Subgroups — C₇×#35102 #13212318

Order 1792.

2902 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2848	C₂	1	2	yes	maximal, complemented
4	C₇×#2847	C₂	1	2	yes	maximal, complemented
5	C₇×#2623	C₂	1	2	yes	maximal, complemented
6	C₇×#2613	C₂	1	2	yes	maximal, complemented
7	C₇×#2603	C₂	1	4	yes	maximal, complemented
8	C₇×#2598	C₂	1	4	yes	maximal, complemented
9	C₇×#2562	C₂	1	2	yes	maximal, complemented
10	C₇×#2540	C₂	1	2	yes	maximal, complemented
11	C₇×#2536	C₂	1	2	yes	maximal, complemented
12	C₇×#2535	C₂	1	2	yes	maximal, complemented
13	C₇×#2321	C₂	1	4	yes	maximal, complemented
14	C₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
17	C₇×#529	—	2	8	no	—
18	C₂×C₇×#126	C₂²	1	2	yes	complemented
19	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₇×#123	C₂²	1	2	yes	—
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
24	C₂×C₇×#121	C₂²	1	1	yes	characteristic
25	C₂×C₇×#121	C₂²	1	4	yes	complemented
26	C₂×C₇×#120	C₂²	1	4	yes	—
27	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×C₇×D₄	—	2	8	no	—
29	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
30	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
33	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
34	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₇×#117	C₂²	1	2	yes	complemented
36	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
39	C₇×#400	C₂²	1	4	yes	complemented
40	C₇×#399	C₂²	1	4	yes	complemented
41	C₇×#398	C₂²	1	4	yes	complemented
42	C₇×#397	C₂²	1	4	yes	complemented
43	C₇×#394	C₂²	1	4	yes	—
44	C₇×#394	C₂²	1	4	yes	—
45	C₇×#392	C₂²	1	4	yes	—
46	C₇×#392	C₂²	1	4	yes	—
47	C₇×#390	C₂²	1	8	yes	complemented
48	C₇×#388	C₂²	1	8	yes	complemented
49	C₇×#388	C₂²	1	8	yes	complemented
50	C₇×#386	C₂²	1	4	yes	—
51	C₇×#386	C₂²	1	8	yes	complemented
52	C₇×#386	C₂²	1	8	yes	complemented
53	C₇×#385	C₂²	1	4	yes	—
54	C₇×#385	C₂²	1	8	yes	complemented
55	C₇×#383	C₂²	1	2	yes	complemented
56	C₇×#382	C₂²	1	2	yes	complemented
57	C₇×#381	C₂²	1	2	yes	—
58	C₇×#380	C₂²	1	2	yes	—
59	C₇×#380	C₂²	1	4	yes	complemented
60	C₇×#380	C₂²	1	4	yes	complemented
61	C₇×#379	C₂²	1	4	yes	—
62	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
63	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₇×#376	C₂²	1	2	yes	complemented
65	#35102	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁵×C₇	C₂³	1	2	yes	—
67	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×D₄	—	2	8	no	—
69	C₂²×C₇×D₄	—	2	4	no	—
70	C₂²×C₇×D₄	C₂³	1	2	yes	—
71	C₂²×C₇×D₄	C₂³	1	2	yes	—
72	C₂²×C₇×D₄	C₂³	1	2	yes	—
73	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
74	C₂²×C₇×D₄	C₂³	1	8	yes	—
75	C₂³×C₄×C₇	—	2	8	no	—
76	C₂³×C₄×C₇	—	4	8	no	—
77	C₂³×C₄×C₇	C₂³	1	4	yes	—
78	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₇	C₂³	1	2	yes	—
81	C₂³×C₄×C₇	C₂³	1	2	yes	—
82	C₂³×C₄×C₇	C₂³	1	4	yes	—
83	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
84	C₇×#126	—	2	8	no	—
85	C₇×#125	—	2	4	no	—
86	C₇×#124	—	2	4	no	—
87	C₇×#123	—	2	8	no	—
88	C₇×C₂²⋊Q₈	—	2	4	no	—
89	C₇×C₂²⋊Q₈	—	4	8	no	—
90	C₇×#121	—	2	4	no	—
91	C₇×#121	—	4	8	no	—
92	C₇×#120	—	2	16	no	—
93	C₄×C₇×Q₈	—	2	4	no	—
94	C₄×C₇×D₄	—	2	8	no	—
95	C₄×C₇×D₄	—	2	8	no	—
96	C₄×C₇×D₄	—	2	8	no	—
97	C₄×C₇×D₄	—	2	8	no	—
98	C₄×C₇×D₄	—	2	8	no	—
99	C₄×C₇×D₄	—	2	4	no	—
100	C₇×#117	—	2	8	no	—
101	C₂×C₇×C₄⋊C₄	—	2	4	no	—
102	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
112	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
113	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
122	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
123	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
124	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
125	C₂×C₄²×C₇	D₄	1	8	yes	complemented
126	C₂×C₄²×C₇	C₂³	1	2	yes	—
127	C₂×C₄²×C₇	C₂³	1	4	yes	—
128	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
132	C₇×#95	C₂³	1	4	yes	—
133	C₇×#95	C₂³	1	4	yes	—
134	C₇×#95	C₂³	1	4	yes	—
135	C₇×#95	C₂³	1	4	yes	—
136	C₇×#95	C₂³	1	8	yes	—
137	C₇×#95	C₂³	1	8	yes	—
138	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
139	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
140	#2848	C₂×C₇	1	2	yes	complemented
141	#2847	C₂×C₇	1	2	yes	complemented
142	#2623	C₂×C₇	1	2	yes	complemented
143	#2613	C₂×C₇	1	2	yes	complemented
144	#2603	C₂×C₇	1	4	yes	complemented
145	#2598	C₂×C₇	1	4	yes	complemented
146	#2562	C₂×C₇	1	2	yes	complemented
147	#2540	C₂×C₇	1	2	yes	complemented
148	#2536	C₂×C₇	1	2	yes	complemented
149	#2535	C₂×C₇	1	2	yes	complemented
150	#2321	C₂×C₇	1	4	yes	complemented
151	#2283	C₂×C₇	1	1	yes	characteristic, complemented
152	C₂⁴×C₇	—	2	4	no	—
153	C₂⁴×C₇	—	2	4	no	—
154	C₂⁴×C₇	—	4	4	no	—
155	C₂⁴×C₇	—	4	4	no	—
156	C₂⁴×C₇	#41	1	8	yes	—
157	C₂⁴×C₇	C₂⁴	1	2	yes	—
158	C₂⁴×C₇	C₂⁴	1	4	yes	—
159	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
160	C₂×C₇×Q₈	—	2	2	no	—
161	C₂×C₇×Q₈	—	2	4	no	—
162	C₂×C₇×D₄	—	2	32	no	—
163	C₂×C₇×D₄	—	2	8	no	—
164	C₂×C₇×D₄	—	2	8	no	—
165	C₂×C₇×D₄	—	2	4	no	—
166	C₂×C₇×D₄	—	2	8	no	—
167	C₂×C₇×D₄	—	2	16	no	—
168	C₂×C₇×D₄	—	2	4	no	—
169	C₂×C₇×D₄	—	2	4	no	—
170	C₂×C₇×D₄	—	2	2	no	—
171	C₂×C₇×D₄	—	2	4	no	—
172	C₂×C₇×D₄	—	4	8	no	—
173	C₂×C₇×D₄	—	4	8	no	—
174	C₂²×C₄×C₇	—	2	4	no	—
175	C₂²×C₄×C₇	—	2	4	no	—
176	C₂²×C₄×C₇	—	2	4	no	—
177	C₂²×C₄×C₇	—	2	4	no	—
178	C₂²×C₄×C₇	—	2	8	no	—
179	C₂²×C₄×C₇	—	2	8	no	—
180	C₂²×C₄×C₇	—	2	8	no	—
181	C₂²×C₄×C₇	—	2	8	no	—
182	C₂²×C₄×C₇	—	4	4	no	—
183	C₂²×C₄×C₇	—	4	4	no	—
184	C₂²×C₄×C₇	—	4	4	no	—
185	C₂²×C₄×C₇	—	4	2	no	—
186	C₂²×C₄×C₇	—	4	4	no	—
187	C₂²×C₄×C₇	—	4	32	no	—
188	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
192	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
202	C₇×C₄⋊C₄	—	2	4	no	—
203	C₇×C₄⋊C₄	—	2	4	no	—
204	C₇×C₄⋊C₄	—	2	4	no	—
205	C₇×C₄⋊C₄	—	2	4	no	—
206	C₇×C₄⋊C₄	—	2	2	no	—
207	C₇×C₄⋊C₄	—	2	4	no	—
208	C₇×C₄⋊C₄	—	2	2	no	—
209	C₇×C₄⋊C₄	—	2	4	no	—
210	C₇×C₄⋊C₄	—	2	8	no	—
211	C₇×C₄⋊C₄	—	4	8	no	—
212	C₇×C₂²⋊C₄	—	2	4	no	—
213	C₇×C₂²⋊C₄	—	2	16	no	—
214	C₇×C₂²⋊C₄	—	2	8	no	—
215	C₇×C₂²⋊C₄	—	2	8	no	—
216	C₇×C₂²⋊C₄	—	2	8	no	—
217	C₇×C₂²⋊C₄	—	2	4	no	—
218	C₇×C₂²⋊C₄	—	2	4	no	—
219	C₇×C₂²⋊C₄	—	2	4	no	—
220	C₇×C₂²⋊C₄	—	2	4	no	—
221	C₇×C₂²⋊C₄	—	4	8	no	—
222	C₇×C₂²⋊C₄	—	4	8	no	—
223	C₇×C₂²⋊C₄	—	4	8	no	—
224	C₄²×C₇	—	2	4	no	—
225	C₄²×C₇	—	4	4	no	—
226	C₄²×C₇	C₂×D₄	1	4	yes	—
227	C₄²×C₇	C₂×D₄	1	4	yes	—
228	C₄²×C₇	C₂×D₄	1	4	yes	—
229	C₄²×C₇	C₂×D₄	1	4	yes	—
230	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
231	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
232	#529	—	2	8	no	—
233	C₂×#126	C₂²×C₇	1	2	yes	complemented
234	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
235	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
236	C₂×#123	C₂²×C₇	1	2	yes	—
237	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
238	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
239	C₂×#121	C₂²×C₇	1	1	yes	characteristic
240	C₂×#121	C₂²×C₇	1	4	yes	complemented
241	C₂×#120	C₂²×C₇	1	4	yes	—
242	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
243	C₂×C₄×D₄	—	2	8	no	—
244	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
246	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
247	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
249	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
250	C₂×#117	C₂²×C₇	1	2	yes	complemented
251	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
253	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
254	#400	C₂²×C₇	1	4	yes	complemented
255	#399	C₂²×C₇	1	4	yes	complemented
256	#398	C₂²×C₇	1	4	yes	complemented
257	#397	C₂²×C₇	1	4	yes	complemented
258	#394	C₂²×C₇	1	4	yes	—
259	#394	C₂²×C₇	1	4	yes	—
260	#392	C₂²×C₇	1	4	yes	—
261	#392	C₂²×C₇	1	4	yes	—
262	#390	C₂²×C₇	1	8	yes	complemented
263	#388	C₂²×C₇	1	8	yes	complemented
264	#388	C₂²×C₇	1	8	yes	complemented
265	#386	C₂²×C₇	1	4	yes	—
266	#386	C₂²×C₇	1	8	yes	complemented
267	#386	C₂²×C₇	1	8	yes	complemented
268	#385	C₂²×C₇	1	4	yes	—
269	#385	C₂²×C₇	1	8	yes	complemented
270	#383	C₂²×C₇	1	2	yes	complemented
271	#382	C₂²×C₇	1	2	yes	complemented
272	#381	C₂²×C₇	1	2	yes	—
273	#380	C₂²×C₇	1	2	yes	—
274	#380	C₂²×C₇	1	4	yes	complemented
275	#380	C₂²×C₇	1	4	yes	complemented
276	#379	C₂²×C₇	1	4	yes	—
277	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
278	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
279	#376	C₂²×C₇	1	2	yes	complemented
280	C₂³×C₇	—	2	2	no	—
281	C₂³×C₇	—	2	2	no	—
282	C₂³×C₇	—	2	16	no	—
283	C₂³×C₇	—	2	4	no	—
284	C₂³×C₇	—	2	4	no	—
285	C₂³×C₇	—	2	4	no	—
286	C₂³×C₇	—	2	4	no	—
287	C₂³×C₇	—	2	4	no	—
288	C₂³×C₇	—	2	4	no	—
289	C₂³×C₇	—	2	2	no	—
290	C₂³×C₇	—	2	4	no	—
291	C₂³×C₇	—	2	4	no	—
292	C₂³×C₇	—	2	4	no	—
293	C₂³×C₇	—	4	16	no	—
294	C₂³×C₇	—	4	8	no	—
295	C₂³×C₇	—	4	8	no	—
296	C₂³×C₇	—	4	16	no	—
297	C₂³×C₇	C₂²×D₄	1	2	yes	—
298	C₂³×C₇	C₂×#41	1	8	yes	—
299	C₂³×C₇	C₂×#41	1	4	yes	—
300	C₂³×C₇	C₂⁵	1	1	yes	characteristic
301	C₇×Q₈	—	4	4	no	—
302	C₇×D₄	—	2	16	no	—
303	C₇×D₄	—	2	16	no	—
304	C₇×D₄	—	4	8	no	—
305	C₇×D₄	—	4	4	no	—
306	C₇×D₄	—	8	16	no	—
307	C₂×C₄×C₇	—	2	8	no	—
308	C₂×C₄×C₇	—	2	2	no	—
309	C₂×C₄×C₇	—	2	2	no	—
310	C₂×C₄×C₇	—	2	2	no	—
311	C₂×C₄×C₇	—	2	2	no	—
312	C₂×C₄×C₇	—	2	2	no	—
313	C₂×C₄×C₇	—	2	8	no	—
314	C₂×C₄×C₇	—	2	2	no	—
315	C₂×C₄×C₇	—	2	2	no	—
316	C₂×C₄×C₇	—	2	2	no	—
317	C₂×C₄×C₇	—	2	4	no	—
318	C₂×C₄×C₇	—	2	4	no	—
319	C₂×C₄×C₇	—	2	8	no	—
320	C₂×C₄×C₇	—	2	8	no	—
321	C₂×C₄×C₇	—	2	4	no	—
322	C₂×C₄×C₇	—	2	4	no	—
323	C₂×C₄×C₇	—	2	4	no	—
324	C₂×C₄×C₇	—	2	8	no	—
325	C₂×C₄×C₇	—	2	4	no	—
326	C₂×C₄×C₇	—	4	4	no	—
327	C₂×C₄×C₇	—	4	8	no	—
328	C₂×C₄×C₇	—	4	16	no	—
329	C₂×C₄×C₇	—	4	8	no	—
330	C₂×C₄×C₇	—	4	16	no	—
331	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
338	C₂⁵	C₂³×C₇	1	2	yes	—
339	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
340	C₂²×D₄	—	2	8	no	—
341	C₂²×D₄	—	2	4	no	—
342	C₂²×D₄	C₂³×C₇	1	2	yes	—
343	C₂²×D₄	C₂³×C₇	1	2	yes	—
344	C₂²×D₄	C₂³×C₇	1	2	yes	—
345	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
346	C₂²×D₄	C₂³×C₇	1	8	yes	—
347	C₂³×C₄	—	2	8	no	—
348	C₂³×C₄	—	4	8	no	—
349	C₂³×C₄	C₂³×C₇	1	4	yes	—
350	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₇	1	2	yes	—
353	C₂³×C₄	C₂³×C₇	1	2	yes	—
354	C₂³×C₄	C₂³×C₇	1	4	yes	—
355	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
356	#126	—	2	8	no	—
357	#125	—	2	4	no	—
358	#124	—	2	4	no	—
359	#123	—	2	8	no	—
360	C₂²⋊Q₈	—	2	4	no	—
361	C₂²⋊Q₈	—	4	8	no	—
362	#121	—	2	4	no	—
363	#121	—	4	8	no	—
364	#120	—	2	16	no	—
365	C₄×Q₈	—	2	4	no	—
366	C₄×D₄	—	2	8	no	—
367	C₄×D₄	—	2	8	no	—
368	C₄×D₄	—	2	8	no	—
369	C₄×D₄	—	2	8	no	—
370	C₄×D₄	—	2	8	no	—
371	C₄×D₄	—	2	4	no	—
372	#117	—	2	8	no	—
373	C₂×C₄⋊C₄	—	2	4	no	—
374	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
384	C₂×C₂²⋊C₄	—	2	8	no	—
385	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
397	C₂×C₄²	C₇×D₄	1	8	yes	complemented
398	C₂×C₄²	C₂³×C₇	1	2	yes	—
399	C₂×C₄²	C₂³×C₇	1	4	yes	—
400	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
404	#95	C₂³×C₇	1	4	yes	—
405	#95	C₂³×C₇	1	4	yes	—
406	#95	C₂³×C₇	1	4	yes	—
407	#95	C₂³×C₇	1	4	yes	—
408	#95	C₂³×C₇	1	8	yes	—
409	#95	C₂³×C₇	1	8	yes	—
410	C₂²×C₇	—	2	2	no	—
411	C₂²×C₇	—	2	2	no	—
412	C₂²×C₇	—	2	8	no	—
413	C₂²×C₇	—	2	8	no	—
414	C₂²×C₇	—	2	8	no	—
415	C₂²×C₇	—	2	8	no	—
416	C₂²×C₇	—	4	32	no	—
417	C₂²×C₇	—	4	4	no	—
418	C₂²×C₇	—	4	4	no	—
419	C₂²×C₇	—	4	4	no	—
420	C₂²×C₇	—	4	4	no	—
421	C₂²×C₇	—	4	2	no	—
422	C₂²×C₇	—	4	2	no	—
423	C₂²×C₇	—	4	2	no	—
424	C₂²×C₇	—	4	8	no	—
425	C₂²×C₇	#525	1	4	yes	—
426	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
427	C₂²×C₇	C₂²×#41	1	2	yes	—
428	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
429	C₂²×C₇	#585	1	2	yes	—
430	C₄×C₇	—	2	2	no	—
431	C₄×C₇	—	2	2	no	—
432	C₄×C₇	—	2	2	no	—
433	C₄×C₇	—	2	2	no	—
434	C₄×C₇	—	2	2	no	—
435	C₄×C₇	—	4	2	no	—
436	C₄×C₇	—	4	4	no	—
437	C₄×C₇	—	4	2	no	—
438	C₄×C₇	—	4	2	no	—
439	C₄×C₇	—	4	8	no	—
440	C₄×C₇	#535	1	4	yes	—
441	C₂⁴	—	2	4	no	—
442	C₂⁴	—	2	4	no	—
443	C₂⁴	—	4	4	no	—
444	C₂⁴	—	4	4	no	—
445	C₂⁴	C₇×#41	1	8	yes	—
446	C₂⁴	C₂⁴×C₇	1	2	yes	—
447	C₂⁴	C₂⁴×C₇	1	4	yes	—
448	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	4	no	—
451	C₂×D₄	—	2	32	no	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	8	no	—
456	C₂×D₄	—	2	16	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	4	8	no	—
462	C₂×D₄	—	4	8	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	8	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	8	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	4	no	—
473	C₂²×C₄	—	4	4	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	—	4	32	no	—
477	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
478	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
479	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
481	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
482	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
483	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
484	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	4	8	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	16	no	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	—	2	8	no	—
505	C₂²⋊C₄	—	2	8	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	4	8	no	—
511	C₂²⋊C₄	—	4	8	no	—
512	C₂²⋊C₄	—	4	8	no	—
513	C₄²	—	2	4	no	—
514	C₄²	—	4	4	no	—
515	C₄²	C₂×C₇×D₄	1	4	yes	—
516	C₄²	C₂×C₇×D₄	1	4	yes	—
517	C₄²	C₂×C₇×D₄	1	4	yes	—
518	C₄²	C₂×C₇×D₄	1	4	yes	—
519	C₂×C₇	—	2	4	no	—
520	C₂×C₇	—	4	8	no	—
521	C₂×C₇	—	8	2	no	—
522	C₂×C₇	C₂×#525	1	1	yes	characteristic
523	C₂×C₇	C₂×#535	1	1	yes	characteristic
524	C₂×C₇	#3449	1	1	yes	characteristic
525	C₂×C₇	#3505	1	4	yes	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	16	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	4	16	no	—
540	C₂³	—	4	8	no	—
541	C₂³	—	4	8	no	—
542	C₂³	—	4	16	no	—
543	C₂³	C₂²×C₇×D₄	1	2	yes	—
544	C₂³	C₂×C₇×#41	1	8	yes	—
545	C₂³	C₂×C₇×#41	1	4	yes	—
546	C₂³	C₂⁵×C₇	1	1	yes	characteristic
547	Q₈	—	4	4	no	—
548	D₄	—	2	16	no	—
549	D₄	—	2	16	no	—
550	D₄	—	4	8	no	—
551	D₄	—	4	4	no	—
552	D₄	—	8	16	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	8	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	8	no	—
574	C₂×C₄	—	4	16	no	—
575	C₂×C₄	—	4	8	no	—
576	C₂×C₄	—	4	16	no	—
577	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
578	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
579	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
580	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
581	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
582	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
583	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
584	C₇	#35102	1	1	yes	characteristic, direct product factor, Sylow
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	8	no	—
588	C₂²	—	2	8	no	—
589	C₂²	—	2	8	no	—
590	C₂²	—	2	8	no	—
591	C₂²	—	4	32	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	8	no	—
600	C₂²	C₇×#525	1	4	yes	—
601	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
602	C₂²	C₂²×C₇×#41	1	2	yes	—
603	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
604	C₂²	C₇×#585	1	2	yes	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	4	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	8	no	—
615	C₄	C₇×#535	1	4	yes	—
616	C₂	—	2	4	no	—
617	C₂	—	4	8	no	—
618	C₂	—	8	2	no	—
619	C₂	C₂×C₇×#525	1	1	yes	characteristic
620	C₂	C₂×C₇×#535	1	1	yes	characteristic
621	C₂	C₇×#3449	1	1	yes	characteristic
622	C₂	C₇×#3505	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#529	C₂	semidirect
2. C₂²×C₄×C₇×D₄	C₂	semidirect
3. C₇×#2848	C₂	semidirect
4. C₇×#2847	C₂	semidirect
5. C₇×#2623	C₂	semidirect
6. C₇×#2613	C₂	semidirect
7. C₇×#2603	C₂	semidirect
8. C₇×#2598	C₂	semidirect
9. C₇×#2562	C₂	semidirect
10. C₇×#2540	C₂	semidirect
11. C₇×#2536	C₂	semidirect
12. C₇×#2535	C₂	semidirect
13. C₇×#2321	C₂	semidirect
14. C₇×#2283	C₂	semidirect
18. C₂×C₇×#126	C₂²	semidirect
19. C₂×C₇×#125	C₂²	semidirect
20. C₂×C₇×#124	C₂²	semidirect
23. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₇×#121	C₂²	semidirect
27. C₂×C₄×C₇×Q₈	C₂²	semidirect
34. C₂×C₄×C₇×D₄	C₂²	semidirect
35. C₂×C₇×#117	C₂²	semidirect
39. C₇×#400	C₂²	semidirect
40. C₇×#399	C₂²	semidirect
41. C₇×#398	C₂²	semidirect
42. C₇×#397	C₂²	semidirect
47. C₇×#390	C₂²	semidirect
48. C₇×#388	C₂²	semidirect
49. C₇×#388	C₂²	semidirect
51. C₇×#386	C₂²	semidirect
52. C₇×#386	C₂²	semidirect
54. C₇×#385	C₂²	semidirect
55. C₇×#383	C₂²	semidirect
56. C₇×#382	C₂²	semidirect
59. C₇×#380	C₂²	semidirect
60. C₇×#380	C₂²	semidirect
62. C₄×C₇×C₄⋊C₄	C₂²	semidirect
64. C₇×#376	C₂²	semidirect
65. #35102	C₇	direct (N × H)
125. C₂×C₄²×C₇	D₄	semidirect
138. C₂×#529	C₂×C₇	semidirect
139. C₂²×C₄×D₄	C₂×C₇	semidirect
140. #2848	C₂×C₇	semidirect
141. #2847	C₂×C₇	semidirect
142. #2623	C₂×C₇	semidirect
143. #2613	C₂×C₇	semidirect
144. #2603	C₂×C₇	semidirect
145. #2598	C₂×C₇	semidirect
146. #2562	C₂×C₇	semidirect
147. #2540	C₂×C₇	semidirect
148. #2536	C₂×C₇	semidirect
149. #2535	C₂×C₇	semidirect
150. #2321	C₂×C₇	semidirect
151. #2283	C₂×C₇	semidirect
233. C₂×#126	C₂²×C₇	semidirect
234. C₂×#125	C₂²×C₇	semidirect
235. C₂×#124	C₂²×C₇	semidirect
238. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
240. C₂×#121	C₂²×C₇	semidirect
242. C₂×C₄×Q₈	C₂²×C₇	semidirect
249. C₂×C₄×D₄	C₂²×C₇	semidirect
250. C₂×#117	C₂²×C₇	semidirect
254. #400	C₂²×C₇	semidirect
255. #399	C₂²×C₇	semidirect
256. #398	C₂²×C₇	semidirect
257. #397	C₂²×C₇	semidirect
262. #390	C₂²×C₇	semidirect
263. #388	C₂²×C₇	semidirect
264. #388	C₂²×C₇	semidirect
266. #386	C₂²×C₇	semidirect
267. #386	C₂²×C₇	semidirect
269. #385	C₂²×C₇	semidirect
270. #383	C₂²×C₇	semidirect
271. #382	C₂²×C₇	semidirect
274. #380	C₂²×C₇	semidirect
275. #380	C₂²×C₇	semidirect
277. C₄×C₄⋊C₄	C₂²×C₇	semidirect
279. #376	C₂²×C₇	semidirect
397. C₂×C₄²	C₇×D₄	semidirect
584. C₇	#35102	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×#529	2
C₂²×C₄×C₇×D₄	2
C₇×#2848	2
C₇×#2847	2
C₇×#2623	2
C₇×#2613	2
C₇×#2603	2
C₇×#2598	2
C₇×#2562	2
C₇×#2540	2
C₇×#2536	2
C₇×#2535	2
C₇×#2321	2
C₇×#2283	2
#35102	7

Subgroups — C7×#35102 #13212318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#35102 #13212318