Subgroups — C₇×#61176 #13238392

Order 1792.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3329	C₂	1	2	yes	maximal, complemented
4	C₇×#3328	C₂	1	2	yes	maximal, complemented
5	C₇×#3327	C₂	1	2	yes	maximal, complemented
6	C₇×#3326	C₂	1	2	yes	maximal, complemented
7	C₇×#3321	C₂	1	2	yes	maximal, complemented
8	C₇×#3320	C₂	1	2	yes	maximal, complemented
9	C₇×#3313	C₂	1	2	yes	maximal, complemented
10	C₇×#3312	C₂	1	2	yes	maximal, complemented
11	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3054	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3004	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₇×#419	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic
27	C₂×C₇×#137	C₂²	1	1	yes	characteristic
28	C₂×C₇×#135	C₂²	1	1	yes	characteristic
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic
30	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
31	C₇×#556	—	2	1	no	—
32	C₇×#556	C₂²	1	2	yes	—
33	C₇×#555	—	2	1	no	—
34	C₇×#555	C₂²	1	2	yes	—
35	C₇×#553	—	2	1	no	—
36	C₇×#553	C₂²	1	2	yes	—
37	C₇×#552	—	2	1	no	—
38	C₇×#552	C₂²	1	2	yes	—
39	C₇×D₄×Q₈	—	2	1	no	—
40	C₇×D₄×Q₈	—	2	1	no	—
41	C₇×D₄×Q₈	C₂²	1	2	yes	—
42	C₇×D₄×Q₈	C₂²	1	2	yes	—
43	C₇×#548	—	2	1	no	—
44	C₇×#548	—	2	1	no	—
45	C₇×#548	C₂²	1	2	yes	—
46	C₇×#548	C₂²	1	2	yes	—
47	C₇×#544	C₂²	1	1	yes	characteristic
48	C₇×#538	—	2	2	no	—
49	C₇×#537	C₂²	1	1	yes	characteristic
50	C₇×#536	—	2	2	no	—
51	C₇×#536	C₂²	1	1	yes	characteristic
52	C₇×#536	C₂²	1	1	yes	characteristic
53	C₇×#529	—	2	2	no	—
54	C₇×#525	—	2	2	no	—
55	C₇×#525	C₂²	1	1	yes	characteristic
56	C₇×#525	C₂²	1	1	yes	characteristic
57	C₇×#525	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#520	C₂²	1	1	yes	characteristic
60	C₇×#519	C₂²	1	1	yes	characteristic
61	C₂×C₇×#117	C₂²	1	1	yes	characteristic
62	C₇×#491	C₂²	1	2	yes	complemented
63	C₇×#489	C₂²	1	2	yes	complemented
64	C₇×#488	C₂²	1	2	yes	complemented
65	C₇×#487	C₂²	1	2	yes	complemented
66	C₇×#485	C₂²	1	2	yes	—
67	C₇×#485	C₂²	1	2	yes	—
68	C₇×#485	C₂²	1	2	yes	complemented
69	C₇×#485	C₂²	1	2	yes	complemented
70	C₇×#484	C₂²	1	2	yes	complemented
71	C₇×#483	C₂²	1	2	yes	complemented
72	C₇×#482	C₂²	1	2	yes	—
73	C₇×#482	C₂²	1	2	yes	—
74	C₇×#479	C₂²	1	2	yes	complemented
75	C₇×#479	C₂²	1	2	yes	complemented
76	C₇×#477	C₂²	1	2	yes	complemented
77	C₇×#475	C₂²	1	2	yes	complemented
78	C₇×#470	C₂²	1	1	yes	characteristic
79	C₇×#470	C₂²	1	1	yes	characteristic
80	C₇×#470	C₂²	1	2	yes	complemented
81	C₇×#469	C₂²	1	1	yes	characteristic
82	C₇×#469	C₂²	1	1	yes	characteristic
83	C₇×#468	C₂²	1	1	yes	characteristic
84	C₇×#468	C₂²	1	1	yes	characteristic
85	C₇×#468	C₂²	1	1	yes	characteristic
86	C₇×#468	C₂²	1	1	yes	characteristic
87	C₇×#468	C₂²	1	2	yes	complemented
88	C₇×#467	C₂²	1	2	yes	complemented
89	C₇×#465	C₂²	1	2	yes	complemented
90	C₇×#464	C₂²	1	2	yes	complemented
91	C₇×#463	C₂²	1	2	yes	complemented
92	C₇×#462	C₂²	1	2	yes	complemented
93	C₇×#461	C₂²	1	2	yes	complemented
94	C₇×#452	C₂²	1	2	yes	complemented
95	C₇×#451	C₂²	1	2	yes	—
96	C₇×#451	C₂²	1	2	yes	—
97	C₇×#451	C₂²	1	2	yes	complemented
98	C₇×#449	C₂²	1	2	yes	complemented
99	C₇×#448	C₂²	1	2	yes	—
100	C₇×#448	C₂²	1	2	yes	—
101	C₇×#448	C₂²	1	2	yes	complemented
102	C₇×#441	C₂²	1	2	yes	complemented
103	C₇×#440	C₂²	1	2	yes	complemented
104	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
105	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
106	C₇×#436	C₂²	1	2	yes	—
107	C₇×#436	C₂²	1	2	yes	—
108	C₇×#435	C₂²	1	2	yes	—
109	C₇×#435	C₂²	1	2	yes	—
110	C₇×#428	C₂²	1	1	yes	characteristic
111	C₇×#428	C₂²	1	1	yes	characteristic
112	C₇×#427	C₂²	1	1	yes	characteristic
113	C₇×#424	C₂²	1	1	yes	characteristic
114	C₇×#419	C₂²	1	1	yes	characteristic
115	C₇×#419	C₂²	1	1	yes	characteristic
116	C₇×#419	C₂²	1	2	yes	—
117	C₇×#419	C₂²	1	2	yes	—
118	C₇×#419	C₂²	1	2	yes	—
119	C₇×#419	C₂²	1	2	yes	—
120	C₇×#419	C₂²	1	2	yes	complemented
121	C₇×#417	C₂²	1	1	yes	characteristic
122	C₇×#417	C₂²	1	1	yes	characteristic
123	C₇×#417	C₂²	1	2	yes	complemented
124	C₇×#416	C₂²	1	1	yes	characteristic
125	C₇×#416	C₂²	1	1	yes	characteristic
126	C₇×#416	C₂²	1	2	yes	complemented
127	C₂×C₇×#103	C₂²	1	1	yes	characteristic
128	C₂×C₇×#103	C₂²	1	1	yes	characteristic
129	C₂×C₇×#103	C₂²	1	1	yes	characteristic
130	C₂×C₇×#103	C₂²	1	1	yes	characteristic
131	C₂×C₇×#103	C₂²	1	2	yes	complemented
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₇×#407	C₂²	1	1	yes	characteristic
134	C₇×#405	C₂²	1	1	yes	characteristic
135	#61176	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₇×2₋¹⁺⁴	—	2	4	no	—
137	C₇×2₋¹⁺⁴	—	4	2	no	—
138	C₂×C₇×#41	—	2	2	no	—
139	C₂×C₇×#41	—	2	1	no	—
140	C₂×C₇×#41	C₂³	1	1	yes	characteristic
141	C₂×C₇×#41	C₂³	1	1	yes	characteristic
142	C₂×C₇×#41	C₂³	1	2	yes	—
143	C₂×C₇×#41	C₂³	1	1	yes	characteristic
144	C₂²×C₇×Q₈	—	2	1	no	—
145	C₂²×C₇×Q₈	—	2	1	no	—
146	C₂²×C₇×Q₈	—	2	1	no	—
147	C₂²×C₇×Q₈	—	2	1	no	—
148	C₂²×C₇×Q₈	—	2	4	no	—
149	C₂²×C₇×Q₈	—	4	2	no	—
150	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₇×Q₈	C₂³	1	2	yes	—
152	C₂²×C₇×Q₈	C₂³	1	2	yes	—
153	C₂²×C₇×Q₈	C₂³	1	2	yes	—
154	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₇	—	2	1	no	—
156	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
157	C₇×#137	—	2	4	no	—
158	C₇×#137	—	4	2	no	—
159	C₇×#135	—	4	2	no	—
160	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
161	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
162	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
163	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
166	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
168	C₇×#131	—	4	2	no	—
169	C₂×C₇×M₁₆	—	4	2	no	—
170	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
171	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
172	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
173	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
174	C₂×C₇×M₁₆	C₂³	1	2	yes	—
175	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
176	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
177	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
178	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
179	C₂²×C₇×C₈	C₂³	1	2	yes	—
180	C₇×C₄⋊Q₈	—	2	1	no	—
181	C₇×C₄⋊Q₈	—	2	2	no	—
182	C₇×C₄⋊Q₈	—	2	2	no	—
183	C₇×C₄⋊Q₈	—	2	1	no	—
184	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
185	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
186	C₇×#126	—	2	2	no	—
187	C₇×#126	—	2	2	no	—
188	C₇×#126	—	2	2	no	—
189	C₇×#126	—	2	2	no	—
190	C₇×#125	—	2	2	no	—
191	C₇×#125	—	2	1	no	—
192	C₇×#125	C₂³	1	2	yes	—
193	C₇×#124	—	2	1	no	—
194	C₇×#124	—	2	2	no	—
195	C₇×#124	—	2	2	no	—
196	C₇×#124	—	2	2	no	—
197	C₇×#124	—	2	2	no	—
198	C₇×#124	—	2	2	no	—
199	C₇×#124	C₂³	1	2	yes	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	—	2	1	no	—
203	C₇×#123	—	2	1	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×#123	—	2	2	no	—
206	C₇×#123	D₄	1	2	yes	—
207	C₇×C₂²⋊Q₈	—	2	1	no	—
208	C₇×C₂²⋊Q₈	—	2	2	no	—
209	C₇×C₂²⋊Q₈	—	2	2	no	—
210	C₇×C₂²⋊Q₈	—	2	1	no	—
211	C₇×C₂²⋊Q₈	—	2	1	no	—
212	C₇×C₂²⋊Q₈	—	2	2	no	—
213	C₇×C₂²⋊Q₈	—	2	2	no	—
214	C₇×C₂²⋊Q₈	—	2	2	no	—
215	C₇×C₂²⋊Q₈	—	2	2	no	—
216	C₇×C₂²⋊Q₈	—	2	2	no	—
217	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
218	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
219	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₇×#121	—	2	2	no	—
227	C₇×#121	—	2	2	no	—
228	C₇×#121	—	2	2	no	—
229	C₇×#121	—	2	1	no	—
230	C₇×#121	—	2	2	no	—
231	C₇×#121	—	2	2	no	—
232	C₇×#121	D₄	1	1	yes	characteristic
233	C₇×#121	D₄	1	1	yes	characteristic
234	C₇×#121	C₂³	1	1	yes	characteristic
235	C₇×#121	C₂³	1	1	yes	characteristic
236	C₇×#121	C₂³	1	1	yes	characteristic
237	C₇×#121	C₂³	1	1	yes	characteristic
238	C₇×#121	C₂³	1	2	yes	—
239	C₇×#120	—	2	1	no	—
240	C₇×#120	—	2	1	no	—
241	C₇×#120	D₄	1	2	yes	—
242	C₄×C₇×Q₈	—	2	1	no	—
243	C₄×C₇×Q₈	—	2	1	no	—
244	C₄×C₇×Q₈	—	2	1	no	—
245	C₄×C₇×Q₈	—	2	2	no	—
246	C₄×C₇×Q₈	C₂³	1	2	yes	—
247	C₄×C₇×Q₈	C₂³	1	2	yes	—
248	C₄×C₇×Q₈	C₂³	1	2	yes	—
249	C₄×C₇×D₄	—	2	2	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	—	2	2	no	—
252	C₄×C₇×D₄	—	2	2	no	—
253	C₄×C₇×D₄	—	2	1	no	—
254	C₄×C₇×D₄	—	2	1	no	—
255	C₄×C₇×D₄	—	2	1	no	—
256	C₄×C₇×D₄	—	2	1	no	—
257	C₄×C₇×D₄	—	2	2	no	—
258	C₄×C₇×D₄	—	2	2	no	—
259	C₄×C₇×D₄	—	2	2	no	—
260	C₄×C₇×D₄	—	2	2	no	—
261	C₄×C₇×D₄	C₂³	1	2	yes	—
262	C₄×C₇×D₄	C₂³	1	2	yes	—
263	C₄×C₇×D₄	C₂³	1	2	yes	—
264	C₇×#117	—	2	1	no	—
265	C₇×#117	—	2	1	no	—
266	C₇×#117	—	2	1	no	—
267	C₇×#117	—	2	2	no	—
268	C₇×#117	—	2	2	no	—
269	C₇×#117	—	2	2	no	—
270	C₇×#117	C₂³	1	2	yes	—
271	C₇×#117	C₂³	1	2	yes	—
272	C₇×#117	C₂³	1	2	yes	—
273	C₇×#117	C₂³	1	1	yes	characteristic
274	C₇×#117	C₂³	1	1	yes	characteristic
275	C₇×#117	C₂³	1	1	yes	characteristic
276	C₂×C₇×C₄⋊C₄	—	2	1	no	—
277	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
278	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₄²×C₇	—	2	1	no	—
282	C₇×#107	C₂³	1	2	yes	—
283	C₇×#107	C₂³	1	1	yes	characteristic
284	C₇×#107	C₂³	1	1	yes	characteristic
285	C₇×#107	C₂³	1	2	yes	—
286	C₇×#106	C₂³	1	1	yes	characteristic
287	C₇×#106	C₂³	1	1	yes	characteristic
288	C₇×#106	C₂³	1	2	yes	—
289	C₇×#106	C₂³	1	2	yes	—
290	C₇×C₄⋊C₈	C₂³	1	2	yes	—
291	C₇×C₄⋊C₈	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×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#103	C₂³	1	2	yes	—
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#103	C₂³	1	2	yes	—
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#103	C₂³	1	2	yes	—
304	C₇×#103	C₂³	1	2	yes	—
305	C₇×#103	C₂³	1	2	yes	—
306	C₇×#103	C₂³	1	2	yes	—
307	C₇×#103	C₂³	1	2	yes	—
308	C₇×#103	C₂³	1	2	yes	—
309	C₇×#103	C₂³	1	2	yes	—
310	C₇×#102	C₂³	1	1	yes	characteristic
311	C₇×#102	C₂³	1	1	yes	characteristic
312	C₇×#102	C₂³	1	1	yes	characteristic
313	C₇×#102	C₂³	1	1	yes	characteristic
314	C₇×#102	C₂³	1	2	yes	—
315	C₇×#102	C₂³	1	2	yes	—
316	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₇×#97	C₂³	1	2	yes	—
321	C₄×C₇×C₈	C₂³	1	2	yes	—
322	#3493	C₂×C₇	1	1	yes	characteristic, complemented
323	#3486	C₂×C₇	1	1	yes	characteristic, complemented
324	#3329	C₂×C₇	1	2	yes	complemented
325	#3328	C₂×C₇	1	2	yes	complemented
326	#3327	C₂×C₇	1	2	yes	complemented
327	#3326	C₂×C₇	1	2	yes	complemented
328	#3321	C₂×C₇	1	2	yes	complemented
329	#3320	C₂×C₇	1	2	yes	complemented
330	#3313	C₂×C₇	1	2	yes	complemented
331	#3312	C₂×C₇	1	2	yes	complemented
332	#3137	C₂×C₇	1	1	yes	characteristic, complemented
333	#3097	C₂×C₇	1	1	yes	characteristic, complemented
334	#3093	C₂×C₇	1	1	yes	characteristic, complemented
335	#3082	C₂×C₇	1	1	yes	characteristic, complemented
336	#3063	C₂×C₇	1	1	yes	characteristic, complemented
337	#3054	C₂×C₇	1	1	yes	characteristic, complemented
338	#3046	C₂×C₇	1	1	yes	characteristic, complemented
339	#3013	C₂×C₇	1	1	yes	characteristic, complemented
340	#3004	C₂×C₇	1	1	yes	characteristic, complemented
341	#2947	C₂×C₇	1	1	yes	characteristic, complemented
342	#2930	C₂×C₇	1	1	yes	characteristic, complemented
343	#2898	C₂×C₇	1	1	yes	characteristic, complemented
344	C₂×#419	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
346	C₇×#41	—	2	2	no	—
347	C₇×#41	—	2	2	no	—
348	C₇×#41	—	2	4	no	—
349	C₇×#41	—	2	2	no	—
350	C₇×#41	—	2	2	no	—
351	C₇×#41	—	2	2	no	—
352	C₇×#41	—	2	2	no	—
353	C₇×#41	—	4	2	no	—
354	C₇×#41	—	4	8	no	—
355	C₇×#41	—	4	4	no	—
356	C₂×C₇×Q₈	—	2	1	no	—
357	C₂×C₇×Q₈	—	2	2	no	—
358	C₂×C₇×Q₈	—	2	2	no	—
359	C₂×C₇×Q₈	—	2	1	no	—
360	C₂×C₇×Q₈	—	2	2	no	—
361	C₂×C₇×Q₈	—	2	2	no	—
362	C₂×C₇×Q₈	—	2	2	no	—
363	C₂×C₇×Q₈	—	2	4	no	—
364	C₂×C₇×Q₈	—	2	4	no	—
365	C₂×C₇×Q₈	—	2	4	no	—
366	C₂×C₇×Q₈	—	2	2	no	—
367	C₂×C₇×Q₈	—	2	2	no	—
368	C₂×C₇×Q₈	—	4	4	no	—
369	C₂×C₇×Q₈	—	4	2	no	—
370	C₂×C₇×Q₈	—	4	2	no	—
371	C₂×C₇×Q₈	—	4	2	no	—
372	C₂×C₇×Q₈	—	4	4	no	—
373	C₂×C₇×Q₈	—	4	4	no	—
374	C₂×C₇×Q₈	—	4	4	no	—
375	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
376	C₂×C₇×Q₈	#41	1	4	yes	—
377	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
378	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
379	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
381	C₂×C₇×D₄	—	2	1	no	—
382	C₂×C₇×D₄	—	2	1	no	—
383	C₂×C₇×D₄	—	2	1	no	—
384	C₂×C₇×D₄	—	2	1	no	—
385	C₂×C₇×D₄	—	2	2	no	—
386	C₂×C₇×D₄	—	2	1	no	—
387	C₂×C₇×D₄	—	2	1	no	—
388	C₂×C₇×D₄	—	2	2	no	—
389	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
390	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
391	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
392	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
393	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
394	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₇	—	2	1	no	—
396	C₂²×C₄×C₇	—	2	2	no	—
397	C₂²×C₄×C₇	—	2	2	no	—
398	C₂²×C₄×C₇	—	2	2	no	—
399	C₂²×C₄×C₇	—	2	2	no	—
400	C₂²×C₄×C₇	—	2	2	no	—
401	C₂²×C₄×C₇	—	2	1	no	—
402	C₂²×C₄×C₇	—	2	1	no	—
403	C₂²×C₄×C₇	—	2	1	no	—
404	C₂²×C₄×C₇	—	2	2	no	—
405	C₂²×C₄×C₇	—	2	1	no	—
406	C₂²×C₄×C₇	—	2	2	no	—
407	C₂²×C₄×C₇	—	2	1	no	—
408	C₂²×C₄×C₇	—	2	2	no	—
409	C₂²×C₄×C₇	—	4	4	no	—
410	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
414	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
417	C₇×Q₁₆	—	2	4	no	—
418	C₇×Q₁₆	—	4	1	no	—
419	C₇×Q₁₆	—	4	2	no	—
420	C₇×SD₁₆	—	2	4	no	—
421	C₇×SD₁₆	—	4	1	no	—
422	C₇×SD₁₆	—	4	1	no	—
423	C₇×SD₁₆	—	4	2	no	—
424	C₇×D₈	—	4	1	no	—
425	C₇×M₁₆	—	2	2	no	—
426	C₇×M₁₆	—	2	2	no	—
427	C₇×M₁₆	—	4	1	no	—
428	C₇×M₁₆	—	4	1	no	—
429	C₇×M₁₆	—	4	1	no	—
430	C₇×M₁₆	—	4	1	no	—
431	C₇×M₁₆	—	4	2	no	—
432	C₂×C₇×C₈	—	2	2	no	—
433	C₂×C₇×C₈	—	2	2	no	—
434	C₂×C₇×C₈	—	4	2	no	—
435	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
436	C₂×C₇×C₈	C₂⁴	1	2	yes	—
437	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
438	C₂×C₇×C₈	C₂⁴	1	2	yes	—
439	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
440	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
441	C₇×C₄⋊C₄	—	2	1	no	—
442	C₇×C₄⋊C₄	—	2	2	no	—
443	C₇×C₄⋊C₄	—	2	1	no	—
444	C₇×C₄⋊C₄	—	2	2	no	—
445	C₇×C₄⋊C₄	—	2	1	no	—
446	C₇×C₄⋊C₄	—	2	2	no	—
447	C₇×C₄⋊C₄	—	2	2	no	—
448	C₇×C₄⋊C₄	—	2	2	no	—
449	C₇×C₄⋊C₄	—	2	2	no	—
450	C₇×C₄⋊C₄	—	2	1	no	—
451	C₇×C₄⋊C₄	—	2	2	no	—
452	C₇×C₄⋊C₄	—	2	2	no	—
453	C₇×C₄⋊C₄	—	2	2	no	—
454	C₇×C₄⋊C₄	—	2	2	no	—
455	C₇×C₄⋊C₄	—	2	1	no	—
456	C₇×C₄⋊C₄	—	2	1	no	—
457	C₇×C₄⋊C₄	—	2	2	no	—
458	C₇×C₄⋊C₄	—	2	2	no	—
459	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
460	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
461	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
462	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
463	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
464	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
465	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
466	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
467	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
468	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
469	C₇×C₂²⋊C₄	—	2	2	no	—
470	C₇×C₂²⋊C₄	—	2	2	no	—
471	C₇×C₂²⋊C₄	—	2	1	no	—
472	C₇×C₂²⋊C₄	—	2	2	no	—
473	C₇×C₂²⋊C₄	—	2	1	no	—
474	C₇×C₂²⋊C₄	—	2	2	no	—
475	C₇×C₂²⋊C₄	—	2	1	no	—
476	C₇×C₂²⋊C₄	—	2	1	no	—
477	C₇×C₂²⋊C₄	—	2	1	no	—
478	C₇×C₂²⋊C₄	—	2	1	no	—
479	C₇×C₂²⋊C₄	—	2	2	no	—
480	C₇×C₂²⋊C₄	—	2	2	no	—
481	C₇×C₂²⋊C₄	—	2	1	no	—
482	C₇×C₂²⋊C₄	—	2	2	no	—
483	C₇×C₂²⋊C₄	—	2	2	no	—
484	C₇×C₂²⋊C₄	—	2	1	no	—
485	C₇×C₂²⋊C₄	—	2	2	no	—
486	C₇×C₂²⋊C₄	—	2	2	no	—
487	C₇×C₂²⋊C₄	—	2	1	no	—
488	C₇×C₂²⋊C₄	—	2	1	no	—
489	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
490	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
491	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
492	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
493	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
494	C₄²×C₇	—	2	2	no	—
495	C₄²×C₇	—	2	2	no	—
496	C₄²×C₇	—	2	2	no	—
497	C₄²×C₇	—	2	2	no	—
498	C₄²×C₇	—	2	2	no	—
499	C₄²×C₇	—	2	2	no	—
500	C₄²×C₇	—	2	1	no	—
501	C₄²×C₇	—	2	1	no	—
502	C₄²×C₇	C₂⁴	1	2	yes	—
503	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
504	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
505	C₂×#137	C₂²×C₇	1	1	yes	characteristic
506	C₂×#137	C₂²×C₇	1	1	yes	characteristic
507	C₂×#135	C₂²×C₇	1	1	yes	characteristic
508	C₂×#131	C₂²×C₇	1	1	yes	characteristic
509	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
510	#556	—	2	1	no	—
511	#556	C₂²×C₇	1	2	yes	—
512	#555	—	2	1	no	—
513	#555	C₂²×C₇	1	2	yes	—
514	#553	—	2	1	no	—
515	#553	C₂²×C₇	1	2	yes	—
516	#552	—	2	1	no	—
517	#552	C₂²×C₇	1	2	yes	—
518	D₄×Q₈	—	2	1	no	—
519	D₄×Q₈	—	2	1	no	—
520	D₄×Q₈	C₂²×C₇	1	2	yes	—
521	D₄×Q₈	C₂²×C₇	1	2	yes	—
522	#548	—	2	1	no	—
523	#548	—	2	1	no	—
524	#548	C₂²×C₇	1	2	yes	—
525	#548	C₂²×C₇	1	2	yes	—
526	#544	C₂²×C₇	1	1	yes	characteristic
527	#538	—	2	2	no	—
528	#537	C₂²×C₇	1	1	yes	characteristic
529	#536	—	2	2	no	—
530	#536	C₂²×C₇	1	1	yes	characteristic
531	#536	C₂²×C₇	1	1	yes	characteristic
532	#529	—	2	2	no	—
533	#525	—	2	2	no	—
534	#525	C₂²×C₇	1	1	yes	characteristic
535	#525	C₂²×C₇	1	1	yes	characteristic
536	#525	C₂²×C₇	1	1	yes	characteristic
537	#520	C₂²×C₇	1	1	yes	characteristic
538	#520	C₂²×C₇	1	1	yes	characteristic
539	#519	C₂²×C₇	1	1	yes	characteristic
540	C₂×#117	C₂²×C₇	1	1	yes	characteristic
541	#491	C₂²×C₇	1	2	yes	complemented
542	#489	C₂²×C₇	1	2	yes	complemented
543	#488	C₂²×C₇	1	2	yes	complemented
544	#487	C₂²×C₇	1	2	yes	complemented
545	#485	C₂²×C₇	1	2	yes	—
546	#485	C₂²×C₇	1	2	yes	—
547	#485	C₂²×C₇	1	2	yes	complemented
548	#485	C₂²×C₇	1	2	yes	complemented
549	#484	C₂²×C₇	1	2	yes	complemented
550	#483	C₂²×C₇	1	2	yes	complemented
551	#482	C₂²×C₇	1	2	yes	—
552	#482	C₂²×C₇	1	2	yes	—
553	#479	C₂²×C₇	1	2	yes	complemented
554	#479	C₂²×C₇	1	2	yes	complemented
555	#477	C₂²×C₇	1	2	yes	complemented
556	#475	C₂²×C₇	1	2	yes	complemented
557	#470	C₂²×C₇	1	1	yes	characteristic
558	#470	C₂²×C₇	1	1	yes	characteristic
559	#470	C₂²×C₇	1	2	yes	complemented
560	#469	C₂²×C₇	1	1	yes	characteristic
561	#469	C₂²×C₇	1	1	yes	characteristic
562	#468	C₂²×C₇	1	1	yes	characteristic
563	#468	C₂²×C₇	1	1	yes	characteristic
564	#468	C₂²×C₇	1	1	yes	characteristic
565	#468	C₂²×C₇	1	1	yes	characteristic
566	#468	C₂²×C₇	1	2	yes	complemented
567	#467	C₂²×C₇	1	2	yes	complemented
568	#465	C₂²×C₇	1	2	yes	complemented
569	#464	C₂²×C₇	1	2	yes	complemented
570	#463	C₂²×C₇	1	2	yes	complemented
571	#462	C₂²×C₇	1	2	yes	complemented
572	#461	C₂²×C₇	1	2	yes	complemented
573	#452	C₂²×C₇	1	2	yes	complemented
574	#451	C₂²×C₇	1	2	yes	—
575	#451	C₂²×C₇	1	2	yes	—
576	#451	C₂²×C₇	1	2	yes	complemented
577	#449	C₂²×C₇	1	2	yes	complemented
578	#448	C₂²×C₇	1	2	yes	—
579	#448	C₂²×C₇	1	2	yes	—
580	#448	C₂²×C₇	1	2	yes	complemented
581	#441	C₂²×C₇	1	2	yes	complemented
582	#440	C₂²×C₇	1	2	yes	complemented
583	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
584	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
585	#436	C₂²×C₇	1	2	yes	—
586	#436	C₂²×C₇	1	2	yes	—
587	#435	C₂²×C₇	1	2	yes	—
588	#435	C₂²×C₇	1	2	yes	—
589	#428	C₂²×C₇	1	1	yes	characteristic
590	#428	C₂²×C₇	1	1	yes	characteristic
591	#427	C₂²×C₇	1	1	yes	characteristic
592	#424	C₂²×C₇	1	1	yes	characteristic
593	#419	C₂²×C₇	1	2	yes	—
594	#419	C₂²×C₇	1	2	yes	—
595	#419	C₂²×C₇	1	1	yes	characteristic
596	#419	C₂²×C₇	1	1	yes	characteristic
597	#419	C₂²×C₇	1	2	yes	—
598	#419	C₂²×C₇	1	2	yes	—
599	#419	C₂²×C₇	1	2	yes	complemented
600	#417	C₂²×C₇	1	1	yes	characteristic
601	#417	C₂²×C₇	1	1	yes	characteristic
602	#417	C₂²×C₇	1	2	yes	complemented
603	#416	C₂²×C₇	1	1	yes	characteristic
604	#416	C₂²×C₇	1	1	yes	characteristic
605	#416	C₂²×C₇	1	2	yes	complemented
606	C₂×#103	C₂²×C₇	1	1	yes	characteristic
607	C₂×#103	C₂²×C₇	1	1	yes	characteristic
608	C₂×#103	C₂²×C₇	1	1	yes	characteristic
609	C₂×#103	C₂²×C₇	1	1	yes	characteristic
610	C₂×#103	C₂²×C₇	1	2	yes	complemented
611	#408	C₂²×C₇	1	1	yes	characteristic
612	#407	C₂²×C₇	1	1	yes	characteristic
613	#405	C₂²×C₇	1	1	yes	characteristic
614	C₂³×C₇	—	2	2	no	—
615	C₂³×C₇	—	2	1	no	—
616	C₂³×C₇	—	2	1	no	—
617	C₂³×C₇	—	4	1	no	—
618	C₂³×C₇	—	4	1	no	—
619	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
620	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
621	C₂³×C₇	C₂²×D₄	1	2	yes	—
622	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
623	C₇×Q₈	—	2	4	no	—
624	C₇×Q₈	—	2	2	no	—
625	C₇×Q₈	—	2	2	no	—
626	C₇×Q₈	—	2	1	no	—
627	C₇×Q₈	—	2	2	no	—
628	C₇×Q₈	—	2	1	no	—
629	C₇×Q₈	—	2	1	no	—
630	C₇×Q₈	—	2	2	no	—
631	C₇×Q₈	—	2	1	no	—
632	C₇×Q₈	—	4	4	no	—
633	C₇×Q₈	—	4	4	no	—
634	C₇×Q₈	—	4	4	no	—
635	C₇×Q₈	—	4	2	no	—
636	C₇×Q₈	—	8	2	no	—
637	C₇×Q₈	C₂×#41	1	4	yes	—
638	C₇×D₄	—	2	4	no	—
639	C₇×D₄	—	2	2	no	—
640	C₇×D₄	—	2	1	no	—
641	C₇×D₄	—	2	1	no	—
642	C₇×D₄	—	2	1	no	—
643	C₇×D₄	—	2	1	no	—
644	C₇×D₄	—	4	2	no	—
645	C₇×D₄	—	4	2	no	—
646	C₇×D₄	—	4	4	no	—
647	C₇×D₄	—	4	2	no	—
648	C₇×D₄	—	4	2	no	—
649	C₇×D₄	—	4	2	no	—
650	C₇×D₄	—	4	2	no	—
651	C₇×D₄	—	8	1	no	—
652	C₇×D₄	—	8	2	no	—
653	C₇×D₄	—	8	1	no	—
654	C₂×C₄×C₇	—	2	2	no	—
655	C₂×C₄×C₇	—	2	4	no	—
656	C₂×C₄×C₇	—	2	2	no	—
657	C₂×C₄×C₇	—	2	2	no	—
658	C₂×C₄×C₇	—	2	2	no	—
659	C₂×C₄×C₇	—	2	1	no	—
660	C₂×C₄×C₇	—	2	1	no	—
661	C₂×C₄×C₇	—	2	2	no	—
662	C₂×C₄×C₇	—	2	2	no	—
663	C₂×C₄×C₇	—	2	1	no	—
664	C₂×C₄×C₇	—	2	1	no	—
665	C₂×C₄×C₇	—	2	2	no	—
666	C₂×C₄×C₇	—	2	1	no	—
667	C₂×C₄×C₇	—	2	1	no	—
668	C₂×C₄×C₇	—	2	1	no	—
669	C₂×C₄×C₇	—	2	1	no	—
670	C₂×C₄×C₇	—	2	2	no	—
671	C₂×C₄×C₇	—	2	1	no	—
672	C₂×C₄×C₇	—	2	2	no	—
673	C₂×C₄×C₇	—	2	1	no	—
674	C₂×C₄×C₇	—	4	4	no	—
675	C₂×C₄×C₇	—	4	4	no	—
676	C₂×C₄×C₇	—	4	4	no	—
677	C₂×C₄×C₇	—	4	4	no	—
678	C₂×C₄×C₇	—	4	2	no	—
679	C₂×C₄×C₇	—	4	2	no	—
680	C₂×C₄×C₇	—	4	2	no	—
681	C₂×C₄×C₇	—	8	2	no	—
682	C₂×C₄×C₇	—	8	1	no	—
683	C₂×C₄×C₇	—	8	2	no	—
684	C₂×C₄×C₇	—	8	1	no	—
685	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
686	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
687	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
688	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
689	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
690	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
691	C₂×C₄×C₇	C₂×#41	1	2	yes	—
692	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
693	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
694	C₇×C₈	—	2	2	no	—
695	C₇×C₈	—	2	1	no	—
696	C₇×C₈	—	2	1	no	—
697	C₇×C₈	—	2	1	no	—
698	C₇×C₈	—	2	1	no	—
699	C₇×C₈	—	2	2	no	—
700	2₋¹⁺⁴	—	2	4	no	—
701	2₋¹⁺⁴	—	4	2	no	—
702	C₂×#41	—	2	2	no	—
703	C₂×#41	—	2	1	no	—
704	C₂×#41	C₂³×C₇	1	1	yes	characteristic
705	C₂×#41	C₂³×C₇	1	1	yes	characteristic
706	C₂×#41	C₂³×C₇	1	2	yes	—
707	C₂×#41	C₂³×C₇	1	1	yes	characteristic
708	C₂²×Q₈	—	2	1	no	—
709	C₂²×Q₈	—	2	1	no	—
710	C₂²×Q₈	—	2	1	no	—
711	C₂²×Q₈	—	2	1	no	—
712	C₂²×Q₈	—	2	4	no	—
713	C₂²×Q₈	—	4	2	no	—
714	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
715	C₂²×Q₈	C₂³×C₇	1	2	yes	—
716	C₂²×Q₈	C₂³×C₇	1	2	yes	—
717	C₂²×Q₈	C₂³×C₇	1	2	yes	—
718	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
719	C₂³×C₄	—	2	1	no	—
720	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
721	#137	—	2	4	no	—
722	#137	—	4	2	no	—
723	#135	—	4	2	no	—
724	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
725	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
726	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
729	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
731	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
732	#131	—	4	2	no	—
733	C₂×M₁₆	—	4	2	no	—
734	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
735	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
736	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
737	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
740	C₂×M₁₆	C₂³×C₇	1	2	yes	—
741	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
742	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
743	C₂²×C₈	C₂³×C₇	1	2	yes	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	—	2	2	no	—
746	C₄⋊Q₈	—	2	2	no	—
747	C₄⋊Q₈	—	2	1	no	—
748	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
749	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#125	—	2	2	no	—
755	#125	—	2	1	no	—
756	#125	C₂³×C₇	1	2	yes	—
757	#124	—	2	1	no	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	C₂³×C₇	1	2	yes	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	1	no	—
767	#123	—	2	1	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	C₇×D₄	1	2	yes	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
782	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
786	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
787	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	C₇×D₄	1	1	yes	characteristic
797	#121	C₇×D₄	1	1	yes	characteristic
798	#121	C₂³×C₇	1	1	yes	characteristic
799	#121	C₂³×C₇	1	1	yes	characteristic
800	#121	C₂³×C₇	1	1	yes	characteristic
801	#121	C₂³×C₇	1	1	yes	characteristic
802	#121	C₂³×C₇	1	2	yes	—
803	#120	—	2	1	no	—
804	#120	—	2	1	no	—
805	#120	C₇×D₄	1	2	yes	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	—	2	2	no	—
810	C₄×Q₈	C₂³×C₇	1	2	yes	—
811	C₄×Q₈	C₂³×C₇	1	2	yes	—
812	C₄×Q₈	C₂³×C₇	1	2	yes	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	C₂³×C₇	1	2	yes	—
826	C₄×D₄	C₂³×C₇	1	2	yes	—
827	C₄×D₄	C₂³×C₇	1	2	yes	—
828	#117	—	2	1	no	—
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	—	2	2	no	—
832	#117	—	2	2	no	—
833	#117	—	2	2	no	—
834	#117	C₂³×C₇	1	2	yes	—
835	#117	C₂³×C₇	1	2	yes	—
836	#117	C₂³×C₇	1	1	yes	characteristic
837	#117	C₂³×C₇	1	1	yes	characteristic
838	#117	C₂³×C₇	1	2	yes	—
839	#117	C₂³×C₇	1	1	yes	characteristic
840	C₂×C₄⋊C₄	—	2	1	no	—
841	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
844	C₂×C₂²⋊C₄	—	2	1	no	—
845	C₂×C₄²	—	2	1	no	—
846	#107	C₂³×C₇	1	1	yes	characteristic
847	#107	C₂³×C₇	1	1	yes	characteristic
848	#107	C₂³×C₇	1	2	yes	—
849	#107	C₂³×C₇	1	2	yes	—
850	#106	C₂³×C₇	1	1	yes	characteristic
851	#106	C₂³×C₇	1	1	yes	characteristic
852	#106	C₂³×C₇	1	2	yes	—
853	#106	C₂³×C₇	1	2	yes	—
854	C₄⋊C₈	C₂³×C₇	1	2	yes	—
855	C₄⋊C₈	C₂³×C₇	1	2	yes	—
856	#103	C₂³×C₇	1	2	yes	—
857	#103	C₂³×C₇	1	2	yes	—
858	#103	C₂³×C₇	1	2	yes	—
859	#103	C₂³×C₇	1	2	yes	—
860	#103	C₂³×C₇	1	2	yes	—
861	#103	C₂³×C₇	1	2	yes	—
862	#103	C₂³×C₇	1	2	yes	—
863	#103	C₂³×C₇	1	2	yes	—
864	#103	C₂³×C₇	1	1	yes	characteristic
865	#103	C₂³×C₇	1	2	yes	—
866	#103	C₂³×C₇	1	2	yes	—
867	#103	C₂³×C₇	1	1	yes	characteristic
868	#103	C₂³×C₇	1	1	yes	characteristic
869	#103	C₂³×C₇	1	1	yes	characteristic
870	#103	C₂³×C₇	1	2	yes	—
871	#103	C₂³×C₇	1	2	yes	—
872	#103	C₂³×C₇	1	2	yes	—
873	#103	C₂³×C₇	1	2	yes	—
874	#102	C₂³×C₇	1	1	yes	characteristic
875	#102	C₂³×C₇	1	1	yes	characteristic
876	#102	C₂³×C₇	1	1	yes	characteristic
877	#102	C₂³×C₇	1	1	yes	characteristic
878	#102	C₂³×C₇	1	2	yes	—
879	#102	C₂³×C₇	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
884	#97	C₂³×C₇	1	2	yes	—
885	C₄×C₈	C₂³×C₇	1	2	yes	—
886	C₂²×C₇	—	2	1	no	—
887	C₂²×C₇	—	2	1	no	—
888	C₂²×C₇	—	2	2	no	—
889	C₂²×C₇	—	2	1	no	—
890	C₂²×C₇	—	2	1	no	—
891	C₂²×C₇	—	2	2	no	—
892	C₂²×C₇	—	2	1	no	—
893	C₂²×C₇	—	2	1	no	—
894	C₂²×C₇	—	2	1	no	—
895	C₂²×C₇	—	2	1	no	—
896	C₂²×C₇	—	2	2	no	—
897	C₂²×C₇	—	4	4	no	—
898	C₂²×C₇	—	4	1	no	—
899	C₂²×C₇	—	4	1	no	—
900	C₂²×C₇	—	4	1	no	—
901	C₂²×C₇	—	4	1	no	—
902	C₂²×C₇	—	4	1	no	—
903	C₂²×C₇	—	4	1	no	—
904	C₂²×C₇	#546	1	2	yes	—
905	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
906	C₄×C₇	—	2	2	no	—
907	C₄×C₇	—	2	2	no	—
908	C₄×C₇	—	2	1	no	—
909	C₄×C₇	—	2	1	no	—
910	C₄×C₇	—	2	4	no	—
911	C₄×C₇	—	2	2	no	—
912	C₄×C₇	—	4	2	no	—
913	C₄×C₇	—	4	1	no	—
914	C₄×C₇	—	4	2	no	—
915	C₄×C₇	—	4	1	no	—
916	C₄×C₇	—	4	1	no	—
917	C₄×C₇	—	4	1	no	—
918	C₄×C₇	—	4	1	no	—
919	C₄×C₇	—	4	2	no	—
920	C₄×C₇	—	4	1	no	—
921	C₄×C₇	#546	1	2	yes	—
922	C₄×C₇	C₂²×#41	1	1	yes	characteristic
923	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
924	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
925	#41	—	2	2	no	—
926	#41	—	2	2	no	—
927	#41	—	2	4	no	—
928	#41	—	2	2	no	—
929	#41	—	2	2	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	4	2	no	—
933	#41	—	4	8	no	—
934	#41	—	4	4	no	—
935	C₂×Q₈	—	2	1	no	—
936	C₂×Q₈	—	2	2	no	—
937	C₂×Q₈	—	2	2	no	—
938	C₂×Q₈	—	2	1	no	—
939	C₂×Q₈	—	2	2	no	—
940	C₂×Q₈	—	2	2	no	—
941	C₂×Q₈	—	2	2	no	—
942	C₂×Q₈	—	2	4	no	—
943	C₂×Q₈	—	2	4	no	—
944	C₂×Q₈	—	2	4	no	—
945	C₂×Q₈	—	2	2	no	—
946	C₂×Q₈	—	2	2	no	—
947	C₂×Q₈	—	4	4	no	—
948	C₂×Q₈	—	4	2	no	—
949	C₂×Q₈	—	4	2	no	—
950	C₂×Q₈	—	4	2	no	—
951	C₂×Q₈	—	4	4	no	—
952	C₂×Q₈	—	4	4	no	—
953	C₂×Q₈	—	4	4	no	—
954	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
955	C₂×Q₈	C₇×#41	1	4	yes	—
956	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
957	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
958	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
959	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	1	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
969	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
970	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
971	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
972	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
973	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	1	no	—
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	2	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	—	4	4	no	—
989	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
990	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
991	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
992	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
993	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
994	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
995	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
996	Q₁₆	—	2	4	no	—
997	Q₁₆	—	4	1	no	—
998	Q₁₆	—	4	2	no	—
999	SD₁₆	—	2	4	no	—
1000	SD₁₆	—	4	1	no	—
1001	SD₁₆	—	4	1	no	—
1002	SD₁₆	—	4	2	no	—
1003	D₈	—	4	1	no	—
1004	M₁₆	—	2	2	no	—
1005	M₁₆	—	2	2	no	—
1006	M₁₆	—	4	1	no	—
1007	M₁₆	—	4	1	no	—
1008	M₁₆	—	4	1	no	—
1009	M₁₆	—	4	1	no	—
1010	M₁₆	—	4	2	no	—
1011	C₂×C₈	—	2	2	no	—
1012	C₂×C₈	—	2	2	no	—
1013	C₂×C₈	—	4	2	no	—
1014	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1015	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1016	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1017	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1018	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1019	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1039	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1040	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1041	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1042	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1043	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1044	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1045	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1046	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1047	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	1	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1069	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1070	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1071	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1072	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1073	C₄²	—	2	2	no	—
1074	C₄²	—	2	2	no	—
1075	C₄²	—	2	2	no	—
1076	C₄²	—	2	2	no	—
1077	C₄²	—	2	2	no	—
1078	C₄²	—	2	2	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	C₂⁴×C₇	1	2	yes	—
1082	C₂×C₇	—	2	2	no	—
1083	C₂×C₇	—	4	2	no	—
1084	C₂×C₇	—	4	1	no	—
1085	C₂×C₇	—	4	1	no	—
1086	C₂×C₇	—	8	1	no	—
1087	C₂×C₇	—	8	1	no	—
1088	C₂×C₇	C₂×#546	1	1	yes	characteristic
1089	C₂×C₇	#3586	1	1	yes	characteristic
1090	C₂×C₇	#3586	1	1	yes	characteristic
1091	C₂³	—	2	2	no	—
1092	C₂³	—	2	1	no	—
1093	C₂³	—	2	1	no	—
1094	C₂³	—	4	1	no	—
1095	C₂³	—	4	1	no	—
1096	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1097	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1098	C₂³	C₂²×C₇×D₄	1	2	yes	—
1099	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1100	Q₈	—	2	2	no	—
1101	Q₈	—	2	4	no	—
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	1	no	—
1104	Q₈	—	2	2	no	—
1105	Q₈	—	2	1	no	—
1106	Q₈	—	2	1	no	—
1107	Q₈	—	2	2	no	—
1108	Q₈	—	2	1	no	—
1109	Q₈	—	4	4	no	—
1110	Q₈	—	4	4	no	—
1111	Q₈	—	4	4	no	—
1112	Q₈	—	4	2	no	—
1113	Q₈	—	8	2	no	—
1114	Q₈	C₂×C₇×#41	1	4	yes	—
1115	D₄	—	2	4	no	—
1116	D₄	—	2	1	no	—
1117	D₄	—	2	1	no	—
1118	D₄	—	2	1	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	2	2	no	—
1121	D₄	—	4	2	no	—
1122	D₄	—	4	2	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	8	1	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	1	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	4	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	4	no	—
1154	C₂×C₄	—	4	4	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	4	2	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	1	no	—
1160	C₂×C₄	—	8	2	no	—
1161	C₂×C₄	—	8	1	no	—
1162	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1163	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1164	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1165	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1166	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1167	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1168	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1169	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1170	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1171	C₈	—	2	2	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	1	no	—
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	2	no	—
1177	C₇	#61176	1	1	yes	characteristic, direct product factor, Sylow
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	1	no	—
1186	C₂²	—	2	1	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	4	4	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	C₇×#546	1	2	yes	—
1197	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1198	C₄	—	2	2	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	2	1	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	4	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	4	2	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	2	no	—
1212	C₄	—	4	1	no	—
1213	C₄	C₇×#546	1	2	yes	—
1214	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1215	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1216	C₂	—	2	2	no	—
1217	C₂	—	4	1	no	—
1218	C₂	—	4	1	no	—
1219	C₂	—	4	2	no	—
1220	C₂	—	8	1	no	—
1221	C₂	—	8	1	no	—
1222	C₂	C₂×C₇×#546	1	1	yes	characteristic
1223	C₂	C₇×#3586	1	1	yes	characteristic
1224	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3493	C₂	semidirect
2. C₇×#3486	C₂	semidirect
3. C₇×#3329	C₂	semidirect
4. C₇×#3328	C₂	semidirect
5. C₇×#3327	C₂	semidirect
6. C₇×#3326	C₂	semidirect
7. C₇×#3321	C₂	semidirect
8. C₇×#3320	C₂	semidirect
9. C₇×#3313	C₂	semidirect
10. C₇×#3312	C₂	semidirect
11. C₇×#3137	C₂	semidirect
12. C₇×#3097	C₂	semidirect
13. C₇×#3093	C₂	semidirect
14. C₇×#3082	C₂	semidirect
15. C₇×#3063	C₂	semidirect
16. C₇×#3054	C₂	semidirect
17. C₇×#3046	C₂	semidirect
18. C₇×#3013	C₂	semidirect
19. C₇×#3004	C₂	semidirect
20. C₇×#2947	C₂	semidirect
21. C₇×#2930	C₂	semidirect
22. C₇×#2898	C₂	semidirect
23. C₂×C₇×#419	C₂	semidirect
62. C₇×#491	C₂²	semidirect
63. C₇×#489	C₂²	semidirect
64. C₇×#488	C₂²	semidirect
65. C₇×#487	C₂²	semidirect
68. C₇×#485	C₂²	semidirect
69. C₇×#485	C₂²	semidirect
70. C₇×#484	C₂²	semidirect
71. C₇×#483	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#479	C₂²	semidirect
76. C₇×#477	C₂²	semidirect
77. C₇×#475	C₂²	semidirect
80. C₇×#470	C₂²	semidirect
87. C₇×#468	C₂²	semidirect
88. C₇×#467	C₂²	semidirect
89. C₇×#465	C₂²	semidirect
90. C₇×#464	C₂²	semidirect
91. C₇×#463	C₂²	semidirect
92. C₇×#462	C₂²	semidirect
93. C₇×#461	C₂²	semidirect
94. C₇×#452	C₂²	semidirect
97. C₇×#451	C₂²	semidirect
98. C₇×#449	C₂²	semidirect
101. C₇×#448	C₂²	semidirect
102. C₇×#441	C₂²	semidirect
103. C₇×#440	C₂²	semidirect
104. C₄×C₇×Q₁₆	C₂²	semidirect
105. C₄×C₇×SD₁₆	C₂²	semidirect
120. C₇×#419	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
126. C₇×#416	C₂²	semidirect
131. C₂×C₇×#103	C₂²	semidirect
135. #61176	C₇	direct (N × H)
322. #3493	C₂×C₇	semidirect
323. #3486	C₂×C₇	semidirect
324. #3329	C₂×C₇	semidirect
325. #3328	C₂×C₇	semidirect
326. #3327	C₂×C₇	semidirect
327. #3326	C₂×C₇	semidirect
328. #3321	C₂×C₇	semidirect
329. #3320	C₂×C₇	semidirect
330. #3313	C₂×C₇	semidirect
331. #3312	C₂×C₇	semidirect
332. #3137	C₂×C₇	semidirect
333. #3097	C₂×C₇	semidirect
334. #3093	C₂×C₇	semidirect
335. #3082	C₂×C₇	semidirect
336. #3063	C₂×C₇	semidirect
337. #3054	C₂×C₇	semidirect
338. #3046	C₂×C₇	semidirect
339. #3013	C₂×C₇	semidirect
340. #3004	C₂×C₇	semidirect
341. #2947	C₂×C₇	semidirect
342. #2930	C₂×C₇	semidirect
343. #2898	C₂×C₇	semidirect
344. C₂×#419	C₂×C₇	semidirect
541. #491	C₂²×C₇	semidirect
542. #489	C₂²×C₇	semidirect
543. #488	C₂²×C₇	semidirect
544. #487	C₂²×C₇	semidirect
547. #485	C₂²×C₇	semidirect
548. #485	C₂²×C₇	semidirect
549. #484	C₂²×C₇	semidirect
550. #483	C₂²×C₇	semidirect
553. #479	C₂²×C₇	semidirect
554. #479	C₂²×C₇	semidirect
555. #477	C₂²×C₇	semidirect
556. #475	C₂²×C₇	semidirect
559. #470	C₂²×C₇	semidirect
566. #468	C₂²×C₇	semidirect
567. #467	C₂²×C₇	semidirect
568. #465	C₂²×C₇	semidirect
569. #464	C₂²×C₇	semidirect
570. #463	C₂²×C₇	semidirect
571. #462	C₂²×C₇	semidirect
572. #461	C₂²×C₇	semidirect
573. #452	C₂²×C₇	semidirect
576. #451	C₂²×C₇	semidirect
577. #449	C₂²×C₇	semidirect
580. #448	C₂²×C₇	semidirect
581. #441	C₂²×C₇	semidirect
582. #440	C₂²×C₇	semidirect
583. C₄×Q₁₆	C₂²×C₇	semidirect
584. C₄×SD₁₆	C₂²×C₇	semidirect
599. #419	C₂²×C₇	semidirect
602. #417	C₂²×C₇	semidirect
605. #416	C₂²×C₇	semidirect
610. C₂×#103	C₂²×C₇	semidirect
1177. C₇	#61176	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×#3493	2
C₇×#3486	2
C₇×#3329	2
C₇×#3328	2
C₇×#3327	2
C₇×#3326	2
C₇×#3321	2
C₇×#3320	2
C₇×#3313	2
C₇×#3312	2
C₇×#3137	2
C₇×#3097	2
C₇×#3093	2
C₇×#3082	2
C₇×#3063	2
C₇×#3054	2
C₇×#3046	2
C₇×#3013	2
C₇×#3004	2
C₇×#2947	2
C₇×#2930	2
C₇×#2898	2
C₂×C₇×#419	2
#61176	7

Subgroups — C7×#61176 #13238392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61176 #13238392