Subgroups — #22590633

Order 9088.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986415	C₂	1	1	yes	maximal, characteristic
2	#17985833	C₂	1	1	yes	maximal, characteristic, complemented
3	#17985832	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₇₁	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556134	C₄	1	1	yes	characteristic
7	#14556068	C₄	1	1	yes	characteristic
8	#14556067	C₄	1	2	yes	—
9	C₁₆×D₇₁	C₂²	1	2	yes	—
10	C₇₁⋊C₃₂	C₂²	1	2	yes	—
11	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
12	C₃₂×C₇₁	C₂²	1	1	yes	characteristic
13	C₃₂×C₇₁	C₂²	1	1	yes	characteristic
14	#11765865	C₈	1	1	yes	characteristic
15	#11765849	C₈	1	1	yes	characteristic
16	#11765848	C₈	1	2	yes	—
17	C₈×D₇₁	C₂×C₄	1	2	yes	—
18	C₇₁⋊C₁₆	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
21	C₁₆×C₇₁	C₂³	1	1	yes	characteristic
22	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
23	C₂²⋊D₇₁	C₁₆	1	2	yes	—
24	D₂₈₄	C₁₆	1	1	yes	characteristic
25	C₄×D₇₁	C₂×C₈	1	2	yes	—
26	Dic₁₄₂	C₁₆	1	1	yes	characteristic
27	C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
28	C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
29	C₇₁⋊C₈	C₂×C₈	1	2	yes	—
30	C₂²×C₇₁	C₂×C₁₆	1	1	yes	characteristic
31	C₂×D₇₁	C₂×C₁₆	1	2	yes	—
32	C₄×C₇₁	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
34	Dic₇₁	C₂×C₁₆	1	2	yes	—
35	C₂×C₇₁	—	2	1	no	—
36	C₂×C₇₁	C₂²×C₁₆	1	1	yes	characteristic
37	D₇₁	—	2	2	no	—
38	#2258	—	71	1	no	maximal, Sylow
39	C₇₁	#2258	1	1	yes	characteristic, complemented, Sylow
40	#504	—	71	1	no	—
41	M₆₄	—	71	1	no	—
42	M₆₄	—	71	2	no	—
43	C₂×C₃₂	—	71	2	no	—
44	C₂×C₃₂	D₇₁	1	1	yes	characteristic, complemented
45	#131	—	71	1	no	—
46	M₃₂	—	71	1	no	—
47	M₃₂	—	71	2	no	—
48	C₂×C₁₆	—	71	2	no	—
49	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
50	C₃₂	—	71	2	no	—
51	C₃₂	C₂×D₇₁	1	1	yes	characteristic
52	C₃₂	C₂×D₇₁	1	1	yes	characteristic
53	#41	—	71	1	no	—
54	M₁₆	—	71	1	no	—
55	M₁₆	—	71	2	no	—
56	C₂×C₈	—	71	2	no	—
57	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
58	C₁₆	—	71	2	no	—
59	C₁₆	C₄×D₇₁	1	1	yes	characteristic
60	C₁₆	C₂²×D₇₁	1	1	yes	characteristic
61	Q₈	—	71	1	no	—
62	D₄	—	71	2	no	—
63	D₄	—	71	1	no	—
64	C₂×C₄	—	71	2	no	—
65	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
66	C₈	—	71	2	no	—
67	C₈	C₈×D₇₁	1	1	yes	characteristic
68	C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
69	C₂²	—	71	2	no	—
70	C₂²	C₁₆×D₇₁	1	1	yes	characteristic
71	C₄	—	71	2	no	—
72	C₄	C₁₆×D₇₁	1	1	yes	characteristic
73	C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	142	2	no	—
76	C₂	C₂×C₁₆×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂×D₇₁
commutator, socle	C₂×C₇₁	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₇₁
Fitting	C₂×C₃₂×C₇₁	C₂
hypercenter	C₂×C₃₂	D₇₁
hypocenter	C₇₁	#2258
LCS	G ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #17985833	C₂	semidirect
3. #17985832	C₂	semidirect
4. C₃₂×D₇₁	C₂	semidirect
5. C₂×C₃₂×C₇₁	C₂	semidirect
39. C₇₁	#2258	semidirect
44. C₂×C₃₂	D₇₁	semidirect