Subgroups — #14557938

Order 2368.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924536	C₂	1	2	yes	maximal
2	#11924470	C₂	1	4	yes	maximal
3	C₄×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₄	—	2	2	no	—
5	C₂×C₈×C₃₇	C₂²	1	2	yes	—
6	C₄²×C₃₇	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₃₇	—	2	2	no	—
8	C₄⋊Dic₃₇	C₂²	1	4	yes	—
9	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
10	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
11	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
12	C₂×Dic₃₇	—	2	4	no	—
13	Dic₇₄	—	4	4	no	—
14	C₈×C₃₇	Q₈	1	4	yes	complemented
15	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
16	C₄×C₃₇	D₈	1	2	yes	—
17	C₄×C₃₇	Q₁₆	1	2	yes	—
18	C₄×C₃₇	C₂×Q₈	1	2	yes	—
19	Dic₃₇	—	4	4	no	—
20	C₂×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
21	C₂×C₃₇	C₂×D₈	1	1	yes	characteristic
22	C₂×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
23	#500	—	37	1	no	maximal, Sylow
24	C₃₇	#500	1	1	yes	characteristic, complemented, Sylow
25	C₄⋊Q₈	—	37	2	no	—
26	#107	—	37	4	no	—
27	C₄×C₈	D₃₇	1	1	yes	characteristic
28	C₂×Q₈	—	74	2	no	—
29	C₂×C₈	C₂×D₃₇	1	2	yes	—
30	C₄⋊C₄	—	37	4	no	—
31	C₄⋊C₄	—	74	2	no	—
32	C₄²	C₂×D₃₇	1	1	yes	characteristic
33	Q₈	—	148	4	no	—
34	C₂×C₄	—	74	4	no	—
35	C₂×C₄	D₁₄₈	1	1	yes	characteristic
36	C₂×C₄	D₁₄₈	1	1	yes	characteristic
37	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
38	C₈	Dic₇₄	1	4	yes	complemented
39	C₂²	C₂×D₁₄₈	1	1	yes	characteristic
40	C₄	—	148	4	no	—
41	C₄	D₂₉₆	1	2	yes	—
42	C₄	Dic₁₄₈	1	2	yes	—
43	C₄	C₂×Dic₇₄	1	2	yes	—
44	C₂	#11924536	1	1	yes	characteristic
45	C₂	C₂×D₂₉₆	1	1	yes	characteristic
46	C₂	C₂×Dic₁₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₄₈
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₄×C₈×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₄
hypercenter	C₄×C₈	D₃₇
hypocenter	C₃₇	#500
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
14. C₈×C₃₇	Q₈	semidirect
24. C₃₇	#500	semidirect
38. C₈	Dic₇₄	semidirect

Maximal subgroups

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

subgroup	index
#11924536	2
#11924470	2
C₄×C₈×C₃₇	2
#500	37