Subgroups — C₃₂×#3866 #18009699

Order 4736.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₆×#3866	C₂	1	1	yes	maximal, characteristic
3	C₃₂×D₃₇	C₂	1	1	yes	maximal, characteristic
4	D₃₇⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×#3866	C₄	1	1	yes	characteristic
6	#11924586	C₄	1	2	yes	complemented
7	C₁₆×D₃₇	C₂²	1	1	yes	characteristic
8	#11924442	C₄	1	1	yes	characteristic, complemented
9	C₃₂×C₃₇	C₄	1	1	yes	characteristic, complemented
10	C₄×#3866	C₈	1	1	yes	characteristic
11	D₃₇⋊C₈	C₈	1	1	yes	characteristic
12	C₈×D₃₇	C₂×C₄	1	1	yes	characteristic
13	#10596927	C₈	1	2	yes	—
14	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
15	#10596925	C₂×C₄	1	1	yes	characteristic
16	C₂×#3866	C₁₆	1	2	yes	—
17	C₄×D₃₇	C₂×C₈	1	1	yes	characteristic
18	#64438	C₁₆	1	2	yes	—
19	C₈×C₃₇	C₄²	1	1	yes	characteristic
20	#64436	C₂×C₈	1	1	yes	characteristic
21	C₂×D₃₇	C₂×C₁₆	1	1	yes	characteristic
22	#3866	C₃₂	1	4	yes	direct product factor
23	C₄×C₃₇	C₄×C₈	1	1	yes	characteristic
24	Dic₃₇	C₂×C₁₆	1	1	yes	characteristic
25	C₄×C₃₂	—	37	1	no	maximal, Sylow
26	C₂×C₃₇	C₄×C₁₆	1	1	yes	characteristic
27	D₃₇	C₂×C₃₂	1	2	yes	—
28	C₂×C₃₂	—	37	1	no	—
29	C₂×C₃₂	—	37	1	no	—
30	C₄×C₁₆	—	37	1	no	—
31	C₃₇	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₁₆	—	37	1	no	—
33	C₂×C₁₆	—	37	1	no	—
34	C₄×C₈	—	37	1	no	—
35	C₃₂	—	37	2	no	—
36	C₃₂	—	37	1	no	—
37	C₃₂	#3866	1	1	yes	characteristic, direct product factor
38	C₂×C₈	—	37	1	no	—
39	C₂×C₈	—	37	1	no	—
40	C₄²	—	37	1	no	—
41	C₁₆	—	37	2	no	—
42	C₁₆	—	37	1	no	—
43	C₁₆	C₂×#3866	1	1	yes	characteristic
44	C₂×C₄	—	37	2	no	—
45	C₂×C₄	—	37	1	no	—
46	C₈	—	37	2	no	—
47	C₈	—	37	1	no	—
48	C₈	C₄×#3866	1	1	yes	characteristic
49	C₂²	—	37	1	no	—
50	C₄	—	37	4	no	—
51	C₄	—	37	1	no	—
52	C₄	C₈×#3866	1	1	yes	characteristic
53	C₂	—	37	2	no	—
54	C₂	C₁₆×#3866	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃₂	#3866
commutator, hypocenter	C₃₇	C₄×C₃₂
Frattini	C₁₆	C₂×#3866
Fitting	C₃₂×C₃₇	C₄
socle	C₂×C₃₇	C₄×C₁₆
prime radical	C₂×D₃₇	C₂×C₁₆
cosocle	C₁₆×D₃₇	C₂²
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
6. #11924586	C₄	semidirect
8. #11924442	C₄	semidirect
9. C₃₂×C₃₇	C₄	semidirect
22. #3866	C₃₂	direct (N × H)
31. C₃₇	C₄×C₃₂	semidirect
37. C₃₂	#3866	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃₇⋊C₃₂	2
C₁₆×#3866	2
C₃₂×D₃₇	2
C₄×C₃₂	37

Subgroups — C32×#3866 #18009699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₂×#3866 #18009699