Subgroups — #14558390

Order 2368.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924591	C₂	1	1	yes	maximal, characteristic
2	#11924591	C₂	1	1	yes	maximal, characteristic
3	#11924527	C₂	1	1	yes	maximal, characteristic
4	C₂×#64438	—	2	1	no	—
5	C₂×#64438	—	2	1	no	—
6	C₄⋊C₄×C₃₇	C₄	1	1	yes	characteristic
7	C₄⋊Dic₃₇	—	2	1	no	—
8	C₄⋊Dic₃₇	C₄	1	1	yes	characteristic
9	#10596936	—	2	1	no	—
10	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₃₇	—	2	1	no	—
12	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₃₇	—	2	1	no	—
14	C₂×Dic₃₇	D₄	1	1	yes	characteristic
15	C₂×Dic₃₇	D₄	1	1	yes	characteristic
16	#64438	—	2	2	no	—
17	#64438	—	2	2	no	—
18	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₃₇	—	2	1	no	—
20	C₄×C₃₇	—	4	1	no	—
21	Dic₃₇	—	2	1	no	—
22	Dic₃₇	—	2	1	no	—
23	Dic₃₇	—	4	1	no	—
24	C₂×C₃₇	#101	1	1	yes	characteristic
25	C₂×C₃₇	#104	1	1	yes	characteristic
26	C₂×C₃₇	#104	1	1	yes	characteristic
27	#330	—	37	1	no	maximal, Sylow
28	C₃₇	#330	1	1	yes	characteristic, complemented, Sylow
29	#125	—	37	1	no	—
30	#97	—	37	1	no	—
31	#97	—	37	1	no	—
32	C₂×C₈	—	74	1	no	—
33	C₂×C₈	—	74	1	no	—
34	C₄⋊C₄	—	37	1	no	—
35	C₄⋊C₄	—	74	1	no	—
36	C₄⋊C₄	—	74	1	no	—
37	C₄⋊C₄	#3866	1	1	yes	characteristic
38	C₄²	—	37	1	no	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	—	37	1	no	—
41	C₂×C₄	—	37	1	no	—
42	C₂×C₄	—	74	1	no	—
43	C₂×C₄	C₂×#3866	1	1	yes	characteristic
44	C₈	—	74	2	no	—
45	C₈	—	74	2	no	—
46	C₂²	C₂²⋊#3866	1	1	yes	characteristic
47	C₄	—	2	1	no	—
48	C₄	—	4	1	no	—
49	C₄	—	74	1	no	—
50	C₄	—	74	1	no	—
51	C₄	—	148	1	no	—
52	C₂	#11924597	1	1	yes	characteristic
53	C₂	#11924600	1	1	yes	characteristic
54	C₂	#11924601	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#3866
commutator	C₂×C₄×C₃₇	C₂×C₄
Frattini	C₂×C₄	C₂×#3866
Fitting	C₄⋊C₄×C₃₇	C₄
socle, prime radical	C₂²×C₃₇	C₂²⋊C₄
cosocle	C₄×Dic₃₇	C₂²
hypercenter	C₄⋊C₄	#3866
hypocenter	C₃₇	#330
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
28. C₃₇	#330	semidirect

Maximal subgroups

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

subgroup	index
#11924591	2
#11924527	2
#330	37