Subgroups — #37531913

Order 23168.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄₄₈	C₂	1	1	yes	maximal, characteristic
2	#26041113	C₂	1	1	yes	maximal, characteristic
3	#368×C₁₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₂₄	—	2	1	no	—
5	Dic₁₄₄₈	—	2	1	no	—
6	Dic₁₄₄₈	C₄	1	2	yes	—
7	#19153722	—	2	1	no	—
8	C₂×C₁₆×C₁₈₁	C₂²	1	1	yes	characteristic
9	#108×C₁₈₁	—	2	1	no	—
10	C₂×Dic₃₆₂	—	4	1	no	—
11	Dic₇₂₄	—	2	2	no	—
12	Dic₇₂₄	—	4	1	no	—
13	M₁₆×C₁₈₁	—	4	1	no	—
14	C₂×C₈×C₁₈₁	D₄	1	1	yes	characteristic
15	C₁₆×C₁₈₁	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₁₈₁	D₄	1	1	yes	characteristic
17	Dic₃₆₂	—	4	2	no	—
18	Dic₃₆₂	—	8	1	no	—
19	C₂×Dic₁₈₁	—	8	1	no	—
20	C₂×C₄×C₁₈₁	D₈	1	1	yes	characteristic
21	C₈×C₁₈₁	—	8	1	no	—
22	C₈×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₈₁	SD₁₆	1	1	yes	characteristic
24	C₂²×C₁₈₁	SD₃₂	1	1	yes	characteristic
25	C₄×C₁₈₁	#102	1	1	yes	characteristic
26	C₄×C₁₈₁	D₁₆	1	1	yes	characteristic
27	Dic₁₈₁	—	8	2	no	—
28	C₂×C₁₈₁	—	2	1	no	—
29	C₂×C₁₈₁	#357	1	1	yes	characteristic
30	C₁₈₁	#1420	1	1	yes	characteristic, complemented, Sylow
31	#1420	—	181	1	no	maximal, Sylow
32	C₂×Q₃₂	—	181	1	no	—
33	M₆₄	—	181	1	no	—
34	#368	D₁₈₁	1	1	yes	characteristic
35	C₂×Q₁₆	—	362	1	no	—
36	Q₃₂	—	362	1	no	—
37	Q₃₂	—	181	2	no	—
38	C₂×C₁₆	C₂×D₁₈₁	1	1	yes	characteristic
39	#108	—	2	1	no	—
40	C₃₂	—	362	1	no	—
41	C₂×Q₈	—	724	1	no	—
42	Q₁₆	—	362	2	no	—
43	Q₁₆	—	724	1	no	—
44	M₁₆	—	4	1	no	—
45	C₂×C₈	C₂²⋊D₁₈₁	1	1	yes	characteristic
46	C₁₆	C₄×D₁₈₁	1	1	yes	characteristic
47	C₁₆	D₇₂₄	1	1	yes	characteristic
48	Q₈	—	1448	1	no	—
49	Q₈	—	724	2	no	—
50	C₂×C₄	—	1448	1	no	—
51	C₂×C₄	#15668434	1	1	yes	characteristic
52	C₈	—	8	1	no	—
53	C₈	#15668426	1	1	yes	characteristic
54	C₈	#15668436	1	1	yes	characteristic
55	C₂²	#19153759	1	1	yes	characteristic
56	C₄	—	1448	2	no	—
57	C₄	#19153736	1	1	yes	characteristic
58	C₄	#19153757	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#26041079	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26041079
commutator	C₁₆×C₁₈₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₈₁
Fitting	#368×C₁₈₁	C₂
socle	C₂×C₁₈₁	#357
prime radical	C₂²×C₁₈₁	SD₃₂
cosocle	C₂×C₁₆×C₁₈₁	C₂²
hypercenter	#368	D₁₈₁
hypocenter	C₁₈₁	#1420
LCS	G ▷ C₁₆×C₁₈₁ ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
30. C₁₈₁	#1420	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₄₄₈	2
#26041113	2
#368×C₁₈₁	2
#1420	181