Subgroups — D₄⋊(C₁₂₇⋊C₈) #22549604

Order 8128.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₁₂₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₂₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₂₇⋊C₈	—	2	1	no	—
5	C₂×C₁₂₇⋊C₈	—	2	1	no	—
6	C₂×D₄×C₁₂₇	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₁₂₇	—	2	1	no	—
8	C₄⋊C₄×C₁₂₇	C₄	1	1	yes	characteristic
9	C₂²⋊C₄×C₁₂₇	—	2	1	no	—
10	C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
11	C₁₂₇⋊C₈	—	2	2	no	—
12	C₁₂₇⋊C₈	—	4	1	no	—
13	C₂³×C₁₂₇	—	2	1	no	—
14	D₄×C₁₂₇	—	2	1	no	—
15	D₄×C₁₂₇	C₈	1	2	yes	complemented
16	C₂×C₄×C₁₂₇	—	2	1	no	—
17	C₂×C₄×C₁₂₇	—	4	1	no	—
18	C₂×C₄×C₁₂₇	—	4	1	no	—
19	C₂×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₂₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₂₇	D₄	1	1	yes	characteristic
22	C₂²×C₁₂₇	—	2	2	no	—
23	C₂²×C₁₂₇	—	4	1	no	—
24	C₂²×C₁₂₇	—	4	1	no	—
25	C₂²×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₄×C₁₂₇	—	2	1	no	—
27	C₄×C₁₂₇	—	4	1	no	—
28	C₄×C₁₂₇	C₂×C₈	1	1	yes	characteristic
29	C₄×C₁₂₇	M₁₆	1	1	yes	characteristic
30	C₄×C₁₂₇	D₈	1	1	yes	characteristic
31	C₄×C₁₂₇	SD₁₆	1	1	yes	characteristic
32	C₂×C₁₂₇	—	4	2	no	—
33	C₂×C₁₂₇	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₁₂₇	#102	1	1	yes	characteristic
35	C₂×C₁₂₇	#104	1	1	yes	characteristic
36	C₁₂₇	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
37	D₄⋊C₈	—	127	1	no	maximal, Sylow
38	C₄×D₄	D₁₂₇	1	1	yes	characteristic
39	C₄⋊C₈	—	127	1	no	—
40	C₄×C₈	—	127	1	no	—
41	C₂×D₄	Dic₁₂₇	1	1	yes	characteristic
42	C₂²×C₄	—	2	1	no	—
43	C₂×C₈	—	254	1	no	—
44	C₂×C₈	—	254	1	no	—
45	C₄⋊C₄	Dic₁₂₇	1	1	yes	characteristic
46	C₂²⋊C₄	—	2	1	no	—
47	C₄²	C₂×D₁₂₇	1	1	yes	characteristic
48	C₂³	—	2	1	no	—
49	D₄	—	2	1	no	—
50	D₄	C₁₂₇⋊C₈	1	2	yes	complemented
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	4	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	C₂×Dic₁₂₇	1	1	yes	characteristic
55	C₂×C₄	C₂²⋊D₁₂₇	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₁₂₇	1	1	yes	characteristic
57	C₈	—	508	1	no	—
58	C₈	—	254	2	no	—
59	C₂²	—	2	2	no	—
60	C₂²	—	4	1	no	—
61	C₂²	—	4	1	no	—
62	C₂²	C₂²⋊Dic₁₂₇	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	—	4	1	no	—
65	C₄	C₂×C₁₂₇⋊C₈	1	1	yes	characteristic
66	C₄	#14523232	1	1	yes	characteristic
67	C₄	#14523233	1	1	yes	characteristic
68	C₄	#14523236	1	1	yes	characteristic
69	C₂	—	4	2	no	—
70	C₂	C₂²⋊(C₁₂₇⋊C₈)	1	1	yes	characteristic
71	C₂	#16861130	1	1	yes	characteristic
72	C₂	#16861136	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₁₂₇
commutator	C₄×C₁₂₇	C₂×C₈
Frattini	C₄²	C₂×D₁₂₇
Fitting	C₄×D₄×C₁₂₇	C₂
socle	C₂²×C₁₂₇	C₂²⋊C₄
hypercenter	C₄×D₄	D₁₂₇
hypocenter	C₁₂₇	D₄⋊C₈
LCS	G ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊(C₁₂₇⋊C₈)	C₂	semidirect
2. C₄×C₁₂₇⋊C₈	C₂	semidirect
15. D₄×C₁₂₇	C₈	semidirect
36. C₁₂₇	D₄⋊C₈	semidirect
50. D₄	C₁₂₇⋊C₈	semidirect

Subgroups — D4⋊(C127⋊C8) #22549604

Conjugacy classes of subgroups

Complements

Subgroups — D₄⋊(C₁₂₇⋊C₈) #22549604