Subgroups — C₂×#11924468 #14557564

Order 2368.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₃₇	C₂	1	2	yes	maximal
2	#11924468	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₃₇	—	2	2	no	—
6	C₂×C₈×C₃₇	C₄	1	4	yes	complemented
7	C₂×C₈×C₃₇	C₂²	1	2	yes	—
8	C₄⋊Dic₃₇	—	2	2	no	—
9	C₄⋊Dic₃₇	C₂²	1	4	yes	—
10	C₂³×C₃₇	D₄	1	1	yes	characteristic
11	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
13	C₂×C₄×C₃₇	Q₈	1	2	yes	—
14	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
15	C₂×Dic₃₇	—	2	4	no	—
16	C₂×Dic₃₇	—	4	4	no	—
17	C₈×C₃₇	C₂×C₄	1	4	yes	complemented
18	C₂²×C₃₇	C₄⋊C₄	1	2	yes	—
19	C₂²×C₃₇	SD₁₆	1	4	yes	—
20	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
21	C₄×C₃₇	C₄⋊C₄	1	2	yes	—
22	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
24	Dic₃₇	—	4	4	no	—
25	C₂×C₃₇	#106	1	4	yes	complemented
26	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₃₇	C₂×SD₁₆	1	2	yes	—
28	C₂×#106	—	37	1	no	maximal, Sylow
29	C₃₇	C₂×#106	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₈	D₃₇	1	1	yes	characteristic
31	C₂×C₄⋊C₄	—	37	2	no	—
32	#106	—	37	4	no	—
33	C₂²×C₄	—	74	2	no	—
34	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
35	C₂×C₈	Dic₃₇	1	4	yes	complemented
36	C₂×C₈	C₂×D₃₇	1	2	yes	—
37	C₄⋊C₄	—	37	4	no	—
38	C₄⋊C₄	—	74	2	no	—
39	C₂³	D₁₄₈	1	1	yes	characteristic
40	C₂×C₄	—	74	4	no	—
41	C₂×C₄	—	148	4	no	—
42	C₂×C₄	Dic₇₄	1	2	yes	—
43	C₂×C₄	D₁₄₈	1	1	yes	characteristic
44	C₂×C₄	C₂×Dic₃₇	1	2	yes	—
45	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
46	C₈	C₂×Dic₃₇	1	4	yes	complemented
47	C₂²	#10596930	1	4	yes	—
48	C₂²	C₄⋊Dic₃₇	1	2	yes	—
49	C₂²	C₂×D₁₄₈	1	1	yes	characteristic
50	C₄	—	148	4	no	—
51	C₄	C₄⋊Dic₃₇	1	2	yes	—
52	C₄	C₂×Dic₇₄	1	1	yes	characteristic
53	C₄	C₂²×Dic₃₇	1	1	yes	characteristic
54	C₂	#11924468	1	4	yes	direct product factor
55	C₂	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
56	C₂	C₂×#10596930	1	2	yes	—

	subgroup	G/H
center	C₂³	D₁₄₈
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₂²×C₈×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	D₄
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	C₂²×C₈	D₃₇
hypocenter	C₃₇	C₂×#106
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #11924468	C₂	direct (N × H)
6. C₂×C₈×C₃₇	C₄	semidirect
17. C₈×C₃₇	C₂×C₄	semidirect
25. C₂×C₃₇	#106	semidirect
29. C₃₇	C₂×#106	semidirect
35. C₂×C₈	Dic₃₇	semidirect
46. C₈	C₂×Dic₃₇	semidirect
54. C₂	#11924468	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×C₄⋊Dic₃₇	2
#11924468	2
C₂²×C₈×C₃₇	2
C₂×#106	37

Subgroups — C2×#11924468 #14557564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924468 #14557564