Subgroups — D₃₇₃⋊M₁₆ #26045877

Order 11936.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20238620	C₂	1	2	yes	maximal, complemented
2	#20238619	C₂	1	2	yes	maximal, complemented
3	D₃₇₃⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₃₇₃	C₂	1	1	yes	maximal, characteristic
5	#15688419	C₂²	1	4	yes	complemented
6	C₂²×D₃₇₃	C₄	1	1	yes	characteristic
7	C₂×Dic₃₇₃	C₂²	1	1	yes	characteristic
8	C₄×D₃₇₃	C₄	1	1	yes	characteristic
9	C₄×D₃₇₃	C₄	1	1	yes	characteristic
10	C₄×D₃₇₃	C₂²	1	1	yes	characteristic
11	C₄×D₃₇₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₃₇₃	C₄	1	1	yes	characteristic
13	C₂²×C₃₇₃	C₂×C₄	1	1	yes	characteristic
14	C₂×D₃₇₃	—	2	2	no	—
15	C₂×D₃₇₃	C₂×C₄	1	1	yes	characteristic
16	C₂×D₃₇₃	C₂×C₄	1	1	yes	characteristic
17	C₄×C₃₇₃	C₂×C₄	1	1	yes	characteristic
18	C₄×C₃₇₃	C₂×C₄	1	1	yes	characteristic
19	Dic₃₇₃	C₂×C₄	1	1	yes	characteristic
20	Dic₃₇₃	C₂³	1	1	yes	characteristic
21	C₂×C₃₇₃	—	2	1	no	—
22	C₂×C₃₇₃	C₂²×C₄	1	1	yes	characteristic
23	D₃₇₃	—	2	1	no	—
24	D₃₇₃	M₁₆	1	2	yes	complemented
25	C₃₇₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	373	1	no	maximal, Sylow
27	C₂²×C₄	—	373	1	no	—
28	M₁₆	—	373	2	no	—
29	M₁₆	—	373	2	no	—
30	C₂×C₈	—	373	2	no	—
31	C₂³	—	373	1	no	—
32	C₂×C₄	—	373	1	no	—
33	C₂×C₄	—	373	1	no	—
34	C₂×C₄	—	373	1	no	—
35	C₂×C₄	—	373	1	no	—
36	C₂×C₄	—	373	1	no	—
37	C₂×C₄	#13093637	1	1	yes	characteristic
38	C₈	—	373	4	no	—
39	C₂²	—	373	1	no	—
40	C₂²	—	373	1	no	—
41	C₂²	—	746	2	no	—
42	C₂²	C₂×#13093637	1	1	yes	characteristic
43	C₄	—	373	1	no	—
44	C₄	—	373	1	no	—
45	C₄	C₂×#13093637	1	1	yes	characteristic
46	C₄	C₂×#13093637	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	373	2	no	—
49	C₂	—	746	1	no	—
50	C₂	C₂²×#13093637	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13093637
commutator, socle	C₂×C₃₇₃	C₂²×C₄
Frattini	C₂	C₂²×#13093637
Fitting	C₂×C₄×C₃₇₃	C₄
prime radical	C₂²×D₃₇₃	C₄
cosocle	Dic₃₇₃	C₂³
hypercenter	C₂×C₄	#13093637
hypocenter	C₃₇₃	C₂×M₁₆
LCS	G ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #20238620	C₂	semidirect
2. #20238619	C₂	semidirect
3. D₃₇₃⋊C₈	C₂	semidirect
5. #15688419	C₂²	semidirect
24. D₃₇₃	M₁₆	semidirect
25. C₃₇₃	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#20238620	2
#20238619	2
D₃₇₃⋊C₈	2
C₂×C₄×D₃₇₃	2
C₂×M₁₆	373

Subgroups — D373⋊M16 #26045877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₇₃⋊M₁₆ #26045877