Group #22589141 — subgroups

Subgroups — #22589141

Order 9088.

332 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 137 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	C₂×#14556128	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556051	C₂	1	4	yes	maximal
3	C₂×C₄×C₇₁⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#384×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₄₂	C₂²	1	2	yes	—
6	C₂²×C₇₁⋊C₈	C₂²	1	2	yes	—
7	#14556128	—	2	2	no	—
8	#14556128	C₄	1	4	yes	complemented
9	C₂×C₄⋊Dic₇₁	—	2	2	no	—
10	#14556051	—	2	8	no	—
11	C₄×C₇₁⋊C₈	—	2	2	no	—
12	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
13	C₂×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
14	C₂×C₄²×C₇₁	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₄₂	—	2	4	no	—
16	C₂×Dic₁₄₂	—	2	4	no	—
17	C₂×Dic₁₄₂	—	2	2	no	—
18	C₂×Dic₁₄₂	C₂×C₄	1	4	yes	—
19	C₂²×Dic₇₁	—	2	2	no	—
20	C₂×C₇₁⋊C₈	—	2	2	no	—
21	C₂×C₇₁⋊C₈	—	2	2	no	—
22	C₂×C₇₁⋊C₈	D₄	1	4	yes	—
23	C₄⋊Dic₇₁	—	2	8	no	—
24	C₂²×C₄×C₇₁	—	2	2	no	—
25	C₂²×C₄×C₇₁	D₄	1	2	yes	—
26	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₇₁	—	2	4	no	—
28	C₄⋊C₄×C₇₁	—	4	4	no	—
29	C₄²×C₇₁	C₂×C₄	1	2	yes	—
30	C₄²×C₇₁	D₄	1	2	yes	—
31	C₂³×C₇₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₁	—	4	2	no	—
33	C₂×C₄×C₇₁	—	4	4	no	—
34	C₂×C₄×C₇₁	C₂²⋊C₄	1	4	yes	—
35	C₂×C₄×C₇₁	SD₁₆	1	4	yes	—
36	C₂×C₄×C₇₁	Q₁₆	1	4	yes	—
37	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₇₁	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₇₁	#41	1	2	yes	—
41	C₂×Dic₇₁	—	2	4	no	—
42	C₂×Dic₇₁	—	4	2	no	—
43	C₂×Dic₇₁	—	4	2	no	—
44	Dic₁₄₂	—	2	8	no	—
45	Dic₁₄₂	—	4	4	no	—
46	C₇₁⋊C₈	—	2	4	no	—
47	C₂²×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₇₁	#124	1	1	yes	characteristic
49	C₂²×C₇₁	#127	1	1	yes	characteristic
50	C₂²×C₇₁	C₂×SD₁₆	1	2	yes	—
51	C₂²×C₇₁	C₂×Q₁₆	1	2	yes	—
52	C₄×C₇₁	—	8	2	no	—
53	C₄×C₇₁	#103	1	8	yes	complemented
54	C₄×C₇₁	C₄×D₄	1	2	yes	—
55	C₄×C₇₁	#121	1	2	yes	—
56	Dic₇₁	—	4	4	no	—
57	C₂×C₇₁	#390	1	1	yes	characteristic
58	C₂×C₇₁	C₂×#103	1	2	yes	—
59	C₂×C₇₁	#487	1	2	yes	—
60	C₂×C₇₁	#492	1	1	yes	characteristic
61	C₂×C₇₁	#494	1	1	yes	characteristic
62	#1956	—	71	1	no	maximal, Sylow
63	C₇₁	#1956	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₄⋊Q₈	—	71	1	no	—
65	C₂×#103	—	71	4	no	—
66	C₂×C₄×C₈	—	71	1	no	—
67	#384	D₇₁	1	1	yes	characteristic
68	C₂²×Q₈	—	71	2	no	—
69	C₂²×C₈	—	71	2	no	—
70	C₄⋊Q₈	—	71	4	no	—
71	C₄⋊Q₈	—	142	2	no	—
72	C₂×C₄⋊C₄	—	2	2	no	—
73	C₂×C₄⋊C₄	—	142	2	no	—
74	C₂×C₄⋊C₄	C₂×D₇₁	1	2	yes	—
75	C₂×C₄²	C₂×D₇₁	1	1	yes	characteristic
76	#103	—	142	8	no	—
77	C₄×C₈	—	142	2	no	—
78	C₂×Q₈	—	71	4	no	—
79	C₂×Q₈	—	142	4	no	—
80	C₂×Q₈	—	142	4	no	—
81	C₂×Q₈	—	142	2	no	—
82	C₂²×C₄	—	2	2	no	—
83	C₂²×C₄	—	142	2	no	—
84	C₂²×C₄	C₂²⋊D₇₁	1	2	yes	—
85	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
86	C₂×C₈	—	71	4	no	—
87	C₂×C₈	—	142	2	no	—
88	C₂×C₈	—	142	2	no	—
89	C₄⋊C₄	—	2	4	no	—
90	C₄⋊C₄	—	4	4	no	—
91	C₄⋊C₄	—	142	8	no	—
92	C₄²	C₄×D₇₁	1	2	yes	—
93	C₄²	D₂₈₄	1	2	yes	—
94	C₂³	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
95	Q₈	—	284	4	no	—
96	Q₈	—	142	8	no	—
97	C₂×C₄	—	4	2	no	—
98	C₂×C₄	—	4	4	no	—
99	C₂×C₄	—	284	2	no	—
100	C₂×C₄	—	284	2	no	—
101	C₂×C₄	—	142	4	no	—
102	C₂×C₄	(C₂×D₇₁)⋊C₄	1	4	yes	—
103	C₂×C₄	#11765853	1	4	yes	—
104	C₂×C₄	#11765855	1	4	yes	—
105	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
106	C₂×C₄	D₄×D₇₁	1	2	yes	—
107	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
108	C₂×C₄	#11765866	1	2	yes	—
109	C₈	—	142	4	no	—
110	C₂²	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
111	C₂²	#14556117	1	1	yes	characteristic
112	C₂²	#14556124	1	1	yes	characteristic
113	C₂²	C₂×#11765853	1	2	yes	—
114	C₂²	C₂×#11765855	1	2	yes	—
115	C₄	—	8	2	no	—
116	C₄	—	284	4	no	—
117	C₄	#14556051	1	8	yes	complemented
118	C₄	#14556090	1	2	yes	—
119	C₄	#14556103	1	2	yes	—
120	C₂	#17985900	1	1	yes	characteristic
121	C₂	C₂×#14556051	1	2	yes	—
122	C₂	#17986351	1	2	yes	—
123	C₂	#17986371	1	1	yes	characteristic
124	C₂	#17986378	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556128

C₂

yes

maximal, characteristic

C₂×#14556051

C₂

yes

maximal

C₂×C₄×C₇₁⋊C₈

C₂

yes

maximal, characteristic

#384×C₇₁

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₂

C₂²

yes

—

C₂²×C₇₁⋊C₈

C₂²

yes

—

#14556128

—

#14556128

C₄

yes

complemented

C₂×C₄⋊Dic₇₁

—

#14556051

—

C₄×C₇₁⋊C₈

—

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄⋊C₄×C₇₁

C₂²

yes

—

C₂×C₄²×C₇₁

C₂²

yes

characteristic

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

C₂×C₄

yes

—

C₂²×Dic₇₁

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

D₄

yes

—

C₄⋊Dic₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

D₄

yes

—

C₂²×C₄×C₇₁

C₂³

yes

characteristic

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

C₂×C₄

yes

—

C₄²×C₇₁

D₄

yes

—

C₂³×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²⋊C₄

yes

—

C₂×C₄×C₇₁

SD₁₆

yes

—

C₂×C₄×C₇₁

Q₁₆

yes

—

C₂×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

#41

yes

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

C₇₁⋊C₈

—

C₂²×C₇₁

C₂×C₂²⋊C₄

yes

C₂²×C₇₁

yes

C₂²×C₇₁

yes

C₂²×C₇₁

C₂×SD₁₆

yes

—

C₂²×C₇₁

C₂×Q₁₆

yes

—

C₄×C₇₁

—

C₄×C₇₁

#103

yes

complemented

C₄×C₇₁

C₄×D₄

yes

—

C₄×C₇₁

#121

yes

—

Dic₇₁

—

C₂×C₇₁

#390

yes

characteristic

C₂×C₇₁

C₂×#103

yes

—

C₂×C₇₁

#487

yes

—

C₂×C₇₁

yes

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

C₂×#103

—

C₂×C₄×C₈

—

#384

D₇₁

yes

characteristic

C₂²×Q₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

142

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

142

—

C₂×C₄⋊C₄

C₂×D₇₁

yes

—

C₂×C₄²

C₂×D₇₁

yes

characteristic

#103

—

142

—

C₄×C₈

—

142

—

C₂×Q₈

—

C₂×Q₈

—

142

—

C₂×Q₈

—

142

—

C₂×Q₈

—

142

—

C₂²×C₄

—

C₂²×C₄

—

142

—

C₂²×C₄

C₂²⋊D₇₁

yes

—

C₂²×C₄

C₂²×D₇₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

142

—

C₂×C₈

—

142

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

142

—

C₄²

C₄×D₇₁

yes

—

C₄²

D₂₈₄

yes

—

C₂³

C₂×C₂²⋊D₇₁

yes

characteristic

Q₈

—

284

—

Q₈

—

142

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

284

—

100

C₂×C₄

—

284

—

101

C₂×C₄

—

142

—

102

C₂×C₄

(C₂×D₇₁)⋊C₄

yes

—

103

C₂×C₄

#11765853

yes

—

104

C₂×C₄

#11765855

yes

—

105

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

106

C₂×C₄

D₄×D₇₁

yes

—

107

C₂×C₄

C₂×D₂₈₄

yes

characteristic

108

C₂×C₄

#11765866

yes

—

109

C₈

—

142

—

110

C₂²

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

111

C₂²

#14556117

yes

characteristic

112

C₂²

#14556124

yes

characteristic

113

C₂²

C₂×#11765853

yes

—

114

C₂²

C₂×#11765855

yes

—

115

C₄

—

116

C₄

—

284

—

117

C₄

#14556051

yes

complemented

118

C₄

#14556090

yes

—

119

C₄

#14556103

yes

—

120

C₂

#17985900

yes

characteristic

121

C₂

C₂×#14556051

yes

—

122

C₂

#17986351

yes

—

123

C₂

#17986371

yes

characteristic

124

C₂

#17986378

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₁
commutator	C₂×C₄×C₇₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₁
Fitting	#384×C₇₁	C₂
socle	C₂³×C₇₁	C₂×D₄
hypercenter	#384	D₇₁
hypocenter	C₇₁	#1956
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₁

commutator

C₂×C₄×C₇₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₁

Fitting

#384×C₇₁

C₂

socle

C₂³×C₇₁

C₂×D₄

D₇₁

C₇₁

G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
8. #14556128	C₄	semidirect
53. C₄×C₇₁	#103	semidirect
63. C₇₁	#1956	semidirect
117. C₄	#14556051	semidirect

H ≅ G/N

type

8. #14556128

C₄

semidirect

53. C₄×C₇₁

#103

semidirect

63. C₇₁

#1956

semidirect

117. C₄

#14556051

semidirect

Subgroups — #22589141

Conjugacy classes of subgroups

Complements