Subgroups — #18009735

Order 4736.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558438	C₂	1	2	yes	maximal
2	#14557899	C₂	1	1	yes	maximal, characteristic
3	#11924595	—	2	2	no	—
4	#11924533	C₂²	1	1	yes	characteristic
5	#11924456	—	2	2	no	—
6	#11924447	C₄	1	1	yes	characteristic, complemented
7	#125×C₃₇	C₄	1	1	yes	characteristic, complemented
8	C₂×D₁₄₈	—	4	1	no	—
9	C₂×D₁₄₈	D₄	1	2	yes	—
10	C₂²⋊#3866	—	4	2	no	—
11	C₄⋊C₄×C₃₇	—	2	1	no	—
12	C₄⋊C₄×C₃₇	—	4	1	no	—
13	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂×#64436	—	2	1	no	—
15	C₂²×D₃₇	—	2	2	no	—
16	C₂×#3866	—	8	2	no	—
17	C₂×C₄×C₃₇	—	2	1	no	—
18	C₂×C₄×C₃₇	—	4	1	no	—
19	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
20	D₁₄₈	—	4	2	no	—
21	D₁₄₈	—	8	2	no	—
22	#64436	—	4	1	no	—
23	C₂²×C₃₇	#99	1	1	yes	characteristic
24	C₂×D₃₇	—	4	2	no	—
25	C₂×D₃₇	—	8	2	no	—
26	#3866	—	16	2	no	—
27	C₄×C₃₇	—	2	1	no	—
28	C₄×C₃₇	—	4	1	no	—
29	C₄×C₃₇	—	8	1	no	—
30	#1412	—	37	1	no	maximal, Sylow
31	C₂×C₃₇	—	2	1	no	—
32	C₂×C₃₇	#354	1	1	yes	characteristic
33	D₃₇	—	8	2	no	—
34	#490	—	37	1	no	—
35	#353	—	37	2	no	—
36	C₃₇	#1412	1	1	yes	characteristic, complemented, Sylow
37	#127	—	37	1	no	—
38	#125	#3866	1	1	yes	characteristic, complemented
39	#102	—	74	2	no	—
40	#99	—	74	2	no	—
41	#97	—	37	1	no	—
42	C₂×D₄	—	37	2	no	—
43	C₂×D₄	—	148	1	no	—
44	C₂×C₈	—	74	1	no	—
45	C₄⋊C₄	—	2	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₂²⋊C₄	—	148	2	no	—
48	C₄²	C₂×#3866	1	1	yes	characteristic
49	C₂³	—	74	2	no	—
50	D₄	—	296	2	no	—
51	D₄	—	148	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	296	2	no	—
55	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
56	C₈	—	148	1	no	—
57	C₂²	—	296	2	no	—
58	C₂²	—	148	2	no	—
59	C₂²	#11924594	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	8	1	no	—
63	C₄	—	592	2	no	—
64	C₂	—	2	1	no	—
65	C₂	—	296	2	no	—
66	C₂	#14558439	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14558439
commutator	C₄²×C₃₇	C₂×C₄
Frattini	C₄²	C₂×#3866
Fitting	#125×C₃₇	C₄
socle	C₂×C₃₇	#354
prime radical, cosocle	#11924533	C₂²
hypercenter	#125	#3866
hypocenter	C₃₇	#1412
LCS	G ▷ C₄²×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
6. #11924447	C₄	semidirect
7. #125×C₃₇	C₄	semidirect
36. C₃₇	#1412	semidirect
38. #125	#3866	semidirect

Maximal subgroups

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

subgroup	index
#14558438	2
#14557899	2
#1412	37