Subgroups — C₇×#61190 #13238406

Order 1792.

2044 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3487	C₂	1	1	yes	maximal, characteristic
3	C₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₇×#3327	C₂	1	2	yes	maximal, complemented
5	C₇×#3317	C₂	1	2	yes	maximal, complemented
6	C₇×#3317	C₂	1	2	yes	maximal, complemented
7	C₇×#3316	C₂	1	2	yes	maximal, complemented
8	C₇×#3313	C₂	1	2	yes	maximal, complemented
9	C₇×#3304	C₂	1	2	yes	maximal, complemented
10	C₇×#3300	C₂	1	2	yes	maximal, complemented
11	C₇×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3057	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3043	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2950	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic
27	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₇×SD₁₆	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	C₂²	1	2	yes	complemented
32	C₇×#554	C₂²	1	2	yes	complemented
33	C₇×#552	—	2	2	no	—
34	C₇×#552	C₂²	1	2	yes	complemented
35	C₇×#552	C₂²	1	2	yes	complemented
36	C₇×#551	—	2	2	no	—
37	C₇×#550	—	2	1	no	—
38	C₇×#550	—	2	1	no	—
39	C₇×#550	C₂²	1	2	yes	—
40	C₇×#550	C₂²	1	2	yes	—
41	C₇×#548	—	2	1	no	—
42	C₇×#548	—	2	1	no	—
43	C₇×#548	C₂²	1	2	yes	—
44	C₇×#548	C₂²	1	2	yes	—
45	C₇×#544	C₂²	1	1	yes	characteristic
46	C₇×#542	—	2	1	no	—
47	C₇×#541	—	2	1	no	—
48	C₇×#536	C₂²	1	1	yes	characteristic
49	C₇×#535	—	2	2	no	—
50	C₇×#535	C₂²	1	1	yes	characteristic
51	C₇×#535	C₂²	1	1	yes	characteristic
52	C₇×#533	—	2	1	no	—
53	C₇×#529	—	2	1	no	—
54	C₇×#525	—	2	2	no	—
55	C₇×#525	C₂²	1	1	yes	characteristic
56	C₇×#525	C₂²	1	1	yes	characteristic
57	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#519	C₂²	1	1	yes	characteristic
60	C₇×#519	C₂²	1	1	yes	characteristic
61	C₂×C₇×#117	C₂²	1	1	yes	characteristic
62	C₇×#490	C₂²	1	2	yes	complemented
63	C₇×#489	C₂²	1	2	yes	complemented
64	C₇×#488	C₂²	1	2	yes	complemented
65	C₇×#486	C₂²	1	2	yes	complemented
66	C₇×#485	C₂²	1	1	yes	characteristic, complemented
67	C₇×#485	C₂²	1	1	yes	characteristic, complemented
68	C₇×#484	C₂²	1	1	yes	characteristic, complemented
69	C₇×#483	C₂²	1	1	yes	characteristic, complemented
70	C₇×#482	C₂²	1	1	yes	characteristic, complemented
71	C₇×#482	C₂²	1	2	yes	complemented
72	C₇×#482	C₂²	1	2	yes	complemented
73	C₇×#482	C₂²	1	1	yes	characteristic, complemented
74	C₇×#481	C₂²	1	2	yes	complemented
75	C₇×#481	C₂²	1	1	yes	characteristic, complemented
76	C₇×#480	C₂²	1	2	yes	complemented
77	C₇×#480	C₂²	1	1	yes	characteristic, complemented
78	C₇×#479	C₂²	1	2	yes	complemented
79	C₇×#479	C₂²	1	2	yes	complemented
80	C₇×#477	C₂²	1	2	yes	complemented
81	C₇×#475	C₂²	1	2	yes	complemented
82	C₇×#470	C₂²	1	2	yes	complemented
83	C₇×#468	C₂²	1	2	yes	complemented
84	C₇×#468	C₂²	1	2	yes	complemented
85	C₇×#468	C₂²	1	2	yes	complemented
86	C₇×#467	C₂²	1	2	yes	complemented
87	C₇×#465	C₂²	1	2	yes	complemented
88	C₇×#465	C₂²	1	2	yes	complemented
89	C₇×#465	C₂²	1	2	yes	complemented
90	C₇×#464	C₂²	1	2	yes	complemented
91	C₇×#464	C₂²	1	2	yes	complemented
92	C₇×#460	C₂²	1	2	yes	complemented
93	C₇×#460	C₂²	1	2	yes	complemented
94	C₇×#452	C₂²	1	2	yes	—
95	C₇×#452	C₂²	1	2	yes	—
96	C₇×#452	C₂²	1	2	yes	—
97	C₇×#452	C₂²	1	2	yes	—
98	C₇×#452	C₂²	1	2	yes	complemented
99	C₇×#452	C₂²	1	2	yes	complemented
100	C₇×#451	C₂²	1	2	yes	complemented
101	C₇×#451	C₂²	1	2	yes	complemented
102	C₇×#441	C₂²	1	2	yes	complemented
103	C₇×#441	C₂²	1	2	yes	complemented
104	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
105	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
106	C₇×#436	C₂²	1	2	yes	complemented
107	C₇×#435	C₂²	1	2	yes	complemented
108	C₇×#435	C₂²	1	2	yes	complemented
109	C₇×C₈×D₄	C₂²	1	2	yes	complemented
110	C₇×#428	C₂²	1	1	yes	characteristic
111	C₇×#427	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	1	yes	characteristic
117	C₇×#419	C₂²	1	2	yes	complemented
118	C₇×#418	C₂²	1	1	yes	characteristic
119	C₇×#418	C₂²	1	1	yes	characteristic
120	C₇×#417	C₂²	1	1	yes	characteristic
121	C₇×#417	C₂²	1	2	yes	—
122	C₇×#417	C₂²	1	2	yes	—
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	—
127	C₇×#416	C₂²	1	2	yes	—
128	C₇×#416	C₂²	1	2	yes	complemented
129	C₂×C₇×#103	C₂²	1	1	yes	characteristic
130	C₂×C₇×#103	C₂²	1	2	yes	complemented
131	C₂×C₇×#102	C₂²	1	1	yes	characteristic
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₇×#405	C₂²	1	1	yes	characteristic
135	#61190	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	—	2	1	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	—	2	4	no	—
143	C₂×C₇×#41	—	4	2	no	—
144	C₂×C₇×#41	C₂³	1	1	yes	characteristic
145	C₂×C₇×#41	C₂³	1	2	yes	—
146	C₂×C₇×#41	C₂³	1	2	yes	—
147	C₂×C₇×#41	C₂³	1	2	yes	—
148	C₂×C₇×#41	C₂³	1	1	yes	characteristic
149	C₂²×C₇×Q₈	—	2	1	no	—
150	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₇×Q₈	C₂³	1	2	yes	—
152	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₇×D₄	—	2	1	no	—
154	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₇	—	2	1	no	—
156	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
157	C₇×#137	—	4	2	no	—
158	C₂×C₇×Q₁₆	—	2	4	no	—
159	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
160	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
161	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
162	C₂×C₇×SD₁₆	—	4	2	no	—
163	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
166	C₇×#131	—	4	2	no	—
167	C₂×C₇×M₁₆	—	4	2	no	—
168	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
169	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
170	C₂×C₇×M₁₆	C₂³	1	2	yes	—
171	C₂×C₇×M₁₆	C₂³	1	2	yes	—
172	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
173	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
174	C₂²×C₇×C₈	C₂³	1	2	yes	—
175	C₂²×C₇×C₈	C₂³	1	2	yes	—
176	C₇×C₄⋊Q₈	—	2	1	no	—
177	C₇×C₄⋊Q₈	—	2	1	no	—
178	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
179	C₇×#127	—	2	2	no	—
180	C₇×#127	—	2	2	no	—
181	C₇×#127	—	2	1	no	—
182	C₇×#127	C₂³	1	2	yes	—
183	C₇×#126	—	2	2	no	—
184	C₇×#126	—	2	2	no	—
185	C₇×#126	—	2	2	no	—
186	C₇×#126	—	2	2	no	—
187	C₇×#125	—	2	1	no	—
188	C₇×#125	—	2	2	no	—
189	C₇×#125	—	2	2	no	—
190	C₇×#125	—	2	2	no	—
191	C₇×#125	C₂³	1	2	yes	—
192	C₇×#124	—	2	1	no	—
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	C₂³	1	2	yes	—
198	C₇×#123	—	2	2	no	—
199	C₇×#123	—	2	2	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	1	no	—
202	C₇×#123	D₄	1	2	yes	—
203	C₇×C₂²⋊Q₈	—	2	1	no	—
204	C₇×C₂²⋊Q₈	—	2	1	no	—
205	C₇×C₂²⋊Q₈	—	2	2	no	—
206	C₇×C₂²⋊Q₈	—	2	2	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	—	2	2	no	—
209	C₇×C₂²⋊Q₈	—	2	2	no	—
210	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
212	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	1	no	—
221	C₇×#121	—	2	1	no	—
222	C₇×#121	—	2	2	no	—
223	C₇×#121	—	2	2	no	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	D₄	1	1	yes	characteristic
227	C₇×#121	D₄	1	1	yes	characteristic
228	C₇×#121	C₂³	1	1	yes	characteristic
229	C₇×#121	C₂³	1	2	yes	—
230	C₇×#121	C₂³	1	2	yes	—
231	C₇×#121	C₂³	1	1	yes	characteristic
232	C₇×#120	—	2	1	no	—
233	C₇×#120	—	2	2	no	—
234	C₇×#120	—	2	2	no	—
235	C₇×#120	D₄	1	2	yes	—
236	C₄×C₇×Q₈	—	2	1	no	—
237	C₄×C₇×Q₈	—	2	1	no	—
238	C₄×C₇×Q₈	—	2	1	no	—
239	C₄×C₇×Q₈	—	2	1	no	—
240	C₄×C₇×Q₈	—	2	1	no	—
241	C₄×C₇×Q₈	—	2	2	no	—
242	C₄×C₇×Q₈	C₂³	1	2	yes	—
243	C₄×C₇×Q₈	C₂³	1	2	yes	—
244	C₄×C₇×Q₈	C₂³	1	2	yes	—
245	C₄×C₇×Q₈	C₂³	1	2	yes	—
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	2	no	—
248	C₄×C₇×D₄	—	2	2	no	—
249	C₄×C₇×D₄	—	2	1	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	2	no	—
254	C₄×C₇×D₄	—	2	2	no	—
255	C₄×C₇×D₄	C₂³	1	2	yes	—
256	C₄×C₇×D₄	C₂³	1	2	yes	—
257	C₇×#117	—	2	1	no	—
258	C₇×#117	—	2	1	no	—
259	C₇×#117	—	2	2	no	—
260	C₇×#117	—	2	2	no	—
261	C₇×#117	—	2	2	no	—
262	C₇×#117	—	2	2	no	—
263	C₇×#117	C₂³	1	2	yes	—
264	C₇×#117	C₂³	1	1	yes	characteristic
265	C₇×#117	C₂³	1	1	yes	characteristic
266	C₇×#117	C₂³	1	1	yes	characteristic
267	C₇×#117	C₂³	1	1	yes	characteristic
268	C₇×#117	C₂³	1	1	yes	characteristic
269	C₇×#117	C₂³	1	1	yes	characteristic
270	C₂×C₇×C₄⋊C₄	—	2	1	no	—
271	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₄²×C₇	—	2	1	no	—
278	C₇×#107	C₂³	1	2	yes	—
279	C₇×#107	C₂³	1	1	yes	characteristic
280	C₇×#107	C₂³	1	1	yes	characteristic
281	C₇×#107	C₂³	1	1	yes	characteristic
282	C₇×#107	C₂³	1	1	yes	characteristic
283	C₇×#106	C₂³	1	2	yes	—
284	C₇×#106	C₂³	1	1	yes	characteristic
285	C₇×#106	C₂³	1	1	yes	characteristic
286	C₇×#106	C₂³	1	1	yes	characteristic
287	C₇×#106	C₂³	1	1	yes	characteristic
288	C₇×C₄⋊C₈	C₂³	1	2	yes	—
289	C₇×C₄⋊C₈	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#103	C₂³	1	1	yes	characteristic
299	C₇×#103	C₂³	1	1	yes	characteristic
300	C₇×#103	C₂³	1	1	yes	characteristic
301	C₇×#103	C₂³	1	2	yes	—
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×#102	C₂³	1	2	yes	—
309	C₇×#102	C₂³	1	1	yes	characteristic
310	C₇×#102	C₂³	1	2	yes	—
311	C₇×#102	C₂³	1	1	yes	characteristic
312	C₇×#102	C₂³	1	1	yes	characteristic
313	C₇×#102	C₂³	1	2	yes	—
314	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
319	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
320	C₇×#97	C₂³	1	2	yes	—
321	C₄×C₇×C₈	C₂³	1	2	yes	—
322	#3495	C₂×C₇	1	1	yes	characteristic, complemented
323	#3487	C₂×C₇	1	1	yes	characteristic
324	#3333	C₂×C₇	1	2	yes	complemented
325	#3327	C₂×C₇	1	2	yes	complemented
326	#3317	C₂×C₇	1	2	yes	complemented
327	#3317	C₂×C₇	1	2	yes	complemented
328	#3316	C₂×C₇	1	2	yes	complemented
329	#3313	C₂×C₇	1	2	yes	complemented
330	#3304	C₂×C₇	1	2	yes	complemented
331	#3300	C₂×C₇	1	2	yes	complemented
332	#3136	C₂×C₇	1	1	yes	characteristic, complemented
333	#3096	C₂×C₇	1	1	yes	characteristic, complemented
334	#3091	C₂×C₇	1	1	yes	characteristic, complemented
335	#3082	C₂×C₇	1	1	yes	characteristic, complemented
336	#3057	C₂×C₇	1	1	yes	characteristic, complemented
337	#3056	C₂×C₇	1	1	yes	characteristic, complemented
338	#3043	C₂×C₇	1	1	yes	characteristic, complemented
339	#3011	C₂×C₇	1	1	yes	characteristic, complemented
340	C₂×#452	C₂×C₇	1	1	yes	characteristic, complemented
341	#2950	C₂×C₇	1	1	yes	characteristic, complemented
342	#2933	C₂×C₇	1	1	yes	characteristic, complemented
343	#2898	C₂×C₇	1	1	yes	characteristic, complemented
344	#2896	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	1	no	—
346	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
347	C₇×#41	—	2	2	no	—
348	C₇×#41	—	2	2	no	—
349	C₇×#41	—	2	4	no	—
350	C₇×#41	—	2	4	no	—
351	C₇×#41	—	2	4	no	—
352	C₇×#41	—	2	2	no	—
353	C₇×#41	—	2	2	no	—
354	C₇×#41	—	4	2	no	—
355	C₇×#41	—	4	2	no	—
356	C₇×#41	—	4	2	no	—
357	C₇×#41	—	4	8	no	—
358	C₇×#41	—	4	4	no	—
359	C₇×#41	—	4	4	no	—
360	C₇×#41	—	4	4	no	—
361	C₂×C₇×Q₈	—	2	1	no	—
362	C₂×C₇×Q₈	—	2	1	no	—
363	C₂×C₇×Q₈	—	2	2	no	—
364	C₂×C₇×Q₈	—	2	2	no	—
365	C₂×C₇×Q₈	—	2	2	no	—
366	C₂×C₇×Q₈	—	2	4	no	—
367	C₂×C₇×Q₈	—	2	2	no	—
368	C₂×C₇×Q₈	—	2	2	no	—
369	C₂×C₇×Q₈	—	4	2	no	—
370	C₂×C₇×Q₈	—	4	4	no	—
371	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
372	C₂×C₇×Q₈	#41	1	4	yes	—
373	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
375	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
376	C₂×C₇×D₄	—	2	1	no	—
377	C₂×C₇×D₄	—	2	2	no	—
378	C₂×C₇×D₄	—	2	2	no	—
379	C₂×C₇×D₄	—	2	2	no	—
380	C₂×C₇×D₄	—	2	2	no	—
381	C₂×C₇×D₄	—	2	2	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	2	no	—
387	C₂×C₇×D₄	—	2	2	no	—
388	C₂×C₇×D₄	—	2	2	no	—
389	C₂×C₇×D₄	—	4	4	no	—
390	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
391	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
392	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
393	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
394	C₂×C₇×D₄	C₂⁴	1	2	yes	—
395	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₇	—	2	1	no	—
397	C₂²×C₄×C₇	—	2	2	no	—
398	C₂²×C₄×C₇	—	2	2	no	—
399	C₂²×C₄×C₇	—	2	1	no	—
400	C₂²×C₄×C₇	—	2	1	no	—
401	C₂²×C₄×C₇	—	2	2	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	2	no	—
406	C₂²×C₄×C₇	—	2	1	no	—
407	C₂²×C₄×C₇	—	2	2	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	1	yes	characteristic
414	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
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	—	2	4	no	—
419	C₇×Q₁₆	—	4	2	no	—
420	C₇×SD₁₆	—	4	2	no	—
421	C₇×SD₁₆	—	4	2	no	—
422	C₇×SD₁₆	—	4	2	no	—
423	C₇×M₁₆	—	2	2	no	—
424	C₇×M₁₆	—	2	2	no	—
425	C₇×M₁₆	—	4	2	no	—
426	C₇×M₁₆	—	4	2	no	—
427	C₂×C₇×C₈	—	2	2	no	—
428	C₂×C₇×C₈	—	2	2	no	—
429	C₂×C₇×C₈	—	4	2	no	—
430	C₂×C₇×C₈	—	4	2	no	—
431	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
432	C₂×C₇×C₈	C₂⁴	1	2	yes	—
433	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
434	C₂×C₇×C₈	C₂⁴	1	2	yes	—
435	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
436	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	2	no	—
439	C₇×C₄⋊C₄	—	2	1	no	—
440	C₇×C₄⋊C₄	—	2	1	no	—
441	C₇×C₄⋊C₄	—	2	1	no	—
442	C₇×C₄⋊C₄	—	2	2	no	—
443	C₇×C₄⋊C₄	—	2	2	no	—
444	C₇×C₄⋊C₄	—	2	2	no	—
445	C₇×C₄⋊C₄	—	2	2	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	1	no	—
452	C₇×C₄⋊C₄	—	2	2	no	—
453	C₇×C₄⋊C₄	—	2	2	no	—
454	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
455	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
456	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
457	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
458	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
459	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
460	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
461	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
462	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
463	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
464	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
465	C₇×C₂²⋊C₄	—	2	1	no	—
466	C₇×C₂²⋊C₄	—	2	1	no	—
467	C₇×C₂²⋊C₄	—	2	1	no	—
468	C₇×C₂²⋊C₄	—	2	1	no	—
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	2	no	—
474	C₇×C₂²⋊C₄	—	2	1	no	—
475	C₇×C₂²⋊C₄	—	2	1	no	—
476	C₇×C₂²⋊C₄	—	2	2	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	2	no	—
482	C₇×C₂²⋊C₄	—	2	2	no	—
483	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
484	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
485	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
486	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
487	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
488	C₄²×C₇	—	2	1	no	—
489	C₄²×C₇	—	2	1	no	—
490	C₄²×C₇	—	2	1	no	—
491	C₄²×C₇	—	2	1	no	—
492	C₄²×C₇	—	2	2	no	—
493	C₄²×C₇	—	2	2	no	—
494	C₄²×C₇	—	2	2	no	—
495	C₄²×C₇	—	2	2	no	—
496	C₄²×C₇	—	2	2	no	—
497	C₄²×C₇	—	2	1	no	—
498	C₄²×C₇	C₂⁴	1	2	yes	—
499	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
500	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
501	C₂×#137	C₂²×C₇	1	1	yes	characteristic
502	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
503	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
504	C₂×#131	C₂²×C₇	1	1	yes	characteristic
505	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
506	#556	C₂²×C₇	1	2	yes	complemented
507	#554	C₂²×C₇	1	2	yes	complemented
508	#552	—	2	2	no	—
509	#552	C₂²×C₇	1	2	yes	complemented
510	#552	C₂²×C₇	1	2	yes	complemented
511	#551	—	2	2	no	—
512	#550	—	2	1	no	—
513	#550	—	2	1	no	—
514	#550	C₂²×C₇	1	2	yes	—
515	#550	C₂²×C₇	1	2	yes	—
516	#548	—	2	1	no	—
517	#548	—	2	1	no	—
518	#548	C₂²×C₇	1	2	yes	—
519	#548	C₂²×C₇	1	2	yes	—
520	#544	C₂²×C₇	1	1	yes	characteristic
521	#542	—	2	1	no	—
522	#541	—	2	1	no	—
523	#536	C₂²×C₇	1	1	yes	characteristic
524	#535	—	2	2	no	—
525	#535	C₂²×C₇	1	1	yes	characteristic
526	#535	C₂²×C₇	1	1	yes	characteristic
527	#533	—	2	1	no	—
528	#529	—	2	1	no	—
529	#525	—	2	2	no	—
530	#525	C₂²×C₇	1	1	yes	characteristic
531	#525	C₂²×C₇	1	1	yes	characteristic
532	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
533	#520	C₂²×C₇	1	1	yes	characteristic
534	#519	C₂²×C₇	1	1	yes	characteristic
535	#519	C₂²×C₇	1	1	yes	characteristic
536	C₂×#117	C₂²×C₇	1	1	yes	characteristic
537	#490	C₂²×C₇	1	2	yes	complemented
538	#489	C₂²×C₇	1	2	yes	complemented
539	#488	C₂²×C₇	1	2	yes	complemented
540	#486	C₂²×C₇	1	2	yes	complemented
541	#485	C₂²×C₇	1	1	yes	characteristic, complemented
542	#485	C₂²×C₇	1	1	yes	characteristic, complemented
543	#484	C₂²×C₇	1	1	yes	characteristic, complemented
544	#483	C₂²×C₇	1	1	yes	characteristic, complemented
545	#482	C₂²×C₇	1	1	yes	characteristic, complemented
546	#482	C₂²×C₇	1	1	yes	characteristic, complemented
547	#482	C₂²×C₇	1	2	yes	complemented
548	#482	C₂²×C₇	1	2	yes	complemented
549	#481	C₂²×C₇	1	1	yes	characteristic, complemented
550	#481	C₂²×C₇	1	2	yes	complemented
551	#480	C₂²×C₇	1	1	yes	characteristic, complemented
552	#480	C₂²×C₇	1	2	yes	complemented
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	2	yes	complemented
558	#468	C₂²×C₇	1	2	yes	complemented
559	#468	C₂²×C₇	1	2	yes	complemented
560	#468	C₂²×C₇	1	2	yes	complemented
561	#467	C₂²×C₇	1	2	yes	complemented
562	#465	C₂²×C₇	1	2	yes	complemented
563	#465	C₂²×C₇	1	2	yes	complemented
564	#465	C₂²×C₇	1	2	yes	complemented
565	#464	C₂²×C₇	1	2	yes	complemented
566	#464	C₂²×C₇	1	2	yes	complemented
567	#460	C₂²×C₇	1	2	yes	complemented
568	#460	C₂²×C₇	1	2	yes	complemented
569	#452	C₂²×C₇	1	2	yes	—
570	#452	C₂²×C₇	1	2	yes	—
571	#452	C₂²×C₇	1	2	yes	—
572	#452	C₂²×C₇	1	2	yes	—
573	#452	C₂²×C₇	1	2	yes	complemented
574	#452	C₂²×C₇	1	2	yes	complemented
575	#451	C₂²×C₇	1	2	yes	complemented
576	#451	C₂²×C₇	1	2	yes	complemented
577	#441	C₂²×C₇	1	2	yes	complemented
578	#441	C₂²×C₇	1	2	yes	complemented
579	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
580	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
581	#436	C₂²×C₇	1	2	yes	complemented
582	#435	C₂²×C₇	1	2	yes	complemented
583	#435	C₂²×C₇	1	2	yes	complemented
584	C₈×D₄	C₂²×C₇	1	2	yes	complemented
585	#428	C₂²×C₇	1	1	yes	characteristic
586	#427	C₂²×C₇	1	1	yes	characteristic
587	#427	C₂²×C₇	1	1	yes	characteristic
588	#424	C₂²×C₇	1	1	yes	characteristic
589	#419	C₂²×C₇	1	1	yes	characteristic
590	#419	C₂²×C₇	1	1	yes	characteristic
591	#419	C₂²×C₇	1	1	yes	characteristic
592	#419	C₂²×C₇	1	2	yes	complemented
593	#418	C₂²×C₇	1	1	yes	characteristic
594	#418	C₂²×C₇	1	1	yes	characteristic
595	#417	C₂²×C₇	1	2	yes	—
596	#417	C₂²×C₇	1	1	yes	characteristic
597	#417	C₂²×C₇	1	2	yes	—
598	#417	C₂²×C₇	1	2	yes	complemented
599	#416	C₂²×C₇	1	1	yes	characteristic
600	#416	C₂²×C₇	1	1	yes	characteristic
601	#416	C₂²×C₇	1	2	yes	—
602	#416	C₂²×C₇	1	2	yes	—
603	#416	C₂²×C₇	1	2	yes	complemented
604	C₂×#103	C₂²×C₇	1	1	yes	characteristic
605	C₂×#103	C₂²×C₇	1	2	yes	complemented
606	C₂×#102	C₂²×C₇	1	1	yes	characteristic
607	#408	C₂²×C₇	1	1	yes	characteristic
608	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
609	#405	C₂²×C₇	1	1	yes	characteristic
610	C₂³×C₇	—	2	2	no	—
611	C₂³×C₇	—	2	2	no	—
612	C₂³×C₇	—	2	1	no	—
613	C₂³×C₇	—	4	1	no	—
614	C₂³×C₇	—	4	1	no	—
615	C₂³×C₇	—	4	2	no	—
616	C₂³×C₇	—	8	1	no	—
617	C₂³×C₇	—	8	1	no	—
618	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
619	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
620	C₂³×C₇	C₂²×D₄	1	2	yes	—
621	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
622	C₇×Q₈	—	2	4	no	—
623	C₇×Q₈	—	2	2	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	—	4	4	no	—
630	C₇×Q₈	—	4	2	no	—
631	C₇×Q₈	—	8	2	no	—
632	C₇×Q₈	C₂×#41	1	4	yes	—
633	C₇×D₄	—	2	4	no	—
634	C₇×D₄	—	2	2	no	—
635	C₇×D₄	—	2	2	no	—
636	C₇×D₄	—	2	1	no	—
637	C₇×D₄	—	2	2	no	—
638	C₇×D₄	—	2	1	no	—
639	C₇×D₄	—	4	2	no	—
640	C₇×D₄	—	4	2	no	—
641	C₇×D₄	—	4	4	no	—
642	C₇×D₄	—	4	4	no	—
643	C₇×D₄	—	4	4	no	—
644	C₇×D₄	—	4	2	no	—
645	C₇×D₄	—	4	2	no	—
646	C₇×D₄	—	8	2	no	—
647	C₇×D₄	—	8	2	no	—
648	C₇×D₄	—	8	2	no	—
649	C₇×D₄	—	8	1	no	—
650	C₇×D₄	—	8	2	no	—
651	C₇×D₄	—	8	1	no	—
652	C₂×C₄×C₇	—	2	2	no	—
653	C₂×C₄×C₇	—	2	4	no	—
654	C₂×C₄×C₇	—	2	2	no	—
655	C₂×C₄×C₇	—	2	2	no	—
656	C₂×C₄×C₇	—	2	2	no	—
657	C₂×C₄×C₇	—	2	1	no	—
658	C₂×C₄×C₇	—	2	1	no	—
659	C₂×C₄×C₇	—	2	2	no	—
660	C₂×C₄×C₇	—	2	1	no	—
661	C₂×C₄×C₇	—	2	2	no	—
662	C₂×C₄×C₇	—	2	1	no	—
663	C₂×C₄×C₇	—	2	1	no	—
664	C₂×C₄×C₇	—	2	1	no	—
665	C₂×C₄×C₇	—	2	1	no	—
666	C₂×C₄×C₇	—	2	1	no	—
667	C₂×C₄×C₇	—	2	1	no	—
668	C₂×C₄×C₇	—	2	2	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	—	4	4	no	—
673	C₂×C₄×C₇	—	4	4	no	—
674	C₂×C₄×C₇	—	4	4	no	—
675	C₂×C₄×C₇	—	4	4	no	—
676	C₂×C₄×C₇	—	4	2	no	—
677	C₂×C₄×C₇	—	4	2	no	—
678	C₂×C₄×C₇	—	4	2	no	—
679	C₂×C₄×C₇	—	8	2	no	—
680	C₂×C₄×C₇	—	8	1	no	—
681	C₂×C₄×C₇	—	8	1	no	—
682	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
683	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
684	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
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	C₂×#41	1	2	yes	—
689	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
690	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
691	C₇×C₈	—	2	1	no	—
692	C₇×C₈	—	2	1	no	—
693	C₇×C₈	—	2	1	no	—
694	C₇×C₈	—	2	1	no	—
695	C₇×C₈	—	2	2	no	—
696	C₇×C₈	—	2	2	no	—
697	2₋¹⁺⁴	—	2	4	no	—
698	2₋¹⁺⁴	—	4	2	no	—
699	C₂×#41	—	2	2	no	—
700	C₂×#41	—	2	1	no	—
701	C₂×#41	—	2	1	no	—
702	C₂×#41	—	2	1	no	—
703	C₂×#41	—	2	4	no	—
704	C₂×#41	—	4	2	no	—
705	C₂×#41	C₂³×C₇	1	1	yes	characteristic
706	C₂×#41	C₂³×C₇	1	2	yes	—
707	C₂×#41	C₂³×C₇	1	2	yes	—
708	C₂×#41	C₂³×C₇	1	2	yes	—
709	C₂×#41	C₂³×C₇	1	1	yes	characteristic
710	C₂²×Q₈	—	2	1	no	—
711	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
712	C₂²×Q₈	C₂³×C₇	1	2	yes	—
713	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
714	C₂²×D₄	—	2	1	no	—
715	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
716	C₂³×C₄	—	2	1	no	—
717	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
718	#137	—	4	2	no	—
719	C₂×Q₁₆	—	2	4	no	—
720	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
721	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
722	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
723	C₂×SD₁₆	—	4	2	no	—
724	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
727	#131	—	4	2	no	—
728	C₂×M₁₆	—	4	2	no	—
729	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
730	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
731	C₂×M₁₆	C₂³×C₇	1	2	yes	—
732	C₂×M₁₆	C₂³×C₇	1	2	yes	—
733	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
734	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
735	C₂²×C₈	C₂³×C₇	1	2	yes	—
736	C₂²×C₈	C₂³×C₇	1	2	yes	—
737	C₄⋊Q₈	—	2	1	no	—
738	C₄⋊Q₈	—	2	1	no	—
739	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
740	#127	—	2	2	no	—
741	#127	—	2	2	no	—
742	#127	—	2	1	no	—
743	#127	C₂³×C₇	1	2	yes	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#125	—	2	1	no	—
749	#125	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	2	no	—
752	#125	C₂³×C₇	1	2	yes	—
753	#124	—	2	1	no	—
754	#124	—	2	1	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	C₂³×C₇	1	2	yes	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	1	no	—
763	#123	C₇×D₄	1	2	yes	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
772	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
773	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	1	no	—
782	#121	—	2	1	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	C₇×D₄	1	1	yes	characteristic
788	#121	C₇×D₄	1	1	yes	characteristic
789	#121	C₂³×C₇	1	1	yes	characteristic
790	#121	C₂³×C₇	1	1	yes	characteristic
791	#121	C₂³×C₇	1	2	yes	—
792	#121	C₂³×C₇	1	2	yes	—
793	#120	—	2	1	no	—
794	#120	—	2	2	no	—
795	#120	—	2	2	no	—
796	#120	C₇×D₄	1	2	yes	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	2	no	—
803	C₄×Q₈	C₂³×C₇	1	2	yes	—
804	C₄×Q₈	C₂³×C₇	1	2	yes	—
805	C₄×Q₈	C₂³×C₇	1	2	yes	—
806	C₄×Q₈	C₂³×C₇	1	2	yes	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	C₂³×C₇	1	2	yes	—
817	C₄×D₄	C₂³×C₇	1	2	yes	—
818	#117	—	2	1	no	—
819	#117	—	2	1	no	—
820	#117	—	2	2	no	—
821	#117	—	2	2	no	—
822	#117	—	2	2	no	—
823	#117	—	2	2	no	—
824	#117	C₂³×C₇	1	1	yes	characteristic
825	#117	C₂³×C₇	1	1	yes	characteristic
826	#117	C₂³×C₇	1	1	yes	characteristic
827	#117	C₂³×C₇	1	1	yes	characteristic
828	#117	C₂³×C₇	1	1	yes	characteristic
829	#117	C₂³×C₇	1	2	yes	—
830	#117	C₂³×C₇	1	1	yes	characteristic
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
834	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
835	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
836	C₂×C₂²⋊C₄	—	2	1	no	—
837	C₂×C₂²⋊C₄	—	2	1	no	—
838	C₂×C₄²	—	2	1	no	—
839	#107	C₂³×C₇	1	1	yes	characteristic
840	#107	C₂³×C₇	1	1	yes	characteristic
841	#107	C₂³×C₇	1	1	yes	characteristic
842	#107	C₂³×C₇	1	1	yes	characteristic
843	#107	C₂³×C₇	1	2	yes	—
844	#106	C₂³×C₇	1	1	yes	characteristic
845	#106	C₂³×C₇	1	1	yes	characteristic
846	#106	C₂³×C₇	1	1	yes	characteristic
847	#106	C₂³×C₇	1	1	yes	characteristic
848	#106	C₂³×C₇	1	2	yes	—
849	C₄⋊C₈	C₂³×C₇	1	2	yes	—
850	C₄⋊C₈	C₂³×C₇	1	2	yes	—
851	#103	C₂³×C₇	1	2	yes	—
852	#103	C₂³×C₇	1	2	yes	—
853	#103	C₂³×C₇	1	1	yes	characteristic
854	#103	C₂³×C₇	1	2	yes	—
855	#103	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	1	yes	characteristic
860	#103	C₂³×C₇	1	1	yes	characteristic
861	#103	C₂³×C₇	1	1	yes	characteristic
862	#103	C₂³×C₇	1	2	yes	—
863	#103	C₂³×C₇	1	2	yes	—
864	#102	C₂³×C₇	1	2	yes	—
865	#102	C₂³×C₇	1	2	yes	—
866	#102	C₂³×C₇	1	1	yes	characteristic
867	#102	C₂³×C₇	1	2	yes	—
868	#102	C₂³×C₇	1	2	yes	—
869	#102	C₂³×C₇	1	2	yes	—
870	#102	C₂³×C₇	1	2	yes	—
871	#102	C₂³×C₇	1	1	yes	characteristic
872	#102	C₂³×C₇	1	1	yes	characteristic
873	#102	C₂³×C₇	1	1	yes	characteristic
874	#102	C₂³×C₇	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
878	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
879	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
881	#97	C₂³×C₇	1	2	yes	—
882	C₄×C₈	C₂³×C₇	1	2	yes	—
883	C₂²×C₇	—	2	1	no	—
884	C₂²×C₇	—	2	1	no	—
885	C₂²×C₇	—	2	2	no	—
886	C₂²×C₇	—	2	1	no	—
887	C₂²×C₇	—	2	1	no	—
888	C₂²×C₇	—	2	1	no	—
889	C₂²×C₇	—	2	2	no	—
890	C₂²×C₇	—	2	1	no	—
891	C₂²×C₇	—	2	1	no	—
892	C₂²×C₇	—	2	1	no	—
893	C₂²×C₇	—	2	2	no	—
894	C₂²×C₇	—	4	1	no	—
895	C₂²×C₇	—	4	2	no	—
896	C₂²×C₇	—	4	1	no	—
897	C₂²×C₇	—	4	2	no	—
898	C₂²×C₇	—	4	1	no	—
899	C₂²×C₇	—	4	2	no	—
900	C₂²×C₇	—	8	2	no	—
901	C₂²×C₇	—	8	4	no	—
902	C₂²×C₇	#546	1	2	yes	—
903	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
904	C₄×C₇	—	2	2	no	—
905	C₄×C₇	—	2	2	no	—
906	C₄×C₇	—	2	1	no	—
907	C₄×C₇	—	2	1	no	—
908	C₄×C₇	—	2	4	no	—
909	C₄×C₇	—	2	2	no	—
910	C₄×C₇	—	4	1	no	—
911	C₄×C₇	—	4	2	no	—
912	C₄×C₇	—	4	1	no	—
913	C₄×C₇	—	4	1	no	—
914	C₄×C₇	—	4	1	no	—
915	C₄×C₇	—	4	1	no	—
916	C₄×C₇	—	4	1	no	—
917	C₄×C₇	—	4	1	no	—
918	C₄×C₇	—	4	2	no	—
919	C₄×C₇	#546	1	2	yes	—
920	C₄×C₇	C₂²×#41	1	1	yes	characteristic
921	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
922	C₂⁴	—	2	1	no	—
923	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
924	#41	—	2	2	no	—
925	#41	—	2	2	no	—
926	#41	—	2	4	no	—
927	#41	—	2	4	no	—
928	#41	—	2	4	no	—
929	#41	—	2	2	no	—
930	#41	—	2	2	no	—
931	#41	—	4	2	no	—
932	#41	—	4	2	no	—
933	#41	—	4	2	no	—
934	#41	—	4	8	no	—
935	#41	—	4	4	no	—
936	#41	—	4	4	no	—
937	#41	—	4	4	no	—
938	C₂×Q₈	—	2	1	no	—
939	C₂×Q₈	—	2	1	no	—
940	C₂×Q₈	—	2	2	no	—
941	C₂×Q₈	—	2	2	no	—
942	C₂×Q₈	—	2	2	no	—
943	C₂×Q₈	—	2	4	no	—
944	C₂×Q₈	—	2	2	no	—
945	C₂×Q₈	—	2	2	no	—
946	C₂×Q₈	—	4	2	no	—
947	C₂×Q₈	—	4	4	no	—
948	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
949	C₂×Q₈	C₇×#41	1	4	yes	—
950	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
951	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
952	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	4	4	no	—
967	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
968	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
969	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
970	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
971	C₂×D₄	C₂⁴×C₇	1	2	yes	—
972	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	4	4	no	—
987	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
988	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
989	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
990	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
991	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
992	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
993	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
994	Q₁₆	—	2	4	no	—
995	Q₁₆	—	2	4	no	—
996	Q₁₆	—	4	2	no	—
997	SD₁₆	—	4	2	no	—
998	SD₁₆	—	4	2	no	—
999	SD₁₆	—	4	2	no	—
1000	M₁₆	—	2	2	no	—
1001	M₁₆	—	2	2	no	—
1002	M₁₆	—	4	2	no	—
1003	M₁₆	—	4	2	no	—
1004	C₂×C₈	—	2	2	no	—
1005	C₂×C₈	—	2	2	no	—
1006	C₂×C₈	—	4	2	no	—
1007	C₂×C₈	—	4	2	no	—
1008	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1009	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1010	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1011	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1012	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1013	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1032	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1033	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1034	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1036	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1037	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1038	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1039	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1040	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1041	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	1	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	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1061	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1062	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1063	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1064	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1065	C₄²	—	2	1	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	—	2	2	no	—
1070	C₄²	—	2	2	no	—
1071	C₄²	—	2	2	no	—
1072	C₄²	—	2	2	no	—
1073	C₄²	—	2	2	no	—
1074	C₄²	—	2	1	no	—
1075	C₄²	C₂⁴×C₇	1	2	yes	—
1076	C₂×C₇	—	2	2	no	—
1077	C₂×C₇	—	4	2	no	—
1078	C₂×C₇	—	4	1	no	—
1079	C₂×C₇	—	4	1	no	—
1080	C₂×C₇	—	8	1	no	—
1081	C₂×C₇	—	8	2	no	—
1082	C₂×C₇	C₂×#546	1	1	yes	characteristic
1083	C₂×C₇	#3584	1	1	yes	characteristic
1084	C₂×C₇	#3586	1	1	yes	characteristic
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	2	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	4	1	no	—
1089	C₂³	—	4	1	no	—
1090	C₂³	—	4	2	no	—
1091	C₂³	—	8	1	no	—
1092	C₂³	—	8	1	no	—
1093	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1094	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1095	C₂³	C₂²×C₇×D₄	1	2	yes	—
1096	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1097	Q₈	—	2	2	no	—
1098	Q₈	—	2	4	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	2	no	—
1101	Q₈	—	2	1	no	—
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	1	no	—
1104	Q₈	—	4	4	no	—
1105	Q₈	—	4	2	no	—
1106	Q₈	—	8	2	no	—
1107	Q₈	C₂×C₇×#41	1	4	yes	—
1108	D₄	—	2	4	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	2	1	no	—
1111	D₄	—	2	2	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	4	2	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	4	4	no	—
1117	D₄	—	4	4	no	—
1118	D₄	—	4	4	no	—
1119	D₄	—	4	2	no	—
1120	D₄	—	4	2	no	—
1121	D₄	—	8	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	1	no	—
1125	D₄	—	8	2	no	—
1126	D₄	—	8	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	4	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	2	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	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	4	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	8	2	no	—
1155	C₂×C₄	—	8	1	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1158	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1159	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1160	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1161	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1162	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1163	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1164	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1165	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1166	C₈	—	2	1	no	—
1167	C₈	—	2	1	no	—
1168	C₈	—	2	1	no	—
1169	C₈	—	2	1	no	—
1170	C₈	—	2	2	no	—
1171	C₈	—	2	2	no	—
1172	C₇	#61190	1	1	yes	characteristic, direct product factor, Sylow
1173	C₂²	—	2	1	no	—
1174	C₂²	—	2	1	no	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	2	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	2	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	8	2	no	—
1191	C₂²	—	8	4	no	—
1192	C₂²	C₇×#546	1	2	yes	—
1193	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1194	C₄	—	2	2	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	1	no	—
1197	C₄	—	2	1	no	—
1198	C₄	—	2	4	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	C₇×#546	1	2	yes	—
1210	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1211	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1212	C₂	—	2	2	no	—
1213	C₂	—	4	1	no	—
1214	C₂	—	4	1	no	—
1215	C₂	—	4	2	no	—
1216	C₂	—	8	2	no	—
1217	C₂	—	8	1	no	—
1218	C₂	C₂×C₇×#546	1	1	yes	characteristic
1219	C₂	C₇×#3584	1	1	yes	characteristic
1220	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3487	C₂
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×#3495	C₂	semidirect
3. C₇×#3333	C₂	semidirect
4. C₇×#3327	C₂	semidirect
5. C₇×#3317	C₂	semidirect
6. C₇×#3317	C₂	semidirect
7. C₇×#3316	C₂	semidirect
8. C₇×#3313	C₂	semidirect
9. C₇×#3304	C₂	semidirect
10. C₇×#3300	C₂	semidirect
11. C₇×#3136	C₂	semidirect
12. C₇×#3096	C₂	semidirect
13. C₇×#3091	C₂	semidirect
14. C₇×#3082	C₂	semidirect
15. C₇×#3057	C₂	semidirect
16. C₇×#3056	C₂	semidirect
17. C₇×#3043	C₂	semidirect
18. C₇×#3011	C₂	semidirect
19. C₂×C₇×#452	C₂	semidirect
20. C₇×#2950	C₂	semidirect
21. C₇×#2933	C₂	semidirect
22. C₇×#2898	C₂	semidirect
23. C₇×#2896	C₂	semidirect
31. C₇×#556	C₂²	semidirect
32. C₇×#554	C₂²	semidirect
34. C₇×#552	C₂²	semidirect
35. C₇×#552	C₂²	semidirect
62. C₇×#490	C₂²	semidirect
63. C₇×#489	C₂²	semidirect
64. C₇×#488	C₂²	semidirect
65. C₇×#486	C₂²	semidirect
66. C₇×#485	C₂²	semidirect
67. C₇×#485	C₂²	semidirect
68. C₇×#484	C₂²	semidirect
69. C₇×#483	C₂²	semidirect
70. C₇×#482	C₂²	semidirect
71. C₇×#482	C₂²	semidirect
72. C₇×#482	C₂²	semidirect
73. C₇×#482	C₂²	semidirect
74. C₇×#481	C₂²	semidirect
75. C₇×#481	C₂²	semidirect
76. C₇×#480	C₂²	semidirect
77. C₇×#480	C₂²	semidirect
78. C₇×#479	C₂²	semidirect
79. C₇×#479	C₂²	semidirect
80. C₇×#477	C₂²	semidirect
81. C₇×#475	C₂²	semidirect
82. C₇×#470	C₂²	semidirect
83. C₇×#468	C₂²	semidirect
84. C₇×#468	C₂²	semidirect
85. C₇×#468	C₂²	semidirect
86. C₇×#467	C₂²	semidirect
87. C₇×#465	C₂²	semidirect
88. C₇×#465	C₂²	semidirect
89. C₇×#465	C₂²	semidirect
90. C₇×#464	C₂²	semidirect
91. C₇×#464	C₂²	semidirect
92. C₇×#460	C₂²	semidirect
93. C₇×#460	C₂²	semidirect
98. C₇×#452	C₂²	semidirect
99. C₇×#452	C₂²	semidirect
100. C₇×#451	C₂²	semidirect
101. C₇×#451	C₂²	semidirect
102. C₇×#441	C₂²	semidirect
103. C₇×#441	C₂²	semidirect
104. C₄×C₇×Q₁₆	C₂²	semidirect
105. C₄×C₇×Q₁₆	C₂²	semidirect
106. C₇×#436	C₂²	semidirect
107. C₇×#435	C₂²	semidirect
108. C₇×#435	C₂²	semidirect
109. C₇×C₈×D₄	C₂²	semidirect
117. C₇×#419	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
128. C₇×#416	C₂²	semidirect
130. C₂×C₇×#103	C₂²	semidirect
135. #61190	C₇	direct (N × H)
322. #3495	C₂×C₇	semidirect
324. #3333	C₂×C₇	semidirect
325. #3327	C₂×C₇	semidirect
326. #3317	C₂×C₇	semidirect
327. #3317	C₂×C₇	semidirect
328. #3316	C₂×C₇	semidirect
329. #3313	C₂×C₇	semidirect
330. #3304	C₂×C₇	semidirect
331. #3300	C₂×C₇	semidirect
332. #3136	C₂×C₇	semidirect
333. #3096	C₂×C₇	semidirect
334. #3091	C₂×C₇	semidirect
335. #3082	C₂×C₇	semidirect
336. #3057	C₂×C₇	semidirect
337. #3056	C₂×C₇	semidirect
338. #3043	C₂×C₇	semidirect
339. #3011	C₂×C₇	semidirect
340. C₂×#452	C₂×C₇	semidirect
341. #2950	C₂×C₇	semidirect
342. #2933	C₂×C₇	semidirect
343. #2898	C₂×C₇	semidirect
344. #2896	C₂×C₇	semidirect
506. #556	C₂²×C₇	semidirect
507. #554	C₂²×C₇	semidirect
509. #552	C₂²×C₇	semidirect
510. #552	C₂²×C₇	semidirect
537. #490	C₂²×C₇	semidirect
538. #489	C₂²×C₇	semidirect
539. #488	C₂²×C₇	semidirect
540. #486	C₂²×C₇	semidirect
541. #485	C₂²×C₇	semidirect
542. #485	C₂²×C₇	semidirect
543. #484	C₂²×C₇	semidirect
544. #483	C₂²×C₇	semidirect
545. #482	C₂²×C₇	semidirect
546. #482	C₂²×C₇	semidirect
547. #482	C₂²×C₇	semidirect
548. #482	C₂²×C₇	semidirect
549. #481	C₂²×C₇	semidirect
550. #481	C₂²×C₇	semidirect
551. #480	C₂²×C₇	semidirect
552. #480	C₂²×C₇	semidirect
553. #479	C₂²×C₇	semidirect
554. #479	C₂²×C₇	semidirect
555. #477	C₂²×C₇	semidirect
556. #475	C₂²×C₇	semidirect
557. #470	C₂²×C₇	semidirect
558. #468	C₂²×C₇	semidirect
559. #468	C₂²×C₇	semidirect
560. #468	C₂²×C₇	semidirect
561. #467	C₂²×C₇	semidirect
562. #465	C₂²×C₇	semidirect
563. #465	C₂²×C₇	semidirect
564. #465	C₂²×C₇	semidirect
565. #464	C₂²×C₇	semidirect
566. #464	C₂²×C₇	semidirect
567. #460	C₂²×C₇	semidirect
568. #460	C₂²×C₇	semidirect
573. #452	C₂²×C₇	semidirect
574. #452	C₂²×C₇	semidirect
575. #451	C₂²×C₇	semidirect
576. #451	C₂²×C₇	semidirect
577. #441	C₂²×C₇	semidirect
578. #441	C₂²×C₇	semidirect
579. C₄×Q₁₆	C₂²×C₇	semidirect
580. C₄×Q₁₆	C₂²×C₇	semidirect
581. #436	C₂²×C₇	semidirect
582. #435	C₂²×C₇	semidirect
583. #435	C₂²×C₇	semidirect
584. C₈×D₄	C₂²×C₇	semidirect
592. #419	C₂²×C₇	semidirect
598. #417	C₂²×C₇	semidirect
603. #416	C₂²×C₇	semidirect
605. C₂×#103	C₂²×C₇	semidirect
1172. C₇	#61190	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×#3495	2
C₇×#3487	2
C₇×#3333	2
C₇×#3327	2
C₇×#3317	2
C₇×#3316	2
C₇×#3313	2
C₇×#3304	2
C₇×#3300	2
C₇×#3136	2
C₇×#3096	2
C₇×#3091	2
C₇×#3082	2
C₇×#3057	2
C₇×#3056	2
C₇×#3043	2
C₇×#3011	2
C₂×C₇×#452	2
C₇×#2950	2
C₇×#2933	2
C₇×#2898	2
C₇×#2896	2
#61190	7

Subgroups — C7×#61190 #13238406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61190 #13238406