Group #22590552 — subgroups

Subgroups — #22590552

Order 9088.

134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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	#17986048	C₂	1	1	yes	maximal, characteristic, complemented
2	#17985821	C₂	1	2	yes	maximal, complemented
3	#17985812	C₂	1	2	yes	maximal, complemented
4	#17985781	C₂	1	1	yes	maximal, characteristic, complemented
5	#469×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11765849	—	2	1	no	—
7	#14556068	C₂²	1	2	yes	—
8	#14556064	—	2	1	no	—
9	#14556064	C₂²	1	2	yes	—
10	C₂×D₈×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
12	#121×C₇₁	—	2	1	no	—
13	#106×C₇₁	C₂²	1	1	yes	characteristic
14	#102×C₇₁	—	2	1	no	—
15	#11765849	—	2	2	no	—
16	#11765849	—	4	1	no	—
17	C₂×C₇₁⋊C₈	—	4	1	no	—
18	C₇₁⋊C₁₆	—	2	2	no	—
19	C₂×D₄×C₇₁	—	2	1	no	—
20	C₂×D₄×C₇₁	—	4	1	no	—
21	C₂²×C₄×C₇₁	D₄	1	1	yes	characteristic
22	D₈×C₇₁	—	2	2	no	—
23	M₁₆×C₇₁	—	2	2	no	—
24	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₇₁	—	2	1	no	—
27	C₂²⋊C₄×C₇₁	—	4	1	no	—
28	C₂³×C₇₁	—	4	1	no	—
29	C₂³×C₇₁	SD₁₆	1	1	yes	characteristic
30	D₄×C₇₁	—	4	1	no	—
31	D₄×C₇₁	—	4	1	no	—
32	D₄×C₇₁	—	8	2	no	—
33	C₂×C₄×C₇₁	—	2	1	no	—
34	C₂×C₄×C₇₁	—	2	1	no	—
35	C₂×C₄×C₇₁	—	4	1	no	—
36	C₂×C₄×C₇₁	SD₁₆	1	1	yes	characteristic
37	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
38	C₈×C₇₁	—	2	1	no	—
39	C₈×C₇₁	#41	1	2	yes	—
40	C₇₁⋊C₈	—	4	2	no	—
41	C₂²×C₇₁	—	2	1	no	—
42	C₂²×C₇₁	—	4	1	no	—
43	C₂²×C₇₁	—	8	1	no	—
44	C₂²×C₇₁	—	8	1	no	—
45	C₂²×C₇₁	—	8	1	no	—
46	C₂²×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
47	C₄×C₇₁	—	2	1	no	—
48	C₄×C₇₁	—	8	1	no	—
49	C₄×C₇₁	#123	1	1	yes	characteristic
50	C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
51	C₂×C₇₁	—	2	1	no	—
52	C₂×C₇₁	—	4	1	no	—
53	C₂×C₇₁	—	16	1	no	—
54	C₂×C₇₁	#481	1	1	yes	characteristic
55	#2238	—	71	1	no	maximal, Sylow
56	C₇₁	#2238	1	1	yes	characteristic, complemented, Sylow
57	#469	D₇₁	1	1	yes	characteristic
58	#430	—	71	1	no	—
59	#365	—	71	2	no	—
60	#361	—	71	2	no	—
61	#349	—	71	1	no	—
62	C₂×D₈	C₂×D₇₁	1	1	yes	characteristic
63	C₂×M₁₆	—	142	1	no	—
64	C₂×M₁₆	C₂×D₇₁	1	1	yes	characteristic
65	#121	—	2	1	no	—
66	M₃₂	—	71	2	no	—
67	#108	—	71	2	no	—
68	#108	—	142	1	no	—
69	#106	C₂×D₇₁	1	1	yes	characteristic
70	#102	—	2	1	no	—
71	C₂×D₄	—	2	1	no	—
72	C₂×D₄	—	4	1	no	—
73	C₂²×C₄	C₂²⋊D₇₁	1	1	yes	characteristic
74	D₈	—	2	2	no	—
75	M₁₆	—	2	2	no	—
76	M₁₆	—	284	1	no	—
77	M₁₆	—	142	2	no	—
78	C₂×C₈	—	284	1	no	—
79	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
80	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
81	C₄⋊C₄	—	2	1	no	—
82	C₂²⋊C₄	—	4	1	no	—
83	C₁₆	—	142	2	no	—
84	C₂³	—	4	1	no	—
85	C₂³	#11765853	1	1	yes	characteristic
86	D₄	—	4	1	no	—
87	D₄	—	4	1	no	—
88	D₄	—	8	2	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	4	1	no	—
92	C₂×C₄	#11765853	1	1	yes	characteristic
93	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	284	2	no	—
96	C₈	#11765864	1	2	yes	—
97	C₂²	—	2	1	no	—
98	C₂²	—	4	1	no	—
99	C₂²	—	8	1	no	—
100	C₂²	—	8	1	no	—
101	C₂²	—	8	1	no	—
102	C₂²	C₂×#11765853	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	8	1	no	—
105	C₄	#14556109	1	1	yes	characteristic
106	C₄	#14556153	1	1	yes	characteristic
107	C₂	—	2	1	no	—
108	C₂	—	4	1	no	—
109	C₂	—	16	1	no	—
110	C₂	#17986315	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986048

C₂

yes

maximal, characteristic, complemented

#17985821

C₂

yes

maximal, complemented

#17985812

C₂

yes

maximal, complemented

#17985781

C₂

yes

maximal, characteristic, complemented

#469×C₇₁

C₂

yes

maximal, characteristic

C₂×#11765849

—

#14556068

C₂²

yes

—

#14556064

—

#14556064

C₂²

yes

—

C₂×D₈×C₇₁

C₂²

yes

characteristic

C₂×M₁₆×C₇₁

C₂²

yes

characteristic

#121×C₇₁

—

#106×C₇₁

C₂²

yes

characteristic

#102×C₇₁

—

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₇₁⋊C₁₆

—

C₂×D₄×C₇₁

—

C₂×D₄×C₇₁

—

C₂²×C₄×C₇₁

D₄

yes

characteristic

D₈×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄⋊C₄×C₇₁

—

C₂²⋊C₄×C₇₁

—

C₂³×C₇₁

—

C₂³×C₇₁

SD₁₆

yes

characteristic

D₄×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

SD₁₆

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

—

C₈×C₇₁

#41

yes

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×SD₁₆

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

yes

C₄×C₇₁

yes

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

#469

D₇₁

yes

—

—

—

—

C₂×D₈

C₂×D₇₁

yes

characteristic

C₂×M₁₆

—

142

—

C₂×M₁₆

C₂×D₇₁

yes

characteristic

#121

—

M₃₂

—

#108

—

#108

—

142

—

#106

C₂×D₇₁

yes

characteristic

#102

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₂²⋊D₇₁

yes

characteristic

D₈

—

M₁₆

—

M₁₆

—

284

—

M₁₆

—

142

—

C₂×C₈

—

284

—

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

142

—

C₂³

—

C₂³

#11765853

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#11765853

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

C₈

—

C₈

—

284

—

C₈

#11765864

yes

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

C₂×#11765853

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

#14556109

yes

characteristic

106

C₄

#14556153

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

—

110

C₂

#17986315

yes

characteristic

	subgroup	G/H
center	C₂	#17986315
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#469×C₇₁	C₂
socle	C₂×C₇₁	#481
hypercenter	#469	D₇₁
hypocenter	C₇₁	#2238
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

subgroup

G/H

center

C₂

#17986315

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#469×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

N	H ≅ G/N	type
1. #17986048	C₂	semidirect
2. #17985821	C₂	semidirect
3. #17985812	C₂	semidirect
4. #17985781	C₂	semidirect
56. C₇₁	#2238	semidirect

H ≅ G/N

type

1. #17986048

C₂

semidirect

2. #17985821

C₂

semidirect

3. #17985812

C₂

semidirect

4. #17985781

C₂

semidirect

56. C₇₁

#2238

semidirect

Subgroups — #22590552

Conjugacy classes of subgroups

Complements