Subgroups — C₇×#34472 #13211688

Order 1792.

2480 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#548	C₂	1	1	yes	maximal, characteristic
2	C₇×#2379	C₂	1	2	yes	maximal, complemented
3	C₇×#2378	C₂	1	2	yes	maximal, complemented
4	C₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2364	C₂	1	2	yes	maximal, complemented
6	C₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2349	C₂	1	2	yes	maximal, complemented
10	C₇×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2337	C₂	1	2	yes	maximal, complemented
14	C₇×#2329	C₂	1	2	yes	maximal, complemented
15	C₇×#2326	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2325	C₂	1	2	yes	maximal, complemented
17	C₇×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2318	C₂	1	2	yes	maximal, complemented
20	C₇×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
26	C₇×#548	C₄	1	16	yes	complemented
27	C₂×C₇×#124	C₂²	1	1	yes	characteristic
28	C₂×C₇×#124	C₂²	1	2	yes	—
29	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₇×#121	C₂²	1	1	yes	characteristic
32	C₂×C₇×#121	C₂²	1	2	yes	—
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
38	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
39	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
40	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
43	C₂×C₇×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
47	C₇×#391	C₂²	1	1	yes	characteristic
48	C₇×#391	C₂²	1	1	yes	characteristic
49	C₇×#391	C₂²	1	2	yes	—
50	C₇×#391	C₂²	1	1	yes	characteristic
51	C₇×#391	C₂²	1	1	yes	characteristic
52	C₇×#391	C₂²	1	2	yes	—
53	C₇×#391	C₂²	1	1	yes	characteristic
54	C₇×#391	C₂²	1	1	yes	characteristic
55	C₇×#391	C₂²	1	2	yes	—
56	C₇×#391	C₂²	1	2	yes	—
57	C₇×#390	C₂²	1	1	yes	characteristic
58	C₇×#390	C₂²	1	1	yes	characteristic
59	C₇×#389	C₂²	1	1	yes	characteristic
60	C₇×#389	C₂²	1	1	yes	characteristic
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	2	yes	—
67	C₇×#388	C₂²	1	2	yes	—
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×#387	C₂²	1	1	yes	characteristic
75	C₇×#387	C₂²	1	1	yes	characteristic
76	C₇×#387	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×#386	C₂²	1	1	yes	characteristic
83	C₇×#386	C₂²	1	1	yes	characteristic
84	C₇×#386	C₂²	1	2	yes	—
85	C₇×#386	C₂²	1	2	yes	—
86	C₇×#386	C₂²	1	2	yes	—
87	C₇×#386	C₂²	1	2	yes	—
88	C₇×#386	C₂²	1	2	yes	—
89	C₇×#386	C₂²	1	2	yes	—
90	C₇×#385	C₂²	1	1	yes	characteristic
91	C₇×#385	C₂²	1	1	yes	characteristic
92	C₇×#385	C₂²	1	2	yes	—
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#385	C₂²	1	2	yes	—
95	C₇×#385	C₂²	1	2	yes	—
96	C₇×#385	C₂²	1	2	yes	—
97	C₇×#385	C₂²	1	2	yes	—
98	C₇×#385	C₂²	1	2	yes	—
99	C₇×#384	C₂²	1	1	yes	characteristic
100	C₇×#383	C₂²	1	2	yes	—
101	C₇×#382	C₂²	1	2	yes	—
102	C₇×#382	C₂²	1	2	yes	—
103	C₇×#381	C₂²	1	2	yes	—
104	C₇×#380	C₂²	1	1	yes	characteristic
105	C₇×#380	C₂²	1	2	yes	—
106	C₇×#380	C₂²	1	2	yes	—
107	C₇×#380	C₂²	1	1	yes	characteristic
108	C₇×#380	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×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₇×C₄⋊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	2	yes	—
117	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₇×#376	C₂²	1	1	yes	characteristic
121	C₂×C₇×#95	C₂²	1	2	yes	—
122	C₂×C₇×#95	C₂²	1	2	yes	—
123	C₂×C₇×#95	C₂²	1	2	yes	—
124	#34472	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂×C₇×#41	—	4	2	no	—
126	C₂×C₇×#41	—	4	2	no	—
127	C₂×C₇×#41	C₂×C₄	1	8	yes	complemented
128	C₂²×C₇×Q₈	—	4	2	no	—
129	C₂²×C₇×Q₈	—	4	2	no	—
130	C₂²×C₇×Q₈	C₂×C₄	1	8	yes	complemented
131	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
132	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
133	C₂²×C₇×Q₈	C₂³	1	2	yes	—
134	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
135	C₂²×C₇×D₄	C₂³	1	2	yes	—
136	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
137	C₂²×C₇×D₄	C₂³	1	2	yes	—
138	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₇	C₂³	1	2	yes	—
145	C₂³×C₄×C₇	C₂³	1	2	yes	—
146	C₂³×C₄×C₇	C₂³	1	2	yes	—
147	C₂³×C₄×C₇	C₂³	1	2	yes	—
148	C₇×#124	C₂×C₄	1	8	yes	complemented
149	C₇×#124	C₂×C₄	1	16	yes	complemented
150	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
151	C₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
152	C₇×#121	C₂×C₄	1	8	yes	complemented
153	C₇×#121	C₂×C₄	1	16	yes	complemented
154	C₄×C₇×Q₈	—	4	2	no	—
155	C₄×C₇×Q₈	—	4	2	no	—
156	C₄×C₇×Q₈	C₂×C₄	1	8	yes	complemented
157	C₄×C₇×D₄	—	4	2	no	—
158	C₄×C₇×D₄	—	4	2	no	—
159	C₄×C₇×D₄	—	4	4	no	—
160	C₄×C₇×D₄	—	4	4	no	—
161	C₄×C₇×D₄	—	4	4	no	—
162	C₄×C₇×D₄	C₂×C₄	1	8	yes	complemented
163	C₄×C₇×D₄	C₂×C₄	1	16	yes	complemented
164	C₇×#117	—	4	2	no	—
165	C₂×C₇×C₄⋊C₄	—	4	2	no	—
166	C₂×C₇×C₄⋊C₄	—	4	2	no	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
172	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₄²×C₇	—	4	2	no	—
208	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₇	C₂³	1	2	yes	—
215	C₂×C₄²×C₇	C₂³	1	2	yes	—
216	C₂×C₄²×C₇	C₂³	1	2	yes	—
217	C₂×C₄²×C₇	C₂³	1	2	yes	—
218	C₂×C₄²×C₇	C₂³	1	2	yes	—
219	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₇	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	1	yes	characteristic
222	C₇×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
233	C₇×#95	C₂³	1	1	yes	characteristic
234	C₇×#95	C₂³	1	1	yes	characteristic
235	C₇×#95	C₂³	1	1	yes	characteristic
236	C₇×#95	C₂³	1	1	yes	characteristic
237	C₇×#95	C₂³	1	2	yes	—
238	C₇×#95	C₂³	1	2	yes	—
239	C₇×#95	C₂³	1	1	yes	characteristic
240	C₇×#95	C₂³	1	2	yes	—
241	C₇×#95	C₂³	1	2	yes	—
242	C₇×#95	C₂³	1	2	yes	—
243	C₇×#95	C₂³	1	1	yes	characteristic
244	C₇×#95	C₂³	1	1	yes	characteristic
245	C₇×#95	C₂³	1	2	yes	—
246	C₇×#95	C₂³	1	2	yes	—
247	C₇×#95	C₂³	1	2	yes	—
248	C₇×#95	C₂³	1	2	yes	—
249	C₇×#95	C₂³	1	1	yes	characteristic
250	C₂×#548	C₂×C₇	1	1	yes	characteristic
251	#2379	C₂×C₇	1	2	yes	complemented
252	#2378	C₂×C₇	1	2	yes	complemented
253	#2367	C₂×C₇	1	1	yes	characteristic, complemented
254	#2364	C₂×C₇	1	2	yes	complemented
255	#2361	C₂×C₇	1	1	yes	characteristic, complemented
256	#2360	C₂×C₇	1	1	yes	characteristic, complemented
257	#2355	C₂×C₇	1	1	yes	characteristic, complemented
258	#2349	C₂×C₇	1	2	yes	complemented
259	D₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
260	Q₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
261	#2339	C₂×C₇	1	1	yes	characteristic, complemented
262	#2337	C₂×C₇	1	2	yes	complemented
263	#2329	C₂×C₇	1	2	yes	complemented
264	#2326	C₂×C₇	1	1	yes	characteristic, complemented
265	#2325	C₂×C₇	1	2	yes	complemented
266	#2323	C₂×C₇	1	1	yes	characteristic, complemented
267	#2320	C₂×C₇	1	1	yes	characteristic, complemented
268	#2318	C₂×C₇	1	2	yes	complemented
269	#2311	C₂×C₇	1	1	yes	characteristic, complemented
270	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
271	C₂×#391	C₂×C₇	1	1	yes	characteristic, complemented
272	#2290	C₂×C₇	1	1	yes	characteristic, complemented
273	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
274	C₂⁴×C₇	C₂⁴	1	2	yes	—
275	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
276	C₇×#41	—	4	16	no	—
277	C₂×C₇×Q₈	—	2	2	no	—
278	C₂×C₇×Q₈	—	2	2	no	—
279	C₂×C₇×Q₈	—	2	2	no	—
280	C₂×C₇×Q₈	—	2	2	no	—
281	C₂×C₇×Q₈	—	4	2	no	—
282	C₂×C₇×Q₈	—	4	2	no	—
283	C₂×C₇×Q₈	—	4	16	no	—
284	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
285	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
286	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	—
287	C₂×C₇×D₄	—	2	4	no	—
288	C₂×C₇×D₄	—	2	2	no	—
289	C₂×C₇×D₄	—	2	4	no	—
290	C₂×C₇×D₄	—	2	2	no	—
291	C₂×C₇×D₄	—	2	2	no	—
292	C₂×C₇×D₄	—	2	2	no	—
293	C₂×C₇×D₄	—	4	2	no	—
294	C₂×C₇×D₄	—	4	2	no	—
295	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
296	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
297	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
298	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
299	C₂²×C₄×C₇	—	2	2	no	—
300	C₂²×C₄×C₇	—	2	2	no	—
301	C₂²×C₄×C₇	—	2	2	no	—
302	C₂²×C₄×C₇	—	2	2	no	—
303	C₂²×C₄×C₇	—	2	2	no	—
304	C₂²×C₄×C₇	—	2	2	no	—
305	C₂²×C₄×C₇	—	2	4	no	—
306	C₂²×C₄×C₇	—	2	2	no	—
307	C₂²×C₄×C₇	—	2	4	no	—
308	C₂²×C₄×C₇	—	4	1	no	—
309	C₂²×C₄×C₇	—	4	1	no	—
310	C₂²×C₄×C₇	—	4	1	no	—
311	C₂²×C₄×C₇	—	4	2	no	—
312	C₂²×C₄×C₇	—	4	2	no	—
313	C₂²×C₄×C₇	—	4	2	no	—
314	C₂²×C₄×C₇	—	4	2	no	—
315	C₂²×C₄×C₇	—	4	2	no	—
316	C₂²×C₄×C₇	—	4	2	no	—
317	C₂²×C₄×C₇	—	4	2	no	—
318	C₂²×C₄×C₇	—	4	2	no	—
319	C₂²×C₄×C₇	—	4	2	no	—
320	C₂²×C₄×C₇	—	4	2	no	—
321	C₂²×C₄×C₇	—	4	2	no	—
322	C₂²×C₄×C₇	—	4	2	no	—
323	C₂²×C₄×C₇	—	4	2	no	—
324	C₂²×C₄×C₇	—	4	2	no	—
325	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
326	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
327	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
328	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
329	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
349	C₇×C₄⋊C₄	—	2	2	no	—
350	C₇×C₄⋊C₄	—	2	2	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	2	no	—
353	C₇×C₄⋊C₄	—	2	2	no	—
354	C₇×C₄⋊C₄	—	4	2	no	—
355	C₇×C₄⋊C₄	—	4	2	no	—
356	C₇×C₄⋊C₄	—	4	1	no	—
357	C₇×C₄⋊C₄	—	4	2	no	—
358	C₇×C₄⋊C₄	—	4	1	no	—
359	C₇×C₄⋊C₄	—	4	1	no	—
360	C₇×C₄⋊C₄	—	4	2	no	—
361	C₇×C₄⋊C₄	—	4	2	no	—
362	C₇×C₄⋊C₄	—	4	2	no	—
363	C₇×C₄⋊C₄	—	4	2	no	—
364	C₇×C₄⋊C₄	—	4	2	no	—
365	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
366	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
367	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
368	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
369	C₇×C₂²⋊C₄	—	2	2	no	—
370	C₇×C₂²⋊C₄	—	2	4	no	—
371	C₇×C₂²⋊C₄	—	2	2	no	—
372	C₇×C₂²⋊C₄	—	2	2	no	—
373	C₇×C₂²⋊C₄	—	4	2	no	—
374	C₇×C₂²⋊C₄	—	4	2	no	—
375	C₇×C₂²⋊C₄	—	4	1	no	—
376	C₇×C₂²⋊C₄	—	4	1	no	—
377	C₇×C₂²⋊C₄	—	4	1	no	—
378	C₇×C₂²⋊C₄	—	4	2	no	—
379	C₇×C₂²⋊C₄	—	4	2	no	—
380	C₇×C₂²⋊C₄	—	4	2	no	—
381	C₇×C₂²⋊C₄	—	4	2	no	—
382	C₇×C₂²⋊C₄	—	4	2	no	—
383	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
384	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
385	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
386	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
387	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
388	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
389	C₄²×C₇	—	2	2	no	—
390	C₄²×C₇	—	2	2	no	—
391	C₄²×C₇	—	2	2	no	—
392	C₄²×C₇	—	2	2	no	—
393	C₄²×C₇	—	4	1	no	—
394	C₄²×C₇	—	4	1	no	—
395	C₄²×C₇	—	4	2	no	—
396	C₄²×C₇	—	4	2	no	—
397	C₄²×C₇	—	4	2	no	—
398	C₄²×C₇	—	4	2	no	—
399	C₄²×C₇	—	4	2	no	—
400	C₄²×C₇	C₂²×C₄	1	8	yes	—
401	C₄²×C₇	C₂²×C₄	1	4	yes	—
402	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
403	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
404	#548	C₄×C₇	1	16	yes	complemented
405	C₂×#124	C₂²×C₇	1	1	yes	characteristic
406	C₂×#124	C₂²×C₇	1	2	yes	—
407	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
408	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
409	C₂×#121	C₂²×C₇	1	2	yes	—
410	C₂×#121	C₂²×C₇	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
412	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
413	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
415	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
416	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
419	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
421	C₂×#117	C₂²×C₇	1	1	yes	characteristic
422	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
423	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
424	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
425	#391	C₂²×C₇	1	1	yes	characteristic
426	#391	C₂²×C₇	1	1	yes	characteristic
427	#391	C₂²×C₇	1	1	yes	characteristic
428	#391	C₂²×C₇	1	1	yes	characteristic
429	#391	C₂²×C₇	1	2	yes	—
430	#391	C₂²×C₇	1	2	yes	—
431	#391	C₂²×C₇	1	2	yes	—
432	#391	C₂²×C₇	1	1	yes	characteristic
433	#391	C₂²×C₇	1	1	yes	characteristic
434	#391	C₂²×C₇	1	2	yes	—
435	#390	C₂²×C₇	1	1	yes	characteristic
436	#390	C₂²×C₇	1	1	yes	characteristic
437	#389	C₂²×C₇	1	1	yes	characteristic
438	#389	C₂²×C₇	1	1	yes	characteristic
439	#389	C₂²×C₇	1	2	yes	—
440	#389	C₂²×C₇	1	2	yes	—
441	#389	C₂²×C₇	1	2	yes	—
442	#388	C₂²×C₇	1	2	yes	—
443	#388	C₂²×C₇	1	2	yes	—
444	#388	C₂²×C₇	1	2	yes	—
445	#388	C₂²×C₇	1	2	yes	—
446	#388	C₂²×C₇	1	2	yes	—
447	#388	C₂²×C₇	1	2	yes	—
448	#388	C₂²×C₇	1	1	yes	characteristic
449	#388	C₂²×C₇	1	2	yes	—
450	#388	C₂²×C₇	1	2	yes	—
451	#388	C₂²×C₇	1	1	yes	characteristic
452	#387	C₂²×C₇	1	2	yes	—
453	#387	C₂²×C₇	1	2	yes	—
454	#387	C₂²×C₇	1	2	yes	—
455	#387	C₂²×C₇	1	2	yes	—
456	#387	C₂²×C₇	1	2	yes	—
457	#387	C₂²×C₇	1	1	yes	characteristic
458	#387	C₂²×C₇	1	2	yes	—
459	#387	C₂²×C₇	1	1	yes	characteristic
460	#386	C₂²×C₇	1	2	yes	—
461	#386	C₂²×C₇	1	2	yes	—
462	#386	C₂²×C₇	1	2	yes	—
463	#386	C₂²×C₇	1	2	yes	—
464	#386	C₂²×C₇	1	1	yes	characteristic
465	#386	C₂²×C₇	1	2	yes	—
466	#386	C₂²×C₇	1	2	yes	—
467	#386	C₂²×C₇	1	1	yes	characteristic
468	#385	C₂²×C₇	1	1	yes	characteristic
469	#385	C₂²×C₇	1	2	yes	—
470	#385	C₂²×C₇	1	2	yes	—
471	#385	C₂²×C₇	1	2	yes	—
472	#385	C₂²×C₇	1	2	yes	—
473	#385	C₂²×C₇	1	2	yes	—
474	#385	C₂²×C₇	1	2	yes	—
475	#385	C₂²×C₇	1	2	yes	—
476	#385	C₂²×C₇	1	1	yes	characteristic
477	#384	C₂²×C₇	1	1	yes	characteristic
478	#383	C₂²×C₇	1	2	yes	—
479	#382	C₂²×C₇	1	2	yes	—
480	#382	C₂²×C₇	1	2	yes	—
481	#381	C₂²×C₇	1	2	yes	—
482	#380	C₂²×C₇	1	2	yes	—
483	#380	C₂²×C₇	1	2	yes	—
484	#380	C₂²×C₇	1	1	yes	characteristic
485	#380	C₂²×C₇	1	2	yes	—
486	#380	C₂²×C₇	1	1	yes	characteristic
487	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
488	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
489	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
491	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
492	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
493	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
494	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
495	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
497	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
498	#376	C₂²×C₇	1	1	yes	characteristic
499	C₂×#95	C₂²×C₇	1	2	yes	—
500	C₂×#95	C₂²×C₇	1	2	yes	—
501	C₂×#95	C₂²×C₇	1	2	yes	—
502	C₂³×C₇	—	2	1	no	—
503	C₂³×C₇	—	2	1	no	—
504	C₂³×C₇	—	2	1	no	—
505	C₂³×C₇	—	2	1	no	—
506	C₂³×C₇	—	2	1	no	—
507	C₂³×C₇	—	2	2	no	—
508	C₂³×C₇	—	2	1	no	—
509	C₂³×C₇	—	2	2	no	—
510	C₂³×C₇	—	2	2	no	—
511	C₂³×C₇	—	2	1	no	—
512	C₂³×C₇	—	2	1	no	—
513	C₂³×C₇	—	2	2	no	—
514	C₂³×C₇	—	2	1	no	—
515	C₂³×C₇	—	2	2	no	—
516	C₂³×C₇	—	2	2	no	—
517	C₂³×C₇	—	2	1	no	—
518	C₂³×C₇	C₂³×C₄	1	2	yes	—
519	C₂³×C₇	C₂³×C₄	1	4	yes	—
520	C₂³×C₇	C₂³×C₄	1	2	yes	—
521	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
522	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
523	C₂³×C₇	C₂⁵	1	1	yes	characteristic
524	C₇×Q₈	—	2	8	no	—
525	C₇×Q₈	—	2	8	no	—
526	C₇×Q₈	—	4	8	no	—
527	C₇×D₄	—	2	8	no	—
528	C₇×D₄	—	2	16	no	—
529	C₇×D₄	—	2	8	no	—
530	C₇×D₄	—	4	8	no	—
531	C₂×C₄×C₇	—	2	1	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	1	no	—
534	C₂×C₄×C₇	—	2	1	no	—
535	C₂×C₄×C₇	—	2	1	no	—
536	C₂×C₄×C₇	—	2	2	no	—
537	C₂×C₄×C₇	—	2	2	no	—
538	C₂×C₄×C₇	—	2	1	no	—
539	C₂×C₄×C₇	—	2	1	no	—
540	C₂×C₄×C₇	—	2	1	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	—	2	1	no	—
545	C₂×C₄×C₇	—	2	2	no	—
546	C₂×C₄×C₇	—	2	1	no	—
547	C₂×C₄×C₇	—	2	8	no	—
548	C₂×C₄×C₇	—	2	8	no	—
549	C₂×C₄×C₇	—	2	1	no	—
550	C₂×C₄×C₇	—	2	1	no	—
551	C₂×C₄×C₇	—	2	1	no	—
552	C₂×C₄×C₇	—	2	1	no	—
553	C₂×C₄×C₇	—	2	1	no	—
554	C₂×C₄×C₇	—	2	1	no	—
555	C₂×C₄×C₇	—	2	1	no	—
556	C₂×C₄×C₇	—	2	1	no	—
557	C₂×C₄×C₇	—	2	2	no	—
558	C₂×C₄×C₇	—	2	2	no	—
559	C₂×C₄×C₇	—	2	2	no	—
560	C₂×C₄×C₇	—	2	2	no	—
561	C₂×C₄×C₇	—	2	2	no	—
562	C₂×C₄×C₇	—	2	2	no	—
563	C₂×C₄×C₇	—	2	1	no	—
564	C₂×C₄×C₇	—	2	1	no	—
565	C₂×C₄×C₇	—	2	2	no	—
566	C₂×C₄×C₇	—	2	2	no	—
567	C₂×C₄×C₇	—	2	1	no	—
568	C₂×C₄×C₇	—	2	1	no	—
569	C₂×C₄×C₇	—	2	1	no	—
570	C₂×C₄×C₇	—	2	1	no	—
571	C₂×C₄×C₇	—	2	1	no	—
572	C₂×C₄×C₇	—	2	2	no	—
573	C₂×C₄×C₇	—	2	1	no	—
574	C₂×C₄×C₇	—	2	1	no	—
575	C₂×C₄×C₇	—	2	1	no	—
576	C₂×C₄×C₇	—	2	1	no	—
577	C₂×C₄×C₇	—	2	1	no	—
578	C₂×C₄×C₇	—	2	2	no	—
579	C₂×C₄×C₇	—	2	1	no	—
580	C₂×C₄×C₇	—	2	2	no	—
581	C₂×C₄×C₇	—	2	2	no	—
582	C₂×C₄×C₇	—	4	8	no	—
583	C₂×C₄×C₇	—	4	8	no	—
584	C₂×C₄×C₇	—	4	4	no	—
585	C₂×C₄×C₇	—	4	4	no	—
586	C₂×C₄×C₇	—	8	4	no	—
587	C₂×C₄×C₇	—	8	4	no	—
588	C₂×C₄×C₇	—	8	4	no	—
589	C₂×C₄×C₇	—	8	4	no	—
590	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
591	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
592	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
593	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
594	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
595	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
596	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
597	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
598	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
599	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
600	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
601	C₂×#41	—	4	2	no	—
602	C₂×#41	—	4	2	no	—
603	C₂×#41	C₂×C₄×C₇	1	8	yes	complemented
604	C₂²×Q₈	—	4	2	no	—
605	C₂²×Q₈	—	4	2	no	—
606	C₂²×Q₈	C₂×C₄×C₇	1	8	yes	complemented
607	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
608	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
609	C₂²×Q₈	C₂³×C₇	1	2	yes	—
610	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₇	1	2	yes	—
612	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
613	C₂²×D₄	C₂³×C₇	1	2	yes	—
614	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₇	1	2	yes	—
618	C₂³×C₄	C₂³×C₇	1	2	yes	—
619	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₇	1	2	yes	—
621	C₂³×C₄	C₂³×C₇	1	2	yes	—
622	C₂³×C₄	C₂³×C₇	1	2	yes	—
623	C₂³×C₄	C₂³×C₇	1	2	yes	—
624	#124	C₂×C₄×C₇	1	8	yes	complemented
625	#124	C₂×C₄×C₇	1	16	yes	complemented
626	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	complemented
627	C₂²⋊Q₈	C₂×C₄×C₇	1	16	yes	complemented
628	#121	C₂×C₄×C₇	1	8	yes	complemented
629	#121	C₂×C₄×C₇	1	16	yes	complemented
630	C₄×Q₈	—	4	2	no	—
631	C₄×Q₈	—	4	2	no	—
632	C₄×Q₈	C₂×C₄×C₇	1	8	yes	complemented
633	C₄×D₄	—	4	2	no	—
634	C₄×D₄	—	4	2	no	—
635	C₄×D₄	—	4	4	no	—
636	C₄×D₄	—	4	4	no	—
637	C₄×D₄	—	4	4	no	—
638	C₄×D₄	C₂×C₄×C₇	1	8	yes	complemented
639	C₄×D₄	C₂×C₄×C₇	1	16	yes	complemented
640	#117	—	4	2	no	—
641	C₂×C₄⋊C₄	—	4	2	no	—
642	C₂×C₄⋊C₄	—	4	2	no	—
643	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
680	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
683	C₂×C₄²	—	4	2	no	—
684	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₇	1	2	yes	—
689	C₂×C₄²	C₂³×C₇	1	2	yes	—
690	C₂×C₄²	C₂³×C₇	1	2	yes	—
691	C₂×C₄²	C₂³×C₇	1	2	yes	—
692	C₂×C₄²	C₂³×C₇	1	2	yes	—
693	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₇	1	2	yes	—
697	#95	C₂³×C₇	1	1	yes	characteristic
698	#95	C₂³×C₇	1	2	yes	—
699	#95	C₂³×C₇	1	2	yes	—
700	#95	C₂³×C₇	1	2	yes	—
701	#95	C₂³×C₇	1	2	yes	—
702	#95	C₂³×C₇	1	2	yes	—
703	#95	C₂³×C₇	1	2	yes	—
704	#95	C₂³×C₇	1	2	yes	—
705	#95	C₂³×C₇	1	2	yes	—
706	#95	C₂³×C₇	1	2	yes	—
707	#95	C₂³×C₇	1	2	yes	—
708	#95	C₂³×C₇	1	1	yes	characteristic
709	#95	C₂³×C₇	1	1	yes	characteristic
710	#95	C₂³×C₇	1	1	yes	characteristic
711	#95	C₂³×C₇	1	1	yes	characteristic
712	#95	C₂³×C₇	1	1	yes	characteristic
713	#95	C₂³×C₇	1	2	yes	—
714	#95	C₂³×C₇	1	2	yes	—
715	#95	C₂³×C₇	1	1	yes	characteristic
716	#95	C₂³×C₇	1	2	yes	—
717	#95	C₂³×C₇	1	2	yes	—
718	#95	C₂³×C₇	1	2	yes	—
719	#95	C₂³×C₇	1	1	yes	characteristic
720	#95	C₂³×C₇	1	1	yes	characteristic
721	#95	C₂³×C₇	1	2	yes	—
722	#95	C₂³×C₇	1	2	yes	—
723	#95	C₂³×C₇	1	2	yes	—
724	#95	C₂³×C₇	1	2	yes	—
725	#95	C₂³×C₇	1	1	yes	characteristic
726	C₂²×C₇	—	2	2	no	—
727	C₂²×C₇	—	2	2	no	—
728	C₂²×C₇	—	2	2	no	—
729	C₂²×C₇	—	2	2	no	—
730	C₂²×C₇	—	2	2	no	—
731	C₂²×C₇	—	2	2	no	—
732	C₂²×C₇	—	2	2	no	—
733	C₂²×C₇	—	2	4	no	—
734	C₂²×C₇	—	2	2	no	—
735	C₂²×C₇	—	2	4	no	—
736	C₂²×C₇	—	2	2	no	—
737	C₂²×C₇	—	2	4	no	—
738	C₂²×C₇	—	4	2	no	—
739	C₂²×C₇	—	4	1	no	—
740	C₂²×C₇	—	4	1	no	—
741	C₂²×C₇	—	4	2	no	—
742	C₂²×C₇	—	4	2	no	—
743	C₂²×C₇	—	4	1	no	—
744	C₂²×C₇	—	4	1	no	—
745	C₂²×C₇	—	4	2	no	—
746	C₂²×C₇	#520	1	4	yes	—
747	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
748	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
749	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
750	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
751	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
752	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
753	C₂²×C₇	#585	1	1	yes	characteristic
754	C₄×C₇	—	2	2	no	—
755	C₄×C₇	—	2	2	no	—
756	C₄×C₇	—	2	4	no	—
757	C₄×C₇	—	2	4	no	—
758	C₄×C₇	—	2	4	no	—
759	C₄×C₇	—	2	2	no	—
760	C₄×C₇	—	2	2	no	—
761	C₄×C₇	—	2	2	no	—
762	C₄×C₇	—	4	1	no	—
763	C₄×C₇	—	4	1	no	—
764	C₄×C₇	—	4	2	no	—
765	C₄×C₇	—	4	1	no	—
766	C₄×C₇	—	4	1	no	—
767	C₄×C₇	—	4	1	no	—
768	C₄×C₇	—	4	1	no	—
769	C₄×C₇	—	4	2	no	—
770	C₄×C₇	—	4	1	no	—
771	C₄×C₇	—	4	2	no	—
772	C₄×C₇	—	4	2	no	—
773	C₄×C₇	#518	1	4	yes	—
774	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
775	C₂⁴	C₂⁴×C₇	1	2	yes	—
776	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
777	#41	—	4	16	no	—
778	C₂×Q₈	—	2	2	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	2	2	no	—
781	C₂×Q₈	—	2	2	no	—
782	C₂×Q₈	—	4	2	no	—
783	C₂×Q₈	—	4	2	no	—
784	C₂×Q₈	—	4	16	no	—
785	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
786	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
787	C₂×Q₈	C₂²×C₄×C₇	1	8	yes	—
788	C₂×D₄	—	2	4	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	4	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
797	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
798	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
799	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	4	no	—
809	C₂²×C₄	—	4	1	no	—
810	C₂²×C₄	—	4	1	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	1	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	—	4	2	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
827	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
828	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
829	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
830	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
845	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	—	4	2	no	—
857	C₄⋊C₄	—	4	1	no	—
858	C₄⋊C₄	—	4	1	no	—
859	C₄⋊C₄	—	4	2	no	—
860	C₄⋊C₄	—	4	2	no	—
861	C₄⋊C₄	—	4	2	no	—
862	C₄⋊C₄	—	4	2	no	—
863	C₄⋊C₄	—	4	2	no	—
864	C₄⋊C₄	—	4	1	no	—
865	C₄⋊C₄	—	4	2	no	—
866	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
867	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
868	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
869	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	4	1	no	—
875	C₂²⋊C₄	—	4	1	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	2	no	—
881	C₂²⋊C₄	—	4	2	no	—
882	C₂²⋊C₄	—	4	2	no	—
883	C₂²⋊C₄	—	4	1	no	—
884	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
885	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
886	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
887	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
888	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
889	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	4	1	no	—
895	C₄²	—	4	1	no	—
896	C₄²	—	4	2	no	—
897	C₄²	—	4	2	no	—
898	C₄²	—	4	2	no	—
899	C₄²	—	4	2	no	—
900	C₄²	—	4	2	no	—
901	C₄²	C₂²×C₄×C₇	1	8	yes	—
902	C₄²	C₂²×C₄×C₇	1	4	yes	—
903	C₂×C₇	—	2	4	no	—
904	C₂×C₇	—	4	2	no	—
905	C₂×C₇	—	4	4	no	—
906	C₂×C₇	C₂×#518	1	1	yes	characteristic
907	C₂×C₇	C₂×#520	1	1	yes	characteristic
908	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
909	C₂×C₇	#3536	1	1	yes	characteristic
910	C₂×C₇	#3541	1	1	yes	characteristic
911	C₂×C₇	#3552	1	1	yes	characteristic
912	C₂×C₇	#3558	1	1	yes	characteristic
913	C₂³	—	2	1	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	1	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	2	2	no	—
928	C₂³	—	2	1	no	—
929	C₂³	C₂³×C₄×C₇	1	2	yes	—
930	C₂³	C₂³×C₄×C₇	1	4	yes	—
931	C₂³	C₂³×C₄×C₇	1	2	yes	—
932	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
933	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
934	C₂³	C₂⁵×C₇	1	1	yes	characteristic
935	Q₈	—	2	8	no	—
936	Q₈	—	2	8	no	—
937	Q₈	—	4	8	no	—
938	D₄	—	2	8	no	—
939	D₄	—	2	16	no	—
940	D₄	—	2	8	no	—
941	D₄	—	4	8	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	8	no	—
959	C₂×C₄	—	2	8	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	4	8	no	—
994	C₂×C₄	—	4	8	no	—
995	C₂×C₄	—	4	4	no	—
996	C₂×C₄	—	4	4	no	—
997	C₂×C₄	—	8	4	no	—
998	C₂×C₄	—	8	4	no	—
999	C₂×C₄	—	8	4	no	—
1000	C₂×C₄	—	8	4	no	—
1001	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1002	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
1003	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1004	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
1005	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1006	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
1007	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1008	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1009	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1010	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1011	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1012	C₇	#34472	1	1	yes	characteristic, direct product factor, Sylow
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	2	4	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	4	no	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	4	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	1	no	—
1031	C₂²	—	4	1	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	C₇×#520	1	4	yes	—
1034	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
1035	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1036	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1037	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1038	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1039	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1040	C₂²	C₇×#585	1	1	yes	characteristic
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	4	no	—
1044	C₄	—	2	4	no	—
1045	C₄	—	2	4	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	2	no	—
1060	C₄	C₇×#518	1	4	yes	—
1061	C₂	—	2	4	no	—
1062	C₂	—	4	2	no	—
1063	C₂	—	4	4	no	—
1064	C₂	C₂×C₇×#518	1	1	yes	characteristic
1065	C₂	C₂×C₇×#520	1	1	yes	characteristic
1066	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1067	C₂	C₇×#3536	1	1	yes	characteristic
1068	C₂	C₇×#3541	1	1	yes	characteristic
1069	C₂	C₇×#3552	1	1	yes	characteristic
1070	C₂	C₇×#3558	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂×C₇×#548	C₂
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×#2379	C₂	semidirect
3. C₇×#2378	C₂	semidirect
4. C₇×#2367	C₂	semidirect
5. C₇×#2364	C₂	semidirect
6. C₇×#2361	C₂	semidirect
7. C₇×#2360	C₂	semidirect
8. C₇×#2355	C₂	semidirect
9. C₇×#2349	C₂	semidirect
10. C₇×D₄×C₄⋊C₄	C₂	semidirect
11. C₇×Q₈×C₂²⋊C₄	C₂	semidirect
12. C₇×#2339	C₂	semidirect
13. C₇×#2337	C₂	semidirect
14. C₇×#2329	C₂	semidirect
15. C₇×#2326	C₂	semidirect
16. C₇×#2325	C₂	semidirect
17. C₇×#2323	C₂	semidirect
18. C₇×#2320	C₂	semidirect
19. C₇×#2318	C₂	semidirect
20. C₇×#2311	C₂	semidirect
21. C₄×C₇×#121	C₂	semidirect
22. C₂×C₇×#391	C₂	semidirect
23. C₇×#2290	C₂	semidirect
26. C₇×#548	C₄	semidirect
124. #34472	C₇	direct (N × H)
127. C₂×C₇×#41	C₂×C₄	semidirect
130. C₂²×C₇×Q₈	C₂×C₄	semidirect
148. C₇×#124	C₂×C₄	semidirect
149. C₇×#124	C₂×C₄	semidirect
150. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
151. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
152. C₇×#121	C₂×C₄	semidirect
153. C₇×#121	C₂×C₄	semidirect
156. C₄×C₇×Q₈	C₂×C₄	semidirect
162. C₄×C₇×D₄	C₂×C₄	semidirect
163. C₄×C₇×D₄	C₂×C₄	semidirect
251. #2379	C₂×C₇	semidirect
252. #2378	C₂×C₇	semidirect
253. #2367	C₂×C₇	semidirect
254. #2364	C₂×C₇	semidirect
255. #2361	C₂×C₇	semidirect
256. #2360	C₂×C₇	semidirect
257. #2355	C₂×C₇	semidirect
258. #2349	C₂×C₇	semidirect
259. D₄×C₄⋊C₄	C₂×C₇	semidirect
260. Q₈×C₂²⋊C₄	C₂×C₇	semidirect
261. #2339	C₂×C₇	semidirect
262. #2337	C₂×C₇	semidirect
263. #2329	C₂×C₇	semidirect
264. #2326	C₂×C₇	semidirect
265. #2325	C₂×C₇	semidirect
266. #2323	C₂×C₇	semidirect
267. #2320	C₂×C₇	semidirect
268. #2318	C₂×C₇	semidirect
269. #2311	C₂×C₇	semidirect
270. C₄×#121	C₂×C₇	semidirect
271. C₂×#391	C₂×C₇	semidirect
272. #2290	C₂×C₇	semidirect
404. #548	C₄×C₇	semidirect
603. C₂×#41	C₂×C₄×C₇	semidirect
606. C₂²×Q₈	C₂×C₄×C₇	semidirect
624. #124	C₂×C₄×C₇	semidirect
625. #124	C₂×C₄×C₇	semidirect
626. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
627. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
628. #121	C₂×C₄×C₇	semidirect
629. #121	C₂×C₄×C₇	semidirect
632. C₄×Q₈	C₂×C₄×C₇	semidirect
638. C₄×D₄	C₂×C₄×C₇	semidirect
639. C₄×D₄	C₂×C₄×C₇	semidirect
1012. C₇	#34472	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×#548	2
C₇×#2379	2
C₇×#2378	2
C₇×#2367	2
C₇×#2364	2
C₇×#2361	2
C₇×#2360	2
C₇×#2355	2
C₇×#2349	2
C₇×D₄×C₄⋊C₄	2
C₇×Q₈×C₂²⋊C₄	2
C₇×#2339	2
C₇×#2337	2
C₇×#2329	2
C₇×#2326	2
C₇×#2325	2
C₇×#2323	2
C₇×#2320	2
C₇×#2318	2
C₇×#2311	2
C₄×C₇×#121	2
C₂×C₇×#391	2
C₇×#2290	2
#34472	7

Subgroups — C7×#34472 #13211688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34472 #13211688