Subgroups — #17994208

Order 4736.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557884	C₂	1	3	yes	maximal, complemented
2	#14557880	C₂	1	3	yes	maximal
3	C₈²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924536	C₂²	1	3	yes	—
5	#11924533	C₂²	1	1	yes	characteristic
6	#11924461	—	2	6	no	—
7	#11924458	—	2	6	no	—
8	C₄×C₈×C₃₇	C₂²	1	3	yes	—
9	C₂×D₁₄₈	—	2	3	no	—
10	C₂×Dic₇₄	—	2	3	no	—
11	C₂×C₈×C₃₇	D₄	1	6	yes	—
12	C₄²×C₃₇	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₃₇	—	2	3	no	—
14	C₄⋊Dic₃₇	—	2	3	no	—
15	C₂²×D₃₇	—	4	1	no	—
16	C₂×C₄×C₃₇	C₂×D₄	1	3	yes	—
17	C₂×Dic₃₇	—	4	3	no	—
18	D₁₄₈	—	4	6	no	—
19	Dic₇₄	—	4	6	no	—
20	C₈×C₃₇	—	2	6	no	—
21	C₂²×C₃₇	#127	1	1	yes	characteristic
22	C₂×D₃₇	—	8	3	no	—
23	C₄×C₃₇	#135	1	6	yes	—
24	Dic₃₇	—	8	3	no	—
25	#1711	—	37	1	no	maximal, Sylow
26	C₂×C₃₇	#495	1	3	yes	—
27	D₃₇	—	16	1	no	—
28	#487	—	37	3	no	—
29	#486	—	37	3	no	—
30	C₈²	D₃₇	1	1	yes	characteristic, complemented
31	C₃₇	#1711	1	1	yes	characteristic, complemented, Sylow
32	C₄⋊Q₈	—	37	3	no	—
33	#127	—	37	1	no	—
34	#103	—	74	6	no	—
35	#102	—	74	6	no	—
36	C₄×C₈	C₂×D₃₇	1	3	yes	—
37	C₂×Q₈	—	74	3	no	—
38	C₂×D₄	—	74	3	no	—
39	C₂×C₈	D₁₄₈	1	6	yes	—
40	C₄⋊C₄	—	74	3	no	—
41	C₄⋊C₄	—	74	3	no	—
42	C₄²	C₂²×D₃₇	1	1	yes	characteristic
43	C₂³	—	148	1	no	—
44	Q₈	—	148	6	no	—
45	D₄	—	148	6	no	—
46	C₂×C₄	—	148	3	no	—
47	C₂×C₄	C₂×D₁₄₈	1	3	yes	—
48	C₈	—	2	6	no	—
49	C₂²	—	296	3	no	—
50	C₂²	#11924533	1	1	yes	characteristic
51	C₄	—	296	3	no	—
52	C₄	#11924558	1	6	yes	—
53	C₂	—	592	1	no	—
54	C₂	#14557917	1	3	yes	—

	subgroup	G/H
center	C₂²	#11924533
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting	C₈²×C₃₇	C₂
socle	C₂²×C₃₇	#127
prime radical	#11924533	C₂²
hypercenter	C₈²	D₃₇
hypocenter	C₃₇	#1711
LCS	G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #14557884	C₂	semidirect
3. C₈²×C₃₇	C₂	semidirect
30. C₈²	D₃₇	semidirect
31. C₃₇	#1711	semidirect

Maximal subgroups

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

subgroup	index
#14557884	2
#14557880	2
C₈²×C₃₇	2
#1711	37