Subgroups — #14557965

Order 2368.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924558	C₂	1	2	yes	maximal, complemented
2	Dic₂₉₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#11924481	C₂	1	2	yes	maximal, complemented
4	D₅₉₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#10596962	—	2	2	no	—
7	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
8	Dic₁₄₈	C₂²	1	2	yes	—
9	D₂₉₆	C₂²	1	2	yes	—
10	#10596930	—	2	2	no	—
11	C₁₆×C₃₇	C₂²	1	1	yes	characteristic
12	C₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
14	C₂²⋊D₃₇	—	4	2	no	—
15	D₁₄₈	—	2	2	no	—
16	C₄×D₃₇	—	4	2	no	—
17	Dic₇₄	—	2	2	no	—
18	C₈×C₃₇	D₄	1	1	yes	characteristic
19	C₈×C₃₇	C₂³	1	1	yes	characteristic
20	C₂²×C₃₇	D₈	1	1	yes	characteristic
21	C₂×D₃₇	—	4	2	no	—
22	C₄×C₃₇	D₈	1	1	yes	characteristic
23	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
24	Dic₃₇	—	4	2	no	—
25	C₂×C₃₇	—	2	1	no	—
26	C₂×C₃₇	C₂×D₈	1	1	yes	characteristic
27	D₃₇	—	8	2	no	—
28	#508	—	37	1	no	maximal, Sylow
29	C₃₇	#508	1	1	yes	characteristic, complemented, Sylow
30	#135	—	37	2	no	—
31	Q₃₂	—	37	1	no	—
32	SD₃₂	—	37	2	no	—
33	D₁₆	—	37	1	no	—
34	C₂×C₁₆	D₃₇	1	1	yes	characteristic, complemented
35	#41	—	74	2	no	—
36	Q₁₆	—	37	2	no	—
37	SD₁₆	—	74	2	no	—
38	D₈	—	37	2	no	—
39	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
40	C₁₆	C₂×D₃₇	1	1	yes	characteristic
41	C₁₆	C₂×D₃₇	1	1	yes	characteristic
42	Q₈	—	74	2	no	—
43	D₄	—	74	2	no	—
44	D₄	—	148	2	no	—
45	C₂×C₄	—	148	2	no	—
46	C₂×C₄	D₁₄₈	1	1	yes	characteristic
47	C₈	D₁₄₈	1	1	yes	characteristic
48	C₈	C₂²×D₃₇	1	1	yes	characteristic
49	C₂²	—	148	2	no	—
50	C₂²	D₂₉₆	1	1	yes	characteristic
51	C₄	—	148	2	no	—
52	C₄	D₂₉₆	1	1	yes	characteristic
53	C₄	C₂×D₁₄₈	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	296	2	no	—
56	C₂	C₂×D₂₉₆	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₂₉₆
commutator, cosocle	C₈×C₃₇	C₂³
Frattini	C₈	C₂²×D₃₇
Fitting	C₂×C₁₆×C₃₇	C₂
socle	C₂×C₃₇	C₂×D₈
hypercenter	C₂×C₁₆	D₃₇
hypocenter	C₃₇	#508
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
1. #11924558	C₂	semidirect
2. Dic₂₉₆	C₂	semidirect
3. #11924481	C₂	semidirect
4. D₅₉₂	C₂	semidirect
5. C₂×C₁₆×C₃₇	C₂	semidirect
29. C₃₇	#508	semidirect
34. C₂×C₁₆	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924558	2
Dic₂₉₆	2
#11924481	2
D₅₉₂	2
C₂×C₁₆×C₃₇	2
#508	37