Subgroups — #14557339

Order 2368.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924558	C₂	1	1	yes	maximal, characteristic
2	C₂×#10596925	C₂	1	1	yes	maximal, characteristic, complemented
3	#108×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#10596962	—	2	1	no	—
5	M₁₆×C₃₇	—	2	1	no	—
6	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
7	Dic₁₄₈	C₄	1	1	yes	characteristic
8	D₂₉₆	C₄	1	1	yes	characteristic
9	#10596930	—	2	1	no	—
10	#10596925	—	2	1	no	—
11	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
12	C₂²⋊D₃₇	—	4	1	no	—
13	D₁₄₈	—	2	1	no	—
14	C₄×D₃₇	—	4	1	no	—
15	Dic₇₄	—	2	1	no	—
16	C₈×C₃₇	—	4	1	no	—
17	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₈×C₃₇	D₄	1	1	yes	characteristic
19	C₂²×C₃₇	SD₁₆	1	1	yes	characteristic
20	C₂×D₃₇	—	4	1	no	—
21	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₃₇	D₈	1	1	yes	characteristic
23	Dic₃₇	—	4	1	no	—
24	C₂×C₃₇	—	2	1	no	—
25	C₂×C₃₇	#102	1	1	yes	characteristic
26	D₃₇	—	8	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	D₃₇	1	1	yes	characteristic, complemented
32	#41	—	74	1	no	—
33	Q₁₆	—	37	1	no	—
34	SD₁₆	—	74	1	no	—
35	D₈	—	37	1	no	—
36	M₁₆	—	2	1	no	—
37	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
38	C₁₆	—	74	1	no	—
39	Q₈	—	74	1	no	—
40	D₄	—	74	1	no	—
41	D₄	—	148	1	no	—
42	C₂×C₄	—	148	1	no	—
43	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
44	C₈	—	4	1	no	—
45	C₈	C₄×D₃₇	1	1	yes	characteristic
46	C₈	D₁₄₈	1	1	yes	characteristic
47	C₂²	—	148	1	no	—
48	C₂²	#10596941	1	1	yes	characteristic
49	C₄	—	148	1	no	—
50	C₄	#10596938	1	1	yes	characteristic
51	C₄	#10596939	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	296	1	no	—
54	C₂	#11924456	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10596939
commutator	C₈×C₃₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₃₇
Fitting	#108×C₃₇	C₂
socle	C₂×C₃₇	#102
prime radical	#11924558	C₂
cosocle	C₂×C₈×C₃₇	C₂²
hypercenter	#108	D₃₇
hypocenter	C₃₇	#359
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×#10596925	C₂	semidirect
3. #108×C₃₇	C₂	semidirect
28. C₃₇	#359	semidirect
31. #108	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
C₂×#10596925	2
#108×C₃₇	2
#359	37