Subgroups — #22586290

Order 9088.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986022	C₂	1	1	yes	maximal, characteristic
2	#17985781	C₂	1	1	yes	maximal, characteristic
3	#349×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11765849	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₇₁	C₄	1	1	yes	characteristic
6	#14556068	—	2	1	no	—
7	Dic₇₁⋊C₈	—	2	1	no	—
8	Dic₇₁⋊C₈	—	2	1	no	—
9	C₂×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
10	M₃₂×C₇₁	—	2	1	no	—
11	C₂²×Dic₇₁	—	2	1	no	—
12	#11765849	—	4	1	no	—
13	C₂×C₇₁⋊C₈	—	2	1	no	—
14	C₄×Dic₇₁	—	2	1	no	—
15	C₄×Dic₇₁	C₈	1	1	yes	characteristic
16	C₄×Dic₇₁	C₈	1	1	yes	characteristic
17	C₇₁⋊C₁₆	—	4	1	no	—
18	C₂²×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
19	M₁₆×C₇₁	—	4	1	no	—
20	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
22	C₁₆×C₇₁	—	4	1	no	—
23	C₂³×C₇₁	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₇₁	—	2	1	no	—
25	C₂×C₄×C₇₁	—	2	1	no	—
26	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₇₁	—	2	1	no	—
29	C₂×Dic₇₁	—	2	1	no	—
30	C₂×Dic₇₁	—	4	2	no	—
31	C₈×C₇₁	—	2	1	no	—
32	C₈×C₇₁	—	2	1	no	—
33	C₇₁⋊C₈	—	4	1	no	—
34	C₂²×C₇₁	—	2	1	no	—
35	C₂²×C₇₁	—	4	1	no	—
36	C₂²×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₇₁	—	2	1	no	—
38	C₄×C₇₁	#99	1	1	yes	characteristic
39	C₄×C₇₁	#101	1	1	yes	characteristic
40	Dic₇₁	—	2	2	no	—
41	Dic₇₁	—	4	1	no	—
42	C₂×C₇₁	—	2	1	no	—
43	C₂×C₇₁	—	4	1	no	—
44	C₂×C₇₁	#324	1	1	yes	characteristic
45	#1327	—	71	1	no	maximal, Sylow
46	C₇₁	#1327	1	1	yes	characteristic, complemented, Sylow
47	#423	—	71	1	no	—
48	#349	—	71	1	no	—
49	#349	D₇₁	1	1	yes	characteristic
50	C₂×M₁₆	—	71	1	no	—
51	C₂×M₁₆	C₂×D₇₁	1	1	yes	characteristic
52	C₂×C₄²	—	71	1	no	—
53	M₃₂	—	2	1	no	—
54	M₃₂	—	142	1	no	—
55	C₄⋊C₈	—	142	1	no	—
56	C₄⋊C₈	—	142	1	no	—
57	C₂²×C₄	—	142	1	no	—
58	C₂²×C₄	C₄×D₇₁	1	1	yes	characteristic
59	M₁₆	—	4	1	no	—
60	M₁₆	—	284	1	no	—
61	C₂×C₈	—	142	1	no	—
62	C₂×C₈	D₂₈₄	1	1	yes	characteristic
63	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
64	C₄²	—	71	1	no	—
65	C₄²	—	71	1	no	—
66	C₄²	—	142	1	no	—
67	C₁₆	—	4	1	no	—
68	C₁₆	—	284	1	no	—
69	C₂³	#11765848	1	1	yes	characteristic
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	284	2	no	—
73	C₂×C₄	—	142	1	no	—
74	C₂×C₄	—	142	1	no	—
75	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
76	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	1	no	—
79	C₈	—	284	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	4	1	no	—
82	C₂²	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	284	1	no	—
85	C₄	—	142	2	no	—
86	C₄	#14556042	1	1	yes	characteristic
87	C₄	#14556046	1	1	yes	characteristic
88	C₂	—	2	1	no	—
89	C₂	—	4	1	no	—
90	C₂	#17985724	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556042
commutator	C₂×C₄×C₇₁	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₇₁
Fitting	#349×C₇₁	C₂
socle	C₂×C₇₁	#324
hypercenter	#349	D₇₁
hypocenter	C₇₁	#1327
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
46. C₇₁	#1327	semidirect