Subgroups — C₇×#22136 #13199352

Order 1792.

896 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2392	C₂	1	1	yes	maximal, characteristic
4	C₇×#1955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1955	C₂	1	2	yes	maximal, complemented
6	C₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1924	C₂	1	2	yes	maximal, complemented
8	C₇×#1869	C₂	1	2	yes	maximal, complemented
9	C₇×#1850	C₂	1	2	yes	maximal, complemented
10	C₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₇×C₈	C₂²	1	2	yes	—
13	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
15	C₂×C₇×#117	C₂²	1	1	yes	characteristic
16	C₇×C₈×D₄	—	2	4	no	—
17	C₇×#433	—	2	4	no	—
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₇×#97	C₂²	1	1	yes	characteristic
30	C₂×C₇×#97	C₂²	1	2	yes	—
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₇×#398	C₄	1	1	yes	characteristic
33	C₇×#397	C₄	1	1	yes	characteristic
34	C₇×#396	C₄	1	2	yes	—
35	C₇×#394	C₄	1	2	yes	—
36	C₇×#394	C₄	1	1	yes	characteristic
37	C₇×#392	C₄	1	1	yes	characteristic
38	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	#22136	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	—	2	4	no	—
49	C₂²×C₇×C₈	—	4	2	no	—
50	C₂²×C₇×C₈	—	4	2	no	—
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇×C₈	C₂³	1	2	yes	—
53	C₂²×C₇×C₈	C₂³	1	2	yes	—
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
57	C₄×C₇×D₄	—	2	2	no	—
58	C₄×C₇×D₄	—	2	2	no	—
59	C₄×C₇×D₄	—	4	2	no	—
60	C₄×C₇×D₄	—	4	2	no	—
61	C₇×#117	—	2	2	no	—
62	C₇×#117	—	2	2	no	—
63	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₇×C₄⋊C₈	—	2	2	no	—
79	C₇×C₄⋊C₈	—	2	2	no	—
80	C₇×C₄⋊C₈	—	2	2	no	—
81	C₇×C₄⋊C₈	—	2	2	no	—
82	C₇×C₄⋊C₈	—	4	2	no	—
83	C₇×C₂²⋊C₈	—	2	2	no	—
84	C₇×C₂²⋊C₈	—	2	2	no	—
85	C₇×C₂²⋊C₈	—	2	4	no	—
86	C₇×C₂²⋊C₈	—	4	2	no	—
87	C₇×C₂²⋊C₈	—	4	2	no	—
88	C₇×C₂²⋊C₈	—	4	2	no	—
89	C₇×#97	—	2	2	no	—
90	C₇×#97	—	4	2	no	—
91	C₄×C₇×C₈	D₄	1	4	yes	complemented
92	C₇×#95	C₂×C₄	1	2	yes	—
93	C₇×#95	C₂×C₄	1	2	yes	—
94	C₇×#95	C₂×C₄	1	1	yes	characteristic
95	C₇×#95	C₂×C₄	1	1	yes	characteristic
96	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
97	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
98	#2392	C₂×C₇	1	1	yes	characteristic
99	#1955	C₂×C₇	1	1	yes	characteristic, complemented
100	#1955	C₂×C₇	1	2	yes	complemented
101	#1940	C₂×C₇	1	1	yes	characteristic, complemented
102	#1924	C₂×C₇	1	2	yes	complemented
103	#1869	C₂×C₇	1	2	yes	complemented
104	#1850	C₂×C₇	1	2	yes	complemented
105	#1798	C₂×C₇	1	1	yes	characteristic, complemented
106	#1770	C₂×C₇	1	1	yes	characteristic, complemented
107	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
108	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
109	C₂×C₇×D₄	—	2	4	no	—
110	C₂×C₇×D₄	—	2	4	no	—
111	C₂×C₇×D₄	—	2	2	no	—
112	C₂×C₇×D₄	—	4	2	no	—
113	C₂×C₇×D₄	—	4	2	no	—
114	C₂²×C₄×C₇	—	2	1	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	2	1	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	1	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	1	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	2	1	no	—
126	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	2	2	no	—
142	C₂×C₇×C₈	—	2	2	no	—
143	C₂×C₇×C₈	—	2	2	no	—
144	C₂×C₇×C₈	—	2	1	no	—
145	C₂×C₇×C₈	—	2	1	no	—
146	C₂×C₇×C₈	—	2	2	no	—
147	C₂×C₇×C₈	—	2	2	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	—	2	2	no	—
150	C₂×C₇×C₈	—	2	1	no	—
151	C₂×C₇×C₈	—	4	8	no	—
152	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
153	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	—	2	2	no	—
156	C₇×C₄⋊C₄	—	2	2	no	—
157	C₇×C₄⋊C₄	—	4	2	no	—
158	C₇×C₄⋊C₄	—	4	2	no	—
159	C₇×C₂²⋊C₄	—	2	4	no	—
160	C₇×C₂²⋊C₄	—	2	2	no	—
161	C₇×C₂²⋊C₄	—	2	2	no	—
162	C₇×C₂²⋊C₄	—	2	4	no	—
163	C₇×C₂²⋊C₄	—	4	2	no	—
164	C₇×C₂²⋊C₄	—	4	2	no	—
165	C₇×C₂²⋊C₄	—	4	2	no	—
166	C₄²×C₇	—	2	1	no	—
167	C₄²×C₇	—	2	1	no	—
168	C₄²×C₇	—	2	2	no	—
169	C₄²×C₇	—	2	2	no	—
170	C₄²×C₇	C₂×D₄	1	2	yes	—
171	C₄²×C₇	#41	1	2	yes	—
172	C₂³×C₈	C₂²×C₇	1	2	yes	—
173	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
174	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
175	C₂×#117	C₂²×C₇	1	1	yes	characteristic
176	C₈×D₄	—	2	4	no	—
177	#433	—	2	4	no	—
178	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
179	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
180	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
181	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
182	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
183	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
184	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
185	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
186	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
187	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
188	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
189	C₂×#97	C₂²×C₇	1	1	yes	characteristic
190	C₂×#97	C₂²×C₇	1	2	yes	—
191	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
192	#398	C₄×C₇	1	1	yes	characteristic
193	#397	C₄×C₇	1	1	yes	characteristic
194	#396	C₄×C₇	1	2	yes	—
195	#394	C₄×C₇	1	2	yes	—
196	#394	C₄×C₇	1	1	yes	characteristic
197	#392	C₄×C₇	1	1	yes	characteristic
198	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
199	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
200	#336	C₂²×C₇	1	2	yes	—
201	#336	C₂²×C₇	1	2	yes	—
202	#336	C₂²×C₇	1	2	yes	—
203	C₂³×C₇	—	2	2	no	—
204	C₂³×C₇	—	2	2	no	—
205	C₂³×C₇	—	2	2	no	—
206	C₂³×C₇	—	2	2	no	—
207	C₂³×C₇	—	2	2	no	—
208	C₂³×C₇	—	2	2	no	—
209	C₂³×C₇	—	2	1	no	—
210	C₂³×C₇	—	2	1	no	—
211	C₂³×C₇	—	2	1	no	—
212	C₂³×C₇	—	2	2	no	—
213	C₂³×C₇	—	2	2	no	—
214	C₂³×C₇	#131	1	4	yes	—
215	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
216	C₇×D₄	—	2	8	no	—
217	C₇×D₄	—	4	8	no	—
218	C₂×C₄×C₇	—	2	2	no	—
219	C₂×C₄×C₇	—	2	2	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	1	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	2	2	no	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	2	2	no	—
228	C₂×C₄×C₇	—	2	1	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	2	no	—
234	C₂×C₄×C₇	—	2	2	no	—
235	C₂×C₄×C₇	—	2	2	no	—
236	C₂×C₄×C₇	—	4	2	no	—
237	C₂×C₄×C₇	—	4	1	no	—
238	C₂×C₄×C₇	—	4	2	no	—
239	C₂×C₄×C₇	—	4	1	no	—
240	C₂×C₄×C₇	—	4	2	no	—
241	C₂×C₄×C₇	—	4	1	no	—
242	C₂×C₄×C₇	—	4	2	no	—
243	C₂×C₄×C₇	—	4	1	no	—
244	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
245	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
246	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
251	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
252	C₇×C₈	—	2	2	no	—
253	C₇×C₈	—	2	2	no	—
254	C₇×C₈	—	4	1	no	—
255	C₇×C₈	—	4	2	no	—
256	C₇×C₈	—	4	1	no	—
257	C₇×C₈	—	4	2	no	—
258	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
259	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
260	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
261	C₂³×C₄	C₂³×C₇	1	2	yes	—
262	C₂²×C₈	—	2	4	no	—
263	C₂²×C₈	—	4	2	no	—
264	C₂²×C₈	—	4	2	no	—
265	C₂²×C₈	C₂³×C₇	1	2	yes	—
266	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₇	1	2	yes	—
268	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
271	C₄×D₄	—	2	2	no	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	—	4	2	no	—
274	C₄×D₄	—	4	2	no	—
275	#117	—	2	2	no	—
276	#117	—	2	2	no	—
277	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
281	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
285	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
288	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
289	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₇	1	2	yes	—
291	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	4	2	no	—
297	C₂²⋊C₈	—	2	2	no	—
298	C₂²⋊C₈	—	2	2	no	—
299	C₂²⋊C₈	—	2	4	no	—
300	C₂²⋊C₈	—	4	2	no	—
301	C₂²⋊C₈	—	4	2	no	—
302	C₂²⋊C₈	—	4	2	no	—
303	#97	—	2	2	no	—
304	#97	—	4	2	no	—
305	C₄×C₈	C₇×D₄	1	4	yes	complemented
306	#95	C₂×C₄×C₇	1	2	yes	—
307	#95	C₂×C₄×C₇	1	2	yes	—
308	#95	C₂×C₄×C₇	1	1	yes	characteristic
309	#95	C₂×C₄×C₇	1	1	yes	characteristic
310	C₂²×C₇	—	2	4	no	—
311	C₂²×C₇	—	2	4	no	—
312	C₂²×C₇	—	2	4	no	—
313	C₂²×C₇	—	4	2	no	—
314	C₂²×C₇	—	4	2	no	—
315	C₂²×C₇	—	4	2	no	—
316	C₂²×C₇	—	4	2	no	—
317	C₂²×C₇	—	4	1	no	—
318	C₂²×C₇	—	4	1	no	—
319	C₂²×C₇	—	4	1	no	—
320	C₂²×C₇	—	4	2	no	—
321	C₂²×C₇	—	4	2	no	—
322	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
323	C₂²×C₇	#518	1	1	yes	characteristic
324	C₂²×C₇	#520	1	1	yes	characteristic
325	C₂²×C₇	C₂×#131	1	2	yes	—
326	C₂²×C₇	#568	1	2	yes	—
327	C₄×C₇	—	2	2	no	—
328	C₄×C₇	—	2	2	no	—
329	C₄×C₇	—	4	2	no	—
330	C₄×C₇	—	4	1	no	—
331	C₄×C₇	—	4	1	no	—
332	C₄×C₇	—	4	1	no	—
333	C₄×C₇	—	4	2	no	—
334	C₄×C₇	—	4	2	no	—
335	C₄×C₇	#535	1	1	yes	characteristic
336	C₄×C₇	#537	1	1	yes	characteristic
337	C₄×C₇	#540	1	1	yes	characteristic
338	C₄×C₇	#542	1	1	yes	characteristic
339	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
340	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
361	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
362	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
363	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
364	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
365	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	4	8	no	—
384	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
385	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	C₂×C₇×D₄	1	2	yes	—
403	C₄²	C₇×#41	1	2	yes	—
404	C₂×C₇	—	4	4	no	—
405	C₂×C₇	—	8	1	no	—
406	C₂×C₇	#2324	1	1	yes	characteristic
407	C₂×C₇	#2929	1	1	yes	characteristic
408	C₂×C₇	#2932	1	1	yes	characteristic
409	C₂×C₇	#2976	1	2	yes	—
410	C₂×C₇	#2992	1	2	yes	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	C₇×#131	1	4	yes	—
423	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
424	D₄	—	2	8	no	—
425	D₄	—	4	8	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
453	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
454	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
455	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
456	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	—	2	2	no	—
462	C₈	—	4	1	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	2	no	—
466	C₇	#22136	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²	—	2	4	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
480	C₂²	C₇×#518	1	1	yes	characteristic
481	C₂²	C₇×#520	1	1	yes	characteristic
482	C₂²	C₂×C₇×#131	1	2	yes	—
483	C₂²	C₇×#568	1	2	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	1	no	—
492	C₄	C₇×#535	1	1	yes	characteristic
493	C₄	C₇×#537	1	1	yes	characteristic
494	C₄	C₇×#540	1	1	yes	characteristic
495	C₄	C₇×#542	1	1	yes	characteristic
496	C₂	—	4	4	no	—
497	C₂	—	8	1	no	—
498	C₂	C₇×#2324	1	1	yes	characteristic
499	C₂	C₇×#2929	1	1	yes	characteristic
500	C₂	C₇×#2932	1	1	yes	characteristic
501	C₂	C₇×#2976	1	2	yes	—
502	C₂	C₇×#2992	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₇×#392	C₄
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. C₂×C₇×C₈×D₄	C₂	semidirect
2. C₂×C₇×#433	C₂	semidirect
4. C₇×#1955	C₂	semidirect
5. C₇×#1955	C₂	semidirect
6. C₇×#1940	C₂	semidirect
7. C₇×#1924	C₂	semidirect
8. C₇×#1869	C₂	semidirect
9. C₇×#1850	C₂	semidirect
10. C₇×#1798	C₂	semidirect
11. C₇×#1770	C₂	semidirect
43. #22136	C₇	direct (N × H)
91. C₄×C₇×C₈	D₄	semidirect
96. C₂×C₈×D₄	C₂×C₇	semidirect
97. C₂×#433	C₂×C₇	semidirect
99. #1955	C₂×C₇	semidirect
100. #1955	C₂×C₇	semidirect
101. #1940	C₂×C₇	semidirect
102. #1924	C₂×C₇	semidirect
103. #1869	C₂×C₇	semidirect
104. #1850	C₂×C₇	semidirect
105. #1798	C₂×C₇	semidirect
106. #1770	C₂×C₇	semidirect
305. C₄×C₈	C₇×D₄	semidirect
466. C₇	#22136	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×C₈×D₄	2
C₂×C₇×#433	2
C₇×#2392	2
C₇×#1955	2
C₇×#1940	2
C₇×#1924	2
C₇×#1869	2
C₇×#1850	2
C₇×#1798	2
C₇×#1770	2
#22136	7

Subgroups — C7×#22136 #13199352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22136 #13199352