Subgroups — D₄⋊#15688419 #37560269

Order 23872.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#15688419	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#15688419	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₃₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688419	—	2	1	no	—
5	C₂×#15688419	—	2	1	no	—
6	C₂²×Dic₃₇₃	—	2	1	no	—
7	C₄⋊Dic₃₇₃	C₄	1	1	yes	characteristic
8	C₂²⋊Dic₃₇₃	—	2	1	no	—
9	C₄×Dic₃₇₃	C₂²	1	1	yes	characteristic
10	C₂×D₄×C₃₇₃	C₄	1	1	yes	characteristic
11	#15688419	—	2	2	no	—
12	#15688419	—	4	1	no	—
13	C₂×Dic₃₇₃	—	2	1	no	—
14	C₂×Dic₃₇₃	—	4	1	no	—
15	C₂×Dic₃₇₃	—	4	1	no	—
16	C₂×Dic₃₇₃	D₄	1	1	yes	characteristic
17	C₂×Dic₃₇₃	D₄	1	1	yes	characteristic
18	C₂³×C₃₇₃	—	2	1	no	—
19	D₄×C₃₇₃	—	2	1	no	—
20	D₄×C₃₇₃	C₈	1	2	yes	complemented
21	C₂×C₄×C₃₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₃₇₃	—	2	2	no	—
23	C₂²×C₃₇₃	—	4	1	no	—
24	C₂²×C₃₇₃	—	4	1	no	—
25	C₂²×C₃₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₄×C₃₇₃	C₂×C₈	1	1	yes	characteristic
27	C₄×C₃₇₃	M₁₆	1	1	yes	characteristic
28	Dic₃₇₃	—	2	1	no	—
29	Dic₃₇₃	—	4	1	no	—
30	Dic₃₇₃	D₈	1	1	yes	characteristic
31	Dic₃₇₃	SD₁₆	1	1	yes	characteristic
32	C₂×C₃₇₃	—	4	2	no	—
33	C₂×C₃₇₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₃₇₃	#102	1	1	yes	characteristic
35	C₂×C₃₇₃	#104	1	1	yes	characteristic
36	C₃₇₃	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
37	D₄⋊C₈	—	373	1	no	maximal, Sylow
38	C₄×D₄	—	373	1	no	—
39	C₄⋊C₈	—	373	1	no	—
40	C₄×C₈	—	373	1	no	—
41	C₂×D₄	#13093637	1	1	yes	characteristic
42	C₂²×C₄	—	746	1	no	—
43	C₂×C₈	—	746	1	no	—
44	C₂×C₈	—	746	1	no	—
45	C₄⋊C₄	—	373	1	no	—
46	C₂²⋊C₄	—	746	1	no	—
47	C₄²	—	373	1	no	—
48	C₂³	—	2	1	no	—
49	D₄	—	2	1	no	—
50	D₄	#15688419	1	2	yes	complemented
51	C₂×C₄	—	373	1	no	—
52	C₂×C₄	—	373	1	no	—
53	C₂×C₄	—	1492	1	no	—
54	C₂×C₄	—	1492	1	no	—
55	C₂×C₄	—	746	1	no	—
56	C₂×C₄	C₂×#13093637	1	1	yes	characteristic
57	C₈	—	1492	1	no	—
58	C₈	—	746	2	no	—
59	C₂²	—	2	2	no	—
60	C₂²	—	4	1	no	—
61	C₂²	—	4	1	no	—
62	C₂²	C₂²⋊#13093637	1	1	yes	characteristic
63	C₄	—	373	1	no	—
64	C₄	—	373	1	no	—
65	C₄	—	1492	1	no	—
66	C₄	—	746	1	no	—
67	C₄	C₂×#15688419	1	1	yes	characteristic
68	C₄	#20238619	1	1	yes	characteristic
69	C₂	—	4	2	no	—
70	C₂	C₂²⋊#15688419	1	1	yes	characteristic
71	C₂	#26045854	1	1	yes	characteristic
72	C₂	#26045856	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#13093637
commutator	C₄×C₃₇₃	C₂×C₈
Frattini	C₂×C₄	C₂×#13093637
Fitting, prime radical	C₂×D₄×C₃₇₃	C₄
socle	C₂²×C₃₇₃	C₂²⋊C₄
cosocle	C₄×Dic₃₇₃	C₂²
hypercenter	C₂×D₄	#13093637
hypocenter	C₃₇₃	D₄⋊C₈
LCS	G ▷ C₄×C₃₇₃ ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊#15688419	C₂	semidirect
2. C₄×#15688419	C₂	semidirect
20. D₄×C₃₇₃	C₈	semidirect
36. C₃₇₃	D₄⋊C₈	semidirect
50. D₄	#15688419	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#15688419	2
C₄×#15688419	2
D₄×Dic₃₇₃	2
D₄⋊C₈	373

Subgroups — D4⋊#15688419 #37560269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄⋊#15688419 #37560269