Subgroups — C₇×#62881 #13240097

Order 1792.

6610 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3559	C₂	1	8	yes	maximal, complemented
2	C₇×#3557	C₂	1	4	yes	maximal, complemented
3	C₇×#3554	C₂	1	8	yes	maximal, complemented
4	C₇×#3548	C₂	1	4	yes	maximal, complemented
5	C₇×#3547	C₂	1	8	yes	maximal, complemented
6	C₇×#3536	C₂	1	8	yes	maximal, complemented
7	C₇×#3535	C₂	1	8	yes	maximal, complemented
8	C₇×#3508	C₂	1	2	yes	maximal, complemented
9	C₇×#3506	C₂	1	2	yes	maximal, complemented
10	C₇×#3504	C₂	1	2	yes	maximal, complemented
11	C₇×#3501	C₂	1	2	yes	maximal, complemented
12	C₇×#3494	C₂	1	4	yes	maximal, complemented
13	C₇×#3458	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3455	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#563	C₂²	1	16	yes	complemented
17	C₇×#562	C₂²	1	16	yes	complemented
18	C₇×#562	C₂²	1	16	yes	complemented
19	C₇×#562	C₂²	1	16	yes	complemented
20	C₇×#559	C₂²	1	8	yes	complemented
21	C₇×#559	C₂²	1	8	yes	complemented
22	C₇×#557	C₂²	1	8	yes	complemented
23	C₇×#556	C₂²	1	4	yes	complemented
24	C₇×#555	C₂²	1	8	yes	complemented
25	C₇×#555	C₂²	1	4	yes	complemented
26	C₇×#554	C₂²	1	16	yes	—
27	C₇×#554	C₂²	1	8	yes	complemented
28	C₇×#554	C₂²	1	8	yes	complemented
29	C₇×#554	C₂²	1	4	yes	complemented
30	C₇×#554	C₂²	1	4	yes	complemented
31	C₇×#554	C₂²	1	8	yes	complemented
32	C₇×#553	C₂²	1	8	yes	complemented
33	C₇×#553	C₂²	1	8	yes	complemented
34	C₇×#553	C₂²	1	8	yes	complemented
35	C₇×#552	C₂²	1	16	yes	complemented
36	C₇×#551	C₂²	1	16	yes	—
37	C₇×#550	C₂²	1	4	yes	complemented
38	C₇×#550	C₂²	1	8	yes	complemented
39	C₇×D₄×Q₈	C₂²	1	4	yes	complemented
40	C₇×D₄×Q₈	C₂²	1	4	yes	complemented
41	C₇×#548	C₂²	1	16	yes	complemented
42	C₇×#547	C₂²	1	8	yes	complemented
43	C₇×#547	C₂²	1	4	yes	complemented
44	C₇×#547	C₂²	1	16	yes	complemented
45	C₇×#547	C₂²	1	16	yes	complemented
46	C₇×#546	C₂²	1	16	yes	—
47	C₇×#546	C₂²	1	16	yes	—
48	C₇×#544	C₂²	1	4	yes	—
49	C₇×#544	C₂²	1	4	yes	—
50	C₇×#544	C₂²	1	4	yes	complemented
51	C₇×#544	C₂²	1	4	yes	complemented
52	C₇×#544	C₂²	1	8	yes	complemented
53	C₇×#543	C₂²	1	4	yes	—
54	C₇×#543	C₂²	1	8	yes	—
55	C₇×#542	C₂²	1	4	yes	complemented
56	C₇×#542	C₂²	1	8	yes	complemented
57	C₇×#542	C₂²	1	16	yes	complemented
58	C₇×#542	C₂²	1	16	yes	complemented
59	C₇×#541	C₂²	1	2	yes	complemented
60	C₇×#540	C₂²	1	8	yes	—
61	C₇×#540	C₂²	1	4	yes	—
62	C₇×#540	C₂²	1	4	yes	—
63	C₇×#540	C₂²	1	2	yes	complemented
64	C₇×#540	C₂²	1	8	yes	complemented
65	C₇×#540	C₂²	1	4	yes	complemented
66	C₇×#540	C₂²	1	4	yes	complemented
67	C₇×#539	C₂²	1	4	yes	—
68	C₇×#539	C₂²	1	16	yes	complemented
69	C₇×#539	C₂²	1	16	yes	complemented
70	C₇×#539	C₂²	1	16	yes	complemented
71	C₇×#538	C₂²	1	4	yes	—
72	C₇×#538	C₂²	1	8	yes	—
73	C₇×#537	C₂²	1	16	yes	complemented
74	C₇×#537	C₂²	1	16	yes	complemented
75	C₇×#536	C₂²	1	16	yes	complemented
76	C₇×#535	C₂²	1	4	yes	—
77	C₇×#533	C₂²	1	1	yes	characteristic
78	C₇×#533	C₂²	1	2	yes	—
79	C₇×#533	C₂²	1	2	yes	—
80	C₇×#533	C₂²	1	4	yes	complemented
81	C₇×#533	C₂²	1	4	yes	complemented
82	C₇×#533	C₂²	1	4	yes	complemented
83	C₇×#532	C₂²	1	1	yes	characteristic
84	C₇×#532	C₂²	1	8	yes	complemented
85	C₇×#532	C₂²	1	8	yes	complemented
86	C₂×C₇×#127	C₂²	1	1	yes	characteristic
87	C₇×#529	C₂²	1	8	yes	complemented
88	C₇×#529	C₂²	1	8	yes	complemented
89	C₂×C₇×#125	C₂²	1	1	yes	characteristic
90	C₂×C₇×#125	C₂²	1	4	yes	complemented
91	C₇×#525	C₂²	1	2	yes	—
92	C₇×#525	C₂²	1	8	yes	—
93	C₂×C₇×#123	C₂²	1	4	yes	—
94	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	—
95	C₂×C₇×#121	C₂²	1	2	yes	—
96	C₂×C₇×#121	C₂²	1	4	yes	—
97	C₇×#520	C₂²	1	4	yes	—
98	C₇×#518	C₂²	1	4	yes	—
99	C₄×C₇×#41	C₂²	1	2	yes	—
100	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
101	C₂×C₇×#117	C₂²	1	1	yes	characteristic
102	C₂×C₇×#117	C₂²	1	2	yes	—
103	#62881	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂×C₇×#41	C₂³	1	2	yes	—
105	C₂×C₇×#41	C₂³	1	8	yes	—
106	C₂×C₇×#41	C₂³	1	16	yes	—
107	C₂×C₇×#41	C₂³	1	16	yes	—
108	C₂²×C₇×Q₈	C₂³	1	8	yes	—
109	C₂²×C₇×D₄	C₂³	1	2	yes	—
110	C₂²×C₇×D₄	C₂³	1	4	yes	—
111	C₂²×C₇×D₄	C₂³	1	4	yes	—
112	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇	C₂³	1	4	yes	—
114	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
117	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
121	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
122	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
123	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
124	C₇×#127	C₂³	1	4	yes	—
125	C₇×#127	C₂³	1	4	yes	—
126	C₇×#127	C₂³	1	1	yes	characteristic
127	C₇×#127	C₂³	1	8	yes	—
128	C₇×#126	C₂³	1	8	yes	—
129	C₇×#126	C₂³	1	8	yes	—
130	C₇×#126	C₂³	1	16	yes	—
131	C₇×#126	C₂³	1	16	yes	—
132	C₇×#126	C₂³	1	16	yes	—
133	C₇×#125	C₂³	1	4	yes	—
134	C₇×#125	C₂³	1	4	yes	—
135	C₇×#125	C₂³	1	2	yes	—
136	C₇×#125	C₂³	1	16	yes	—
137	C₇×#125	C₂³	1	8	yes	—
138	C₇×#125	C₂³	1	8	yes	—
139	C₇×#125	C₂³	1	8	yes	—
140	C₇×#125	C₂³	1	2	yes	—
141	C₇×#125	C₂³	1	2	yes	—
142	C₇×#125	C₂³	1	4	yes	—
143	C₇×#125	C₂³	1	8	yes	—
144	C₇×#125	C₂³	1	8	yes	—
145	C₇×#125	C₂³	1	16	yes	—
146	C₇×#124	C₂³	1	8	yes	—
147	C₇×#124	C₂³	1	8	yes	—
148	C₇×#124	C₂³	1	2	yes	—
149	C₇×#124	C₂³	1	16	yes	—
150	C₇×#124	C₂³	1	16	yes	—
151	C₇×#124	C₂³	1	16	yes	—
152	C₇×#124	C₂³	1	16	yes	—
153	C₇×#123	C₂³	1	16	yes	—
154	C₇×#123	C₂³	1	16	yes	—
155	C₇×#123	C₂³	1	16	yes	—
156	C₇×#123	C₂³	1	4	yes	—
157	C₇×#123	C₂³	1	8	yes	—
158	C₇×#123	C₂³	1	8	yes	—
159	C₇×#123	C₂³	1	16	yes	—
160	C₇×#123	C₂³	1	16	yes	—
161	C₇×#123	C₂³	1	16	yes	—
162	C₇×#123	C₂³	1	16	yes	—
163	C₇×#123	C₂³	1	16	yes	—
164	C₇×#123	C₂³	1	16	yes	—
165	C₇×#123	C₂³	1	16	yes	—
166	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
167	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
168	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
169	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
170	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
171	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
172	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
173	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
174	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
175	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
176	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
177	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
178	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
180	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
181	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
182	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
183	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
184	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
185	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
186	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
187	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
188	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
189	C₇×#121	C₂³	1	8	yes	—
190	C₇×#121	C₂³	1	16	yes	—
191	C₇×#121	C₂³	1	16	yes	—
192	C₇×#121	C₂³	1	8	yes	—
193	C₇×#121	C₂³	1	4	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	8	yes	—
199	C₇×#121	C₂³	1	16	yes	—
200	C₇×#121	C₂³	1	16	yes	—
201	C₇×#121	C₂³	1	16	yes	—
202	C₇×#121	C₂³	1	16	yes	—
203	C₇×#121	C₂³	1	16	yes	—
204	C₇×#121	C₂³	1	16	yes	—
205	C₇×#121	C₂³	1	16	yes	—
206	C₇×#120	C₂³	1	16	yes	—
207	C₇×#120	C₂³	1	4	yes	—
208	C₄×C₇×Q₈	C₂³	1	4	yes	—
209	C₄×C₇×Q₈	C₂³	1	8	yes	—
210	C₄×C₇×Q₈	C₂³	1	4	yes	—
211	C₄×C₇×Q₈	C₂³	1	4	yes	—
212	C₄×C₇×Q₈	C₂³	1	4	yes	—
213	C₄×C₇×Q₈	C₂³	1	8	yes	—
214	C₄×C₇×Q₈	C₂³	1	16	yes	—
215	C₄×C₇×D₄	C₂³	1	4	yes	—
216	C₄×C₇×D₄	C₂³	1	4	yes	—
217	C₄×C₇×D₄	C₂³	1	4	yes	—
218	C₄×C₇×D₄	C₂³	1	4	yes	—
219	C₄×C₇×D₄	C₂³	1	8	yes	—
220	C₄×C₇×D₄	C₂³	1	4	yes	—
221	C₄×C₇×D₄	C₂³	1	8	yes	—
222	C₄×C₇×D₄	C₂³	1	8	yes	—
223	C₄×C₇×D₄	C₂³	1	8	yes	—
224	C₄×C₇×D₄	C₂³	1	8	yes	—
225	C₄×C₇×D₄	C₂³	1	16	yes	—
226	C₄×C₇×D₄	C₂³	1	8	yes	—
227	C₄×C₇×D₄	C₂³	1	8	yes	—
228	C₄×C₇×D₄	C₂³	1	16	yes	—
229	C₄×C₇×D₄	C₂³	1	4	yes	—
230	C₄×C₇×D₄	C₂³	1	16	yes	—
231	C₄×C₇×D₄	C₂³	1	16	yes	—
232	C₄×C₇×D₄	C₂³	1	16	yes	—
233	C₇×#117	C₂³	1	4	yes	—
234	C₇×#117	C₂³	1	4	yes	—
235	C₇×#117	C₂³	1	2	yes	—
236	C₇×#117	C₂³	1	2	yes	—
237	C₇×#117	C₂³	1	4	yes	—
238	C₇×#117	C₂³	1	4	yes	—
239	C₇×#117	C₂³	1	2	yes	—
240	C₇×#117	C₂³	1	2	yes	—
241	C₇×#117	C₂³	1	2	yes	—
242	C₇×#117	C₂³	1	4	yes	—
243	C₇×#117	C₂³	1	8	yes	—
244	C₇×#117	C₂³	1	8	yes	—
245	C₇×#117	C₂³	1	16	yes	—
246	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
248	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
249	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
250	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
251	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
252	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
253	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
254	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
255	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
256	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
257	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
258	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
259	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
260	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
261	C₂×C₄²×C₇	C₂³	1	4	yes	—
262	C₂×C₄²×C₇	C₂³	1	4	yes	—
263	#3559	C₂×C₇	1	8	yes	complemented
264	#3557	C₂×C₇	1	4	yes	complemented
265	#3554	C₂×C₇	1	8	yes	complemented
266	#3548	C₂×C₇	1	4	yes	complemented
267	#3547	C₂×C₇	1	8	yes	complemented
268	#3536	C₂×C₇	1	8	yes	complemented
269	#3535	C₂×C₇	1	8	yes	complemented
270	#3508	C₂×C₇	1	2	yes	complemented
271	#3506	C₂×C₇	1	2	yes	complemented
272	#3504	C₂×C₇	1	2	yes	complemented
273	#3501	C₂×C₇	1	2	yes	complemented
274	#3494	C₂×C₇	1	4	yes	complemented
275	#3458	C₂×C₇	1	1	yes	characteristic, complemented
276	#3455	C₂×C₇	1	1	yes	characteristic, complemented
277	C₂×#540	C₂×C₇	1	1	yes	characteristic, complemented
278	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
279	C₂⁴×C₇	C₂⁴	1	4	yes	—
280	C₇×#41	—	2	8	no	—
281	C₇×#41	—	8	8	no	—
282	C₇×#41	—	8	16	no	—
283	C₇×#41	—	8	16	no	—
284	C₂×C₇×Q₈	—	8	8	no	—
285	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
286	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
287	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
288	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
289	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
290	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
291	C₂×C₇×D₄	—	2	8	no	—
292	C₂×C₇×D₄	—	8	4	no	—
293	C₂×C₇×D₄	—	8	4	no	—
294	C₂×C₇×D₄	C₂⁴	1	4	yes	—
295	C₂×C₇×D₄	C₂⁴	1	4	yes	—
296	C₂×C₇×D₄	C₂⁴	1	4	yes	—
297	C₂×C₇×D₄	C₂⁴	1	2	yes	—
298	C₂×C₇×D₄	C₂⁴	1	8	yes	—
299	C₂×C₇×D₄	C₂⁴	1	16	yes	—
300	C₂×C₇×D₄	C₂⁴	1	16	yes	—
301	C₂×C₇×D₄	C₂⁴	1	16	yes	—
302	C₂×C₇×D₄	C₂⁴	1	4	yes	—
303	C₂×C₇×D₄	C₂⁴	1	16	yes	—
304	C₂²×C₄×C₇	—	2	4	no	—
305	C₂²×C₄×C₇	—	8	4	no	—
306	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
308	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
315	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
316	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
317	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
318	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
319	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
320	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
321	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
322	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
324	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
325	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
326	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
327	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
328	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
329	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
330	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
331	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
332	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
333	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
334	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
335	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
336	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
337	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
338	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
339	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
340	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
341	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
342	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
343	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
344	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
345	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
346	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
347	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
348	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
349	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
350	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
351	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
352	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
353	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
354	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
355	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
356	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
357	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
358	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
359	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
360	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
361	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
362	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
363	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
364	C₄²×C₇	C₂⁴	1	2	yes	—
365	C₄²×C₇	C₂⁴	1	4	yes	—
366	C₄²×C₇	C₂⁴	1	2	yes	—
367	C₄²×C₇	C₂⁴	1	4	yes	—
368	C₄²×C₇	C₂⁴	1	1	yes	characteristic
369	C₄²×C₇	C₂⁴	1	1	yes	characteristic
370	C₄²×C₇	C₂⁴	1	4	yes	—
371	C₄²×C₇	C₂⁴	1	8	yes	—
372	C₄²×C₇	C₂⁴	1	2	yes	—
373	C₄²×C₇	C₂⁴	1	8	yes	—
374	C₄²×C₇	C₂⁴	1	16	yes	—
375	#563	C₂²×C₇	1	16	yes	complemented
376	#562	C₂²×C₇	1	16	yes	complemented
377	#562	C₂²×C₇	1	16	yes	complemented
378	#562	C₂²×C₇	1	16	yes	complemented
379	#559	C₂²×C₇	1	8	yes	complemented
380	#559	C₂²×C₇	1	8	yes	complemented
381	#557	C₂²×C₇	1	8	yes	complemented
382	#556	C₂²×C₇	1	4	yes	complemented
383	#555	C₂²×C₇	1	8	yes	complemented
384	#555	C₂²×C₇	1	4	yes	complemented
385	#554	C₂²×C₇	1	16	yes	—
386	#554	C₂²×C₇	1	8	yes	complemented
387	#554	C₂²×C₇	1	8	yes	complemented
388	#554	C₂²×C₇	1	4	yes	complemented
389	#554	C₂²×C₇	1	4	yes	complemented
390	#554	C₂²×C₇	1	8	yes	complemented
391	#553	C₂²×C₇	1	8	yes	complemented
392	#553	C₂²×C₇	1	8	yes	complemented
393	#553	C₂²×C₇	1	8	yes	complemented
394	#552	C₂²×C₇	1	16	yes	complemented
395	#551	C₂²×C₇	1	16	yes	—
396	#550	C₂²×C₇	1	4	yes	complemented
397	#550	C₂²×C₇	1	8	yes	complemented
398	D₄×Q₈	C₂²×C₇	1	4	yes	complemented
399	D₄×Q₈	C₂²×C₇	1	4	yes	complemented
400	#548	C₂²×C₇	1	16	yes	complemented
401	#547	C₂²×C₇	1	8	yes	complemented
402	#547	C₂²×C₇	1	4	yes	complemented
403	#547	C₂²×C₇	1	16	yes	complemented
404	#547	C₂²×C₇	1	16	yes	complemented
405	#546	C₂²×C₇	1	16	yes	—
406	#546	C₂²×C₇	1	16	yes	—
407	#544	C₂²×C₇	1	4	yes	—
408	#544	C₂²×C₇	1	4	yes	—
409	#544	C₂²×C₇	1	4	yes	complemented
410	#544	C₂²×C₇	1	4	yes	complemented
411	#544	C₂²×C₇	1	8	yes	complemented
412	#543	C₂²×C₇	1	4	yes	—
413	#543	C₂²×C₇	1	8	yes	—
414	#542	C₂²×C₇	1	4	yes	complemented
415	#542	C₂²×C₇	1	8	yes	complemented
416	#542	C₂²×C₇	1	16	yes	complemented
417	#542	C₂²×C₇	1	16	yes	complemented
418	#541	C₂²×C₇	1	2	yes	complemented
419	#540	C₂²×C₇	1	8	yes	—
420	#540	C₂²×C₇	1	4	yes	—
421	#540	C₂²×C₇	1	4	yes	—
422	#540	C₂²×C₇	1	2	yes	complemented
423	#540	C₂²×C₇	1	8	yes	complemented
424	#540	C₂²×C₇	1	4	yes	complemented
425	#540	C₂²×C₇	1	4	yes	complemented
426	#539	C₂²×C₇	1	4	yes	—
427	#539	C₂²×C₇	1	16	yes	complemented
428	#539	C₂²×C₇	1	16	yes	complemented
429	#539	C₂²×C₇	1	16	yes	complemented
430	#538	C₂²×C₇	1	4	yes	—
431	#538	C₂²×C₇	1	8	yes	—
432	#537	C₂²×C₇	1	16	yes	complemented
433	#537	C₂²×C₇	1	16	yes	complemented
434	#536	C₂²×C₇	1	16	yes	complemented
435	#535	C₂²×C₇	1	4	yes	—
436	#533	C₂²×C₇	1	1	yes	characteristic
437	#533	C₂²×C₇	1	2	yes	—
438	#533	C₂²×C₇	1	2	yes	—
439	#533	C₂²×C₇	1	4	yes	complemented
440	#533	C₂²×C₇	1	4	yes	complemented
441	#533	C₂²×C₇	1	4	yes	complemented
442	#532	C₂²×C₇	1	1	yes	characteristic
443	#532	C₂²×C₇	1	8	yes	complemented
444	#532	C₂²×C₇	1	8	yes	complemented
445	C₂×#127	C₂²×C₇	1	1	yes	characteristic
446	#529	C₂²×C₇	1	8	yes	complemented
447	#529	C₂²×C₇	1	8	yes	complemented
448	C₂×#125	C₂²×C₇	1	1	yes	characteristic
449	C₂×#125	C₂²×C₇	1	4	yes	complemented
450	#525	C₂²×C₇	1	2	yes	—
451	#525	C₂²×C₇	1	8	yes	—
452	C₂×#123	C₂²×C₇	1	4	yes	—
453	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	—
454	C₂×#121	C₂²×C₇	1	2	yes	—
455	C₂×#121	C₂²×C₇	1	4	yes	—
456	#520	C₂²×C₇	1	4	yes	—
457	#518	C₂²×C₇	1	4	yes	—
458	C₄×#41	C₂²×C₇	1	2	yes	—
459	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
460	C₂×#117	C₂²×C₇	1	1	yes	characteristic
461	C₂×#117	C₂²×C₇	1	2	yes	—
462	C₂³×C₇	—	2	2	no	—
463	C₂³×C₇	—	2	8	no	—
464	C₂³×C₇	—	4	4	no	—
465	C₂³×C₇	—	4	2	no	—
466	C₂³×C₇	—	4	4	no	—
467	C₂³×C₇	C₂⁵	1	2	yes	—
468	C₂³×C₇	C₂⁵	1	8	yes	—
469	C₂³×C₇	C₂⁵	1	4	yes	—
470	C₂³×C₇	C₂⁵	1	1	yes	characteristic
471	C₇×Q₈	—	2	4	no	—
472	C₇×Q₈	—	4	4	no	—
473	C₇×Q₈	—	4	4	no	—
474	C₇×Q₈	—	4	16	no	—
475	C₇×Q₈	—	4	4	no	—
476	C₇×Q₈	—	4	8	no	—
477	C₇×D₄	—	2	8	no	—
478	C₇×D₄	—	2	8	no	—
479	C₇×D₄	—	2	8	no	—
480	C₇×D₄	—	2	4	no	—
481	C₇×D₄	—	4	16	no	—
482	C₇×D₄	—	4	16	no	—
483	C₇×D₄	—	4	16	no	—
484	C₇×D₄	—	4	4	no	—
485	C₇×D₄	—	4	8	no	—
486	C₇×D₄	—	4	16	no	—
487	C₂×C₄×C₇	—	2	2	no	—
488	C₂×C₄×C₇	—	2	4	no	—
489	C₂×C₄×C₇	—	2	4	no	—
490	C₂×C₄×C₇	—	2	8	no	—
491	C₂×C₄×C₇	—	4	2	no	—
492	C₂×C₄×C₇	—	4	4	no	—
493	C₂×C₄×C₇	—	4	8	no	—
494	C₂×C₄×C₇	—	4	8	no	—
495	C₂×C₄×C₇	—	4	2	no	—
496	C₂×C₄×C₇	—	4	16	no	—
497	C₂×C₄×C₇	—	4	16	no	—
498	C₂×C₄×C₇	—	4	16	no	—
499	C₂×C₄×C₇	—	4	8	no	—
500	C₂×C₄×C₇	—	4	8	no	—
501	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
502	C₂×C₄×C₇	C₂⁵	1	4	yes	—
503	C₂×C₄×C₇	C₂⁵	1	2	yes	—
504	C₂×C₄×C₇	C₂⁵	1	8	yes	—
505	C₂×C₄×C₇	C₂⁵	1	4	yes	—
506	C₂×C₄×C₇	C₂⁵	1	2	yes	—
507	C₂×C₄×C₇	C₂⁵	1	8	yes	—
508	C₂×C₄×C₇	C₂⁵	1	2	yes	—
509	C₂×C₄×C₇	C₂⁵	1	8	yes	—
510	C₂×C₄×C₇	C₂⁵	1	8	yes	—
511	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
512	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
513	C₂×#41	C₂³×C₇	1	2	yes	—
514	C₂×#41	C₂³×C₇	1	8	yes	—
515	C₂×#41	C₂³×C₇	1	16	yes	—
516	C₂×#41	C₂³×C₇	1	16	yes	—
517	C₂²×Q₈	C₂³×C₇	1	8	yes	—
518	C₂²×D₄	C₂³×C₇	1	2	yes	—
519	C₂²×D₄	C₂³×C₇	1	4	yes	—
520	C₂²×D₄	C₂³×C₇	1	4	yes	—
521	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₇	1	4	yes	—
523	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
524	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
525	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
526	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
527	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
528	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
529	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
530	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
531	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
532	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
533	#127	C₂³×C₇	1	4	yes	—
534	#127	C₂³×C₇	1	4	yes	—
535	#127	C₂³×C₇	1	1	yes	characteristic
536	#127	C₂³×C₇	1	8	yes	—
537	#126	C₂³×C₇	1	8	yes	—
538	#126	C₂³×C₇	1	8	yes	—
539	#126	C₂³×C₇	1	16	yes	—
540	#126	C₂³×C₇	1	16	yes	—
541	#126	C₂³×C₇	1	16	yes	—
542	#125	C₂³×C₇	1	4	yes	—
543	#125	C₂³×C₇	1	4	yes	—
544	#125	C₂³×C₇	1	2	yes	—
545	#125	C₂³×C₇	1	16	yes	—
546	#125	C₂³×C₇	1	8	yes	—
547	#125	C₂³×C₇	1	8	yes	—
548	#125	C₂³×C₇	1	8	yes	—
549	#125	C₂³×C₇	1	2	yes	—
550	#125	C₂³×C₇	1	2	yes	—
551	#125	C₂³×C₇	1	4	yes	—
552	#125	C₂³×C₇	1	8	yes	—
553	#125	C₂³×C₇	1	8	yes	—
554	#125	C₂³×C₇	1	16	yes	—
555	#124	C₂³×C₇	1	8	yes	—
556	#124	C₂³×C₇	1	8	yes	—
557	#124	C₂³×C₇	1	2	yes	—
558	#124	C₂³×C₇	1	16	yes	—
559	#124	C₂³×C₇	1	16	yes	—
560	#124	C₂³×C₇	1	16	yes	—
561	#124	C₂³×C₇	1	16	yes	—
562	#123	C₂³×C₇	1	16	yes	—
563	#123	C₂³×C₇	1	16	yes	—
564	#123	C₂³×C₇	1	16	yes	—
565	#123	C₂³×C₇	1	4	yes	—
566	#123	C₂³×C₇	1	8	yes	—
567	#123	C₂³×C₇	1	8	yes	—
568	#123	C₂³×C₇	1	16	yes	—
569	#123	C₂³×C₇	1	16	yes	—
570	#123	C₂³×C₇	1	16	yes	—
571	#123	C₂³×C₇	1	16	yes	—
572	#123	C₂³×C₇	1	16	yes	—
573	#123	C₂³×C₇	1	16	yes	—
574	#123	C₂³×C₇	1	16	yes	—
575	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
576	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
577	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
578	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
579	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
580	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
581	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
582	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
583	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
584	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
585	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
586	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
587	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
588	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
589	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
590	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
591	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
592	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
593	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
594	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
595	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
596	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
597	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
598	#121	C₂³×C₇	1	8	yes	—
599	#121	C₂³×C₇	1	16	yes	—
600	#121	C₂³×C₇	1	16	yes	—
601	#121	C₂³×C₇	1	8	yes	—
602	#121	C₂³×C₇	1	4	yes	—
603	#121	C₂³×C₇	1	4	yes	—
604	#121	C₂³×C₇	1	8	yes	—
605	#121	C₂³×C₇	1	8	yes	—
606	#121	C₂³×C₇	1	8	yes	—
607	#121	C₂³×C₇	1	8	yes	—
608	#121	C₂³×C₇	1	16	yes	—
609	#121	C₂³×C₇	1	16	yes	—
610	#121	C₂³×C₇	1	16	yes	—
611	#121	C₂³×C₇	1	16	yes	—
612	#121	C₂³×C₇	1	16	yes	—
613	#121	C₂³×C₇	1	16	yes	—
614	#121	C₂³×C₇	1	16	yes	—
615	#120	C₂³×C₇	1	16	yes	—
616	#120	C₂³×C₇	1	4	yes	—
617	C₄×Q₈	C₂³×C₇	1	4	yes	—
618	C₄×Q₈	C₂³×C₇	1	8	yes	—
619	C₄×Q₈	C₂³×C₇	1	4	yes	—
620	C₄×Q₈	C₂³×C₇	1	4	yes	—
621	C₄×Q₈	C₂³×C₇	1	4	yes	—
622	C₄×Q₈	C₂³×C₇	1	8	yes	—
623	C₄×Q₈	C₂³×C₇	1	16	yes	—
624	C₄×D₄	C₂³×C₇	1	4	yes	—
625	C₄×D₄	C₂³×C₇	1	4	yes	—
626	C₄×D₄	C₂³×C₇	1	4	yes	—
627	C₄×D₄	C₂³×C₇	1	4	yes	—
628	C₄×D₄	C₂³×C₇	1	8	yes	—
629	C₄×D₄	C₂³×C₇	1	4	yes	—
630	C₄×D₄	C₂³×C₇	1	8	yes	—
631	C₄×D₄	C₂³×C₇	1	8	yes	—
632	C₄×D₄	C₂³×C₇	1	8	yes	—
633	C₄×D₄	C₂³×C₇	1	8	yes	—
634	C₄×D₄	C₂³×C₇	1	16	yes	—
635	C₄×D₄	C₂³×C₇	1	8	yes	—
636	C₄×D₄	C₂³×C₇	1	8	yes	—
637	C₄×D₄	C₂³×C₇	1	16	yes	—
638	C₄×D₄	C₂³×C₇	1	4	yes	—
639	C₄×D₄	C₂³×C₇	1	16	yes	—
640	C₄×D₄	C₂³×C₇	1	16	yes	—
641	C₄×D₄	C₂³×C₇	1	16	yes	—
642	#117	C₂³×C₇	1	4	yes	—
643	#117	C₂³×C₇	1	4	yes	—
644	#117	C₂³×C₇	1	2	yes	—
645	#117	C₂³×C₇	1	2	yes	—
646	#117	C₂³×C₇	1	4	yes	—
647	#117	C₂³×C₇	1	4	yes	—
648	#117	C₂³×C₇	1	2	yes	—
649	#117	C₂³×C₇	1	2	yes	—
650	#117	C₂³×C₇	1	2	yes	—
651	#117	C₂³×C₇	1	4	yes	—
652	#117	C₂³×C₇	1	8	yes	—
653	#117	C₂³×C₇	1	8	yes	—
654	#117	C₂³×C₇	1	16	yes	—
655	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
657	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
659	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
660	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
661	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
662	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
668	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₇	1	4	yes	—
671	C₂×C₄²	C₂³×C₇	1	4	yes	—
672	C₂²×C₇	—	2	2	no	—
673	C₂²×C₇	—	2	2	no	—
674	C₂²×C₇	—	2	4	no	—
675	C₂²×C₇	—	2	8	no	—
676	C₂²×C₇	—	2	8	no	—
677	C₂²×C₇	—	2	8	no	—
678	C₂²×C₇	—	2	4	no	—
679	C₂²×C₇	—	2	8	no	—
680	C₂²×C₇	—	8	2	no	—
681	C₂²×C₇	—	8	8	no	—
682	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
683	C₂²×C₇	C₂⁶	1	1	yes	characteristic
684	C₄×C₇	—	2	2	no	—
685	C₄×C₇	—	2	4	no	—
686	C₄×C₇	—	2	2	no	—
687	C₄×C₇	—	2	8	no	—
688	C₄×C₇	—	2	8	no	—
689	C₄×C₇	—	2	8	no	—
690	C₄×C₇	—	2	2	no	—
691	C₄×C₇	—	2	4	no	—
692	C₄×C₇	—	2	8	no	—
693	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
694	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
695	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
696	C₂⁴	C₂⁴×C₇	1	4	yes	—
697	#41	—	2	8	no	—
698	#41	—	8	8	no	—
699	#41	—	8	16	no	—
700	#41	—	8	16	no	—
701	C₂×Q₈	—	8	8	no	—
702	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
703	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
704	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
705	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
706	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
707	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
708	C₂×D₄	—	2	8	no	—
709	C₂×D₄	—	8	4	no	—
710	C₂×D₄	—	8	4	no	—
711	C₂×D₄	C₂⁴×C₇	1	4	yes	—
712	C₂×D₄	C₂⁴×C₇	1	4	yes	—
713	C₂×D₄	C₂⁴×C₇	1	4	yes	—
714	C₂×D₄	C₂⁴×C₇	1	2	yes	—
715	C₂×D₄	C₂⁴×C₇	1	8	yes	—
716	C₂×D₄	C₂⁴×C₇	1	16	yes	—
717	C₂×D₄	C₂⁴×C₇	1	16	yes	—
718	C₂×D₄	C₂⁴×C₇	1	16	yes	—
719	C₂×D₄	C₂⁴×C₇	1	4	yes	—
720	C₂×D₄	C₂⁴×C₇	1	16	yes	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	8	4	no	—
723	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
725	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
730	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
731	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
732	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
733	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
734	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
735	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
736	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
737	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
738	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
739	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
740	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
741	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
742	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
743	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
744	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
745	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
746	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
747	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
748	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
749	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
750	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
751	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
752	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
753	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
754	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
755	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
756	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
757	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
758	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
759	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
760	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
761	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
762	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
763	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
764	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
765	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
766	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
767	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
768	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
769	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
770	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
771	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
772	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
773	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
774	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
775	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
776	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
777	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
778	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
779	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
780	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
781	C₄²	C₂⁴×C₇	1	2	yes	—
782	C₄²	C₂⁴×C₇	1	4	yes	—
783	C₄²	C₂⁴×C₇	1	2	yes	—
784	C₄²	C₂⁴×C₇	1	4	yes	—
785	C₄²	C₂⁴×C₇	1	1	yes	characteristic
786	C₄²	C₂⁴×C₇	1	1	yes	characteristic
787	C₄²	C₂⁴×C₇	1	4	yes	—
788	C₄²	C₂⁴×C₇	1	8	yes	—
789	C₄²	C₂⁴×C₇	1	2	yes	—
790	C₄²	C₂⁴×C₇	1	8	yes	—
791	C₄²	C₂⁴×C₇	1	16	yes	—
792	C₂×C₇	—	2	2	no	—
793	C₂×C₇	—	4	4	no	—
794	C₂×C₇	—	4	2	no	—
795	C₂×C₇	—	4	8	no	—
796	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
797	C₂×C₇	H(7,𝔽₂)	1	2	yes	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	8	no	—
800	C₂³	—	4	4	no	—
801	C₂³	—	4	2	no	—
802	C₂³	—	4	4	no	—
803	C₂³	C₂⁵×C₇	1	2	yes	—
804	C₂³	C₂⁵×C₇	1	8	yes	—
805	C₂³	C₂⁵×C₇	1	4	yes	—
806	C₂³	C₂⁵×C₇	1	1	yes	characteristic
807	Q₈	—	2	4	no	—
808	Q₈	—	4	4	no	—
809	Q₈	—	4	4	no	—
810	Q₈	—	4	16	no	—
811	Q₈	—	4	4	no	—
812	Q₈	—	4	8	no	—
813	D₄	—	2	8	no	—
814	D₄	—	2	8	no	—
815	D₄	—	2	8	no	—
816	D₄	—	2	4	no	—
817	D₄	—	4	16	no	—
818	D₄	—	4	16	no	—
819	D₄	—	4	16	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	16	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	8	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	8	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	16	no	—
833	C₂×C₄	—	4	16	no	—
834	C₂×C₄	—	4	16	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
838	C₂×C₄	C₂⁵×C₇	1	4	yes	—
839	C₂×C₄	C₂⁵×C₇	1	2	yes	—
840	C₂×C₄	C₂⁵×C₇	1	8	yes	—
841	C₂×C₄	C₂⁵×C₇	1	4	yes	—
842	C₂×C₄	C₂⁵×C₇	1	2	yes	—
843	C₂×C₄	C₂⁵×C₇	1	8	yes	—
844	C₂×C₄	C₂⁵×C₇	1	2	yes	—
845	C₂×C₄	C₂⁵×C₇	1	8	yes	—
846	C₂×C₄	C₂⁵×C₇	1	8	yes	—
847	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
848	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
849	C₇	#62881	1	1	yes	characteristic, direct product factor, Sylow
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	8	no	—
854	C₂²	—	2	8	no	—
855	C₂²	—	2	8	no	—
856	C₂²	—	2	4	no	—
857	C₂²	—	2	8	no	—
858	C₂²	—	8	2	no	—
859	C₂²	—	8	8	no	—
860	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
861	C₂²	C₂⁶×C₇	1	1	yes	characteristic
862	C₄	—	2	2	no	—
863	C₄	—	2	4	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	8	no	—
866	C₄	—	2	8	no	—
867	C₄	—	2	8	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	8	no	—
871	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
872	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
873	C₂	—	2	2	no	—
874	C₂	—	4	2	no	—
875	C₂	—	4	8	no	—
876	C₂	—	4	4	no	—
877	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
878	C₂	C₇×H(7,𝔽₂)	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×#3559	C₂	semidirect
2. C₇×#3557	C₂	semidirect
3. C₇×#3554	C₂	semidirect
4. C₇×#3548	C₂	semidirect
5. C₇×#3547	C₂	semidirect
6. C₇×#3536	C₂	semidirect
7. C₇×#3535	C₂	semidirect
8. C₇×#3508	C₂	semidirect
9. C₇×#3506	C₂	semidirect
10. C₇×#3504	C₂	semidirect
11. C₇×#3501	C₂	semidirect
12. C₇×#3494	C₂	semidirect
13. C₇×#3458	C₂	semidirect
14. C₇×#3455	C₂	semidirect
15. C₂×C₇×#540	C₂	semidirect
16. C₇×#563	C₂²	semidirect
17. C₇×#562	C₂²	semidirect
18. C₇×#562	C₂²	semidirect
19. C₇×#562	C₂²	semidirect
20. C₇×#559	C₂²	semidirect
21. C₇×#559	C₂²	semidirect
22. C₇×#557	C₂²	semidirect
23. C₇×#556	C₂²	semidirect
24. C₇×#555	C₂²	semidirect
25. C₇×#555	C₂²	semidirect
27. C₇×#554	C₂²	semidirect
28. C₇×#554	C₂²	semidirect
29. C₇×#554	C₂²	semidirect
30. C₇×#554	C₂²	semidirect
31. C₇×#554	C₂²	semidirect
32. C₇×#553	C₂²	semidirect
33. C₇×#553	C₂²	semidirect
34. C₇×#553	C₂²	semidirect
35. C₇×#552	C₂²	semidirect
37. C₇×#550	C₂²	semidirect
38. C₇×#550	C₂²	semidirect
39. C₇×D₄×Q₈	C₂²	semidirect
40. C₇×D₄×Q₈	C₂²	semidirect
41. C₇×#548	C₂²	semidirect
42. C₇×#547	C₂²	semidirect
43. C₇×#547	C₂²	semidirect
44. C₇×#547	C₂²	semidirect
45. C₇×#547	C₂²	semidirect
50. C₇×#544	C₂²	semidirect
51. C₇×#544	C₂²	semidirect
52. C₇×#544	C₂²	semidirect
55. C₇×#542	C₂²	semidirect
56. C₇×#542	C₂²	semidirect
57. C₇×#542	C₂²	semidirect
58. C₇×#542	C₂²	semidirect
59. C₇×#541	C₂²	semidirect
63. C₇×#540	C₂²	semidirect
64. C₇×#540	C₂²	semidirect
65. C₇×#540	C₂²	semidirect
66. C₇×#540	C₂²	semidirect
68. C₇×#539	C₂²	semidirect
69. C₇×#539	C₂²	semidirect
70. C₇×#539	C₂²	semidirect
73. C₇×#537	C₂²	semidirect
74. C₇×#537	C₂²	semidirect
75. C₇×#536	C₂²	semidirect
80. C₇×#533	C₂²	semidirect
81. C₇×#533	C₂²	semidirect
82. C₇×#533	C₂²	semidirect
84. C₇×#532	C₂²	semidirect
85. C₇×#532	C₂²	semidirect
87. C₇×#529	C₂²	semidirect
88. C₇×#529	C₂²	semidirect
90. C₂×C₇×#125	C₂²	semidirect
103. #62881	C₇	direct (N × H)
263. #3559	C₂×C₇	semidirect
264. #3557	C₂×C₇	semidirect
265. #3554	C₂×C₇	semidirect
266. #3548	C₂×C₇	semidirect
267. #3547	C₂×C₇	semidirect
268. #3536	C₂×C₇	semidirect
269. #3535	C₂×C₇	semidirect
270. #3508	C₂×C₇	semidirect
271. #3506	C₂×C₇	semidirect
272. #3504	C₂×C₇	semidirect
273. #3501	C₂×C₇	semidirect
274. #3494	C₂×C₇	semidirect
275. #3458	C₂×C₇	semidirect
276. #3455	C₂×C₇	semidirect
277. C₂×#540	C₂×C₇	semidirect
375. #563	C₂²×C₇	semidirect
376. #562	C₂²×C₇	semidirect
377. #562	C₂²×C₇	semidirect
378. #562	C₂²×C₇	semidirect
379. #559	C₂²×C₇	semidirect
380. #559	C₂²×C₇	semidirect
381. #557	C₂²×C₇	semidirect
382. #556	C₂²×C₇	semidirect
383. #555	C₂²×C₇	semidirect
384. #555	C₂²×C₇	semidirect
386. #554	C₂²×C₇	semidirect
387. #554	C₂²×C₇	semidirect
388. #554	C₂²×C₇	semidirect
389. #554	C₂²×C₇	semidirect
390. #554	C₂²×C₇	semidirect
391. #553	C₂²×C₇	semidirect
392. #553	C₂²×C₇	semidirect
393. #553	C₂²×C₇	semidirect
394. #552	C₂²×C₇	semidirect
396. #550	C₂²×C₇	semidirect
397. #550	C₂²×C₇	semidirect
398. D₄×Q₈	C₂²×C₇	semidirect
399. D₄×Q₈	C₂²×C₇	semidirect
400. #548	C₂²×C₇	semidirect
401. #547	C₂²×C₇	semidirect
402. #547	C₂²×C₇	semidirect
403. #547	C₂²×C₇	semidirect
404. #547	C₂²×C₇	semidirect
409. #544	C₂²×C₇	semidirect
410. #544	C₂²×C₇	semidirect
411. #544	C₂²×C₇	semidirect
414. #542	C₂²×C₇	semidirect
415. #542	C₂²×C₇	semidirect
416. #542	C₂²×C₇	semidirect
417. #542	C₂²×C₇	semidirect
418. #541	C₂²×C₇	semidirect
422. #540	C₂²×C₇	semidirect
423. #540	C₂²×C₇	semidirect
424. #540	C₂²×C₇	semidirect
425. #540	C₂²×C₇	semidirect
427. #539	C₂²×C₇	semidirect
428. #539	C₂²×C₇	semidirect
429. #539	C₂²×C₇	semidirect
432. #537	C₂²×C₇	semidirect
433. #537	C₂²×C₇	semidirect
434. #536	C₂²×C₇	semidirect
439. #533	C₂²×C₇	semidirect
440. #533	C₂²×C₇	semidirect
441. #533	C₂²×C₇	semidirect
443. #532	C₂²×C₇	semidirect
444. #532	C₂²×C₇	semidirect
446. #529	C₂²×C₇	semidirect
447. #529	C₂²×C₇	semidirect
449. C₂×#125	C₂²×C₇	semidirect
849. C₇	#62881	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×#3559	2
C₇×#3557	2
C₇×#3554	2
C₇×#3548	2
C₇×#3547	2
C₇×#3536	2
C₇×#3535	2
C₇×#3508	2
C₇×#3506	2
C₇×#3504	2
C₇×#3501	2
C₇×#3494	2
C₇×#3458	2
C₇×#3455	2
C₂×C₇×#540	2
#62881	7

Subgroups — C7×#62881 #13240097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62881 #13240097