Subgroups — C₇×#62071 #13239287

Order 1792.

1844 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3311	C₂	1	2	yes	maximal, complemented
9	C₇×#3304	C₂	1	2	yes	maximal, complemented
10	C₇×#3303	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3282	C₂	1	2	yes	maximal, complemented
12	C₇×D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3271	C₂	1	2	yes	maximal, complemented
15	C₇×#3263	C₂	1	2	yes	maximal, complemented
16	C₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3224	C₂	1	2	yes	maximal, complemented
18	C₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3121	C₂	1	2	yes	maximal, complemented
20	C₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3043	C₂	1	2	yes	maximal, complemented
22	C₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	2	yes	complemented
25	C₂×C₇×#135	C₂²	1	2	yes	complemented
26	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
27	C₇×#560	—	2	2	no	—
28	C₇×Q₈²	C₂²	1	1	yes	characteristic, complemented
29	C₇×#556	—	2	2	no	—
30	C₇×#556	—	2	1	no	—
31	C₇×#556	C₂²	1	1	yes	characteristic
32	C₇×#556	C₂²	1	1	yes	characteristic, complemented
33	C₇×#556	C₂²	1	2	yes	complemented
34	C₇×#555	—	2	1	no	—
35	C₇×#555	C₂²	1	1	yes	characteristic
36	C₇×#553	—	2	1	no	—
37	C₇×#550	C₂²	1	2	yes	—
38	C₇×#550	C₂²	1	1	yes	characteristic
39	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
40	C₇×#548	C₂²	1	2	yes	complemented
41	C₇×#547	C₂²	1	1	yes	characteristic
42	C₇×#546	—	2	1	no	—
43	C₇×#546	C₂²	1	2	yes	—
44	C₇×D₄²	C₂²	1	1	yes	characteristic
45	C₇×#542	—	2	2	no	—
46	C₇×#542	C₂²	1	2	yes	—
47	C₇×#542	C₂²	1	2	yes	complemented
48	C₇×#538	—	2	2	no	—
49	C₇×#537	—	2	1	no	—
50	C₇×#535	—	2	1	no	—
51	C₇×#535	C₂²	1	2	yes	—
52	C₇×#533	—	2	1	no	—
53	C₇×#533	C₂²	1	1	yes	characteristic, complemented
54	C₇×#532	C₂²	1	1	yes	characteristic
55	C₇×#532	C₂²	1	1	yes	characteristic
56	C₇×#529	—	2	1	no	—
57	C₇×#529	C₂²	1	1	yes	characteristic
58	C₇×#519	C₂²	1	2	yes	complemented
59	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
60	C₇×#496	C₂²	1	2	yes	complemented
61	C₇×#495	C₂²	1	2	yes	—
62	C₇×#494	C₂²	1	1	yes	characteristic, complemented
63	C₇×#492	C₂²	1	1	yes	characteristic
64	C₇×#489	C₂²	1	2	yes	—
65	C₇×#487	C₂²	1	1	yes	characteristic, complemented
66	C₇×#486	C₂²	1	1	yes	characteristic
67	C₇×#486	C₂²	1	2	yes	complemented
68	C₇×#485	C₂²	1	2	yes	complemented
69	C₇×#482	C₂²	1	2	yes	—
70	C₇×#482	C₂²	1	1	yes	characteristic
71	C₇×#482	C₂²	1	1	yes	characteristic, complemented
72	C₇×#477	C₂²	1	1	yes	characteristic, complemented
73	C₇×#476	C₂²	1	1	yes	characteristic
74	C₇×#476	C₂²	1	1	yes	characteristic, complemented
75	C₇×#476	C₂²	1	1	yes	characteristic, complemented
76	C₇×#476	C₂²	1	2	yes	complemented
77	C₇×#475	C₂²	1	2	yes	complemented
78	C₇×#475	C₂²	1	2	yes	complemented
79	C₇×#470	C₂²	1	2	yes	complemented
80	C₇×#469	C₂²	1	2	yes	—
81	C₇×#465	C₂²	1	2	yes	—
82	C₇×#465	C₂²	1	2	yes	—
83	C₇×#465	C₂²	1	2	yes	complemented
84	C₇×#465	C₂²	1	2	yes	complemented
85	C₇×#464	C₂²	1	2	yes	—
86	C₇×#464	C₂²	1	2	yes	—
87	C₇×#464	C₂²	1	2	yes	complemented
88	C₇×#464	C₂²	1	2	yes	complemented
89	C₇×#464	C₂²	1	2	yes	complemented
90	C₇×#464	C₂²	1	2	yes	complemented
91	C₇×#463	C₂²	1	2	yes	complemented
92	C₇×#463	C₂²	1	2	yes	complemented
93	C₇×#462	C₂²	1	1	yes	characteristic, complemented
94	C₇×#461	C₂²	1	1	yes	characteristic
95	C₇×#461	C₂²	1	1	yes	characteristic, complemented
96	C₇×#461	C₂²	1	1	yes	characteristic, complemented
97	C₇×#460	C₂²	1	2	yes	—
98	C₇×#460	C₂²	1	1	yes	characteristic
99	C₇×#460	C₂²	1	1	yes	characteristic
100	C₇×#460	C₂²	1	2	yes	complemented
101	C₇×#460	C₂²	1	2	yes	complemented
102	C₇×#459	C₂²	1	1	yes	characteristic
103	C₇×#459	C₂²	1	1	yes	characteristic
104	C₇×#452	C₂²	1	2	yes	complemented
105	C₇×#452	C₂²	1	2	yes	complemented
106	C₇×#452	C₂²	1	2	yes	complemented
107	C₇×#451	C₂²	1	2	yes	complemented
108	C₇×#450	C₂²	1	2	yes	—
109	C₇×#449	C₂²	1	1	yes	characteristic
110	C₇×#449	C₂²	1	2	yes	complemented
111	C₇×#449	C₂²	1	1	yes	characteristic, complemented
112	C₇×#448	C₂²	1	2	yes	—
113	C₇×#447	C₂²	1	2	yes	—
114	C₇×#446	C₂²	1	1	yes	characteristic, complemented
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	C₇×#441	C₂²	1	2	yes	complemented
117	C₇×#440	C₂²	1	2	yes	complemented
118	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
119	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
122	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
123	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
124	C₇×#436	C₂²	1	1	yes	characteristic
125	C₇×#435	C₂²	1	2	yes	complemented
126	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
127	C₇×C₈×D₄	C₂²	1	2	yes	complemented
128	C₇×#433	C₂²	1	2	yes	complemented
129	C₇×#431	C₂²	1	1	yes	characteristic, complemented
130	C₇×#424	C₂²	1	2	yes	complemented
131	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₇×#418	C₂²	1	2	yes	—
133	C₇×#416	C₂²	1	2	yes	complemented
134	C₇×#416	C₂²	1	2	yes	complemented
135	#62071	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	C₂³	1	1	yes	characteristic
139	C₂×C₇×#41	C₂³	1	2	yes	—
140	C₂×C₇×#41	C₂³	1	2	yes	—
141	C₂²×C₇×Q₈	C₂³	1	2	yes	—
142	C₂²×C₇×D₄	—	2	1	no	—
143	C₂²×C₇×D₄	C₂³	1	2	yes	—
144	C₇×#137	—	4	4	no	—
145	C₇×#135	—	4	4	no	—
146	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₇×SD₁₆	—	4	4	no	—
150	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₇×D₈	C₂³	1	2	yes	—
159	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
160	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
161	C₂×C₇×M₁₆	C₂³	1	2	yes	—
162	C₂²×C₇×C₈	C₂³	1	2	yes	—
163	C₂²×C₇×C₈	C₂³	1	2	yes	—
164	C₇×C₄⋊Q₈	—	2	1	no	—
165	C₇×C₄⋊Q₈	—	2	1	no	—
166	C₇×C₄⋊Q₈	—	2	2	no	—
167	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₇×#127	—	2	2	no	—
173	C₇×#127	C₂³	1	1	yes	characteristic
174	C₇×#127	C₂³	1	2	yes	—
175	C₇×#127	C₂³	1	1	yes	characteristic
176	C₇×#126	—	2	2	no	—
177	C₇×#126	—	2	2	no	—
178	C₇×#126	—	2	2	no	—
179	C₇×#126	—	2	2	no	—
180	C₇×#126	—	2	2	no	—
181	C₇×#126	—	2	2	no	—
182	C₇×#126	D₄	1	2	yes	—
183	C₇×#125	—	2	1	no	—
184	C₇×#125	D₄	1	1	yes	characteristic
185	C₇×#124	—	2	2	no	—
186	C₇×#124	—	2	2	no	—
187	C₇×#124	—	2	2	no	—
188	C₇×#124	—	2	2	no	—
189	C₇×#124	—	2	2	no	—
190	C₇×#124	—	2	1	no	—
191	C₇×#124	D₄	1	1	yes	characteristic
192	C₇×#124	C₂³	1	2	yes	—
193	C₇×#124	C₂³	1	2	yes	—
194	C₇×#124	C₂³	1	2	yes	—
195	C₇×#123	—	2	2	no	—
196	C₇×#123	—	2	2	no	—
197	C₇×#123	—	2	2	no	—
198	C₇×#123	—	2	2	no	—
199	C₇×#123	D₄	1	2	yes	—
200	C₇×C₂²⋊Q₈	—	2	1	no	—
201	C₇×C₂²⋊Q₈	—	2	1	no	—
202	C₇×C₂²⋊Q₈	—	2	1	no	—
203	C₇×C₂²⋊Q₈	—	2	2	no	—
204	C₇×C₂²⋊Q₈	—	2	2	no	—
205	C₇×C₂²⋊Q₈	—	2	2	no	—
206	C₇×C₂²⋊Q₈	—	2	2	no	—
207	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₇×#121	—	2	1	no	—
212	C₇×#121	—	2	1	no	—
213	C₇×#121	—	2	2	no	—
214	C₇×#121	—	2	1	no	—
215	C₇×#121	—	2	1	no	—
216	C₇×#121	—	2	1	no	—
217	C₇×#121	—	2	1	no	—
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	1	no	—
221	C₇×#121	—	2	2	no	—
222	C₇×#121	—	2	2	no	—
223	C₇×#121	—	2	2	no	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	D₄	1	1	yes	characteristic
226	C₇×#121	C₂³	1	2	yes	—
227	C₇×#121	C₂³	1	2	yes	—
228	C₇×#121	C₂³	1	1	yes	characteristic
229	C₇×#121	C₂³	1	1	yes	characteristic
230	C₇×#120	—	2	2	no	—
231	C₇×#120	—	2	2	no	—
232	C₇×#120	—	2	2	no	—
233	C₇×#120	—	2	2	no	—
234	C₄×C₇×Q₈	—	2	1	no	—
235	C₄×C₇×Q₈	—	2	2	no	—
236	C₄×C₇×Q₈	—	2	2	no	—
237	C₄×C₇×Q₈	—	2	2	no	—
238	C₄×C₇×Q₈	—	2	1	no	—
239	C₄×C₇×Q₈	C₂³	1	2	yes	—
240	C₄×C₇×Q₈	C₂³	1	2	yes	—
241	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
242	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
243	C₄×C₇×Q₈	C₂³	1	2	yes	—
244	C₄×C₇×Q₈	C₂³	1	2	yes	—
245	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	1	no	—
248	C₄×C₇×D₄	—	2	1	no	—
249	C₄×C₇×D₄	—	2	2	no	—
250	C₄×C₇×D₄	—	2	2	no	—
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	—	2	1	no	—
253	C₄×C₇×D₄	—	2	1	no	—
254	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
255	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
256	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
257	C₄×C₇×D₄	C₂³	1	2	yes	—
258	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
259	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₇×#117	—	2	1	no	—
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	1	no	—
264	C₇×#117	—	2	1	no	—
265	C₇×#117	—	2	2	no	—
266	C₇×#117	—	2	2	no	—
267	C₇×#117	—	2	1	no	—
268	C₇×#117	C₂³	1	1	yes	characteristic
269	C₇×#117	C₂³	1	2	yes	—
270	C₇×#117	C₂³	1	2	yes	—
271	C₂×C₇×C₄⋊C₄	—	2	1	no	—
272	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²×C₇	—	2	1	no	—
274	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₇×#107	C₂³	1	1	yes	characteristic
276	C₇×#107	C₂³	1	1	yes	characteristic
277	C₇×#106	C₂³	1	2	yes	—
278	C₇×#106	C₂³	1	1	yes	characteristic
279	C₇×#106	C₂³	1	1	yes	characteristic
280	C₇×#106	C₂³	1	2	yes	—
281	C₇×C₄⋊C₈	C₂³	1	2	yes	—
282	C₇×C₄⋊C₈	C₂³	1	2	yes	—
283	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	1	yes	characteristic
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
302	C₇×#102	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	1	yes	characteristic
304	C₇×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
309	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	2	yes	—
315	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
316	#3546	C₂×C₇	1	1	yes	characteristic, complemented
317	#3518	C₂×C₇	1	1	yes	characteristic, complemented
318	#3397	C₂×C₇	1	1	yes	characteristic, complemented
319	#3393	C₂×C₇	1	1	yes	characteristic, complemented
320	#3369	C₂×C₇	1	1	yes	characteristic, complemented
321	#3362	C₂×C₇	1	1	yes	characteristic, complemented
322	#3325	C₂×C₇	1	1	yes	characteristic, complemented
323	#3311	C₂×C₇	1	2	yes	complemented
324	#3304	C₂×C₇	1	2	yes	complemented
325	#3303	C₂×C₇	1	1	yes	characteristic, complemented
326	#3282	C₂×C₇	1	2	yes	complemented
327	D₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
328	#3276	C₂×C₇	1	1	yes	characteristic, complemented
329	#3271	C₂×C₇	1	2	yes	complemented
330	#3263	C₂×C₇	1	2	yes	complemented
331	#3246	C₂×C₇	1	1	yes	characteristic, complemented
332	#3224	C₂×C₇	1	2	yes	complemented
333	#3210	C₂×C₇	1	1	yes	characteristic, complemented
334	#3121	C₂×C₇	1	2	yes	complemented
335	#3106	C₂×C₇	1	1	yes	characteristic, complemented
336	#3043	C₂×C₇	1	2	yes	complemented
337	#3035	C₂×C₇	1	1	yes	characteristic, complemented
338	#2994	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂⁴×C₇	—	2	2	no	—
340	C₇×#41	—	2	2	no	—
341	C₇×#41	—	4	1	no	—
342	C₇×#41	—	4	2	no	—
343	C₇×#41	—	4	2	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	C₂×C₇×Q₈	—	2	2	no	—
349	C₂×C₇×Q₈	—	2	1	no	—
350	C₂×C₇×Q₈	—	2	2	no	—
351	C₂×C₇×Q₈	—	2	1	no	—
352	C₂×C₇×Q₈	—	2	4	no	—
353	C₂×C₇×Q₈	—	4	2	no	—
354	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
355	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
356	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
357	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₇×D₄	—	2	1	no	—
359	C₂×C₇×D₄	—	2	2	no	—
360	C₂×C₇×D₄	—	2	1	no	—
361	C₂×C₇×D₄	—	2	2	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	—	2	2	no	—
364	C₂×C₇×D₄	—	2	1	no	—
365	C₂×C₇×D₄	—	2	1	no	—
366	C₂×C₇×D₄	—	2	1	no	—
367	C₂×C₇×D₄	—	2	1	no	—
368	C₂×C₇×D₄	—	2	2	no	—
369	C₂×C₇×D₄	—	2	1	no	—
370	C₂×C₇×D₄	—	2	2	no	—
371	C₂×C₇×D₄	—	2	2	no	—
372	C₂×C₇×D₄	—	4	2	no	—
373	C₂×C₇×D₄	—	4	2	no	—
374	C₂×C₇×D₄	—	8	2	no	—
375	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
376	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
377	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
378	C₂×C₇×D₄	C₂⁴	1	2	yes	—
379	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₇	—	2	2	no	—
382	C₂²×C₄×C₇	—	2	1	no	—
383	C₂²×C₄×C₇	—	2	1	no	—
384	C₂²×C₄×C₇	—	2	1	no	—
385	C₂²×C₄×C₇	—	2	1	no	—
386	C₂²×C₄×C₇	—	2	1	no	—
387	C₂²×C₄×C₇	—	2	2	no	—
388	C₂²×C₄×C₇	—	2	2	no	—
389	C₂²×C₄×C₇	—	2	2	no	—
390	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
394	C₇×Q₁₆	—	2	4	no	—
395	C₇×Q₁₆	—	4	2	no	—
396	C₇×Q₁₆	—	4	2	no	—
397	C₇×SD₁₆	—	2	2	no	—
398	C₇×SD₁₆	—	2	4	no	—
399	C₇×SD₁₆	—	2	2	no	—
400	C₇×SD₁₆	—	4	2	no	—
401	C₇×SD₁₆	—	4	2	no	—
402	C₇×SD₁₆	—	4	2	no	—
403	C₇×SD₁₆	—	4	2	no	—
404	C₇×SD₁₆	—	4	2	no	—
405	C₇×D₈	—	4	1	no	—
406	C₇×D₈	—	4	1	no	—
407	C₇×D₈	—	4	2	no	—
408	C₇×M₁₆	—	4	2	no	—
409	C₂×C₇×C₈	—	4	2	no	—
410	C₂×C₇×C₈	—	4	2	no	—
411	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
412	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
413	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
414	C₂×C₇×C₈	C₂⁴	1	2	yes	—
415	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
416	C₂×C₇×C₈	C₂⁴	1	2	yes	—
417	C₇×C₄⋊C₄	—	2	1	no	—
418	C₇×C₄⋊C₄	—	2	2	no	—
419	C₇×C₄⋊C₄	—	2	1	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	2	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	1	no	—
428	C₇×C₄⋊C₄	—	2	1	no	—
429	C₇×C₄⋊C₄	—	2	1	no	—
430	C₇×C₄⋊C₄	—	2	2	no	—
431	C₇×C₄⋊C₄	—	2	2	no	—
432	C₇×C₄⋊C₄	—	2	2	no	—
433	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
434	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
435	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
436	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
437	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
438	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
443	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
448	C₇×C₂²⋊C₄	—	2	2	no	—
449	C₇×C₂²⋊C₄	—	2	1	no	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	1	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	1	no	—
457	C₇×C₂²⋊C₄	—	2	2	no	—
458	C₇×C₂²⋊C₄	—	2	2	no	—
459	C₇×C₂²⋊C₄	—	2	2	no	—
460	C₇×C₂²⋊C₄	—	2	2	no	—
461	C₇×C₂²⋊C₄	—	2	1	no	—
462	C₇×C₂²⋊C₄	—	2	2	no	—
463	C₇×C₂²⋊C₄	—	2	1	no	—
464	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
465	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
466	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
467	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
468	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
469	C₄²×C₇	—	2	1	no	—
470	C₄²×C₇	—	2	1	no	—
471	C₄²×C₇	—	2	1	no	—
472	C₄²×C₇	—	2	2	no	—
473	C₄²×C₇	—	2	2	no	—
474	C₄²×C₇	—	2	2	no	—
475	C₄²×C₇	—	2	2	no	—
476	C₄²×C₇	—	2	2	no	—
477	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
478	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
479	C₄²×C₇	C₂⁴	1	1	yes	characteristic
480	C₄²×C₇	C₂⁴	1	2	yes	—
481	C₄²×C₇	C₂⁴	1	1	yes	characteristic
482	C₂×#137	C₂²×C₇	1	2	yes	complemented
483	C₂×#135	C₂²×C₇	1	2	yes	complemented
484	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
485	#560	—	2	2	no	—
486	Q₈²	C₂²×C₇	1	1	yes	characteristic, complemented
487	#556	—	2	2	no	—
488	#556	—	2	1	no	—
489	#556	C₂²×C₇	1	1	yes	characteristic
490	#556	C₂²×C₇	1	1	yes	characteristic, complemented
491	#556	C₂²×C₇	1	2	yes	complemented
492	#555	—	2	1	no	—
493	#555	C₂²×C₇	1	1	yes	characteristic
494	#553	—	2	1	no	—
495	#550	C₂²×C₇	1	2	yes	—
496	#550	C₂²×C₇	1	1	yes	characteristic
497	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
498	#548	C₂²×C₇	1	2	yes	complemented
499	#547	C₂²×C₇	1	1	yes	characteristic
500	#546	—	2	1	no	—
501	#546	C₂²×C₇	1	2	yes	—
502	D₄²	C₂²×C₇	1	1	yes	characteristic
503	#542	—	2	2	no	—
504	#542	C₂²×C₇	1	2	yes	—
505	#542	C₂²×C₇	1	2	yes	complemented
506	#538	—	2	2	no	—
507	#537	—	2	1	no	—
508	#535	—	2	1	no	—
509	#535	C₂²×C₇	1	2	yes	—
510	#533	—	2	1	no	—
511	#533	C₂²×C₇	1	1	yes	characteristic, complemented
512	#532	C₂²×C₇	1	1	yes	characteristic
513	#532	C₂²×C₇	1	1	yes	characteristic
514	#529	—	2	1	no	—
515	#529	C₂²×C₇	1	1	yes	characteristic
516	#519	C₂²×C₇	1	2	yes	complemented
517	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
518	#496	C₂²×C₇	1	2	yes	complemented
519	#495	C₂²×C₇	1	2	yes	—
520	#494	C₂²×C₇	1	1	yes	characteristic, complemented
521	#492	C₂²×C₇	1	1	yes	characteristic
522	#489	C₂²×C₇	1	2	yes	—
523	#487	C₂²×C₇	1	1	yes	characteristic, complemented
524	#486	C₂²×C₇	1	1	yes	characteristic
525	#486	C₂²×C₇	1	2	yes	complemented
526	#485	C₂²×C₇	1	2	yes	complemented
527	#482	C₂²×C₇	1	1	yes	characteristic
528	#482	C₂²×C₇	1	2	yes	—
529	#482	C₂²×C₇	1	1	yes	characteristic, complemented
530	#477	C₂²×C₇	1	1	yes	characteristic, complemented
531	#476	C₂²×C₇	1	1	yes	characteristic
532	#476	C₂²×C₇	1	1	yes	characteristic, complemented
533	#476	C₂²×C₇	1	1	yes	characteristic, complemented
534	#476	C₂²×C₇	1	2	yes	complemented
535	#475	C₂²×C₇	1	2	yes	complemented
536	#475	C₂²×C₇	1	2	yes	complemented
537	#470	C₂²×C₇	1	2	yes	complemented
538	#469	C₂²×C₇	1	2	yes	—
539	#465	C₂²×C₇	1	2	yes	—
540	#465	C₂²×C₇	1	2	yes	—
541	#465	C₂²×C₇	1	2	yes	complemented
542	#465	C₂²×C₇	1	2	yes	complemented
543	#464	C₂²×C₇	1	2	yes	—
544	#464	C₂²×C₇	1	2	yes	—
545	#464	C₂²×C₇	1	2	yes	complemented
546	#464	C₂²×C₇	1	2	yes	complemented
547	#464	C₂²×C₇	1	2	yes	complemented
548	#464	C₂²×C₇	1	2	yes	complemented
549	#463	C₂²×C₇	1	2	yes	complemented
550	#463	C₂²×C₇	1	2	yes	complemented
551	#462	C₂²×C₇	1	1	yes	characteristic, complemented
552	#461	C₂²×C₇	1	1	yes	characteristic
553	#461	C₂²×C₇	1	1	yes	characteristic, complemented
554	#461	C₂²×C₇	1	1	yes	characteristic, complemented
555	#460	C₂²×C₇	1	1	yes	characteristic
556	#460	C₂²×C₇	1	1	yes	characteristic
557	#460	C₂²×C₇	1	2	yes	—
558	#460	C₂²×C₇	1	2	yes	complemented
559	#460	C₂²×C₇	1	2	yes	complemented
560	#459	C₂²×C₇	1	1	yes	characteristic
561	#459	C₂²×C₇	1	1	yes	characteristic
562	#452	C₂²×C₇	1	2	yes	complemented
563	#452	C₂²×C₇	1	2	yes	complemented
564	#452	C₂²×C₇	1	2	yes	complemented
565	#451	C₂²×C₇	1	2	yes	complemented
566	#450	C₂²×C₇	1	2	yes	—
567	#449	C₂²×C₇	1	1	yes	characteristic
568	#449	C₂²×C₇	1	1	yes	characteristic, complemented
569	#449	C₂²×C₇	1	2	yes	complemented
570	#448	C₂²×C₇	1	2	yes	—
571	#447	C₂²×C₇	1	2	yes	—
572	#446	C₂²×C₇	1	1	yes	characteristic, complemented
573	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
574	#441	C₂²×C₇	1	2	yes	complemented
575	#440	C₂²×C₇	1	2	yes	complemented
576	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
577	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
578	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
579	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
580	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
581	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
582	#436	C₂²×C₇	1	1	yes	characteristic
583	#435	C₂²×C₇	1	2	yes	complemented
584	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
585	C₈×D₄	C₂²×C₇	1	2	yes	complemented
586	#433	C₂²×C₇	1	2	yes	complemented
587	#431	C₂²×C₇	1	1	yes	characteristic, complemented
588	#424	C₂²×C₇	1	2	yes	complemented
589	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
590	#418	C₂²×C₇	1	2	yes	—
591	#416	C₂²×C₇	1	2	yes	complemented
592	#416	C₂²×C₇	1	2	yes	complemented
593	C₂³×C₇	—	2	1	no	—
594	C₂³×C₇	—	2	1	no	—
595	C₂³×C₇	—	2	2	no	—
596	C₂³×C₇	—	2	1	no	—
597	C₂³×C₇	—	8	2	no	—
598	C₂³×C₇	—	8	2	no	—
599	C₂³×C₇	—	8	2	no	—
600	C₂³×C₇	C₂²×D₄	1	2	yes	—
601	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
602	C₇×Q₈	—	2	2	no	—
603	C₇×Q₈	—	2	1	no	—
604	C₇×Q₈	—	2	2	no	—
605	C₇×Q₈	—	2	2	no	—
606	C₇×Q₈	—	2	2	no	—
607	C₇×Q₈	—	2	2	no	—
608	C₇×Q₈	—	4	4	no	—
609	C₇×Q₈	—	8	1	no	—
610	C₇×Q₈	—	8	2	no	—
611	C₇×Q₈	—	8	1	no	—
612	C₇×Q₈	H(5,𝔽₂)	1	2	yes	—
613	C₇×D₄	—	2	2	no	—
614	C₇×D₄	—	2	1	no	—
615	C₇×D₄	—	2	2	no	—
616	C₇×D₄	—	2	1	no	—
617	C₇×D₄	—	2	1	no	—
618	C₇×D₄	—	2	1	no	—
619	C₇×D₄	—	2	1	no	—
620	C₇×D₄	—	2	1	no	—
621	C₇×D₄	—	2	2	no	—
622	C₇×D₄	—	4	2	no	—
623	C₇×D₄	—	4	2	no	—
624	C₇×D₄	—	4	2	no	—
625	C₇×D₄	—	8	1	no	—
626	C₇×D₄	—	8	1	no	—
627	C₇×D₄	—	8	2	no	—
628	C₇×D₄	—	8	2	no	—
629	C₇×D₄	—	8	1	no	—
630	C₇×D₄	—	8	2	no	—
631	C₇×D₄	—	8	2	no	—
632	C₇×D₄	—	8	2	no	—
633	C₇×D₄	—	8	2	no	—
634	C₇×D₄	—	8	2	no	—
635	C₇×D₄	—	8	1	no	—
636	C₇×D₄	—	8	1	no	—
637	C₂×C₄×C₇	—	2	1	no	—
638	C₂×C₄×C₇	—	2	2	no	—
639	C₂×C₄×C₇	—	2	1	no	—
640	C₂×C₄×C₇	—	2	2	no	—
641	C₂×C₄×C₇	—	2	2	no	—
642	C₂×C₄×C₇	—	2	1	no	—
643	C₂×C₄×C₇	—	2	1	no	—
644	C₂×C₄×C₇	—	2	2	no	—
645	C₂×C₄×C₇	—	2	2	no	—
646	C₂×C₄×C₇	—	2	1	no	—
647	C₂×C₄×C₇	—	2	1	no	—
648	C₂×C₄×C₇	—	2	2	no	—
649	C₂×C₄×C₇	—	2	1	no	—
650	C₂×C₄×C₇	—	4	1	no	—
651	C₂×C₄×C₇	—	4	2	no	—
652	C₂×C₄×C₇	—	4	4	no	—
653	C₂×C₄×C₇	—	4	2	no	—
654	C₂×C₄×C₇	—	4	2	no	—
655	C₂×C₄×C₇	—	4	2	no	—
656	C₂×C₄×C₇	—	8	1	no	—
657	C₂×C₄×C₇	—	8	2	no	—
658	C₂×C₄×C₇	—	8	2	no	—
659	C₂×C₄×C₇	—	8	2	no	—
660	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
661	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
662	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
663	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
664	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
665	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
666	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
667	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
668	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
669	C₇×C₈	—	2	1	no	—
670	C₇×C₈	—	2	2	no	—
671	C₇×C₈	—	2	2	no	—
672	C₇×C₈	—	2	1	no	—
673	C₇×C₈	—	2	1	no	—
674	C₇×C₈	—	2	1	no	—
675	C₂×#41	—	2	1	no	—
676	C₂×#41	—	2	1	no	—
677	C₂×#41	C₂³×C₇	1	1	yes	characteristic
678	C₂×#41	C₂³×C₇	1	2	yes	—
679	C₂×#41	C₂³×C₇	1	2	yes	—
680	C₂²×Q₈	C₂³×C₇	1	2	yes	—
681	C₂²×D₄	—	2	1	no	—
682	C₂²×D₄	C₂³×C₇	1	2	yes	—
683	#137	—	4	4	no	—
684	#135	—	4	4	no	—
685	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
686	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
687	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
688	C₂×SD₁₆	—	4	4	no	—
689	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
690	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
692	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
693	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
694	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
695	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
696	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
697	C₂×D₈	C₂³×C₇	1	2	yes	—
698	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
699	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
700	C₂×M₁₆	C₂³×C₇	1	2	yes	—
701	C₂²×C₈	C₂³×C₇	1	2	yes	—
702	C₂²×C₈	C₂³×C₇	1	2	yes	—
703	C₄⋊Q₈	—	2	1	no	—
704	C₄⋊Q₈	—	2	1	no	—
705	C₄⋊Q₈	—	2	2	no	—
706	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
711	#127	—	2	2	no	—
712	#127	C₂³×C₇	1	1	yes	characteristic
713	#127	C₂³×C₇	1	1	yes	characteristic
714	#127	C₂³×C₇	1	2	yes	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	C₇×D₄	1	2	yes	—
722	#125	—	2	1	no	—
723	#125	C₇×D₄	1	1	yes	characteristic
724	#124	—	2	2	no	—
725	#124	—	2	2	no	—
726	#124	—	2	2	no	—
727	#124	—	2	2	no	—
728	#124	—	2	2	no	—
729	#124	—	2	1	no	—
730	#124	C₇×D₄	1	1	yes	characteristic
731	#124	C₂³×C₇	1	2	yes	—
732	#124	C₂³×C₇	1	2	yes	—
733	#124	C₂³×C₇	1	2	yes	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	C₇×D₄	1	2	yes	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
747	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
748	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
749	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
750	#121	—	2	1	no	—
751	#121	—	2	1	no	—
752	#121	—	2	2	no	—
753	#121	—	2	1	no	—
754	#121	—	2	1	no	—
755	#121	—	2	1	no	—
756	#121	—	2	1	no	—
757	#121	—	2	2	no	—
758	#121	—	2	2	no	—
759	#121	—	2	1	no	—
760	#121	—	2	2	no	—
761	#121	—	2	2	no	—
762	#121	—	2	2	no	—
763	#121	—	2	2	no	—
764	#121	C₇×D₄	1	1	yes	characteristic
765	#121	C₂³×C₇	1	1	yes	characteristic
766	#121	C₂³×C₇	1	1	yes	characteristic
767	#121	C₂³×C₇	1	2	yes	—
768	#121	C₂³×C₇	1	2	yes	—
769	#120	—	2	2	no	—
770	#120	—	2	2	no	—
771	#120	—	2	2	no	—
772	#120	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	2	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	—	2	2	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₇	1	2	yes	—
781	C₄×Q₈	C₂³×C₇	1	2	yes	—
782	C₄×Q₈	C₂³×C₇	1	2	yes	—
783	C₄×Q₈	C₂³×C₇	1	2	yes	—
784	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₇	1	2	yes	—
798	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₇	1	2	yes	—
800	#117	—	2	1	no	—
801	#117	—	2	1	no	—
802	#117	—	2	1	no	—
803	#117	—	2	1	no	—
804	#117	—	2	2	no	—
805	#117	—	2	2	no	—
806	#117	—	2	1	no	—
807	#117	C₂³×C₇	1	1	yes	characteristic
808	#117	C₂³×C₇	1	2	yes	—
809	#117	C₂³×C₇	1	2	yes	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₂²⋊C₄	—	2	2	no	—
812	C₂×C₄²	—	2	1	no	—
813	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
814	#107	C₂³×C₇	1	1	yes	characteristic
815	#107	C₂³×C₇	1	1	yes	characteristic
816	#106	C₂³×C₇	1	1	yes	characteristic
817	#106	C₂³×C₇	1	2	yes	—
818	#106	C₂³×C₇	1	1	yes	characteristic
819	#106	C₂³×C₇	1	2	yes	—
820	C₄⋊C₈	C₂³×C₇	1	2	yes	—
821	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₇	1	2	yes	—
825	C₄⋊C₈	C₂³×C₇	1	2	yes	—
826	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
827	#103	C₂³×C₇	1	2	yes	—
828	#103	C₂³×C₇	1	2	yes	—
829	#103	C₂³×C₇	1	2	yes	—
830	#103	C₂³×C₇	1	1	yes	characteristic
831	#103	C₂³×C₇	1	1	yes	characteristic
832	#103	C₂³×C₇	1	2	yes	—
833	#103	C₂³×C₇	1	2	yes	—
834	#103	C₂³×C₇	1	2	yes	—
835	#102	C₂³×C₇	1	1	yes	characteristic
836	#102	C₂³×C₇	1	2	yes	—
837	#102	C₂³×C₇	1	2	yes	—
838	#102	C₂³×C₇	1	2	yes	—
839	#102	C₂³×C₇	1	1	yes	characteristic
840	#102	C₂³×C₇	1	2	yes	—
841	#102	C₂³×C₇	1	2	yes	—
842	#102	C₂³×C₇	1	1	yes	characteristic
843	#102	C₂³×C₇	1	1	yes	characteristic
844	#102	C₂³×C₇	1	1	yes	characteristic
845	#102	C₂³×C₇	1	2	yes	—
846	#102	C₂³×C₇	1	1	yes	characteristic
847	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
848	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
849	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
850	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
851	#97	C₂³×C₇	1	2	yes	—
852	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
853	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
854	C₄×C₈	C₂³×C₇	1	2	yes	—
855	C₂²×C₇	—	2	1	no	—
856	C₂²×C₇	—	2	2	no	—
857	C₂²×C₇	—	2	2	no	—
858	C₂²×C₇	—	2	1	no	—
859	C₂²×C₇	—	2	1	no	—
860	C₂²×C₇	—	2	2	no	—
861	C₂²×C₇	—	4	1	no	—
862	C₂²×C₇	—	4	1	no	—
863	C₂²×C₇	—	4	2	no	—
864	C₂²×C₇	—	4	1	no	—
865	C₂²×C₇	—	4	1	no	—
866	C₂²×C₇	—	4	1	no	—
867	C₂²×C₇	—	4	2	no	—
868	C₂²×C₇	—	4	1	no	—
869	C₂²×C₇	—	4	1	no	—
870	C₂²×C₇	—	4	1	no	—
871	C₂²×C₇	—	4	1	no	—
872	C₂²×C₇	—	4	2	no	—
873	C₂²×C₇	—	16	4	no	—
874	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
875	C₄×C₇	—	2	1	no	—
876	C₄×C₇	—	2	1	no	—
877	C₄×C₇	—	2	2	no	—
878	C₄×C₇	—	2	1	no	—
879	C₄×C₇	—	2	2	no	—
880	C₄×C₇	—	2	2	no	—
881	C₄×C₇	—	2	1	no	—
882	C₄×C₇	—	2	2	no	—
883	C₄×C₇	—	4	1	no	—
884	C₄×C₇	—	4	2	no	—
885	C₄×C₇	—	4	2	no	—
886	C₄×C₇	—	4	2	no	—
887	C₄×C₇	—	4	1	no	—
888	C₄×C₇	—	4	1	no	—
889	C₄×C₇	—	4	1	no	—
890	C₄×C₇	#577	1	2	yes	—
891	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
892	C₄×C₇	#585	1	1	yes	characteristic
893	C₂⁴	—	2	2	no	—
894	#41	—	2	2	no	—
895	#41	—	4	1	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	4	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
911	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	8	2	no	—
929	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
930	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
931	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
932	C₂×D₄	C₂⁴×C₇	1	2	yes	—
933	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
945	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
948	Q₁₆	—	2	4	no	—
949	Q₁₆	—	4	2	no	—
950	Q₁₆	—	4	2	no	—
951	SD₁₆	—	2	2	no	—
952	SD₁₆	—	2	4	no	—
953	SD₁₆	—	2	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	2	no	—
959	D₈	—	4	1	no	—
960	D₈	—	4	1	no	—
961	D₈	—	4	2	no	—
962	M₁₆	—	4	2	no	—
963	C₂×C₈	—	4	2	no	—
964	C₂×C₈	—	4	2	no	—
965	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₇	1	2	yes	—
970	C₂×C₈	C₂⁴×C₇	1	2	yes	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
988	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
989	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
990	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
991	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
992	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1019	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1020	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1021	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1022	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1032	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₇	1	2	yes	—
1035	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1036	C₂×C₇	—	4	1	no	—
1037	C₂×C₇	—	4	2	no	—
1038	C₂×C₇	—	8	1	no	—
1039	C₂×C₇	—	8	1	no	—
1040	C₂×C₇	—	8	2	no	—
1041	C₂×C₇	—	8	1	no	—
1042	C₂×C₇	#3488	1	1	yes	characteristic
1043	C₂×C₇	C₂×#577	1	1	yes	characteristic
1044	C₂×C₇	#3584	1	1	yes	characteristic
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	8	2	no	—
1050	C₂³	—	8	2	no	—
1051	C₂³	—	8	2	no	—
1052	C₂³	C₂²×C₇×D₄	1	2	yes	—
1053	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1054	Q₈	—	2	1	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	2	no	—
1058	Q₈	—	2	2	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	4	4	no	—
1061	Q₈	—	8	1	no	—
1062	Q₈	—	8	2	no	—
1063	Q₈	—	8	1	no	—
1064	Q₈	C₇×H(5,𝔽₂)	1	2	yes	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	4	2	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	1	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	1	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	8	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	4	1	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	4	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	8	1	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1113	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1114	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1115	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1116	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1117	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1118	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1119	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1120	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1121	C₈	—	2	1	no	—
1122	C₈	—	2	2	no	—
1123	C₈	—	2	2	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	1	no	—
1127	C₇	#62071	1	1	yes	characteristic, direct product factor, Sylow
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	16	4	no	—
1147	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	2	no	—
1163	C₄	C₇×#577	1	2	yes	—
1164	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1165	C₄	C₇×#585	1	1	yes	characteristic
1166	C₂	—	4	2	no	—
1167	C₂	—	4	1	no	—
1168	C₂	—	8	1	no	—
1169	C₂	—	8	2	no	—
1170	C₂	—	8	1	no	—
1171	C₂	—	8	1	no	—
1172	C₂	C₇×#3488	1	1	yes	characteristic
1173	C₂	C₂×C₇×#577	1	1	yes	characteristic
1174	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×#3546	C₂	semidirect
2. C₇×#3518	C₂	semidirect
3. C₇×#3397	C₂	semidirect
4. C₇×#3393	C₂	semidirect
5. C₇×#3369	C₂	semidirect
6. C₇×#3362	C₂	semidirect
7. C₇×#3325	C₂	semidirect
8. C₇×#3311	C₂	semidirect
9. C₇×#3304	C₂	semidirect
10. C₇×#3303	C₂	semidirect
11. C₇×#3282	C₂	semidirect
12. C₇×D₄×SD₁₆	C₂	semidirect
13. C₇×#3276	C₂	semidirect
14. C₇×#3271	C₂	semidirect
15. C₇×#3263	C₂	semidirect
16. C₇×#3246	C₂	semidirect
17. C₇×#3224	C₂	semidirect
18. C₇×#3210	C₂	semidirect
19. C₇×#3121	C₂	semidirect
20. C₇×#3106	C₂	semidirect
21. C₇×#3043	C₂	semidirect
22. C₇×#3035	C₂	semidirect
23. C₇×#2994	C₂	semidirect
24. C₂×C₇×#137	C₂²	semidirect
25. C₂×C₇×#135	C₂²	semidirect
28. C₇×Q₈²	C₂²	semidirect
32. C₇×#556	C₂²	semidirect
33. C₇×#556	C₂²	semidirect
40. C₇×#548	C₂²	semidirect
47. C₇×#542	C₂²	semidirect
53. C₇×#533	C₂²	semidirect
58. C₇×#519	C₂²	semidirect
59. C₄×C₇×#41	C₂²	semidirect
60. C₇×#496	C₂²	semidirect
62. C₇×#494	C₂²	semidirect
65. C₇×#487	C₂²	semidirect
67. C₇×#486	C₂²	semidirect
68. C₇×#485	C₂²	semidirect
71. C₇×#482	C₂²	semidirect
72. C₇×#477	C₂²	semidirect
74. C₇×#476	C₂²	semidirect
75. C₇×#476	C₂²	semidirect
76. C₇×#476	C₂²	semidirect
77. C₇×#475	C₂²	semidirect
78. C₇×#475	C₂²	semidirect
79. C₇×#470	C₂²	semidirect
83. C₇×#465	C₂²	semidirect
84. C₇×#465	C₂²	semidirect
87. C₇×#464	C₂²	semidirect
88. C₇×#464	C₂²	semidirect
89. C₇×#464	C₂²	semidirect
90. C₇×#464	C₂²	semidirect
91. C₇×#463	C₂²	semidirect
92. C₇×#463	C₂²	semidirect
93. C₇×#462	C₂²	semidirect
95. C₇×#461	C₂²	semidirect
96. C₇×#461	C₂²	semidirect
100. C₇×#460	C₂²	semidirect
101. C₇×#460	C₂²	semidirect
104. C₇×#452	C₂²	semidirect
105. C₇×#452	C₂²	semidirect
106. C₇×#452	C₂²	semidirect
107. C₇×#451	C₂²	semidirect
110. C₇×#449	C₂²	semidirect
111. C₇×#449	C₂²	semidirect
114. C₇×#446	C₂²	semidirect
115. C₇×C₈×Q₈	C₂²	semidirect
116. C₇×#441	C₂²	semidirect
117. C₇×#440	C₂²	semidirect
118. C₄×C₇×Q₁₆	C₂²	semidirect
120. C₄×C₇×SD₁₆	C₂²	semidirect
121. C₄×C₇×SD₁₆	C₂²	semidirect
123. C₄×C₇×D₈	C₂²	semidirect
125. C₇×#435	C₂²	semidirect
127. C₇×C₈×D₄	C₂²	semidirect
128. C₇×#433	C₂²	semidirect
129. C₇×#431	C₂²	semidirect
130. C₇×#424	C₂²	semidirect
131. C₂×C₇×C₄⋊C₈	C₂²	semidirect
133. C₇×#416	C₂²	semidirect
134. C₇×#416	C₂²	semidirect
135. #62071	C₇	direct (N × H)
316. #3546	C₂×C₇	semidirect
317. #3518	C₂×C₇	semidirect
318. #3397	C₂×C₇	semidirect
319. #3393	C₂×C₇	semidirect
320. #3369	C₂×C₇	semidirect
321. #3362	C₂×C₇	semidirect
322. #3325	C₂×C₇	semidirect
323. #3311	C₂×C₇	semidirect
324. #3304	C₂×C₇	semidirect
325. #3303	C₂×C₇	semidirect
326. #3282	C₂×C₇	semidirect
327. D₄×SD₁₆	C₂×C₇	semidirect
328. #3276	C₂×C₇	semidirect
329. #3271	C₂×C₇	semidirect
330. #3263	C₂×C₇	semidirect
331. #3246	C₂×C₇	semidirect
332. #3224	C₂×C₇	semidirect
333. #3210	C₂×C₇	semidirect
334. #3121	C₂×C₇	semidirect
335. #3106	C₂×C₇	semidirect
336. #3043	C₂×C₇	semidirect
337. #3035	C₂×C₇	semidirect
338. #2994	C₂×C₇	semidirect
482. C₂×#137	C₂²×C₇	semidirect
483. C₂×#135	C₂²×C₇	semidirect
486. Q₈²	C₂²×C₇	semidirect
490. #556	C₂²×C₇	semidirect
491. #556	C₂²×C₇	semidirect
498. #548	C₂²×C₇	semidirect
505. #542	C₂²×C₇	semidirect
511. #533	C₂²×C₇	semidirect
516. #519	C₂²×C₇	semidirect
517. C₄×#41	C₂²×C₇	semidirect
518. #496	C₂²×C₇	semidirect
520. #494	C₂²×C₇	semidirect
523. #487	C₂²×C₇	semidirect
525. #486	C₂²×C₇	semidirect
526. #485	C₂²×C₇	semidirect
529. #482	C₂²×C₇	semidirect
530. #477	C₂²×C₇	semidirect
532. #476	C₂²×C₇	semidirect
533. #476	C₂²×C₇	semidirect
534. #476	C₂²×C₇	semidirect
535. #475	C₂²×C₇	semidirect
536. #475	C₂²×C₇	semidirect
537. #470	C₂²×C₇	semidirect
541. #465	C₂²×C₇	semidirect
542. #465	C₂²×C₇	semidirect
545. #464	C₂²×C₇	semidirect
546. #464	C₂²×C₇	semidirect
547. #464	C₂²×C₇	semidirect
548. #464	C₂²×C₇	semidirect
549. #463	C₂²×C₇	semidirect
550. #463	C₂²×C₇	semidirect
551. #462	C₂²×C₇	semidirect
553. #461	C₂²×C₇	semidirect
554. #461	C₂²×C₇	semidirect
558. #460	C₂²×C₇	semidirect
559. #460	C₂²×C₇	semidirect
562. #452	C₂²×C₇	semidirect
563. #452	C₂²×C₇	semidirect
564. #452	C₂²×C₇	semidirect
565. #451	C₂²×C₇	semidirect
568. #449	C₂²×C₇	semidirect
569. #449	C₂²×C₇	semidirect
572. #446	C₂²×C₇	semidirect
573. C₈×Q₈	C₂²×C₇	semidirect
574. #441	C₂²×C₇	semidirect
575. #440	C₂²×C₇	semidirect
576. C₄×Q₁₆	C₂²×C₇	semidirect
578. C₄×SD₁₆	C₂²×C₇	semidirect
579. C₄×SD₁₆	C₂²×C₇	semidirect
581. C₄×D₈	C₂²×C₇	semidirect
583. #435	C₂²×C₇	semidirect
585. C₈×D₄	C₂²×C₇	semidirect
586. #433	C₂²×C₇	semidirect
587. #431	C₂²×C₇	semidirect
588. #424	C₂²×C₇	semidirect
589. C₂×C₄⋊C₈	C₂²×C₇	semidirect
591. #416	C₂²×C₇	semidirect
592. #416	C₂²×C₇	semidirect
1127. C₇	#62071	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×#3546	2
C₇×#3518	2
C₇×#3397	2
C₇×#3393	2
C₇×#3369	2
C₇×#3362	2
C₇×#3325	2
C₇×#3311	2
C₇×#3304	2
C₇×#3303	2
C₇×#3282	2
C₇×D₄×SD₁₆	2
C₇×#3276	2
C₇×#3271	2
C₇×#3263	2
C₇×#3246	2
C₇×#3224	2
C₇×#3210	2
C₇×#3121	2
C₇×#3106	2
C₇×#3043	2
C₇×#3035	2
C₇×#2994	2
#62071	7

Subgroups — C7×#62071 #13239287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62071 #13239287