Subgroups — C₂×D₃₇₃⋊C₁₆ #37560476

Order 23872.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇₃⋊C₁₆	C₂	1	4	yes	maximal, direct product factor
2	C₂×#20238613	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₃₇₃	C₂	1	1	yes	maximal, characteristic
4	#20238613	C₂²	1	4	yes	complemented
5	C₂×C₄×D₃₇₃	C₄	1	1	yes	characteristic
6	C₂×#15688412	C₂²	1	1	yes	characteristic
7	C₈×D₃₇₃	C₄	1	2	yes	—
8	C₈×D₃₇₃	C₂²	1	2	yes	—
9	C₂×C₈×C₃₇₃	C₄	1	1	yes	characteristic
10	C₂²×D₃₇₃	C₈	1	1	yes	characteristic
11	C₂×Dic₃₇₃	C₈	1	1	yes	characteristic
12	C₄×D₃₇₃	C₈	1	2	yes	—
13	C₄×D₃₇₃	C₂×C₄	1	2	yes	—
14	#15688412	C₂×C₄	1	1	yes	characteristic
15	#15688412	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₃₇₃	C₂×C₄	1	1	yes	characteristic
17	C₈×C₃₇₃	C₂×C₄	1	2	yes	—
18	C₂²×C₃₇₃	C₂×C₈	1	1	yes	characteristic
19	C₂×D₃₇₃	C₁₆	1	4	yes	complemented
20	C₂×D₃₇₃	C₂×C₈	1	2	yes	—
21	C₄×C₃₇₃	C₂×C₈	1	1	yes	characteristic
22	C₄×C₃₇₃	C₂²×C₄	1	1	yes	characteristic
23	Dic₃₇₃	C₂×C₈	1	2	yes	—
24	C₂×C₃₇₃	C₂×C₁₆	1	2	yes	complemented
25	C₂×C₃₇₃	C₂²×C₈	1	1	yes	characteristic
26	D₃₇₃	C₂×C₁₆	1	4	yes	complemented
27	C₃₇₃	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₁₆	—	373	1	no	maximal, Sylow
29	C₂²×C₈	—	373	1	no	—
30	C₂×C₁₆	—	373	2	no	—
31	C₂×C₁₆	—	373	4	no	—
32	C₂²×C₄	—	373	1	no	—
33	C₂×C₈	—	373	1	no	—
34	C₂×C₈	—	373	2	no	—
35	C₂×C₈	—	373	2	no	—
36	C₂×C₈	#13093637	1	1	yes	characteristic
37	C₁₆	—	373	4	no	—
38	C₂³	—	373	1	no	—
39	C₂×C₄	—	373	1	no	—
40	C₂×C₄	—	373	2	no	—
41	C₂×C₄	—	373	2	no	—
42	C₂×C₄	C₂×#13093637	1	1	yes	characteristic
43	C₈	—	373	1	no	—
44	C₈	—	373	1	no	—
45	C₈	C₂×#13093637	1	2	yes	—
46	C₂²	—	373	4	no	—
47	C₂²	—	373	2	no	—
48	C₂²	D₃₇₃⋊C₈	1	1	yes	characteristic
49	C₄	—	373	2	no	—
50	C₄	D₃₇₃⋊C₈	1	1	yes	characteristic
51	C₄	C₂²×#13093637	1	1	yes	characteristic
52	C₂	—	373	4	no	—
53	C₂	D₃₇₃⋊C₁₆	1	2	yes	direct product factor
54	C₂	C₂×D₃₇₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	#13093637
commutator, hypocenter	C₃₇₃	C₂²×C₁₆
Frattini	C₄	C₂²×#13093637
Fitting	C₂×C₈×C₃₇₃	C₄
socle	C₂²×C₃₇₃	C₂×C₈
prime radical	C₂²×D₃₇₃	C₈
cosocle	#15688412	C₂³
LCS	G ▷ C₃₇₃
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. D₃₇₃⋊C₁₆	C₂	direct (N × H)
2. C₂×#20238613	C₂	semidirect
4. #20238613	C₂²	semidirect
19. C₂×D₃₇₃	C₁₆	semidirect
24. C₂×C₃₇₃	C₂×C₁₆	semidirect
26. D₃₇₃	C₂×C₁₆	semidirect
27. C₃₇₃	C₂²×C₁₆	semidirect
53. C₂	D₃₇₃⋊C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃₇₃⋊C₁₆	2
C₂×#20238613	2
C₂×C₈×D₃₇₃	2
C₂²×C₁₆	373

Subgroups — C2×D373⋊C16 #37560476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₇₃⋊C₁₆ #37560476