Subgroups — #17992797

Order 4736.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924442	C₂	1	1	yes	maximal, characteristic
2	#14557359	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#366	C₂	1	1	yes	maximal, characteristic
4	#11924470	—	2	1	no	—
5	#11924442	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
7	#107×C₃₇	—	2	1	no	—
8	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
9	C₄⋊C₄×C₃₇	—	4	1	no	—
10	C₄⋊Dic₃₇	—	4	1	no	—
11	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₃₇	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₃₇	—	8	1	no	—
14	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
15	C₂×Dic₃₇	—	8	1	no	—
16	C₈×C₃₇	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
18	C₂²×C₃₇	D₁₆	1	1	yes	characteristic
19	C₄×C₃₇	—	16	1	no	—
20	C₄×C₃₇	#107	1	1	yes	characteristic
21	C₄×C₃₇	Q₃₂	1	1	yes	characteristic
22	Dic₃₇	—	16	1	no	—
23	#1424	—	37	1	no	maximal, Sylow
24	C₂×C₃₇	#366	1	1	yes	characteristic
25	C₂×C₃₇	SD₆₄	1	1	yes	characteristic
26	C₂×C₃₇	SD₆₄	1	1	yes	characteristic
27	C₂×C₃₂	—	37	1	no	—
28	#366	—	37	1	no	—
29	#366	D₃₇	1	1	yes	characteristic
30	C₃₇	#1424	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	74	1	no	—
34	C₃₂	—	37	2	no	—
35	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	148	1	no	—
38	C₁₆	Dic₇₄	1	1	yes	characteristic
39	C₁₆	C₄×D₃₇	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	296	1	no	—
42	C₂×C₄	#10596939	1	1	yes	characteristic
43	C₈	#10596936	1	1	yes	characteristic
44	C₈	#10596942	1	1	yes	characteristic
45	C₂²	#11924477	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	592	1	no	—
48	C₄	#11924469	1	1	yes	characteristic
49	C₄	#11924482	1	1	yes	characteristic
50	C₂	#14557358	1	1	yes	characteristic
51	C₂	#14557370	1	1	yes	characteristic
52	C₂	#14557371	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11924477
commutator	C₁₆×C₃₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₃₇
Fitting	C₃₇×#366	C₂
socle, prime radical	C₂²×C₃₇	D₁₆
cosocle	C₂×C₁₆×C₃₇	C₂²
hypercenter	#366	D₃₇
hypocenter	C₃₇	#1424
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. #11924442	C₄	semidirect
30. C₃₇	#1424	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924442	2
#14557359	2
C₃₇×#366	2
#1424	37