Subgroups — C₂×#11924476 #14557948

Order 2368.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924476	C₂	1	4	yes	maximal, direct product factor
2	C₂×#10596925	C₂	1	2	yes	maximal, complemented
3	C₂²×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₃₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₃₇	C₄	1	1	yes	characteristic
6	C₂×C₈×C₃₇	C₄	1	2	yes	—
7	C₂×C₈×C₃₇	C₂²	1	2	yes	—
8	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	#10596925	C₂²	1	4	yes	complemented
10	C₂³×C₃₇	C₈	1	1	yes	characteristic
11	C₂×C₄×C₃₇	C₈	1	2	yes	—
12	C₂×C₄×C₃₇	C₈	1	1	yes	characteristic
13	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₈×C₃₇	C₂×C₄	1	2	yes	—
16	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₈×C₃₇	C₂³	1	1	yes	characteristic
18	C₂²×C₃₇	—	2	2	no	—
19	C₂²×C₃₇	C₂×C₈	1	2	yes	—
20	C₂²×C₃₇	C₂×C₈	1	1	yes	characteristic
21	C₄×C₃₇	C₂×C₈	1	2	yes	—
22	C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
23	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₃₇	—	2	2	no	—
25	C₂×C₃₇	M₃₂	1	2	yes	complemented
26	C₂×C₃₇	C₂²×C₈	1	1	yes	characteristic
27	C₂×M₃₂	—	37	1	no	maximal, Sylow
28	C₃₇	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₈	D₃₇	1	1	yes	characteristic
30	M₃₂	—	37	4	no	—
31	C₂×C₁₆	—	37	2	no	—
32	C₂²×C₄	Dic₃₇	1	1	yes	characteristic
33	C₂×C₈	Dic₃₇	1	1	yes	characteristic
34	C₂×C₈	Dic₃₇	1	2	yes	—
35	C₂×C₈	C₂×D₃₇	1	2	yes	—
36	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
37	C₁₆	—	37	4	no	—
38	C₂³	#64436	1	1	yes	characteristic
39	C₂×C₄	#64436	1	2	yes	—
40	C₂×C₄	#64436	1	1	yes	characteristic
41	C₂×C₄	C₂×Dic₃₇	1	2	yes	—
42	C₂×C₄	C₂×Dic₃₇	1	1	yes	characteristic
43	C₈	C₂×Dic₃₇	1	2	yes	—
44	C₈	C₂×Dic₃₇	1	1	yes	characteristic
45	C₈	C₂²×D₃₇	1	1	yes	characteristic
46	C₂²	—	2	2	no	—
47	C₂²	C₂×#64436	1	2	yes	—
48	C₂²	C₂×#64436	1	1	yes	characteristic
49	C₄	C₂×#64436	1	2	yes	—
50	C₄	C₂×#64436	1	1	yes	characteristic
51	C₄	C₂²×Dic₃₇	1	1	yes	characteristic
52	C₂	—	2	2	no	—
53	C₂	#11924476	1	2	yes	direct product factor
54	C₂	C₂²×#64436	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃₇
commutator	C₂×C₃₇	C₂²×C₈
Frattini	C₈	C₂²×D₃₇
Fitting	C₂²×C₈×C₃₇	C₂
socle	C₂²×C₃₇	C₂×C₈
prime radical	C₂³×C₃₇	C₈
cosocle	C₈×C₃₇	C₂³
hypercenter	C₂²×C₈	D₃₇
hypocenter	C₃₇	C₂×M₃₂
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. #11924476	C₂	direct (N × H)
2. C₂×#10596925	C₂	semidirect
9. #10596925	C₂²	semidirect
25. C₂×C₃₇	M₃₂	semidirect
28. C₃₇	C₂×M₃₂	semidirect
53. C₂	#11924476	direct (N × H)

Maximal subgroups

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

subgroup	index
#11924476	2
C₂×#10596925	2
C₂²×C₈×C₃₇	2
C₂×M₃₂	37

Subgroups — C2×#11924476 #14557948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924476 #14557948