Subgroups — #37559239

Order 23872.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄₉₂	C₂	1	1	yes	maximal, characteristic
2	#26045728	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₃₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₄₆	—	2	1	no	—
5	Dic₁₄₉₂	—	2	1	no	—
6	Dic₁₄₉₂	C₄	1	2	yes	—
7	#20238594	—	2	1	no	—
8	C₂×C₈×C₃₇₃	C₂²	1	1	yes	characteristic
9	C₁₆×C₃₇₃	—	2	1	no	—
10	Dic₇₄₆	—	2	2	no	—
11	Dic₇₄₆	—	4	1	no	—
12	C₂×Dic₃₇₃	—	4	1	no	—
13	#15688412	—	4	1	no	—
14	C₂×C₄×C₃₇₃	D₄	1	1	yes	characteristic
15	C₈×C₃₇₃	C₂×C₄	1	1	yes	characteristic
16	C₈×C₃₇₃	D₄	1	1	yes	characteristic
17	C₂²×C₃₇₃	SD₁₆	1	1	yes	characteristic
18	C₄×C₃₇₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₃₇₃	D₈	1	1	yes	characteristic
20	Dic₃₇₃	—	4	2	no	—
21	C₂×C₃₇₃	—	2	1	no	—
22	C₂×C₃₇₃	#102	1	1	yes	characteristic
23	C₃₇₃	#362	1	1	yes	characteristic, complemented, Sylow
24	#362	—	373	1	no	maximal, Sylow
25	C₂×Q₁₆	—	373	1	no	—
26	M₃₂	D₃₇₃	1	1	yes	characteristic
27	#108	—	373	1	no	—
28	C₂×Q₈	—	746	1	no	—
29	Q₁₆	—	373	2	no	—
30	Q₁₆	—	746	1	no	—
31	M₁₆	—	746	1	no	—
32	C₂×C₈	C₂×D₃₇₃	1	1	yes	characteristic
33	C₁₆	—	2	1	no	—
34	Q₈	—	1492	1	no	—
35	Q₈	—	746	2	no	—
36	C₂×C₄	—	1492	1	no	—
37	C₂×C₄	D₁₄₉₂	1	1	yes	characteristic
38	C₈	—	1492	1	no	—
39	C₈	C₄×D₃₇₃	1	1	yes	characteristic
40	C₈	C₂²⋊D₃₇₃	1	1	yes	characteristic
41	C₂²	#20238599	1	1	yes	characteristic
42	C₄	—	1492	2	no	—
43	C₄	#20238587	1	1	yes	characteristic
44	C₄	D₂₉₈₄	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#26045714	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26045714
commutator	C₈×C₃₇₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₃₇₃
Fitting	M₃₂×C₃₇₃	C₂
socle	C₂×C₃₇₃	#102
prime radical	C₂²×C₃₇₃	SD₁₆
cosocle	C₂×C₈×C₃₇₃	C₂²
hypercenter	M₃₂	D₃₇₃
hypocenter	C₃₇₃	#362
LCS	G ▷ C₈×C₃₇₃ ▷ C₄×C₃₇₃ ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
23. C₃₇₃	#362	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₄₉₂	2
#26045728	2
M₃₂×C₃₇₃	2
#362	373