Subgroups — #17992789

Order 4736.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557367	C₂	1	1	yes	maximal, characteristic
2	#14557363	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic
4	#11924472	—	2	1	no	—
5	#11924442	—	2	1	no	—
6	C₂×Q₁₆×C₃₇	—	2	1	no	—
7	Q₃₂×C₃₇	—	2	1	no	—
8	Q₃₂×C₃₇	C₄	1	2	yes	—
9	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×Q₈×C₃₇	—	4	1	no	—
11	Q₁₆×C₃₇	—	2	2	no	—
12	Q₁₆×C₃₇	—	4	1	no	—
13	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
14	#10596934	—	4	1	no	—
15	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₃₇	D₄	1	1	yes	characteristic
17	Q₈×C₃₇	—	4	2	no	—
18	Q₈×C₃₇	—	8	1	no	—
19	C₂×C₄×C₃₇	—	8	1	no	—
20	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
21	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
23	#64436	—	8	1	no	—
24	C₂²×C₃₇	SD₃₂	1	1	yes	characteristic
25	C₄×C₃₇	—	8	2	no	—
26	C₄×C₃₇	#102	1	1	yes	characteristic
27	C₄×C₃₇	D₁₆	1	1	yes	characteristic
28	#1420	—	37	1	no	maximal, Sylow
29	C₂×C₃₇	—	2	1	no	—
30	C₂×C₃₇	#357	1	1	yes	characteristic
31	C₂×Q₃₂	D₃₇	1	1	yes	characteristic
32	M₆₄	—	37	1	no	—
33	#368	—	37	1	no	—
34	C₃₇	#1420	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₁₆	—	2	1	no	—
36	Q₃₂	—	2	1	no	—
37	Q₃₂	Dic₃₇	1	2	yes	—
38	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
39	#108	—	74	1	no	—
40	C₃₂	—	74	1	no	—
41	C₂×Q₈	—	4	1	no	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	4	1	no	—
44	M₁₆	—	148	1	no	—
45	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
46	C₁₆	C₂×Dic₃₇	1	1	yes	characteristic
47	C₁₆	C₂²⋊D₃₇	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	8	1	no	—
50	C₂×C₄	—	8	1	no	—
51	C₂×C₄	#10596939	1	1	yes	characteristic
52	C₈	—	296	1	no	—
53	C₈	#10596940	1	1	yes	characteristic
54	C₈	C₂²⋊Dic₃₇	1	1	yes	characteristic
55	C₂²	#11924480	1	1	yes	characteristic
56	C₄	—	8	2	no	—
57	C₄	#11924457	1	1	yes	characteristic
58	C₄	#11924477	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#14557334	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14557334
commutator	C₁₆×C₃₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₃₇
Fitting	C₂×Q₃₂×C₃₇	C₂
socle	C₂×C₃₇	#357
prime radical	C₂²×C₃₇	SD₃₂
cosocle	C₂×C₁₆×C₃₇	C₂²
hypercenter	C₂×Q₃₂	D₃₇
hypocenter	C₃₇	#1420
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

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

Maximal subgroups

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

subgroup	index
#14557367	2
#14557363	2
C₂×Q₃₂×C₃₇	2
#1420	37