Subgroups — C₇×#61186 #13238402

Order 1792.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1202 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×#3486	C₂	1	1	yes	maximal, characteristic
3	C₇×#3328	C₂	1	2	yes	maximal, complemented
4	C₇×#3327	C₂	1	2	yes	maximal, complemented
5	C₇×#3316	C₂	1	2	yes	maximal, complemented
6	C₇×#3313	C₂	1	2	yes	maximal, complemented
7	C₇×#3312	C₂	1	2	yes	maximal, complemented
8	C₇×#3312	C₂	1	2	yes	maximal, complemented
9	C₇×#3300	C₂	1	2	yes	maximal, complemented
10	C₇×#3299	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×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3059	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₇×#451	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	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	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₇×Q₁₆	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	—
32	C₇×#554	C₂²	1	2	yes	—
33	C₇×#552	—	2	2	no	—
34	C₇×#552	C₂²	1	2	yes	—
35	C₇×#552	C₂²	1	2	yes	—
36	C₇×#551	—	2	2	no	—
37	C₇×D₄×Q₈	—	2	1	no	—
38	C₇×D₄×Q₈	—	2	1	no	—
39	C₇×D₄×Q₈	C₂²	1	2	yes	—
40	C₇×D₄×Q₈	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	—	2	2	no	—
49	C₇×#536	C₂²	1	1	yes	characteristic
50	C₇×#536	C₂²	1	1	yes	characteristic
51	C₇×#536	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×#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	1	yes	characteristic
67	C₇×#485	C₂²	1	1	yes	characteristic
68	C₇×#485	C₂²	1	2	yes	complemented
69	C₇×#485	C₂²	1	2	yes	complemented
70	C₇×#484	C₂²	1	1	yes	characteristic
71	C₇×#484	C₂²	1	2	yes	complemented
72	C₇×#483	C₂²	1	1	yes	characteristic
73	C₇×#483	C₂²	1	2	yes	complemented
74	C₇×#482	C₂²	1	1	yes	characteristic
75	C₇×#482	C₂²	1	1	yes	characteristic
76	C₇×#481	C₂²	1	1	yes	characteristic
77	C₇×#480	C₂²	1	1	yes	characteristic
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	—
83	C₇×#470	C₂²	1	2	yes	complemented
84	C₇×#470	C₂²	1	2	yes	complemented
85	C₇×#468	C₂²	1	2	yes	—
86	C₇×#467	C₂²	1	2	yes	—
87	C₇×#467	C₂²	1	2	yes	complemented
88	C₇×#467	C₂²	1	2	yes	complemented
89	C₇×#465	C₂²	1	2	yes	—
90	C₇×#464	C₂²	1	2	yes	complemented
91	C₇×#464	C₂²	1	2	yes	complemented
92	C₇×#462	C₂²	1	2	yes	complemented
93	C₇×#462	C₂²	1	2	yes	complemented
94	C₇×#452	C₂²	1	2	yes	complemented
95	C₇×#452	C₂²	1	2	yes	complemented
96	C₇×#451	C₂²	1	2	yes	—
97	C₇×#451	C₂²	1	2	yes	—
98	C₇×#451	C₂²	1	2	yes	—
99	C₇×#451	C₂²	1	2	yes	—
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	—
107	C₇×#435	C₂²	1	2	yes	—
108	C₇×#435	C₂²	1	2	yes	—
109	C₇×C₈×D₄	C₂²	1	2	yes	—
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	1	yes	characteristic
118	C₇×#419	C₂²	1	2	yes	—
119	C₇×#419	C₂²	1	2	yes	—
120	C₇×#419	C₂²	1	1	yes	characteristic
121	C₇×#419	C₂²	1	2	yes	complemented
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	2	yes	—
130	C₂×C₇×#103	C₂²	1	2	yes	—
131	C₂×C₇×#103	C₂²	1	2	yes	complemented
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	#61186	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	2	yes	—
142	C₂×C₇×#41	C₂³	1	1	yes	characteristic
143	C₂²×C₇×Q₈	—	2	1	no	—
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	4	no	—
148	C₂²×C₇×Q₈	—	4	2	no	—
149	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
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	—	4	2	no	—
158	C₂×C₇×Q₁₆	—	2	4	no	—
159	C₂×C₇×Q₁₆	—	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	2	yes	—
163	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
164	C₂×C₇×Q₁₆	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	—	2	1	no	—
179	C₇×C₄⋊Q₈	—	2	2	no	—
180	C₇×C₄⋊Q₈	—	2	2	no	—
181	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
182	C₇×C₄⋊Q₈	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	2	no	—
202	C₇×#123	—	2	1	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	D₄	1	2	yes	—
205	C₇×C₂²⋊Q₈	—	2	1	no	—
206	C₇×C₂²⋊Q₈	—	2	1	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	—	2	2	no	—
209	C₇×C₂²⋊Q₈	—	2	1	no	—
210	C₇×C₂²⋊Q₈	—	2	1	no	—
211	C₇×C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
218	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
219	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
220	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₇×#121	—	2	2	no	—
229	C₇×#121	—	2	2	no	—
230	C₇×#121	D₄	1	1	yes	characteristic
231	C₇×#121	D₄	1	1	yes	characteristic
232	C₇×#121	C₂³	1	1	yes	characteristic
233	C₇×#121	C₂³	1	1	yes	characteristic
234	C₇×#120	—	2	1	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	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	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	1	yes	characteristic
264	C₇×#117	C₂³	1	1	yes	characteristic
265	C₇×#117	C₂³	1	2	yes	—
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	1	yes	characteristic
272	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
298	C₇×#103	C₂³	1	2	yes	—
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×#103	C₂³	1	1	yes	characteristic
304	C₇×#103	C₂³	1	1	yes	characteristic
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×#102	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
315	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	#3495	C₂×C₇	1	1	yes	characteristic, complemented
323	#3486	C₂×C₇	1	1	yes	characteristic
324	#3328	C₂×C₇	1	2	yes	complemented
325	#3327	C₂×C₇	1	2	yes	complemented
326	#3316	C₂×C₇	1	2	yes	complemented
327	#3313	C₂×C₇	1	2	yes	complemented
328	#3312	C₂×C₇	1	2	yes	complemented
329	#3312	C₂×C₇	1	2	yes	complemented
330	#3300	C₂×C₇	1	2	yes	complemented
331	#3299	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	#3091	C₂×C₇	1	1	yes	characteristic, complemented
335	#3082	C₂×C₇	1	1	yes	characteristic, complemented
336	#3059	C₂×C₇	1	1	yes	characteristic, complemented
337	#3056	C₂×C₇	1	1	yes	characteristic, complemented
338	#3044	C₂×C₇	1	1	yes	characteristic, complemented
339	#3011	C₂×C₇	1	1	yes	characteristic, complemented
340	C₂×#451	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	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	—	4	2	no	—
352	C₇×#41	—	4	8	no	—
353	C₇×#41	—	4	4	no	—
354	C₂×C₇×Q₈	—	2	1	no	—
355	C₂×C₇×Q₈	—	2	1	no	—
356	C₂×C₇×Q₈	—	2	2	no	—
357	C₂×C₇×Q₈	—	2	2	no	—
358	C₂×C₇×Q₈	—	2	1	no	—
359	C₂×C₇×Q₈	—	2	2	no	—
360	C₂×C₇×Q₈	—	2	2	no	—
361	C₂×C₇×Q₈	—	2	2	no	—
362	C₂×C₇×Q₈	—	2	4	no	—
363	C₂×C₇×Q₈	—	2	4	no	—
364	C₂×C₇×Q₈	—	2	4	no	—
365	C₂×C₇×Q₈	—	2	2	no	—
366	C₂×C₇×Q₈	—	2	2	no	—
367	C₂×C₇×Q₈	—	2	2	no	—
368	C₂×C₇×Q₈	—	2	2	no	—
369	C₂×C₇×Q₈	—	4	4	no	—
370	C₂×C₇×Q₈	—	4	2	no	—
371	C₂×C₇×Q₈	—	4	2	no	—
372	C₂×C₇×Q₈	—	4	2	no	—
373	C₂×C₇×Q₈	—	4	4	no	—
374	C₂×C₇×Q₈	—	4	4	no	—
375	C₂×C₇×Q₈	—	4	4	no	—
376	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
377	C₂×C₇×Q₈	#41	1	4	yes	—
378	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
379	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
381	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
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	C₂×D₄	1	2	yes	—
387	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
388	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
389	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
390	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₇	—	2	1	no	—
392	C₂²×C₄×C₇	—	2	2	no	—
393	C₂²×C₄×C₇	—	2	2	no	—
394	C₂²×C₄×C₇	—	2	1	no	—
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	1	no	—
400	C₂²×C₄×C₇	—	2	1	no	—
401	C₂²×C₄×C₇	—	2	1	no	—
402	C₂²×C₄×C₇	—	2	2	no	—
403	C₂²×C₄×C₇	—	2	2	no	—
404	C₂²×C₄×C₇	—	2	1	no	—
405	C₂²×C₄×C₇	—	4	4	no	—
406	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
411	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
413	C₇×Q₁₆	—	2	4	no	—
414	C₇×Q₁₆	—	2	4	no	—
415	C₇×Q₁₆	—	4	2	no	—
416	C₇×Q₁₆	—	4	2	no	—
417	C₇×Q₁₆	—	4	2	no	—
418	C₇×SD₁₆	—	4	2	no	—
419	C₇×M₁₆	—	2	2	no	—
420	C₇×M₁₆	—	2	2	no	—
421	C₇×M₁₆	—	4	2	no	—
422	C₇×M₁₆	—	4	2	no	—
423	C₂×C₇×C₈	—	2	2	no	—
424	C₂×C₇×C₈	—	2	2	no	—
425	C₂×C₇×C₈	—	4	2	no	—
426	C₂×C₇×C₈	—	4	2	no	—
427	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
428	C₂×C₇×C₈	C₂⁴	1	2	yes	—
429	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
430	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
431	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
432	C₂×C₇×C₈	C₂⁴	1	2	yes	—
433	C₇×C₄⋊C₄	—	2	2	no	—
434	C₇×C₄⋊C₄	—	2	2	no	—
435	C₇×C₄⋊C₄	—	2	1	no	—
436	C₇×C₄⋊C₄	—	2	1	no	—
437	C₇×C₄⋊C₄	—	2	1	no	—
438	C₇×C₄⋊C₄	—	2	2	no	—
439	C₇×C₄⋊C₄	—	2	2	no	—
440	C₇×C₄⋊C₄	—	2	2	no	—
441	C₇×C₄⋊C₄	—	2	2	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	2	no	—
478	C₇×C₂²⋊C₄	—	2	2	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	1	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	C₂³×Q₈	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×Q₁₆	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	—
507	#554	C₂²×C₇	1	2	yes	—
508	#552	—	2	2	no	—
509	#552	C₂²×C₇	1	2	yes	—
510	#552	C₂²×C₇	1	2	yes	—
511	#551	—	2	2	no	—
512	D₄×Q₈	—	2	1	no	—
513	D₄×Q₈	—	2	1	no	—
514	D₄×Q₈	C₂²×C₇	1	2	yes	—
515	D₄×Q₈	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	—	2	2	no	—
524	#536	C₂²×C₇	1	1	yes	characteristic
525	#536	C₂²×C₇	1	1	yes	characteristic
526	#536	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	#491	C₂²×C₇	1	2	yes	complemented
538	#489	C₂²×C₇	1	2	yes	complemented
539	#488	C₂²×C₇	1	2	yes	complemented
540	#487	C₂²×C₇	1	2	yes	complemented
541	#485	C₂²×C₇	1	1	yes	characteristic
542	#485	C₂²×C₇	1	1	yes	characteristic
543	#485	C₂²×C₇	1	2	yes	complemented
544	#485	C₂²×C₇	1	2	yes	complemented
545	#484	C₂²×C₇	1	1	yes	characteristic
546	#484	C₂²×C₇	1	2	yes	complemented
547	#483	C₂²×C₇	1	1	yes	characteristic
548	#483	C₂²×C₇	1	2	yes	complemented
549	#482	C₂²×C₇	1	1	yes	characteristic
550	#482	C₂²×C₇	1	1	yes	characteristic
551	#481	C₂²×C₇	1	1	yes	characteristic
552	#480	C₂²×C₇	1	1	yes	characteristic
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	—
558	#470	C₂²×C₇	1	2	yes	complemented
559	#470	C₂²×C₇	1	2	yes	complemented
560	#468	C₂²×C₇	1	2	yes	—
561	#467	C₂²×C₇	1	2	yes	—
562	#467	C₂²×C₇	1	2	yes	complemented
563	#467	C₂²×C₇	1	2	yes	complemented
564	#465	C₂²×C₇	1	2	yes	—
565	#464	C₂²×C₇	1	2	yes	complemented
566	#464	C₂²×C₇	1	2	yes	complemented
567	#462	C₂²×C₇	1	2	yes	complemented
568	#462	C₂²×C₇	1	2	yes	complemented
569	#452	C₂²×C₇	1	2	yes	complemented
570	#452	C₂²×C₇	1	2	yes	complemented
571	#451	C₂²×C₇	1	2	yes	—
572	#451	C₂²×C₇	1	2	yes	—
573	#451	C₂²×C₇	1	2	yes	—
574	#451	C₂²×C₇	1	2	yes	—
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	—
582	#435	C₂²×C₇	1	2	yes	—
583	#435	C₂²×C₇	1	2	yes	—
584	C₈×D₄	C₂²×C₇	1	2	yes	—
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	2	yes	—
590	#419	C₂²×C₇	1	1	yes	characteristic
591	#419	C₂²×C₇	1	1	yes	characteristic
592	#419	C₂²×C₇	1	1	yes	characteristic
593	#419	C₂²×C₇	1	1	yes	characteristic
594	#419	C₂²×C₇	1	2	yes	—
595	#419	C₂²×C₇	1	1	yes	characteristic
596	#419	C₂²×C₇	1	2	yes	complemented
597	#417	C₂²×C₇	1	1	yes	characteristic
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	complemented
602	C₂×#103	C₂²×C₇	1	1	yes	characteristic
603	C₂×#103	C₂²×C₇	1	1	yes	characteristic
604	C₂×#103	C₂²×C₇	1	2	yes	—
605	C₂×#103	C₂²×C₇	1	2	yes	—
606	C₂×#103	C₂²×C₇	1	2	yes	complemented
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	C₂²×D₄	1	1	yes	characteristic
615	C₂³×C₇	C₂²×D₄	1	2	yes	—
616	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
617	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
618	C₇×Q₈	—	2	4	no	—
619	C₇×Q₈	—	2	2	no	—
620	C₇×Q₈	—	2	2	no	—
621	C₇×Q₈	—	2	2	no	—
622	C₇×Q₈	—	2	2	no	—
623	C₇×Q₈	—	2	1	no	—
624	C₇×Q₈	—	2	2	no	—
625	C₇×Q₈	—	2	2	no	—
626	C₇×Q₈	—	2	1	no	—
627	C₇×Q₈	—	4	4	no	—
628	C₇×Q₈	—	4	4	no	—
629	C₇×Q₈	—	4	4	no	—
630	C₇×Q₈	—	4	2	no	—
631	C₇×Q₈	—	4	2	no	—
632	C₇×Q₈	—	8	2	no	—
633	C₇×Q₈	C₂×#41	1	4	yes	—
634	C₇×D₄	—	2	4	no	—
635	C₇×D₄	—	2	4	no	—
636	C₇×D₄	—	2	2	no	—
637	C₇×D₄	—	2	1	no	—
638	C₇×D₄	—	2	1	no	—
639	C₇×D₄	—	4	2	no	—
640	C₇×D₄	—	4	4	no	—
641	C₇×D₄	—	4	2	no	—
642	C₇×D₄	—	4	2	no	—
643	C₇×D₄	—	4	2	no	—
644	C₂×C₄×C₇	—	2	2	no	—
645	C₂×C₄×C₇	—	2	4	no	—
646	C₂×C₄×C₇	—	2	2	no	—
647	C₂×C₄×C₇	—	2	2	no	—
648	C₂×C₄×C₇	—	2	2	no	—
649	C₂×C₄×C₇	—	2	1	no	—
650	C₂×C₄×C₇	—	2	1	no	—
651	C₂×C₄×C₇	—	2	2	no	—
652	C₂×C₄×C₇	—	2	1	no	—
653	C₂×C₄×C₇	—	2	2	no	—
654	C₂×C₄×C₇	—	2	1	no	—
655	C₂×C₄×C₇	—	2	1	no	—
656	C₂×C₄×C₇	—	2	1	no	—
657	C₂×C₄×C₇	—	2	1	no	—
658	C₂×C₄×C₇	—	2	1	no	—
659	C₂×C₄×C₇	—	2	1	no	—
660	C₂×C₄×C₇	—	2	2	no	—
661	C₂×C₄×C₇	—	2	1	no	—
662	C₂×C₄×C₇	—	2	2	no	—
663	C₂×C₄×C₇	—	2	2	no	—
664	C₂×C₄×C₇	—	2	1	no	—
665	C₂×C₄×C₇	—	4	4	no	—
666	C₂×C₄×C₇	—	4	4	no	—
667	C₂×C₄×C₇	—	4	4	no	—
668	C₂×C₄×C₇	—	4	4	no	—
669	C₂×C₄×C₇	—	4	2	no	—
670	C₂×C₄×C₇	—	4	2	no	—
671	C₂×C₄×C₇	—	4	2	no	—
672	C₂×C₄×C₇	—	4	2	no	—
673	C₂×C₄×C₇	—	8	2	no	—
674	C₂×C₄×C₇	—	8	1	no	—
675	C₂×C₄×C₇	—	8	1	no	—
676	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
677	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
678	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
679	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
680	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
681	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
682	C₂×C₄×C₇	C₂×#41	1	2	yes	—
683	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
684	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
685	C₇×C₈	—	2	1	no	—
686	C₇×C₈	—	2	1	no	—
687	C₇×C₈	—	2	1	no	—
688	C₇×C₈	—	2	1	no	—
689	C₇×C₈	—	2	2	no	—
690	C₇×C₈	—	2	2	no	—
691	2₋¹⁺⁴	—	2	4	no	—
692	2₋¹⁺⁴	—	4	2	no	—
693	C₂×#41	—	2	2	no	—
694	C₂×#41	—	2	1	no	—
695	C₂×#41	C₂³×C₇	1	1	yes	characteristic
696	C₂×#41	C₂³×C₇	1	2	yes	—
697	C₂×#41	C₂³×C₇	1	1	yes	characteristic
698	C₂²×Q₈	—	2	1	no	—
699	C₂²×Q₈	—	2	1	no	—
700	C₂²×Q₈	—	2	1	no	—
701	C₂²×Q₈	—	2	1	no	—
702	C₂²×Q₈	—	2	4	no	—
703	C₂²×Q₈	—	4	2	no	—
704	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
705	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
706	C₂²×Q₈	C₂³×C₇	1	2	yes	—
707	C₂²×Q₈	C₂³×C₇	1	2	yes	—
708	C₂²×Q₈	C₂³×C₇	1	2	yes	—
709	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
710	C₂³×C₄	—	2	1	no	—
711	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
712	#137	—	4	2	no	—
713	C₂×Q₁₆	—	2	4	no	—
714	C₂×Q₁₆	—	4	2	no	—
715	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
716	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
717	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
718	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
719	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
721	#131	—	4	2	no	—
722	C₂×M₁₆	—	4	2	no	—
723	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
724	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
725	C₂×M₁₆	C₂³×C₇	1	2	yes	—
726	C₂×M₁₆	C₂³×C₇	1	2	yes	—
727	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
728	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₇	1	2	yes	—
730	C₂²×C₈	C₂³×C₇	1	2	yes	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	1	no	—
734	C₄⋊Q₈	—	2	2	no	—
735	C₄⋊Q₈	—	2	2	no	—
736	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
737	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#125	—	2	1	no	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	C₂³×C₇	1	2	yes	—
747	#124	—	2	1	no	—
748	#124	—	2	1	no	—
749	#124	—	2	2	no	—
750	#124	—	2	2	no	—
751	#124	—	2	2	no	—
752	#124	C₂³×C₇	1	2	yes	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	1	no	—
758	#123	—	2	2	no	—
759	#123	C₇×D₄	1	2	yes	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
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	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
774	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
778	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
779	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
780	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
781	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
782	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	C₇×D₄	1	1	yes	characteristic
786	#121	C₇×D₄	1	1	yes	characteristic
787	#121	C₂³×C₇	1	1	yes	characteristic
788	#121	C₂³×C₇	1	1	yes	characteristic
789	#120	—	2	1	no	—
790	#120	C₇×D₄	1	2	yes	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	2	no	—
797	C₄×Q₈	C₂³×C₇	1	2	yes	—
798	C₄×Q₈	C₂³×C₇	1	2	yes	—
799	C₄×Q₈	C₂³×C₇	1	2	yes	—
800	C₄×Q₈	C₂³×C₇	1	2	yes	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	C₂³×C₇	1	2	yes	—
811	C₄×D₄	C₂³×C₇	1	2	yes	—
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	—	2	2	no	—
815	#117	—	2	2	no	—
816	#117	—	2	2	no	—
817	#117	—	2	2	no	—
818	#117	C₂³×C₇	1	1	yes	characteristic
819	#117	C₂³×C₇	1	1	yes	characteristic
820	#117	C₂³×C₇	1	1	yes	characteristic
821	#117	C₂³×C₇	1	1	yes	characteristic
822	#117	C₂³×C₇	1	1	yes	characteristic
823	#117	C₂³×C₇	1	2	yes	—
824	#117	C₂³×C₇	1	1	yes	characteristic
825	C₂×C₄⋊C₄	—	2	1	no	—
826	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
830	C₂×C₂²⋊C₄	—	2	1	no	—
831	C₂×C₂²⋊C₄	—	2	1	no	—
832	C₂×C₄²	—	2	1	no	—
833	#107	C₂³×C₇	1	1	yes	characteristic
834	#107	C₂³×C₇	1	1	yes	characteristic
835	#107	C₂³×C₇	1	1	yes	characteristic
836	#107	C₂³×C₇	1	1	yes	characteristic
837	#107	C₂³×C₇	1	2	yes	—
838	#106	C₂³×C₇	1	1	yes	characteristic
839	#106	C₂³×C₇	1	1	yes	characteristic
840	#106	C₂³×C₇	1	1	yes	characteristic
841	#106	C₂³×C₇	1	1	yes	characteristic
842	#106	C₂³×C₇	1	2	yes	—
843	C₄⋊C₈	C₂³×C₇	1	2	yes	—
844	C₄⋊C₈	C₂³×C₇	1	2	yes	—
845	#103	C₂³×C₇	1	2	yes	—
846	#103	C₂³×C₇	1	2	yes	—
847	#103	C₂³×C₇	1	2	yes	—
848	#103	C₂³×C₇	1	2	yes	—
849	#103	C₂³×C₇	1	2	yes	—
850	#103	C₂³×C₇	1	2	yes	—
851	#103	C₂³×C₇	1	2	yes	—
852	#103	C₂³×C₇	1	2	yes	—
853	#103	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
865	#102	C₂³×C₇	1	1	yes	characteristic
866	#102	C₂³×C₇	1	1	yes	characteristic
867	#102	C₂³×C₇	1	1	yes	characteristic
868	#102	C₂³×C₇	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
870	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
875	#97	C₂³×C₇	1	2	yes	—
876	C₄×C₈	C₂³×C₇	1	2	yes	—
877	C₂²×C₇	—	2	1	no	—
878	C₂²×C₇	—	2	1	no	—
879	C₂²×C₇	—	2	1	no	—
880	C₂²×C₇	—	2	1	no	—
881	C₂²×C₇	—	2	2	no	—
882	C₂²×C₇	—	2	1	no	—
883	C₂²×C₇	—	2	1	no	—
884	C₂²×C₇	—	2	2	no	—
885	C₂²×C₇	—	2	2	no	—
886	C₂²×C₇	—	2	1	no	—
887	C₂²×C₇	—	4	4	no	—
888	C₂²×C₇	—	4	1	no	—
889	C₂²×C₇	—	4	1	no	—
890	C₂²×C₇	—	4	1	no	—
891	C₂²×C₇	#546	1	2	yes	—
892	C₂²×C₇	#578	1	2	yes	—
893	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
894	C₄×C₇	—	2	2	no	—
895	C₄×C₇	—	2	1	no	—
896	C₄×C₇	—	2	1	no	—
897	C₄×C₇	—	2	4	no	—
898	C₄×C₇	—	2	2	no	—
899	C₄×C₇	—	2	2	no	—
900	C₄×C₇	—	4	1	no	—
901	C₄×C₇	—	4	2	no	—
902	C₄×C₇	—	4	1	no	—
903	C₄×C₇	—	4	1	no	—
904	C₄×C₇	—	4	1	no	—
905	C₄×C₇	—	4	2	no	—
906	C₄×C₇	—	4	2	no	—
907	C₄×C₇	—	4	1	no	—
908	C₄×C₇	—	4	1	no	—
909	C₄×C₇	—	4	1	no	—
910	C₄×C₇	#546	1	2	yes	—
911	C₄×C₇	C₂²×#41	1	1	yes	characteristic
912	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
913	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
914	#41	—	2	2	no	—
915	#41	—	2	2	no	—
916	#41	—	2	4	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	4	2	no	—
920	#41	—	4	8	no	—
921	#41	—	4	4	no	—
922	C₂×Q₈	—	2	1	no	—
923	C₂×Q₈	—	2	1	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	—	2	2	no	—
926	C₂×Q₈	—	2	1	no	—
927	C₂×Q₈	—	2	2	no	—
928	C₂×Q₈	—	2	2	no	—
929	C₂×Q₈	—	2	2	no	—
930	C₂×Q₈	—	2	4	no	—
931	C₂×Q₈	—	2	4	no	—
932	C₂×Q₈	—	2	4	no	—
933	C₂×Q₈	—	2	2	no	—
934	C₂×Q₈	—	2	2	no	—
935	C₂×Q₈	—	2	2	no	—
936	C₂×Q₈	—	2	2	no	—
937	C₂×Q₈	—	4	4	no	—
938	C₂×Q₈	—	4	2	no	—
939	C₂×Q₈	—	4	2	no	—
940	C₂×Q₈	—	4	2	no	—
941	C₂×Q₈	—	4	4	no	—
942	C₂×Q₈	—	4	4	no	—
943	C₂×Q₈	—	4	4	no	—
944	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
945	C₂×Q₈	C₇×#41	1	4	yes	—
946	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
947	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
948	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
949	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
955	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
956	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
957	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
958	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	4	4	no	—
974	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
975	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
976	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
979	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
980	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
981	Q₁₆	—	2	4	no	—
982	Q₁₆	—	2	4	no	—
983	Q₁₆	—	4	2	no	—
984	Q₁₆	—	4	2	no	—
985	Q₁₆	—	4	2	no	—
986	SD₁₆	—	4	2	no	—
987	M₁₆	—	2	2	no	—
988	M₁₆	—	2	2	no	—
989	M₁₆	—	4	2	no	—
990	M₁₆	—	4	2	no	—
991	C₂×C₈	—	2	2	no	—
992	C₂×C₈	—	2	2	no	—
993	C₂×C₈	—	4	2	no	—
994	C₂×C₈	—	4	2	no	—
995	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₇	1	2	yes	—
997	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
999	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1023	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1024	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1025	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1026	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1027	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1028	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1029	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1030	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1031	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1032	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1052	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1053	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1054	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1055	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1056	C₄²	—	2	1	no	—
1057	C₄²	—	2	1	no	—
1058	C₄²	—	2	1	no	—
1059	C₄²	—	2	1	no	—
1060	C₄²	—	2	2	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	—	2	2	no	—
1063	C₄²	—	2	2	no	—
1064	C₄²	—	2	2	no	—
1065	C₄²	—	2	1	no	—
1066	C₄²	C₂⁴×C₇	1	2	yes	—
1067	C₂×C₇	—	2	2	no	—
1068	C₂×C₇	—	2	2	no	—
1069	C₂×C₇	—	4	2	no	—
1070	C₂×C₇	—	4	1	no	—
1071	C₂×C₇	—	8	1	no	—
1072	C₂×C₇	C₂×#546	1	1	yes	characteristic
1073	C₂×C₇	C₂×#578	1	1	yes	characteristic
1074	C₂×C₇	#3586	1	1	yes	characteristic
1075	C₂³	—	2	2	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	4	1	no	—
1079	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1080	C₂³	C₂²×C₇×D₄	1	2	yes	—
1081	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1082	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1083	Q₈	—	2	2	no	—
1084	Q₈	—	2	4	no	—
1085	Q₈	—	2	2	no	—
1086	Q₈	—	2	2	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	2	1	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	2	no	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	4	4	no	—
1093	Q₈	—	4	4	no	—
1094	Q₈	—	4	4	no	—
1095	Q₈	—	4	2	no	—
1096	Q₈	—	4	2	no	—
1097	Q₈	—	8	2	no	—
1098	Q₈	C₂×C₇×#41	1	4	yes	—
1099	D₄	—	2	4	no	—
1100	D₄	—	2	4	no	—
1101	D₄	—	2	1	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	4	2	no	—
1105	D₄	—	4	4	no	—
1106	D₄	—	4	2	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	4	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	2	no	—
1135	C₂×C₄	—	4	2	no	—
1136	C₂×C₄	—	4	2	no	—
1137	C₂×C₄	—	4	2	no	—
1138	C₂×C₄	—	8	2	no	—
1139	C₂×C₄	—	8	1	no	—
1140	C₂×C₄	—	8	1	no	—
1141	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1142	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1143	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1144	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1145	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1146	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1147	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1148	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1149	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₈	—	2	1	no	—
1154	C₈	—	2	2	no	—
1155	C₈	—	2	2	no	—
1156	C₇	#61186	1	1	yes	characteristic, direct product factor, Sylow
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	1	no	—
1159	C₂²	—	2	1	no	—
1160	C₂²	—	2	1	no	—
1161	C₂²	—	2	2	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	1	no	—
1165	C₂²	—	2	1	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	4	4	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	C₇×#546	1	2	yes	—
1172	C₂²	C₇×#578	1	2	yes	—
1173	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1174	C₄	—	2	2	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	1	no	—
1177	C₄	—	2	1	no	—
1178	C₄	—	2	4	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	2	no	—
1190	C₄	C₇×#546	1	2	yes	—
1191	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1192	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1193	C₂	—	2	2	no	—
1194	C₂	—	2	2	no	—
1195	C₂	—	4	1	no	—
1196	C₂	—	4	2	no	—
1197	C₂	—	8	1	no	—
1198	C₂	C₂×C₇×#546	1	1	yes	characteristic
1199	C₂	C₂×C₇×#578	1	1	yes	characteristic
1200	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×#3486	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×#3328	C₂	semidirect
4. C₇×#3327	C₂	semidirect
5. C₇×#3316	C₂	semidirect
6. C₇×#3313	C₂	semidirect
7. C₇×#3312	C₂	semidirect
8. C₇×#3312	C₂	semidirect
9. C₇×#3300	C₂	semidirect
10. C₇×#3299	C₂	semidirect
11. C₇×#3137	C₂	semidirect
12. C₇×#3097	C₂	semidirect
13. C₇×#3091	C₂	semidirect
14. C₇×#3082	C₂	semidirect
15. C₇×#3059	C₂	semidirect
16. C₇×#3056	C₂	semidirect
17. C₇×#3044	C₂	semidirect
18. C₇×#3011	C₂	semidirect
19. C₂×C₇×#451	C₂	semidirect
20. C₇×#2950	C₂	semidirect
21. C₇×#2933	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
71. C₇×#484	C₂²	semidirect
73. C₇×#483	C₂²	semidirect
78. C₇×#479	C₂²	semidirect
79. C₇×#479	C₂²	semidirect
80. C₇×#477	C₂²	semidirect
81. C₇×#475	C₂²	semidirect
83. C₇×#470	C₂²	semidirect
84. C₇×#470	C₂²	semidirect
87. C₇×#467	C₂²	semidirect
88. C₇×#467	C₂²	semidirect
90. C₇×#464	C₂²	semidirect
91. C₇×#464	C₂²	semidirect
92. C₇×#462	C₂²	semidirect
93. C₇×#462	C₂²	semidirect
94. C₇×#452	C₂²	semidirect
95. 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
121. C₇×#419	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
126. C₇×#416	C₂²	semidirect
131. C₂×C₇×#103	C₂²	semidirect
135. #61186	C₇	direct (N × H)
322. #3495	C₂×C₇	semidirect
324. #3328	C₂×C₇	semidirect
325. #3327	C₂×C₇	semidirect
326. #3316	C₂×C₇	semidirect
327. #3313	C₂×C₇	semidirect
328. #3312	C₂×C₇	semidirect
329. #3312	C₂×C₇	semidirect
330. #3300	C₂×C₇	semidirect
331. #3299	C₂×C₇	semidirect
332. #3137	C₂×C₇	semidirect
333. #3097	C₂×C₇	semidirect
334. #3091	C₂×C₇	semidirect
335. #3082	C₂×C₇	semidirect
336. #3059	C₂×C₇	semidirect
337. #3056	C₂×C₇	semidirect
338. #3044	C₂×C₇	semidirect
339. #3011	C₂×C₇	semidirect
340. C₂×#451	C₂×C₇	semidirect
341. #2950	C₂×C₇	semidirect
342. #2933	C₂×C₇	semidirect
343. #2898	C₂×C₇	semidirect
344. C₂×#419	C₂×C₇	semidirect
537. #491	C₂²×C₇	semidirect
538. #489	C₂²×C₇	semidirect
539. #488	C₂²×C₇	semidirect
540. #487	C₂²×C₇	semidirect
543. #485	C₂²×C₇	semidirect
544. #485	C₂²×C₇	semidirect
546. #484	C₂²×C₇	semidirect
548. #483	C₂²×C₇	semidirect
553. #479	C₂²×C₇	semidirect
554. #479	C₂²×C₇	semidirect
555. #477	C₂²×C₇	semidirect
556. #475	C₂²×C₇	semidirect
558. #470	C₂²×C₇	semidirect
559. #470	C₂²×C₇	semidirect
562. #467	C₂²×C₇	semidirect
563. #467	C₂²×C₇	semidirect
565. #464	C₂²×C₇	semidirect
566. #464	C₂²×C₇	semidirect
567. #462	C₂²×C₇	semidirect
568. #462	C₂²×C₇	semidirect
569. #452	C₂²×C₇	semidirect
570. #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
596. #419	C₂²×C₇	semidirect
598. #417	C₂²×C₇	semidirect
601. #416	C₂²×C₇	semidirect
606. C₂×#103	C₂²×C₇	semidirect
1156. C₇	#61186	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×#3486	2
C₇×#3328	2
C₇×#3327	2
C₇×#3316	2
C₇×#3313	2
C₇×#3312	2
C₇×#3300	2
C₇×#3299	2
C₇×#3137	2
C₇×#3097	2
C₇×#3091	2
C₇×#3082	2
C₇×#3059	2
C₇×#3056	2
C₇×#3044	2
C₇×#3011	2
C₂×C₇×#451	2
C₇×#2950	2
C₇×#2933	2
C₇×#2898	2
C₂×C₇×#419	2
#61186	7

Subgroups — C7×#61186 #13238402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61186 #13238402