Subgroups — C₇×#36609 #13213825

Order 1792.

1938 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2858	C₂	1	2	yes	maximal
3	C₇×#2592	C₂	1	4	yes	maximal, complemented
4	C₇×#2580	C₂	1	2	yes	maximal, complemented
5	C₇×#2513	C₂	1	4	yes	maximal, complemented
6	C₇×#2448	C₂	1	4	yes	maximal, complemented
7	C₇×#2447	C₂	1	4	yes	maximal, complemented
8	C₇×#2367	C₂	1	4	yes	maximal, complemented
9	C₇×#2357	C₂	1	2	yes	maximal, complemented
10	C₄×C₇×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
11	C₄×C₇×#127	C₂	1	1	yes	maximal, characteristic
12	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₇×#127	C₂²	1	1	yes	characteristic
15	C₂×C₇×#124	C₂²	1	4	yes	—
16	C₂×C₇×#124	C₂²	1	4	yes	—
17	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
19	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	—
20	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
21	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
22	C₇×#399	C₂²	1	4	yes	—
23	C₇×#397	C₂²	1	8	yes	—
24	C₇×#397	C₂²	1	8	yes	—
25	C₇×#393	C₂²	1	4	yes	—
26	C₇×#391	C₂²	1	4	yes	—
27	C₇×#391	C₂²	1	4	yes	—
28	C₇×#391	C₂²	1	4	yes	—
29	C₇×#390	C₂²	1	4	yes	—
30	C₇×#390	C₂²	1	4	yes	—
31	C₇×#390	C₂²	1	4	yes	—
32	C₇×#390	C₂²	1	2	yes	—
33	C₇×#390	C₂²	1	4	yes	—
34	C₇×#390	C₂²	1	4	yes	—
35	C₇×#389	C₂²	1	4	yes	—
36	C₇×#389	C₂²	1	4	yes	—
37	C₇×#388	C₂²	1	8	yes	—
38	C₇×#388	C₂²	1	8	yes	—
39	C₇×#388	C₂²	1	8	yes	—
40	C₇×#385	C₂²	1	8	yes	—
41	C₇×#384	C₂²	1	1	yes	characteristic
42	C₇×#382	C₂²	1	2	yes	—
43	C₇×#382	C₂²	1	2	yes	—
44	C₇×#381	C₂²	1	4	yes	—
45	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
46	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
47	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
48	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
49	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
51	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
52	C₄×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
53	C₄³×C₇	C₂²	1	1	yes	characteristic
54	C₄³×C₇	C₂²	1	2	yes	—
55	#36609	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇×Q₈	C₂³	1	4	yes	—
58	C₂²×C₇×D₄	C₂³	1	4	yes	—
59	C₂²×C₇×D₄	C₂³	1	2	yes	—
60	C₂³×C₄×C₇	C₂³	1	4	yes	—
61	C₇×C₄⋊Q₈	—	2	8	no	—
62	C₇×#127	—	2	4	no	—
63	C₇×#124	—	2	16	no	—
64	C₇×#124	—	4	8	no	—
65	C₄×C₇×Q₈	—	2	4	no	—
66	C₄×C₇×Q₈	—	2	8	no	—
67	C₄×C₇×Q₈	—	4	8	no	—
68	C₄×C₇×D₄	—	2	8	no	—
69	C₄×C₇×D₄	—	4	8	no	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
77	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
80	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
82	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₄²×C₇	C₂³	1	2	yes	—
87	C₂×C₄²×C₇	C₂³	1	2	yes	—
88	C₂×C₄²×C₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇	C₂³	1	2	yes	—
91	C₂×C₄²×C₇	C₂³	1	2	yes	—
92	C₂×C₄²×C₇	C₂³	1	2	yes	—
93	C₂×C₄²×C₇	C₂³	1	2	yes	—
94	C₂×C₄²×C₇	C₂³	1	8	yes	—
95	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇	C₂³	1	2	yes	—
97	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
98	C₇×#95	C₂³	1	1	yes	characteristic
99	C₇×#95	C₂³	1	4	yes	—
100	C₇×#95	C₂³	1	1	yes	characteristic
101	C₇×#95	C₂³	1	2	yes	—
102	C₇×#95	C₂³	1	2	yes	—
103	C₇×#95	C₂³	1	8	yes	—
104	C₇×#95	C₂³	1	8	yes	—
105	C₇×#95	C₂³	1	4	yes	—
106	C₇×#95	C₂³	1	8	yes	—
107	#2862	C₂×C₇	1	1	yes	characteristic, complemented
108	#2858	C₂×C₇	1	2	yes	—
109	#2592	C₂×C₇	1	4	yes	complemented
110	#2580	C₂×C₇	1	2	yes	complemented
111	#2513	C₂×C₇	1	4	yes	complemented
112	#2448	C₂×C₇	1	4	yes	complemented
113	#2447	C₂×C₇	1	4	yes	complemented
114	#2367	C₂×C₇	1	4	yes	complemented
115	#2357	C₂×C₇	1	2	yes	complemented
116	C₄×C₄⋊Q₈	C₂×C₇	1	2	yes	complemented
117	C₄×#127	C₂×C₇	1	1	yes	characteristic
118	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
119	C₂⁴×C₇	C₂⁴	1	4	yes	—
120	C₂×C₇×Q₈	—	2	2	no	—
121	C₂×C₇×Q₈	—	2	4	no	—
122	C₂×C₇×Q₈	—	2	8	no	—
123	C₂×C₇×Q₈	—	2	8	no	—
124	C₂×C₇×Q₈	—	2	8	no	—
125	C₂×C₇×D₄	—	2	4	no	—
126	C₂×C₇×D₄	—	2	8	no	—
127	C₂×C₇×D₄	—	2	4	no	—
128	C₂×C₇×D₄	—	2	8	no	—
129	C₂×C₇×D₄	—	2	8	no	—
130	C₂×C₇×D₄	—	2	4	no	—
131	C₂²×C₄×C₇	—	2	8	no	—
132	C₂²×C₄×C₇	—	4	8	no	—
133	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
136	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
144	C₇×C₄⋊C₄	—	2	4	no	—
145	C₇×C₄⋊C₄	—	2	4	no	—
146	C₇×C₄⋊C₄	—	2	4	no	—
147	C₇×C₄⋊C₄	—	2	4	no	—
148	C₇×C₄⋊C₄	—	2	4	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	8	no	—
151	C₇×C₄⋊C₄	—	2	8	no	—
152	C₇×C₄⋊C₄	—	2	8	no	—
153	C₇×C₄⋊C₄	—	4	8	no	—
154	C₇×C₂²⋊C₄	—	2	8	no	—
155	C₇×C₂²⋊C₄	—	2	16	no	—
156	C₇×C₂²⋊C₄	—	2	16	no	—
157	C₇×C₂²⋊C₄	—	4	8	no	—
158	C₇×C₂²⋊C₄	—	4	8	no	—
159	C₇×C₂²⋊C₄	—	4	8	no	—
160	C₄²×C₇	—	2	4	no	—
161	C₄²×C₇	—	2	4	no	—
162	C₄²×C₇	—	2	4	no	—
163	C₄²×C₇	—	2	4	no	—
164	C₄²×C₇	—	2	4	no	—
165	C₄²×C₇	—	2	4	no	—
166	C₄²×C₇	—	2	4	no	—
167	C₄²×C₇	—	2	2	no	—
168	C₄²×C₇	—	4	8	no	—
169	C₄²×C₇	#41	1	4	yes	—
170	C₄²×C₇	#41	1	8	yes	—
171	C₄²×C₇	#41	1	4	yes	—
172	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
173	C₂×#127	C₂²×C₇	1	1	yes	characteristic
174	C₂×#124	C₂²×C₇	1	4	yes	—
175	C₂×#124	C₂²×C₇	1	4	yes	—
176	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
177	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
178	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	—
179	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
180	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
181	#399	C₂²×C₇	1	4	yes	—
182	#397	C₂²×C₇	1	8	yes	—
183	#397	C₂²×C₇	1	8	yes	—
184	#393	C₂²×C₇	1	4	yes	—
185	#391	C₂²×C₇	1	4	yes	—
186	#391	C₂²×C₇	1	4	yes	—
187	#391	C₂²×C₇	1	4	yes	—
188	#390	C₂²×C₇	1	4	yes	—
189	#390	C₂²×C₇	1	2	yes	—
190	#390	C₂²×C₇	1	4	yes	—
191	#390	C₂²×C₇	1	4	yes	—
192	#390	C₂²×C₇	1	4	yes	—
193	#390	C₂²×C₇	1	4	yes	—
194	#389	C₂²×C₇	1	4	yes	—
195	#389	C₂²×C₇	1	4	yes	—
196	#388	C₂²×C₇	1	8	yes	—
197	#388	C₂²×C₇	1	8	yes	—
198	#388	C₂²×C₇	1	8	yes	—
199	#385	C₂²×C₇	1	8	yes	—
200	#384	C₂²×C₇	1	1	yes	characteristic
201	#382	C₂²×C₇	1	2	yes	—
202	#382	C₂²×C₇	1	2	yes	—
203	#381	C₂²×C₇	1	4	yes	—
204	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
205	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
206	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
207	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
208	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
209	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
210	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
211	C₄×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
212	C₄³	C₂²×C₇	1	1	yes	characteristic
213	C₄³	C₂²×C₇	1	2	yes	—
214	C₂³×C₇	—	2	8	no	—
215	C₂³×C₇	—	2	4	no	—
216	C₂³×C₇	—	2	4	no	—
217	C₂³×C₇	—	2	8	no	—
218	C₂³×C₇	—	2	4	no	—
219	C₂³×C₇	C₂⁵	1	1	yes	characteristic
220	C₇×Q₈	—	2	8	no	—
221	C₇×Q₈	—	4	16	no	—
222	C₇×D₄	—	4	8	no	—
223	C₇×D₄	—	4	16	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	2	2	no	—
226	C₂×C₄×C₇	—	2	2	no	—
227	C₂×C₄×C₇	—	2	2	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	8	no	—
234	C₂×C₄×C₇	—	2	4	no	—
235	C₂×C₄×C₇	—	2	8	no	—
236	C₂×C₄×C₇	—	2	2	no	—
237	C₂×C₄×C₇	—	2	2	no	—
238	C₂×C₄×C₇	—	2	2	no	—
239	C₂×C₄×C₇	—	2	2	no	—
240	C₂×C₄×C₇	—	2	8	no	—
241	C₂×C₄×C₇	—	2	8	no	—
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	2	no	—
244	C₂×C₄×C₇	—	8	8	no	—
245	C₂×C₄×C₇	C₂×#41	1	4	yes	—
246	C₂×C₄×C₇	C₂×#41	1	2	yes	—
247	C₂×C₄×C₇	C₂×#41	1	4	yes	—
248	C₂×C₄×C₇	C₂×#41	1	2	yes	—
249	C₂×C₄×C₇	C₂×#41	1	2	yes	—
250	C₂×C₄×C₇	C₂×#41	1	2	yes	—
251	C₂×C₄×C₇	C₂×#41	1	4	yes	—
252	C₂×C₄×C₇	C₂×#41	1	4	yes	—
253	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
254	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
255	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
256	C₂²×Q₈	C₂³×C₇	1	4	yes	—
257	C₂²×D₄	C₂³×C₇	1	4	yes	—
258	C₂²×D₄	C₂³×C₇	1	2	yes	—
259	C₂³×C₄	C₂³×C₇	1	4	yes	—
260	C₄⋊Q₈	—	2	8	no	—
261	#127	—	2	4	no	—
262	#124	—	2	16	no	—
263	#124	—	4	8	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	8	no	—
266	C₄×Q₈	—	4	8	no	—
267	C₄×D₄	—	2	8	no	—
268	C₄×D₄	—	4	8	no	—
269	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
285	C₂×C₄²	C₂³×C₇	1	2	yes	—
286	C₂×C₄²	C₂³×C₇	1	2	yes	—
287	C₂×C₄²	C₂³×C₇	1	2	yes	—
288	C₂×C₄²	C₂³×C₇	1	2	yes	—
289	C₂×C₄²	C₂³×C₇	1	2	yes	—
290	C₂×C₄²	C₂³×C₇	1	2	yes	—
291	C₂×C₄²	C₂³×C₇	1	2	yes	—
292	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₇	1	8	yes	—
294	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₇	1	2	yes	—
296	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
297	#95	C₂³×C₇	1	1	yes	characteristic
298	#95	C₂³×C₇	1	4	yes	—
299	#95	C₂³×C₇	1	1	yes	characteristic
300	#95	C₂³×C₇	1	2	yes	—
301	#95	C₂³×C₇	1	2	yes	—
302	#95	C₂³×C₇	1	8	yes	—
303	#95	C₂³×C₇	1	8	yes	—
304	#95	C₂³×C₇	1	4	yes	—
305	#95	C₂³×C₇	1	8	yes	—
306	C₂²×C₇	—	4	4	no	—
307	C₂²×C₇	—	4	4	no	—
308	C₂²×C₇	—	4	8	no	—
309	C₂²×C₇	—	4	4	no	—
310	C₂²×C₇	—	4	8	no	—
311	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
312	C₂²×C₇	C₂²×#41	1	2	yes	—
313	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
314	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
315	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
316	C₄×C₇	—	2	4	no	—
317	C₄×C₇	—	2	2	no	—
318	C₄×C₇	—	2	2	no	—
319	C₄×C₇	—	2	4	no	—
320	C₄×C₇	—	4	8	no	—
321	C₄×C₇	—	4	2	no	—
322	C₄×C₇	—	4	4	no	—
323	C₄×C₇	—	4	2	no	—
324	C₄×C₇	—	4	2	no	—
325	C₄×C₇	#556	1	4	yes	—
326	C₄×C₇	#559	1	8	yes	—
327	C₂⁴	C₂⁴×C₇	1	4	yes	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	2	8	no	—
331	C₂×Q₈	—	2	8	no	—
332	C₂×Q₈	—	2	8	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	8	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂²×C₄	—	2	8	no	—
340	C₂²×C₄	—	4	8	no	—
341	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
343	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
344	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
345	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
346	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
347	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
348	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
350	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	4	8	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	16	no	—
364	C₂²⋊C₄	—	2	16	no	—
365	C₂²⋊C₄	—	4	8	no	—
366	C₂²⋊C₄	—	4	8	no	—
367	C₂²⋊C₄	—	4	8	no	—
368	C₄²	—	2	4	no	—
369	C₄²	—	2	4	no	—
370	C₄²	—	2	4	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	4	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	4	8	no	—
377	C₄²	C₇×#41	1	4	yes	—
378	C₄²	C₇×#41	1	8	yes	—
379	C₄²	C₇×#41	1	4	yes	—
380	C₂×C₇	—	8	4	no	—
381	C₂×C₇	#3444	1	1	yes	characteristic
382	C₂×C₇	C₂×#556	1	1	yes	characteristic
383	C₂×C₇	C₂×#559	1	2	yes	—
384	C₂×C₇	#3508	1	1	yes	characteristic
385	C₂×C₇	#3511	1	2	yes	—
386	C₂³	—	2	8	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	8	no	—
390	C₂³	—	2	4	no	—
391	C₂³	C₂⁵×C₇	1	1	yes	characteristic
392	Q₈	—	2	8	no	—
393	Q₈	—	4	16	no	—
394	D₄	—	4	8	no	—
395	D₄	—	4	16	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	8	8	no	—
417	C₂×C₄	C₂×C₇×#41	1	4	yes	—
418	C₂×C₄	C₂×C₇×#41	1	2	yes	—
419	C₂×C₄	C₂×C₇×#41	1	4	yes	—
420	C₂×C₄	C₂×C₇×#41	1	2	yes	—
421	C₂×C₄	C₂×C₇×#41	1	2	yes	—
422	C₂×C₄	C₂×C₇×#41	1	2	yes	—
423	C₂×C₄	C₂×C₇×#41	1	4	yes	—
424	C₂×C₄	C₂×C₇×#41	1	4	yes	—
425	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
426	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
427	C₇	#36609	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	8	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	8	no	—
433	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
434	C₂²	C₂²×C₇×#41	1	2	yes	—
435	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
436	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
437	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	4	no	—
442	C₄	—	4	8	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	C₇×#556	1	4	yes	—
448	C₄	C₇×#559	1	8	yes	—
449	C₂	—	8	4	no	—
450	C₂	C₇×#3444	1	1	yes	characteristic
451	C₂	C₂×C₇×#556	1	1	yes	characteristic
452	C₂	C₂×C₇×#559	1	2	yes	—
453	C₂	C₇×#3508	1	1	yes	characteristic
454	C₂	C₇×#3511	1	2	yes	—

	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×#2862	C₂	semidirect
3. C₇×#2592	C₂	semidirect
4. C₇×#2580	C₂	semidirect
5. C₇×#2513	C₂	semidirect
6. C₇×#2448	C₂	semidirect
7. C₇×#2447	C₂	semidirect
8. C₇×#2367	C₂	semidirect
9. C₇×#2357	C₂	semidirect
10. C₄×C₇×C₄⋊Q₈	C₂	semidirect
12. C₄²×C₇×Q₈	C₂	semidirect
55. #36609	C₇	direct (N × H)
107. #2862	C₂×C₇	semidirect
109. #2592	C₂×C₇	semidirect
110. #2580	C₂×C₇	semidirect
111. #2513	C₂×C₇	semidirect
112. #2448	C₂×C₇	semidirect
113. #2447	C₂×C₇	semidirect
114. #2367	C₂×C₇	semidirect
115. #2357	C₂×C₇	semidirect
116. C₄×C₄⋊Q₈	C₂×C₇	semidirect
118. C₄²×Q₈	C₂×C₇	semidirect
427. C₇	#36609	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×#2862	2
C₇×#2858	2
C₇×#2592	2
C₇×#2580	2
C₇×#2513	2
C₇×#2448	2
C₇×#2447	2
C₇×#2367	2
C₇×#2357	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#127	2
C₄²×C₇×Q₈	2
#36609	7

Subgroups — C7×#36609 #13213825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36609 #13213825