Subgroups — C₄⋊#20238613 #37560342

Order 23872.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20238613	C₂	1	2	yes	maximal
2	C₄×#15688412	C₂	1	1	yes	maximal, characteristic
3	#20238613	—	2	2	no	—
4	C₂×#15688412	C₄	1	1	yes	characteristic
5	C₂×#15688412	C₂²	1	1	yes	characteristic
6	C₄²×C₃₇₃	C₄	1	1	yes	characteristic
7	#15688412	—	2	1	no	—
8	#15688412	D₄	1	1	yes	characteristic
9	#15688412	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₃₇₃	C₈	1	1	yes	characteristic
11	C₂×C₄×C₃₇₃	C₈	1	1	yes	characteristic
12	C₂×C₄×C₃₇₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₃₇₃	C₂×C₈	1	1	yes	characteristic
14	C₄×C₃₇₃	—	2	1	no	—
15	C₄×C₃₇₃	C₁₆	1	2	yes	complemented
16	C₄×C₃₇₃	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₃₇₃	M₁₆	1	1	yes	characteristic
18	C₂×C₃₇₃	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₃₇₃	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₃₇₃	M₃₂	1	1	yes	characteristic
21	C₃₇₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	373	1	no	maximal, Sylow
23	C₂×C₁₆	—	373	2	no	—
24	C₄×C₈	—	373	1	no	—
25	C₂×C₈	—	373	1	no	—
26	C₂×C₈	—	373	1	no	—
27	C₄²	#13093637	1	1	yes	characteristic
28	C₁₆	—	746	2	no	—
29	C₂×C₄	#15688419	1	1	yes	characteristic
30	C₂×C₄	#15688419	1	1	yes	characteristic
31	C₂×C₄	C₂×#13093637	1	1	yes	characteristic
32	C₈	—	373	1	no	—
33	C₈	—	373	1	no	—
34	C₈	—	746	1	no	—
35	C₂²	C₂×#15688419	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	#20238613	1	2	yes	complemented
38	C₄	C₄⋊#13093637	1	1	yes	characteristic
39	C₄	#20238620	1	1	yes	characteristic
40	C₂	C₄⋊#15688419	1	1	yes	characteristic
41	C₂	C₂×#20238613	1	1	yes	characteristic
42	C₂	#26045866	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#13093637
commutator	C₂×C₃₇₃	C₂×C₁₆
Fitting	C₄²×C₃₇₃	C₄
socle, prime radical	C₂²×C₃₇₃	C₂×C₈
cosocle	C₂×#15688412	C₂²
hypercenter	C₄²	#13093637
hypocenter	C₃₇₃	C₄⋊C₁₆
LCS	G ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
15. C₄×C₃₇₃	C₁₆	semidirect
21. C₃₇₃	C₄⋊C₁₆	semidirect
37. C₄	#20238613	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20238613	2
C₄×#15688412	2
C₄⋊C₁₆	373

Subgroups — C4⋊#20238613 #37560342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#20238613 #37560342