Subgroups — C₂×#11924604 #14558541

Order 2368.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#3866	C₂	1	2	yes	maximal
2	#11924604	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#3866	—	2	2	no	—
5	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
6	C₄⋊#3866	—	2	2	no	—
7	C₄⋊#3866	C₂²	1	4	yes	—
8	C₂×C₈×C₃₇	C₄	1	1	yes	characteristic, complemented
9	C₂×#64436	C₄	1	1	yes	characteristic, complemented
10	C₈×D₃₇	C₄	1	2	yes	complemented
11	C₈×D₃₇	C₂²	1	2	yes	—
12	C₂²×D₃₇	D₄	1	1	yes	characteristic
13	C₂×#3866	—	2	4	no	—
14	C₂×#3866	—	4	4	no	—
15	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₃₇	Q₈	1	1	yes	characteristic
17	C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
18	C₄×D₃₇	D₄	1	1	yes	characteristic
19	C₄×D₃₇	Q₈	1	1	yes	characteristic
20	C₄×D₃₇	C₂³	1	1	yes	characteristic
21	C₈×C₃₇	C₂×C₄	1	2	yes	complemented
22	#64436	C₂×C₄	1	2	yes	complemented
23	C₂²×C₃₇	C₄⋊C₄	1	1	yes	characteristic
24	C₂×D₃₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₃₇	SD₁₆	1	4	yes	—
26	C₂×D₃₇	C₂×D₄	1	1	yes	characteristic
27	#3866	—	4	4	no	—
28	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
29	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
30	Dic₃₇	C₄⋊C₄	1	1	yes	characteristic
31	Dic₃₇	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₃₇	#106	1	2	yes	complemented
33	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
34	D₃₇	#106	1	2	yes	complemented
35	D₃₇	C₂×SD₁₆	1	2	yes	—
36	C₂×#106	—	37	1	no	maximal, Sylow
37	C₃₇	C₂×#106	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₈	—	37	1	no	—
39	C₂×C₄⋊C₄	—	37	2	no	—
40	#106	—	37	4	no	—
41	C₂²×C₄	—	37	1	no	—
42	C₂²×C₄	—	74	2	no	—
43	C₂×C₈	—	37	1	no	—
44	C₂×C₈	—	37	2	no	—
45	C₂×C₈	—	37	2	no	—
46	C₂×C₈	#3866	1	1	yes	characteristic, complemented
47	C₄⋊C₄	—	37	4	no	—
48	C₄⋊C₄	—	74	2	no	—
49	C₂³	—	37	1	no	—
50	C₂×C₄	—	37	1	no	—
51	C₂×C₄	—	37	1	no	—
52	C₂×C₄	—	37	1	no	—
53	C₂×C₄	—	37	1	no	—
54	C₂×C₄	—	37	1	no	—
55	C₂×C₄	—	74	4	no	—
56	C₂×C₄	—	148	4	no	—
57	C₂×C₄	C₂×#3866	1	1	yes	characteristic
58	C₈	—	37	2	no	—
59	C₈	C₂×#3866	1	2	yes	complemented
60	C₂²	—	37	4	no	—
61	C₂²	—	37	1	no	—
62	C₂²	—	37	1	no	—
63	C₂²	C₄⋊#3866	1	1	yes	characteristic
64	C₄	—	37	1	no	—
65	C₄	—	37	1	no	—
66	C₄	—	148	4	no	—
67	C₄	C₄⋊#3866	1	1	yes	characteristic
68	C₄	C₂²×#3866	1	1	yes	characteristic
69	C₂	—	37	2	no	—
70	C₂	—	37	2	no	—
71	C₂	#11924604	1	2	yes	direct product factor
72	C₂	C₂×C₄⋊#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#3866
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₄	C₂²×#3866
Fitting	C₂×C₈×C₃₇	C₄
socle	C₂²×C₃₇	C₄⋊C₄
prime radical	C₂²×D₃₇	D₄
cosocle	C₄×D₃₇	C₂³
hypercenter	C₂×C₈	#3866
hypocenter	C₃₇	C₂×#106
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #11924604	C₂	direct (N × H)
8. C₂×C₈×C₃₇	C₄	semidirect
9. C₂×#64436	C₄	semidirect
10. C₈×D₃₇	C₄	semidirect
21. C₈×C₃₇	C₂×C₄	semidirect
22. #64436	C₂×C₄	semidirect
32. C₂×C₃₇	#106	semidirect
34. D₃₇	#106	semidirect
37. C₃₇	C₂×#106	semidirect
46. C₂×C₈	#3866	semidirect
59. C₈	C₂×#3866	semidirect
71. C₂	#11924604	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⋊#3866	2
#11924604	2
C₂×C₈×D₃₇	2
C₂×#106	37

Subgroups — C2×#11924604 #14558541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924604 #14558541