Subgroups — #37536030

Order 23168.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26041711	C₂	1	2	yes	maximal, complemented
2	Dic₂₈₉₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#26041118	C₂	1	2	yes	maximal, complemented
4	D₅₇₉₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₂×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#19153838	—	2	2	no	—
7	Dic₁₄₄₈	C₂²	1	2	yes	—
8	#19153761	—	2	2	no	—
9	D₂₈₉₆	C₂²	1	2	yes	—
10	C₂×C₁₆×C₁₈₁	C₂²	1	1	yes	characteristic
11	C₃₂×C₁₈₁	C₂²	1	1	yes	characteristic
12	C₃₂×C₁₈₁	C₂²	1	1	yes	characteristic
13	#15668449	—	4	2	no	—
14	Dic₇₂₄	—	2	2	no	—
15	#15668438	—	4	2	no	—
16	D₁₄₄₈	—	2	2	no	—
17	C₂×C₈×C₁₈₁	D₄	1	1	yes	characteristic
18	C₁₆×C₁₈₁	D₄	1	1	yes	characteristic
19	C₁₆×C₁₈₁	C₂³	1	1	yes	characteristic
20	Dic₃₆₂	—	4	2	no	—
21	D₇₂₄	—	4	2	no	—
22	C₂²⋊D₁₈₁	—	8	2	no	—
23	C₄×D₁₈₁	—	8	2	no	—
24	C₂×C₄×C₁₈₁	D₈	1	1	yes	characteristic
25	C₈×C₁₈₁	D₈	1	1	yes	characteristic
26	C₈×C₁₈₁	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₁₈₁	D₁₆	1	1	yes	characteristic
28	C₂×D₁₈₁	—	8	2	no	—
29	C₄×C₁₈₁	D₁₆	1	1	yes	characteristic
30	C₄×C₁₈₁	C₂×D₈	1	1	yes	characteristic
31	Dic₁₈₁	—	8	2	no	—
32	C₂×C₁₈₁	—	2	1	no	—
33	C₂×C₁₈₁	C₂×D₁₆	1	1	yes	characteristic
34	D₁₈₁	—	16	2	no	—
35	C₁₈₁	#2262	1	1	yes	characteristic, complemented, Sylow
36	#2262	—	181	1	no	maximal, Sylow
37	#508	—	181	2	no	—
38	Q₆₄	—	181	1	no	—
39	SD₆₄	—	181	2	no	—
40	D₃₂	—	181	1	no	—
41	C₂×C₃₂	D₁₈₁	1	1	yes	characteristic, complemented
42	#135	—	362	2	no	—
43	Q₃₂	—	181	2	no	—
44	SD₃₂	—	362	2	no	—
45	D₁₆	—	181	2	no	—
46	C₂×C₁₆	C₂×D₁₈₁	1	1	yes	characteristic
47	C₃₂	C₂×D₁₈₁	1	1	yes	characteristic
48	C₃₂	C₂×D₁₈₁	1	1	yes	characteristic
49	#41	—	724	2	no	—
50	Q₁₆	—	362	2	no	—
51	SD₁₆	—	724	2	no	—
52	D₈	—	362	2	no	—
53	C₂×C₈	D₇₂₄	1	1	yes	characteristic
54	C₁₆	D₇₂₄	1	1	yes	characteristic
55	C₁₆	C₂²×D₁₈₁	1	1	yes	characteristic
56	Q₈	—	724	2	no	—
57	D₄	—	1448	2	no	—
58	D₄	—	724	2	no	—
59	C₂×C₄	—	1448	2	no	—
60	C₂×C₄	D₁₄₄₈	1	1	yes	characteristic
61	C₈	D₁₄₄₈	1	1	yes	characteristic
62	C₈	C₂×D₇₂₄	1	1	yes	characteristic
63	C₂²	—	1448	2	no	—
64	C₂²	D₂₈₉₆	1	1	yes	characteristic
65	C₄	—	1448	2	no	—
66	C₄	D₂₈₉₆	1	1	yes	characteristic
67	C₄	C₂×D₁₄₄₈	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	2896	2	no	—
70	C₂	C₂×D₂₈₉₆	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₂₈₉₆
commutator, cosocle	C₁₆×C₁₈₁	C₂³
Frattini	C₁₆	C₂²×D₁₈₁
Fitting	C₂×C₃₂×C₁₈₁	C₂
socle	C₂×C₁₈₁	C₂×D₁₆
hypercenter	C₂×C₃₂	D₁₈₁
hypocenter	C₁₈₁	#2262
LCS	G ▷ C₁₆×C₁₈₁ ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #26041711	C₂	semidirect
2. Dic₂₈₉₆	C₂	semidirect
3. #26041118	C₂	semidirect
4. D₅₇₉₂	C₂	semidirect
5. C₂×C₃₂×C₁₈₁	C₂	semidirect
35. C₁₈₁	#2262	semidirect
41. C₂×C₃₂	D₁₈₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#26041711	2
Dic₂₈₉₆	2
#26041118	2
D₅₇₉₂	2
C₂×C₃₂×C₁₈₁	2
#2262	181