Subgroups — C₂²×#10596953 #14558607

Order 2368.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596953	C₂	1	12	yes	maximal, direct product factor
2	C₂²×#64438	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂³×D₃₇	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₃₇	C₄	1	1	yes	characteristic
6	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₃₇	C₄	1	6	yes	—
8	C₂×C₄×D₃₇	C₂²	1	6	yes	—
9	C₂×#64438	C₂²	1	12	yes	complemented
10	#10596953	C₂²	1	16	yes	direct product factor
11	C₂³×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×D₃₇	—	2	4	no	—
13	C₂²×D₃₇	C₂×C₄	1	6	yes	—
14	C₂×C₄×C₃₇	C₂×C₄	1	6	yes	—
15	C₂×Dic₃₇	C₂×C₄	1	3	yes	—
16	C₂×Dic₃₇	C₂³	1	3	yes	—
17	C₄×D₃₇	C₂×C₄	1	12	yes	—
18	C₄×D₃₇	C₂³	1	4	yes	—
19	#64438	C₂³	1	8	yes	complemented
20	C₂²×C₃₇	M₁₆	1	4	yes	complemented
21	C₂²×C₃₇	C₂²×C₄	1	3	yes	—
22	C₂×D₃₇	—	2	12	no	—
23	C₂×D₃₇	C₂²×C₄	1	4	yes	—
24	C₄×C₃₇	C₂²×C₄	1	4	yes	—
25	Dic₃₇	C₂²×C₄	1	3	yes	—
26	Dic₃₇	C₂⁴	1	1	yes	characteristic
27	C₂×C₃₇	C₂×M₁₆	1	6	yes	complemented
28	C₂×C₃₇	C₂³×C₄	1	1	yes	characteristic
29	D₃₇	—	2	4	no	—
30	C₂²×M₁₆	—	37	1	no	maximal, Sylow
31	C₃₇	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
32	C₂³×C₄	—	37	1	no	—
33	C₂×M₁₆	—	37	12	no	—
34	C₂²×C₈	—	37	2	no	—
35	C₂⁴	—	37	1	no	—
36	C₂²×C₄	—	37	1	no	—
37	C₂²×C₄	—	37	6	no	—
38	C₂²×C₄	—	37	6	no	—
39	C₂²×C₄	#3866	1	1	yes	characteristic
40	M₁₆	—	37	16	no	—
41	C₂×C₈	—	37	12	no	—
42	C₂³	—	37	6	no	—
43	C₂³	—	74	4	no	—
44	C₂³	C₂×#3866	1	1	yes	characteristic
45	C₂×C₄	—	37	3	no	—
46	C₂×C₄	—	37	3	no	—
47	C₂×C₄	—	37	4	no	—
48	C₂×C₄	—	37	12	no	—
49	C₂×C₄	C₂×#3866	1	6	yes	—
50	C₈	—	37	8	no	—
51	C₂²	—	37	4	no	—
52	C₂²	—	74	12	no	—
53	C₂²	#10596953	1	4	yes	direct product factor
54	C₂²	C₂²×#3866	1	3	yes	—
55	C₄	—	37	1	no	—
56	C₄	—	37	3	no	—
57	C₄	C₂²×#3866	1	4	yes	—
58	C₂	—	74	4	no	—
59	C₂	C₂×#10596953	1	6	yes	direct product factor
60	C₂	C₂³×#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#3866
commutator	C₂×C₃₇	C₂³×C₄
Frattini	C₂	C₂³×#3866
Fitting	C₂²×C₄×C₃₇	C₄
socle	C₂³×C₃₇	C₂×C₄
prime radical	C₂³×D₃₇	C₄
cosocle	Dic₃₇	C₂⁴
hypercenter	C₂²×C₄	#3866
hypocenter	C₃₇	C₂²×M₁₆
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#10596953	C₂	direct (N × H)
2. C₂²×#64438	C₂	semidirect
9. C₂×#64438	C₂²	semidirect
10. #10596953	C₂²	direct (N × H)
19. #64438	C₂³	semidirect
20. C₂²×C₃₇	M₁₆	semidirect
27. C₂×C₃₇	C₂×M₁₆	semidirect
31. C₃₇	C₂²×M₁₆	semidirect
53. C₂²	#10596953	direct (N × H)
59. C₂	C₂×#10596953	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×#10596953	2
C₂²×#64438	2
C₂²×C₄×D₃₇	2
C₂²×M₁₆	37

Subgroups — C22×#10596953 #14558607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10596953 #14558607