Subgroups — D₄⋊#14555667 #31800849

Order 17728.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14555667	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#14555667	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₂₇₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#14555667	—	2	1	no	—
5	C₂×#14555667	—	2	1	no	—
6	C₂²×Dic₂₇₇	—	2	1	no	—
7	C₄⋊Dic₂₇₇	C₄	1	1	yes	characteristic
8	C₂²⋊Dic₂₇₇	—	2	1	no	—
9	C₄×Dic₂₇₇	C₂²	1	1	yes	characteristic
10	C₂×D₄×C₂₇₇	C₄	1	1	yes	characteristic
11	#14555667	—	2	2	no	—
12	#14555667	—	4	1	no	—
13	C₂×Dic₂₇₇	—	2	1	no	—
14	C₂×Dic₂₇₇	—	4	1	no	—
15	C₂×Dic₂₇₇	—	4	1	no	—
16	C₂×Dic₂₇₇	D₄	1	1	yes	characteristic
17	C₂×Dic₂₇₇	D₄	1	1	yes	characteristic
18	C₂³×C₂₇₇	—	2	1	no	—
19	D₄×C₂₇₇	—	2	1	no	—
20	D₄×C₂₇₇	C₈	1	2	yes	complemented
21	C₂×C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₂₇₇	—	2	2	no	—
23	C₂²×C₂₇₇	—	4	1	no	—
24	C₂²×C₂₇₇	—	4	1	no	—
25	C₂²×C₂₇₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₄×C₂₇₇	C₂×C₈	1	1	yes	characteristic
27	C₄×C₂₇₇	M₁₆	1	1	yes	characteristic
28	Dic₂₇₇	—	2	1	no	—
29	Dic₂₇₇	—	4	1	no	—
30	Dic₂₇₇	D₈	1	1	yes	characteristic
31	Dic₂₇₇	SD₁₆	1	1	yes	characteristic
32	C₂×C₂₇₇	—	4	2	no	—
33	C₂×C₂₇₇	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₂₇₇	#102	1	1	yes	characteristic
35	C₂×C₂₇₇	#104	1	1	yes	characteristic
36	C₂₇₇	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
37	D₄⋊C₈	—	277	1	no	maximal, Sylow
38	C₄×D₄	—	277	1	no	—
39	C₄⋊C₈	—	277	1	no	—
40	C₄×C₈	—	277	1	no	—
41	C₂×D₄	#11764308	1	1	yes	characteristic
42	C₂²×C₄	—	554	1	no	—
43	C₂×C₈	—	554	1	no	—
44	C₂×C₈	—	554	1	no	—
45	C₄⋊C₄	—	277	1	no	—
46	C₂²⋊C₄	—	554	1	no	—
47	C₄²	—	277	1	no	—
48	C₂³	—	2	1	no	—
49	D₄	—	2	1	no	—
50	D₄	#14555667	1	2	yes	complemented
51	C₂×C₄	—	277	1	no	—
52	C₂×C₄	—	277	1	no	—
53	C₂×C₄	—	554	1	no	—
54	C₂×C₄	—	1108	1	no	—
55	C₂×C₄	—	1108	1	no	—
56	C₂×C₄	C₂×#11764308	1	1	yes	characteristic
57	C₈	—	554	2	no	—
58	C₈	—	1108	1	no	—
59	C₂²	—	2	2	no	—
60	C₂²	—	4	1	no	—
61	C₂²	—	4	1	no	—
62	C₂²	C₂²⋊#11764308	1	1	yes	characteristic
63	C₄	—	277	1	no	—
64	C₄	—	277	1	no	—
65	C₄	—	554	1	no	—
66	C₄	—	1108	1	no	—
67	C₄	C₂×#14555667	1	1	yes	characteristic
68	C₄	#17984572	1	1	yes	characteristic
69	C₂	—	4	2	no	—
70	C₂	C₂²⋊#14555667	1	1	yes	characteristic
71	C₂	#22579942	1	1	yes	characteristic
72	C₂	#22579944	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#11764308
commutator	C₄×C₂₇₇	C₂×C₈
Frattini	C₂×C₄	C₂×#11764308
Fitting, prime radical	C₂×D₄×C₂₇₇	C₄
socle	C₂²×C₂₇₇	C₂²⋊C₄
cosocle	C₄×Dic₂₇₇	C₂²
hypercenter	C₂×D₄	#11764308
hypocenter	C₂₇₇	D₄⋊C₈
LCS	G ▷ C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
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⋊#14555667	C₂	semidirect
2. C₄×#14555667	C₂	semidirect
20. D₄×C₂₇₇	C₈	semidirect
36. C₂₇₇	D₄⋊C₈	semidirect
50. D₄	#14555667	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14555667	2
C₄×#14555667	2
D₄×Dic₂₇₇	2
D₄⋊C₈	277

Subgroups — D4⋊#14555667 #31800849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄⋊#14555667 #31800849