Subgroups — C₂²×#11924442 #17996885

Order 4736.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924442	C₂	1	6	yes	maximal, direct product factor
2	C₂²×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
3	#11924442	C₂²	1	4	yes	direct product factor
4	C₂²×C₈×C₃₇	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₃₇	C₄	1	3	yes	—
6	C₂×C₁₆×C₃₇	C₂²	1	3	yes	—
7	C₂²×C₄×C₃₇	C₈	1	1	yes	characteristic
8	C₂×C₈×C₃₇	C₈	1	3	yes	—
9	C₂×C₈×C₃₇	C₂×C₄	1	3	yes	—
10	C₁₆×C₃₇	C₂×C₄	1	3	yes	—
11	C₁₆×C₃₇	C₂³	1	1	yes	characteristic
12	C₂³×C₃₇	C₁₆	1	1	yes	characteristic
13	C₂×C₄×C₃₇	C₁₆	1	3	yes	—
14	C₂×C₄×C₃₇	C₂×C₈	1	3	yes	—
15	C₈×C₃₇	C₂×C₈	1	3	yes	—
16	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
17	C₂²×C₃₇	C₃₂	1	4	yes	complemented
18	C₂²×C₃₇	C₂×C₁₆	1	3	yes	—
19	C₄×C₃₇	C₂×C₁₆	1	3	yes	—
20	C₄×C₃₇	C₂²×C₈	1	1	yes	characteristic
21	C₂²×C₃₂	—	37	1	no	maximal, Sylow
22	C₂×C₃₇	C₂×C₃₂	1	6	yes	complemented
23	C₂×C₃₇	C₂²×C₁₆	1	1	yes	characteristic
24	C₂²×C₁₆	D₃₇	1	1	yes	characteristic
25	C₂×C₃₂	—	37	6	no	—
26	C₃₇	C₂²×C₃₂	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₈	Dic₃₇	1	1	yes	characteristic
28	C₂×C₁₆	Dic₃₇	1	3	yes	—
29	C₂×C₁₆	C₂×D₃₇	1	3	yes	—
30	C₃₂	—	37	4	no	—
31	C₂²×C₄	#64436	1	1	yes	characteristic
32	C₂×C₈	#64436	1	3	yes	—
33	C₂×C₈	C₂×Dic₃₇	1	3	yes	—
34	C₁₆	C₂×Dic₃₇	1	3	yes	—
35	C₁₆	C₂²×D₃₇	1	1	yes	characteristic
36	C₂³	#10596925	1	1	yes	characteristic
37	C₂×C₄	#10596925	1	3	yes	—
38	C₂×C₄	C₂×#64436	1	3	yes	—
39	C₈	C₂×#64436	1	3	yes	—
40	C₈	C₂²×Dic₃₇	1	1	yes	characteristic
41	C₂²	#11924442	1	4	yes	direct product factor
42	C₂²	C₂×#10596925	1	3	yes	—
43	C₄	C₂×#10596925	1	3	yes	—
44	C₄	C₂²×#64436	1	1	yes	characteristic
45	C₂	C₂×#11924442	1	6	yes	direct product factor
46	C₂	C₂²×#10596925	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₁₆	D₃₇
commutator, hypocenter	C₃₇	C₂²×C₃₂
Frattini	C₁₆	C₂²×D₃₇
Fitting	C₂²×C₁₆×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	C₁₆
cosocle	C₁₆×C₃₇	C₂³
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#11924442	C₂	direct (N × H)
3. #11924442	C₂²	direct (N × H)
17. C₂²×C₃₇	C₃₂	semidirect
22. C₂×C₃₇	C₂×C₃₂	semidirect
26. C₃₇	C₂²×C₃₂	semidirect
41. C₂²	#11924442	direct (N × H)
45. C₂	C₂×#11924442	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×#11924442	2
C₂²×C₁₆×C₃₇	2
C₂²×C₃₂	37

Subgroups — C22×#11924442 #17996885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11924442 #17996885