Subgroups — #37548789

Order 23168.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042289	C₂	1	2	yes	maximal
2	C₂×#19153755	C₂	1	1	yes	maximal, characteristic
3	#19153895	—	2	2	no	—
4	#19153885	—	2	2	no	—
5	#19153884	C₄	1	4	yes	complemented
6	C₂×C₈×D₁₈₁	C₂²	1	1	yes	characteristic
7	#19153755	—	2	2	no	—
8	C₂×#15668424	C₄	1	1	yes	characteristic, complemented
9	C₂×C₁₆×C₁₈₁	C₄	1	1	yes	characteristic, complemented
10	C₄⋊#10624382	—	2	4	no	—
11	C₂²⋊#10624382	—	4	2	no	—
12	C₄×#10624382	—	4	2	no	—
13	C₂×C₄×D₁₈₁	D₄	1	1	yes	characteristic
14	C₂×#13089678	Q₈	1	1	yes	characteristic
15	C₈×D₁₈₁	C₂×C₄	1	2	yes	—
16	C₈×D₁₈₁	D₄	1	2	yes	—
17	#15668424	—	2	1	no	—
18	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₁₈₁	—	2	1	no	—
20	C₂×#10624382	—	4	4	no	—
21	C₂²×D₁₈₁	D₈	1	1	yes	characteristic
22	C₂×Dic₁₈₁	Q₁₆	1	1	yes	characteristic
23	C₄×D₁₈₁	C₂²⋊C₄	1	2	yes	—
24	C₄×D₁₈₁	SD₁₆	1	2	yes	—
25	#13089678	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
27	C₈×C₁₈₁	C₄²	1	1	yes	characteristic
28	C₈×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₁₈₁	#107	1	1	yes	characteristic
30	C₂×D₁₈₁	—	4	1	no	—
31	C₂×D₁₈₁	#102	1	2	yes	—
32	#10624382	—	8	4	no	—
33	C₄×C₁₈₁	#95	1	1	yes	characteristic
34	C₄×C₁₈₁	#106	1	1	yes	characteristic
35	Dic₁₈₁	#103	1	2	yes	—
36	C₂×C₁₈₁	—	2	1	no	—
37	C₂×C₁₈₁	#340	1	1	yes	characteristic
38	D₁₈₁	—	2	2	no	—
39	C₁₈₁	#1384	1	1	yes	characteristic, complemented, Sylow
40	#1384	—	181	1	no	maximal, Sylow
41	C₂×M₃₂	—	181	1	no	—
42	#427	—	181	2	no	—
43	C₂²×C₈	—	181	1	no	—
44	#117	—	362	2	no	—
45	M₃₂	—	362	2	no	—
46	C₂×C₁₆	—	181	1	no	—
47	C₂×C₁₆	#10624382	1	1	yes	characteristic, complemented
48	#107	—	362	2	no	—
49	#106	—	181	4	no	—
50	C₂²×C₄	—	181	1	no	—
51	C₂×C₈	—	181	1	no	—
52	C₂×C₈	—	181	2	no	—
53	C₂×C₈	—	181	2	no	—
54	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
55	C₄⋊C₄	—	362	4	no	—
56	C₂²⋊C₄	—	724	2	no	—
57	C₄²	—	724	2	no	—
58	C₁₆	—	2	1	no	—
59	C₁₆	—	362	1	no	—
60	C₂³	—	181	1	no	—
61	C₂×C₄	—	181	1	no	—
62	C₂×C₄	—	181	2	no	—
63	C₂×C₄	—	181	2	no	—
64	C₂×C₄	—	724	4	no	—
65	C₂×C₄	C₄⋊#10624382	1	1	yes	characteristic
66	C₈	—	181	2	no	—
67	C₈	C₄×#10624382	1	1	yes	characteristic
68	C₈	C₂²⋊#10624382	1	1	yes	characteristic
69	C₂²	—	181	2	no	—
70	C₂²	—	724	1	no	—
71	C₂²	#19153885	1	1	yes	characteristic
72	C₄	—	1448	4	no	—
73	C₄	—	181	2	no	—
74	C₄	(C₂×#10624382)⋊C₄	1	1	yes	characteristic
75	C₄	#19153884	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	362	2	no	—
78	C₂	#26042153	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19153884
commutator	C₈×C₁₈₁	C₄²
Frattini	C₂×C₈	C₂×#10624382
Fitting	C₂×C₁₆×C₁₈₁	C₄
socle	C₂×C₁₈₁	#340
prime radical	C₂²×D₁₈₁	D₈
cosocle	C₂×C₈×D₁₈₁	C₂²
hypercenter	C₂×C₁₆	#10624382
hypocenter	C₁₈₁	#1384
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
5. #19153884	C₄	semidirect
8. C₂×#15668424	C₄	semidirect
9. C₂×C₁₆×C₁₈₁	C₄	semidirect
39. C₁₈₁	#1384	semidirect
47. C₂×C₁₆	#10624382	semidirect

Maximal subgroups

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

subgroup	index
#26042289	2
C₂×#19153755	2
#1384	181