Subgroups — #18009600

Order 4736.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558425	C₂	1	2	yes	maximal, complemented
2	#14557899	C₂	1	1	yes	maximal, characteristic
3	#11924610	—	2	2	no	—
4	#11924533	C₄	1	1	yes	characteristic
5	#11924456	—	2	2	no	—
6	#11924447	C₂²	1	1	yes	characteristic
7	#125×C₃₇	C₄	1	1	yes	characteristic
8	C₂×D₁₄₈	—	2	1	no	—
9	C₂×D₁₄₈	—	4	1	no	—
10	C₄⋊C₄×C₃₇	—	2	1	no	—
11	C₄⋊C₄×C₃₇	—	4	1	no	—
12	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂×#64436	D₄	1	2	yes	—
14	#10596927	—	2	4	no	—
15	C₂²×D₃₇	—	4	1	no	—
16	C₂×C₄×C₃₇	—	2	1	no	—
17	C₂×C₄×C₃₇	—	4	1	no	—
18	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
19	D₁₄₈	—	4	2	no	—
20	D₁₄₈	—	8	2	no	—
21	#64436	—	2	2	no	—
22	C₂²×C₃₇	#100	1	1	yes	characteristic
23	C₂×D₃₇	—	8	2	no	—
24	C₂×D₃₇	—	8	1	no	—
25	C₄×C₃₇	—	4	1	no	—
26	C₄×C₃₇	—	8	1	no	—
27	C₄×C₃₇	#104	1	2	yes	—
28	#1355	—	37	1	no	maximal, Sylow
29	C₂×C₃₇	—	2	1	no	—
30	C₂×C₃₇	#329	1	1	yes	characteristic
31	D₃₇	—	16	1	no	—
32	#490	—	37	1	no	—
33	#347	—	37	2	no	—
34	C₃₇	#1355	1	1	yes	characteristic, complemented, Sylow
35	#127	—	37	1	no	—
36	#125	#3866	1	1	yes	characteristic
37	M₃₂	—	74	2	no	—
38	#102	—	74	2	no	—
39	#97	—	37	1	no	—
40	C₂×D₄	—	74	1	no	—
41	C₂×D₄	—	148	1	no	—
42	C₂×C₈	—	37	2	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	4	1	no	—
45	C₄²	C₂×#3866	1	1	yes	characteristic
46	C₁₆	—	74	4	no	—
47	C₂³	—	148	1	no	—
48	D₄	—	296	2	no	—
49	D₄	—	148	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
53	C₈	—	74	2	no	—
54	C₂²	—	296	2	no	—
55	C₂²	—	296	1	no	—
56	C₂²	#11924596	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	1	no	—
59	C₄	#11924601	1	2	yes	—
60	C₂	—	2	1	no	—
61	C₂	—	592	1	no	—
62	C₂	#14558389	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14558389
commutator	C₄²×C₃₇	C₂×C₄
Frattini	C₄²	C₂×#3866
Fitting	#125×C₃₇	C₄
socle	C₂×C₃₇	#329
prime radical	#11924533	C₄
cosocle	#11924447	C₂²
hypercenter	#125	#3866
hypocenter	C₃₇	#1355
LCS	G ▷ C₄²×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #14558425	C₂	semidirect
34. C₃₇	#1355	semidirect

Maximal subgroups

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

subgroup	index
#14558425	2
#14557899	2
#1355	37