Subgroups — #18009752

Order 4736.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558466	C₂	1	1	yes	maximal, characteristic
2	#14558462	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×D₃₇	C₂	1	1	yes	maximal, characteristic
4	#11924607	—	2	1	no	—
5	#11924586	—	2	1	no	—
6	Q₁₆×D₃₇	—	2	1	no	—
7	Dic₂₉₆	C₄	1	1	yes	characteristic
8	#11924482	—	2	1	no	—
9	C₁₆×D₃₇	C₂²	1	1	yes	characteristic
10	Q₃₂×C₃₇	C₄	1	1	yes	characteristic
11	Q₈×D₃₇	—	4	1	no	—
12	#10596953	—	4	1	no	—
13	Q₁₆×C₃₇	—	2	1	no	—
14	#10596942	—	4	1	no	—
15	Dic₁₄₈	—	2	1	no	—
16	C₈×D₃₇	D₄	1	1	yes	characteristic
17	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
18	#10596925	D₄	1	1	yes	characteristic
19	Q₈×C₃₇	—	4	1	no	—
20	C₄×D₃₇	—	8	1	no	—
21	C₄×D₃₇	D₈	1	1	yes	characteristic
22	Dic₇₄	—	4	1	no	—
23	Dic₇₄	—	8	1	no	—
24	#64438	—	8	1	no	—
25	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
26	#64436	SD₁₆	1	1	yes	characteristic
27	C₂×D₃₇	SD₃₂	1	1	yes	characteristic
28	C₄×C₃₇	—	8	1	no	—
29	C₄×C₃₇	#102	1	1	yes	characteristic
30	Dic₃₇	—	8	1	no	—
31	Dic₃₇	D₁₆	1	1	yes	characteristic
32	#1420	—	37	1	no	maximal, Sylow
33	C₂×C₃₇	#357	1	1	yes	characteristic
34	D₃₇	—	2	1	no	—
35	C₂×Q₃₂	—	37	1	no	—
36	M₆₄	—	37	1	no	—
37	#368	—	37	1	no	—
38	C₃₇	#1420	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₁₆	—	74	1	no	—
40	Q₃₂	—	37	1	no	—
41	Q₃₂	—	74	1	no	—
42	Q₃₂	#3866	1	1	yes	characteristic
43	C₂×C₁₆	—	37	1	no	—
44	#108	—	74	1	no	—
45	C₃₂	—	74	1	no	—
46	C₂×Q₈	—	148	1	no	—
47	Q₁₆	—	2	1	no	—
48	Q₁₆	—	74	1	no	—
49	Q₁₆	—	148	1	no	—
50	M₁₆	—	148	1	no	—
51	C₂×C₈	—	37	1	no	—
52	C₁₆	—	37	1	no	—
53	C₁₆	C₂×#3866	1	1	yes	characteristic
54	Q₈	—	4	1	no	—
55	Q₈	—	296	1	no	—
56	Q₈	—	148	1	no	—
57	C₂×C₄	—	37	1	no	—
58	C₂×C₄	—	296	1	no	—
59	C₈	—	37	1	no	—
60	C₈	—	296	1	no	—
61	C₈	C₂²⋊#3866	1	1	yes	characteristic
62	C₂²	—	37	1	no	—
63	C₄	—	8	1	no	—
64	C₄	—	37	1	no	—
65	C₄	—	296	1	no	—
66	C₄	#11924598	1	1	yes	characteristic
67	C₂	—	74	1	no	—
68	C₂	#14558445	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14558445
commutator	C₁₆×C₃₇	C₂×C₄
Frattini	C₁₆	C₂×#3866
Fitting	Q₃₂×C₃₇	C₄
socle	C₂×C₃₇	#357
prime radical	C₂×D₃₇	SD₃₂
cosocle	C₁₆×D₃₇	C₂²
hypercenter	Q₃₂	#3866
hypocenter	C₃₇	#1420
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
38. C₃₇	#1420	semidirect

Maximal subgroups

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

subgroup	index
#14558466	2
#14558462	2
Q₃₂×D₃₇	2
#1420	37