Subgroups — #18009664

Order 4736.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558543	C₂	1	2	yes	maximal
2	C₂×#11924475	C₂	1	1	yes	maximal, characteristic
3	#11924615	—	2	2	no	—
4	#11924605	—	2	2	no	—
5	#11924604	C₄	1	4	yes	complemented
6	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
7	#11924475	—	2	2	no	—
8	C₂×#10596925	C₄	1	1	yes	characteristic, complemented
9	C₂×C₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
10	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
11	C₂²⋊#3866	—	4	2	no	—
12	C₄⋊#3866	—	2	4	no	—
13	C₄×#3866	—	4	2	no	—
14	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×#64436	Q₈	1	1	yes	characteristic
16	C₈×D₃₇	C₂×C₄	1	2	yes	—
17	C₈×D₃₇	D₄	1	2	yes	—
18	C₁₆×C₃₇	—	2	1	no	—
19	#10596925	—	2	1	no	—
20	C₂²×D₃₇	D₈	1	1	yes	characteristic
21	C₂×#3866	—	4	4	no	—
22	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
23	C₂×Dic₃₇	Q₁₆	1	1	yes	characteristic
24	C₄×D₃₇	C₂²⋊C₄	1	2	yes	—
25	C₄×D₃₇	SD₁₆	1	2	yes	—
26	C₈×C₃₇	C₄²	1	1	yes	characteristic
27	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
28	#64436	C₄⋊C₄	1	2	yes	—
29	C₂²×C₃₇	#107	1	1	yes	characteristic
30	C₂×D₃₇	—	4	1	no	—
31	C₂×D₃₇	#102	1	2	yes	—
32	#3866	—	8	4	no	—
33	C₄×C₃₇	#95	1	1	yes	characteristic
34	C₄×C₃₇	#106	1	1	yes	characteristic
35	Dic₃₇	#103	1	2	yes	—
36	#1384	—	37	1	no	maximal, Sylow
37	C₂×C₃₇	—	2	1	no	—
38	C₂×C₃₇	#340	1	1	yes	characteristic
39	D₃₇	—	2	2	no	—
40	C₂×M₃₂	—	37	1	no	—
41	#427	—	37	2	no	—
42	C₃₇	#1384	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₈	—	37	1	no	—
44	#117	—	74	2	no	—
45	M₃₂	—	74	2	no	—
46	C₂×C₁₆	—	37	1	no	—
47	C₂×C₁₆	#3866	1	1	yes	characteristic, complemented
48	#107	—	74	2	no	—
49	#106	—	37	4	no	—
50	C₂²×C₄	—	37	1	no	—
51	C₂×C₈	—	37	1	no	—
52	C₂×C₈	—	37	2	no	—
53	C₂×C₈	—	37	2	no	—
54	C₂×C₈	C₂×#3866	1	1	yes	characteristic
55	C₄⋊C₄	—	74	4	no	—
56	C₂²⋊C₄	—	148	2	no	—
57	C₄²	—	148	2	no	—
58	C₁₆	—	2	1	no	—
59	C₁₆	—	74	1	no	—
60	C₂³	—	37	1	no	—
61	C₂×C₄	—	37	1	no	—
62	C₂×C₄	—	37	2	no	—
63	C₂×C₄	—	37	2	no	—
64	C₂×C₄	—	148	4	no	—
65	C₂×C₄	C₄⋊#3866	1	1	yes	characteristic
66	C₈	—	37	2	no	—
67	C₈	C₄×#3866	1	1	yes	characteristic
68	C₈	C₂²⋊#3866	1	1	yes	characteristic
69	C₂²	—	37	2	no	—
70	C₂²	—	148	1	no	—
71	C₂²	#11924605	1	1	yes	characteristic
72	C₄	—	37	2	no	—
73	C₄	—	296	4	no	—
74	C₄	(C₂×#3866)⋊C₄	1	1	yes	characteristic
75	C₄	#11924604	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	74	2	no	—
78	C₂	#14558407	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924604
commutator	C₈×C₃₇	C₄²
Frattini	C₂×C₈	C₂×#3866
Fitting	C₂×C₁₆×C₃₇	C₄
socle	C₂×C₃₇	#340
prime radical	C₂²×D₃₇	D₈
cosocle	C₂×C₈×D₃₇	C₂²
hypercenter	C₂×C₁₆	#3866
hypocenter	C₃₇	#1384
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
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. #11924604	C₄	semidirect
8. C₂×#10596925	C₄	semidirect
9. C₂×C₁₆×C₃₇	C₄	semidirect
42. C₃₇	#1384	semidirect
47. C₂×C₁₆	#3866	semidirect

Maximal subgroups

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

subgroup	index
#14558543	2
C₂×#11924475	2
#1384	37