Subgroups — C₇×#34482 #13211698

Order 1792.

2024 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#552	C₂	1	1	yes	maximal, characteristic
2	C₇×#2382	C₂	1	2	yes	maximal, complemented
3	C₇×#2376	C₂	1	2	yes	maximal
4	C₇×#2373	C₂	1	2	yes	maximal, complemented
5	C₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2352	C₂	1	1	yes	maximal, characteristic
9	C₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2346	C₂	1	2	yes	maximal, complemented
11	C₇×#2346	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2345	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2335	C₂	1	2	yes	maximal
14	C₇×#2334	C₂	1	2	yes	maximal, complemented
15	C₇×#2330	C₂	1	2	yes	maximal, complemented
16	C₇×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2317	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2316	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2314	C₂	1	2	yes	maximal, complemented
21	C₄×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2293	C₂	1	1	yes	maximal, characteristic
24	C₇×#552	C₄	1	16	yes	complemented
25	C₂×C₇×#126	C₂²	1	2	yes	—
26	C₂×C₇×#125	C₂²	1	1	yes	characteristic
27	C₂×C₇×#125	C₂²	1	2	yes	—
28	C₂×C₇×#123	C₂²	1	2	yes	—
29	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₇×#117	C₂²	1	1	yes	characteristic
36	C₂×C₇×#117	C₂²	1	1	yes	characteristic
37	C₂×C₇×#117	C₂²	1	1	yes	characteristic
38	C₂×C₇×#117	C₂²	1	1	yes	characteristic
39	C₂×C₇×#117	C₂²	1	2	yes	—
40	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₇×#391	C₂²	1	1	yes	characteristic
43	C₇×#391	C₂²	1	1	yes	characteristic
44	C₇×#390	C₂²	1	1	yes	characteristic
45	C₇×#390	C₂²	1	1	yes	characteristic
46	C₇×#389	C₂²	1	1	yes	characteristic
47	C₇×#389	C₂²	1	1	yes	characteristic
48	C₇×#389	C₂²	1	1	yes	characteristic
49	C₇×#389	C₂²	1	1	yes	characteristic
50	C₇×#389	C₂²	1	1	yes	characteristic
51	C₇×#389	C₂²	1	1	yes	characteristic
52	C₇×#389	C₂²	1	2	yes	—
53	C₇×#389	C₂²	1	1	yes	characteristic
54	C₇×#389	C₂²	1	1	yes	characteristic
55	C₇×#389	C₂²	1	2	yes	—
56	C₇×#389	C₂²	1	1	yes	characteristic
57	C₇×#389	C₂²	1	1	yes	characteristic
58	C₇×#389	C₂²	1	2	yes	—
59	C₇×#389	C₂²	1	2	yes	—
60	C₇×#389	C₂²	1	2	yes	—
61	C₇×#389	C₂²	1	2	yes	—
62	C₇×#389	C₂²	1	2	yes	—
63	C₇×#389	C₂²	1	2	yes	—
64	C₇×#388	C₂²	1	1	yes	characteristic
65	C₇×#388	C₂²	1	1	yes	characteristic
66	C₇×#388	C₂²	1	1	yes	characteristic
67	C₇×#388	C₂²	1	1	yes	characteristic
68	C₇×#388	C₂²	1	2	yes	—
69	C₇×#388	C₂²	1	2	yes	—
70	C₇×#388	C₂²	1	2	yes	—
71	C₇×#388	C₂²	1	2	yes	—
72	C₇×#388	C₂²	1	2	yes	—
73	C₇×#388	C₂²	1	2	yes	—
74	C₇×#388	C₂²	1	2	yes	—
75	C₇×#388	C₂²	1	2	yes	—
76	C₇×#388	C₂²	1	2	yes	—
77	C₇×#387	C₂²	1	2	yes	—
78	C₇×#387	C₂²	1	2	yes	—
79	C₇×#387	C₂²	1	2	yes	—
80	C₇×#387	C₂²	1	2	yes	—
81	C₇×#387	C₂²	1	2	yes	—
82	C₇×#387	C₂²	1	2	yes	—
83	C₇×#387	C₂²	1	2	yes	—
84	C₇×#387	C₂²	1	2	yes	—
85	C₇×#387	C₂²	1	2	yes	—
86	C₇×#387	C₂²	1	2	yes	—
87	C₇×#387	C₂²	1	2	yes	—
88	C₇×#387	C₂²	1	2	yes	—
89	C₇×#387	C₂²	1	2	yes	—
90	C₇×#386	C₂²	1	2	yes	—
91	C₇×#385	C₂²	1	2	yes	—
92	C₇×#385	C₂²	1	2	yes	—
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#384	C₂²	1	2	yes	—
95	C₇×#382	C₂²	1	1	yes	characteristic
96	C₇×#382	C₂²	1	2	yes	—
97	C₇×#382	C₂²	1	2	yes	—
98	C₇×#382	C₂²	1	2	yes	—
99	C₇×#380	C₂²	1	2	yes	—
100	C₇×#380	C₂²	1	2	yes	—
101	C₇×#380	C₂²	1	2	yes	—
102	C₇×#380	C₂²	1	1	yes	characteristic
103	C₇×#380	C₂²	1	1	yes	characteristic
104	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
106	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
108	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
111	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
112	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
119	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₇×#376	C₂²	1	2	yes	—
122	C₇×#376	C₂²	1	2	yes	—
123	C₄³×C₇	C₂²	1	1	yes	characteristic
124	#34482	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
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	2	yes	—
131	C₇×#126	C₂×C₄	1	16	yes	—
132	C₇×#125	C₂×C₄	1	16	yes	complemented
133	C₇×#125	C₂×C₄	1	8	yes	complemented
134	C₇×#123	C₂×C₄	1	16	yes	—
135	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
136	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
137	C₄×C₇×Q₈	—	4	2	no	—
138	C₄×C₇×Q₈	—	4	2	no	—
139	C₄×C₇×Q₈	C₂×C₄	1	8	yes	complemented
140	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
141	C₇×#117	—	4	2	no	—
142	C₇×#117	—	4	2	no	—
143	C₇×#117	—	4	2	no	—
144	C₇×#117	C₂×C₄	1	8	yes	—
145	C₇×#117	C₂×C₄	1	16	yes	complemented
146	C₂×C₇×C₄⋊C₄	—	4	2	no	—
147	C₂×C₇×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
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	1	yes	characteristic
151	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
166	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
170	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
186	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇	C₂³	1	2	yes	—
205	C₂×C₄²×C₇	C₂³	1	2	yes	—
206	C₂×C₄²×C₇	C₂³	1	2	yes	—
207	C₂×C₄²×C₇	C₂³	1	2	yes	—
208	C₂×C₄²×C₇	C₂³	1	2	yes	—
209	C₂×C₄²×C₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₇	C₂³	1	2	yes	—
214	C₇×#95	C₂³	1	2	yes	—
215	C₇×#95	C₂³	1	1	yes	characteristic
216	C₇×#95	C₂³	1	2	yes	—
217	C₇×#95	C₂³	1	2	yes	—
218	C₇×#95	C₂³	1	2	yes	—
219	C₇×#95	C₂³	1	2	yes	—
220	C₇×#95	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
227	C₇×#95	C₂³	1	1	yes	characteristic
228	C₇×#95	C₂³	1	1	yes	characteristic
229	C₇×#95	C₂³	1	1	yes	characteristic
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	C₇×#95	C₂³	1	2	yes	—
239	C₇×#95	C₂³	1	2	yes	—
240	C₇×#95	C₂³	1	2	yes	—
241	C₂×#552	C₂×C₇	1	1	yes	characteristic
242	#2382	C₂×C₇	1	2	yes	complemented
243	#2376	C₂×C₇	1	2	yes	—
244	#2373	C₂×C₇	1	2	yes	complemented
245	#2370	C₂×C₇	1	1	yes	characteristic, complemented
246	#2362	C₂×C₇	1	1	yes	characteristic, complemented
247	#2360	C₂×C₇	1	1	yes	characteristic, complemented
248	#2352	C₂×C₇	1	1	yes	characteristic
249	#2351	C₂×C₇	1	1	yes	characteristic, complemented
250	#2346	C₂×C₇	1	1	yes	characteristic, complemented
251	#2346	C₂×C₇	1	2	yes	complemented
252	#2345	C₂×C₇	1	1	yes	characteristic, complemented
253	#2335	C₂×C₇	1	2	yes	—
254	#2334	C₂×C₇	1	2	yes	complemented
255	#2330	C₂×C₇	1	2	yes	complemented
256	#2323	C₂×C₇	1	1	yes	characteristic, complemented
257	#2323	C₂×C₇	1	1	yes	characteristic, complemented
258	#2317	C₂×C₇	1	1	yes	characteristic, complemented
259	#2316	C₂×C₇	1	1	yes	characteristic, complemented
260	#2314	C₂×C₇	1	2	yes	complemented
261	C₄×#125	C₂×C₇	1	1	yes	characteristic, complemented
262	#2295	C₂×C₇	1	1	yes	characteristic, complemented
263	#2293	C₂×C₇	1	1	yes	characteristic
264	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
266	C₂×C₇×Q₈	—	2	2	no	—
267	C₂×C₇×Q₈	—	2	2	no	—
268	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
269	C₂×C₇×D₄	—	4	1	no	—
270	C₂×C₇×D₄	—	4	1	no	—
271	C₂×C₇×D₄	C₂²×C₄	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	—	4	2	no	—
277	C₂²×C₄×C₇	—	4	2	no	—
278	C₂²×C₄×C₇	—	4	2	no	—
279	C₂²×C₄×C₇	—	4	2	no	—
280	C₂²×C₄×C₇	—	4	2	no	—
281	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
282	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
283	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
284	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	2	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	4	2	no	—
310	C₇×C₄⋊C₄	—	4	2	no	—
311	C₇×C₄⋊C₄	—	4	2	no	—
312	C₇×C₄⋊C₄	—	4	2	no	—
313	C₇×C₄⋊C₄	—	4	2	no	—
314	C₇×C₄⋊C₄	—	4	1	no	—
315	C₇×C₄⋊C₄	—	4	1	no	—
316	C₇×C₄⋊C₄	—	4	2	no	—
317	C₇×C₄⋊C₄	—	4	2	no	—
318	C₇×C₄⋊C₄	—	4	2	no	—
319	C₇×C₄⋊C₄	—	4	2	no	—
320	C₇×C₄⋊C₄	—	4	1	no	—
321	C₇×C₄⋊C₄	—	4	1	no	—
322	C₇×C₄⋊C₄	—	4	1	no	—
323	C₇×C₄⋊C₄	—	4	1	no	—
324	C₇×C₄⋊C₄	—	4	2	no	—
325	C₇×C₄⋊C₄	—	4	2	no	—
326	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
327	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
328	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
329	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
330	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
331	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
332	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
333	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
334	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
335	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
336	C₇×C₂²⋊C₄	—	2	2	no	—
337	C₇×C₂²⋊C₄	—	2	2	no	—
338	C₇×C₂²⋊C₄	—	4	1	no	—
339	C₇×C₂²⋊C₄	—	4	2	no	—
340	C₇×C₂²⋊C₄	—	4	1	no	—
341	C₇×C₂²⋊C₄	—	4	2	no	—
342	C₇×C₂²⋊C₄	—	4	1	no	—
343	C₇×C₂²⋊C₄	—	4	1	no	—
344	C₇×C₂²⋊C₄	—	4	1	no	—
345	C₇×C₂²⋊C₄	—	4	1	no	—
346	C₇×C₂²⋊C₄	—	4	2	no	—
347	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
348	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
349	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
350	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
351	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
352	C₄²×C₇	—	2	2	no	—
353	C₄²×C₇	—	2	2	no	—
354	C₄²×C₇	—	2	2	no	—
355	C₄²×C₇	—	2	2	no	—
356	C₄²×C₇	—	2	4	no	—
357	C₄²×C₇	—	2	2	no	—
358	C₄²×C₇	—	4	2	no	—
359	C₄²×C₇	—	4	1	no	—
360	C₄²×C₇	—	4	2	no	—
361	C₄²×C₇	—	4	1	no	—
362	C₄²×C₇	—	4	2	no	—
363	C₄²×C₇	—	4	2	no	—
364	C₄²×C₇	—	4	1	no	—
365	C₄²×C₇	—	4	2	no	—
366	C₄²×C₇	—	4	2	no	—
367	C₄²×C₇	—	4	2	no	—
368	C₄²×C₇	C₂²×C₄	1	8	yes	—
369	C₄²×C₇	C₂²×C₄	1	8	yes	—
370	C₄²×C₇	C₂²×C₄	1	4	yes	—
371	#552	C₄×C₇	1	16	yes	complemented
372	C₂×#126	C₂²×C₇	1	2	yes	—
373	C₂×#125	C₂²×C₇	1	1	yes	characteristic
374	C₂×#125	C₂²×C₇	1	2	yes	—
375	C₂×#123	C₂²×C₇	1	2	yes	—
376	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
377	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
379	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
380	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
382	C₂×#117	C₂²×C₇	1	1	yes	characteristic
383	C₂×#117	C₂²×C₇	1	1	yes	characteristic
384	C₂×#117	C₂²×C₇	1	1	yes	characteristic
385	C₂×#117	C₂²×C₇	1	1	yes	characteristic
386	C₂×#117	C₂²×C₇	1	2	yes	—
387	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
389	#391	C₂²×C₇	1	1	yes	characteristic
390	#391	C₂²×C₇	1	1	yes	characteristic
391	#390	C₂²×C₇	1	1	yes	characteristic
392	#390	C₂²×C₇	1	1	yes	characteristic
393	#389	C₂²×C₇	1	1	yes	characteristic
394	#389	C₂²×C₇	1	1	yes	characteristic
395	#389	C₂²×C₇	1	1	yes	characteristic
396	#389	C₂²×C₇	1	2	yes	—
397	#389	C₂²×C₇	1	1	yes	characteristic
398	#389	C₂²×C₇	1	1	yes	characteristic
399	#389	C₂²×C₇	1	2	yes	—
400	#389	C₂²×C₇	1	1	yes	characteristic
401	#389	C₂²×C₇	1	1	yes	characteristic
402	#389	C₂²×C₇	1	2	yes	—
403	#389	C₂²×C₇	1	2	yes	—
404	#389	C₂²×C₇	1	1	yes	characteristic
405	#389	C₂²×C₇	1	2	yes	—
406	#389	C₂²×C₇	1	2	yes	—
407	#389	C₂²×C₇	1	2	yes	—
408	#389	C₂²×C₇	1	2	yes	—
409	#389	C₂²×C₇	1	1	yes	characteristic
410	#389	C₂²×C₇	1	1	yes	characteristic
411	#388	C₂²×C₇	1	1	yes	characteristic
412	#388	C₂²×C₇	1	2	yes	—
413	#388	C₂²×C₇	1	2	yes	—
414	#388	C₂²×C₇	1	2	yes	—
415	#388	C₂²×C₇	1	2	yes	—
416	#388	C₂²×C₇	1	2	yes	—
417	#388	C₂²×C₇	1	2	yes	—
418	#388	C₂²×C₇	1	1	yes	characteristic
419	#388	C₂²×C₇	1	2	yes	—
420	#388	C₂²×C₇	1	2	yes	—
421	#388	C₂²×C₇	1	2	yes	—
422	#388	C₂²×C₇	1	1	yes	characteristic
423	#388	C₂²×C₇	1	1	yes	characteristic
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	#387	C₂²×C₇	1	2	yes	—
432	#387	C₂²×C₇	1	2	yes	—
433	#387	C₂²×C₇	1	2	yes	—
434	#387	C₂²×C₇	1	2	yes	—
435	#387	C₂²×C₇	1	2	yes	—
436	#387	C₂²×C₇	1	2	yes	—
437	#386	C₂²×C₇	1	2	yes	—
438	#385	C₂²×C₇	1	2	yes	—
439	#385	C₂²×C₇	1	2	yes	—
440	#385	C₂²×C₇	1	2	yes	—
441	#384	C₂²×C₇	1	2	yes	—
442	#382	C₂²×C₇	1	1	yes	characteristic
443	#382	C₂²×C₇	1	2	yes	—
444	#382	C₂²×C₇	1	2	yes	—
445	#382	C₂²×C₇	1	2	yes	—
446	#380	C₂²×C₇	1	2	yes	—
447	#380	C₂²×C₇	1	2	yes	—
448	#380	C₂²×C₇	1	2	yes	—
449	#380	C₂²×C₇	1	1	yes	characteristic
450	#380	C₂²×C₇	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
453	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
461	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
463	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
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	#376	C₂²×C₇	1	2	yes	—
469	#376	C₂²×C₇	1	2	yes	—
470	C₄³	C₂²×C₇	1	1	yes	characteristic
471	C₂³×C₇	—	2	1	no	—
472	C₂³×C₇	—	2	1	no	—
473	C₂³×C₇	—	2	1	no	—
474	C₂³×C₇	—	2	1	no	—
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	C₂³×C₄	1	2	yes	—
484	C₂³×C₇	C₂³×C₄	1	2	yes	—
485	C₂³×C₇	C₂⁵	1	1	yes	characteristic
486	C₇×Q₈	—	2	8	no	—
487	C₇×D₄	—	4	4	no	—
488	C₂×C₄×C₇	—	2	1	no	—
489	C₂×C₄×C₇	—	2	2	no	—
490	C₂×C₄×C₇	—	2	1	no	—
491	C₂×C₄×C₇	—	2	1	no	—
492	C₂×C₄×C₇	—	2	2	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	2	no	—
497	C₂×C₄×C₇	—	2	1	no	—
498	C₂×C₄×C₇	—	2	1	no	—
499	C₂×C₄×C₇	—	2	2	no	—
500	C₂×C₄×C₇	—	2	2	no	—
501	C₂×C₄×C₇	—	2	2	no	—
502	C₂×C₄×C₇	—	2	1	no	—
503	C₂×C₄×C₇	—	2	1	no	—
504	C₂×C₄×C₇	—	2	2	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	2	8	no	—
507	C₂×C₄×C₇	—	2	8	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	1	no	—
512	C₂×C₄×C₇	—	2	1	no	—
513	C₂×C₄×C₇	—	2	1	no	—
514	C₂×C₄×C₇	—	2	2	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	1	no	—
518	C₂×C₄×C₇	—	2	2	no	—
519	C₂×C₄×C₇	—	2	1	no	—
520	C₂×C₄×C₇	—	2	1	no	—
521	C₂×C₄×C₇	—	2	1	no	—
522	C₂×C₄×C₇	—	2	2	no	—
523	C₂×C₄×C₇	—	2	1	no	—
524	C₂×C₄×C₇	—	2	2	no	—
525	C₂×C₄×C₇	—	2	1	no	—
526	C₂×C₄×C₇	—	2	1	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	1	no	—
529	C₂×C₄×C₇	—	2	1	no	—
530	C₂×C₄×C₇	—	2	1	no	—
531	C₂×C₄×C₇	—	2	1	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	1	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	1	no	—
540	C₂×C₄×C₇	—	2	2	no	—
541	C₂×C₄×C₇	—	4	8	no	—
542	C₂×C₄×C₇	—	8	4	no	—
543	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
544	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
545	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
546	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
547	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
548	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
549	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
550	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
551	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
552	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
553	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
554	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
555	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₇	1	2	yes	—
560	C₂³×C₄	C₂³×C₇	1	2	yes	—
561	#126	C₂×C₄×C₇	1	16	yes	—
562	#125	C₂×C₄×C₇	1	16	yes	complemented
563	#125	C₂×C₄×C₇	1	8	yes	complemented
564	#123	C₂×C₄×C₇	1	16	yes	—
565	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
566	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	complemented
567	C₄×Q₈	—	4	2	no	—
568	C₄×Q₈	—	4	2	no	—
569	C₄×Q₈	C₂×C₄×C₇	1	8	yes	complemented
570	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
571	#117	—	4	2	no	—
572	#117	—	4	2	no	—
573	#117	—	4	2	no	—
574	#117	C₂×C₄×C₇	1	8	yes	—
575	#117	C₂×C₄×C₇	1	16	yes	complemented
576	C₂×C₄⋊C₄	—	4	2	no	—
577	C₂×C₄⋊C₄	C₂×C₄×C₇	1	8	yes	complemented
578	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
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	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
625	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₇	1	2	yes	—
631	C₂×C₄²	C₂³×C₇	1	2	yes	—
632	C₂×C₄²	C₂³×C₇	1	2	yes	—
633	C₂×C₄²	C₂³×C₇	1	2	yes	—
634	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₇	1	2	yes	—
638	C₂×C₄²	C₂³×C₇	1	2	yes	—
639	C₂×C₄²	C₂³×C₇	1	2	yes	—
640	C₂×C₄²	C₂³×C₇	1	2	yes	—
641	C₂×C₄²	C₂³×C₇	1	2	yes	—
642	C₂×C₄²	C₂³×C₇	1	2	yes	—
643	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
644	#95	C₂³×C₇	1	2	yes	—
645	#95	C₂³×C₇	1	1	yes	characteristic
646	#95	C₂³×C₇	1	2	yes	—
647	#95	C₂³×C₇	1	2	yes	—
648	#95	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
661	#95	C₂³×C₇	1	2	yes	—
662	#95	C₂³×C₇	1	2	yes	—
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	C₂²×C₇	—	2	2	no	—
672	C₂²×C₇	—	2	2	no	—
673	C₂²×C₇	—	2	2	no	—
674	C₂²×C₇	—	2	2	no	—
675	C₂²×C₇	—	2	2	no	—
676	C₂²×C₇	—	2	2	no	—
677	C₂²×C₇	—	4	1	no	—
678	C₂²×C₇	—	4	1	no	—
679	C₂²×C₇	—	4	1	no	—
680	C₂²×C₇	—	4	1	no	—
681	C₂²×C₇	—	4	1	no	—
682	C₂²×C₇	—	4	1	no	—
683	C₂²×C₇	—	4	1	no	—
684	C₂²×C₇	—	4	1	no	—
685	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
686	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
688	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
689	C₂²×C₇	#585	1	1	yes	characteristic
690	C₂²×C₇	#585	1	1	yes	characteristic
691	C₂²×C₇	#585	1	1	yes	characteristic
692	C₄×C₇	—	2	2	no	—
693	C₄×C₇	—	2	2	no	—
694	C₄×C₇	—	2	4	no	—
695	C₄×C₇	—	2	4	no	—
696	C₄×C₇	—	2	4	no	—
697	C₄×C₇	—	2	2	no	—
698	C₄×C₇	—	2	2	no	—
699	C₄×C₇	—	2	4	no	—
700	C₄×C₇	—	2	2	no	—
701	C₄×C₇	—	4	1	no	—
702	C₄×C₇	—	4	1	no	—
703	C₄×C₇	—	4	1	no	—
704	C₄×C₇	—	4	2	no	—
705	C₄×C₇	—	4	1	no	—
706	C₄×C₇	—	4	1	no	—
707	C₄×C₇	—	4	1	no	—
708	C₄×C₇	—	4	2	no	—
709	C₄×C₇	—	4	2	no	—
710	C₄×C₇	—	4	1	no	—
711	C₄×C₇	—	4	2	no	—
712	C₄×C₇	#520	1	4	yes	—
713	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
714	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	2	2	no	—
717	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
718	C₂×D₄	—	4	1	no	—
719	C₂×D₄	—	4	1	no	—
720	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
731	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
732	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
733	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	1	no	—
760	C₄⋊C₄	—	4	1	no	—
761	C₄⋊C₄	—	4	1	no	—
762	C₄⋊C₄	—	4	1	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	1	no	—
770	C₄⋊C₄	—	4	1	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
776	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
777	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
778	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
779	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
780	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
781	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
782	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
783	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
784	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	4	1	no	—
788	C₂²⋊C₄	—	4	1	no	—
789	C₂²⋊C₄	—	4	1	no	—
790	C₂²⋊C₄	—	4	1	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₂²⋊C₄	—	4	1	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	4	1	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
797	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
798	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
799	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
800	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	4	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	4	2	no	—
808	C₄²	—	4	2	no	—
809	C₄²	—	4	2	no	—
810	C₄²	—	4	2	no	—
811	C₄²	—	4	1	no	—
812	C₄²	—	4	2	no	—
813	C₄²	—	4	1	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	1	no	—
817	C₄²	C₂²×C₄×C₇	1	8	yes	—
818	C₄²	C₂²×C₄×C₇	1	8	yes	—
819	C₄²	C₂²×C₄×C₇	1	4	yes	—
820	C₂×C₇	—	4	2	no	—
821	C₂×C₇	—	4	2	no	—
822	C₂×C₇	C₂×#520	1	1	yes	characteristic
823	C₂×C₇	#3428	1	1	yes	characteristic
824	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
825	C₂×C₇	#3547	1	1	yes	characteristic
826	C₂×C₇	#3551	1	1	yes	characteristic
827	C₂×C₇	#3563	1	1	yes	characteristic
828	C₂×C₇	#3565	1	1	yes	characteristic
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	C₂³×C₄×C₇	1	2	yes	—
842	C₂³	C₂³×C₄×C₇	1	2	yes	—
843	C₂³	C₂⁵×C₇	1	1	yes	characteristic
844	Q₈	—	2	8	no	—
845	D₄	—	4	4	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	8	no	—
865	C₂×C₄	—	2	8	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	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	4	8	no	—
900	C₂×C₄	—	8	4	no	—
901	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
902	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
903	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
904	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
905	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
906	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
907	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
908	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
909	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
910	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
911	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
912	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
913	C₇	#34482	1	1	yes	characteristic, direct product factor, Sylow
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
929	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
930	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
931	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
932	C₂²	C₇×#585	1	1	yes	characteristic
933	C₂²	C₇×#585	1	1	yes	characteristic
934	C₂²	C₇×#585	1	1	yes	characteristic
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	2	4	no	—
939	C₄	—	2	4	no	—
940	C₄	—	2	4	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	1	no	—
955	C₄	C₇×#520	1	4	yes	—
956	C₂	—	4	2	no	—
957	C₂	—	4	2	no	—
958	C₂	C₂×C₇×#520	1	1	yes	characteristic
959	C₂	C₇×#3428	1	1	yes	characteristic
960	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
961	C₂	C₇×#3547	1	1	yes	characteristic
962	C₂	C₇×#3551	1	1	yes	characteristic
963	C₂	C₇×#3563	1	1	yes	characteristic
964	C₂	C₇×#3565	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₇×#2382	C₂	semidirect
4. C₇×#2373	C₂	semidirect
5. C₇×#2370	C₂	semidirect
6. C₇×#2362	C₂	semidirect
7. C₇×#2360	C₂	semidirect
9. C₇×#2351	C₂	semidirect
10. C₇×#2346	C₂	semidirect
11. C₇×#2346	C₂	semidirect
12. C₇×#2345	C₂	semidirect
14. C₇×#2334	C₂	semidirect
15. C₇×#2330	C₂	semidirect
16. C₇×#2323	C₂	semidirect
17. C₇×#2323	C₂	semidirect
18. C₇×#2317	C₂	semidirect
19. C₇×#2316	C₂	semidirect
20. C₇×#2314	C₂	semidirect
21. C₄×C₇×#125	C₂	semidirect
22. C₇×#2295	C₂	semidirect
24. C₇×#552	C₄	semidirect
124. #34482	C₇	direct (N × H)
132. C₇×#125	C₂×C₄	semidirect
133. C₇×#125	C₂×C₄	semidirect
136. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
139. C₄×C₇×Q₈	C₂×C₄	semidirect
145. C₇×#117	C₂×C₄	semidirect
147. C₂×C₇×C₄⋊C₄	C₂×C₄	semidirect
242. #2382	C₂×C₇	semidirect
244. #2373	C₂×C₇	semidirect
245. #2370	C₂×C₇	semidirect
246. #2362	C₂×C₇	semidirect
247. #2360	C₂×C₇	semidirect
249. #2351	C₂×C₇	semidirect
250. #2346	C₂×C₇	semidirect
251. #2346	C₂×C₇	semidirect
252. #2345	C₂×C₇	semidirect
254. #2334	C₂×C₇	semidirect
255. #2330	C₂×C₇	semidirect
256. #2323	C₂×C₇	semidirect
257. #2323	C₂×C₇	semidirect
258. #2317	C₂×C₇	semidirect
259. #2316	C₂×C₇	semidirect
260. #2314	C₂×C₇	semidirect
261. C₄×#125	C₂×C₇	semidirect
262. #2295	C₂×C₇	semidirect
371. #552	C₄×C₇	semidirect
562. #125	C₂×C₄×C₇	semidirect
563. #125	C₂×C₄×C₇	semidirect
566. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
569. C₄×Q₈	C₂×C₄×C₇	semidirect
575. #117	C₂×C₄×C₇	semidirect
577. C₂×C₄⋊C₄	C₂×C₄×C₇	semidirect
913. C₇	#34482	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#552	2
C₇×#2382	2
C₇×#2376	2
C₇×#2373	2
C₇×#2370	2
C₇×#2362	2
C₇×#2360	2
C₇×#2352	2
C₇×#2351	2
C₇×#2346	2
C₇×#2345	2
C₇×#2335	2
C₇×#2334	2
C₇×#2330	2
C₇×#2323	2
C₇×#2317	2
C₇×#2316	2
C₇×#2314	2
C₄×C₇×#125	2
C₇×#2295	2
C₇×#2293	2
#34482	7

Subgroups — C7×#34482 #13211698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34482 #13211698