Subgroups — #17993898

Order 4736.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557899	C₂	1	3	yes	maximal
2	#14557275	C₂	1	3	yes	maximal, complemented
3	C₃₇×#564	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924533	C₂²	1	1	yes	characteristic
5	#11924456	—	2	6	no	—
6	#11924447	C₂²	1	3	yes	—
7	#125×C₃₇	—	2	6	no	—
8	#125×C₃₇	C₂²	1	3	yes	—
9	C₂×D₁₄₈	—	2	3	no	—
10	C₄⋊C₄×C₃₇	—	2	6	no	—
11	C₄⋊C₄×C₃₇	—	2	6	no	—
12	C₄⋊C₄×C₃₇	D₄	1	6	yes	—
13	C₄²×C₃₇	—	2	2	no	—
14	C₄²×C₃₇	C₂³	1	1	yes	characteristic
15	C₂×#64436	—	2	3	no	—
16	C₂²×D₃₇	—	4	1	no	—
17	C₂×C₄×C₃₇	—	2	6	no	—
18	C₂×C₄×C₃₇	C₂×D₄	1	3	yes	—
19	D₁₄₈	—	4	6	no	—
20	#64436	—	4	3	no	—
21	C₂²×C₃₇	#120	1	1	yes	characteristic
22	C₂×D₃₇	—	8	3	no	—
23	C₄×C₃₇	—	2	3	no	—
24	C₄×C₃₇	—	4	6	no	—
25	#1658	—	37	1	no	maximal, Sylow
26	C₂×C₃₇	#454	1	3	yes	—
27	D₃₇	—	16	1	no	—
28	#564	D₃₇	1	1	yes	characteristic, complemented
29	#490	—	37	3	no	—
30	#330	—	37	3	no	—
31	C₃₇	#1658	1	1	yes	characteristic, complemented, Sylow
32	#127	—	37	1	no	—
33	#125	—	2	6	no	—
34	#125	C₂×D₃₇	1	3	yes	—
35	#102	—	74	6	no	—
36	#97	—	37	3	no	—
37	C₂×D₄	—	74	3	no	—
38	C₂×C₈	—	74	3	no	—
39	C₄⋊C₄	—	2	6	no	—
40	C₄⋊C₄	—	2	6	no	—
41	C₄⋊C₄	C₂²⋊D₃₇	1	6	yes	—
42	C₄²	—	2	2	no	—
43	C₄²	C₂²×D₃₇	1	1	yes	characteristic
44	C₂³	—	148	1	no	—
45	D₄	—	148	6	no	—
46	C₂×C₄	—	2	6	no	—
47	C₂×C₄	C₂×C₂²⋊D₃₇	1	3	yes	—
48	C₈	—	148	3	no	—
49	C₂²	—	296	3	no	—
50	C₂²	#11924505	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	—	4	6	no	—
53	C₂	—	592	1	no	—
54	C₂	#14557706	1	3	yes	—

	subgroup	G/H
center	C₂²	#11924505
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting	C₃₇×#564	C₂
socle	C₂²×C₃₇	#120
prime radical	#11924533	C₂²
hypercenter	#564	D₃₇
hypocenter	C₃₇	#1658
LCS	G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #564

Complements

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

N	H ≅ G/N	type
2. #14557275	C₂	semidirect
3. C₃₇×#564	C₂	semidirect
28. #564	D₃₇	semidirect
31. C₃₇	#1658	semidirect

Maximal subgroups

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

subgroup	index
#14557899	2
#14557275	2
C₃₇×#564	2
#1658	37