Subgroups — #14557314

Order 2368.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596929	C₂	1	1	yes	maximal, characteristic
2	#11924476	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₃₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
6	C₂×#64436	C₄	1	1	yes	characteristic
7	#10596929	—	2	1	no	—
8	#10596929	—	2	1	no	—
9	C₁₆×C₃₇	—	2	1	no	—
10	#10596925	—	2	1	no	—
11	C₂²×D₃₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₃₇	C₈	1	1	yes	characteristic
14	C₄×D₃₇	—	2	1	no	—
15	C₄×D₃₇	—	2	1	no	—
16	C₈×C₃₇	D₄	1	1	yes	characteristic
17	C₈×C₃₇	D₄	1	1	yes	characteristic
18	#64436	—	2	1	no	—
19	C₂²×C₃₇	C₂×C₈	1	1	yes	characteristic
20	C₂×D₃₇	—	2	1	no	—
21	C₂×D₃₇	—	4	1	no	—
22	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₃₇	M₁₆	1	1	yes	characteristic
24	Dic₃₇	—	2	1	no	—
25	C₂×C₃₇	—	2	1	no	—
26	C₂×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
27	D₃₇	—	4	1	no	—
28	#349	—	37	1	no	maximal, Sylow
29	C₃₇	#349	1	1	yes	characteristic, complemented, Sylow
30	C₂×M₁₆	—	37	1	no	—
31	M₃₂	—	37	1	no	—
32	M₃₂	D₃₇	1	1	yes	characteristic, complemented
33	C₂²×C₄	—	37	1	no	—
34	M₁₆	—	74	1	no	—
35	M₁₆	—	74	1	no	—
36	C₂×C₈	—	37	1	no	—
37	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	—	74	1	no	—
40	C₂³	—	37	1	no	—
41	C₂×C₄	—	37	1	no	—
42	C₂×C₄	—	74	1	no	—
43	C₂×C₄	—	74	1	no	—
44	C₂×C₄	C₄×D₃₇	1	1	yes	characteristic
45	C₈	—	74	1	no	—
46	C₈	D₁₄₈	1	1	yes	characteristic
47	C₈	C₂²⋊D₃₇	1	1	yes	characteristic
48	C₂²	—	74	1	no	—
49	C₂²	—	148	1	no	—
50	C₂²	C₈×D₃₇	1	1	yes	characteristic
51	C₄	—	74	1	no	—
52	C₄	#10596929	1	1	yes	characteristic
53	C₄	#10596938	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	148	1	no	—
56	C₂	#11924448	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10596938
commutator	C₂²×C₃₇	C₂×C₈
Frattini	C₂×C₈	C₂×D₃₇
Fitting	M₃₂×C₃₇	C₂
socle	C₂×C₃₇	C₂²⋊C₈
prime radical	C₂²×D₃₇	C₈
cosocle	C₂×C₈×C₃₇	C₂²
hypercenter	M₃₂	D₃₇
hypocenter	C₃₇	#349
LCS	G ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #11924476	C₂	semidirect
3. M₃₂×C₃₇	C₂	semidirect
29. C₃₇	#349	semidirect
32. M₃₂	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596929	2
#11924476	2
M₃₂×C₃₇	2
#349	37