Subgroups — #37560427

Order 23872.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20238620	C₂	1	2	yes	maximal
2	#26045859	C₂	1	4	yes	maximal, complemented
3	C₄²×D₃₇₃	C₂	1	1	yes	maximal, characteristic
4	#20238620	—	2	4	no	—
5	C₂×#15688419	C₂²	1	4	yes	—
6	C₂×C₄×D₃₇₃	C₄	1	2	yes	—
7	C₂×C₄×D₃₇₃	C₂²	1	1	yes	characteristic
8	C₄×Dic₃₇₃	C₄	1	1	yes	characteristic
9	C₄×Dic₃₇₃	C₂²	1	2	yes	—
10	C₄²×C₃₇₃	C₄	1	1	yes	characteristic
11	#15688419	—	2	4	no	—
12	C₂²×D₃₇₃	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₃₇₃	C₂×C₄	1	2	yes	—
14	C₂×Dic₃₇₃	C₂³	1	1	yes	characteristic
15	C₄×D₃₇₃	—	2	4	no	—
16	C₄×D₃₇₃	D₄	1	2	yes	—
17	C₄×D₃₇₃	Q₈	1	2	yes	—
18	C₂×C₄×C₃₇₃	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₃₇₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₃₇₃	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₃₇₃	—	2	2	no	—
22	C₂×D₃₇₃	C₄⋊C₄	1	2	yes	—
23	C₄×C₃₇₃	—	2	2	no	—
24	C₄×C₃₇₃	C₄⋊C₄	1	2	yes	—
25	Dic₃₇₃	M₁₆	1	4	yes	complemented
26	Dic₃₇₃	C₂×D₄	1	1	yes	characteristic
27	Dic₃₇₃	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₃₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₃₇₃	C₂×M₁₆	1	2	yes	—
30	D₃₇₃	—	2	2	no	—
31	C₃₇₃	#423	1	1	yes	characteristic, complemented, Sylow
32	#423	—	373	1	no	maximal, Sylow
33	C₂×M₁₆	—	373	2	no	—
34	C₂×C₄²	—	373	1	no	—
35	C₄⋊C₈	—	373	4	no	—
36	C₂²×C₄	—	373	1	no	—
37	C₂²×C₄	—	373	2	no	—
38	M₁₆	—	746	4	no	—
39	C₂×C₈	—	373	4	no	—
40	C₄²	—	373	2	no	—
41	C₄²	—	373	1	no	—
42	C₄²	#13093637	1	1	yes	characteristic
43	C₂³	—	373	1	no	—
44	C₂×C₄	—	373	1	no	—
45	C₂×C₄	—	373	2	no	—
46	C₂×C₄	—	373	2	no	—
47	C₂×C₄	—	373	2	no	—
48	C₂×C₄	—	746	4	no	—
49	C₂×C₄	C₂×#13093637	1	2	yes	—
50	C₂×C₄	C₂×#13093637	1	1	yes	characteristic
51	C₈	—	746	4	no	—
52	C₂²	—	373	2	no	—
53	C₂²	—	746	2	no	—
54	C₂²	C₂²×#13093637	1	1	yes	characteristic
55	C₄	—	2	2	no	—
56	C₄	—	373	1	no	—
57	C₄	—	373	1	no	—
58	C₄	—	373	4	no	—
59	C₄	C₄⋊#13093637	1	2	yes	—
60	C₂	—	746	2	no	—
61	C₂	C₂×C₄⋊#13093637	1	1	yes	characteristic
62	C₂	D₃₇₃⋊M₁₆	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#13093637
commutator, socle	C₂²×C₃₇₃	C₂²×C₄
Fitting	C₄²×C₃₇₃	C₄
prime radical	C₂²×D₃₇₃	C₂×C₄
cosocle	C₂×Dic₃₇₃	C₂³
hypercenter	C₄²	#13093637
hypocenter	C₃₇₃	#423
LCS	G ▷ C₂²×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #26045859	C₂	semidirect
25. Dic₃₇₃	M₁₆	semidirect
31. C₃₇₃	#423	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20238620	2
#26045859	2
C₄²×D₃₇₃	2
#423	373