Subgroups — C₂×#14557401 #17996986

Order 4736.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557401	C₂	1	8	yes	maximal, direct product factor
2	C₂×#11924443	C₂	1	6	yes	maximal
3	C₂²×C₄²×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₃₇	C₂²	1	4	yes	—
5	#11924443	C₂²	1	24	yes	—
6	C₂³×C₄×C₃₇	C₂²	1	3	yes	—
7	C₂×C₄²×C₃₇	C₄	1	8	yes	complemented
8	C₂×C₄²×C₃₇	C₂²	1	4	yes	—
9	C₂⁴×C₃₇	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₃₇	—	2	12	no	—
11	C₂²×C₄×C₃₇	C₂×C₄	1	12	yes	—
12	C₂²×C₄×C₃₇	C₂³	1	6	yes	—
13	C₂²×Dic₃₇	—	2	24	no	—
14	C₂²×Dic₃₇	C₂³	1	8	yes	—
15	C₄²×C₃₇	C₂×C₄	1	16	yes	complemented
16	C₂³×C₃₇	C₂²×C₄	1	2	yes	—
17	C₂³×C₃₇	#41	1	12	yes	—
18	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
19	C₂×C₄×C₃₇	—	2	24	no	—
20	C₂×C₄×C₃₇	—	2	12	no	—
21	C₂×C₄×C₃₇	C₂²×C₄	1	12	yes	—
22	C₂×Dic₃₇	—	2	24	no	—
23	C₂×Dic₃₇	—	4	16	no	—
24	C₂²×C₃₇	#117	1	12	yes	—
25	C₂²×C₃₇	#126	1	16	yes	—
26	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
27	C₂²×C₃₇	C₂×#41	1	6	yes	—
28	C₄×C₃₇	—	2	12	no	—
29	Dic₃₇	—	4	8	no	—
30	C₂×#383	—	37	1	no	maximal, Sylow
31	C₂×C₃₇	#383	1	8	yes	complemented
32	C₂×C₃₇	C₂×#117	1	3	yes	—
33	C₂×C₃₇	C₂×#126	1	4	yes	—
34	C₂²×C₄²	D₃₇	1	1	yes	characteristic
35	#383	—	37	8	no	—
36	C₂×#95	—	37	6	no	—
37	C₃₇	C₂×#383	1	1	yes	characteristic, complemented, Sylow
38	C₂³×C₄	—	37	4	no	—
39	C₂³×C₄	C₂×D₃₇	1	3	yes	—
40	C₂×C₄²	Dic₃₇	1	8	yes	complemented
41	C₂×C₄²	C₂×D₃₇	1	4	yes	—
42	#95	—	37	24	no	—
43	C₂⁴	C₂²×D₃₇	1	1	yes	characteristic
44	C₂²×C₄	—	2	12	no	—
45	C₂²×C₄	—	37	8	no	—
46	C₂²×C₄	—	74	24	no	—
47	C₂²×C₄	C₂×Dic₃₇	1	12	yes	—
48	C₂²×C₄	C₂²×D₃₇	1	6	yes	—
49	C₄²	C₂×Dic₃₇	1	16	yes	complemented
50	C₂³	#10596962	1	12	yes	—
51	C₂³	C₂²×Dic₃₇	1	2	yes	—
52	C₂³	C₂³×D₃₇	1	1	yes	characteristic
53	C₂×C₄	—	2	24	no	—
54	C₂×C₄	—	2	12	no	—
55	C₂×C₄	—	74	24	no	—
56	C₂×C₄	—	148	16	no	—
57	C₂×C₄	C₂²×Dic₃₇	1	12	yes	—
58	C₂²	#11924495	1	12	yes	—
59	C₂²	#11924530	1	16	yes	—
60	C₂²	C₂³×Dic₃₇	1	1	yes	characteristic
61	C₂²	C₂×#10596962	1	6	yes	—
62	C₄	—	2	12	no	—
63	C₄	—	148	8	no	—
64	C₂	#14557401	1	8	yes	direct product factor
65	C₂	C₂×#11924495	1	3	yes	—
66	C₂	C₂×#11924530	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₃₇
commutator	C₂²×C₃₇	C₂³×C₄
Frattini	C₂³	C₂³×D₃₇
Fitting	C₂²×C₄²×C₃₇	C₂
socle, prime radical	C₂⁴×C₃₇	C₂³
cosocle	C₂³×C₃₇	C₂⁴
hypercenter	C₂²×C₄²	D₃₇
hypocenter	C₃₇	C₂×#383
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
1. #14557401	C₂	direct (N × H)
7. C₂×C₄²×C₃₇	C₄	semidirect
15. C₄²×C₃₇	C₂×C₄	semidirect
31. C₂×C₃₇	#383	semidirect
37. C₃₇	C₂×#383	semidirect
40. C₂×C₄²	Dic₃₇	semidirect
49. C₄²	C₂×Dic₃₇	semidirect
64. C₂	#14557401	direct (N × H)

Maximal subgroups

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

subgroup	index
#14557401	2
C₂×#11924443	2
C₂²×C₄²×C₃₇	2
C₂×#383	37

Subgroups — C2×#14557401 #17996986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14557401 #17996986