Subgroups — C₇×#62888 #13240104

Order 1792.

6906 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3562	C₂	1	8	yes	maximal, complemented
2	C₇×#3560	C₂	1	8	yes	maximal, complemented
3	C₇×#3559	C₂	1	8	yes	maximal, complemented
4	C₇×#3552	C₂	1	8	yes	maximal, complemented
5	C₇×#3541	C₂	1	8	yes	maximal, complemented
6	C₇×#3539	C₂	1	4	yes	maximal, complemented
7	C₇×#3538	C₂	1	4	yes	maximal, complemented
8	C₇×#3512	C₂	1	2	yes	maximal, complemented
9	C₇×#3507	C₂	1	2	yes	maximal, complemented
10	C₇×#3499	C₂	1	2	yes	maximal, complemented
11	C₇×#3497	C₂	1	2	yes	maximal, complemented
12	C₇×#3489	C₂	1	4	yes	maximal, complemented
13	C₇×#3455	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3449	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×2₋¹⁺⁴	C₂²	1	4	yes	complemented
17	C₂²×C₇×#41	C₂²	1	2	yes	—
18	C₇×#563	C₂²	1	16	yes	complemented
19	C₇×#563	C₂²	1	16	yes	complemented
20	C₇×#562	C₂²	1	16	yes	complemented
21	C₇×#560	C₂²	1	16	yes	complemented
22	C₇×#559	C₂²	1	4	yes	complemented
23	C₇×#557	C₂²	1	4	yes	complemented
24	C₇×#556	C₂²	1	8	yes	complemented
25	C₇×#556	C₂²	1	4	yes	complemented
26	C₇×#554	C₂²	1	4	yes	complemented
27	C₇×#554	C₂²	1	16	yes	complemented
28	C₇×#553	C₂²	1	16	yes	complemented
29	C₇×#553	C₂²	1	16	yes	complemented
30	C₇×#553	C₂²	1	16	yes	complemented
31	C₇×#553	C₂²	1	8	yes	complemented
32	C₇×#552	C₂²	1	8	yes	complemented
33	C₇×#552	C₂²	1	8	yes	complemented
34	C₇×#551	C₂²	1	16	yes	complemented
35	C₇×#550	C₂²	1	4	yes	complemented
36	C₇×#550	C₂²	1	4	yes	complemented
37	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
38	C₇×D₄×Q₈	C₂²	1	4	yes	complemented
39	C₇×D₄×Q₈	C₂²	1	4	yes	complemented
40	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
41	C₇×#548	C₂²	1	8	yes	—
42	C₇×#548	C₂²	1	8	yes	complemented
43	C₇×#548	C₂²	1	8	yes	complemented
44	C₇×#547	C₂²	1	8	yes	—
45	C₇×#547	C₂²	1	16	yes	complemented
46	C₇×#547	C₂²	1	16	yes	complemented
47	C₇×#547	C₂²	1	8	yes	complemented
48	C₇×#546	C₂²	1	16	yes	—
49	C₇×#546	C₂²	1	8	yes	complemented
50	C₇×#544	C₂²	1	16	yes	complemented
51	C₇×#542	C₂²	1	16	yes	complemented
52	C₇×#542	C₂²	1	4	yes	complemented
53	C₇×#541	C₂²	1	8	yes	complemented
54	C₇×#541	C₂²	1	4	yes	complemented
55	C₇×#541	C₂²	1	4	yes	complemented
56	C₇×#541	C₂²	1	2	yes	complemented
57	C₇×#541	C₂²	1	4	yes	complemented
58	C₇×#540	C₂²	1	4	yes	complemented
59	C₇×#540	C₂²	1	16	yes	complemented
60	C₇×#540	C₂²	1	2	yes	complemented
61	C₇×#539	C₂²	1	8	yes	complemented
62	C₇×#539	C₂²	1	16	yes	complemented
63	C₇×#539	C₂²	1	16	yes	complemented
64	C₇×#539	C₂²	1	4	yes	complemented
65	C₇×#539	C₂²	1	16	yes	complemented
66	C₇×#538	C₂²	1	4	yes	—
67	C₇×#538	C₂²	1	16	yes	complemented
68	C₇×#538	C₂²	1	16	yes	complemented
69	C₇×#537	C₂²	1	4	yes	—
70	C₇×#537	C₂²	1	8	yes	—
71	C₇×#537	C₂²	1	8	yes	complemented
72	C₇×#537	C₂²	1	4	yes	complemented
73	C₇×#536	C₂²	1	4	yes	—
74	C₇×#536	C₂²	1	8	yes	—
75	C₇×#536	C₂²	1	8	yes	complemented
76	C₇×#536	C₂²	1	4	yes	complemented
77	C₇×#535	C₂²	1	4	yes	—
78	C₇×#534	C₂²	1	4	yes	—
79	C₇×#533	C₂²	1	1	yes	characteristic, complemented
80	C₇×#532	C₂²	1	2	yes	—
81	C₇×#532	C₂²	1	2	yes	—
82	C₇×#532	C₂²	1	8	yes	complemented
83	C₇×#532	C₂²	1	4	yes	complemented
84	C₇×#532	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	complemented
87	C₇×#529	C₂²	1	8	yes	complemented
88	C₇×#529	C₂²	1	8	yes	complemented
89	C₇×#529	C₂²	1	8	yes	complemented
90	C₂×C₇×#126	C₂²	1	4	yes	—
91	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₇×#125	C₂²	1	4	yes	complemented
93	C₇×#525	C₂²	1	4	yes	—
94	C₇×#525	C₂²	1	4	yes	—
95	C₇×#525	C₂²	1	2	yes	—
96	C₇×#525	C₂²	1	8	yes	complemented
97	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
98	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
99	C₇×#520	C₂²	1	4	yes	complemented
100	C₄×C₇×#41	C₂²	1	2	yes	complemented
101	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
102	C₂×C₇×#117	C₂²	1	1	yes	characteristic
103	#62888	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₇×2₋¹⁺⁴	—	4	16	no	—
105	C₂×C₇×#41	—	4	8	no	—
106	C₂×C₇×#41	C₂³	1	4	yes	—
107	C₂×C₇×#41	C₂³	1	2	yes	—
108	C₂×C₇×#41	C₂³	1	4	yes	—
109	C₂×C₇×#41	C₂³	1	4	yes	—
110	C₂×C₇×#41	C₂³	1	4	yes	—
111	C₂×C₇×#41	C₂³	1	8	yes	—
112	C₂×C₇×#41	C₂³	1	8	yes	—
113	C₂×C₇×#41	C₂³	1	16	yes	—
114	C₂²×C₇×Q₈	C₂³	1	2	yes	—
115	C₂²×C₇×Q₈	C₂³	1	2	yes	—
116	C₂²×C₇×Q₈	C₂³	1	8	yes	—
117	C₂²×C₇×Q₈	C₂³	1	8	yes	—
118	C₂²×C₇×D₄	C₂³	1	4	yes	—
119	C₂²×C₇×D₄	C₂³	1	2	yes	—
120	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇	C₂³	1	4	yes	—
122	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
124	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
125	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
126	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
127	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
128	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
130	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
132	C₇×#127	C₂³	1	2	yes	—
133	C₇×#127	C₂³	1	2	yes	—
134	C₇×#127	C₂³	1	1	yes	characteristic
135	C₇×#127	C₂³	1	8	yes	—
136	C₇×#126	C₂³	1	16	yes	—
137	C₇×#126	C₂³	1	16	yes	—
138	C₇×#126	C₂³	1	8	yes	—
139	C₇×#126	C₂³	1	16	yes	—
140	C₇×#126	C₂³	1	16	yes	—
141	C₇×#126	C₂³	1	8	yes	—
142	C₇×#126	C₂³	1	16	yes	—
143	C₇×#126	C₂³	1	16	yes	—
144	C₇×#125	C₂³	1	4	yes	—
145	C₇×#125	C₂³	1	16	yes	—
146	C₇×#125	C₂³	1	4	yes	—
147	C₇×#125	C₂³	1	16	yes	—
148	C₇×#125	C₂³	1	8	yes	—
149	C₇×#125	C₂³	1	8	yes	—
150	C₇×#125	C₂³	1	2	yes	—
151	C₇×#125	C₂³	1	16	yes	—
152	C₇×#125	C₂³	1	16	yes	—
153	C₇×#124	C₂³	1	4	yes	—
154	C₇×#124	C₂³	1	8	yes	—
155	C₇×#124	C₂³	1	8	yes	—
156	C₇×#124	C₂³	1	4	yes	—
157	C₇×#124	C₂³	1	8	yes	—
158	C₇×#124	C₂³	1	16	yes	—
159	C₇×#124	C₂³	1	2	yes	—
160	C₇×#124	C₂³	1	16	yes	—
161	C₇×#123	C₂³	1	8	yes	—
162	C₇×#123	C₂³	1	8	yes	—
163	C₇×#123	C₂³	1	4	yes	—
164	C₇×#123	C₂³	1	16	yes	—
165	C₇×#123	C₂³	1	16	yes	—
166	C₇×#123	C₂³	1	8	yes	—
167	C₇×#123	C₂³	1	8	yes	—
168	C₇×#123	C₂³	1	16	yes	—
169	C₇×#123	C₂³	1	16	yes	—
170	C₇×#123	C₂³	1	16	yes	—
171	C₇×#123	C₂³	1	16	yes	—
172	C₇×#123	C₂³	1	16	yes	—
173	C₇×#123	C₂³	1	16	yes	—
174	C₇×#123	C₂³	1	16	yes	—
175	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
176	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
177	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
178	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
180	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
181	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
182	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
183	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
184	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
185	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
186	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
187	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
188	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
189	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
190	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
191	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
192	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
193	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
194	C₇×#121	C₂³	1	4	yes	—
195	C₇×#121	C₂³	1	8	yes	—
196	C₇×#121	C₂³	1	8	yes	—
197	C₇×#121	C₂³	1	8	yes	—
198	C₇×#121	C₂³	1	4	yes	—
199	C₇×#121	C₂³	1	8	yes	—
200	C₇×#121	C₂³	1	8	yes	—
201	C₇×#121	C₂³	1	4	yes	—
202	C₇×#121	C₂³	1	8	yes	—
203	C₇×#121	C₂³	1	4	yes	—
204	C₇×#121	C₂³	1	16	yes	—
205	C₇×#121	C₂³	1	16	yes	—
206	C₇×#121	C₂³	1	16	yes	—
207	C₇×#121	C₂³	1	16	yes	—
208	C₇×#121	C₂³	1	16	yes	—
209	C₇×#121	C₂³	1	16	yes	—
210	C₇×#121	C₂³	1	16	yes	—
211	C₇×#121	C₂³	1	16	yes	—
212	C₇×#120	C₂³	1	8	yes	—
213	C₇×#120	C₂³	1	8	yes	—
214	C₇×#120	C₂³	1	4	yes	—
215	C₇×#120	C₂³	1	16	yes	—
216	C₄×C₇×Q₈	C₂³	1	4	yes	—
217	C₄×C₇×Q₈	C₂³	1	4	yes	—
218	C₄×C₇×Q₈	C₂³	1	4	yes	—
219	C₄×C₇×Q₈	C₂³	1	4	yes	—
220	C₄×C₇×Q₈	C₂³	1	4	yes	—
221	C₄×C₇×Q₈	C₂³	1	8	yes	—
222	C₄×C₇×Q₈	C₂³	1	4	yes	—
223	C₄×C₇×Q₈	C₂³	1	8	yes	—
224	C₄×C₇×D₄	C₂³	1	8	yes	—
225	C₄×C₇×D₄	C₂³	1	4	yes	—
226	C₄×C₇×D₄	C₂³	1	16	yes	—
227	C₄×C₇×D₄	C₂³	1	8	yes	—
228	C₄×C₇×D₄	C₂³	1	8	yes	—
229	C₄×C₇×D₄	C₂³	1	4	yes	—
230	C₄×C₇×D₄	C₂³	1	4	yes	—
231	C₄×C₇×D₄	C₂³	1	8	yes	—
232	C₄×C₇×D₄	C₂³	1	16	yes	—
233	C₄×C₇×D₄	C₂³	1	16	yes	—
234	C₄×C₇×D₄	C₂³	1	4	yes	—
235	C₄×C₇×D₄	C₂³	1	8	yes	—
236	C₄×C₇×D₄	C₂³	1	16	yes	—
237	C₄×C₇×D₄	C₂³	1	16	yes	—
238	C₄×C₇×D₄	C₂³	1	16	yes	—
239	C₄×C₇×D₄	C₂³	1	8	yes	—
240	C₄×C₇×D₄	C₂³	1	8	yes	—
241	C₇×#117	C₂³	1	2	yes	—
242	C₇×#117	C₂³	1	2	yes	—
243	C₇×#117	C₂³	1	4	yes	—
244	C₇×#117	C₂³	1	2	yes	—
245	C₇×#117	C₂³	1	4	yes	—
246	C₇×#117	C₂³	1	8	yes	—
247	C₇×#117	C₂³	1	16	yes	—
248	C₇×#117	C₂³	1	16	yes	—
249	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
250	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
251	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
252	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
253	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
254	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
255	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
256	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
257	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
258	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
259	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
260	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
261	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
263	C₂×C₄²×C₇	C₂³	1	4	yes	—
264	C₂×C₄²×C₇	C₂³	1	4	yes	—
265	#3562	C₂×C₇	1	8	yes	complemented
266	#3560	C₂×C₇	1	8	yes	complemented
267	#3559	C₂×C₇	1	8	yes	complemented
268	#3552	C₂×C₇	1	8	yes	complemented
269	#3541	C₂×C₇	1	8	yes	complemented
270	#3539	C₂×C₇	1	4	yes	complemented
271	#3538	C₂×C₇	1	4	yes	complemented
272	#3512	C₂×C₇	1	2	yes	complemented
273	#3507	C₂×C₇	1	2	yes	complemented
274	#3499	C₂×C₇	1	2	yes	complemented
275	#3497	C₂×C₇	1	2	yes	complemented
276	#3489	C₂×C₇	1	4	yes	complemented
277	#3455	C₂×C₇	1	1	yes	characteristic, complemented
278	C₂×#541	C₂×C₇	1	1	yes	characteristic, complemented
279	#3449	C₂×C₇	1	1	yes	characteristic, complemented
280	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
281	C₂⁴×C₇	C₂⁴	1	4	yes	—
282	C₇×#41	—	2	16	no	—
283	C₇×#41	—	2	8	no	—
284	C₇×#41	—	4	8	no	—
285	C₇×#41	—	4	8	no	—
286	C₇×#41	—	4	32	no	—
287	C₇×#41	—	4	8	no	—
288	C₇×#41	—	4	16	no	—
289	C₇×#41	—	4	16	no	—
290	C₂×C₇×Q₈	—	2	8	no	—
291	C₂×C₇×Q₈	—	4	4	no	—
292	C₂×C₇×Q₈	—	4	16	no	—
293	C₂×C₇×Q₈	—	4	16	no	—
294	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
295	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
296	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
297	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
298	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
299	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
300	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
301	C₂×C₇×D₄	—	4	4	no	—
302	C₂×C₇×D₄	—	4	8	no	—
303	C₂×C₇×D₄	C₂⁴	1	4	yes	—
304	C₂×C₇×D₄	C₂⁴	1	8	yes	—
305	C₂×C₇×D₄	C₂⁴	1	2	yes	—
306	C₂×C₇×D₄	C₂⁴	1	4	yes	—
307	C₂×C₇×D₄	C₂⁴	1	8	yes	—
308	C₂×C₇×D₄	C₂⁴	1	8	yes	—
309	C₂×C₇×D₄	C₂⁴	1	4	yes	—
310	C₂×C₇×D₄	C₂⁴	1	4	yes	—
311	C₂×C₇×D₄	C₂⁴	1	16	yes	—
312	C₂×C₇×D₄	C₂⁴	1	4	yes	—
313	C₂×C₇×D₄	C₂⁴	1	8	yes	—
314	C₂×C₇×D₄	C₂⁴	1	16	yes	—
315	C₂×C₇×D₄	C₂⁴	1	4	yes	—
316	C₂²×C₄×C₇	—	2	4	no	—
317	C₂²×C₄×C₇	—	4	8	no	—
318	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
319	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
320	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
322	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
327	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
328	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
329	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
330	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
331	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
332	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
333	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
334	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
335	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
336	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
337	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
338	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
339	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
340	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
341	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
342	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
343	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
344	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
345	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
346	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
347	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
348	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
349	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
350	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
351	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
352	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
353	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
354	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
355	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
356	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
357	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
358	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
359	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
360	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
361	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
362	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
363	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
364	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
365	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
366	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
367	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
368	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
369	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
370	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
371	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
372	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
373	C₄²×C₇	C₂⁴	1	2	yes	—
374	C₄²×C₇	C₂⁴	1	2	yes	—
375	C₄²×C₇	C₂⁴	1	1	yes	characteristic
376	C₄²×C₇	C₂⁴	1	4	yes	—
377	C₄²×C₇	C₂⁴	1	1	yes	characteristic
378	C₄²×C₇	C₂⁴	1	8	yes	—
379	C₄²×C₇	C₂⁴	1	2	yes	—
380	C₄²×C₇	C₂⁴	1	8	yes	—
381	C₄²×C₇	C₂⁴	1	8	yes	—
382	C₄²×C₇	C₂⁴	1	16	yes	—
383	C₂×2₋¹⁺⁴	C₂²×C₇	1	4	yes	complemented
384	C₂²×#41	C₂²×C₇	1	2	yes	—
385	#563	C₂²×C₇	1	16	yes	complemented
386	#563	C₂²×C₇	1	16	yes	complemented
387	#562	C₂²×C₇	1	16	yes	complemented
388	#560	C₂²×C₇	1	16	yes	complemented
389	#559	C₂²×C₇	1	4	yes	complemented
390	#557	C₂²×C₇	1	4	yes	complemented
391	#556	C₂²×C₇	1	4	yes	complemented
392	#556	C₂²×C₇	1	8	yes	complemented
393	#554	C₂²×C₇	1	4	yes	complemented
394	#554	C₂²×C₇	1	16	yes	complemented
395	#553	C₂²×C₇	1	8	yes	complemented
396	#553	C₂²×C₇	1	16	yes	complemented
397	#553	C₂²×C₇	1	16	yes	complemented
398	#553	C₂²×C₇	1	16	yes	complemented
399	#552	C₂²×C₇	1	8	yes	complemented
400	#552	C₂²×C₇	1	8	yes	complemented
401	#551	C₂²×C₇	1	16	yes	complemented
402	#550	C₂²×C₇	1	4	yes	complemented
403	#550	C₂²×C₇	1	4	yes	complemented
404	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
405	D₄×Q₈	C₂²×C₇	1	4	yes	complemented
406	D₄×Q₈	C₂²×C₇	1	4	yes	complemented
407	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
408	#548	C₂²×C₇	1	8	yes	—
409	#548	C₂²×C₇	1	8	yes	complemented
410	#548	C₂²×C₇	1	8	yes	complemented
411	#547	C₂²×C₇	1	8	yes	—
412	#547	C₂²×C₇	1	16	yes	complemented
413	#547	C₂²×C₇	1	8	yes	complemented
414	#547	C₂²×C₇	1	16	yes	complemented
415	#546	C₂²×C₇	1	16	yes	—
416	#546	C₂²×C₇	1	8	yes	complemented
417	#544	C₂²×C₇	1	16	yes	complemented
418	#542	C₂²×C₇	1	4	yes	complemented
419	#542	C₂²×C₇	1	16	yes	complemented
420	#541	C₂²×C₇	1	4	yes	complemented
421	#541	C₂²×C₇	1	4	yes	complemented
422	#541	C₂²×C₇	1	8	yes	complemented
423	#541	C₂²×C₇	1	2	yes	complemented
424	#541	C₂²×C₇	1	4	yes	complemented
425	#540	C₂²×C₇	1	2	yes	complemented
426	#540	C₂²×C₇	1	4	yes	complemented
427	#540	C₂²×C₇	1	16	yes	complemented
428	#539	C₂²×C₇	1	4	yes	complemented
429	#539	C₂²×C₇	1	8	yes	complemented
430	#539	C₂²×C₇	1	16	yes	complemented
431	#539	C₂²×C₇	1	16	yes	complemented
432	#539	C₂²×C₇	1	16	yes	complemented
433	#538	C₂²×C₇	1	4	yes	—
434	#538	C₂²×C₇	1	16	yes	complemented
435	#538	C₂²×C₇	1	16	yes	complemented
436	#537	C₂²×C₇	1	4	yes	—
437	#537	C₂²×C₇	1	8	yes	—
438	#537	C₂²×C₇	1	4	yes	complemented
439	#537	C₂²×C₇	1	8	yes	complemented
440	#536	C₂²×C₇	1	4	yes	—
441	#536	C₂²×C₇	1	8	yes	—
442	#536	C₂²×C₇	1	4	yes	complemented
443	#536	C₂²×C₇	1	8	yes	complemented
444	#535	C₂²×C₇	1	4	yes	—
445	#534	C₂²×C₇	1	4	yes	—
446	#533	C₂²×C₇	1	1	yes	characteristic, complemented
447	#532	C₂²×C₇	1	2	yes	—
448	#532	C₂²×C₇	1	2	yes	—
449	#532	C₂²×C₇	1	1	yes	characteristic, complemented
450	#532	C₂²×C₇	1	8	yes	complemented
451	#532	C₂²×C₇	1	4	yes	complemented
452	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
453	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	complemented
454	#529	C₂²×C₇	1	8	yes	complemented
455	#529	C₂²×C₇	1	8	yes	complemented
456	#529	C₂²×C₇	1	8	yes	complemented
457	C₂×#126	C₂²×C₇	1	4	yes	—
458	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
459	C₂×#125	C₂²×C₇	1	4	yes	complemented
460	#525	C₂²×C₇	1	4	yes	—
461	#525	C₂²×C₇	1	4	yes	—
462	#525	C₂²×C₇	1	2	yes	—
463	#525	C₂²×C₇	1	8	yes	complemented
464	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
465	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	complemented
466	#520	C₂²×C₇	1	4	yes	complemented
467	C₄×#41	C₂²×C₇	1	2	yes	complemented
468	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
469	C₂×#117	C₂²×C₇	1	1	yes	characteristic
470	C₂³×C₇	—	2	2	no	—
471	C₂³×C₇	—	4	4	no	—
472	C₂³×C₇	—	4	2	no	—
473	C₂³×C₇	—	4	8	no	—
474	C₂³×C₇	C₂⁵	1	2	yes	—
475	C₂³×C₇	C₂⁵	1	8	yes	—
476	C₂³×C₇	C₂⁵	1	4	yes	—
477	C₂³×C₇	C₂⁵	1	1	yes	characteristic
478	C₇×Q₈	—	2	8	no	—
479	C₇×Q₈	—	2	8	no	—
480	C₇×Q₈	—	2	4	no	—
481	C₇×Q₈	—	2	8	no	—
482	C₇×Q₈	—	4	16	no	—
483	C₇×Q₈	—	4	4	no	—
484	C₇×Q₈	—	4	4	no	—
485	C₇×D₄	—	2	16	no	—
486	C₇×D₄	—	2	8	no	—
487	C₇×D₄	—	2	8	no	—
488	C₇×D₄	—	2	4	no	—
489	C₇×D₄	—	4	4	no	—
490	C₇×D₄	—	4	8	no	—
491	C₇×D₄	—	4	8	no	—
492	C₇×D₄	—	4	16	no	—
493	C₇×D₄	—	4	8	no	—
494	C₇×D₄	—	4	4	no	—
495	C₇×D₄	—	4	4	no	—
496	C₇×D₄	—	4	4	no	—
497	C₇×D₄	—	4	16	no	—
498	C₂×C₄×C₇	—	2	2	no	—
499	C₂×C₄×C₇	—	2	8	no	—
500	C₂×C₄×C₇	—	2	4	no	—
501	C₂×C₄×C₇	—	2	4	no	—
502	C₂×C₄×C₇	—	2	16	no	—
503	C₂×C₄×C₇	—	2	8	no	—
504	C₂×C₄×C₇	—	4	4	no	—
505	C₂×C₄×C₇	—	4	8	no	—
506	C₂×C₄×C₇	—	4	2	no	—
507	C₂×C₄×C₇	—	4	4	no	—
508	C₂×C₄×C₇	—	4	16	no	—
509	C₂×C₄×C₇	—	4	8	no	—
510	C₂×C₄×C₇	—	4	2	no	—
511	C₂×C₄×C₇	—	4	16	no	—
512	C₂×C₄×C₇	—	4	16	no	—
513	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
514	C₂×C₄×C₇	C₂⁵	1	2	yes	—
515	C₂×C₄×C₇	C₂⁵	1	2	yes	—
516	C₂×C₄×C₇	C₂⁵	1	8	yes	—
517	C₂×C₄×C₇	C₂⁵	1	4	yes	—
518	C₂×C₄×C₇	C₂⁵	1	8	yes	—
519	C₂×C₄×C₇	C₂⁵	1	4	yes	—
520	C₂×C₄×C₇	C₂⁵	1	8	yes	—
521	C₂×C₄×C₇	C₂⁵	1	8	yes	—
522	C₂×C₄×C₇	C₂⁵	1	2	yes	—
523	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
524	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
525	2₋¹⁺⁴	—	4	16	no	—
526	C₂×#41	—	4	8	no	—
527	C₂×#41	C₂³×C₇	1	2	yes	—
528	C₂×#41	C₂³×C₇	1	4	yes	—
529	C₂×#41	C₂³×C₇	1	4	yes	—
530	C₂×#41	C₂³×C₇	1	8	yes	—
531	C₂×#41	C₂³×C₇	1	8	yes	—
532	C₂×#41	C₂³×C₇	1	16	yes	—
533	C₂×#41	C₂³×C₇	1	4	yes	—
534	C₂×#41	C₂³×C₇	1	4	yes	—
535	C₂²×Q₈	C₂³×C₇	1	2	yes	—
536	C₂²×Q₈	C₂³×C₇	1	8	yes	—
537	C₂²×Q₈	C₂³×C₇	1	8	yes	—
538	C₂²×Q₈	C₂³×C₇	1	2	yes	—
539	C₂²×D₄	C₂³×C₇	1	4	yes	—
540	C₂²×D₄	C₂³×C₇	1	2	yes	—
541	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₇	1	4	yes	—
543	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
544	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
545	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
546	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
547	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
548	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
551	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
553	#127	C₂³×C₇	1	2	yes	—
554	#127	C₂³×C₇	1	2	yes	—
555	#127	C₂³×C₇	1	1	yes	characteristic
556	#127	C₂³×C₇	1	8	yes	—
557	#126	C₂³×C₇	1	16	yes	—
558	#126	C₂³×C₇	1	16	yes	—
559	#126	C₂³×C₇	1	8	yes	—
560	#126	C₂³×C₇	1	16	yes	—
561	#126	C₂³×C₇	1	16	yes	—
562	#126	C₂³×C₇	1	8	yes	—
563	#126	C₂³×C₇	1	16	yes	—
564	#126	C₂³×C₇	1	16	yes	—
565	#125	C₂³×C₇	1	4	yes	—
566	#125	C₂³×C₇	1	16	yes	—
567	#125	C₂³×C₇	1	4	yes	—
568	#125	C₂³×C₇	1	16	yes	—
569	#125	C₂³×C₇	1	8	yes	—
570	#125	C₂³×C₇	1	8	yes	—
571	#125	C₂³×C₇	1	2	yes	—
572	#125	C₂³×C₇	1	16	yes	—
573	#125	C₂³×C₇	1	16	yes	—
574	#124	C₂³×C₇	1	4	yes	—
575	#124	C₂³×C₇	1	8	yes	—
576	#124	C₂³×C₇	1	8	yes	—
577	#124	C₂³×C₇	1	4	yes	—
578	#124	C₂³×C₇	1	8	yes	—
579	#124	C₂³×C₇	1	16	yes	—
580	#124	C₂³×C₇	1	2	yes	—
581	#124	C₂³×C₇	1	16	yes	—
582	#123	C₂³×C₇	1	8	yes	—
583	#123	C₂³×C₇	1	8	yes	—
584	#123	C₂³×C₇	1	4	yes	—
585	#123	C₂³×C₇	1	16	yes	—
586	#123	C₂³×C₇	1	16	yes	—
587	#123	C₂³×C₇	1	8	yes	—
588	#123	C₂³×C₇	1	8	yes	—
589	#123	C₂³×C₇	1	16	yes	—
590	#123	C₂³×C₇	1	16	yes	—
591	#123	C₂³×C₇	1	16	yes	—
592	#123	C₂³×C₇	1	16	yes	—
593	#123	C₂³×C₇	1	16	yes	—
594	#123	C₂³×C₇	1	16	yes	—
595	#123	C₂³×C₇	1	16	yes	—
596	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
597	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
598	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
599	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
600	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
601	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
602	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
603	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
604	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
605	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
606	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
607	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
608	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
609	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
610	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
611	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
612	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
613	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
614	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
615	#121	C₂³×C₇	1	4	yes	—
616	#121	C₂³×C₇	1	8	yes	—
617	#121	C₂³×C₇	1	8	yes	—
618	#121	C₂³×C₇	1	8	yes	—
619	#121	C₂³×C₇	1	4	yes	—
620	#121	C₂³×C₇	1	8	yes	—
621	#121	C₂³×C₇	1	8	yes	—
622	#121	C₂³×C₇	1	4	yes	—
623	#121	C₂³×C₇	1	8	yes	—
624	#121	C₂³×C₇	1	4	yes	—
625	#121	C₂³×C₇	1	16	yes	—
626	#121	C₂³×C₇	1	16	yes	—
627	#121	C₂³×C₇	1	16	yes	—
628	#121	C₂³×C₇	1	16	yes	—
629	#121	C₂³×C₇	1	16	yes	—
630	#121	C₂³×C₇	1	16	yes	—
631	#121	C₂³×C₇	1	16	yes	—
632	#121	C₂³×C₇	1	16	yes	—
633	#120	C₂³×C₇	1	8	yes	—
634	#120	C₂³×C₇	1	8	yes	—
635	#120	C₂³×C₇	1	4	yes	—
636	#120	C₂³×C₇	1	16	yes	—
637	C₄×Q₈	C₂³×C₇	1	4	yes	—
638	C₄×Q₈	C₂³×C₇	1	4	yes	—
639	C₄×Q₈	C₂³×C₇	1	4	yes	—
640	C₄×Q₈	C₂³×C₇	1	4	yes	—
641	C₄×Q₈	C₂³×C₇	1	4	yes	—
642	C₄×Q₈	C₂³×C₇	1	8	yes	—
643	C₄×Q₈	C₂³×C₇	1	4	yes	—
644	C₄×Q₈	C₂³×C₇	1	8	yes	—
645	C₄×D₄	C₂³×C₇	1	8	yes	—
646	C₄×D₄	C₂³×C₇	1	4	yes	—
647	C₄×D₄	C₂³×C₇	1	16	yes	—
648	C₄×D₄	C₂³×C₇	1	8	yes	—
649	C₄×D₄	C₂³×C₇	1	8	yes	—
650	C₄×D₄	C₂³×C₇	1	4	yes	—
651	C₄×D₄	C₂³×C₇	1	4	yes	—
652	C₄×D₄	C₂³×C₇	1	8	yes	—
653	C₄×D₄	C₂³×C₇	1	16	yes	—
654	C₄×D₄	C₂³×C₇	1	16	yes	—
655	C₄×D₄	C₂³×C₇	1	4	yes	—
656	C₄×D₄	C₂³×C₇	1	8	yes	—
657	C₄×D₄	C₂³×C₇	1	16	yes	—
658	C₄×D₄	C₂³×C₇	1	16	yes	—
659	C₄×D₄	C₂³×C₇	1	16	yes	—
660	C₄×D₄	C₂³×C₇	1	8	yes	—
661	C₄×D₄	C₂³×C₇	1	8	yes	—
662	#117	C₂³×C₇	1	2	yes	—
663	#117	C₂³×C₇	1	2	yes	—
664	#117	C₂³×C₇	1	4	yes	—
665	#117	C₂³×C₇	1	2	yes	—
666	#117	C₂³×C₇	1	4	yes	—
667	#117	C₂³×C₇	1	8	yes	—
668	#117	C₂³×C₇	1	16	yes	—
669	#117	C₂³×C₇	1	16	yes	—
670	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
673	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
674	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
675	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
676	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
677	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
678	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
682	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₇	1	4	yes	—
685	C₂×C₄²	C₂³×C₇	1	4	yes	—
686	C₂²×C₇	—	2	2	no	—
687	C₂²×C₇	—	2	2	no	—
688	C₂²×C₇	—	2	4	no	—
689	C₂²×C₇	—	2	8	no	—
690	C₂²×C₇	—	2	8	no	—
691	C₂²×C₇	—	2	8	no	—
692	C₂²×C₇	—	2	8	no	—
693	C₂²×C₇	—	2	4	no	—
694	C₂²×C₇	—	8	2	no	—
695	C₂²×C₇	—	8	8	no	—
696	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
697	C₂²×C₇	C₂⁶	1	1	yes	characteristic
698	C₄×C₇	—	2	2	no	—
699	C₄×C₇	—	2	8	no	—
700	C₄×C₇	—	2	4	no	—
701	C₄×C₇	—	2	8	no	—
702	C₄×C₇	—	2	8	no	—
703	C₄×C₇	—	2	4	no	—
704	C₄×C₇	—	2	8	no	—
705	C₄×C₇	—	2	2	no	—
706	C₄×C₇	—	2	2	no	—
707	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
708	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
709	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
710	C₂⁴	C₂⁴×C₇	1	4	yes	—
711	#41	—	2	16	no	—
712	#41	—	2	8	no	—
713	#41	—	4	8	no	—
714	#41	—	4	8	no	—
715	#41	—	4	32	no	—
716	#41	—	4	8	no	—
717	#41	—	4	16	no	—
718	#41	—	4	16	no	—
719	C₂×Q₈	—	2	8	no	—
720	C₂×Q₈	—	4	4	no	—
721	C₂×Q₈	—	4	16	no	—
722	C₂×Q₈	—	4	16	no	—
723	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
724	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
725	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
726	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
727	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
728	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
729	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
730	C₂×D₄	—	4	4	no	—
731	C₂×D₄	—	4	8	no	—
732	C₂×D₄	C₂⁴×C₇	1	4	yes	—
733	C₂×D₄	C₂⁴×C₇	1	8	yes	—
734	C₂×D₄	C₂⁴×C₇	1	2	yes	—
735	C₂×D₄	C₂⁴×C₇	1	4	yes	—
736	C₂×D₄	C₂⁴×C₇	1	8	yes	—
737	C₂×D₄	C₂⁴×C₇	1	8	yes	—
738	C₂×D₄	C₂⁴×C₇	1	4	yes	—
739	C₂×D₄	C₂⁴×C₇	1	4	yes	—
740	C₂×D₄	C₂⁴×C₇	1	16	yes	—
741	C₂×D₄	C₂⁴×C₇	1	4	yes	—
742	C₂×D₄	C₂⁴×C₇	1	8	yes	—
743	C₂×D₄	C₂⁴×C₇	1	16	yes	—
744	C₂×D₄	C₂⁴×C₇	1	4	yes	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	4	8	no	—
747	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
748	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
749	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
751	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
756	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
757	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
758	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
759	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
760	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
761	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
762	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
763	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
764	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
765	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
766	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
767	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
768	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
769	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
770	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
771	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
772	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
773	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
774	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
775	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
776	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
777	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
778	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
779	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
780	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
781	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
782	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
783	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
784	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
785	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
786	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
787	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
788	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
789	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
790	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
791	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
792	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
793	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
794	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
795	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
796	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
797	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
798	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
799	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
800	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
801	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
802	C₄²	C₂⁴×C₇	1	2	yes	—
803	C₄²	C₂⁴×C₇	1	2	yes	—
804	C₄²	C₂⁴×C₇	1	1	yes	characteristic
805	C₄²	C₂⁴×C₇	1	4	yes	—
806	C₄²	C₂⁴×C₇	1	1	yes	characteristic
807	C₄²	C₂⁴×C₇	1	8	yes	—
808	C₄²	C₂⁴×C₇	1	2	yes	—
809	C₄²	C₂⁴×C₇	1	8	yes	—
810	C₄²	C₂⁴×C₇	1	8	yes	—
811	C₄²	C₂⁴×C₇	1	16	yes	—
812	C₂×C₇	—	2	2	no	—
813	C₂×C₇	—	4	4	no	—
814	C₂×C₇	—	4	8	no	—
815	C₂×C₇	—	4	2	no	—
816	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
817	C₂×C₇	2₋¹⁺⁶	1	2	yes	—
818	C₂³	—	2	2	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	4	2	no	—
821	C₂³	—	4	8	no	—
822	C₂³	C₂⁵×C₇	1	2	yes	—
823	C₂³	C₂⁵×C₇	1	8	yes	—
824	C₂³	C₂⁵×C₇	1	4	yes	—
825	C₂³	C₂⁵×C₇	1	1	yes	characteristic
826	Q₈	—	2	8	no	—
827	Q₈	—	2	8	no	—
828	Q₈	—	2	4	no	—
829	Q₈	—	2	8	no	—
830	Q₈	—	4	16	no	—
831	Q₈	—	4	4	no	—
832	Q₈	—	4	4	no	—
833	D₄	—	2	16	no	—
834	D₄	—	2	8	no	—
835	D₄	—	2	8	no	—
836	D₄	—	2	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	8	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	16	no	—
841	D₄	—	4	8	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	16	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	8	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	16	no	—
851	C₂×C₄	—	2	8	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	8	no	—
854	C₂×C₄	—	4	2	no	—
855	C₂×C₄	—	4	4	no	—
856	C₂×C₄	—	4	16	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	4	16	no	—
860	C₂×C₄	—	4	16	no	—
861	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
862	C₂×C₄	C₂⁵×C₇	1	2	yes	—
863	C₂×C₄	C₂⁵×C₇	1	2	yes	—
864	C₂×C₄	C₂⁵×C₇	1	8	yes	—
865	C₂×C₄	C₂⁵×C₇	1	4	yes	—
866	C₂×C₄	C₂⁵×C₇	1	8	yes	—
867	C₂×C₄	C₂⁵×C₇	1	4	yes	—
868	C₂×C₄	C₂⁵×C₇	1	8	yes	—
869	C₂×C₄	C₂⁵×C₇	1	8	yes	—
870	C₂×C₄	C₂⁵×C₇	1	2	yes	—
871	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
872	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
873	C₇	#62888	1	1	yes	characteristic, direct product factor, Sylow
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	8	no	—
878	C₂²	—	2	8	no	—
879	C₂²	—	2	8	no	—
880	C₂²	—	2	8	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	8	2	no	—
883	C₂²	—	8	8	no	—
884	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
885	C₂²	C₂⁶×C₇	1	1	yes	characteristic
886	C₄	—	2	2	no	—
887	C₄	—	2	8	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	8	no	—
890	C₄	—	2	8	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	8	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
896	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
897	C₂	—	2	2	no	—
898	C₂	—	4	2	no	—
899	C₂	—	4	8	no	—
900	C₂	—	4	4	no	—
901	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂	C₇×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3562	C₂	semidirect
2. C₇×#3560	C₂	semidirect
3. C₇×#3559	C₂	semidirect
4. C₇×#3552	C₂	semidirect
5. C₇×#3541	C₂	semidirect
6. C₇×#3539	C₂	semidirect
7. C₇×#3538	C₂	semidirect
8. C₇×#3512	C₂	semidirect
9. C₇×#3507	C₂	semidirect
10. C₇×#3499	C₂	semidirect
11. C₇×#3497	C₂	semidirect
12. C₇×#3489	C₂	semidirect
13. C₇×#3455	C₂	semidirect
14. C₂×C₇×#541	C₂	semidirect
15. C₇×#3449	C₂	semidirect
16. C₂×C₇×2₋¹⁺⁴	C₂²	semidirect
18. C₇×#563	C₂²	semidirect
19. C₇×#563	C₂²	semidirect
20. C₇×#562	C₂²	semidirect
21. C₇×#560	C₂²	semidirect
22. C₇×#559	C₂²	semidirect
23. C₇×#557	C₂²	semidirect
24. C₇×#556	C₂²	semidirect
25. C₇×#556	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
27. C₇×#554	C₂²	semidirect
28. C₇×#553	C₂²	semidirect
29. C₇×#553	C₂²	semidirect
30. C₇×#553	C₂²	semidirect
31. C₇×#553	C₂²	semidirect
32. C₇×#552	C₂²	semidirect
33. C₇×#552	C₂²	semidirect
34. C₇×#551	C₂²	semidirect
35. C₇×#550	C₂²	semidirect
36. C₇×#550	C₂²	semidirect
37. C₇×D₄×Q₈	C₂²	semidirect
38. C₇×D₄×Q₈	C₂²	semidirect
39. C₇×D₄×Q₈	C₂²	semidirect
40. C₇×D₄×Q₈	C₂²	semidirect
42. C₇×#548	C₂²	semidirect
43. C₇×#548	C₂²	semidirect
45. C₇×#547	C₂²	semidirect
46. C₇×#547	C₂²	semidirect
47. C₇×#547	C₂²	semidirect
49. C₇×#546	C₂²	semidirect
50. C₇×#544	C₂²	semidirect
51. C₇×#542	C₂²	semidirect
52. C₇×#542	C₂²	semidirect
53. C₇×#541	C₂²	semidirect
54. C₇×#541	C₂²	semidirect
55. C₇×#541	C₂²	semidirect
56. C₇×#541	C₂²	semidirect
57. C₇×#541	C₂²	semidirect
58. C₇×#540	C₂²	semidirect
59. C₇×#540	C₂²	semidirect
60. C₇×#540	C₂²	semidirect
61. C₇×#539	C₂²	semidirect
62. C₇×#539	C₂²	semidirect
63. C₇×#539	C₂²	semidirect
64. C₇×#539	C₂²	semidirect
65. C₇×#539	C₂²	semidirect
67. C₇×#538	C₂²	semidirect
68. C₇×#538	C₂²	semidirect
71. C₇×#537	C₂²	semidirect
72. C₇×#537	C₂²	semidirect
75. C₇×#536	C₂²	semidirect
76. C₇×#536	C₂²	semidirect
79. C₇×#533	C₂²	semidirect
82. C₇×#532	C₂²	semidirect
83. C₇×#532	C₂²	semidirect
84. C₇×#532	C₂²	semidirect
85. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
86. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
87. C₇×#529	C₂²	semidirect
88. C₇×#529	C₂²	semidirect
89. C₇×#529	C₂²	semidirect
91. C₂×C₇×#125	C₂²	semidirect
92. C₂×C₇×#125	C₂²	semidirect
96. C₇×#525	C₂²	semidirect
98. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
99. C₇×#520	C₂²	semidirect
100. C₄×C₇×#41	C₂²	semidirect
101. C₂×C₄×C₇×Q₈	C₂²	semidirect
103. #62888	C₇	direct (N × H)
265. #3562	C₂×C₇	semidirect
266. #3560	C₂×C₇	semidirect
267. #3559	C₂×C₇	semidirect
268. #3552	C₂×C₇	semidirect
269. #3541	C₂×C₇	semidirect
270. #3539	C₂×C₇	semidirect
271. #3538	C₂×C₇	semidirect
272. #3512	C₂×C₇	semidirect
273. #3507	C₂×C₇	semidirect
274. #3499	C₂×C₇	semidirect
275. #3497	C₂×C₇	semidirect
276. #3489	C₂×C₇	semidirect
277. #3455	C₂×C₇	semidirect
278. C₂×#541	C₂×C₇	semidirect
279. #3449	C₂×C₇	semidirect
383. C₂×2₋¹⁺⁴	C₂²×C₇	semidirect
385. #563	C₂²×C₇	semidirect
386. #563	C₂²×C₇	semidirect
387. #562	C₂²×C₇	semidirect
388. #560	C₂²×C₇	semidirect
389. #559	C₂²×C₇	semidirect
390. #557	C₂²×C₇	semidirect
391. #556	C₂²×C₇	semidirect
392. #556	C₂²×C₇	semidirect
393. #554	C₂²×C₇	semidirect
394. #554	C₂²×C₇	semidirect
395. #553	C₂²×C₇	semidirect
396. #553	C₂²×C₇	semidirect
397. #553	C₂²×C₇	semidirect
398. #553	C₂²×C₇	semidirect
399. #552	C₂²×C₇	semidirect
400. #552	C₂²×C₇	semidirect
401. #551	C₂²×C₇	semidirect
402. #550	C₂²×C₇	semidirect
403. #550	C₂²×C₇	semidirect
404. D₄×Q₈	C₂²×C₇	semidirect
405. D₄×Q₈	C₂²×C₇	semidirect
406. D₄×Q₈	C₂²×C₇	semidirect
407. D₄×Q₈	C₂²×C₇	semidirect
409. #548	C₂²×C₇	semidirect
410. #548	C₂²×C₇	semidirect
412. #547	C₂²×C₇	semidirect
413. #547	C₂²×C₇	semidirect
414. #547	C₂²×C₇	semidirect
416. #546	C₂²×C₇	semidirect
417. #544	C₂²×C₇	semidirect
418. #542	C₂²×C₇	semidirect
419. #542	C₂²×C₇	semidirect
420. #541	C₂²×C₇	semidirect
421. #541	C₂²×C₇	semidirect
422. #541	C₂²×C₇	semidirect
423. #541	C₂²×C₇	semidirect
424. #541	C₂²×C₇	semidirect
425. #540	C₂²×C₇	semidirect
426. #540	C₂²×C₇	semidirect
427. #540	C₂²×C₇	semidirect
428. #539	C₂²×C₇	semidirect
429. #539	C₂²×C₇	semidirect
430. #539	C₂²×C₇	semidirect
431. #539	C₂²×C₇	semidirect
432. #539	C₂²×C₇	semidirect
434. #538	C₂²×C₇	semidirect
435. #538	C₂²×C₇	semidirect
438. #537	C₂²×C₇	semidirect
439. #537	C₂²×C₇	semidirect
442. #536	C₂²×C₇	semidirect
443. #536	C₂²×C₇	semidirect
446. #533	C₂²×C₇	semidirect
449. #532	C₂²×C₇	semidirect
450. #532	C₂²×C₇	semidirect
451. #532	C₂²×C₇	semidirect
452. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
453. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
454. #529	C₂²×C₇	semidirect
455. #529	C₂²×C₇	semidirect
456. #529	C₂²×C₇	semidirect
458. C₂×#125	C₂²×C₇	semidirect
459. C₂×#125	C₂²×C₇	semidirect
463. #525	C₂²×C₇	semidirect
465. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
466. #520	C₂²×C₇	semidirect
467. C₄×#41	C₂²×C₇	semidirect
468. C₂×C₄×Q₈	C₂²×C₇	semidirect
873. C₇	#62888	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×#3562	2
C₇×#3560	2
C₇×#3559	2
C₇×#3552	2
C₇×#3541	2
C₇×#3539	2
C₇×#3538	2
C₇×#3512	2
C₇×#3507	2
C₇×#3499	2
C₇×#3497	2
C₇×#3489	2
C₇×#3455	2
C₂×C₇×#541	2
C₇×#3449	2
#62888	7

Subgroups — C7×#62888 #13240104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62888 #13240104