Subgroups — #14557899

Order 2368.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924533	C₂	1	1	yes	maximal, characteristic
2	#11924456	C₂	1	4	yes	maximal, complemented
3	#11924447	C₂	1	1	yes	maximal, characteristic, complemented
4	#125×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₄₈	—	2	2	no	—
6	C₂×D₁₄₈	C₂²	1	2	yes	—
7	C₄⋊C₄×C₃₇	—	2	2	no	—
8	C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
9	C₄²×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×#64436	C₂²	1	2	yes	—
11	C₂²×D₃₇	—	2	2	no	—
12	C₂×C₄×C₃₇	—	2	2	no	—
13	C₂×C₄×C₃₇	D₄	1	2	yes	—
14	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
15	D₁₄₈	—	2	4	no	—
16	D₁₄₈	—	4	4	no	—
17	#64436	—	2	2	no	—
18	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
19	C₂×D₃₇	—	4	2	no	—
20	C₂×D₃₇	—	4	4	no	—
21	C₄×C₃₇	—	2	2	no	—
22	C₄×C₃₇	—	4	2	no	—
23	C₄×C₃₇	#41	1	2	yes	—
24	C₂×C₃₇	#124	1	1	yes	characteristic
25	C₂×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
26	D₃₇	—	8	2	no	—
27	#490	—	37	1	no	maximal, Sylow
28	C₃₇	#490	1	1	yes	characteristic, complemented, Sylow
29	#127	—	37	1	no	—
30	#125	D₃₇	1	1	yes	characteristic, complemented
31	#102	—	37	4	no	—
32	#97	—	37	1	no	—
33	C₂×D₄	—	37	2	no	—
34	C₂×D₄	—	74	2	no	—
35	C₂×C₈	—	37	2	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	C₂×D₃₇	1	2	yes	—
38	C₄²	C₂×D₃₇	1	1	yes	characteristic
39	C₂³	—	74	2	no	—
40	D₄	—	74	4	no	—
41	D₄	—	148	4	no	—
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	C₂²⋊D₃₇	1	2	yes	—
44	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
45	C₈	—	74	2	no	—
46	C₂²	—	148	2	no	—
47	C₂²	—	148	4	no	—
48	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	4	2	no	—
51	C₄	#10596966	1	2	yes	—
52	C₂	—	296	2	no	—
53	C₂	#11924525	1	1	yes	characteristic
54	C₂	#11924561	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#125×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
prime radical	#11924533	C₂
hypercenter	#125	D₃₇
hypocenter	C₃₇	#490
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
2. #11924456	C₂	semidirect
3. #11924447	C₂	semidirect
4. #125×C₃₇	C₂	semidirect
28. C₃₇	#490	semidirect
30. #125	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924533	2
#11924456	2
#11924447	2
#125×C₃₇	2
#490	37