Subgroups — #18009607

Order 4736.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558456	C₂	1	2	yes	maximal, complemented
2	#14557907	C₂	1	1	yes	maximal, characteristic
3	#11924610	—	2	2	no	—
4	C₂×#10596941	—	2	2	no	—
5	#11924533	C₄	1	1	yes	characteristic
6	C₄×#64436	C₂²	1	1	yes	characteristic
7	C₄⋊Q₈×C₃₇	C₄	1	1	yes	characteristic
8	C₂×Q₈×C₃₇	—	2	1	no	—
9	C₂×D₁₄₈	—	2	1	no	—
10	C₂×D₁₄₈	—	4	1	no	—
11	C₄⋊C₄×C₃₇	—	4	1	no	—
12	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
13	#10596941	—	4	2	no	—
14	#10596941	—	4	2	no	—
15	C₂×#64436	D₄	1	2	yes	—
16	#10596927	—	4	2	no	—
17	C₂²×D₃₇	—	4	1	no	—
18	Q₈×C₃₇	—	4	2	no	—
19	C₂×C₄×C₃₇	—	2	1	no	—
20	C₂×C₄×C₃₇	—	4	1	no	—
21	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
22	D₁₄₈	—	4	2	no	—
23	D₁₄₈	—	8	2	no	—
24	#64436	D₈	1	2	yes	—
25	#64436	SD₁₆	1	2	yes	—
26	C₂²×C₃₇	#100	1	1	yes	characteristic
27	C₂×D₃₇	—	8	2	no	—
28	C₂×D₃₇	—	8	1	no	—
29	C₄×C₃₇	—	2	2	no	—
30	C₄×C₃₇	—	8	1	no	—
31	C₄×C₃₇	#102	1	2	yes	—
32	#1359	—	37	1	no	maximal, Sylow
33	C₂×C₃₇	—	2	1	no	—
34	C₂×C₃₇	#331	1	1	yes	characteristic
35	D₃₇	—	16	1	no	—
36	#492	—	37	1	no	—
37	#364	—	37	2	no	—
38	C₃₇	#1359	1	1	yes	characteristic, complemented, Sylow
39	C₂×SD₁₆	—	74	2	no	—
40	C₄⋊Q₈	#3866	1	1	yes	characteristic
41	#127	—	37	1	no	—
42	M₃₂	—	74	2	no	—
43	C₄×C₈	—	37	1	no	—
44	C₂×Q₈	—	2	1	no	—
45	C₂×D₄	—	74	1	no	—
46	C₂×D₄	—	148	1	no	—
47	SD₁₆	—	148	2	no	—
48	SD₁₆	—	148	2	no	—
49	C₂×C₈	—	37	2	no	—
50	C₄⋊C₄	—	4	1	no	—
51	C₄²	C₂×#3866	1	1	yes	characteristic
52	C₁₆	—	148	2	no	—
53	C₂³	—	148	1	no	—
54	Q₈	—	4	2	no	—
55	D₄	—	296	2	no	—
56	D₄	—	148	2	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
60	C₈	—	37	2	no	—
61	C₈	—	37	2	no	—
62	C₂²	—	296	2	no	—
63	C₂²	—	296	1	no	—
64	C₂²	#11924596	1	1	yes	characteristic
65	C₄	—	2	2	no	—
66	C₄	—	8	1	no	—
67	C₄	#11924598	1	2	yes	—
68	C₂	—	2	1	no	—
69	C₂	—	592	1	no	—
70	C₂	#14558391	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14558391
commutator	C₄²×C₃₇	C₂×C₄
Frattini	C₄²	C₂×#3866
Fitting	C₄⋊Q₈×C₃₇	C₄
socle	C₂×C₃₇	#331
prime radical	#11924533	C₄
cosocle	C₄×#64436	C₂²
hypercenter	C₄⋊Q₈	#3866
hypocenter	C₃₇	#1359
LCS	G ▷ C₄²×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #14558456	C₂	semidirect
38. C₃₇	#1359	semidirect

Maximal subgroups

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

subgroup	index
#14558456	2
#14557907	2
#1359	37