Subgroups — C₇×#34772 #13211988

Order 1792.

1944 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2522	C₂	1	2	yes	maximal, complemented
2	C₇×#2520	C₂	1	2	yes	maximal, complemented
3	C₇×#2511	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2507	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2505	C₂	1	2	yes	maximal, complemented
6	C₇×#2502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2487	C₂	1	1	yes	maximal, characteristic
10	C₇×#2450	C₂	1	2	yes	maximal
11	C₇×#2440	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2417	C₂	1	1	yes	maximal, characteristic
13	C₇×#2402	C₂	1	2	yes	maximal, complemented
14	C₇×#2396	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
19	C₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2290	C₂	1	2	yes	maximal
21	C₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic
23	C₂×C₄×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₇×#117	C₂²	1	2	yes	—
34	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₇	C₂²	1	2	yes	—
39	C₇×#400	C₂²	1	2	yes	—
40	C₇×#400	C₂²	1	2	yes	—
41	C₇×#400	C₂²	1	2	yes	—
42	C₇×#400	C₂²	1	2	yes	—
43	C₇×#400	C₂²	1	2	yes	—
44	C₇×#399	C₂²	1	2	yes	—
45	C₇×#398	C₂²	1	2	yes	—
46	C₇×#398	C₂²	1	2	yes	—
47	C₇×#398	C₂²	1	2	yes	—
48	C₇×#398	C₂²	1	2	yes	—
49	C₇×#398	C₂²	1	2	yes	—
50	C₇×#398	C₂²	1	2	yes	—
51	C₇×#396	C₂²	1	2	yes	—
52	C₇×#396	C₂²	1	2	yes	—
53	C₇×#395	C₂²	1	2	yes	—
54	C₇×#393	C₂²	1	2	yes	—
55	C₇×#391	C₂²	1	1	yes	characteristic
56	C₇×#391	C₂²	1	2	yes	—
57	C₇×#391	C₂²	1	1	yes	characteristic
58	C₇×#391	C₂²	1	1	yes	characteristic
59	C₇×#391	C₂²	1	2	yes	—
60	C₇×#391	C₂²	1	1	yes	characteristic
61	C₇×#389	C₂²	1	1	yes	characteristic
62	C₇×#389	C₂²	1	1	yes	characteristic
63	C₇×#389	C₂²	1	1	yes	characteristic
64	C₇×#389	C₂²	1	1	yes	characteristic
65	C₇×#389	C₂²	1	1	yes	characteristic
66	C₇×#389	C₂²	1	1	yes	characteristic
67	C₇×#389	C₂²	1	2	yes	—
68	C₇×#389	C₂²	1	2	yes	—
69	C₇×#388	C₂²	1	2	yes	—
70	C₇×#388	C₂²	1	2	yes	—
71	C₇×#387	C₂²	1	2	yes	—
72	C₇×#387	C₂²	1	2	yes	—
73	C₇×#387	C₂²	1	2	yes	—
74	C₇×#387	C₂²	1	2	yes	—
75	C₇×#387	C₂²	1	2	yes	—
76	C₇×#387	C₂²	1	2	yes	—
77	C₇×#387	C₂²	1	2	yes	—
78	C₇×#387	C₂²	1	2	yes	—
79	C₇×#386	C₂²	1	2	yes	—
80	C₇×#386	C₂²	1	2	yes	—
81	C₇×#385	C₂²	1	2	yes	—
82	C₇×#385	C₂²	1	2	yes	—
83	C₇×#385	C₂²	1	2	yes	—
84	C₇×#385	C₂²	1	2	yes	—
85	C₇×#385	C₂²	1	2	yes	—
86	C₇×#385	C₂²	1	2	yes	—
87	C₇×#384	C₂²	1	1	yes	characteristic
88	C₇×#384	C₂²	1	1	yes	characteristic
89	C₇×#384	C₂²	1	1	yes	characteristic
90	C₇×#382	C₂²	1	2	yes	—
91	C₇×#380	C₂²	1	1	yes	characteristic
92	C₇×#380	C₂²	1	2	yes	—
93	C₇×#380	C₂²	1	1	yes	characteristic
94	C₇×#380	C₂²	1	2	yes	—
95	C₇×#380	C₂²	1	1	yes	characteristic
96	C₇×#380	C₂²	1	1	yes	characteristic
97	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
102	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
103	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
104	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₇×#376	C₂²	1	2	yes	—
121	C₂×C₇×#95	C₂²	1	2	yes	—
122	C₄³×C₇	C₂²	1	1	yes	characteristic
123	#34772	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₇×Q₈	C₂³	1	2	yes	—
126	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₇	C₂³	1	2	yes	—
135	C₇×C₄⋊Q₈	—	2	4	no	—
136	C₇×C₂²⋊Q₈	—	2	4	no	—
137	C₇×C₂²⋊Q₈	—	2	4	no	—
138	C₇×C₂²⋊Q₈	—	2	8	no	—
139	C₄×C₇×Q₈	—	2	4	no	—
140	C₄×C₇×Q₈	—	4	4	no	—
141	C₄×C₇×D₄	—	2	4	no	—
142	C₄×C₇×D₄	—	2	4	no	—
143	C₄×C₇×D₄	Q₈	1	8	yes	complemented
144	C₇×#117	—	4	4	no	—
145	C₂×C₇×C₄⋊C₄	—	2	4	no	—
146	C₂×C₇×C₄⋊C₄	—	2	4	no	—
147	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₇	—	2	4	no	—
188	C₂×C₄²×C₇	—	2	4	no	—
189	C₂×C₄²×C₇	—	4	4	no	—
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇	C₂³	1	2	yes	—
202	C₂×C₄²×C₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₇	C₂³	1	2	yes	—
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇	C₂³	1	2	yes	—
206	C₂×C₄²×C₇	C₂³	1	2	yes	—
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
209	C₇×#95	C₂³	1	2	yes	—
210	C₇×#95	C₂³	1	2	yes	—
211	C₇×#95	C₂³	1	2	yes	—
212	C₇×#95	C₂³	1	2	yes	—
213	C₇×#95	C₂³	1	2	yes	—
214	C₇×#95	C₂³	1	2	yes	—
215	C₇×#95	C₂³	1	2	yes	—
216	C₇×#95	C₂³	1	2	yes	—
217	C₇×#95	C₂³	1	1	yes	characteristic
218	C₇×#95	C₂³	1	1	yes	characteristic
219	C₇×#95	C₂³	1	1	yes	characteristic
220	C₇×#95	C₂³	1	1	yes	characteristic
221	C₇×#95	C₂³	1	1	yes	characteristic
222	C₇×#95	C₂³	1	1	yes	characteristic
223	C₇×#95	C₂³	1	2	yes	—
224	C₇×#95	C₂³	1	2	yes	—
225	C₇×#95	C₂³	1	2	yes	—
226	C₇×#95	C₂³	1	2	yes	—
227	C₇×#95	C₂³	1	2	yes	—
228	C₇×#95	C₂³	1	2	yes	—
229	C₇×#95	C₂³	1	2	yes	—
230	C₇×#95	C₂³	1	2	yes	—
231	C₇×#95	C₂³	1	2	yes	—
232	C₇×#95	C₂³	1	2	yes	—
233	C₇×#95	C₂³	1	2	yes	—
234	C₇×#95	C₂³	1	2	yes	—
235	C₇×#95	C₂³	1	2	yes	—
236	C₇×#95	C₂³	1	2	yes	—
237	C₇×#95	C₂³	1	2	yes	—
238	#2522	C₂×C₇	1	2	yes	complemented
239	#2520	C₂×C₇	1	2	yes	complemented
240	#2511	C₂×C₇	1	1	yes	characteristic, complemented
241	#2507	C₂×C₇	1	1	yes	characteristic, complemented
242	#2505	C₂×C₇	1	2	yes	complemented
243	#2502	C₂×C₇	1	1	yes	characteristic, complemented
244	#2497	C₂×C₇	1	1	yes	characteristic, complemented
245	#2492	C₂×C₇	1	1	yes	characteristic, complemented
246	#2487	C₂×C₇	1	1	yes	characteristic
247	#2450	C₂×C₇	1	2	yes	—
248	#2440	C₂×C₇	1	1	yes	characteristic, complemented
249	#2417	C₂×C₇	1	1	yes	characteristic
250	#2402	C₂×C₇	1	2	yes	complemented
251	#2396	C₂×C₇	1	2	yes	complemented
252	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
253	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
254	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
255	C₄×C₂²⋊Q₈	C₂×C₇	1	2	yes	complemented
256	#2295	C₂×C₇	1	1	yes	characteristic, complemented
257	#2290	C₂×C₇	1	2	yes	—
258	#2285	C₂×C₇	1	1	yes	characteristic, complemented
259	C₄²×D₄	C₂×C₇	1	1	yes	characteristic
260	C₂×C₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
261	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
263	C₂×C₇×Q₈	—	2	2	no	—
264	C₂×C₇×Q₈	—	2	4	no	—
265	C₂×C₇×Q₈	—	2	2	no	—
266	C₂×C₇×Q₈	—	2	2	no	—
267	C₂×C₇×Q₈	—	2	4	no	—
268	C₂×C₇×Q₈	—	4	2	no	—
269	C₂×C₇×D₄	—	2	2	no	—
270	C₂×C₇×D₄	—	2	2	no	—
271	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
272	C₂²×C₄×C₇	—	2	2	no	—
273	C₂²×C₄×C₇	—	2	2	no	—
274	C₂²×C₄×C₇	—	2	2	no	—
275	C₂²×C₄×C₇	—	2	2	no	—
276	C₂²×C₄×C₇	—	2	2	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	4	no	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	4	no	—
281	C₂²×C₄×C₇	—	2	2	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	2	no	—
284	C₂²×C₄×C₇	—	2	4	no	—
285	C₂²×C₄×C₇	—	2	2	no	—
286	C₂²×C₄×C₇	—	2	2	no	—
287	C₂²×C₄×C₇	—	2	2	no	—
288	C₂²×C₄×C₇	—	4	2	no	—
289	C₂²×C₄×C₇	—	4	2	no	—
290	C₂²×C₄×C₇	—	4	1	no	—
291	C₂²×C₄×C₇	—	4	1	no	—
292	C₂²×C₄×C₇	—	4	2	no	—
293	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
294	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
295	C₂²×C₄×C₇	#41	1	4	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
317	C₇×C₄⋊C₄	—	2	4	no	—
318	C₇×C₄⋊C₄	—	2	4	no	—
319	C₇×C₄⋊C₄	—	2	2	no	—
320	C₇×C₄⋊C₄	—	2	2	no	—
321	C₇×C₄⋊C₄	—	2	2	no	—
322	C₇×C₄⋊C₄	—	2	2	no	—
323	C₇×C₄⋊C₄	—	2	2	no	—
324	C₇×C₄⋊C₄	—	2	2	no	—
325	C₇×C₄⋊C₄	—	2	4	no	—
326	C₇×C₄⋊C₄	—	2	4	no	—
327	C₇×C₄⋊C₄	—	2	2	no	—
328	C₇×C₄⋊C₄	—	2	4	no	—
329	C₇×C₄⋊C₄	—	2	4	no	—
330	C₇×C₄⋊C₄	—	2	4	no	—
331	C₇×C₄⋊C₄	—	2	4	no	—
332	C₇×C₄⋊C₄	—	2	4	no	—
333	C₇×C₄⋊C₄	—	2	2	no	—
334	C₇×C₄⋊C₄	—	4	2	no	—
335	C₇×C₄⋊C₄	—	4	2	no	—
336	C₇×C₄⋊C₄	—	4	2	no	—
337	C₇×C₄⋊C₄	—	4	2	no	—
338	C₇×C₄⋊C₄	—	4	2	no	—
339	C₇×C₄⋊C₄	—	4	2	no	—
340	C₇×C₄⋊C₄	—	4	2	no	—
341	C₇×C₄⋊C₄	—	4	2	no	—
342	C₇×C₄⋊C₄	—	4	2	no	—
343	C₇×C₄⋊C₄	C₂×Q₈	1	4	yes	—
344	C₇×C₄⋊C₄	#41	1	4	yes	—
345	C₇×C₂²⋊C₄	—	2	2	no	—
346	C₇×C₂²⋊C₄	—	2	4	no	—
347	C₇×C₂²⋊C₄	—	2	4	no	—
348	C₇×C₂²⋊C₄	—	2	2	no	—
349	C₇×C₂²⋊C₄	—	2	2	no	—
350	C₇×C₂²⋊C₄	—	2	4	no	—
351	C₇×C₂²⋊C₄	—	4	2	no	—
352	C₇×C₂²⋊C₄	—	4	2	no	—
353	C₇×C₂²⋊C₄	—	4	2	no	—
354	C₇×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
355	C₇×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
356	C₇×C₂²⋊C₄	#41	1	4	yes	—
357	C₄²×C₇	—	2	2	no	—
358	C₄²×C₇	—	2	2	no	—
359	C₄²×C₇	—	2	2	no	—
360	C₄²×C₇	—	2	2	no	—
361	C₄²×C₇	—	2	2	no	—
362	C₄²×C₇	—	2	2	no	—
363	C₄²×C₇	—	2	2	no	—
364	C₄²×C₇	—	2	2	no	—
365	C₄²×C₇	—	2	4	no	—
366	C₄²×C₇	—	2	2	no	—
367	C₄²×C₇	—	2	4	no	—
368	C₄²×C₇	—	2	4	no	—
369	C₄²×C₇	—	2	4	no	—
370	C₄²×C₇	—	2	2	no	—
371	C₄²×C₇	—	4	2	no	—
372	C₄²×C₇	—	4	2	no	—
373	C₄²×C₇	—	4	1	no	—
374	C₄²×C₇	C₂×Q₈	1	4	yes	—
375	C₄²×C₇	#41	1	4	yes	—
376	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
377	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
378	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
379	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
380	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
381	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
382	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
385	C₂×#117	C₂²×C₇	1	2	yes	—
386	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
387	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
388	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
389	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
390	C₂²×C₄²	C₂²×C₇	1	2	yes	—
391	#400	C₂²×C₇	1	2	yes	—
392	#400	C₂²×C₇	1	2	yes	—
393	#400	C₂²×C₇	1	2	yes	—
394	#400	C₂²×C₇	1	2	yes	—
395	#400	C₂²×C₇	1	2	yes	—
396	#399	C₂²×C₇	1	2	yes	—
397	#398	C₂²×C₇	1	2	yes	—
398	#398	C₂²×C₇	1	2	yes	—
399	#398	C₂²×C₇	1	2	yes	—
400	#398	C₂²×C₇	1	2	yes	—
401	#398	C₂²×C₇	1	2	yes	—
402	#398	C₂²×C₇	1	2	yes	—
403	#396	C₂²×C₇	1	2	yes	—
404	#396	C₂²×C₇	1	2	yes	—
405	#395	C₂²×C₇	1	2	yes	—
406	#393	C₂²×C₇	1	2	yes	—
407	#391	C₂²×C₇	1	2	yes	—
408	#391	C₂²×C₇	1	1	yes	characteristic
409	#391	C₂²×C₇	1	1	yes	characteristic
410	#391	C₂²×C₇	1	1	yes	characteristic
411	#391	C₂²×C₇	1	2	yes	—
412	#391	C₂²×C₇	1	1	yes	characteristic
413	#389	C₂²×C₇	1	1	yes	characteristic
414	#389	C₂²×C₇	1	1	yes	characteristic
415	#389	C₂²×C₇	1	2	yes	—
416	#389	C₂²×C₇	1	1	yes	characteristic
417	#389	C₂²×C₇	1	1	yes	characteristic
418	#389	C₂²×C₇	1	1	yes	characteristic
419	#389	C₂²×C₇	1	1	yes	characteristic
420	#389	C₂²×C₇	1	2	yes	—
421	#388	C₂²×C₇	1	2	yes	—
422	#388	C₂²×C₇	1	2	yes	—
423	#387	C₂²×C₇	1	2	yes	—
424	#387	C₂²×C₇	1	2	yes	—
425	#387	C₂²×C₇	1	2	yes	—
426	#387	C₂²×C₇	1	2	yes	—
427	#387	C₂²×C₇	1	2	yes	—
428	#387	C₂²×C₇	1	2	yes	—
429	#387	C₂²×C₇	1	2	yes	—
430	#387	C₂²×C₇	1	2	yes	—
431	#386	C₂²×C₇	1	2	yes	—
432	#386	C₂²×C₇	1	2	yes	—
433	#385	C₂²×C₇	1	2	yes	—
434	#385	C₂²×C₇	1	2	yes	—
435	#385	C₂²×C₇	1	2	yes	—
436	#385	C₂²×C₇	1	2	yes	—
437	#385	C₂²×C₇	1	2	yes	—
438	#385	C₂²×C₇	1	2	yes	—
439	#384	C₂²×C₇	1	1	yes	characteristic
440	#384	C₂²×C₇	1	1	yes	characteristic
441	#384	C₂²×C₇	1	1	yes	characteristic
442	#382	C₂²×C₇	1	2	yes	—
443	#380	C₂²×C₇	1	1	yes	characteristic
444	#380	C₂²×C₇	1	2	yes	—
445	#380	C₂²×C₇	1	1	yes	characteristic
446	#380	C₂²×C₇	1	2	yes	—
447	#380	C₂²×C₇	1	1	yes	characteristic
448	#380	C₂²×C₇	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
452	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
456	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
460	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
461	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
464	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
465	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
467	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
468	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
469	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
470	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
471	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
472	#376	C₂²×C₇	1	2	yes	—
473	C₂×#95	C₂²×C₇	1	2	yes	—
474	C₄³	C₂²×C₇	1	1	yes	characteristic
475	C₂³×C₇	—	2	1	no	—
476	C₂³×C₇	—	2	1	no	—
477	C₂³×C₇	—	2	1	no	—
478	C₂³×C₇	—	2	1	no	—
479	C₂³×C₇	—	2	1	no	—
480	C₂³×C₇	—	2	1	no	—
481	C₂³×C₇	—	2	1	no	—
482	C₂³×C₇	—	2	1	no	—
483	C₂³×C₇	—	2	1	no	—
484	C₂³×C₇	—	2	1	no	—
485	C₂³×C₇	C₂²×Q₈	1	2	yes	—
486	C₂³×C₇	C₂²×Q₈	1	2	yes	—
487	C₂³×C₇	C₂×#41	1	2	yes	—
488	C₂³×C₇	C₂×#41	1	2	yes	—
489	C₂³×C₇	C₂⁵	1	1	yes	characteristic
490	C₇×Q₈	—	4	8	no	—
491	C₇×Q₈	—	4	4	no	—
492	C₇×D₄	—	2	8	no	—
493	C₂×C₄×C₇	—	2	1	no	—
494	C₂×C₄×C₇	—	2	1	no	—
495	C₂×C₄×C₇	—	2	1	no	—
496	C₂×C₄×C₇	—	2	1	no	—
497	C₂×C₄×C₇	—	2	1	no	—
498	C₂×C₄×C₇	—	2	1	no	—
499	C₂×C₄×C₇	—	2	1	no	—
500	C₂×C₄×C₇	—	2	1	no	—
501	C₂×C₄×C₇	—	2	1	no	—
502	C₂×C₄×C₇	—	2	1	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	2	2	no	—
505	C₂×C₄×C₇	—	2	1	no	—
506	C₂×C₄×C₇	—	2	1	no	—
507	C₂×C₄×C₇	—	2	1	no	—
508	C₂×C₄×C₇	—	2	1	no	—
509	C₂×C₄×C₇	—	2	1	no	—
510	C₂×C₄×C₇	—	2	1	no	—
511	C₂×C₄×C₇	—	2	8	no	—
512	C₂×C₄×C₇	—	2	8	no	—
513	C₂×C₄×C₇	—	2	8	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	2	2	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	1	no	—
522	C₂×C₄×C₇	—	2	1	no	—
523	C₂×C₄×C₇	—	2	2	no	—
524	C₂×C₄×C₇	—	2	2	no	—
525	C₂×C₄×C₇	—	2	2	no	—
526	C₂×C₄×C₇	—	2	1	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	2	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	2	no	—
535	C₂×C₄×C₇	—	2	2	no	—
536	C₂×C₄×C₇	—	2	2	no	—
537	C₂×C₄×C₇	—	2	1	no	—
538	C₂×C₄×C₇	—	2	1	no	—
539	C₂×C₄×C₇	—	2	2	no	—
540	C₂×C₄×C₇	—	2	2	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	2	2	no	—
543	C₂×C₄×C₇	—	2	1	no	—
544	C₂×C₄×C₇	—	4	4	no	—
545	C₂×C₄×C₇	—	4	4	no	—
546	C₂×C₄×C₇	—	4	8	no	—
547	C₂×C₄×C₇	—	4	8	no	—
548	C₂×C₄×C₇	—	4	4	no	—
549	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
550	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
551	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
552	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
553	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
554	C₂×C₄×C₇	C₂×#41	1	2	yes	—
555	C₂×C₄×C₇	C₂×#41	1	2	yes	—
556	C₂×C₄×C₇	C₂×#41	1	2	yes	—
557	C₂×C₄×C₇	C₂×#41	1	4	yes	—
558	C₂×C₄×C₇	C₂×#41	1	2	yes	—
559	C₂×C₄×C₇	C₂×#41	1	2	yes	—
560	C₂×C₄×C₇	C₂×#41	1	2	yes	—
561	C₂×C₄×C₇	C₂×#41	1	2	yes	—
562	C₂×C₄×C₇	C₂×#41	1	2	yes	—
563	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
564	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₇	1	2	yes	—
566	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₇	1	2	yes	—
569	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₇	1	2	yes	—
575	C₄⋊Q₈	—	2	4	no	—
576	C₂²⋊Q₈	—	2	4	no	—
577	C₂²⋊Q₈	—	2	4	no	—
578	C₂²⋊Q₈	—	2	8	no	—
579	C₄×Q₈	—	2	4	no	—
580	C₄×Q₈	—	4	4	no	—
581	C₄×D₄	—	2	4	no	—
582	C₄×D₄	—	2	4	no	—
583	C₄×D₄	C₇×Q₈	1	8	yes	complemented
584	#117	—	4	4	no	—
585	C₂×C₄⋊C₄	—	2	4	no	—
586	C₂×C₄⋊C₄	—	2	4	no	—
587	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
627	C₂×C₄²	—	2	4	no	—
628	C₂×C₄²	—	2	4	no	—
629	C₂×C₄²	—	4	4	no	—
630	C₂×C₄²	C₂³×C₇	1	2	yes	—
631	C₂×C₄²	C₂³×C₇	1	2	yes	—
632	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₇	1	2	yes	—
636	C₂×C₄²	C₂³×C₇	1	2	yes	—
637	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₇	1	2	yes	—
646	C₂×C₄²	C₂³×C₇	1	2	yes	—
647	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
649	#95	C₂³×C₇	1	2	yes	—
650	#95	C₂³×C₇	1	2	yes	—
651	#95	C₂³×C₇	1	2	yes	—
652	#95	C₂³×C₇	1	2	yes	—
653	#95	C₂³×C₇	1	2	yes	—
654	#95	C₂³×C₇	1	2	yes	—
655	#95	C₂³×C₇	1	2	yes	—
656	#95	C₂³×C₇	1	2	yes	—
657	#95	C₂³×C₇	1	1	yes	characteristic
658	#95	C₂³×C₇	1	1	yes	characteristic
659	#95	C₂³×C₇	1	1	yes	characteristic
660	#95	C₂³×C₇	1	1	yes	characteristic
661	#95	C₂³×C₇	1	1	yes	characteristic
662	#95	C₂³×C₇	1	1	yes	characteristic
663	#95	C₂³×C₇	1	2	yes	—
664	#95	C₂³×C₇	1	2	yes	—
665	#95	C₂³×C₇	1	2	yes	—
666	#95	C₂³×C₇	1	2	yes	—
667	#95	C₂³×C₇	1	2	yes	—
668	#95	C₂³×C₇	1	2	yes	—
669	#95	C₂³×C₇	1	2	yes	—
670	#95	C₂³×C₇	1	2	yes	—
671	#95	C₂³×C₇	1	2	yes	—
672	#95	C₂³×C₇	1	2	yes	—
673	#95	C₂³×C₇	1	2	yes	—
674	#95	C₂³×C₇	1	2	yes	—
675	#95	C₂³×C₇	1	2	yes	—
676	#95	C₂³×C₇	1	2	yes	—
677	#95	C₂³×C₇	1	2	yes	—
678	C₂²×C₇	—	2	2	no	—
679	C₂²×C₇	—	2	2	no	—
680	C₂²×C₇	—	2	2	no	—
681	C₂²×C₇	—	2	2	no	—
682	C₂²×C₇	—	2	2	no	—
683	C₂²×C₇	—	2	2	no	—
684	C₂²×C₇	—	2	2	no	—
685	C₂²×C₇	—	2	2	no	—
686	C₂²×C₇	—	2	2	no	—
687	C₂²×C₇	—	4	1	no	—
688	C₂²×C₇	—	4	1	no	—
689	C₂²×C₇	—	4	1	no	—
690	C₂²×C₇	—	4	1	no	—
691	C₂²×C₇	#533	1	4	yes	—
692	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
693	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
694	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
695	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
696	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
697	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
698	C₂²×C₇	#585	1	1	yes	characteristic
699	C₄×C₇	—	2	2	no	—
700	C₄×C₇	—	2	2	no	—
701	C₄×C₇	—	2	2	no	—
702	C₄×C₇	—	2	2	no	—
703	C₄×C₇	—	2	2	no	—
704	C₄×C₇	—	2	2	no	—
705	C₄×C₇	—	2	2	no	—
706	C₄×C₇	—	2	4	no	—
707	C₄×C₇	—	2	2	no	—
708	C₄×C₇	—	4	1	no	—
709	C₄×C₇	—	4	2	no	—
710	C₄×C₇	—	4	1	no	—
711	C₄×C₇	—	4	2	no	—
712	C₄×C₇	—	4	2	no	—
713	C₄×C₇	—	4	2	no	—
714	C₄×C₇	—	4	2	no	—
715	C₄×C₇	—	4	1	no	—
716	C₄×C₇	—	4	2	no	—
717	C₄×C₇	—	4	2	no	—
718	C₄×C₇	#529	1	4	yes	—
719	C₄×C₇	#554	1	4	yes	—
720	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
721	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	4	no	—
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	2	4	no	—
727	C₂×Q₈	—	4	2	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	1	no	—
750	C₂²×C₄	—	4	1	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
753	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
754	C₂²×C₄	C₇×#41	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	4	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₄⋊C₄	C₂×C₇×Q₈	1	4	yes	—
803	C₄⋊C₄	C₇×#41	1	4	yes	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	C₂×C₇×Q₈	1	4	yes	—
814	C₂²⋊C₄	C₂×C₇×Q₈	1	4	yes	—
815	C₂²⋊C₄	C₇×#41	1	4	yes	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	4	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	4	no	—
827	C₄²	—	2	4	no	—
828	C₄²	—	2	4	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	4	2	no	—
831	C₄²	—	4	2	no	—
832	C₄²	—	4	1	no	—
833	C₄²	C₂×C₇×Q₈	1	4	yes	—
834	C₄²	C₇×#41	1	4	yes	—
835	C₂×C₇	—	2	4	no	—
836	C₂×C₇	—	4	2	no	—
837	C₂×C₇	C₂×#529	1	1	yes	characteristic
838	C₂×C₇	C₂×#533	1	1	yes	characteristic
839	C₂×C₇	#3460	1	1	yes	characteristic
840	C₂×C₇	C₂×#554	1	1	yes	characteristic
841	C₂×C₇	#3475	1	1	yes	characteristic
842	C₂×C₇	Q₈×#41	1	1	yes	characteristic
843	C₂×C₇	#3481	1	1	yes	characteristic
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	C₂²×C₇×Q₈	1	2	yes	—
855	C₂³	C₂²×C₇×Q₈	1	2	yes	—
856	C₂³	C₂×C₇×#41	1	2	yes	—
857	C₂³	C₂×C₇×#41	1	2	yes	—
858	C₂³	C₂⁵×C₇	1	1	yes	characteristic
859	Q₈	—	4	8	no	—
860	Q₈	—	4	4	no	—
861	D₄	—	2	8	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	8	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	8	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	4	8	no	—
916	C₂×C₄	—	4	8	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
919	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
920	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
921	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
922	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
923	C₂×C₄	C₂×C₇×#41	1	2	yes	—
924	C₂×C₄	C₂×C₇×#41	1	2	yes	—
925	C₂×C₄	C₂×C₇×#41	1	2	yes	—
926	C₂×C₄	C₂×C₇×#41	1	4	yes	—
927	C₂×C₄	C₂×C₇×#41	1	2	yes	—
928	C₂×C₄	C₂×C₇×#41	1	2	yes	—
929	C₂×C₄	C₂×C₇×#41	1	2	yes	—
930	C₂×C₄	C₂×C₇×#41	1	2	yes	—
931	C₂×C₄	C₂×C₇×#41	1	2	yes	—
932	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
933	C₇	#34772	1	1	yes	characteristic, direct product factor, Sylow
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	no	—
947	C₂²	C₇×#533	1	4	yes	—
948	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
949	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
950	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
951	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
952	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
953	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
954	C₂²	C₇×#585	1	1	yes	characteristic
955	C₄	—	2	2	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	4	no	—
963	C₄	—	2	2	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	C₇×#529	1	4	yes	—
975	C₄	C₇×#554	1	4	yes	—
976	C₂	—	2	4	no	—
977	C₂	—	4	2	no	—
978	C₂	C₂×C₇×#529	1	1	yes	characteristic
979	C₂	C₂×C₇×#533	1	1	yes	characteristic
980	C₂	C₇×#3460	1	1	yes	characteristic
981	C₂	C₂×C₇×#554	1	1	yes	characteristic
982	C₂	C₇×#3475	1	1	yes	characteristic
983	C₂	C₇×Q₈×#41	1	1	yes	characteristic
984	C₂	C₇×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2522	C₂	semidirect
2. C₇×#2520	C₂	semidirect
3. C₇×#2511	C₂	semidirect
4. C₇×#2507	C₂	semidirect
5. C₇×#2505	C₂	semidirect
6. C₇×#2502	C₂	semidirect
7. C₇×#2497	C₂	semidirect
8. C₇×#2492	C₂	semidirect
11. C₇×#2440	C₂	semidirect
13. C₇×#2402	C₂	semidirect
14. C₇×#2396	C₂	semidirect
15. C₄×C₇×C₄⋊Q₈	C₂	semidirect
16. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
17. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
19. C₇×#2295	C₂	semidirect
21. C₇×#2285	C₂	semidirect
23. C₂×C₄×C₇×C₄⋊C₄	C₂	semidirect
123. #34772	C₇	direct (N × H)
143. C₄×C₇×D₄	Q₈	semidirect
238. #2522	C₂×C₇	semidirect
239. #2520	C₂×C₇	semidirect
240. #2511	C₂×C₇	semidirect
241. #2507	C₂×C₇	semidirect
242. #2505	C₂×C₇	semidirect
243. #2502	C₂×C₇	semidirect
244. #2497	C₂×C₇	semidirect
245. #2492	C₂×C₇	semidirect
248. #2440	C₂×C₇	semidirect
250. #2402	C₂×C₇	semidirect
251. #2396	C₂×C₇	semidirect
252. C₄×C₄⋊Q₈	C₂×C₇	semidirect
253. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
254. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
255. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
256. #2295	C₂×C₇	semidirect
258. #2285	C₂×C₇	semidirect
260. C₂×C₄×C₄⋊C₄	C₂×C₇	semidirect
583. C₄×D₄	C₇×Q₈	semidirect
933. C₇	#34772	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×#2522	2
C₇×#2520	2
C₇×#2511	2
C₇×#2507	2
C₇×#2505	2
C₇×#2502	2
C₇×#2497	2
C₇×#2492	2
C₇×#2487	2
C₇×#2450	2
C₇×#2440	2
C₇×#2417	2
C₇×#2402	2
C₇×#2396	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#2295	2
C₇×#2290	2
C₇×#2285	2
C₄²×C₇×D₄	2
C₂×C₄×C₇×C₄⋊C₄	2
#34772	7

Subgroups — C7×#34772 #13211988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34772 #13211988