Subgroups — C₇×#62052 #13239268

Order 1792.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3320	C₂	1	2	yes	maximal, complemented
9	C₇×#3303	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3301	C₂	1	2	yes	maximal, complemented
11	C₇×D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×D₄×SD₁₆	C₂	1	2	yes	maximal, complemented
13	C₇×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3265	C₂	1	2	yes	maximal, complemented
15	C₇×#3260	C₂	1	2	yes	maximal, complemented
16	C₇×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3221	C₂	1	2	yes	maximal, complemented
18	C₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3123	C₂	1	2	yes	maximal, complemented
20	C₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3042	C₂	1	2	yes	maximal, complemented
22	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
26	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
27	C₇×#563	—	2	2	no	—
28	C₇×#557	C₂²	1	1	yes	characteristic, complemented
29	C₇×#556	C₂²	1	1	yes	characteristic, complemented
30	C₇×#555	C₂²	1	1	yes	characteristic
31	C₇×#554	—	2	1	no	—
32	C₇×#554	C₂²	1	1	yes	characteristic
33	C₇×#553	—	2	1	no	—
34	C₇×#553	—	2	1	no	—
35	C₇×#553	C₂²	1	2	yes	—
36	C₇×#550	C₂²	1	1	yes	characteristic
37	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
38	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₇×#548	C₂²	1	2	yes	complemented
40	C₇×#547	C₂²	1	1	yes	characteristic, complemented
41	C₇×#546	—	2	1	no	—
42	C₇×#546	—	2	2	no	—
43	C₇×D₄²	C₂²	1	2	yes	—
44	C₇×D₄²	C₂²	1	1	yes	characteristic
45	C₇×#544	—	2	1	no	—
46	C₇×#542	—	2	1	no	—
47	C₇×#541	C₂²	1	2	yes	complemented
48	C₇×#540	C₂²	1	2	yes	—
49	C₇×#539	—	2	2	no	—
50	C₇×#538	—	2	2	no	—
51	C₇×#536	C₂²	1	2	yes	complemented
52	C₇×#532	C₂²	1	1	yes	characteristic
53	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₇×#529	C₂²	1	1	yes	characteristic
55	C₇×#529	C₂²	1	1	yes	characteristic, complemented
56	C₇×#525	—	2	1	no	—
57	C₂×C₇×#121	—	2	1	no	—
58	C₇×#518	C₂²	1	2	yes	—
59	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
60	C₇×#496	C₂²	1	2	yes	complemented
61	C₇×#492	C₂²	1	1	yes	characteristic, complemented
62	C₇×#492	C₂²	1	1	yes	characteristic, complemented
63	C₇×#492	C₂²	1	2	yes	complemented
64	C₇×#491	C₂²	1	2	yes	complemented
65	C₇×#488	C₂²	1	2	yes	complemented
66	C₇×#487	C₂²	1	1	yes	characteristic, complemented
67	C₇×#487	C₂²	1	1	yes	characteristic, complemented
68	C₇×#485	C₂²	1	2	yes	complemented
69	C₇×#485	C₂²	1	2	yes	complemented
70	C₇×#484	C₂²	1	1	yes	characteristic, complemented
71	C₇×#481	C₂²	1	1	yes	characteristic, complemented
72	C₇×#479	C₂²	1	2	yes	complemented
73	C₇×#479	C₂²	1	2	yes	complemented
74	C₇×#478	C₂²	1	1	yes	characteristic
75	C₇×#478	C₂²	1	2	yes	complemented
76	C₇×#478	C₂²	1	1	yes	characteristic, complemented
77	C₇×#477	C₂²	1	1	yes	characteristic, complemented
78	C₇×#476	C₂²	1	1	yes	characteristic, complemented
79	C₇×#468	C₂²	1	2	yes	complemented
80	C₇×#468	C₂²	1	2	yes	complemented
81	C₇×#466	C₂²	1	2	yes	complemented
82	C₇×#465	C₂²	1	2	yes	complemented
83	C₇×#465	C₂²	1	2	yes	complemented
84	C₇×#465	C₂²	1	2	yes	complemented
85	C₇×#463	C₂²	1	2	yes	—
86	C₇×#463	C₂²	1	1	yes	characteristic
87	C₇×#463	C₂²	1	1	yes	characteristic, complemented
88	C₇×#463	C₂²	1	2	yes	complemented
89	C₇×#463	C₂²	1	2	yes	complemented
90	C₇×#461	C₂²	1	1	yes	characteristic
91	C₇×#461	C₂²	1	1	yes	characteristic
92	C₇×#461	C₂²	1	2	yes	—
93	C₇×#461	C₂²	1	2	yes	—
94	C₇×#461	C₂²	1	2	yes	complemented
95	C₇×#461	C₂²	1	2	yes	complemented
96	C₇×#461	C₂²	1	2	yes	complemented
97	C₇×#461	C₂²	1	1	yes	characteristic, complemented
98	C₇×#461	C₂²	1	1	yes	characteristic, complemented
99	C₇×#461	C₂²	1	2	yes	complemented
100	C₇×#460	C₂²	1	1	yes	characteristic, complemented
101	C₇×#460	C₂²	1	2	yes	complemented
102	C₇×#460	C₂²	1	2	yes	complemented
103	C₇×#459	C₂²	1	1	yes	characteristic, complemented
104	C₇×#450	C₂²	1	2	yes	—
105	C₇×#450	C₂²	1	2	yes	—
106	C₇×#450	C₂²	1	1	yes	characteristic
107	C₇×#449	C₂²	1	2	yes	complemented
108	C₇×#449	C₂²	1	2	yes	complemented
109	C₇×#448	C₂²	1	2	yes	complemented
110	C₇×#448	C₂²	1	2	yes	complemented
111	C₇×#448	C₂²	1	2	yes	complemented
112	C₇×#448	C₂²	1	2	yes	complemented
113	C₇×#447	C₂²	1	1	yes	characteristic
114	C₇×#446	C₂²	1	1	yes	characteristic, complemented
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	C₇×#440	C₂²	1	2	yes	—
117	C₇×#440	C₂²	1	2	yes	complemented
118	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
119	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
121	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
123	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
124	C₇×#436	C₂²	1	1	yes	characteristic, complemented
125	C₇×#435	C₂²	1	2	yes	complemented
126	C₇×C₈×D₄	C₂²	1	2	yes	complemented
127	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
128	C₇×#433	C₂²	1	2	yes	complemented
129	C₇×#431	C₂²	1	1	yes	characteristic, complemented
130	C₇×#424	C₂²	1	2	yes	complemented
131	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₇×#419	C₂²	1	2	yes	complemented
133	C₇×#416	C₂²	1	2	yes	complemented
134	C₂×C₇×#103	C₂²	1	2	yes	complemented
135	#62052	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	—	2	1	no	—
138	C₂×C₇×#41	C₂³	1	2	yes	—
139	C₂²×C₇×Q₈	C₂³	1	2	yes	—
140	C₂²×C₇×Q₈	C₂³	1	2	yes	—
141	C₂²×C₇×D₄	—	2	1	no	—
142	C₂²×C₇×D₄	—	2	2	no	—
143	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
144	C₂²×C₇×D₄	C₂³	1	2	yes	—
145	C₂³×C₄×C₇	—	2	1	no	—
146	C₇×AGL(1,ℤ/8)	—	4	4	no	—
147	C₂×C₇×SD₁₆	—	4	4	no	—
148	C₂×C₇×SD₁₆	—	4	4	no	—
149	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
160	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
161	C₂×C₇×D₈	C₂³	1	2	yes	—
162	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
163	C₂×C₇×M₁₆	C₂³	1	2	yes	—
164	C₂²×C₇×C₈	C₂³	1	2	yes	—
165	C₂²×C₇×C₈	C₂³	1	2	yes	—
166	C₇×C₄⋊Q₈	—	2	1	no	—
167	C₇×C₄⋊Q₈	—	2	2	no	—
168	C₇×C₄⋊Q₈	—	2	1	no	—
169	C₇×C₄⋊Q₈	—	2	1	no	—
170	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
175	C₇×#127	C₂³	1	1	yes	characteristic
176	C₇×#127	C₂³	1	2	yes	—
177	C₇×#126	—	2	2	no	—
178	C₇×#126	—	2	2	no	—
179	C₇×#126	—	2	2	no	—
180	C₇×#126	—	2	2	no	—
181	C₇×#126	—	2	1	no	—
182	C₇×#126	D₄	1	2	yes	—
183	C₇×#125	—	2	2	no	—
184	C₇×#125	—	2	2	no	—
185	C₇×#125	—	2	2	no	—
186	C₇×#125	—	2	1	no	—
187	C₇×#125	D₄	1	1	yes	characteristic
188	C₇×#125	C₂³	1	1	yes	characteristic
189	C₇×#125	C₂³	1	2	yes	—
190	C₇×#124	—	2	2	no	—
191	C₇×#124	—	2	2	no	—
192	C₇×#124	—	2	1	no	—
193	C₇×#124	D₄	1	1	yes	characteristic
194	C₇×#124	C₂³	1	2	yes	—
195	C₇×#124	C₂³	1	1	yes	characteristic
196	C₇×#123	—	2	1	no	—
197	C₇×#123	—	2	2	no	—
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	2	no	—
203	C₇×#123	D₄	1	2	yes	—
204	C₇×C₂²⋊Q₈	—	2	1	no	—
205	C₇×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	—	2	2	no	—
213	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
214	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₇×#121	—	2	2	no	—
218	C₇×#121	—	2	1	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	1	no	—
221	C₇×#121	—	2	1	no	—
222	C₇×#121	—	2	1	no	—
223	C₇×#121	—	2	1	no	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	2	no	—
227	C₇×#121	—	2	2	no	—
228	C₇×#121	D₄	1	1	yes	characteristic
229	C₇×#121	C₂³	1	1	yes	characteristic
230	C₇×#121	C₂³	1	2	yes	—
231	C₇×#121	C₂³	1	2	yes	—
232	C₇×#121	C₂³	1	2	yes	—
233	C₇×#120	—	2	2	no	—
234	C₇×#120	—	2	2	no	—
235	C₇×#120	—	2	2	no	—
236	C₄×C₇×Q₈	—	2	1	no	—
237	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
238	C₄×C₇×Q₈	C₂³	1	2	yes	—
239	C₄×C₇×Q₈	C₂³	1	2	yes	—
240	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
241	C₄×C₇×D₄	—	2	2	no	—
242	C₄×C₇×D₄	—	2	1	no	—
243	C₄×C₇×D₄	—	2	1	no	—
244	C₄×C₇×D₄	—	2	2	no	—
245	C₄×C₇×D₄	—	2	2	no	—
246	C₄×C₇×D₄	—	2	2	no	—
247	C₄×C₇×D₄	—	2	2	no	—
248	C₄×C₇×D₄	—	2	1	no	—
249	C₄×C₇×D₄	—	2	1	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
252	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
253	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
254	C₄×C₇×D₄	C₂³	1	2	yes	—
255	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
256	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
257	C₄×C₇×D₄	C₂³	1	2	yes	—
258	C₄×C₇×D₄	C₂³	1	2	yes	—
259	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₇×#117	—	2	1	no	—
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	1	no	—
264	C₇×#117	C₂³	1	2	yes	—
265	C₇×#117	C₂³	1	2	yes	—
266	C₂×C₇×C₄⋊C₄	—	2	1	no	—
267	C₂×C₇×C₄⋊C₄	—	2	1	no	—
268	C₂×C₇×C₄⋊C₄	—	2	1	no	—
269	C₂×C₇×C₄⋊C₄	—	2	1	no	—
270	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₇×#107	C₂³	1	2	yes	—
276	C₇×#107	C₂³	1	1	yes	characteristic
277	C₇×#107	C₂³	1	1	yes	characteristic
278	C₇×#106	C₂³	1	2	yes	—
279	C₇×#106	C₂³	1	1	yes	characteristic
280	C₇×#106	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₇×C₄⋊C₈	C₂³	1	2	yes	—
285	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₄⋊C₈	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	1	yes	characteristic
294	C₇×#103	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	1	yes	characteristic
302	C₇×#102	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	1	yes	characteristic
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×#102	C₂³	1	1	yes	characteristic
306	C₇×#102	C₂³	1	1	yes	characteristic
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	#3552	C₂×C₇	1	1	yes	characteristic, complemented
317	#3519	C₂×C₇	1	1	yes	characteristic, complemented
318	#3397	C₂×C₇	1	1	yes	characteristic, complemented
319	#3392	C₂×C₇	1	1	yes	characteristic, complemented
320	#3372	C₂×C₇	1	1	yes	characteristic, complemented
321	#3360	C₂×C₇	1	1	yes	characteristic, complemented
322	#3329	C₂×C₇	1	1	yes	characteristic, complemented
323	#3320	C₂×C₇	1	2	yes	complemented
324	#3303	C₂×C₇	1	1	yes	characteristic, complemented
325	#3301	C₂×C₇	1	2	yes	complemented
326	D₄×SD₁₆	C₂×C₇	1	2	yes	complemented
327	D₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
328	#3272	C₂×C₇	1	1	yes	characteristic, complemented
329	#3265	C₂×C₇	1	2	yes	complemented
330	#3260	C₂×C₇	1	2	yes	complemented
331	#3247	C₂×C₇	1	1	yes	characteristic, complemented
332	#3221	C₂×C₇	1	2	yes	complemented
333	#3206	C₂×C₇	1	1	yes	characteristic, complemented
334	#3123	C₂×C₇	1	2	yes	complemented
335	#3105	C₂×C₇	1	1	yes	characteristic, complemented
336	#3042	C₂×C₇	1	2	yes	complemented
337	C₂×#461	C₂×C₇	1	1	yes	characteristic, complemented
338	#2994	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂⁴×C₇	—	2	1	no	—
340	C₂⁴×C₇	—	2	2	no	—
341	C₇×#41	—	4	2	no	—
342	C₇×#41	—	4	2	no	—
343	C₇×#41	—	8	2	no	—
344	C₇×#41	—	8	2	no	—
345	C₂×C₇×Q₈	—	2	2	no	—
346	C₂×C₇×Q₈	—	2	1	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	—	4	2	no	—
349	C₂×C₇×Q₈	—	4	2	no	—
350	C₂×C₇×Q₈	—	4	2	no	—
351	C₂×C₇×Q₈	—	4	2	no	—
352	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
353	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
354	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
355	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
356	C₂×C₇×D₄	—	2	2	no	—
357	C₂×C₇×D₄	—	2	4	no	—
358	C₂×C₇×D₄	—	2	1	no	—
359	C₂×C₇×D₄	—	2	2	no	—
360	C₂×C₇×D₄	—	2	2	no	—
361	C₂×C₇×D₄	—	2	2	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	—	2	2	no	—
364	C₂×C₇×D₄	—	2	1	no	—
365	C₂×C₇×D₄	—	2	1	no	—
366	C₂×C₇×D₄	—	2	2	no	—
367	C₂×C₇×D₄	—	2	1	no	—
368	C₂×C₇×D₄	—	2	2	no	—
369	C₂×C₇×D₄	—	4	1	no	—
370	C₂×C₇×D₄	—	4	2	no	—
371	C₂×C₇×D₄	—	8	2	no	—
372	C₂×C₇×D₄	—	8	4	no	—
373	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
374	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
375	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
376	C₂×C₇×D₄	C₂⁴	1	2	yes	—
377	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
378	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₇	—	2	1	no	—
380	C₂²×C₄×C₇	—	2	2	no	—
381	C₂²×C₄×C₇	—	2	2	no	—
382	C₂²×C₄×C₇	—	2	1	no	—
383	C₂²×C₄×C₇	—	2	1	no	—
384	C₂²×C₄×C₇	—	2	1	no	—
385	C₂²×C₄×C₇	—	2	1	no	—
386	C₂²×C₄×C₇	—	2	2	no	—
387	C₂²×C₄×C₇	—	2	2	no	—
388	C₂²×C₄×C₇	—	2	2	no	—
389	C₂²×C₄×C₇	—	2	2	no	—
390	C₂²×C₄×C₇	—	2	1	no	—
391	C₂²×C₄×C₇	—	8	2	no	—
392	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
396	C₇×SD₁₆	—	2	2	no	—
397	C₇×SD₁₆	—	2	4	no	—
398	C₇×SD₁₆	—	2	4	no	—
399	C₇×SD₁₆	—	4	2	no	—
400	C₇×SD₁₆	—	4	2	no	—
401	C₇×SD₁₆	—	4	2	no	—
402	C₇×SD₁₆	—	4	2	no	—
403	C₇×SD₁₆	—	4	2	no	—
404	C₇×SD₁₆	—	4	1	no	—
405	C₇×SD₁₆	—	4	2	no	—
406	C₇×SD₁₆	—	4	2	no	—
407	C₇×D₈	—	2	2	no	—
408	C₇×D₈	—	4	1	no	—
409	C₇×D₈	—	4	2	no	—
410	C₇×M₁₆	—	4	2	no	—
411	C₂×C₇×C₈	—	4	2	no	—
412	C₂×C₇×C₈	—	4	2	no	—
413	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
414	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
415	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
416	C₂×C₇×C₈	C₂⁴	1	2	yes	—
417	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
418	C₂×C₇×C₈	C₂⁴	1	2	yes	—
419	C₇×C₄⋊C₄	—	2	1	no	—
420	C₇×C₄⋊C₄	—	2	1	no	—
421	C₇×C₄⋊C₄	—	2	1	no	—
422	C₇×C₄⋊C₄	—	2	2	no	—
423	C₇×C₄⋊C₄	—	2	1	no	—
424	C₇×C₄⋊C₄	—	2	2	no	—
425	C₇×C₄⋊C₄	—	2	2	no	—
426	C₇×C₄⋊C₄	—	2	2	no	—
427	C₇×C₄⋊C₄	—	2	1	no	—
428	C₇×C₄⋊C₄	—	2	1	no	—
429	C₇×C₄⋊C₄	—	2	1	no	—
430	C₇×C₄⋊C₄	—	2	1	no	—
431	C₇×C₄⋊C₄	—	2	2	no	—
432	C₇×C₄⋊C₄	—	2	2	no	—
433	C₇×C₄⋊C₄	—	2	2	no	—
434	C₇×C₄⋊C₄	—	2	1	no	—
435	C₇×C₄⋊C₄	—	2	2	no	—
436	C₇×C₄⋊C₄	—	2	2	no	—
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	1	no	—
439	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
442	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
443	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
444	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
445	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
446	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	1	no	—
452	C₇×C₂²⋊C₄	—	2	2	no	—
453	C₇×C₂²⋊C₄	—	2	2	no	—
454	C₇×C₂²⋊C₄	—	2	1	no	—
455	C₇×C₂²⋊C₄	—	2	2	no	—
456	C₇×C₂²⋊C₄	—	2	1	no	—
457	C₇×C₂²⋊C₄	—	2	2	no	—
458	C₇×C₂²⋊C₄	—	2	1	no	—
459	C₇×C₂²⋊C₄	—	2	2	no	—
460	C₇×C₂²⋊C₄	—	2	1	no	—
461	C₇×C₂²⋊C₄	—	2	2	no	—
462	C₇×C₂²⋊C₄	—	2	2	no	—
463	C₇×C₂²⋊C₄	—	2	1	no	—
464	C₇×C₂²⋊C₄	—	2	1	no	—
465	C₇×C₂²⋊C₄	—	2	2	no	—
466	C₇×C₂²⋊C₄	—	2	2	no	—
467	C₇×C₂²⋊C₄	—	2	1	no	—
468	C₇×C₂²⋊C₄	—	2	2	no	—
469	C₇×C₂²⋊C₄	—	2	1	no	—
470	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
471	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
472	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
473	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
474	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
475	C₄²×C₇	—	2	2	no	—
476	C₄²×C₇	—	2	1	no	—
477	C₄²×C₇	—	2	2	no	—
478	C₄²×C₇	—	2	2	no	—
479	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
480	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
481	C₄²×C₇	C₂⁴	1	1	yes	characteristic
482	C₄²×C₇	C₂⁴	1	2	yes	—
483	C₄²×C₇	C₂⁴	1	1	yes	characteristic
484	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
485	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
486	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
487	#563	—	2	2	no	—
488	#557	C₂²×C₇	1	1	yes	characteristic, complemented
489	#556	C₂²×C₇	1	1	yes	characteristic, complemented
490	#555	C₂²×C₇	1	1	yes	characteristic
491	#554	—	2	1	no	—
492	#554	C₂²×C₇	1	1	yes	characteristic
493	#553	—	2	1	no	—
494	#553	—	2	1	no	—
495	#553	C₂²×C₇	1	2	yes	—
496	#550	C₂²×C₇	1	1	yes	characteristic
497	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
498	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
499	#548	C₂²×C₇	1	2	yes	complemented
500	#547	C₂²×C₇	1	1	yes	characteristic, complemented
501	#546	—	2	1	no	—
502	#546	—	2	2	no	—
503	D₄²	C₂²×C₇	1	2	yes	—
504	D₄²	C₂²×C₇	1	1	yes	characteristic
505	#544	—	2	1	no	—
506	#542	—	2	1	no	—
507	#541	C₂²×C₇	1	2	yes	complemented
508	#540	C₂²×C₇	1	2	yes	—
509	#539	—	2	2	no	—
510	#538	—	2	2	no	—
511	#536	C₂²×C₇	1	2	yes	complemented
512	#532	C₂²×C₇	1	1	yes	characteristic
513	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
514	#529	C₂²×C₇	1	1	yes	characteristic
515	#529	C₂²×C₇	1	1	yes	characteristic, complemented
516	#525	—	2	1	no	—
517	C₂×#121	—	2	1	no	—
518	#518	C₂²×C₇	1	2	yes	—
519	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
520	#496	C₂²×C₇	1	2	yes	complemented
521	#492	C₂²×C₇	1	1	yes	characteristic, complemented
522	#492	C₂²×C₇	1	2	yes	complemented
523	#492	C₂²×C₇	1	1	yes	characteristic, complemented
524	#491	C₂²×C₇	1	2	yes	complemented
525	#488	C₂²×C₇	1	2	yes	complemented
526	#487	C₂²×C₇	1	1	yes	characteristic, complemented
527	#487	C₂²×C₇	1	1	yes	characteristic, complemented
528	#485	C₂²×C₇	1	2	yes	complemented
529	#485	C₂²×C₇	1	2	yes	complemented
530	#484	C₂²×C₇	1	1	yes	characteristic, complemented
531	#481	C₂²×C₇	1	1	yes	characteristic, complemented
532	#479	C₂²×C₇	1	2	yes	complemented
533	#479	C₂²×C₇	1	2	yes	complemented
534	#478	C₂²×C₇	1	1	yes	characteristic
535	#478	C₂²×C₇	1	1	yes	characteristic, complemented
536	#478	C₂²×C₇	1	2	yes	complemented
537	#477	C₂²×C₇	1	1	yes	characteristic, complemented
538	#476	C₂²×C₇	1	1	yes	characteristic, complemented
539	#468	C₂²×C₇	1	2	yes	complemented
540	#468	C₂²×C₇	1	2	yes	complemented
541	#466	C₂²×C₇	1	2	yes	complemented
542	#465	C₂²×C₇	1	2	yes	complemented
543	#465	C₂²×C₇	1	2	yes	complemented
544	#465	C₂²×C₇	1	2	yes	complemented
545	#463	C₂²×C₇	1	2	yes	—
546	#463	C₂²×C₇	1	1	yes	characteristic
547	#463	C₂²×C₇	1	1	yes	characteristic, complemented
548	#463	C₂²×C₇	1	2	yes	complemented
549	#463	C₂²×C₇	1	2	yes	complemented
550	#461	C₂²×C₇	1	1	yes	characteristic
551	#461	C₂²×C₇	1	1	yes	characteristic
552	#461	C₂²×C₇	1	2	yes	—
553	#461	C₂²×C₇	1	2	yes	—
554	#461	C₂²×C₇	1	1	yes	characteristic, complemented
555	#461	C₂²×C₇	1	2	yes	complemented
556	#461	C₂²×C₇	1	1	yes	characteristic, complemented
557	#461	C₂²×C₇	1	2	yes	complemented
558	#461	C₂²×C₇	1	2	yes	complemented
559	#461	C₂²×C₇	1	2	yes	complemented
560	#460	C₂²×C₇	1	1	yes	characteristic, complemented
561	#460	C₂²×C₇	1	2	yes	complemented
562	#460	C₂²×C₇	1	2	yes	complemented
563	#459	C₂²×C₇	1	1	yes	characteristic, complemented
564	#450	C₂²×C₇	1	1	yes	characteristic
565	#450	C₂²×C₇	1	2	yes	—
566	#450	C₂²×C₇	1	2	yes	—
567	#449	C₂²×C₇	1	2	yes	complemented
568	#449	C₂²×C₇	1	2	yes	complemented
569	#448	C₂²×C₇	1	2	yes	complemented
570	#448	C₂²×C₇	1	2	yes	complemented
571	#448	C₂²×C₇	1	2	yes	complemented
572	#448	C₂²×C₇	1	2	yes	complemented
573	#447	C₂²×C₇	1	1	yes	characteristic
574	#446	C₂²×C₇	1	1	yes	characteristic, complemented
575	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
576	#440	C₂²×C₇	1	2	yes	—
577	#440	C₂²×C₇	1	2	yes	complemented
578	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
579	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
580	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
581	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
582	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
583	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
584	#436	C₂²×C₇	1	1	yes	characteristic, complemented
585	#435	C₂²×C₇	1	2	yes	complemented
586	C₈×D₄	C₂²×C₇	1	2	yes	complemented
587	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
588	#433	C₂²×C₇	1	2	yes	complemented
589	#431	C₂²×C₇	1	1	yes	characteristic, complemented
590	#424	C₂²×C₇	1	2	yes	complemented
591	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
592	#419	C₂²×C₇	1	2	yes	complemented
593	#416	C₂²×C₇	1	2	yes	complemented
594	C₂×#103	C₂²×C₇	1	2	yes	complemented
595	C₂³×C₇	—	2	1	no	—
596	C₂³×C₇	—	2	1	no	—
597	C₂³×C₇	—	2	1	no	—
598	C₂³×C₇	—	2	2	no	—
599	C₂³×C₇	—	4	2	no	—
600	C₂³×C₇	—	4	4	no	—
601	C₂³×C₇	—	4	2	no	—
602	C₂³×C₇	—	8	1	no	—
603	C₂³×C₇	—	8	2	no	—
604	C₂³×C₇	—	8	2	no	—
605	C₂³×C₇	C₂²×D₄	1	2	yes	—
606	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
607	C₇×Q₈	—	2	2	no	—
608	C₇×Q₈	—	2	1	no	—
609	C₇×Q₈	—	2	2	no	—
610	C₇×Q₈	—	2	2	no	—
611	C₇×Q₈	—	2	2	no	—
612	C₇×Q₈	—	2	1	no	—
613	C₇×Q₈	—	2	2	no	—
614	C₇×Q₈	—	8	2	no	—
615	C₇×Q₈	—	8	2	no	—
616	C₇×Q₈	—	8	1	no	—
617	C₇×D₄	—	2	4	no	—
618	C₇×D₄	—	2	2	no	—
619	C₇×D₄	—	2	1	no	—
620	C₇×D₄	—	2	2	no	—
621	C₇×D₄	—	2	1	no	—
622	C₇×D₄	—	2	1	no	—
623	C₇×D₄	—	2	1	no	—
624	C₇×D₄	—	2	1	no	—
625	C₇×D₄	—	2	2	no	—
626	C₇×D₄	—	4	4	no	—
627	C₇×D₄	—	4	2	no	—
628	C₇×D₄	—	4	2	no	—
629	C₇×D₄	—	4	4	no	—
630	C₇×D₄	—	4	2	no	—
631	C₇×D₄	—	8	2	no	—
632	C₇×D₄	—	8	1	no	—
633	C₇×D₄	—	8	2	no	—
634	C₇×D₄	—	8	2	no	—
635	C₇×D₄	—	8	2	no	—
636	C₇×D₄	—	8	2	no	—
637	C₇×D₄	H(5,𝔽₂)	1	2	yes	—
638	C₂×C₄×C₇	—	2	2	no	—
639	C₂×C₄×C₇	—	2	2	no	—
640	C₂×C₄×C₇	—	2	1	no	—
641	C₂×C₄×C₇	—	2	2	no	—
642	C₂×C₄×C₇	—	2	1	no	—
643	C₂×C₄×C₇	—	2	2	no	—
644	C₂×C₄×C₇	—	2	1	no	—
645	C₂×C₄×C₇	—	2	1	no	—
646	C₂×C₄×C₇	—	2	1	no	—
647	C₂×C₄×C₇	—	2	2	no	—
648	C₂×C₄×C₇	—	2	1	no	—
649	C₂×C₄×C₇	—	2	2	no	—
650	C₂×C₄×C₇	—	2	2	no	—
651	C₂×C₄×C₇	—	2	1	no	—
652	C₂×C₄×C₇	—	4	2	no	—
653	C₂×C₄×C₇	—	4	2	no	—
654	C₂×C₄×C₇	—	4	2	no	—
655	C₂×C₄×C₇	—	8	1	no	—
656	C₂×C₄×C₇	—	8	1	no	—
657	C₂×C₄×C₇	—	8	2	no	—
658	C₂×C₄×C₇	—	8	2	no	—
659	C₂×C₄×C₇	—	8	2	no	—
660	C₂×C₄×C₇	—	8	2	no	—
661	C₂×C₄×C₇	—	8	1	no	—
662	C₂×C₄×C₇	—	8	2	no	—
663	C₂×C₄×C₇	—	8	2	no	—
664	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
665	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
666	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
667	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
668	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
669	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
670	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
671	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
672	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
673	C₇×C₈	—	2	1	no	—
674	C₇×C₈	—	2	2	no	—
675	C₇×C₈	—	2	2	no	—
676	C₇×C₈	—	2	1	no	—
677	C₇×C₈	—	2	1	no	—
678	C₇×C₈	—	2	1	no	—
679	C₂×#41	—	2	1	no	—
680	C₂×#41	—	2	1	no	—
681	C₂×#41	C₂³×C₇	1	2	yes	—
682	C₂²×Q₈	C₂³×C₇	1	2	yes	—
683	C₂²×Q₈	C₂³×C₇	1	2	yes	—
684	C₂²×D₄	—	2	1	no	—
685	C₂²×D₄	—	2	2	no	—
686	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
687	C₂²×D₄	C₂³×C₇	1	2	yes	—
688	C₂³×C₄	—	2	1	no	—
689	AGL(1,ℤ/8)	—	4	4	no	—
690	C₂×SD₁₆	—	4	4	no	—
691	C₂×SD₁₆	—	4	4	no	—
692	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
693	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
694	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
695	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
696	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
697	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
698	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
699	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
700	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
701	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
702	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
703	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
704	C₂×D₈	C₂³×C₇	1	2	yes	—
705	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
706	C₂×M₁₆	C₂³×C₇	1	2	yes	—
707	C₂²×C₈	C₂³×C₇	1	2	yes	—
708	C₂²×C₈	C₂³×C₇	1	2	yes	—
709	C₄⋊Q₈	—	2	1	no	—
710	C₄⋊Q₈	—	2	2	no	—
711	C₄⋊Q₈	—	2	1	no	—
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
714	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
717	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
718	#127	C₂³×C₇	1	1	yes	characteristic
719	#127	C₂³×C₇	1	2	yes	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	1	no	—
725	#126	C₇×D₄	1	2	yes	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	1	no	—
730	#125	C₇×D₄	1	1	yes	characteristic
731	#125	C₂³×C₇	1	1	yes	characteristic
732	#125	C₂³×C₇	1	2	yes	—
733	#124	—	2	2	no	—
734	#124	—	2	2	no	—
735	#124	—	2	1	no	—
736	#124	C₇×D₄	1	1	yes	characteristic
737	#124	C₂³×C₇	1	1	yes	characteristic
738	#124	C₂³×C₇	1	2	yes	—
739	#123	—	2	1	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	C₇×D₄	1	2	yes	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
757	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
760	#121	—	2	2	no	—
761	#121	—	2	1	no	—
762	#121	—	2	2	no	—
763	#121	—	2	1	no	—
764	#121	—	2	1	no	—
765	#121	—	2	1	no	—
766	#121	—	2	1	no	—
767	#121	—	2	2	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	C₇×D₄	1	1	yes	characteristic
772	#121	C₂³×C₇	1	1	yes	characteristic
773	#121	C₂³×C₇	1	2	yes	—
774	#121	C₂³×C₇	1	2	yes	—
775	#121	C₂³×C₇	1	2	yes	—
776	#120	—	2	2	no	—
777	#120	—	2	2	no	—
778	#120	—	2	2	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₇	1	2	yes	—
782	C₄×Q₈	C₂³×C₇	1	2	yes	—
783	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₇	1	2	yes	—
799	C₄×D₄	C₂³×C₇	1	2	yes	—
800	C₄×D₄	C₂³×C₇	1	2	yes	—
801	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₇	1	2	yes	—
804	#117	—	2	1	no	—
805	#117	—	2	1	no	—
806	#117	—	2	1	no	—
807	#117	C₂³×C₇	1	2	yes	—
808	#117	C₂³×C₇	1	2	yes	—
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
814	C₂×C₂²⋊C₄	—	2	1	no	—
815	C₂×C₂²⋊C₄	—	2	2	no	—
816	C₂×C₂²⋊C₄	—	2	2	no	—
817	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
818	#107	C₂³×C₇	1	1	yes	characteristic
819	#107	C₂³×C₇	1	1	yes	characteristic
820	#107	C₂³×C₇	1	2	yes	—
821	#106	C₂³×C₇	1	2	yes	—
822	#106	C₂³×C₇	1	1	yes	characteristic
823	#106	C₂³×C₇	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₇	1	2	yes	—
825	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₇	1	2	yes	—
829	C₄⋊C₈	C₂³×C₇	1	2	yes	—
830	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
831	#103	C₂³×C₇	1	2	yes	—
832	#103	C₂³×C₇	1	2	yes	—
833	#103	C₂³×C₇	1	2	yes	—
834	#103	C₂³×C₇	1	2	yes	—
835	#103	C₂³×C₇	1	2	yes	—
836	#103	C₂³×C₇	1	1	yes	characteristic
837	#103	C₂³×C₇	1	2	yes	—
838	#103	C₂³×C₇	1	2	yes	—
839	#103	C₂³×C₇	1	2	yes	—
840	#103	C₂³×C₇	1	1	yes	characteristic
841	#103	C₂³×C₇	1	2	yes	—
842	#102	C₂³×C₇	1	1	yes	characteristic
843	#102	C₂³×C₇	1	2	yes	—
844	#102	C₂³×C₇	1	1	yes	characteristic
845	#102	C₂³×C₇	1	1	yes	characteristic
846	#102	C₂³×C₇	1	1	yes	characteristic
847	#102	C₂³×C₇	1	1	yes	characteristic
848	#102	C₂³×C₇	1	1	yes	characteristic
849	#102	C₂³×C₇	1	2	yes	—
850	#102	C₂³×C₇	1	2	yes	—
851	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
852	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
853	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
854	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
855	#97	C₂³×C₇	1	2	yes	—
856	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
857	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
858	C₄×C₈	C₂³×C₇	1	2	yes	—
859	C₂²×C₇	—	2	1	no	—
860	C₂²×C₇	—	2	1	no	—
861	C₂²×C₇	—	2	2	no	—
862	C₂²×C₇	—	2	2	no	—
863	C₂²×C₇	—	2	2	no	—
864	C₂²×C₇	—	2	2	no	—
865	C₂²×C₇	—	4	1	no	—
866	C₂²×C₇	—	4	1	no	—
867	C₂²×C₇	—	4	1	no	—
868	C₂²×C₇	—	4	1	no	—
869	C₂²×C₇	—	4	2	no	—
870	C₂²×C₇	—	4	1	no	—
871	C₂²×C₇	—	4	1	no	—
872	C₂²×C₇	—	4	2	no	—
873	C₂²×C₇	—	4	2	no	—
874	C₂²×C₇	—	4	1	no	—
875	C₂²×C₇	—	4	1	no	—
876	C₂²×C₇	—	8	4	no	—
877	C₂²×C₇	—	16	4	no	—
878	C₂²×C₇	#577	1	2	yes	—
879	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
880	C₄×C₇	—	2	2	no	—
881	C₄×C₇	—	2	1	no	—
882	C₄×C₇	—	2	1	no	—
883	C₄×C₇	—	2	1	no	—
884	C₄×C₇	—	2	1	no	—
885	C₄×C₇	—	2	2	no	—
886	C₄×C₇	—	2	2	no	—
887	C₄×C₇	—	4	2	no	—
888	C₄×C₇	—	4	1	no	—
889	C₄×C₇	—	4	2	no	—
890	C₄×C₇	—	4	1	no	—
891	C₄×C₇	—	4	1	no	—
892	C₄×C₇	—	4	1	no	—
893	C₄×C₇	—	4	2	no	—
894	C₄×C₇	—	4	1	no	—
895	C₄×C₇	#577	1	2	yes	—
896	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
897	C₄×C₇	#585	1	1	yes	characteristic
898	C₂⁴	—	2	1	no	—
899	C₂⁴	—	2	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	8	2	no	—
903	#41	—	8	2	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	4	2	no	—
909	C₂×Q₈	—	4	2	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	4	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	4	1	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	8	2	no	—
931	C₂×D₄	—	8	4	no	—
932	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
933	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₇	1	2	yes	—
936	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	8	2	no	—
951	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
952	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	2	4	no	—
957	SD₁₆	—	2	4	no	—
958	SD₁₆	—	4	2	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	2	no	—
962	SD₁₆	—	4	2	no	—
963	SD₁₆	—	4	1	no	—
964	SD₁₆	—	4	2	no	—
965	SD₁₆	—	4	2	no	—
966	D₈	—	2	2	no	—
967	D₈	—	4	1	no	—
968	D₈	—	4	2	no	—
969	M₁₆	—	4	2	no	—
970	C₂×C₈	—	4	2	no	—
971	C₂×C₈	—	4	2	no	—
972	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₇	1	2	yes	—
976	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₇	1	2	yes	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
999	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1000	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1001	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1002	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1003	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1004	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1006	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1008	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1030	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1031	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1032	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1033	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1034	C₄²	—	2	2	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1039	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1040	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₇	1	2	yes	—
1042	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1043	C₂×C₇	—	2	2	no	—
1044	C₂×C₇	—	4	2	no	—
1045	C₂×C₇	—	4	2	no	—
1046	C₂×C₇	—	8	1	no	—
1047	C₂×C₇	—	8	1	no	—
1048	C₂×C₇	—	8	2	no	—
1049	C₂×C₇	#3488	1	1	yes	characteristic
1050	C₂×C₇	C₂×#577	1	1	yes	characteristic
1051	C₂×C₇	C₂×#577	1	1	yes	characteristic
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	4	2	no	—
1057	C₂³	—	4	4	no	—
1058	C₂³	—	4	2	no	—
1059	C₂³	—	8	1	no	—
1060	C₂³	—	8	2	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	C₂²×C₇×D₄	1	2	yes	—
1063	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1064	Q₈	—	2	2	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	2	no	—
1071	Q₈	—	8	2	no	—
1072	Q₈	—	8	2	no	—
1073	Q₈	—	8	1	no	—
1074	D₄	—	2	4	no	—
1075	D₄	—	2	1	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	2	1	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	4	4	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	4	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	1	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	C₇×H(5,𝔽₂)	1	2	yes	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	8	1	no	—
1113	C₂×C₄	—	8	1	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1122	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1123	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1124	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1125	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1126	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1127	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1128	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1129	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1130	C₈	—	2	1	no	—
1131	C₈	—	2	2	no	—
1132	C₈	—	2	2	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₇	#62052	1	1	yes	characteristic, direct product factor, Sylow
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	8	4	no	—
1155	C₂²	—	16	4	no	—
1156	C₂²	C₇×#577	1	2	yes	—
1157	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	2	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	2	no	—
1173	C₄	C₇×#577	1	2	yes	—
1174	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1175	C₄	C₇×#585	1	1	yes	characteristic
1176	C₂	—	2	2	no	—
1177	C₂	—	4	2	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	1	no	—
1180	C₂	—	8	2	no	—
1181	C₂	—	8	1	no	—
1182	C₂	C₇×#3488	1	1	yes	characteristic
1183	C₂	C₂×C₇×#577	1	1	yes	characteristic
1184	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3552	C₂	semidirect
2. C₇×#3519	C₂	semidirect
3. C₇×#3397	C₂	semidirect
4. C₇×#3392	C₂	semidirect
5. C₇×#3372	C₂	semidirect
6. C₇×#3360	C₂	semidirect
7. C₇×#3329	C₂	semidirect
8. C₇×#3320	C₂	semidirect
9. C₇×#3303	C₂	semidirect
10. C₇×#3301	C₂	semidirect
11. C₇×D₄×SD₁₆	C₂	semidirect
12. C₇×D₄×SD₁₆	C₂	semidirect
13. C₇×#3272	C₂	semidirect
14. C₇×#3265	C₂	semidirect
15. C₇×#3260	C₂	semidirect
16. C₇×#3247	C₂	semidirect
17. C₇×#3221	C₂	semidirect
18. C₇×#3206	C₂	semidirect
19. C₇×#3123	C₂	semidirect
20. C₇×#3105	C₂	semidirect
21. C₇×#3042	C₂	semidirect
22. C₂×C₇×#461	C₂	semidirect
23. C₇×#2994	C₂	semidirect
28. C₇×#557	C₂²	semidirect
29. C₇×#556	C₂²	semidirect
37. C₇×D₄×Q₈	C₂²	semidirect
38. C₇×D₄×Q₈	C₂²	semidirect
39. C₇×#548	C₂²	semidirect
40. C₇×#547	C₂²	semidirect
47. C₇×#541	C₂²	semidirect
51. C₇×#536	C₂²	semidirect
53. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
55. C₇×#529	C₂²	semidirect
60. C₇×#496	C₂²	semidirect
61. C₇×#492	C₂²	semidirect
62. C₇×#492	C₂²	semidirect
63. C₇×#492	C₂²	semidirect
64. C₇×#491	C₂²	semidirect
65. C₇×#488	C₂²	semidirect
66. C₇×#487	C₂²	semidirect
67. C₇×#487	C₂²	semidirect
68. C₇×#485	C₂²	semidirect
69. C₇×#485	C₂²	semidirect
70. C₇×#484	C₂²	semidirect
71. C₇×#481	C₂²	semidirect
72. C₇×#479	C₂²	semidirect
73. C₇×#479	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#478	C₂²	semidirect
77. C₇×#477	C₂²	semidirect
78. C₇×#476	C₂²	semidirect
79. C₇×#468	C₂²	semidirect
80. C₇×#468	C₂²	semidirect
81. C₇×#466	C₂²	semidirect
82. C₇×#465	C₂²	semidirect
83. C₇×#465	C₂²	semidirect
84. C₇×#465	C₂²	semidirect
87. C₇×#463	C₂²	semidirect
88. C₇×#463	C₂²	semidirect
89. C₇×#463	C₂²	semidirect
94. C₇×#461	C₂²	semidirect
95. C₇×#461	C₂²	semidirect
96. C₇×#461	C₂²	semidirect
97. C₇×#461	C₂²	semidirect
98. C₇×#461	C₂²	semidirect
99. C₇×#461	C₂²	semidirect
100. C₇×#460	C₂²	semidirect
101. C₇×#460	C₂²	semidirect
102. C₇×#460	C₂²	semidirect
103. C₇×#459	C₂²	semidirect
107. C₇×#449	C₂²	semidirect
108. C₇×#449	C₂²	semidirect
109. C₇×#448	C₂²	semidirect
110. C₇×#448	C₂²	semidirect
111. C₇×#448	C₂²	semidirect
112. C₇×#448	C₂²	semidirect
114. C₇×#446	C₂²	semidirect
115. C₇×C₈×Q₈	C₂²	semidirect
117. C₇×#440	C₂²	semidirect
120. C₄×C₇×SD₁₆	C₂²	semidirect
121. C₄×C₇×SD₁₆	C₂²	semidirect
123. C₄×C₇×D₈	C₂²	semidirect
124. C₇×#436	C₂²	semidirect
125. C₇×#435	C₂²	semidirect
126. C₇×C₈×D₄	C₂²	semidirect
127. C₇×C₈×D₄	C₂²	semidirect
128. C₇×#433	C₂²	semidirect
129. C₇×#431	C₂²	semidirect
130. C₇×#424	C₂²	semidirect
131. C₂×C₇×C₄⋊C₈	C₂²	semidirect
132. C₇×#419	C₂²	semidirect
133. C₇×#416	C₂²	semidirect
134. C₂×C₇×#103	C₂²	semidirect
135. #62052	C₇	direct (N × H)
316. #3552	C₂×C₇	semidirect
317. #3519	C₂×C₇	semidirect
318. #3397	C₂×C₇	semidirect
319. #3392	C₂×C₇	semidirect
320. #3372	C₂×C₇	semidirect
321. #3360	C₂×C₇	semidirect
322. #3329	C₂×C₇	semidirect
323. #3320	C₂×C₇	semidirect
324. #3303	C₂×C₇	semidirect
325. #3301	C₂×C₇	semidirect
326. D₄×SD₁₆	C₂×C₇	semidirect
327. D₄×SD₁₆	C₂×C₇	semidirect
328. #3272	C₂×C₇	semidirect
329. #3265	C₂×C₇	semidirect
330. #3260	C₂×C₇	semidirect
331. #3247	C₂×C₇	semidirect
332. #3221	C₂×C₇	semidirect
333. #3206	C₂×C₇	semidirect
334. #3123	C₂×C₇	semidirect
335. #3105	C₂×C₇	semidirect
336. #3042	C₂×C₇	semidirect
337. C₂×#461	C₂×C₇	semidirect
338. #2994	C₂×C₇	semidirect
488. #557	C₂²×C₇	semidirect
489. #556	C₂²×C₇	semidirect
497. D₄×Q₈	C₂²×C₇	semidirect
498. D₄×Q₈	C₂²×C₇	semidirect
499. #548	C₂²×C₇	semidirect
500. #547	C₂²×C₇	semidirect
507. #541	C₂²×C₇	semidirect
511. #536	C₂²×C₇	semidirect
513. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
515. #529	C₂²×C₇	semidirect
520. #496	C₂²×C₇	semidirect
521. #492	C₂²×C₇	semidirect
522. #492	C₂²×C₇	semidirect
523. #492	C₂²×C₇	semidirect
524. #491	C₂²×C₇	semidirect
525. #488	C₂²×C₇	semidirect
526. #487	C₂²×C₇	semidirect
527. #487	C₂²×C₇	semidirect
528. #485	C₂²×C₇	semidirect
529. #485	C₂²×C₇	semidirect
530. #484	C₂²×C₇	semidirect
531. #481	C₂²×C₇	semidirect
532. #479	C₂²×C₇	semidirect
533. #479	C₂²×C₇	semidirect
535. #478	C₂²×C₇	semidirect
536. #478	C₂²×C₇	semidirect
537. #477	C₂²×C₇	semidirect
538. #476	C₂²×C₇	semidirect
539. #468	C₂²×C₇	semidirect
540. #468	C₂²×C₇	semidirect
541. #466	C₂²×C₇	semidirect
542. #465	C₂²×C₇	semidirect
543. #465	C₂²×C₇	semidirect
544. #465	C₂²×C₇	semidirect
547. #463	C₂²×C₇	semidirect
548. #463	C₂²×C₇	semidirect
549. #463	C₂²×C₇	semidirect
554. #461	C₂²×C₇	semidirect
555. #461	C₂²×C₇	semidirect
556. #461	C₂²×C₇	semidirect
557. #461	C₂²×C₇	semidirect
558. #461	C₂²×C₇	semidirect
559. #461	C₂²×C₇	semidirect
560. #460	C₂²×C₇	semidirect
561. #460	C₂²×C₇	semidirect
562. #460	C₂²×C₇	semidirect
563. #459	C₂²×C₇	semidirect
567. #449	C₂²×C₇	semidirect
568. #449	C₂²×C₇	semidirect
569. #448	C₂²×C₇	semidirect
570. #448	C₂²×C₇	semidirect
571. #448	C₂²×C₇	semidirect
572. #448	C₂²×C₇	semidirect
574. #446	C₂²×C₇	semidirect
575. C₈×Q₈	C₂²×C₇	semidirect
577. #440	C₂²×C₇	semidirect
580. C₄×SD₁₆	C₂²×C₇	semidirect
581. C₄×SD₁₆	C₂²×C₇	semidirect
583. C₄×D₈	C₂²×C₇	semidirect
584. #436	C₂²×C₇	semidirect
585. #435	C₂²×C₇	semidirect
586. C₈×D₄	C₂²×C₇	semidirect
587. C₈×D₄	C₂²×C₇	semidirect
588. #433	C₂²×C₇	semidirect
589. #431	C₂²×C₇	semidirect
590. #424	C₂²×C₇	semidirect
591. C₂×C₄⋊C₈	C₂²×C₇	semidirect
592. #419	C₂²×C₇	semidirect
593. #416	C₂²×C₇	semidirect
594. C₂×#103	C₂²×C₇	semidirect
1136. C₇	#62052	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×#3552	2
C₇×#3519	2
C₇×#3397	2
C₇×#3392	2
C₇×#3372	2
C₇×#3360	2
C₇×#3329	2
C₇×#3320	2
C₇×#3303	2
C₇×#3301	2
C₇×D₄×SD₁₆	2
C₇×#3272	2
C₇×#3265	2
C₇×#3260	2
C₇×#3247	2
C₇×#3221	2
C₇×#3206	2
C₇×#3123	2
C₇×#3105	2
C₇×#3042	2
C₂×C₇×#461	2
C₇×#2994	2
#62052	7

Subgroups — C7×#62052 #13239268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62052 #13239268