Group #22624881 — subgroups

Subgroups — D₄⋊#11924031 #22624881

Order 9344.

110 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11924031	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#11924031	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#10596831	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924031	—	2	1	no	—
5	C₂×#11924031	—	2	1	no	—
6	C₂²×#10596831	—	2	1	no	—
7	C₄⋊#10596831	C₄	1	1	yes	characteristic
8	C₂²⋊#10596831	—	2	1	no	—
9	C₄×#10596831	C₂²	1	1	yes	characteristic
10	C₄×D₄×C₇₃	C₄	1	1	yes	characteristic
11	#11924031	—	2	2	no	—
12	#11924031	—	4	1	no	—
13	C₂×#10596831	—	2	1	no	—
14	C₂×#10596831	—	4	1	no	—
15	C₂×#10596831	—	4	1	no	—
16	C₂×#10596831	D₄	1	1	yes	characteristic
17	C₂×#10596831	D₄	1	1	yes	characteristic
18	C₂×D₄×C₇₃	C₈	1	1	yes	characteristic
19	C₂²×C₄×C₇₃	—	2	1	no	—
20	C₄⋊C₄×C₇₃	C₈	1	1	yes	characteristic
21	C₂²⋊C₄×C₇₃	—	2	1	no	—
22	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₇₃	—	2	1	no	—
24	D₄×C₇₃	—	2	1	no	—
25	D₄×C₇₃	C₁₆	1	2	yes	complemented
26	C₂×C₄×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	—	4	1	no	—
28	C₂×C₄×C₇₃	—	4	1	no	—
29	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
32	#10596831	—	2	1	no	—
33	#10596831	—	4	1	no	—
34	#10596831	D₈	1	1	yes	characteristic
35	#10596831	SD₁₆	1	1	yes	characteristic
36	C₂²×C₇₃	—	2	2	no	—
37	C₂²×C₇₃	—	4	1	no	—
38	C₂²×C₇₃	—	4	1	no	—
39	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₇₃	—	2	1	no	—
41	C₄×C₇₃	—	4	1	no	—
42	C₄×C₇₃	#102	1	1	yes	characteristic
43	C₄×C₇₃	#104	1	1	yes	characteristic
44	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
45	C₄×C₇₃	M₃₂	1	1	yes	characteristic
46	C₂×C₇₃	—	4	2	no	—
47	C₂×C₇₃	D₄⋊C₈	1	1	yes	characteristic
48	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
49	C₂×C₇₃	#350	1	1	yes	characteristic
50	D₄⋊C₁₆	—	73	1	no	maximal, Sylow
51	C₇₃	D₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
52	C₈×D₄	—	73	1	no	—
53	C₄⋊C₁₆	—	73	1	no	—
54	C₄×C₁₆	—	73	1	no	—
55	C₂²×C₈	—	146	1	no	—
56	C₄×D₄	#64408	1	1	yes	characteristic
57	C₂×C₁₆	—	146	1	no	—
58	C₂×C₁₆	—	146	1	no	—
59	C₄⋊C₈	—	73	1	no	—
60	C₂²⋊C₈	—	146	1	no	—
61	C₄×C₈	—	73	1	no	—
62	C₂×D₄	#10596833	1	1	yes	characteristic
63	C₂²×C₄	—	2	1	no	—
64	C₂×C₈	—	292	1	no	—
65	C₂×C₈	—	292	1	no	—
66	C₂×C₈	—	73	1	no	—
67	C₂×C₈	—	73	1	no	—
68	C₂×C₈	—	146	1	no	—
69	C₄⋊C₄	#10596833	1	1	yes	characteristic
70	C₂²⋊C₄	—	2	1	no	—
71	C₄²	C₂×#64408	1	1	yes	characteristic
72	C₁₆	—	292	1	no	—
73	C₁₆	—	146	2	no	—
74	C₂³	—	2	1	no	—
75	D₄	—	2	1	no	—
76	D₄	#11924031	1	2	yes	complemented
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	4	1	no	—
79	C₂×C₄	—	4	1	no	—
80	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
81	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
82	C₂×C₄	#11924037	1	1	yes	characteristic
83	C₈	—	292	1	no	—
84	C₈	—	73	1	no	—
85	C₈	—	73	1	no	—
86	C₈	—	146	1	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	4	1	no	—
89	C₂²	—	4	1	no	—
90	C₂²	C₂²⋊#10596833	1	1	yes	characteristic
91	C₄	—	2	1	no	—
92	C₄	—	4	1	no	—
93	C₄	#14556653	1	1	yes	characteristic
94	C₄	#14556655	1	1	yes	characteristic
95	C₄	C₂×#11924031	1	1	yes	characteristic
96	C₄	#14556665	1	1	yes	characteristic
97	C₂	—	4	2	no	—
98	C₂	D₄⋊#10596833	1	1	yes	characteristic
99	C₂	C₂²⋊#11924031	1	1	yes	characteristic
100	C₂	#17989485	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#11924031

C₂

yes

maximal, characteristic, complemented

C₄×#11924031

C₂

yes

maximal, characteristic, complemented

D₄×#10596831

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

characteristic

C₂²⋊#10596831

—

C₄×#10596831

C₂²

yes

characteristic

C₄×D₄×C₇₃

C₄

yes

—

—

—

—

—

D₄

yes

characteristic

C₂×#10596831

D₄

yes

characteristic

C₂×D₄×C₇₃

C₈

yes

characteristic

C₂²×C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₈

yes

characteristic

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

C₁₆

yes

complemented

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

—

—

D₈

yes

characteristic

#10596831

SD₁₆

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

C₂×C₁₆

yes

characteristic

C₄×C₇₃

M₃₂

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

D₄⋊C₈

yes

characteristic

C₂×C₇₃

C₂²⋊C₁₆

yes

characteristic

C₂×C₇₃

#350

yes

characteristic

D₄⋊C₁₆

—

maximal, Sylow

C₇₃

D₄⋊C₁₆

yes

characteristic, complemented, Sylow

C₈×D₄

—

C₄⋊C₁₆

—

C₄×C₁₆

—

C₂²×C₈

—

146

—

C₄×D₄

#64408

yes

characteristic

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

C₄⋊C₈

—

C₂²⋊C₈

—

146

—

C₄×C₈

—

C₂×D₄

#10596833

yes

characteristic

C₂²×C₄

—

C₂×C₈

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

#10596833

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂×#64408

yes

characteristic

C₁₆

—

292

—

C₁₆

—

146

—

C₂³

—

D₄

—

D₄

#11924031

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

292

—

C₈

—

C₈

—

C₈

—

146

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂²⋊#10596833

yes

characteristic

C₄

—

C₄

—

C₄

yes

C₄

yes

C₄

yes

C₄

yes

C₂

—

C₂

yes

C₂

yes

100

C₂

#17989485

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#64408
commutator	C₄×C₇₃	C₂×C₁₆
Frattini	C₄²	C₂×#64408
Fitting	C₄×D₄×C₇₃	C₄
socle	C₂²×C₇₃	C₂²⋊C₈
hypercenter	C₄×D₄	#64408
hypocenter	C₇₃	D₄⋊C₁₆
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₄

subgroup

G/H

center

C₂×C₄

C₂²⋊#64408

commutator

C₄×C₇₃

C₂×C₁₆

Frattini

C₄²

C₂×#64408

Fitting

C₄×D₄×C₇₃

C₄

socle

C₂²×C₇₃

C₂²⋊C₈

hypercenter

C₄×D₄

#64408

hypocenter

C₇₃

D₄⋊C₁₆

LCS

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₄

N	H ≅ G/N	type
1. C₄⋊#11924031	C₂	semidirect
2. C₄×#11924031	C₂	semidirect
25. D₄×C₇₃	C₁₆	semidirect
51. C₇₃	D₄⋊C₁₆	semidirect
76. D₄	#11924031	semidirect

H ≅ G/N

type

1. C₄⋊#11924031

C₂

semidirect

2. C₄×#11924031

C₂

semidirect

25. D₄×C₇₃

C₁₆

semidirect

51. C₇₃

D₄⋊C₁₆

semidirect

76. D₄

#11924031

semidirect

Subgroups — D₄⋊#11924031 #22624881

Conjugacy classes of subgroups

Complements

Subgroups — D4⋊#11924031 #22624881

Conjugacy classes of subgroups

Complements

Subgroups — D₄⋊#11924031 #22624881