Subgroups — #14557351

Order 2368.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596925	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
5	C₄×Dic₃₇	C₄	1	1	yes	characteristic
6	C₂×#64436	C₄	1	1	yes	characteristic
7	C₁₆×C₃₇	—	2	1	no	—
8	#10596925	—	2	1	no	—
9	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₃₇	C₈	1	1	yes	characteristic
11	C₂×Dic₃₇	C₈	1	1	yes	characteristic
12	C₈×C₃₇	D₄	1	1	yes	characteristic
13	C₈×C₃₇	Q₈	1	1	yes	characteristic
14	#64436	—	2	1	no	—
15	C₂²×C₃₇	C₂×C₈	1	1	yes	characteristic
16	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₃₇	M₁₆	1	1	yes	characteristic
18	Dic₃₇	—	2	1	no	—
19	Dic₃₇	C₁₆	1	2	yes	complemented
20	C₂×C₃₇	C₄⋊C₈	1	1	yes	characteristic
21	C₂×C₃₇	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₃₇	M₃₂	1	1	yes	characteristic
23	C₄⋊C₁₆	—	37	1	no	maximal, Sylow
24	C₃₇	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₆	—	37	1	no	—
26	C₂×C₁₆	D₃₇	1	1	yes	characteristic
27	C₄×C₈	—	37	1	no	—
28	C₂×C₈	—	37	1	no	—
29	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
30	C₄²	—	37	1	no	—
31	C₁₆	—	2	1	no	—
32	C₁₆	—	74	1	no	—
33	C₂×C₄	—	37	1	no	—
34	C₂×C₄	—	37	1	no	—
35	C₂×C₄	C₄×D₃₇	1	1	yes	characteristic
36	C₈	—	74	1	no	—
37	C₈	Dic₇₄	1	1	yes	characteristic
38	C₈	C₂²⋊D₃₇	1	1	yes	characteristic
39	C₂²	C₈×D₃₇	1	1	yes	characteristic
40	C₄	—	37	2	no	—
41	C₄	—	74	1	no	—
42	C₄	#10596929	1	1	yes	characteristic
43	C₄	#10596936	1	1	yes	characteristic
44	C₂	#11924465	1	1	yes	characteristic
45	C₂	C₁₆×D₃₇	1	1	yes	characteristic
46	C₂	#11924475	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₃₇
commutator	C₂×C₃₇	C₂×C₁₆
Fitting	C₂×C₁₆×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×C₈
cosocle	C₂×C₈×C₃₇	C₂²
hypercenter	C₂×C₁₆	D₃₇
hypocenter	C₃₇	C₄⋊C₁₆
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
19. Dic₃₇	C₁₆	semidirect
24. C₃₇	C₄⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596925	2
C₈×Dic₃₇	2
C₂×C₁₆×C₃₇	2
C₄⋊C₁₆	37