Group #22624885 — subgroups

Subgroups — #22624885

Order 9344.

110 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 40 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	#17989473	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989450	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924031	—	2	1	no	—
5	C₄⋊#10596833	—	2	1	no	—
6	D₄×Dic₇₃	—	2	1	no	—
7	#14556525	C₄	1	1	yes	characteristic
8	#14556512	—	2	1	no	—
9	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
10	C₂×D₈×C₇₃	C₄	1	1	yes	characteristic
11	C₂×#10596833	—	4	1	no	—
12	#11924031	—	2	2	no	—
13	C₂²×Dic₇₃	—	4	1	no	—
14	C₂×#10596831	D₄	1	1	yes	characteristic
15	C₄⋊Dic₇₃	—	2	1	no	—
16	C₂²⋊Dic₇₃	—	4	1	no	—
17	C₄×Dic₇₃	D₄	1	1	yes	characteristic
18	C₂×D₄×C₇₃	—	2	1	no	—
19	D₈×C₇₃	—	2	1	no	—
20	D₈×C₇₃	C₈	1	2	yes	complemented
21	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₇₃	—	4	1	no	—
23	D₄×C₇₃	—	2	2	no	—
24	D₄×C₇₃	—	4	1	no	—
25	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₇₃	—	4	1	no	—
27	C₂×Dic₇₃	—	8	1	no	—
28	C₂×Dic₇₃	—	8	1	no	—
29	C₂×Dic₇₃	D₈	1	1	yes	characteristic
30	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
31	#10596833	—	8	1	no	—
32	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
33	C₈×C₇₃	M₁₆	1	1	yes	characteristic
34	#10596831	—	2	1	no	—
35	C₂²×C₇₃	—	4	2	no	—
36	C₂²×C₇₃	—	8	1	no	—
37	C₂²×C₇₃	—	8	1	no	—
38	C₂²×C₇₃	#102	1	1	yes	characteristic
39	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₇₃	#104	1	1	yes	characteristic
41	Dic₇₃	—	2	1	no	—
42	Dic₇₃	—	8	1	no	—
43	Dic₇₃	D₁₆	1	1	yes	characteristic
44	Dic₇₃	SD₃₂	1	1	yes	characteristic
45	C₂×C₇₃	—	8	2	no	—
46	C₂×C₇₃	D₄⋊C₈	1	1	yes	characteristic
47	C₂×C₇₃	#357	1	1	yes	characteristic
48	C₂×C₇₃	#359	1	1	yes	characteristic
49	#1331	—	73	1	no	maximal, Sylow
50	C₇₃	#1331	1	1	yes	characteristic, complemented, Sylow
51	C₄×D₈	—	73	1	no	—
52	C₄×C₁₆	—	73	1	no	—
53	#335	—	73	1	no	—
54	C₂×D₈	#64408	1	1	yes	characteristic
55	C₄×D₄	—	146	1	no	—
56	C₂×C₁₆	—	146	1	no	—
57	#107	—	73	1	no	—
58	C₄⋊C₈	—	146	1	no	—
59	#102	—	146	1	no	—
60	C₄×C₈	—	73	1	no	—
61	C₂×D₄	—	2	1	no	—
62	C₂²×C₄	—	292	1	no	—
63	D₈	—	2	1	no	—
64	D₈	#10596833	1	2	yes	complemented
65	C₂×C₈	—	292	1	no	—
66	C₂×C₈	—	73	1	no	—
67	C₂×C₈	C₂×#64408	1	1	yes	characteristic
68	C₄⋊C₄	—	146	1	no	—
69	C₂²⋊C₄	—	292	1	no	—
70	C₄²	—	73	1	no	—
71	C₁₆	—	146	2	no	—
72	C₂³	—	4	1	no	—
73	D₄	—	2	2	no	—
74	D₄	—	4	1	no	—
75	C₂×C₄	—	292	1	no	—
76	C₂×C₄	—	584	1	no	—
77	C₂×C₄	—	584	1	no	—
78	C₂×C₄	—	73	1	no	—
79	C₂×C₄	—	73	1	no	—
80	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
81	C₈	—	584	1	no	—
82	C₈	—	146	1	no	—
83	C₈	C₂×#10596833	1	1	yes	characteristic
84	C₈	#11924037	1	1	yes	characteristic
85	C₂²	—	4	2	no	—
86	C₂²	—	8	1	no	—
87	C₂²	—	8	1	no	—
88	C₂²	#14556653	1	1	yes	characteristic
89	C₄	—	584	1	no	—
90	C₄	—	73	1	no	—
91	C₄	—	73	1	no	—
92	C₄	—	146	1	no	—
93	C₄	C₂²⋊#10596833	1	1	yes	characteristic
94	C₄	#14556655	1	1	yes	characteristic
95	C₂	—	8	2	no	—
96	C₂	D₄⋊#10596833	1	1	yes	characteristic
97	C₂	#17989499	1	1	yes	characteristic
98	C₂	#17989501	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989473

C₂

yes

maximal, characteristic, complemented

#17989450

C₂

yes

maximal, characteristic, complemented

D₈×Dic₇₃

C₂

yes

maximal, characteristic

C₂×#11924031

—

C₄⋊#10596833

—

D₄×Dic₇₃

—

#14556525

C₄

yes

characteristic

#14556512

—

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×D₈×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

#11924031

—

C₂²×Dic₇₃

—

C₂×#10596831

D₄

yes

characteristic

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

D₄

yes

characteristic

C₂×D₄×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

C₈

yes

complemented

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

D₈

yes

characteristic

C₂×Dic₇₃

SD₁₆

yes

characteristic

#10596833

—

C₈×C₇₃

C₂×C₈

yes

characteristic

C₈×C₇₃

M₁₆

yes

characteristic

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#102

yes

characteristic

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

#104

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

D₁₆

yes

characteristic

Dic₇₃

SD₃₂

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

D₄⋊C₈

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₄×D₈

—

C₄×C₁₆

—

#335

—

C₂×D₈

#64408

yes

characteristic

C₄×D₄

—

146

—

C₂×C₁₆

—

146

—

#107

—

C₄⋊C₈

—

146

—

#102

—

146

—

C₄×C₈

—

C₂×D₄

—

C₂²×C₄

—

292

—

D₈

—

D₈

#10596833

yes

complemented

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

292

—

C₄²

—

C₁₆

—

146

—

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

—

584

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#64408

yes

characteristic

C₈

—

584

—

C₈

—

146

—

C₈

yes

C₈

yes

C₂²

—

C₂²

—

C₂²

—

C₂²

#14556653

yes

characteristic

C₄

—

584

—

C₄

—

C₄

—

C₄

—

146

—

C₄

yes

C₄

yes

C₂

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	#14556653
commutator	C₈×C₇₃	C₂×C₈
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×D₈×C₇₃	C₄
socle	C₂²×C₇₃	#102
hypercenter	C₂×D₈	#64408
hypocenter	C₇₃	#1331
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

subgroup

G/H

center

C₂²

#14556653

commutator

C₈×C₇₃

C₂×C₈

Frattini

C₂×C₈

C₂×#64408

Fitting

C₂×D₈×C₇₃

C₄

C₂²×C₇₃

C₂×D₈

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

N	H ≅ G/N	type
1. #17989473	C₂	semidirect
2. #17989450	C₂	semidirect
20. D₈×C₇₃	C₈	semidirect
50. C₇₃	#1331	semidirect
64. D₈	#10596833	semidirect

H ≅ G/N

type

1. #17989473

C₂

semidirect

2. #17989450

C₂

semidirect

20. D₈×C₇₃

C₈

semidirect

50. C₇₃

#1331

semidirect

64. D₈

#10596833

semidirect

Subgroups — #22624885

Conjugacy classes of subgroups

Complements