Subgroups — #37548836

Order 23168.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042211	C₂	1	2	yes	maximal, complemented
2	C₂×#19153756	C₂	1	1	yes	maximal, characteristic
3	#19153866	—	2	2	no	—
4	#19153756	—	2	2	no	—
5	C₂×#15668424	C₄	1	1	yes	characteristic
6	C₂×#15668424	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₈₁	C₄	1	1	yes	characteristic
8	#15668424	—	2	1	no	—
9	#15668424	D₄	1	2	yes	—
10	C₂²×C₄×C₁₈₁	C₈	1	1	yes	characteristic
11	C₂×C₈×C₁₈₁	—	2	1	no	—
12	C₂×C₈×C₁₈₁	—	2	1	no	—
13	C₂×C₈×C₁₈₁	C₈	1	1	yes	characteristic
14	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₁₈₁	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₁₈₁	—	2	1	no	—
17	C₂×C₄×C₁₈₁	—	2	1	no	—
18	C₂×C₄×C₁₈₁	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
20	C₈×C₁₈₁	—	2	1	no	—
21	C₈×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
23	C₂²×C₁₈₁	—	2	1	no	—
24	C₂²×C₁₈₁	—	4	1	no	—
25	C₂²×C₁₈₁	C₂×C₁₆	1	1	yes	characteristic
26	C₄×C₁₈₁	—	2	1	no	—
27	C₄×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₁₈₁	M₃₂	1	1	yes	characteristic
29	C₂×C₁₈₁	—	2	1	no	—
30	C₂×C₁₈₁	—	4	1	no	—
31	C₂×C₁₈₁	C₂²⋊C₁₆	1	1	yes	characteristic
32	C₁₈₁	#1400	1	1	yes	characteristic, complemented, Sylow
33	#1400	—	181	1	no	maximal, Sylow
34	C₂×M₃₂	—	181	1	no	—
35	M₆₄	—	181	2	no	—
36	C₂²×C₈	#10624382	1	1	yes	characteristic
37	M₃₂	—	362	2	no	—
38	C₂×C₁₆	—	181	1	no	—
39	C₂×C₁₆	—	181	1	no	—
40	C₃₂	—	362	2	no	—
41	C₂²×C₄	#13089685	1	1	yes	characteristic
42	C₂×C₈	—	2	1	no	—
43	C₂×C₈	—	2	1	no	—
44	C₂×C₈	#13089685	1	1	yes	characteristic
45	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
46	C₁₆	—	362	1	no	—
47	C₁₆	—	181	2	no	—
48	C₂³	#15668452	1	1	yes	characteristic
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	#15668452	1	1	yes	characteristic
52	C₂×C₄	C₂×#13089685	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	C₂²⋊#10624382	1	1	yes	characteristic
55	C₈	#15668458	1	1	yes	characteristic
56	C₂²	—	2	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂×#15668452	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	C₂²⋊#13089685	1	1	yes	characteristic
61	C₄	#19153890	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	4	1	no	—
64	C₂	C₂²⋊#15668452	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#10624382
commutator	C₂²×C₁₈₁	C₂×C₁₆
Frattini	C₂×C₈	C₂×#10624382
Fitting	C₂²×C₈×C₁₈₁	C₄
socle	C₂×C₁₈₁	C₂²⋊C₁₆
prime radical	C₂³×C₁₈₁	C₁₆
cosocle	C₂×#15668424	C₂²
hypercenter	C₂²×C₈	#10624382
hypocenter	C₁₈₁	#1400
LCS	G ▷ C₂²×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. #26042211	C₂	semidirect
32. C₁₈₁	#1400	semidirect

Maximal subgroups

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

subgroup	index
#26042211	2
C₂×#19153756	2
#1400	181