Subgroups — C₂²×#10596964 #14558359

Order 2368.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596964	C₂	1	24	yes	maximal, direct product factor
2	C₂²×Dic₇₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂²⋊D₃₇	C₂	1	2	yes	maximal, complemented
4	C₂³×Dic₃₇	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁴×C₃₇	C₂²	1	2	yes	—
8	C₂³×D₃₇	C₂²	1	1	yes	characteristic
9	C₂×D₄×C₃₇	C₂²	1	12	yes	complemented
10	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊D₃₇	C₂²	1	24	yes	complemented
12	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
13	C₂²×Dic₃₇	C₂²	1	2	yes	—
14	C₂²×Dic₃₇	C₂²	1	24	yes	complemented
15	#10596964	C₂²	1	64	yes	direct product factor
16	C₂×C₄×D₃₇	C₂²	1	12	yes	complemented
17	C₂×Dic₇₄	C₂²	1	12	yes	complemented
18	C₂³×C₃₇	—	2	8	no	—
19	C₂³×C₃₇	C₂³	1	12	yes	—
20	C₂³×C₃₇	C₂³	1	1	yes	characteristic
21	C₂²×D₃₇	—	2	4	no	—
22	C₂²×D₃₇	C₂³	1	6	yes	—
23	D₄×C₃₇	C₂³	1	16	yes	complemented
24	C₂×C₄×C₃₇	C₂³	1	6	yes	—
25	C₂²⋊D₃₇	C₂³	1	32	yes	complemented
26	C₂×Dic₃₇	C₂³	1	12	yes	—
27	C₂×Dic₃₇	C₂³	1	6	yes	—
28	C₂×Dic₃₇	C₂³	1	32	yes	complemented
29	C₄×D₃₇	C₂³	1	16	yes	complemented
30	Dic₇₄	C₂³	1	16	yes	complemented
31	C₂²×C₃₇	—	2	24	no	—
32	C₂²×C₃₇	#41	1	4	yes	complemented
33	C₂²×C₃₇	C₂⁴	1	8	yes	—
34	C₂²×C₃₇	C₂⁴	1	3	yes	—
35	C₂×D₃₇	—	2	12	no	—
36	C₂×D₃₇	C₂⁴	1	4	yes	—
37	C₄×C₃₇	C₂⁴	1	4	yes	—
38	Dic₃₇	C₂⁴	1	8	yes	—
39	Dic₃₇	C₂⁴	1	4	yes	—
40	C₂×C₃₇	—	2	8	no	—
41	C₂×C₃₇	C₂×#41	1	6	yes	complemented
42	C₂×C₃₇	C₂⁵	1	1	yes	characteristic
43	D₃₇	—	2	4	no	—
44	C₂²×#41	—	37	1	no	maximal, Sylow
45	C₃₇	C₂²×#41	1	1	yes	characteristic, complemented, Sylow
46	C₂×#41	—	37	24	no	—
47	C₂²×Q₈	—	37	1	no	—
48	C₂²×D₄	—	37	2	no	—
49	C₂²×D₄	D₃₇	1	1	yes	characteristic, complemented
50	C₂³×C₄	—	37	2	no	—
51	C₂³×C₄	—	37	1	no	—
52	C₂⁴	—	37	1	no	—
53	C₂⁴	C₂×D₃₇	1	2	yes	—
54	#41	—	37	64	no	—
55	C₂×Q₈	—	37	12	no	—
56	C₂×D₄	—	37	24	no	—
57	C₂×D₄	C₂×D₃₇	1	12	yes	complemented
58	C₂²×C₄	—	37	24	no	—
59	C₂²×C₄	—	37	1	no	—
60	C₂²×C₄	—	37	2	no	—
61	C₂²×C₄	—	37	12	no	—
62	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
63	C₂³	—	2	8	no	—
64	C₂³	—	37	6	no	—
65	C₂³	—	74	4	no	—
66	C₂³	C₂²×D₃₇	1	12	yes	—
67	C₂³	C₂²×D₃₇	1	1	yes	characteristic
68	Q₈	—	37	16	no	—
69	D₄	—	37	32	no	—
70	D₄	C₂²×D₃₇	1	16	yes	complemented
71	C₂×C₄	—	37	6	no	—
72	C₂×C₄	—	37	12	no	—
73	C₂×C₄	—	37	32	no	—
74	C₂×C₄	—	37	16	no	—
75	C₂×C₄	C₂²×D₃₇	1	6	yes	—
76	C₂²	—	2	24	no	—
77	C₂²	—	37	4	no	—
78	C₂²	—	74	12	no	—
79	C₂²	#10596964	1	4	yes	direct product factor
80	C₂²	C₂³×D₃₇	1	8	yes	—
81	C₂²	C₂³×D₃₇	1	3	yes	—
82	C₄	—	37	4	no	—
83	C₄	—	37	8	no	—
84	C₄	C₂³×D₃₇	1	4	yes	—
85	C₂	—	2	8	no	—
86	C₂	—	74	4	no	—
87	C₂	C₂×#10596964	1	6	yes	direct product factor
88	C₂	C₂⁴×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃₇
commutator, cosocle	C₂×C₃₇	C₂⁵
Frattini	C₂	C₂⁴×D₃₇
Fitting	C₂²×D₄×C₃₇	C₂
socle	C₂³×C₃₇	C₂³
hypercenter	C₂²×D₄	D₃₇
hypocenter	C₃₇	C₂²×#41
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#10596964	C₂	direct (N × H)
2. C₂²×Dic₇₄	C₂	semidirect
3. C₂²×C₂²⋊D₃₇	C₂	semidirect
4. C₂³×Dic₃₇	C₂	semidirect
5. C₂²×C₄×D₃₇	C₂	semidirect
6. C₂²×D₄×C₃₇	C₂	semidirect
9. C₂×D₄×C₃₇	C₂²	semidirect
11. C₂×C₂²⋊D₃₇	C₂²	semidirect
14. C₂²×Dic₃₇	C₂²	semidirect
15. #10596964	C₂²	direct (N × H)
16. C₂×C₄×D₃₇	C₂²	semidirect
17. C₂×Dic₇₄	C₂²	semidirect
23. D₄×C₃₇	C₂³	semidirect
25. C₂²⋊D₃₇	C₂³	semidirect
28. C₂×Dic₃₇	C₂³	semidirect
29. C₄×D₃₇	C₂³	semidirect
30. Dic₇₄	C₂³	semidirect
32. C₂²×C₃₇	#41	semidirect
41. C₂×C₃₇	C₂×#41	semidirect
45. C₃₇	C₂²×#41	semidirect
49. C₂²×D₄	D₃₇	semidirect
57. C₂×D₄	C₂×D₃₇	semidirect
70. D₄	C₂²×D₃₇	semidirect
79. C₂²	#10596964	direct (N × H)
87. C₂	C₂×#10596964	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×#10596964	2
C₂²×Dic₇₄	2
C₂²×C₂²⋊D₃₇	2
C₂³×Dic₃₇	2
C₂²×C₄×D₃₇	2
C₂²×D₄×C₃₇	2
C₂²×#41	37

Subgroups — C22×#10596964 #14558359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10596964 #14558359