Subgroups — #14557571

Order 2368.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924495	C₂	1	2	yes	maximal
2	#11924470	C₂	1	2	yes	maximal, complemented
3	#11924468	C₂	1	2	yes	maximal, complemented
4	C₂²×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₇	C₄	1	4	yes	complemented
7	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂²⋊Dic₃₇	—	2	2	no	—
10	C₄⋊Dic₃₇	C₂²	1	4	yes	—
11	C₄×Dic₃₇	—	2	2	no	—
12	C₂³×C₃₇	D₄	1	1	yes	characteristic
13	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₃₇	Q₈	1	2	yes	—
16	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
17	C₂×Dic₃₇	—	2	4	no	—
18	C₈×C₃₇	C₂×C₄	1	2	yes	—
19	C₈×C₃₇	C₂×C₄	1	2	yes	—
20	C₂²×C₃₇	—	2	2	no	—
21	C₂²×C₃₇	C₄⋊C₄	1	2	yes	—
22	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
23	C₄×C₃₇	C₄⋊C₄	1	2	yes	—
24	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
26	Dic₃₇	—	4	4	no	—
27	C₂×C₃₇	—	2	2	no	—
28	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₃₇	#135	1	2	yes	—
30	#427	—	37	1	no	maximal, Sylow
31	C₃₇	#427	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₈	D₃₇	1	1	yes	characteristic
33	#117	—	37	2	no	—
34	#107	—	37	2	no	—
35	#106	—	37	2	no	—
36	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
37	C₂×C₈	Dic₃₇	1	4	yes	complemented
38	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
39	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
40	C₄⋊C₄	—	37	4	no	—
41	C₂²⋊C₄	—	74	2	no	—
42	C₄²	—	74	2	no	—
43	C₂³	D₁₄₈	1	1	yes	characteristic
44	C₂×C₄	—	74	4	no	—
45	C₂×C₄	Dic₇₄	1	2	yes	—
46	C₂×C₄	D₁₄₈	1	1	yes	characteristic
47	C₂×C₄	C₂×Dic₃₇	1	2	yes	—
48	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
49	C₈	C₂×Dic₃₇	1	2	yes	—
50	C₈	C₂×Dic₃₇	1	2	yes	—
51	C₂²	—	2	2	no	—
52	C₂²	C₄⋊Dic₃₇	1	2	yes	—
53	C₂²	C₂×D₁₄₈	1	1	yes	characteristic
54	C₄	—	148	4	no	—
55	C₄	C₄⋊Dic₃₇	1	2	yes	—
56	C₄	C₂×Dic₇₄	1	1	yes	characteristic
57	C₄	C₂²×Dic₃₇	1	1	yes	characteristic
58	C₂	—	2	2	no	—
59	C₂	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
60	C₂	#11924558	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₁₄₈
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₂²×C₈×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
prime radical	C₂³×C₃₇	D₄
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	C₂²×C₈	D₃₇
hypocenter	C₃₇	#427
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #11924470	C₂	semidirect
3. #11924468	C₂	semidirect
6. C₂×C₈×C₃₇	C₄	semidirect
31. C₃₇	#427	semidirect
37. C₂×C₈	Dic₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924495	2
#11924470	2
#11924468	2
C₂²×C₈×C₃₇	2
#427	37