Subgroups — #14558447

Order 2368.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#11924607	C₂	1	1	yes	maximal, characteristic, complemented
3	#11924555	C₂	1	1	yes	maximal, characteristic
4	#10596964	—	2	1	no	—
5	#10596953	—	2	1	no	—
6	D₈×C₃₇	C₄	1	1	yes	characteristic
7	#10596940	—	2	1	no	—
8	Dic₁₄₈	C₄	1	1	yes	characteristic
9	C₈×D₃₇	C₂²	1	1	yes	characteristic
10	#10596927	—	2	1	no	—
11	D₄×C₃₇	—	2	1	no	—
12	C₂²⋊D₃₇	—	4	1	no	—
13	C₂×Dic₃₇	—	4	1	no	—
14	C₄×D₃₇	D₄	1	1	yes	characteristic
15	Dic₇₄	—	2	1	no	—
16	#64438	—	4	1	no	—
17	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
18	#64436	D₄	1	1	yes	characteristic
19	C₂²×C₃₇	—	4	1	no	—
20	C₂×D₃₇	SD₁₆	1	1	yes	characteristic
21	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₃₇	—	4	1	no	—
23	Dic₃₇	D₈	1	1	yes	characteristic
24	C₂×C₃₇	—	8	1	no	—
25	C₂×C₃₇	#102	1	1	yes	characteristic
26	D₃₇	—	2	1	no	—
27	#359	—	37	1	no	maximal, Sylow
28	C₃₇	#359	1	1	yes	characteristic, complemented, Sylow
29	#135	—	37	1	no	—
30	C₂×C₁₆	—	37	1	no	—
31	#108	—	37	1	no	—
32	#41	—	74	1	no	—
33	Q₁₆	—	37	1	no	—
34	SD₁₆	—	74	1	no	—
35	D₈	#3866	1	1	yes	characteristic
36	M₁₆	—	74	1	no	—
37	C₂×C₈	—	37	1	no	—
38	C₁₆	—	74	1	no	—
39	Q₈	—	74	1	no	—
40	D₄	—	2	1	no	—
41	D₄	—	148	1	no	—
42	C₂×C₄	—	37	1	no	—
43	C₂×C₄	—	148	1	no	—
44	C₈	—	37	1	no	—
45	C₈	—	148	1	no	—
46	C₈	C₂×#3866	1	1	yes	characteristic
47	C₂²	—	4	1	no	—
48	C₂²	—	37	1	no	—
49	C₄	—	37	1	no	—
50	C₄	—	148	1	no	—
51	C₄	C₂²⋊#3866	1	1	yes	characteristic
52	C₂	—	8	1	no	—
53	C₂	—	74	1	no	—
54	C₂	#11924598	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11924598
commutator	C₈×C₃₇	C₂×C₄
Frattini	C₈	C₂×#3866
Fitting	D₈×C₃₇	C₄
socle	C₂×C₃₇	#102
prime radical	#11924555	C₂
cosocle	C₈×D₃₇	C₂²
hypercenter	D₈	#3866
hypocenter	C₃₇	#359
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₃₇⋊C₁₆	C₂	semidirect
2. #11924607	C₂	semidirect
28. C₃₇	#359	semidirect

Maximal subgroups

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

subgroup	index
D₃₇⋊C₁₆	2
#11924607	2
#11924555	2
#359	37