Subgroups — C₃₇×#7546 #22628799

Order 9472.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#1423	C₂	1	2	yes	maximal
3	C₂×C₃₂×C₃₇	C₂²	1	1	yes	characteristic
4	C₃₇×#366	—	2	2	no	—
5	C₃₇×C₆₄	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₃₇	D₄	1	1	yes	characteristic
7	#107×C₃₇	—	4	2	no	—
8	C₃₂×C₃₇	C₂×C₄	1	1	yes	characteristic
9	C₃₂×C₃₇	Q₈	1	1	yes	characteristic
10	C₂×C₈×C₃₇	D₈	1	1	yes	characteristic
11	C₄⋊C₄×C₃₇	—	8	2	no	—
12	C₁₆×C₃₇	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆×C₃₇	Q₁₆	1	1	yes	characteristic
14	C₂×C₄×C₃₇	—	16	2	no	—
15	C₂×C₄×C₃₇	D₁₆	1	1	yes	characteristic
16	C₈×C₃₇	#107	1	1	yes	characteristic
17	C₈×C₃₇	Q₃₂	1	1	yes	characteristic
18	#7546	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₃₇	D₃₂	1	1	yes	characteristic
20	C₄×C₃₇	—	32	2	no	—
21	C₄×C₃₇	#366	1	1	yes	characteristic
22	C₄×C₃₇	Q₆₄	1	1	yes	characteristic
23	C₂×C₆₄	C₂×C₃₇	1	1	yes	characteristic
24	#1423	C₂×C₃₇	1	2	yes	—
25	C₂×C₃₇	#1423	1	1	yes	characteristic
26	C₂×C₃₇	SD₁₂₈	1	2	yes	—
27	C₂×C₃₂	C₂²×C₃₇	1	1	yes	characteristic
28	#366	—	2	2	no	—
29	C₆₄	C₄×C₃₇	1	2	yes	complemented
30	C₃₇	#7546	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₁₆	D₄×C₃₇	1	1	yes	characteristic
32	#107	—	4	2	no	—
33	C₃₂	C₂×C₄×C₃₇	1	1	yes	characteristic
34	C₃₂	Q₈×C₃₇	1	1	yes	characteristic
35	C₂×C₈	D₈×C₃₇	1	1	yes	characteristic
36	C₄⋊C₄	—	8	2	no	—
37	C₁₆	C₄⋊C₄×C₃₇	1	1	yes	characteristic
38	C₁₆	Q₁₆×C₃₇	1	1	yes	characteristic
39	C₂×C₄	—	16	2	no	—
40	C₂×C₄	D₁₆×C₃₇	1	1	yes	characteristic
41	C₈	#107×C₃₇	1	1	yes	characteristic
42	C₈	Q₃₂×C₃₇	1	1	yes	characteristic
43	C₂²	C₃₇×D₃₂	1	1	yes	characteristic
44	C₄	—	32	2	no	—
45	C₄	C₃₇×#366	1	1	yes	characteristic
46	C₄	C₃₇×Q₆₄	1	1	yes	characteristic
47	C₂	C₃₇×#1423	1	1	yes	characteristic
48	C₂	C₃₇×SD₁₂₈	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₇	D₃₂
commutator	C₃₂	C₂×C₄×C₃₇
Frattini, cosocle	C₂×C₃₂	C₂²×C₃₇
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄×C₃₇ ◁ C₂×C₈×C₃₇ ◁ C₂×C₁₆×C₃₇ ◁ C₂×C₃₂×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₃₇×C₆₄	C₄	semidirect
18. #7546	C₃₇	direct (N × H)
29. C₆₄	C₄×C₃₇	semidirect
30. C₃₇	#7546	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₇×C₆₄	2
C₃₇×#1423	2
#7546	37

Subgroups — C37×#7546 #22628799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#7546 #22628799