Group #22626977 — subgroups

Subgroups — #22626977

Order 9344.

110 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 31 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	#64408⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989677	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×#64408	C₂	1	1	yes	maximal, characteristic
4	#14556686	—	2	1	no	—
5	C₄⋊#10596842	—	2	1	no	—
6	D₄×#64408	—	2	1	no	—
7	#14556660	C₄	1	1	yes	characteristic
8	#14556653	—	2	1	no	—
9	C₈×#64408	C₂²	1	1	yes	characteristic
10	D₈×D₇₃	C₄	1	1	yes	characteristic
11	C₂×#10596842	—	4	1	no	—
12	#11924040	—	2	2	no	—
13	C₂²×#64408	—	4	1	no	—
14	#11924036	D₄	1	1	yes	characteristic
15	C₄⋊#64408	—	2	1	no	—
16	C₂²⋊#64408	—	4	1	no	—
17	C₄×#64408	D₄	1	1	yes	characteristic
18	D₄×D₇₃	—	2	1	no	—
19	D₅₈₄	C₈	1	1	yes	characteristic, complemented
20	#11924013	—	2	1	no	—
21	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
22	D₈×C₇₃	C₈	1	1	yes	characteristic, complemented
23	C₂²×D₇₃	—	4	1	no	—
24	C₂×#64408	—	4	1	no	—
25	C₂×#64408	—	8	1	no	—
26	C₂×#64408	—	8	1	no	—
27	C₂×#64408	D₈	1	1	yes	characteristic
28	C₂×#64408	SD₁₆	1	1	yes	characteristic
29	#10596842	—	8	1	no	—
30	D₄×C₇₃	—	2	1	no	—
31	C₂²⋊D₇₃	—	4	1	no	—
32	D₂₉₂	—	2	1	no	—
33	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
34	#10596833	—	2	1	no	—
35	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
36	#10596831	M₁₆	1	1	yes	characteristic
37	C₂²×C₇₃	—	4	1	no	—
38	C₂×D₇₃	—	4	1	no	—
39	C₂×D₇₃	—	8	1	no	—
40	C₂×D₇₃	—	8	1	no	—
41	C₂×D₇₃	#102	1	1	yes	characteristic
42	#64408	—	2	1	no	—
43	#64408	—	8	1	no	—
44	#64408	D₁₆	1	1	yes	characteristic
45	#64408	SD₃₂	1	1	yes	characteristic
46	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
47	Dic₇₃	#104	1	1	yes	characteristic
48	C₂×C₇₃	—	8	1	no	—
49	C₂×C₇₃	D₄⋊C₈	1	1	yes	characteristic
50	D₇₃	—	8	1	no	—
51	D₇₃	#357	1	1	yes	characteristic
52	D₇₃	#359	1	1	yes	characteristic
53	#1331	—	73	1	no	maximal, Sylow
54	C₇₃	#1331	1	1	yes	characteristic, complemented, Sylow
55	C₄×D₈	—	73	1	no	—
56	C₄×C₁₆	—	73	1	no	—
57	#335	—	73	1	no	—
58	C₂×D₈	—	73	1	no	—
59	C₄×D₄	—	146	1	no	—
60	C₂×C₁₆	—	146	1	no	—
61	#107	—	73	1	no	—
62	C₄⋊C₈	—	146	1	no	—
63	#102	—	146	1	no	—
64	C₄×C₈	—	73	1	no	—
65	C₂×D₄	—	146	1	no	—
66	C₂²×C₄	—	292	1	no	—
67	D₈	—	73	1	no	—
68	D₈	—	146	1	no	—
69	D₈	#10596842	1	1	yes	characteristic, complemented
70	C₂×C₈	—	292	1	no	—
71	C₂×C₈	—	73	1	no	—
72	C₂×C₈	—	73	1	no	—
73	C₄⋊C₄	—	146	1	no	—
74	C₂²⋊C₄	—	292	1	no	—
75	C₄²	—	73	1	no	—
76	C₁₆	—	146	2	no	—
77	C₂³	—	292	1	no	—
78	D₄	—	2	1	no	—
79	D₄	—	292	1	no	—
80	D₄	—	146	1	no	—
81	C₂×C₄	—	292	1	no	—
82	C₂×C₄	—	584	1	no	—
83	C₂×C₄	—	584	1	no	—
84	C₂×C₄	—	73	1	no	—
85	C₂×C₄	—	73	1	no	—
86	C₂×C₄	—	73	1	no	—
87	C₈	—	584	1	no	—
88	C₈	—	73	1	no	—
89	C₈	—	146	1	no	—
90	C₈	C₂×#10596842	1	1	yes	characteristic
91	C₂²	—	4	1	no	—
92	C₂²	—	292	1	no	—
93	C₂²	—	584	1	no	—
94	C₂²	—	584	1	no	—
95	C₂²	—	73	1	no	—
96	C₄	—	584	1	no	—
97	C₄	—	73	1	no	—
98	C₄	—	73	1	no	—
99	C₄	—	73	1	no	—
100	C₄	—	146	1	no	—
101	C₄	C₂²⋊#10596842	1	1	yes	characteristic
102	C₂	—	8	1	no	—
103	C₂	—	584	1	no	—
104	C₂	—	73	1	no	—
105	C₂	—	73	1	no	—
106	C₂	D₄⋊#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#64408⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#17989677

C₂

yes

maximal, characteristic, complemented

D₈×#64408

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

characteristic

#14556653

—

C₈×#64408

C₂²

yes

characteristic

D₈×D₇₃

C₄

yes

characteristic

C₂×#10596842

—

#11924040

—

C₂²×#64408

—

#11924036

D₄

yes

—

—

D₄

yes

characteristic

D₄×D₇₃

—

D₅₈₄

C₈

yes

characteristic, complemented

#11924013

—

C₈×D₇₃

C₂×C₄

yes

characteristic

D₈×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

—

—

—

—

D₈

yes

characteristic

C₂×#64408

SD₁₆

yes

characteristic

#10596842

—

D₄×C₇₃

—

C₂²⋊D₇₃

—

D₂₉₂

—

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

#10596833

—

C₈×C₇₃

C₂×C₈

yes

characteristic

#10596831

M₁₆

yes

characteristic

C₂²×C₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

yes

—

—

D₁₆

yes

characteristic

#64408

SD₃₂

yes

characteristic

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

Dic₇₃

#104

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

D₄⋊C₈

yes

characteristic

D₇₃

—

D₇₃

yes

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₄×D₈

—

C₄×C₁₆

—

#335

—

C₂×D₈

—

C₄×D₄

—

146

—

C₂×C₁₆

—

146

—

#107

—

C₄⋊C₈

—

146

—

#102

—

146

—

C₄×C₈

—

C₂×D₄

—

146

—

C₂²×C₄

—

292

—

D₈

—

D₈

—

146

—

D₈

#10596842

yes

characteristic, complemented

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

292

—

C₄²

—

C₁₆

—

146

—

C₂³

—

292

—

D₄

—

D₄

—

292

—

D₄

—

146

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

—

584

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₈

—

584

—

C₈

—

C₈

—

146

—

C₈

C₂×#10596842

yes

characteristic

C₂²

—

C₂²

—

292

—

C₂²

—

584

—

C₂²

—

584

—

C₂²

—

C₄

—

584

—

C₄

—

C₄

—

C₄

—

100

C₄

—

146

—

101

C₄

C₂²⋊#10596842

yes

characteristic

102

C₂

—

103

C₂

—

584

—

104

C₂

—

105

C₂

—

106

C₂

D₄⋊#10596842

yes

characteristic

	subgroup	G/H
center	C₂	D₄⋊#10596842
commutator	C₈×C₇₃	C₂×C₈
Frattini	C₈	C₂×#10596842
Fitting	D₈×C₇₃	C₈
socle	C₂×C₇₃	D₄⋊C₈
hypercenter	D₈	#10596842
hypocenter	C₇₃	#1331
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

subgroup

G/H

center

C₂

D₄⋊#10596842

commutator

C₈×C₇₃

C₂×C₈

Frattini

C₈

C₂×#10596842

Fitting

D₈×C₇₃

C₈

socle

C₂×C₇₃

D₄⋊C₈

D₈

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

N	H ≅ G/N	type
1. #64408⋊C₁₆	C₂	semidirect
2. #17989677	C₂	semidirect
19. D₅₈₄	C₈	semidirect
22. D₈×C₇₃	C₈	semidirect
54. C₇₃	#1331	semidirect
69. D₈	#10596842	semidirect

H ≅ G/N

type

1. #64408⋊C₁₆

C₂

semidirect

2. #17989677

C₂

semidirect

19. D₅₈₄

C₈

semidirect

22. D₈×C₇₃

C₈

semidirect

54. C₇₃

#1331

semidirect

69. D₈

#10596842

semidirect

Subgroups — #22626977

Conjugacy classes of subgroups

Complements