Subgroups — C₇×#36591 #13213807

Order 1792.

1838 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2861	C₂	1	2	yes	maximal, complemented
2	C₇×#2858	C₂	1	1	yes	maximal, characteristic
3	C₇×#2595	C₂	1	4	yes	maximal, complemented
4	C₇×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2548	C₂	1	1	yes	maximal, characteristic
6	C₇×#2516	C₂	1	4	yes	maximal, complemented
7	C₇×#2513	C₂	1	2	yes	maximal, complemented
8	C₇×#2448	C₂	1	2	yes	maximal, complemented
9	C₇×#2448	C₂	1	2	yes	maximal, complemented
10	C₇×#2447	C₂	1	2	yes	maximal, complemented
11	C₇×#2367	C₂	1	2	yes	maximal, complemented
12	C₇×#2366	C₂	1	1	yes	maximal, characteristic
13	C₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2357	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×#124	C₂	1	2	yes	maximal, complemented
17	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×#127	C₂²	1	1	yes	characteristic
20	C₂×C₇×#125	C₂²	1	1	yes	characteristic
21	C₂×C₇×#124	C₂²	1	2	yes	—
22	C₂×C₇×#124	C₂²	1	2	yes	—
23	C₂×C₇×#124	C₂²	1	2	yes	—
24	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
28	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
29	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
30	C₇×#400	C₂²	1	4	yes	—
31	C₇×#399	C₂²	1	4	yes	—
32	C₇×#397	C₂²	1	4	yes	—
33	C₇×#397	C₂²	1	4	yes	—
34	C₇×#397	C₂²	1	4	yes	—
35	C₇×#394	C₂²	1	4	yes	—
36	C₇×#391	C₂²	1	2	yes	—
37	C₇×#391	C₂²	1	2	yes	—
38	C₇×#391	C₂²	1	2	yes	—
39	C₇×#391	C₂²	1	2	yes	—
40	C₇×#390	C₂²	1	2	yes	—
41	C₇×#390	C₂²	1	2	yes	—
42	C₇×#390	C₂²	1	2	yes	—
43	C₇×#390	C₂²	1	2	yes	—
44	C₇×#390	C₂²	1	2	yes	—
45	C₇×#390	C₂²	1	2	yes	—
46	C₇×#390	C₂²	1	2	yes	—
47	C₇×#390	C₂²	1	2	yes	—
48	C₇×#390	C₂²	1	2	yes	—
49	C₇×#389	C₂²	1	1	yes	characteristic
50	C₇×#389	C₂²	1	1	yes	characteristic
51	C₇×#389	C₂²	1	2	yes	—
52	C₇×#388	C₂²	1	4	yes	—
53	C₇×#388	C₂²	1	4	yes	—
54	C₇×#388	C₂²	1	4	yes	—
55	C₇×#388	C₂²	1	4	yes	—
56	C₇×#388	C₂²	1	4	yes	—
57	C₇×#388	C₂²	1	4	yes	—
58	C₇×#388	C₂²	1	4	yes	—
59	C₇×#388	C₂²	1	4	yes	—
60	C₇×#387	C₂²	1	2	yes	—
61	C₇×#387	C₂²	1	4	yes	—
62	C₇×#387	C₂²	1	2	yes	—
63	C₇×#386	C₂²	1	4	yes	—
64	C₇×#385	C₂²	1	4	yes	—
65	C₇×#382	C₂²	1	2	yes	—
66	C₇×#382	C₂²	1	1	yes	characteristic
67	C₇×#381	C₂²	1	4	yes	—
68	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
70	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
73	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
79	C₄×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₄×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
81	C₄³×C₇	C₂²	1	2	yes	—
82	C₄³×C₇	C₂²	1	1	yes	characteristic
83	#36591	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂²×C₇×Q₈	C₂³	1	2	yes	—
85	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×D₄	C₂³	1	2	yes	—
87	C₂²×C₇×D₄	C₂³	1	2	yes	—
88	C₂²×C₇×D₄	C₂³	1	2	yes	—
89	C₂³×C₄×C₇	C₂³	1	4	yes	—
90	C₇×C₄⋊Q₈	—	2	4	no	—
91	C₇×#127	—	2	4	no	—
92	C₇×#125	—	2	4	no	—
93	C₇×#124	—	2	8	no	—
94	C₇×#124	—	2	8	no	—
95	C₇×#124	—	4	4	no	—
96	C₄×C₇×Q₈	—	2	4	no	—
97	C₄×C₇×Q₈	—	2	4	no	—
98	C₄×C₇×Q₈	—	2	4	no	—
99	C₄×C₇×Q₈	—	4	4	no	—
100	C₄×C₇×D₄	—	2	8	no	—
101	C₄×C₇×D₄	—	4	4	no	—
102	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₄²×C₇	C₂³	1	2	yes	—
131	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₇	C₂³	1	2	yes	—
134	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₇	C₂³	1	2	yes	—
136	C₂×C₄²×C₇	C₂³	1	2	yes	—
137	C₂×C₄²×C₇	C₂³	1	2	yes	—
138	C₂×C₄²×C₇	C₂³	1	2	yes	—
139	C₂×C₄²×C₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₇	C₂³	1	2	yes	—
143	C₂×C₄²×C₇	C₂³	1	4	yes	—
144	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
146	C₇×#95	C₂³	1	2	yes	—
147	C₇×#95	C₂³	1	2	yes	—
148	C₇×#95	C₂³	1	4	yes	—
149	C₇×#95	C₂³	1	4	yes	—
150	C₇×#95	C₂³	1	2	yes	—
151	C₇×#95	C₂³	1	2	yes	—
152	C₇×#95	C₂³	1	2	yes	—
153	C₇×#95	C₂³	1	2	yes	—
154	C₇×#95	C₂³	1	4	yes	—
155	C₇×#95	C₂³	1	2	yes	—
156	C₇×#95	C₂³	1	2	yes	—
157	C₇×#95	C₂³	1	2	yes	—
158	C₇×#95	C₂³	1	4	yes	—
159	C₇×#95	C₂³	1	4	yes	—
160	C₇×#95	C₂³	1	4	yes	—
161	#2861	C₂×C₇	1	2	yes	complemented
162	#2858	C₂×C₇	1	1	yes	characteristic
163	#2595	C₂×C₇	1	4	yes	complemented
164	#2568	C₂×C₇	1	1	yes	characteristic, complemented
165	#2548	C₂×C₇	1	1	yes	characteristic
166	#2516	C₂×C₇	1	4	yes	complemented
167	#2513	C₂×C₇	1	2	yes	complemented
168	#2448	C₂×C₇	1	2	yes	complemented
169	#2448	C₂×C₇	1	2	yes	complemented
170	#2447	C₂×C₇	1	2	yes	complemented
171	#2367	C₂×C₇	1	2	yes	complemented
172	#2366	C₂×C₇	1	1	yes	characteristic
173	#2365	C₂×C₇	1	1	yes	characteristic, complemented
174	#2357	C₂×C₇	1	2	yes	complemented
175	C₄×#125	C₂×C₇	1	1	yes	characteristic, complemented
176	C₄×#124	C₂×C₇	1	2	yes	complemented
177	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
178	C₂⁴×C₇	C₂⁴	1	4	yes	—
179	C₂×C₇×Q₈	—	2	2	no	—
180	C₂×C₇×Q₈	—	2	2	no	—
181	C₂×C₇×Q₈	—	2	4	no	—
182	C₂×C₇×Q₈	—	2	4	no	—
183	C₂×C₇×Q₈	—	2	4	no	—
184	C₂×C₇×Q₈	#41	1	4	yes	—
185	C₂×C₇×D₄	—	2	4	no	—
186	C₂×C₇×D₄	—	2	4	no	—
187	C₂×C₇×D₄	—	2	4	no	—
188	C₂×C₇×D₄	—	2	4	no	—
189	C₂×C₇×D₄	—	2	4	no	—
190	C₂×C₇×D₄	—	2	4	no	—
191	C₂×C₇×D₄	—	2	4	no	—
192	C₂×C₇×D₄	—	4	2	no	—
193	C₂×C₇×D₄	—	4	2	no	—
194	C₂²×C₄×C₇	—	2	8	no	—
195	C₂²×C₄×C₇	—	4	4	no	—
196	C₂²×C₄×C₇	—	4	4	no	—
197	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
213	C₇×C₄⋊C₄	—	2	4	no	—
214	C₇×C₄⋊C₄	—	2	4	no	—
215	C₇×C₄⋊C₄	—	2	4	no	—
216	C₇×C₄⋊C₄	—	2	2	no	—
217	C₇×C₄⋊C₄	—	2	2	no	—
218	C₇×C₄⋊C₄	—	2	4	no	—
219	C₇×C₄⋊C₄	—	2	4	no	—
220	C₇×C₄⋊C₄	—	2	2	no	—
221	C₇×C₄⋊C₄	—	2	2	no	—
222	C₇×C₄⋊C₄	—	2	4	no	—
223	C₇×C₄⋊C₄	—	2	4	no	—
224	C₇×C₄⋊C₄	—	2	2	no	—
225	C₇×C₄⋊C₄	—	2	2	no	—
226	C₇×C₄⋊C₄	—	4	2	no	—
227	C₇×C₄⋊C₄	—	4	2	no	—
228	C₇×C₄⋊C₄	—	4	4	no	—
229	C₇×C₄⋊C₄	#41	1	4	yes	—
230	C₇×C₂²⋊C₄	—	2	8	no	—
231	C₇×C₂²⋊C₄	—	2	8	no	—
232	C₇×C₂²⋊C₄	—	2	8	no	—
233	C₇×C₂²⋊C₄	—	2	8	no	—
234	C₇×C₂²⋊C₄	—	2	8	no	—
235	C₇×C₂²⋊C₄	—	4	4	no	—
236	C₇×C₂²⋊C₄	—	4	4	no	—
237	C₇×C₂²⋊C₄	—	4	4	no	—
238	C₇×C₂²⋊C₄	—	4	4	no	—
239	C₇×C₂²⋊C₄	—	4	4	no	—
240	C₇×C₂²⋊C₄	—	4	4	no	—
241	C₄²×C₇	—	2	4	no	—
242	C₄²×C₇	—	2	4	no	—
243	C₄²×C₇	—	2	4	no	—
244	C₄²×C₇	—	2	2	no	—
245	C₄²×C₇	—	2	2	no	—
246	C₄²×C₇	—	2	4	no	—
247	C₄²×C₇	—	2	4	no	—
248	C₄²×C₇	—	2	4	no	—
249	C₄²×C₇	—	2	2	no	—
250	C₄²×C₇	—	4	2	no	—
251	C₄²×C₇	—	4	1	no	—
252	C₄²×C₇	—	4	1	no	—
253	C₄²×C₇	—	4	2	no	—
254	C₄²×C₇	—	4	4	no	—
255	C₄²×C₇	#41	1	4	yes	—
256	C₄²×C₇	#41	1	4	yes	—
257	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
258	C₂×#127	C₂²×C₇	1	1	yes	characteristic
259	C₂×#125	C₂²×C₇	1	1	yes	characteristic
260	C₂×#124	C₂²×C₇	1	2	yes	—
261	C₂×#124	C₂²×C₇	1	2	yes	—
262	C₂×#124	C₂²×C₇	1	2	yes	—
263	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
264	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
265	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
267	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
268	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
269	#400	C₂²×C₇	1	4	yes	—
270	#399	C₂²×C₇	1	4	yes	—
271	#397	C₂²×C₇	1	4	yes	—
272	#397	C₂²×C₇	1	4	yes	—
273	#397	C₂²×C₇	1	4	yes	—
274	#394	C₂²×C₇	1	4	yes	—
275	#391	C₂²×C₇	1	2	yes	—
276	#391	C₂²×C₇	1	2	yes	—
277	#391	C₂²×C₇	1	2	yes	—
278	#391	C₂²×C₇	1	2	yes	—
279	#390	C₂²×C₇	1	2	yes	—
280	#390	C₂²×C₇	1	2	yes	—
281	#390	C₂²×C₇	1	2	yes	—
282	#390	C₂²×C₇	1	2	yes	—
283	#390	C₂²×C₇	1	2	yes	—
284	#390	C₂²×C₇	1	2	yes	—
285	#390	C₂²×C₇	1	2	yes	—
286	#390	C₂²×C₇	1	2	yes	—
287	#390	C₂²×C₇	1	2	yes	—
288	#389	C₂²×C₇	1	1	yes	characteristic
289	#389	C₂²×C₇	1	1	yes	characteristic
290	#389	C₂²×C₇	1	2	yes	—
291	#388	C₂²×C₇	1	4	yes	—
292	#388	C₂²×C₇	1	4	yes	—
293	#388	C₂²×C₇	1	4	yes	—
294	#388	C₂²×C₇	1	4	yes	—
295	#388	C₂²×C₇	1	4	yes	—
296	#388	C₂²×C₇	1	4	yes	—
297	#388	C₂²×C₇	1	4	yes	—
298	#388	C₂²×C₇	1	4	yes	—
299	#387	C₂²×C₇	1	2	yes	—
300	#387	C₂²×C₇	1	2	yes	—
301	#387	C₂²×C₇	1	4	yes	—
302	#386	C₂²×C₇	1	4	yes	—
303	#385	C₂²×C₇	1	4	yes	—
304	#382	C₂²×C₇	1	1	yes	characteristic
305	#382	C₂²×C₇	1	2	yes	—
306	#381	C₂²×C₇	1	4	yes	—
307	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
308	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
309	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
310	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
311	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
312	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
313	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
314	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
315	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
316	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
317	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
318	C₄×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
319	C₄×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
320	C₄³	C₂²×C₇	1	1	yes	characteristic
321	C₄³	C₂²×C₇	1	2	yes	—
322	C₂³×C₇	—	2	4	no	—
323	C₂³×C₇	—	2	4	no	—
324	C₂³×C₇	—	2	4	no	—
325	C₂³×C₇	—	2	4	no	—
326	C₂³×C₇	—	2	4	no	—
327	C₂³×C₇	—	2	4	no	—
328	C₂³×C₇	—	2	4	no	—
329	C₂³×C₇	C₂⁵	1	1	yes	characteristic
330	C₇×Q₈	—	2	8	no	—
331	C₇×Q₈	—	4	8	no	—
332	C₇×D₄	—	4	8	no	—
333	C₇×D₄	—	4	8	no	—
334	C₇×D₄	—	8	4	no	—
335	C₂×C₄×C₇	—	2	1	no	—
336	C₂×C₄×C₇	—	2	1	no	—
337	C₂×C₄×C₇	—	2	2	no	—
338	C₂×C₄×C₇	—	2	2	no	—
339	C₂×C₄×C₇	—	2	2	no	—
340	C₂×C₄×C₇	—	2	1	no	—
341	C₂×C₄×C₇	—	2	1	no	—
342	C₂×C₄×C₇	—	2	2	no	—
343	C₂×C₄×C₇	—	2	1	no	—
344	C₂×C₄×C₇	—	2	1	no	—
345	C₂×C₄×C₇	—	2	2	no	—
346	C₂×C₄×C₇	—	2	2	no	—
347	C₂×C₄×C₇	—	2	2	no	—
348	C₂×C₄×C₇	—	2	2	no	—
349	C₂×C₄×C₇	—	2	1	no	—
350	C₂×C₄×C₇	—	2	1	no	—
351	C₂×C₄×C₇	—	2	2	no	—
352	C₂×C₄×C₇	—	2	2	no	—
353	C₂×C₄×C₇	—	2	4	no	—
354	C₂×C₄×C₇	—	2	2	no	—
355	C₂×C₄×C₇	—	2	2	no	—
356	C₂×C₄×C₇	—	2	4	no	—
357	C₂×C₄×C₇	—	2	1	no	—
358	C₂×C₄×C₇	—	2	1	no	—
359	C₂×C₄×C₇	—	2	2	no	—
360	C₂×C₄×C₇	—	2	2	no	—
361	C₂×C₄×C₇	—	2	4	no	—
362	C₂×C₄×C₇	—	2	2	no	—
363	C₂×C₄×C₇	—	2	2	no	—
364	C₂×C₄×C₇	—	2	2	no	—
365	C₂×C₄×C₇	—	2	2	no	—
366	C₂×C₄×C₇	—	2	1	no	—
367	C₂×C₄×C₇	—	2	1	no	—
368	C₂×C₄×C₇	—	2	2	no	—
369	C₂×C₄×C₇	—	2	2	no	—
370	C₂×C₄×C₇	—	2	2	no	—
371	C₂×C₄×C₇	—	2	2	no	—
372	C₂×C₄×C₇	—	8	8	no	—
373	C₂×C₄×C₇	C₂×#41	1	4	yes	—
374	C₂×C₄×C₇	C₂×#41	1	4	yes	—
375	C₂×C₄×C₇	C₂×#41	1	2	yes	—
376	C₂×C₄×C₇	C₂×#41	1	2	yes	—
377	C₂×C₄×C₇	C₂×#41	1	2	yes	—
378	C₂×C₄×C₇	C₂×#41	1	2	yes	—
379	C₂×C₄×C₇	C₂×#41	1	2	yes	—
380	C₂×C₄×C₇	C₂×#41	1	2	yes	—
381	C₂×C₄×C₇	C₂×#41	1	2	yes	—
382	C₂×C₄×C₇	C₂×#41	1	2	yes	—
383	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
384	C₂²×Q₈	C₂³×C₇	1	2	yes	—
385	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
386	C₂²×D₄	C₂³×C₇	1	2	yes	—
387	C₂²×D₄	C₂³×C₇	1	2	yes	—
388	C₂²×D₄	C₂³×C₇	1	2	yes	—
389	C₂³×C₄	C₂³×C₇	1	4	yes	—
390	C₄⋊Q₈	—	2	4	no	—
391	#127	—	2	4	no	—
392	#125	—	2	4	no	—
393	#124	—	2	8	no	—
394	#124	—	2	8	no	—
395	#124	—	4	4	no	—
396	C₄×Q₈	—	2	4	no	—
397	C₄×Q₈	—	2	4	no	—
398	C₄×Q₈	—	2	4	no	—
399	C₄×Q₈	—	4	4	no	—
400	C₄×D₄	—	2	8	no	—
401	C₄×D₄	—	4	4	no	—
402	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
430	C₂×C₄²	C₂³×C₇	1	2	yes	—
431	C₂×C₄²	C₂³×C₇	1	2	yes	—
432	C₂×C₄²	C₂³×C₇	1	2	yes	—
433	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₇	1	2	yes	—
436	C₂×C₄²	C₂³×C₇	1	2	yes	—
437	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₇	1	2	yes	—
439	C₂×C₄²	C₂³×C₇	1	4	yes	—
440	C₂×C₄²	C₂³×C₇	1	2	yes	—
441	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₇	1	2	yes	—
444	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
446	#95	C₂³×C₇	1	2	yes	—
447	#95	C₂³×C₇	1	2	yes	—
448	#95	C₂³×C₇	1	4	yes	—
449	#95	C₂³×C₇	1	4	yes	—
450	#95	C₂³×C₇	1	2	yes	—
451	#95	C₂³×C₇	1	2	yes	—
452	#95	C₂³×C₇	1	2	yes	—
453	#95	C₂³×C₇	1	2	yes	—
454	#95	C₂³×C₇	1	4	yes	—
455	#95	C₂³×C₇	1	2	yes	—
456	#95	C₂³×C₇	1	2	yes	—
457	#95	C₂³×C₇	1	2	yes	—
458	#95	C₂³×C₇	1	4	yes	—
459	#95	C₂³×C₇	1	4	yes	—
460	#95	C₂³×C₇	1	4	yes	—
461	C₂²×C₇	—	4	4	no	—
462	C₂²×C₇	—	4	4	no	—
463	C₂²×C₇	—	4	4	no	—
464	C₂²×C₇	—	4	4	no	—
465	C₂²×C₇	—	4	4	no	—
466	C₂²×C₇	—	4	4	no	—
467	C₂²×C₇	—	4	4	no	—
468	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
469	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
470	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
471	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
472	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×C₇	#585	1	1	yes	characteristic
474	C₂²×C₇	#585	1	1	yes	characteristic
475	C₄×C₇	—	2	4	no	—
476	C₄×C₇	—	2	2	no	—
477	C₄×C₇	—	2	2	no	—
478	C₄×C₇	—	2	2	no	—
479	C₄×C₇	—	2	4	no	—
480	C₄×C₇	—	4	4	no	—
481	C₄×C₇	—	4	2	no	—
482	C₄×C₇	—	4	2	no	—
483	C₄×C₇	—	4	2	no	—
484	C₄×C₇	—	4	1	no	—
485	C₄×C₇	—	4	2	no	—
486	C₄×C₇	—	4	2	no	—
487	C₄×C₇	—	4	1	no	—
488	C₄×C₇	—	4	2	no	—
489	C₄×C₇	#529	1	4	yes	—
490	C₄×C₇	#559	1	4	yes	—
491	C₂⁴	C₂⁴×C₇	1	4	yes	—
492	C₂×Q₈	—	2	2	no	—
493	C₂×Q₈	—	2	2	no	—
494	C₂×Q₈	—	2	4	no	—
495	C₂×Q₈	—	2	4	no	—
496	C₂×Q₈	—	2	4	no	—
497	C₂×Q₈	C₇×#41	1	4	yes	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	2	4	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	4	2	no	—
506	C₂×D₄	—	4	2	no	—
507	C₂²×C₄	—	2	8	no	—
508	C₂²×C₄	—	4	4	no	—
509	C₂²×C₄	—	4	4	no	—
510	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
514	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
515	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	4	4	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	C₇×#41	1	4	yes	—
543	C₂²⋊C₄	—	2	8	no	—
544	C₂²⋊C₄	—	2	8	no	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	—	2	8	no	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	4	4	no	—
549	C₂²⋊C₄	—	4	4	no	—
550	C₂²⋊C₄	—	4	4	no	—
551	C₂²⋊C₄	—	4	4	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	4	4	no	—
554	C₄²	—	2	4	no	—
555	C₄²	—	2	4	no	—
556	C₄²	—	2	4	no	—
557	C₄²	—	2	2	no	—
558	C₄²	—	2	2	no	—
559	C₄²	—	2	4	no	—
560	C₄²	—	2	4	no	—
561	C₄²	—	2	4	no	—
562	C₄²	—	2	2	no	—
563	C₄²	—	4	4	no	—
564	C₄²	—	4	2	no	—
565	C₄²	—	4	1	no	—
566	C₄²	—	4	1	no	—
567	C₄²	—	4	2	no	—
568	C₄²	C₇×#41	1	4	yes	—
569	C₄²	C₇×#41	1	4	yes	—
570	C₂×C₇	—	8	4	no	—
571	C₂×C₇	C₂×#529	1	1	yes	characteristic
572	C₂×C₇	C₂×#559	1	1	yes	characteristic
573	C₂×C₇	#3480	1	1	yes	characteristic
574	C₂×C₇	#3480	1	1	yes	characteristic
575	C₂×C₇	#3510	1	1	yes	characteristic
576	C₂×C₇	#3514	1	1	yes	characteristic
577	C₂×C₇	#3517	1	1	yes	characteristic
578	C₂³	—	2	4	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	4	no	—
582	C₂³	—	2	4	no	—
583	C₂³	—	2	4	no	—
584	C₂³	—	2	4	no	—
585	C₂³	C₂⁵×C₇	1	1	yes	characteristic
586	Q₈	—	2	8	no	—
587	Q₈	—	4	8	no	—
588	D₄	—	4	8	no	—
589	D₄	—	4	8	no	—
590	D₄	—	8	4	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	8	8	no	—
629	C₂×C₄	C₂×C₇×#41	1	4	yes	—
630	C₂×C₄	C₂×C₇×#41	1	4	yes	—
631	C₂×C₄	C₂×C₇×#41	1	2	yes	—
632	C₂×C₄	C₂×C₇×#41	1	2	yes	—
633	C₂×C₄	C₂×C₇×#41	1	2	yes	—
634	C₂×C₄	C₂×C₇×#41	1	2	yes	—
635	C₂×C₄	C₂×C₇×#41	1	2	yes	—
636	C₂×C₄	C₂×C₇×#41	1	2	yes	—
637	C₂×C₄	C₂×C₇×#41	1	2	yes	—
638	C₂×C₄	C₂×C₇×#41	1	2	yes	—
639	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
640	C₇	#36591	1	1	yes	characteristic, direct product factor, Sylow
641	C₂²	—	4	4	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	4	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
649	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
650	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
651	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
652	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
653	C₂²	C₇×#585	1	1	yes	characteristic
654	C₂²	C₇×#585	1	1	yes	characteristic
655	C₄	—	2	4	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	4	4	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	C₇×#529	1	4	yes	—
670	C₄	C₇×#559	1	4	yes	—
671	C₂	—	8	4	no	—
672	C₂	C₂×C₇×#529	1	1	yes	characteristic
673	C₂	C₂×C₇×#559	1	1	yes	characteristic
674	C₂	C₇×#3480	1	1	yes	characteristic
675	C₂	C₇×#3480	1	1	yes	characteristic
676	C₂	C₇×#3510	1	1	yes	characteristic
677	C₂	C₇×#3514	1	1	yes	characteristic
678	C₂	C₇×#3517	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂×C₇×#127	C₂²
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. C₇×#2861	C₂	semidirect
3. C₇×#2595	C₂	semidirect
4. C₇×#2568	C₂	semidirect
6. C₇×#2516	C₂	semidirect
7. C₇×#2513	C₂	semidirect
8. C₇×#2448	C₂	semidirect
9. C₇×#2448	C₂	semidirect
10. C₇×#2447	C₂	semidirect
11. C₇×#2367	C₂	semidirect
13. C₇×#2365	C₂	semidirect
14. C₇×#2357	C₂	semidirect
15. C₄×C₇×#125	C₂	semidirect
16. C₄×C₇×#124	C₂	semidirect
17. C₄²×C₇×Q₈	C₂	semidirect
83. #36591	C₇	direct (N × H)
161. #2861	C₂×C₇	semidirect
163. #2595	C₂×C₇	semidirect
164. #2568	C₂×C₇	semidirect
166. #2516	C₂×C₇	semidirect
167. #2513	C₂×C₇	semidirect
168. #2448	C₂×C₇	semidirect
169. #2448	C₂×C₇	semidirect
170. #2447	C₂×C₇	semidirect
171. #2367	C₂×C₇	semidirect
173. #2365	C₂×C₇	semidirect
174. #2357	C₂×C₇	semidirect
175. C₄×#125	C₂×C₇	semidirect
176. C₄×#124	C₂×C₇	semidirect
177. C₄²×Q₈	C₂×C₇	semidirect
640. C₇	#36591	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×#2861	2
C₇×#2858	2
C₇×#2595	2
C₇×#2568	2
C₇×#2548	2
C₇×#2516	2
C₇×#2513	2
C₇×#2448	2
C₇×#2447	2
C₇×#2367	2
C₇×#2366	2
C₇×#2365	2
C₇×#2357	2
C₄×C₇×#125	2
C₄×C₇×#124	2
C₄²×C₇×Q₈	2
#36591	7

Subgroups — C7×#36591 #13213807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36591 #13213807