Subgroups — C₇×#61316 #13238532

Order 1792.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×Q₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3377	C₂	1	2	yes	maximal, complemented
4	C₇×#3376	C₂	1	2	yes	maximal, complemented
5	C₇×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3374	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3373	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3372	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3371	C₂	1	2	yes	maximal, complemented
10	C₇×#3370	C₂	1	2	yes	maximal, complemented
11	C₇×#3369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3368	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3367	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3366	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3135	C₂	1	2	yes	maximal, complemented
16	C₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3076	C₂	1	2	yes	maximal, complemented
19	C₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3035	C₂	1	2	yes	maximal, complemented
21	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2943	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×#559	C₂²	1	2	yes	—
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×#557	C₂²	1	1	yes	characteristic
31	C₇×#557	C₂²	1	2	yes	—
32	C₇×#556	C₂²	1	1	yes	characteristic
33	C₇×#556	C₂²	1	2	yes	—
34	C₇×#554	—	2	1	no	—
35	C₇×#554	—	2	2	no	—
36	C₇×#554	C₂²	1	1	yes	characteristic
37	C₇×#554	C₂²	1	2	yes	—
38	C₇×#553	—	2	1	no	—
39	C₇×#553	—	2	2	no	—
40	C₇×#550	C₂²	1	1	yes	characteristic
41	C₇×D₄×Q₈	—	2	1	no	—
42	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
43	C₇×#548	—	2	1	no	—
44	C₇×#533	—	2	1	no	—
45	C₇×#533	—	2	2	no	—
46	C₇×#533	C₂²	1	1	yes	characteristic
47	C₇×#533	C₂²	1	2	yes	—
48	C₇×#532	C₂²	1	1	yes	characteristic
49	C₇×#532	C₂²	1	2	yes	—
50	C₇×#529	—	2	1	no	—
51	C₇×#529	—	2	2	no	—
52	C₄×C₇×#41	—	2	1	no	—
53	C₄×C₇×#41	C₂²	1	1	yes	characteristic
54	C₄×C₇×#41	C₂²	1	1	yes	characteristic
55	C₄×C₇×#41	C₂²	1	2	yes	—
56	C₄×C₇×#41	C₂²	1	2	yes	—
57	C₂×C₄×C₇×Q₈	—	2	1	no	—
58	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
59	C₇×#491	C₂²	1	2	yes	—
60	C₇×#491	C₂²	1	2	yes	—
61	C₇×#490	C₂²	1	2	yes	—
62	C₇×#490	C₂²	1	2	yes	—
63	C₇×#489	C₂²	1	2	yes	—
64	C₇×#489	C₂²	1	2	yes	—
65	C₇×#489	C₂²	1	2	yes	—
66	C₇×#489	C₂²	1	2	yes	—
67	C₇×#488	C₂²	1	2	yes	—
68	C₇×#488	C₂²	1	2	yes	—
69	C₇×#487	C₂²	1	1	yes	characteristic
70	C₇×#487	C₂²	1	1	yes	characteristic
71	C₇×#486	C₂²	1	1	yes	characteristic
72	C₇×#486	C₂²	1	1	yes	characteristic
73	C₇×#479	C₂²	1	2	yes	—
74	C₇×#479	C₂²	1	2	yes	—
75	C₇×#479	C₂²	1	2	yes	—
76	C₇×#478	C₂²	1	2	yes	—
77	C₇×#478	C₂²	1	2	yes	—
78	C₇×#478	C₂²	1	2	yes	—
79	C₇×#477	C₂²	1	2	yes	—
80	C₇×#477	C₂²	1	1	yes	characteristic
81	C₇×#476	C₂²	1	1	yes	characteristic
82	C₇×#476	C₂²	1	2	yes	—
83	C₇×#475	C₂²	1	2	yes	—
84	C₇×#475	C₂²	1	1	yes	characteristic
85	C₇×#474	C₂²	1	1	yes	characteristic
86	C₇×#474	C₂²	1	2	yes	—
87	C₇×#464	C₂²	1	2	yes	—
88	C₇×#464	C₂²	1	2	yes	—
89	C₇×#464	C₂²	1	2	yes	—
90	C₇×#463	C₂²	1	2	yes	—
91	C₇×#463	C₂²	1	2	yes	—
92	C₇×#463	C₂²	1	2	yes	—
93	C₇×#462	C₂²	1	1	yes	characteristic
94	C₇×#462	C₂²	1	2	yes	—
95	C₇×#461	C₂²	1	1	yes	characteristic
96	C₇×#461	C₂²	1	2	yes	—
97	C₇×#460	C₂²	1	2	yes	—
98	C₇×#460	C₂²	1	1	yes	characteristic
99	C₇×#459	C₂²	1	2	yes	—
100	C₇×#459	C₂²	1	1	yes	characteristic
101	C₇×#446	C₂²	1	1	yes	characteristic
102	C₇×#446	C₂²	1	1	yes	characteristic
103	C₇×#446	C₂²	1	1	yes	characteristic
104	C₇×#446	C₂²	1	1	yes	characteristic
105	C₇×#446	C₂²	1	2	yes	—
106	C₇×#446	C₂²	1	2	yes	—
107	C₇×#442	C₂²	1	2	yes	—
108	C₇×#442	C₂²	1	2	yes	—
109	C₇×#441	C₂²	1	2	yes	—
110	C₇×#441	C₂²	1	2	yes	—
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	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
116	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
117	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
118	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
121	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
122	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
123	C₇×#427	C₂²	1	1	yes	characteristic
124	C₇×#427	C₂²	1	2	yes	—
125	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
127	C₇×#416	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	1	yes	characteristic
129	C₇×#416	C₂²	1	2	yes	—
130	C₇×#416	C₂²	1	2	yes	—
131	C₇×#416	C₂²	1	2	yes	—
132	C₇×#416	C₂²	1	2	yes	—
133	C₂×C₇×#97	C₂²	1	2	yes	—
134	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
135	#61316	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	C₂³	1	1	yes	characteristic
138	C₂×C₇×#41	C₂³	1	2	yes	—
139	C₂×C₇×#41	C₂³	1	1	yes	characteristic
140	C₂²×C₇×Q₈	—	2	1	no	—
141	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
142	C₇×#135	—	2	4	no	—
143	C₇×#135	—	2	8	no	—
144	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
146	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
151	C₂×C₇×D₈	C₂³	1	2	yes	—
152	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
154	C₂²×C₇×C₈	C₂³	1	2	yes	—
155	C₇×C₄⋊Q₈	—	2	1	no	—
156	C₇×C₄⋊Q₈	—	2	2	no	—
157	C₇×C₄⋊Q₈	—	2	1	no	—
158	C₇×C₄⋊Q₈	—	2	2	no	—
159	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₇×#127	C₂³	1	1	yes	characteristic
166	C₇×#127	C₂³	1	2	yes	—
167	C₇×#126	—	2	2	no	—
168	C₇×#126	—	2	2	no	—
169	C₇×#126	—	2	2	no	—
170	C₇×#125	—	2	1	no	—
171	C₇×#125	—	2	2	no	—
172	C₇×#125	—	2	2	no	—
173	C₇×#125	—	2	2	no	—
174	C₇×#125	—	2	2	no	—
175	C₇×#125	C₂³	1	2	yes	—
176	C₇×#125	C₂³	1	2	yes	—
177	C₇×#125	C₂³	1	2	yes	—
178	C₇×#124	—	2	1	no	—
179	C₇×#124	—	2	2	no	—
180	C₇×#124	C₂³	1	2	yes	—
181	C₇×#124	C₂³	1	2	yes	—
182	C₇×#124	C₂³	1	2	yes	—
183	C₇×#123	—	2	2	no	—
184	C₇×#123	—	2	2	no	—
185	C₇×#123	—	2	2	no	—
186	C₇×C₂²⋊Q₈	—	2	1	no	—
187	C₇×C₂²⋊Q₈	—	2	2	no	—
188	C₇×C₂²⋊Q₈	—	2	1	no	—
189	C₇×C₂²⋊Q₈	—	2	2	no	—
190	C₇×C₂²⋊Q₈	—	2	1	no	—
191	C₇×C₂²⋊Q₈	—	2	2	no	—
192	C₇×C₂²⋊Q₈	—	2	1	no	—
193	C₇×C₂²⋊Q₈	—	2	2	no	—
194	C₇×C₂²⋊Q₈	—	2	1	no	—
195	C₇×C₂²⋊Q₈	—	2	2	no	—
196	C₇×C₂²⋊Q₈	—	2	2	no	—
197	C₇×C₂²⋊Q₈	—	2	2	no	—
198	C₇×C₂²⋊Q₈	—	2	2	no	—
199	C₇×#121	—	2	1	no	—
200	C₇×#121	—	2	2	no	—
201	C₇×#121	—	2	1	no	—
202	C₇×#121	—	2	2	no	—
203	C₇×#121	—	2	1	no	—
204	C₇×#121	—	2	2	no	—
205	C₄×C₇×Q₈	—	2	1	no	—
206	C₄×C₇×Q₈	—	2	1	no	—
207	C₄×C₇×Q₈	—	2	1	no	—
208	C₄×C₇×Q₈	—	2	2	no	—
209	C₄×C₇×Q₈	—	2	1	no	—
210	C₄×C₇×Q₈	—	2	2	no	—
211	C₄×C₇×Q₈	—	2	2	no	—
212	C₄×C₇×Q₈	—	2	1	no	—
213	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
214	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
215	C₄×C₇×Q₈	D₄	1	2	yes	—
216	C₄×C₇×Q₈	C₂³	1	2	yes	—
217	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
218	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
219	C₄×C₇×Q₈	C₂³	1	2	yes	—
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	2	yes	—
224	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
225	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
226	C₄×C₇×Q₈	C₂³	1	2	yes	—
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	1	no	—
232	C₄×C₇×D₄	—	2	2	no	—
233	C₄×C₇×D₄	—	2	1	no	—
234	C₄×C₇×D₄	—	2	2	no	—
235	C₄×C₇×D₄	—	2	2	no	—
236	C₄×C₇×D₄	—	2	1	no	—
237	C₄×C₇×D₄	—	2	1	no	—
238	C₄×C₇×D₄	—	2	2	no	—
239	C₄×C₇×D₄	—	2	2	no	—
240	C₄×C₇×D₄	—	2	1	no	—
241	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
242	C₄×C₇×D₄	C₂³	1	2	yes	—
243	C₄×C₇×D₄	C₂³	1	2	yes	—
244	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
245	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
246	C₄×C₇×D₄	C₂³	1	2	yes	—
247	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
248	C₄×C₇×D₄	C₂³	1	2	yes	—
249	C₇×#117	—	2	2	no	—
250	C₇×#117	—	2	1	no	—
251	C₇×#117	—	2	2	no	—
252	C₇×#117	—	2	1	no	—
253	C₇×#117	—	2	2	no	—
254	C₇×#117	—	2	1	no	—
255	C₇×#117	C₂³	1	1	yes	characteristic
256	C₇×#117	C₂³	1	1	yes	characteristic
257	C₇×#117	C₂³	1	2	yes	—
258	C₂×C₇×C₄⋊C₄	—	2	1	no	—
259	C₂×C₇×C₄⋊C₄	—	2	2	no	—
260	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
261	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
262	C₂×C₄²×C₇	—	2	1	no	—
263	C₂×C₄²×C₇	—	2	2	no	—
264	C₂×C₄²×C₇	—	2	1	no	—
265	C₂×C₄²×C₇	—	2	2	no	—
266	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
267	C₂×C₄²×C₇	C₂³	1	2	yes	—
268	C₇×#107	C₂³	1	1	yes	characteristic
269	C₇×#107	C₂³	1	2	yes	—
270	C₇×#107	C₂³	1	2	yes	—
271	C₇×#107	C₂³	1	1	yes	characteristic
272	C₇×#106	C₂³	1	1	yes	characteristic
273	C₇×#106	C₂³	1	2	yes	—
274	C₇×#106	C₂³	1	2	yes	—
275	C₇×#106	C₂³	1	1	yes	characteristic
276	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₇×C₄⋊C₈	C₂³	1	2	yes	—
278	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₇×C₄⋊C₈	C₂³	1	2	yes	—
280	C₇×C₄⋊C₈	C₂³	1	2	yes	—
281	C₇×C₄⋊C₈	C₂³	1	2	yes	—
282	C₇×C₄⋊C₈	C₂³	1	2	yes	—
283	C₇×#103	C₂³	1	2	yes	—
284	C₇×#103	C₂³	1	2	yes	—
285	C₇×#103	C₂³	1	2	yes	—
286	C₇×#103	C₂³	1	2	yes	—
287	C₇×#103	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
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×#103	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	1	yes	characteristic
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×#97	C₂³	1	2	yes	—
308	C₇×#97	C₂³	1	2	yes	—
309	C₇×#97	C₂³	1	2	yes	—
310	C₇×#97	C₂³	1	2	yes	—
311	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	#3480	C₂×C₇	1	1	yes	characteristic, complemented
316	Q₈×#41	C₂×C₇	1	1	yes	characteristic, complemented
317	#3377	C₂×C₇	1	2	yes	complemented
318	#3376	C₂×C₇	1	2	yes	complemented
319	#3375	C₂×C₇	1	1	yes	characteristic, complemented
320	#3374	C₂×C₇	1	1	yes	characteristic, complemented
321	#3373	C₂×C₇	1	1	yes	characteristic, complemented
322	#3372	C₂×C₇	1	1	yes	characteristic, complemented
323	#3371	C₂×C₇	1	2	yes	complemented
324	#3370	C₂×C₇	1	2	yes	complemented
325	#3369	C₂×C₇	1	1	yes	characteristic, complemented
326	#3368	C₂×C₇	1	1	yes	characteristic, complemented
327	#3367	C₂×C₇	1	1	yes	characteristic, complemented
328	#3366	C₂×C₇	1	1	yes	characteristic, complemented
329	#3135	C₂×C₇	1	2	yes	complemented
330	#3131	C₂×C₇	1	1	yes	characteristic, complemented
331	#3076	C₂×C₇	1	1	yes	characteristic, complemented
332	#3076	C₂×C₇	1	2	yes	complemented
333	#3035	C₂×C₇	1	1	yes	characteristic, complemented
334	#3035	C₂×C₇	1	2	yes	complemented
335	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
336	#2943	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	2	no	—
340	C₇×#41	—	2	4	no	—
341	C₇×#41	—	2	2	no	—
342	C₇×#41	—	2	4	no	—
343	C₇×#41	—	4	4	no	—
344	C₇×#41	#41	1	4	yes	complemented
345	C₂×C₇×Q₈	—	2	2	no	—
346	C₂×C₇×Q₈	—	2	1	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	—	2	1	no	—
349	C₂×C₇×Q₈	—	4	2	no	—
350	C₂×C₇×Q₈	—	4	4	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	C₂×D₄	1	2	yes	—
354	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
355	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
356	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
357	C₂×C₇×D₄	—	2	1	no	—
358	C₂×C₇×D₄	—	2	1	no	—
359	C₂×C₇×D₄	—	2	2	no	—
360	C₂×C₇×D₄	—	2	2	no	—
361	C₂×C₇×D₄	—	2	1	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	—	2	1	no	—
364	C₂×C₇×D₄	C₂⁴	1	2	yes	—
365	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
366	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₇	—	2	1	no	—
368	C₂²×C₄×C₇	—	2	2	no	—
369	C₂²×C₄×C₇	—	2	1	no	—
370	C₂²×C₄×C₇	—	2	2	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	1	no	—
375	C₂²×C₄×C₇	—	2	2	no	—
376	C₂²×C₄×C₇	—	2	1	no	—
377	C₂²×C₄×C₇	—	2	2	no	—
378	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
381	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
382	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
383	C₇×Q₁₆	—	2	2	no	—
384	C₇×Q₁₆	—	2	4	no	—
385	C₇×SD₁₆	—	2	2	no	—
386	C₇×SD₁₆	—	2	4	no	—
387	C₇×SD₁₆	—	2	2	no	—
388	C₇×SD₁₆	—	2	4	no	—
389	C₇×D₈	—	2	2	no	—
390	C₇×D₈	—	2	4	no	—
391	C₂×C₇×C₈	—	2	2	no	—
392	C₂×C₇×C₈	—	2	4	no	—
393	C₂×C₇×C₈	—	2	2	no	—
394	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
395	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
396	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
397	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
398	C₂×C₇×C₈	C₂⁴	1	2	yes	—
399	C₂×C₇×C₈	C₂⁴	1	2	yes	—
400	C₇×C₄⋊C₄	—	2	2	no	—
401	C₇×C₄⋊C₄	—	2	2	no	—
402	C₇×C₄⋊C₄	—	2	2	no	—
403	C₇×C₄⋊C₄	—	2	2	no	—
404	C₇×C₄⋊C₄	—	2	1	no	—
405	C₇×C₄⋊C₄	—	2	2	no	—
406	C₇×C₄⋊C₄	—	2	1	no	—
407	C₇×C₄⋊C₄	—	2	2	no	—
408	C₇×C₄⋊C₄	—	2	1	no	—
409	C₇×C₄⋊C₄	—	2	2	no	—
410	C₇×C₄⋊C₄	—	2	1	no	—
411	C₇×C₄⋊C₄	—	2	2	no	—
412	C₇×C₄⋊C₄	—	2	2	no	—
413	C₇×C₄⋊C₄	—	2	1	no	—
414	C₇×C₄⋊C₄	—	2	1	no	—
415	C₇×C₄⋊C₄	—	2	2	no	—
416	C₇×C₄⋊C₄	—	2	1	no	—
417	C₇×C₄⋊C₄	—	2	2	no	—
418	C₇×C₄⋊C₄	—	2	1	no	—
419	C₇×C₄⋊C₄	—	2	2	no	—
420	C₇×C₄⋊C₄	—	2	2	no	—
421	C₇×C₄⋊C₄	—	2	2	no	—
422	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
423	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
424	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
425	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
426	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
427	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
428	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
429	C₇×C₄⋊C₄	C₂⁴	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	1	yes	characteristic
434	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
435	C₇×C₂²⋊C₄	—	2	1	no	—
436	C₇×C₂²⋊C₄	—	2	1	no	—
437	C₇×C₂²⋊C₄	—	2	2	no	—
438	C₇×C₂²⋊C₄	—	2	2	no	—
439	C₇×C₂²⋊C₄	—	2	2	no	—
440	C₇×C₂²⋊C₄	—	2	2	no	—
441	C₇×C₂²⋊C₄	—	2	2	no	—
442	C₇×C₂²⋊C₄	—	2	1	no	—
443	C₇×C₂²⋊C₄	—	2	2	no	—
444	C₇×C₂²⋊C₄	—	2	2	no	—
445	C₇×C₂²⋊C₄	—	2	1	no	—
446	C₇×C₂²⋊C₄	—	2	1	no	—
447	C₇×C₂²⋊C₄	—	2	2	no	—
448	C₇×C₂²⋊C₄	—	2	1	no	—
449	C₇×C₂²⋊C₄	—	2	2	no	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₄²×C₇	—	2	1	no	—
453	C₄²×C₇	—	2	2	no	—
454	C₄²×C₇	—	2	2	no	—
455	C₄²×C₇	—	2	1	no	—
456	C₄²×C₇	—	2	1	no	—
457	C₄²×C₇	—	2	2	no	—
458	C₄²×C₇	—	2	2	no	—
459	C₄²×C₇	—	2	1	no	—
460	C₄²×C₇	—	2	1	no	—
461	C₄²×C₇	—	2	1	no	—
462	C₄²×C₇	—	2	2	no	—
463	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
464	C₄²×C₇	C₂×D₄	1	2	yes	—
465	C₄²×C₇	C₂×D₄	1	2	yes	—
466	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
467	C₄²×C₇	C₂⁴	1	1	yes	characteristic
468	C₄²×C₇	C₂⁴	1	1	yes	characteristic
469	C₄²×C₇	C₂⁴	1	2	yes	—
470	C₄²×C₇	C₂⁴	1	2	yes	—
471	C₂×#135	C₂²×C₇	1	1	yes	characteristic
472	C₂×#135	C₂²×C₇	1	2	yes	—
473	#559	C₂²×C₇	1	2	yes	—
474	#559	C₂²×C₇	1	1	yes	characteristic
475	Q₈²	C₂²×C₇	1	1	yes	characteristic
476	#557	C₂²×C₇	1	1	yes	characteristic
477	#557	C₂²×C₇	1	1	yes	characteristic
478	#557	C₂²×C₇	1	2	yes	—
479	#556	C₂²×C₇	1	1	yes	characteristic
480	#556	C₂²×C₇	1	2	yes	—
481	#554	—	2	1	no	—
482	#554	—	2	2	no	—
483	#554	C₂²×C₇	1	1	yes	characteristic
484	#554	C₂²×C₇	1	2	yes	—
485	#553	—	2	1	no	—
486	#553	—	2	2	no	—
487	#550	C₂²×C₇	1	1	yes	characteristic
488	D₄×Q₈	—	2	1	no	—
489	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
490	#548	—	2	1	no	—
491	#533	—	2	1	no	—
492	#533	—	2	2	no	—
493	#533	C₂²×C₇	1	1	yes	characteristic
494	#533	C₂²×C₇	1	2	yes	—
495	#532	C₂²×C₇	1	1	yes	characteristic
496	#532	C₂²×C₇	1	2	yes	—
497	#529	—	2	1	no	—
498	#529	—	2	2	no	—
499	C₄×#41	—	2	1	no	—
500	C₄×#41	C₂²×C₇	1	1	yes	characteristic
501	C₄×#41	C₂²×C₇	1	2	yes	—
502	C₄×#41	C₂²×C₇	1	1	yes	characteristic
503	C₄×#41	C₂²×C₇	1	2	yes	—
504	C₂×C₄×Q₈	—	2	1	no	—
505	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
506	#491	C₂²×C₇	1	2	yes	—
507	#491	C₂²×C₇	1	2	yes	—
508	#490	C₂²×C₇	1	2	yes	—
509	#490	C₂²×C₇	1	2	yes	—
510	#489	C₂²×C₇	1	2	yes	—
511	#489	C₂²×C₇	1	2	yes	—
512	#489	C₂²×C₇	1	2	yes	—
513	#489	C₂²×C₇	1	2	yes	—
514	#488	C₂²×C₇	1	2	yes	—
515	#488	C₂²×C₇	1	2	yes	—
516	#487	C₂²×C₇	1	1	yes	characteristic
517	#487	C₂²×C₇	1	1	yes	characteristic
518	#486	C₂²×C₇	1	1	yes	characteristic
519	#486	C₂²×C₇	1	1	yes	characteristic
520	#479	C₂²×C₇	1	2	yes	—
521	#479	C₂²×C₇	1	2	yes	—
522	#479	C₂²×C₇	1	2	yes	—
523	#478	C₂²×C₇	1	2	yes	—
524	#478	C₂²×C₇	1	2	yes	—
525	#478	C₂²×C₇	1	2	yes	—
526	#477	C₂²×C₇	1	2	yes	—
527	#477	C₂²×C₇	1	1	yes	characteristic
528	#476	C₂²×C₇	1	1	yes	characteristic
529	#476	C₂²×C₇	1	2	yes	—
530	#475	C₂²×C₇	1	2	yes	—
531	#475	C₂²×C₇	1	1	yes	characteristic
532	#474	C₂²×C₇	1	1	yes	characteristic
533	#474	C₂²×C₇	1	2	yes	—
534	#464	C₂²×C₇	1	2	yes	—
535	#464	C₂²×C₇	1	2	yes	—
536	#464	C₂²×C₇	1	2	yes	—
537	#463	C₂²×C₇	1	2	yes	—
538	#463	C₂²×C₇	1	2	yes	—
539	#463	C₂²×C₇	1	2	yes	—
540	#462	C₂²×C₇	1	1	yes	characteristic
541	#462	C₂²×C₇	1	2	yes	—
542	#461	C₂²×C₇	1	1	yes	characteristic
543	#461	C₂²×C₇	1	2	yes	—
544	#460	C₂²×C₇	1	2	yes	—
545	#460	C₂²×C₇	1	1	yes	characteristic
546	#459	C₂²×C₇	1	2	yes	—
547	#459	C₂²×C₇	1	1	yes	characteristic
548	#446	C₂²×C₇	1	1	yes	characteristic
549	#446	C₂²×C₇	1	1	yes	characteristic
550	#446	C₂²×C₇	1	1	yes	characteristic
551	#446	C₂²×C₇	1	1	yes	characteristic
552	#446	C₂²×C₇	1	2	yes	—
553	#446	C₂²×C₇	1	2	yes	—
554	#442	C₂²×C₇	1	2	yes	—
555	#442	C₂²×C₇	1	2	yes	—
556	#441	C₂²×C₇	1	2	yes	—
557	#441	C₂²×C₇	1	2	yes	—
558	#440	C₂²×C₇	1	2	yes	—
559	#440	C₂²×C₇	1	2	yes	—
560	#440	C₂²×C₇	1	2	yes	—
561	#440	C₂²×C₇	1	2	yes	—
562	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
563	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
564	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
565	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
566	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
567	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
568	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
569	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
570	#427	C₂²×C₇	1	1	yes	characteristic
571	#427	C₂²×C₇	1	2	yes	—
572	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
573	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
574	#416	C₂²×C₇	1	2	yes	—
575	#416	C₂²×C₇	1	2	yes	—
576	#416	C₂²×C₇	1	2	yes	—
577	#416	C₂²×C₇	1	2	yes	—
578	#416	C₂²×C₇	1	1	yes	characteristic
579	#416	C₂²×C₇	1	1	yes	characteristic
580	C₂×#97	C₂²×C₇	1	2	yes	—
581	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
582	C₂³×C₇	—	2	1	no	—
583	C₂³×C₇	—	2	2	no	—
584	C₂³×C₇	—	2	1	no	—
585	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
586	C₇×Q₈	—	2	2	no	—
587	C₇×Q₈	—	2	2	no	—
588	C₇×Q₈	—	2	1	no	—
589	C₇×Q₈	—	2	1	no	—
590	C₇×Q₈	—	2	2	no	—
591	C₇×Q₈	—	2	2	no	—
592	C₇×Q₈	—	2	1	no	—
593	C₇×Q₈	—	4	2	no	—
594	C₇×Q₈	—	4	4	no	—
595	C₇×Q₈	—	4	2	no	—
596	C₇×Q₈	—	8	2	no	—
597	C₇×Q₈	—	8	1	no	—
598	C₇×Q₈	C₂×#41	1	2	yes	—
599	C₇×D₄	—	2	4	no	—
600	C₇×D₄	—	2	1	no	—
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	—	4	4	no	—
606	C₇×D₄	—	4	2	no	—
607	C₇×D₄	—	4	4	no	—
608	C₇×D₄	—	4	2	no	—
609	C₇×D₄	—	8	2	no	—
610	C₇×D₄	—	8	1	no	—
611	C₇×D₄	C₂×#41	1	2	yes	—
612	C₂×C₄×C₇	—	2	1	no	—
613	C₂×C₄×C₇	—	2	4	no	—
614	C₂×C₄×C₇	—	2	2	no	—
615	C₂×C₄×C₇	—	2	1	no	—
616	C₂×C₄×C₇	—	2	1	no	—
617	C₂×C₄×C₇	—	2	1	no	—
618	C₂×C₄×C₇	—	2	2	no	—
619	C₂×C₄×C₇	—	2	2	no	—
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	—	4	1	no	—
624	C₂×C₄×C₇	—	4	2	no	—
625	C₂×C₄×C₇	—	4	2	no	—
626	C₂×C₄×C₇	—	4	4	no	—
627	C₂×C₄×C₇	—	4	4	no	—
628	C₂×C₄×C₇	—	4	2	no	—
629	C₂×C₄×C₇	—	4	4	no	—
630	C₂×C₄×C₇	—	4	2	no	—
631	C₂×C₄×C₇	—	4	2	no	—
632	C₂×C₄×C₇	—	8	1	no	—
633	C₂×C₄×C₇	—	8	1	no	—
634	C₂×C₄×C₇	—	8	2	no	—
635	C₂×C₄×C₇	—	8	2	no	—
636	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
637	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
638	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
639	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
640	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
641	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
642	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
643	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄×C₇	C₂×#41	1	2	yes	—
646	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
647	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
648	C₇×C₈	—	2	1	no	—
649	C₇×C₈	—	2	2	no	—
650	C₇×C₈	—	2	1	no	—
651	C₇×C₈	—	2	2	no	—
652	C₇×C₈	—	2	1	no	—
653	C₇×C₈	—	2	1	no	—
654	C₂×#41	—	2	1	no	—
655	C₂×#41	C₂³×C₇	1	1	yes	characteristic
656	C₂×#41	C₂³×C₇	1	2	yes	—
657	C₂×#41	C₂³×C₇	1	1	yes	characteristic
658	C₂²×Q₈	—	2	1	no	—
659	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
660	#135	—	2	4	no	—
661	#135	—	2	8	no	—
662	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
663	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
664	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
665	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
666	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
667	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
668	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
669	C₂×D₈	C₂³×C₇	1	2	yes	—
670	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
671	C₂²×C₈	C₂³×C₇	1	2	yes	—
672	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
673	C₄⋊Q₈	—	2	1	no	—
674	C₄⋊Q₈	—	2	2	no	—
675	C₄⋊Q₈	—	2	1	no	—
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
678	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
679	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
680	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
681	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
682	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
683	#127	C₂³×C₇	1	1	yes	characteristic
684	#127	C₂³×C₇	1	2	yes	—
685	#126	—	2	2	no	—
686	#126	—	2	2	no	—
687	#126	—	2	2	no	—
688	#125	—	2	1	no	—
689	#125	—	2	2	no	—
690	#125	—	2	2	no	—
691	#125	—	2	2	no	—
692	#125	—	2	2	no	—
693	#125	C₂³×C₇	1	2	yes	—
694	#125	C₂³×C₇	1	2	yes	—
695	#125	C₂³×C₇	1	2	yes	—
696	#124	—	2	1	no	—
697	#124	—	2	2	no	—
698	#124	C₂³×C₇	1	2	yes	—
699	#124	C₂³×C₇	1	2	yes	—
700	#124	C₂³×C₇	1	2	yes	—
701	#123	—	2	2	no	—
702	#123	—	2	2	no	—
703	#123	—	2	2	no	—
704	C₂²⋊Q₈	—	2	1	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	—	2	1	no	—
707	C₂²⋊Q₈	—	2	2	no	—
708	C₂²⋊Q₈	—	2	1	no	—
709	C₂²⋊Q₈	—	2	2	no	—
710	C₂²⋊Q₈	—	2	1	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	1	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	2	no	—
717	#121	—	2	1	no	—
718	#121	—	2	2	no	—
719	#121	—	2	1	no	—
720	#121	—	2	2	no	—
721	#121	—	2	1	no	—
722	#121	—	2	2	no	—
723	C₄×Q₈	—	2	1	no	—
724	C₄×Q₈	—	2	1	no	—
725	C₄×Q₈	—	2	1	no	—
726	C₄×Q₈	—	2	2	no	—
727	C₄×Q₈	—	2	1	no	—
728	C₄×Q₈	—	2	2	no	—
729	C₄×Q₈	—	2	2	no	—
730	C₄×Q₈	—	2	1	no	—
731	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
732	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
733	C₄×Q₈	C₇×D₄	1	2	yes	—
734	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
735	C₄×Q₈	C₂³×C₇	1	2	yes	—
736	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
737	C₄×Q₈	C₂³×C₇	1	2	yes	—
738	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
739	C₄×Q₈	C₂³×C₇	1	2	yes	—
740	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
741	C₄×Q₈	C₂³×C₇	1	2	yes	—
742	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
743	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
744	C₄×Q₈	C₂³×C₇	1	2	yes	—
745	C₄×D₄	—	2	1	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	1	no	—
748	C₄×D₄	—	2	2	no	—
749	C₄×D₄	—	2	1	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	1	no	—
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	1	no	—
755	C₄×D₄	—	2	1	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	1	no	—
759	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
760	C₄×D₄	C₂³×C₇	1	2	yes	—
761	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
762	C₄×D₄	C₂³×C₇	1	2	yes	—
763	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
764	C₄×D₄	C₂³×C₇	1	2	yes	—
765	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
766	C₄×D₄	C₂³×C₇	1	2	yes	—
767	#117	—	2	2	no	—
768	#117	—	2	1	no	—
769	#117	—	2	2	no	—
770	#117	—	2	1	no	—
771	#117	—	2	2	no	—
772	#117	—	2	1	no	—
773	#117	C₂³×C₇	1	1	yes	characteristic
774	#117	C₂³×C₇	1	1	yes	characteristic
775	#117	C₂³×C₇	1	2	yes	—
776	C₂×C₄⋊C₄	—	2	1	no	—
777	C₂×C₄⋊C₄	—	2	2	no	—
778	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
779	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
780	C₂×C₄²	—	2	1	no	—
781	C₂×C₄²	—	2	2	no	—
782	C₂×C₄²	—	2	1	no	—
783	C₂×C₄²	—	2	2	no	—
784	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
785	C₂×C₄²	C₂³×C₇	1	2	yes	—
786	#107	C₂³×C₇	1	1	yes	characteristic
787	#107	C₂³×C₇	1	1	yes	characteristic
788	#107	C₂³×C₇	1	2	yes	—
789	#107	C₂³×C₇	1	2	yes	—
790	#106	C₂³×C₇	1	1	yes	characteristic
791	#106	C₂³×C₇	1	1	yes	characteristic
792	#106	C₂³×C₇	1	2	yes	—
793	#106	C₂³×C₇	1	2	yes	—
794	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
795	C₄⋊C₈	C₂³×C₇	1	2	yes	—
796	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
797	C₄⋊C₈	C₂³×C₇	1	2	yes	—
798	C₄⋊C₈	C₂³×C₇	1	2	yes	—
799	C₄⋊C₈	C₂³×C₇	1	2	yes	—
800	C₄⋊C₈	C₂³×C₇	1	2	yes	—
801	#103	C₂³×C₇	1	1	yes	characteristic
802	#103	C₂³×C₇	1	1	yes	characteristic
803	#103	C₂³×C₇	1	1	yes	characteristic
804	#103	C₂³×C₇	1	1	yes	characteristic
805	#103	C₂³×C₇	1	2	yes	—
806	#103	C₂³×C₇	1	2	yes	—
807	#103	C₂³×C₇	1	2	yes	—
808	#103	C₂³×C₇	1	2	yes	—
809	#103	C₂³×C₇	1	2	yes	—
810	#103	C₂³×C₇	1	2	yes	—
811	#103	C₂³×C₇	1	2	yes	—
812	#103	C₂³×C₇	1	2	yes	—
813	#102	C₂³×C₇	1	1	yes	characteristic
814	#102	C₂³×C₇	1	1	yes	characteristic
815	#102	C₂³×C₇	1	1	yes	characteristic
816	#102	C₂³×C₇	1	1	yes	characteristic
817	#102	C₂³×C₇	1	2	yes	—
818	#102	C₂³×C₇	1	2	yes	—
819	#102	C₂³×C₇	1	2	yes	—
820	#102	C₂³×C₇	1	2	yes	—
821	#102	C₂³×C₇	1	2	yes	—
822	#102	C₂³×C₇	1	2	yes	—
823	#102	C₂³×C₇	1	2	yes	—
824	#102	C₂³×C₇	1	2	yes	—
825	#97	C₂³×C₇	1	2	yes	—
826	#97	C₂³×C₇	1	2	yes	—
827	#97	C₂³×C₇	1	2	yes	—
828	#97	C₂³×C₇	1	2	yes	—
829	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
830	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
831	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
832	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
833	C₂²×C₇	—	2	1	no	—
834	C₂²×C₇	—	2	1	no	—
835	C₂²×C₇	—	2	2	no	—
836	C₂²×C₇	—	4	1	no	—
837	C₂²×C₇	—	4	1	no	—
838	C₂²×C₇	—	4	1	no	—
839	C₂²×C₇	—	4	2	no	—
840	C₂²×C₇	—	4	2	no	—
841	C₂²×C₇	—	4	1	no	—
842	C₂²×C₇	—	4	2	no	—
843	C₂²×C₇	—	4	1	no	—
844	C₂²×C₇	#548	1	2	yes	—
845	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
846	C₄×C₇	—	2	1	no	—
847	C₄×C₇	—	2	2	no	—
848	C₄×C₇	—	2	2	no	—
849	C₄×C₇	—	2	1	no	—
850	C₄×C₇	—	2	2	no	—
851	C₄×C₇	—	2	1	no	—
852	C₄×C₇	—	2	2	no	—
853	C₄×C₇	—	2	2	no	—
854	C₄×C₇	—	4	1	no	—
855	C₄×C₇	—	4	1	no	—
856	C₄×C₇	—	4	2	no	—
857	C₄×C₇	—	4	1	no	—
858	C₄×C₇	—	4	2	no	—
859	C₄×C₇	—	4	1	no	—
860	C₄×C₇	—	4	2	no	—
861	C₄×C₇	—	4	1	no	—
862	C₄×C₇	#548	1	2	yes	—
863	C₄×C₇	#575	1	2	yes	—
864	C₄×C₇	C₂²×#41	1	1	yes	characteristic
865	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
866	#41	—	2	2	no	—
867	#41	—	2	2	no	—
868	#41	—	2	4	no	—
869	#41	—	2	2	no	—
870	#41	—	2	4	no	—
871	#41	—	4	4	no	—
872	#41	C₇×#41	1	4	yes	complemented
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	2	1	no	—
875	C₂×Q₈	—	2	2	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	4	2	no	—
878	C₂×Q₈	—	4	4	no	—
879	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
880	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
881	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
882	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
884	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
893	C₂×D₄	C₂⁴×C₇	1	2	yes	—
894	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
907	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
908	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
909	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
911	Q₁₆	—	2	2	no	—
912	Q₁₆	—	2	4	no	—
913	SD₁₆	—	2	2	no	—
914	SD₁₆	—	2	4	no	—
915	SD₁₆	—	2	2	no	—
916	SD₁₆	—	2	4	no	—
917	D₈	—	2	2	no	—
918	D₈	—	2	4	no	—
919	C₂×C₈	—	2	2	no	—
920	C₂×C₈	—	2	4	no	—
921	C₂×C₈	—	2	2	no	—
922	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
925	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
926	C₂×C₈	C₂⁴×C₇	1	2	yes	—
927	C₂×C₈	C₂⁴×C₇	1	2	yes	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
951	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
952	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
953	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
954	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
955	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
956	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
957	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
960	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	1	no	—
991	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
992	C₄²	C₂×C₇×D₄	1	2	yes	—
993	C₄²	C₂×C₇×D₄	1	2	yes	—
994	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
995	C₄²	C₂⁴×C₇	1	1	yes	characteristic
996	C₄²	C₂⁴×C₇	1	1	yes	characteristic
997	C₄²	C₂⁴×C₇	1	2	yes	—
998	C₄²	C₂⁴×C₇	1	2	yes	—
999	C₂×C₇	—	2	2	no	—
1000	C₂×C₇	—	4	2	no	—
1001	C₂×C₇	—	8	2	no	—
1002	C₂×C₇	—	8	1	no	—
1003	C₂×C₇	C₂×#548	1	1	yes	characteristic
1004	C₂×C₇	C₂×#575	1	1	yes	characteristic
1005	C₂×C₇	#3584	1	1	yes	characteristic
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1010	Q₈	—	2	1	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	2	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	2	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	2	no	—
1017	Q₈	—	4	2	no	—
1018	Q₈	—	4	4	no	—
1019	Q₈	—	4	2	no	—
1020	Q₈	—	8	2	no	—
1021	Q₈	—	8	1	no	—
1022	Q₈	C₂×C₇×#41	1	2	yes	—
1023	D₄	—	2	4	no	—
1024	D₄	—	2	1	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	2	2	no	—
1029	D₄	—	4	4	no	—
1030	D₄	—	4	2	no	—
1031	D₄	—	4	4	no	—
1032	D₄	—	4	2	no	—
1033	D₄	—	8	2	no	—
1034	D₄	—	8	1	no	—
1035	D₄	C₂×C₇×#41	1	2	yes	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	4	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	4	1	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	4	4	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	8	1	no	—
1057	C₂×C₄	—	8	1	no	—
1058	C₂×C₄	—	8	2	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1061	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1062	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1063	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1064	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1065	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1066	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1067	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1068	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1069	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1070	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1071	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1072	C₈	—	2	1	no	—
1073	C₈	—	2	2	no	—
1074	C₈	—	2	1	no	—
1075	C₈	—	2	2	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₇	#61316	1	1	yes	characteristic, direct product factor, Sylow
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	C₇×#548	1	2	yes	—
1091	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1092	C₄	—	2	1	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	C₇×#548	1	2	yes	—
1109	C₄	C₇×#575	1	2	yes	—
1110	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1111	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1112	C₂	—	2	2	no	—
1113	C₂	—	4	2	no	—
1114	C₂	—	8	2	no	—
1115	C₂	—	8	1	no	—
1116	C₂	C₂×C₇×#548	1	1	yes	characteristic
1117	C₂	C₂×C₇×#575	1	1	yes	characteristic
1118	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3480	C₂	semidirect
2. C₇×Q₈×#41	C₂	semidirect
3. C₇×#3377	C₂	semidirect
4. C₇×#3376	C₂	semidirect
5. C₇×#3375	C₂	semidirect
6. C₇×#3374	C₂	semidirect
7. C₇×#3373	C₂	semidirect
8. C₇×#3372	C₂	semidirect
9. C₇×#3371	C₂	semidirect
10. C₇×#3370	C₂	semidirect
11. C₇×#3369	C₂	semidirect
12. C₇×#3368	C₂	semidirect
13. C₇×#3367	C₂	semidirect
14. C₇×#3366	C₂	semidirect
15. C₇×#3135	C₂	semidirect
16. C₇×#3131	C₂	semidirect
17. C₇×#3076	C₂	semidirect
18. C₇×#3076	C₂	semidirect
19. C₇×#3035	C₂	semidirect
20. C₇×#3035	C₂	semidirect
21. C₂×C₇×#446	C₂	semidirect
22. C₇×#2943	C₂	semidirect
23. C₄×C₇×#135	C₂	semidirect
135. #61316	C₇	direct (N × H)
315. #3480	C₂×C₇	semidirect
316. Q₈×#41	C₂×C₇	semidirect
317. #3377	C₂×C₇	semidirect
318. #3376	C₂×C₇	semidirect
319. #3375	C₂×C₇	semidirect
320. #3374	C₂×C₇	semidirect
321. #3373	C₂×C₇	semidirect
322. #3372	C₂×C₇	semidirect
323. #3371	C₂×C₇	semidirect
324. #3370	C₂×C₇	semidirect
325. #3369	C₂×C₇	semidirect
326. #3368	C₂×C₇	semidirect
327. #3367	C₂×C₇	semidirect
328. #3366	C₂×C₇	semidirect
329. #3135	C₂×C₇	semidirect
330. #3131	C₂×C₇	semidirect
331. #3076	C₂×C₇	semidirect
332. #3076	C₂×C₇	semidirect
333. #3035	C₂×C₇	semidirect
334. #3035	C₂×C₇	semidirect
335. C₂×#446	C₂×C₇	semidirect
336. #2943	C₂×C₇	semidirect
337. C₄×#135	C₂×C₇	semidirect
344. C₇×#41	#41	semidirect
872. #41	C₇×#41	semidirect
1078. C₇	#61316	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×#3480	2
C₇×Q₈×#41	2
C₇×#3377	2
C₇×#3376	2
C₇×#3375	2
C₇×#3374	2
C₇×#3373	2
C₇×#3372	2
C₇×#3371	2
C₇×#3370	2
C₇×#3369	2
C₇×#3368	2
C₇×#3367	2
C₇×#3366	2
C₇×#3135	2
C₇×#3131	2
C₇×#3076	2
C₇×#3035	2
C₂×C₇×#446	2
C₇×#2943	2
C₄×C₇×#135	2
#61316	7

Subgroups — C7×#61316 #13238532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61316 #13238532