yes	—
754	C₄×Q₈	C₂³×C₇	1	2	yes	—
755	C₄×Q₈	C₂³×C₇	1	2	yes	—
756	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
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	1	no	—
762	C₄×D₄	—	2	1	no	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
773	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
774	C₄×D₄	C₂³×C₇	1	2	yes	—
775	C₄×D₄	C₂³×C₇	1	2	yes	—
776	C₄×D₄	C₂³×C₇	1	2	yes	—
777	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
778	C₄×D₄	C₂³×C₇	1	2	yes	—
779	#117	—	2	1	no	—
780	#117	—	2	2	no	—
781	#117	—	2	2	no	—
782	#117	—	2	2	no	—
783	#117	—	2	1	no	—
784	#117	—	2	1	no	—
785	#117	C₂³×C₇	1	1	yes	characteristic
786	#117	C₂³×C₇	1	1	yes	characteristic
787	#117	C₂³×C₇	1	2	yes	—
788	C₂×C₄⋊C₄	—	2	2	no	—
789	C₂×C₄⋊C₄	—	2	2	no	—
790	C₂×C₄⋊C₄	—	2	1	no	—
791	C₂×C₄⋊C₄	—	2	2	no	—
792	C₂×C₄⋊C₄	—	2	1	no	—
793	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
794	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
795	C₂×C₄²	—	2	1	no	—
796	C₂×C₄²	—	2	1	no	—
797	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
798	#107	C₂³×C₇	1	1	yes	characteristic
799	#107	C₂³×C₇	1	1	yes	characteristic
800	#107	C₂³×C₇	1	2	yes	—
801	#107	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	#106	C₂³×C₇	1	2	yes	—
806	#106	C₂³×C₇	1	1	yes	characteristic
807	#106	C₂³×C₇	1	2	yes	—
808	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
809	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
810	C₄⋊C₈	C₂³×C₇	1	2	yes	—
811	C₄⋊C₈	C₂³×C₇	1	2	yes	—
812	#103	C₂³×C₇	1	1	yes	characteristic
813	#103	C₂³×C₇	1	1	yes	characteristic
814	#103	C₂³×C₇	1	1	yes	characteristic
815	#103	C₂³×C₇	1	1	yes	characteristic
816	#103	C₂³×C₇	1	2	yes	—
817	#103	C₂³×C₇	1	2	yes	—
818	#103	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic
823	#102	C₂³×C₇	1	1	yes	characteristic
824	#102	C₂³×C₇	1	1	yes	characteristic
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	#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	#97	C₂³×C₇	1	2	yes	—
836	#97	C₂³×C₇	1	2	yes	—
837	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
838	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
839	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
840	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
841	C₄×C₈	C₂³×C₇	1	2	yes	—
842	C₂²×C₇	—	2	1	no	—
843	C₂²×C₇	—	2	2	no	—
844	C₂²×C₇	—	2	1	no	—
845	C₂²×C₇	—	2	2	no	—
846	C₂²×C₇	—	2	2	no	—
847	C₂²×C₇	—	2	1	no	—
848	C₂²×C₇	—	2	2	no	—
849	C₂²×C₇	—	4	1	no	—
850	C₂²×C₇	—	4	1	no	—
851	C₂²×C₇	—	4	1	no	—
852	C₂²×C₇	—	4	2	no	—
853	C₂²×C₇	—	4	1	no	—
854	C₂²×C₇	—	4	2	no	—
855	C₂²×C₇	—	4	1	no	—
856	C₂²×C₇	—	4	2	no	—
857	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
858	C₄×C₇	—	2	1	no	—
859	C₄×C₇	—	2	1	no	—
860	C₄×C₇	—	2	2	no	—
861	C₄×C₇	—	2	1	no	—
862	C₄×C₇	—	2	2	no	—
863	C₄×C₇	—	2	2	no	—
864	C₄×C₇	—	2	1	no	—
865	C₄×C₇	—	2	2	no	—
866	C₄×C₇	—	4	1	no	—
867	C₄×C₇	—	4	2	no	—
868	C₄×C₇	—	4	1	no	—
869	C₄×C₇	—	4	1	no	—
870	C₄×C₇	—	4	2	no	—
871	C₄×C₇	—	4	1	no	—
872	C₄×C₇	—	4	1	no	—
873	C₄×C₇	—	4	2	no	—
874	C₄×C₇	#577	1	2	yes	—
875	C₄×C₇	C₂²×#41	1	1	yes	characteristic
876	C₄×C₇	#585	1	1	yes	characteristic
877	#41	—	2	2	no	—
878	#41	—	2	4	no	—
879	#41	—	2	2	no	—
880	#41	—	2	4	no	—
881	#41	—	4	1	no	—
882	#41	—	4	1	no	—
883	#41	—	4	2	no	—
884	#41	—	4	2	no	—
885	#41	—	8	2	no	—
886	#41	—	8	2	no	—
887	#41	—	8	2	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
893	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
906	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
907	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
908	C₂×D₄	C₂⁴×C₇	1	2	yes	—
909	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
924	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
927	Q₁₆	—	2	2	no	—
928	Q₁₆	—	2	4	no	—
929	SD₁₆	—	2	2	no	—
930	SD₁₆	—	2	4	no	—
931	SD₁₆	—	4	2	no	—
932	SD₁₆	—	4	2	no	—
933	SD₁₆	—	4	2	no	—
934	SD₁₆	C₇×#41	1	4	yes	complemented
935	D₈	—	2	2	no	—
936	D₈	—	2	4	no	—
937	M₁₆	—	4	2	no	—
938	C₂×C₈	—	2	2	no	—
939	C₂×C₈	—	2	4	no	—
940	C₂×C₈	—	4	1	no	—
941	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
943	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₇	1	2	yes	—
945	C₂×C₈	C₂⁴×C₇	1	2	yes	—
946	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	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	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
970	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
971	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
972	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
973	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
974	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	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	C₂×C₇×D₄	1	2	yes	—
997	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
998	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
999	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1000	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1011	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1012	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₇	1	2	yes	—
1015	C₂×C₇	—	4	1	no	—
1016	C₂×C₇	—	4	2	no	—
1017	C₂×C₇	—	4	2	no	—
1018	C₂×C₇	—	8	1	no	—
1019	C₂×C₇	—	8	2	no	—
1020	C₂×C₇	D₄×#41	1	1	yes	characteristic
1021	C₂×C₇	C₂×#577	1	1	yes	characteristic
1022	C₂×C₇	#3584	1	1	yes	characteristic
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	2	no	—
1026	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1027	C₂³	C₂²×C₇×D₄	1	2	yes	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	2	2	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	1	no	—
1036	Q₈	C₂×C₇×#41	1	2	yes	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	4	2	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	4	4	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	8	1	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	2	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	C₂×C₇×#41	1	2	yes	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	4	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	4	4	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	8	1	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1085	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1086	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1087	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1088	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1089	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1090	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1091	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1092	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1093	C₈	—	2	1	no	—
1094	C₈	—	2	2	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	1	no	—
1097	C₈	—	2	2	no	—
1098	C₈	C₂×C₇×#41	1	2	yes	—
1099	C₇	#61476	1	1	yes	characteristic, direct product factor, Sylow
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	C₇×#577	1	2	yes	—
1133	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1134	C₄	C₇×#585	1	1	yes	characteristic
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	8	2	no	—
1140	C₂	C₇×D₄×#41	1	1	yes	characteristic
1141	C₂	C₂×C₇×#577	1	1	yes	characteristic
1142	C₂	C₇×#3584	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3517	C₂	semidirect
2. C₇×#3515	C₂	semidirect
3. C₇×#3392	C₂	semidirect
4. C₇×#3381	C₂	semidirect
5. C₇×#3374	C₂	semidirect
6. C₇×#3366	C₂	semidirect
7. C₇×#3337	C₂	semidirect
8. C₇×#3335	C₂	semidirect
9. C₇×#3333	C₂	semidirect
10. C₇×#3330	C₂	semidirect
11. C₇×#3317	C₂	semidirect
12. C₇×#3307	C₂	semidirect
13. C₇×#3284	C₂	semidirect
14. C₇×#3284	C₂	semidirect
15. C₇×#3174	C₂	semidirect
16. C₇×#3167	C₂	semidirect
17. C₇×#3120	C₂	semidirect
18. C₇×#3119	C₂	semidirect
19. C₇×#3116	C₂	semidirect
20. C₇×#3115	C₂	semidirect
21. C₇×#2966	C₂	semidirect
22. C₇×#2952	C₂	semidirect
23. C₄×C₇×#135	C₂	semidirect
135. #61476	C₇	direct (N × H)
315. #3517	C₂×C₇	semidirect
316. #3515	C₂×C₇	semidirect
317. #3392	C₂×C₇	semidirect
318. #3381	C₂×C₇	semidirect
319. #3374	C₂×C₇	semidirect
320. #3366	C₂×C₇	semidirect
321. #3337	C₂×C₇	semidirect
322. #3335	C₂×C₇	semidirect
323. #3333	C₂×C₇	semidirect
324. #3330	C₂×C₇	semidirect
325. #3317	C₂×C₇	semidirect
326. #3307	C₂×C₇	semidirect
327. #3284	C₂×C₇	semidirect
328. #3284	C₂×C₇	semidirect
329. #3174	C₂×C₇	semidirect
330. #3167	C₂×C₇	semidirect
331. #3120	C₂×C₇	semidirect
332. #3119	C₂×C₇	semidirect
333. #3116	C₂×C₇	semidirect
334. #3115	C₂×C₇	semidirect
335. #2966	C₂×C₇	semidirect
336. #2952	C₂×C₇	semidirect
337. C₄×#135	C₂×C₇	semidirect
395. C₇×SD₁₆	#41	semidirect
934. SD₁₆	C₇×#41	semidirect
1099. C₇	#61476	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×#3517	2
C₇×#3515	2
C₇×#3392	2
C₇×#3381	2
C₇×#3374	2
C₇×#3366	2
C₇×#3337	2
C₇×#3335	2
C₇×#3333	2
C₇×#3330	2
C₇×#3317	2
C₇×#3307	2
C₇×#3284	2
C₇×#3174	2
C₇×#3167	2
C₇×#3120	2
C₇×#3119	2
C₇×#3116	2
C₇×#3115	2
C₇×#2966	2
C₇×#2952	2
C₄×C₇×#135	2
#61476	7

Subgroups — C7×#61476 #13238692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61476 #13238692