Group #22590514 — subgroups

Subgroups — #22590514

Order 9088.

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

normal subgroups only

This group has 120 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	#17986399	C₂	1	1	yes	maximal, characteristic, complemented
2	#17986116	C₂	1	1	yes	maximal, characteristic
3	#17985822	C₂	1	1	yes	maximal, characteristic, complemented
4	#17985821	C₂	1	1	yes	maximal, characteristic, complemented
5	#17985819	C₂	1	1	yes	maximal, characteristic, complemented
6	#17985809	C₂	1	1	yes	maximal, characteristic
7	#360×C₇₁	C₂	1	1	yes	maximal, characteristic
8	#14556135	—	2	1	no	—
9	#14556119	—	2	1	no	—
10	#14556068	C₂²	1	1	yes	characteristic
11	#14556064	C₂²	1	1	yes	characteristic
12	#14556061	—	2	1	no	—
13	#14556060	C₂²	1	1	yes	characteristic
14	#14556055	—	2	1	no	—
15	C₈×Dic₇₁	C₂²	1	1	yes	characteristic
16	#135×C₇₁	C₂²	1	1	yes	characteristic
17	M₃₂×C₇₁	C₂²	1	1	yes	characteristic
18	#106×C₇₁	C₂²	1	1	yes	characteristic
19	#11765849	—	2	1	no	—
20	#11765849	—	4	1	no	—
21	C₂×C₇₁⋊C₈	—	4	1	no	—
22	C₂×C₇₁⋊C₈	D₄	1	1	yes	characteristic
23	C₄⋊Dic₇₁	—	2	1	no	—
24	C₄⋊Dic₇₁	—	4	1	no	—
25	Dic₇₁⋊C₄	—	4	1	no	—
26	C₄×Dic₇₁	D₄	1	1	yes	characteristic
27	C₇₁⋊C₁₆	—	2	1	no	—
28	#41×C₇₁	—	2	1	no	—
29	Q₁₆×C₇₁	Q₈	1	1	yes	characteristic
30	SD₁₆×C₇₁	—	2	1	no	—
31	D₈×C₇₁	Q₈	1	1	yes	characteristic
32	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
33	C₄⋊C₄×C₇₁	—	2	1	no	—
34	C₁₆×C₇₁	—	2	1	no	—
35	Q₈×C₇₁	—	2	1	no	—
36	D₄×C₇₁	—	2	1	no	—
37	D₄×C₇₁	—	4	1	no	—
38	C₂×C₄×C₇₁	—	4	1	no	—
39	C₂×C₄×C₇₁	—	4	1	no	—
40	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₇₁	—	2	1	no	—
42	C₂×Dic₇₁	—	4	1	no	—
43	C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
44	C₈×C₇₁	#41	1	1	yes	characteristic
45	C₇₁⋊C₈	—	4	1	no	—
46	C₇₁⋊C₈	SD₁₆	1	1	yes	characteristic
47	C₇₁⋊C₈	SD₁₆	1	1	yes	characteristic
48	C₂²×C₇₁	—	4	1	no	—
49	C₂²×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
50	C₄×C₇₁	—	4	1	no	—
51	C₄×C₇₁	—	8	1	no	—
52	C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
53	C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
54	Dic₇₁	—	4	1	no	—
55	Dic₇₁	—	8	1	no	—
56	C₂×C₇₁	—	2	1	no	—
57	C₂×C₇₁	—	8	1	no	—
58	C₂×C₇₁	#476	1	1	yes	characteristic
59	#2231	—	71	1	no	maximal, Sylow
60	C₇₁	#2231	1	1	yes	characteristic, complemented, Sylow
61	#499	—	71	1	no	—
62	#443	—	71	1	no	—
63	#365	—	71	1	no	—
64	#365	—	71	1	no	—
65	#364	—	71	1	no	—
66	#360	—	71	1	no	—
67	#360	D₇₁	1	1	yes	characteristic
68	#135	C₂×D₇₁	1	1	yes	characteristic
69	#131	—	142	1	no	—
70	#125	—	142	1	no	—
71	M₃₂	—	71	1	no	—
72	M₃₂	C₂×D₇₁	1	1	yes	characteristic
73	#108	—	71	1	no	—
74	#107	—	142	1	no	—
75	#106	—	71	1	no	—
76	#106	C₂×D₇₁	1	1	yes	characteristic
77	#104	—	142	1	no	—
78	C₄×C₈	—	71	1	no	—
79	#41	—	2	1	no	—
80	Q₁₆	Dic₁₄₂	1	1	yes	characteristic
81	SD₁₆	—	2	1	no	—
82	D₈	Dic₁₄₂	1	1	yes	characteristic
83	M₁₆	—	284	1	no	—
84	M₁₆	—	142	1	no	—
85	C₂×C₈	—	284	1	no	—
86	C₂×C₈	—	71	1	no	—
87	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
88	C₄⋊C₄	—	2	1	no	—
89	C₄⋊C₄	—	284	1	no	—
90	C₄⋊C₄	—	284	1	no	—
91	C₄⋊C₄	—	142	1	no	—
92	C₄²	—	71	1	no	—
93	C₁₆	—	2	1	no	—
94	C₁₆	—	142	1	no	—
95	Q₈	—	2	1	no	—
96	D₄	—	2	1	no	—
97	D₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	4	1	no	—
100	C₂×C₄	—	284	1	no	—
101	C₂×C₄	—	142	1	no	—
102	C₂×C₄	D₄×D₇₁	1	1	yes	characteristic
103	C₈	—	284	1	no	—
104	C₈	—	71	1	no	—
105	C₈	—	71	1	no	—
106	C₈	C₂×Dic₁₄₂	1	1	yes	characteristic
107	C₈	#11765864	1	1	yes	characteristic
108	C₂²	—	4	1	no	—
109	C₂²	#14556152	1	1	yes	characteristic
110	C₄	—	4	1	no	—
111	C₄	—	8	1	no	—
112	C₄	—	284	1	no	—
113	C₄	—	568	1	no	—
114	C₄	#14556105	1	1	yes	characteristic
115	C₄	SD₁₆×D₇₁	1	1	yes	characteristic
116	C₂	—	2	1	no	—
117	C₂	—	8	1	no	—
118	C₂	#17986287	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986399

C₂

yes

maximal, characteristic, complemented

#17986116

C₂

yes

maximal, characteristic

#17985822

C₂

yes

maximal, characteristic, complemented

#17985821

C₂

yes

maximal, characteristic, complemented

#17985819

C₂

yes

maximal, characteristic, complemented

#17985809

C₂

yes

maximal, characteristic

#360×C₇₁

C₂

yes

maximal, characteristic

#14556135

—

#14556119

—

#14556068

C₂²

yes

characteristic

#14556064

C₂²

yes

characteristic

#14556061

—

#14556060

C₂²

yes

characteristic

#14556055

—

C₈×Dic₇₁

C₂²

yes

characteristic

#135×C₇₁

C₂²

yes

characteristic

M₃₂×C₇₁

C₂²

yes

characteristic

#106×C₇₁

C₂²

yes

characteristic

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

C₄×Dic₇₁

D₄

yes

characteristic

C₇₁⋊C₁₆

—

#41×C₇₁

—

Q₁₆×C₇₁

Q₈

yes

characteristic

SD₁₆×C₇₁

—

D₈×C₇₁

Q₈

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄⋊C₄×C₇₁

—

C₁₆×C₇₁

—

Q₈×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₈×C₇₁

C₂×Q₈

yes

characteristic

C₈×C₇₁

#41

yes

characteristic

C₇₁⋊C₈

—

C₇₁⋊C₈

SD₁₆

yes

characteristic

C₇₁⋊C₈

SD₁₆

yes

characteristic

C₂²×C₇₁

—

C₂²×C₇₁

AGL(1,ℤ/8)

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

C₄×C₇₁

C₂×SD₁₆

yes

characteristic

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

—

—

—

—

—

—

D₇₁

yes

characteristic

#135

C₂×D₇₁

yes

characteristic

#131

—

142

—

#125

—

142

—

M₃₂

—

M₃₂

C₂×D₇₁

yes

characteristic

#108

—

#107

—

142

—

#106

—

#106

C₂×D₇₁

yes

characteristic

#104

—

142

—

C₄×C₈

—

#41

—

Q₁₆

Dic₁₄₂

yes

characteristic

SD₁₆

—

D₈

Dic₁₄₂

yes

characteristic

M₁₆

—

284

—

M₁₆

—

142

—

C₂×C₈

—

284

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

284

—

C₄⋊C₄

—

284

—

C₄⋊C₄

—

142

—

C₄²

—

C₁₆

—

C₁₆

—

142

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

284

—

101

C₂×C₄

—

142

—

102

C₂×C₄

D₄×D₇₁

yes

characteristic

103

C₈

—

284

—

104

C₈

—

105

C₈

—

106

C₈

C₂×Dic₁₄₂

yes

characteristic

107

C₈

#11765864

yes

characteristic

108

C₂²

—

109

C₂²

#14556152

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

284

—

113

C₄

—

568

—

114

C₄

#14556105

yes

characteristic

115

C₄

SD₁₆×D₇₁

yes

characteristic

116

C₂

—

117

C₂

—

118

C₂

#17986287

yes

characteristic

	subgroup	G/H
center	C₂	#17986287
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#360×C₇₁	C₂
socle	C₂×C₇₁	#476
hypercenter	#360	D₇₁
hypocenter	C₇₁	#2231
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #360

subgroup

G/H

center

C₂

#17986287

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#360×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #360

N	H ≅ G/N	type
1. #17986399	C₂	semidirect
3. #17985822	C₂	semidirect
4. #17985821	C₂	semidirect
5. #17985819	C₂	semidirect
60. C₇₁	#2231	semidirect

H ≅ G/N

type

1. #17986399

C₂

semidirect

3. #17985822

C₂

semidirect

4. #17985821

C₂

semidirect

5. #17985819

C₂

semidirect

60. C₇₁

#2231

semidirect

Subgroups — #22590514

Conjugacy classes of subgroups

Complements