Subgroups — C₇×#36635 #13213851

Order 1792.

2006 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2864	C₂	1	2	yes	maximal, complemented
2	C₇×#2863	C₂	1	4	yes	maximal, complemented
3	C₇×#2862	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2859	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2857	C₂	1	2	yes	maximal
6	C₇×#2855	C₂	1	4	yes	maximal
7	C₇×#2851	C₂	1	2	yes	maximal
8	C₄×C₇×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
9	C₄×C₇×#125	C₂	1	2	yes	maximal, complemented
10	C₄×C₇×C₂²⋊Q₈	C₂	1	4	yes	maximal
11	C₇×#2295	C₂	1	4	yes	maximal, complemented
12	C₇×#2283	C₂	1	2	yes	maximal
13	C₂×C₄³×C₇	C₂	1	1	yes	maximal, characteristic
14	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₇×#125	C₂²	1	2	yes	—
16	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
17	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	—
18	C₂²×C₄²×C₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₇	C₂²	1	2	yes	—
21	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
23	C₇×#391	C₂²	1	4	yes	—
24	C₇×#391	C₂²	1	4	yes	—
25	C₇×#391	C₂²	1	4	yes	—
26	C₇×#391	C₂²	1	4	yes	—
27	C₇×#389	C₂²	1	4	yes	—
28	C₇×#389	C₂²	1	4	yes	—
29	C₇×#389	C₂²	1	4	yes	—
30	C₇×#389	C₂²	1	4	yes	—
31	C₇×#389	C₂²	1	4	yes	—
32	C₇×#389	C₂²	1	4	yes	—
33	C₇×#387	C₂²	1	8	yes	—
34	C₇×#387	C₂²	1	8	yes	—
35	C₇×#387	C₂²	1	8	yes	—
36	C₇×#387	C₂²	1	8	yes	—
37	C₇×#385	C₂²	1	8	yes	—
38	C₇×#384	C₂²	1	2	yes	—
39	C₇×#383	C₂²	1	4	yes	—
40	C₇×#382	C₂²	1	2	yes	—
41	C₇×#382	C₂²	1	2	yes	—
42	C₇×#382	C₂²	1	2	yes	—
43	C₇×#381	C₂²	1	4	yes	—
44	C₇×#380	C₂²	1	4	yes	—
45	C₇×#380	C₂²	1	4	yes	—
46	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
47	C₄×C₇×C₄⋊C₄	C₂²	1	8	yes	—
48	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
49	C₄×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
50	C₇×#376	C₂²	1	4	yes	—
51	C₄³×C₇	C₂²	1	2	yes	—
52	C₄³×C₇	C₂²	1	1	yes	characteristic
53	C₄³×C₇	C₂²	1	1	yes	characteristic
54	C₄³×C₇	C₂²	1	1	yes	characteristic
55	C₄³×C₇	C₂²	1	2	yes	—
56	C₄³×C₇	C₂²	1	1	yes	characteristic
57	#36635	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂²×C₇×Q₈	C₂³	1	4	yes	—
59	C₂³×C₄×C₇	C₂³	1	2	yes	—
60	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₇	C₂³	1	2	yes	—
64	C₇×C₄⋊Q₈	—	2	8	no	—
65	C₇×#125	—	2	8	no	—
66	C₇×C₂²⋊Q₈	—	2	16	no	—
67	C₄×C₇×Q₈	—	2	16	no	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
73	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
74	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
76	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
77	C₂×C₄²×C₇	—	2	8	no	—
78	C₂×C₄²×C₇	—	2	8	no	—
79	C₂×C₄²×C₇	—	2	4	no	—
80	C₂×C₄²×C₇	—	2	4	no	—
81	C₂×C₄²×C₇	Q₈	1	8	yes	complemented
82	C₂×C₄²×C₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₇	C₂³	1	2	yes	—
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	8	yes	—
94	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₇	C₂³	1	2	yes	—
101	C₇×#95	C₂³	1	8	yes	—
102	C₇×#95	C₂³	1	4	yes	—
103	C₇×#95	C₂³	1	4	yes	—
104	C₇×#95	C₂³	1	4	yes	—
105	C₇×#95	C₂³	1	4	yes	—
106	C₇×#95	C₂³	1	8	yes	—
107	C₇×#95	C₂³	1	8	yes	—
108	C₇×#95	C₂³	1	8	yes	—
109	C₇×#95	C₂³	1	8	yes	—
110	#2864	C₂×C₇	1	2	yes	complemented
111	#2863	C₂×C₇	1	4	yes	complemented
112	#2862	C₂×C₇	1	1	yes	characteristic, complemented
113	#2859	C₂×C₇	1	1	yes	characteristic, complemented
114	#2857	C₂×C₇	1	2	yes	—
115	#2855	C₂×C₇	1	4	yes	—
116	#2851	C₂×C₇	1	2	yes	—
117	C₄×C₄⋊Q₈	C₂×C₇	1	2	yes	complemented
118	C₄×#125	C₂×C₇	1	2	yes	complemented
119	C₄×C₂²⋊Q₈	C₂×C₇	1	4	yes	—
120	#2295	C₂×C₇	1	4	yes	complemented
121	#2283	C₂×C₇	1	2	yes	—
122	C₂×C₄³	C₂×C₇	1	1	yes	characteristic
123	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
124	C₂×C₇×Q₈	—	2	8	no	—
125	C₂×C₇×Q₈	—	2	8	no	—
126	C₂×C₇×Q₈	—	2	8	no	—
127	C₂²×C₄×C₇	—	2	4	no	—
128	C₂²×C₄×C₇	—	2	4	no	—
129	C₂²×C₄×C₇	—	2	4	no	—
130	C₂²×C₄×C₇	—	2	4	no	—
131	C₂²×C₄×C₇	—	2	4	no	—
132	C₂²×C₄×C₇	—	2	4	no	—
133	C₂²×C₄×C₇	—	2	4	no	—
134	C₂²×C₄×C₇	—	2	2	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
137	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
138	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
139	C₂²×C₄×C₇	#41	1	8	yes	—
140	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
141	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
142	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
152	C₇×C₄⋊C₄	—	2	8	no	—
153	C₇×C₄⋊C₄	—	2	16	no	—
154	C₇×C₄⋊C₄	—	2	8	no	—
155	C₇×C₄⋊C₄	—	2	16	no	—
156	C₇×C₄⋊C₄	—	2	16	no	—
157	C₇×C₄⋊C₄	—	2	8	no	—
158	C₇×C₄⋊C₄	—	2	8	no	—
159	C₇×C₄⋊C₄	—	2	8	no	—
160	C₇×C₂²⋊C₄	—	2	16	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	4	no	—
168	C₄²×C₇	—	2	4	no	—
169	C₄²×C₇	—	2	4	no	—
170	C₄²×C₇	—	2	2	no	—
171	C₄²×C₇	—	2	2	no	—
172	C₄²×C₇	—	2	16	no	—
173	C₄²×C₇	C₂×Q₈	1	4	yes	—
174	C₄²×C₇	C₂×Q₈	1	4	yes	—
175	C₄²×C₇	C₂×Q₈	1	4	yes	—
176	C₄²×C₇	C₂×Q₈	1	4	yes	—
177	C₄²×C₇	#41	1	8	yes	—
178	C₄²×C₇	#41	1	4	yes	—
179	C₄²×C₇	#41	1	4	yes	—
180	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
181	C₂×#125	C₂²×C₇	1	2	yes	—
182	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
183	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	—
184	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
185	C₂²×C₄²	C₂²×C₇	1	2	yes	—
186	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
187	C₂²×C₄²	C₂²×C₇	1	2	yes	—
188	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
189	#391	C₂²×C₇	1	4	yes	—
190	#391	C₂²×C₇	1	4	yes	—
191	#391	C₂²×C₇	1	4	yes	—
192	#391	C₂²×C₇	1	4	yes	—
193	#389	C₂²×C₇	1	4	yes	—
194	#389	C₂²×C₇	1	4	yes	—
195	#389	C₂²×C₇	1	4	yes	—
196	#389	C₂²×C₇	1	4	yes	—
197	#389	C₂²×C₇	1	4	yes	—
198	#389	C₂²×C₇	1	4	yes	—
199	#387	C₂²×C₇	1	8	yes	—
200	#387	C₂²×C₇	1	8	yes	—
201	#387	C₂²×C₇	1	8	yes	—
202	#387	C₂²×C₇	1	8	yes	—
203	#385	C₂²×C₇	1	8	yes	—
204	#384	C₂²×C₇	1	2	yes	—
205	#383	C₂²×C₇	1	4	yes	—
206	#382	C₂²×C₇	1	2	yes	—
207	#382	C₂²×C₇	1	2	yes	—
208	#382	C₂²×C₇	1	2	yes	—
209	#381	C₂²×C₇	1	4	yes	—
210	#380	C₂²×C₇	1	4	yes	—
211	#380	C₂²×C₇	1	4	yes	—
212	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
213	C₄×C₄⋊C₄	C₂²×C₇	1	8	yes	—
214	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
215	C₄×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
216	#376	C₂²×C₇	1	4	yes	—
217	C₄³	C₂²×C₇	1	1	yes	characteristic
218	C₄³	C₂²×C₇	1	1	yes	characteristic
219	C₄³	C₂²×C₇	1	1	yes	characteristic
220	C₄³	C₂²×C₇	1	2	yes	—
221	C₄³	C₂²×C₇	1	1	yes	characteristic
222	C₄³	C₂²×C₇	1	2	yes	—
223	C₂³×C₇	—	2	1	no	—
224	C₂³×C₇	—	2	2	no	—
225	C₂³×C₇	—	2	1	no	—
226	C₂³×C₇	C₂²×Q₈	1	2	yes	—
227	C₂³×C₇	C₂×#41	1	4	yes	—
228	C₂³×C₇	C₂⁵	1	1	yes	characteristic
229	C₇×Q₈	—	4	16	no	—
230	C₂×C₄×C₇	—	2	16	no	—
231	C₂×C₄×C₇	—	2	8	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	2	no	—
234	C₂×C₄×C₇	—	2	1	no	—
235	C₂×C₄×C₇	—	2	2	no	—
236	C₂×C₄×C₇	—	2	2	no	—
237	C₂×C₄×C₇	—	2	2	no	—
238	C₂×C₄×C₇	—	2	1	no	—
239	C₂×C₄×C₇	—	2	2	no	—
240	C₂×C₄×C₇	—	2	2	no	—
241	C₂×C₄×C₇	—	2	2	no	—
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	16	no	—
244	C₂×C₄×C₇	—	2	8	no	—
245	C₂×C₄×C₇	—	2	8	no	—
246	C₂×C₄×C₇	—	2	8	no	—
247	C₂×C₄×C₇	—	2	8	no	—
248	C₂×C₄×C₇	—	2	8	no	—
249	C₂×C₄×C₇	—	2	8	no	—
250	C₂×C₄×C₇	—	2	8	no	—
251	C₂×C₄×C₇	—	2	8	no	—
252	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
253	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
254	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
255	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
256	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
257	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
258	C₂×C₄×C₇	C₂×#41	1	4	yes	—
259	C₂×C₄×C₇	C₂×#41	1	4	yes	—
260	C₂×C₄×C₇	C₂×#41	1	4	yes	—
261	C₂×C₄×C₇	C₂×#41	1	4	yes	—
262	C₂×C₄×C₇	C₂×#41	1	4	yes	—
263	C₂×C₄×C₇	C₂×#41	1	4	yes	—
264	C₂×C₄×C₇	C₂×#41	1	4	yes	—
265	C₂×C₄×C₇	C₂×#41	1	2	yes	—
266	C₂×C₄×C₇	C₂×#41	1	2	yes	—
267	C₂²×Q₈	C₂³×C₇	1	4	yes	—
268	C₂³×C₄	C₂³×C₇	1	2	yes	—
269	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
270	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₇	1	2	yes	—
273	C₄⋊Q₈	—	2	8	no	—
274	#125	—	2	8	no	—
275	C₂²⋊Q₈	—	2	16	no	—
276	C₄×Q₈	—	2	16	no	—
277	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
279	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
281	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
282	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
283	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
284	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
286	C₂×C₄²	—	2	8	no	—
287	C₂×C₄²	—	2	8	no	—
288	C₂×C₄²	—	2	4	no	—
289	C₂×C₄²	—	2	4	no	—
290	C₂×C₄²	C₇×Q₈	1	8	yes	complemented
291	C₂×C₄²	C₂³×C₇	1	8	yes	—
292	C₂×C₄²	C₂³×C₇	1	2	yes	—
293	C₂×C₄²	C₂³×C₇	1	2	yes	—
294	C₂×C₄²	C₂³×C₇	1	2	yes	—
295	C₂×C₄²	C₂³×C₇	1	2	yes	—
296	C₂×C₄²	C₂³×C₇	1	2	yes	—
297	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₇	1	2	yes	—
300	C₂×C₄²	C₂³×C₇	1	2	yes	—
301	C₂×C₄²	C₂³×C₇	1	2	yes	—
302	C₂×C₄²	C₂³×C₇	1	2	yes	—
303	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₇	1	2	yes	—
308	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
310	#95	C₂³×C₇	1	8	yes	—
311	#95	C₂³×C₇	1	4	yes	—
312	#95	C₂³×C₇	1	4	yes	—
313	#95	C₂³×C₇	1	4	yes	—
314	#95	C₂³×C₇	1	4	yes	—
315	#95	C₂³×C₇	1	8	yes	—
316	#95	C₂³×C₇	1	8	yes	—
317	#95	C₂³×C₇	1	8	yes	—
318	#95	C₂³×C₇	1	8	yes	—
319	C₂²×C₇	—	2	4	no	—
320	C₂²×C₇	—	2	2	no	—
321	C₂²×C₇	—	2	2	no	—
322	C₂²×C₇	—	2	4	no	—
323	C₂²×C₇	#533	1	4	yes	—
324	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
325	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
326	C₂²×C₇	C₂²×#41	1	2	yes	—
327	C₂²×C₇	C₂²×#41	1	2	yes	—
328	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
329	C₄×C₇	—	2	4	no	—
330	C₄×C₇	—	2	2	no	—
331	C₄×C₇	—	2	2	no	—
332	C₄×C₇	—	2	2	no	—
333	C₄×C₇	—	2	2	no	—
334	C₄×C₇	—	2	4	no	—
335	C₄×C₇	—	2	4	no	—
336	C₄×C₇	—	4	8	no	—
337	C₄×C₇	—	4	8	no	—
338	C₄×C₇	#529	1	8	yes	—
339	C₄×C₇	#533	1	4	yes	—
340	C₄×C₇	#533	1	4	yes	—
341	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
342	C₂×Q₈	—	2	8	no	—
343	C₂×Q₈	—	2	8	no	—
344	C₂×Q₈	—	2	8	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
355	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
356	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
357	C₂²×C₄	C₇×#41	1	8	yes	—
358	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
359	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
360	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	16	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	16	no	—
374	C₄⋊C₄	—	2	16	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	8	no	—
378	C₂²⋊C₄	—	2	16	no	—
379	C₄²	—	2	4	no	—
380	C₄²	—	2	4	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	2	4	no	—
383	C₄²	—	2	4	no	—
384	C₄²	—	2	4	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	16	no	—
391	C₄²	C₂×C₇×Q₈	1	4	yes	—
392	C₄²	C₂×C₇×Q₈	1	4	yes	—
393	C₄²	C₂×C₇×Q₈	1	4	yes	—
394	C₄²	C₂×C₇×Q₈	1	4	yes	—
395	C₄²	C₇×#41	1	8	yes	—
396	C₄²	C₇×#41	1	4	yes	—
397	C₄²	C₇×#41	1	4	yes	—
398	C₂×C₇	—	2	4	no	—
399	C₂×C₇	C₂×#529	1	2	yes	—
400	C₂×C₇	C₂×#533	1	1	yes	characteristic
401	C₂×C₇	C₂×#533	1	1	yes	characteristic
402	C₂×C₇	C₂×#533	1	1	yes	characteristic
403	C₂×C₇	#3444	1	2	yes	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	1	no	—
407	C₂³	C₂²×C₇×Q₈	1	2	yes	—
408	C₂³	C₂×C₇×#41	1	4	yes	—
409	C₂³	C₂⁵×C₇	1	1	yes	characteristic
410	Q₈	—	4	16	no	—
411	C₂×C₄	—	2	16	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	16	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
434	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
435	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
436	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
437	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
438	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
439	C₂×C₄	C₂×C₇×#41	1	4	yes	—
440	C₂×C₄	C₂×C₇×#41	1	4	yes	—
441	C₂×C₄	C₂×C₇×#41	1	4	yes	—
442	C₂×C₄	C₂×C₇×#41	1	4	yes	—
443	C₂×C₄	C₂×C₇×#41	1	4	yes	—
444	C₂×C₄	C₂×C₇×#41	1	4	yes	—
445	C₂×C₄	C₂×C₇×#41	1	4	yes	—
446	C₂×C₄	C₂×C₇×#41	1	2	yes	—
447	C₂×C₄	C₂×C₇×#41	1	2	yes	—
448	C₇	#36635	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²	—	2	4	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	4	no	—
453	C₂²	C₇×#533	1	4	yes	—
454	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
455	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
456	C₂²	C₂²×C₇×#41	1	2	yes	—
457	C₂²	C₂²×C₇×#41	1	2	yes	—
458	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
459	C₄	—	2	4	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	4	no	—
465	C₄	—	2	4	no	—
466	C₄	—	4	8	no	—
467	C₄	—	4	8	no	—
468	C₄	C₇×#529	1	8	yes	—
469	C₄	C₇×#533	1	4	yes	—
470	C₄	C₇×#533	1	4	yes	—
471	C₂	—	2	4	no	—
472	C₂	C₂×C₇×#529	1	2	yes	—
473	C₂	C₂×C₇×#533	1	1	yes	characteristic
474	C₂	C₂×C₇×#533	1	1	yes	characteristic
475	C₂	C₂×C₇×#533	1	1	yes	characteristic
476	C₂	C₇×#3444	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₇×#2864	C₂	semidirect
2. C₇×#2863	C₂	semidirect
3. C₇×#2862	C₂	semidirect
4. C₇×#2859	C₂	semidirect
8. C₄×C₇×C₄⋊Q₈	C₂	semidirect
9. C₄×C₇×#125	C₂	semidirect
11. C₇×#2295	C₂	semidirect
57. #36635	C₇	direct (N × H)
81. C₂×C₄²×C₇	Q₈	semidirect
110. #2864	C₂×C₇	semidirect
111. #2863	C₂×C₇	semidirect
112. #2862	C₂×C₇	semidirect
113. #2859	C₂×C₇	semidirect
117. C₄×C₄⋊Q₈	C₂×C₇	semidirect
118. C₄×#125	C₂×C₇	semidirect
120. #2295	C₂×C₇	semidirect
290. C₂×C₄²	C₇×Q₈	semidirect
448. C₇	#36635	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×#2864	2
C₇×#2863	2
C₇×#2862	2
C₇×#2859	2
C₇×#2857	2
C₇×#2855	2
C₇×#2851	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#125	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#2295	2
C₇×#2283	2
C₂×C₄³×C₇	2
#36635	7

Subgroups — C7×#36635 #13213851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36635 #13213851