Subgroups — #18009603

Order 4736.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558425	C₂	1	2	yes	maximal
2	#14557903	C₂	1	1	yes	maximal, characteristic
3	#11924610	—	2	2	no	—
4	#11924536	C₄	1	1	yes	characteristic
5	#11924459	—	2	2	no	—
6	#11924447	C₂²	1	1	yes	characteristic
7	#125×C₃₇	C₄	1	1	yes	characteristic
8	C₂×Dic₇₄	—	2	1	no	—
9	C₄⋊C₄×C₃₇	—	2	1	no	—
10	C₄⋊C₄×C₃₇	—	4	1	no	—
11	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₄⋊Dic₃₇	—	4	1	no	—
13	C₂×#64436	D₄	1	2	yes	—
14	#10596927	—	2	4	no	—
15	C₂×C₄×C₃₇	—	2	1	no	—
16	C₂×C₄×C₃₇	—	4	1	no	—
17	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×Dic₃₇	—	4	1	no	—
19	Dic₇₄	—	4	2	no	—
20	#64436	—	2	2	no	—
21	C₂²×C₃₇	#100	1	1	yes	characteristic
22	C₄×C₃₇	—	4	1	no	—
23	C₄×C₃₇	—	8	1	no	—
24	C₄×C₃₇	#104	1	2	yes	—
25	Dic₃₇	—	8	1	no	—
26	#1356	—	37	1	no	maximal, Sylow
27	C₂×C₃₇	—	2	1	no	—
28	C₂×C₃₇	#329	1	1	yes	characteristic
29	#491	—	37	1	no	—
30	#347	—	37	2	no	—
31	C₃₇	#1356	1	1	yes	characteristic, complemented, Sylow
32	C₄⋊Q₈	—	37	1	no	—
33	#125	#3866	1	1	yes	characteristic
34	M₃₂	—	74	2	no	—
35	#103	—	74	2	no	—
36	#97	—	37	1	no	—
37	C₂×Q₈	—	74	1	no	—
38	C₂×C₈	—	37	2	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	4	1	no	—
41	C₄⋊C₄	—	148	1	no	—
42	C₄²	C₂×#3866	1	1	yes	characteristic
43	C₁₆	—	74	4	no	—
44	Q₈	—	148	2	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	—	148	1	no	—
48	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
49	C₈	—	74	2	no	—
50	C₂²	#11924596	1	1	yes	characteristic
51	C₄	—	4	1	no	—
52	C₄	—	8	1	no	—
53	C₄	—	296	1	no	—
54	C₄	#11924601	1	2	yes	—
55	C₂	—	2	1	no	—
56	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	C₂²×C₃₇	#100
cosocle	#11924447	C₂²
hypercenter	#125	#3866
hypocenter	C₃₇	#1356
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
31. C₃₇	#1356	semidirect

Maximal subgroups

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

subgroup	index
#14558425	2
#14557903	2
#1356	37