Subgroups — C₂×#11924505 #14558019

Order 2368.

662 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊D₃₇	C₂	1	3	yes	maximal, complemented
2	#11924505	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₂²⋊Dic₃₇	C₂	1	3	yes	maximal, complemented
4	C₂⁵×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×C₃₇	—	2	12	no	—
6	C₂⁴×C₃₇	C₂²	1	3	yes	—
7	C₂⁴×C₃₇	C₂²	1	4	yes	complemented
8	C₂³×D₃₇	C₂²	1	1	yes	characteristic, complemented
9	C₂×C₂²⋊D₃₇	—	2	12	no	—
10	C₂×C₂²⋊D₃₇	C₂²	1	12	yes	complemented
11	C₂²×Dic₃₇	C₂²	1	3	yes	complemented
12	C₂²⋊Dic₃₇	C₂²	1	12	yes	complemented
13	C₂³×C₃₇	—	2	32	no	—
14	C₂³×C₃₇	—	2	12	no	—
15	C₂³×C₃₇	—	2	24	no	—
16	C₂³×C₃₇	D₄	1	12	yes	complemented
17	C₂³×C₃₇	C₂³	1	6	yes	—
18	C₂³×C₃₇	C₂³	1	1	yes	characteristic
19	C₂²×D₃₇	—	2	6	no	—
20	C₂²×D₃₇	C₂³	1	2	yes	complemented
21	C₂²⋊D₃₇	—	2	24	no	—
22	C₂×Dic₃₇	—	2	6	no	—
23	C₂×Dic₃₇	C₂³	1	6	yes	complemented
24	C₂²×C₃₇	—	2	32	no	—
25	C₂²×C₃₇	—	2	24	no	—
26	C₂²×C₃₇	—	2	12	no	—
27	C₂²×C₃₇	C₂×D₄	1	6	yes	—
28	C₂²×C₃₇	C₂×D₄	1	12	yes	complemented
29	C₂²×C₃₇	C₂⁴	1	1	yes	characteristic
30	C₂×D₃₇	—	2	6	no	—
31	C₂×D₃₇	—	4	4	no	—
32	Dic₃₇	—	2	6	no	—
33	C₂×C₃₇	—	2	12	no	—
34	C₂×C₃₇	#120	1	4	yes	complemented
35	C₂×C₃₇	C₂²×D₄	1	3	yes	—
36	D₃₇	—	4	2	no	—
37	C₂×#120	—	37	1	no	maximal, Sylow
38	C₃₇	C₂×#120	1	1	yes	characteristic, complemented, Sylow
39	C₂⁵	D₃₇	1	1	yes	characteristic, complemented
40	C₂²×D₄	—	37	3	no	—
41	#120	—	37	8	no	—
42	C₂×C₂²⋊C₄	—	37	3	no	—
43	C₂⁴	—	2	12	no	—
44	C₂⁴	—	37	1	no	—
45	C₂⁴	C₂×D₃₇	1	3	yes	—
46	C₂⁴	C₂×D₃₇	1	4	yes	complemented
47	C₂×D₄	—	37	12	no	—
48	C₂×D₄	—	74	12	no	—
49	C₂²×C₄	—	37	3	no	—
50	C₂²⋊C₄	—	37	12	no	—
51	C₂³	—	2	32	no	—
52	C₂³	—	2	12	no	—
53	C₂³	—	2	24	no	—
54	C₂³	—	37	2	no	—
55	C₂³	—	74	6	no	—
56	C₂³	C₂²⋊D₃₇	1	12	yes	complemented
57	C₂³	C₂²×D₃₇	1	6	yes	—
58	C₂³	C₂²×D₃₇	1	1	yes	characteristic
59	D₄	—	74	24	no	—
60	C₂×C₄	—	37	6	no	—
61	C₂×C₄	—	74	6	no	—
62	C₂²	—	2	32	no	—
63	C₂²	—	2	24	no	—
64	C₂²	—	2	12	no	—
65	C₂²	—	74	6	no	—
66	C₂²	—	148	4	no	—
67	C₂²	C₂×C₂²⋊D₃₇	1	6	yes	—
68	C₂²	C₂×C₂²⋊D₃₇	1	12	yes	complemented
69	C₂²	C₂³×D₃₇	1	1	yes	characteristic
70	C₄	—	74	6	no	—
71	C₂	—	2	12	no	—
72	C₂	—	148	2	no	—
73	C₂	#11924505	1	4	yes	direct product factor
74	C₂	C₂²×C₂²⋊D₃₇	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₃₇
commutator, cosocle	C₂²×C₃₇	C₂⁴
Frattini	C₂²	C₂³×D₃₇
Fitting	C₂⁵×C₃₇	C₂
socle	C₂³×C₃₇	C₂³
hypercenter	C₂⁵	D₃₇
hypocenter	C₃₇	C₂×#120
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊D₃₇	C₂	semidirect
2. #11924505	C₂	direct (N × H)
3. C₂×C₂²⋊Dic₃₇	C₂	semidirect
4. C₂⁵×C₃₇	C₂	semidirect
7. C₂⁴×C₃₇	C₂²	semidirect
8. C₂³×D₃₇	C₂²	semidirect
10. C₂×C₂²⋊D₃₇	C₂²	semidirect
11. C₂²×Dic₃₇	C₂²	semidirect
12. C₂²⋊Dic₃₇	C₂²	semidirect
16. C₂³×C₃₇	D₄	semidirect
20. C₂²×D₃₇	C₂³	semidirect
23. C₂×Dic₃₇	C₂³	semidirect
28. C₂²×C₃₇	C₂×D₄	semidirect
34. C₂×C₃₇	#120	semidirect
38. C₃₇	C₂×#120	semidirect
39. C₂⁵	D₃₇	semidirect
46. C₂⁴	C₂×D₃₇	semidirect
56. C₂³	C₂²⋊D₃₇	semidirect
68. C₂²	C₂×C₂²⋊D₃₇	semidirect
73. C₂	#11924505	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊D₃₇	2
#11924505	2
C₂×C₂²⋊Dic₃₇	2
C₂⁵×C₃₇	2
C₂×#120	37

Subgroups — C2×#11924505 #14558019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924505 #14558019