Group #22611469 — subgroups

Subgroups — #22611469

Order 9344.

254 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14556524	C₂	1	2	yes	maximal
2	C₂×#14556515	C₂	1	2	yes	maximal
3	#17988457	C₂	1	1	yes	maximal, characteristic
4	#17988342	C₂	1	1	yes	maximal, characteristic
5	#391×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10596831	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₇₃	—	2	2	no	—
8	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
9	#14556524	—	2	4	no	—
10	#14556515	—	2	4	no	—
11	C₂²×Q₈×C₇₃	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
14	#95×C₇₃	—	2	2	no	—
15	C₂²×Dic₇₃	—	2	2	no	—
16	C₂×#10596831	—	2	2	no	—
17	C₂×#10596831	—	2	2	no	—
18	C₂×#10596831	D₄	1	4	yes	—
19	C₄⋊Dic₇₃	—	2	2	no	—
20	C₄⋊Dic₇₃	—	2	2	no	—
21	C₄⋊Dic₇₃	—	4	4	no	—
22	C₂×Q₈×C₇₃	—	2	1	no	—
23	C₂×Q₈×C₇₃	—	2	2	no	—
24	C₂×Q₈×C₇₃	—	2	2	no	—
25	C₂×Q₈×C₇₃	Q₈	1	2	yes	—
26	C₂²×C₄×C₇₃	—	2	1	no	—
27	C₂²×C₄×C₇₃	—	2	1	no	—
28	C₂²×C₄×C₇₃	D₄	1	2	yes	—
29	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
30	C₄⋊C₄×C₇₃	—	2	2	no	—
31	C₄²×C₇₃	—	2	2	no	—
32	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
33	Q₈×C₇₃	—	2	4	no	—
34	Q₈×C₇₃	—	4	2	no	—
35	C₂×C₄×C₇₃	—	2	2	no	—
36	C₂×C₄×C₇₃	—	2	2	no	—
37	C₂×C₄×C₇₃	—	2	2	no	—
38	C₂×C₄×C₇₃	—	4	1	no	—
39	C₂×C₄×C₇₃	—	4	1	no	—
40	C₂×C₄×C₇₃	—	4	1	no	—
41	C₂×C₄×C₇₃	—	4	2	no	—
42	C₂×C₄×C₇₃	Q₁₆	1	4	yes	—
43	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₇₃	#41	1	2	yes	—
46	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
47	C₂×Dic₇₃	—	4	2	no	—
48	C₂×Dic₇₃	—	4	4	no	—
49	#10596831	—	2	4	no	—
50	C₂²×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
51	C₂²×C₇₃	#123	1	1	yes	characteristic
52	C₂²×C₇₃	#127	1	1	yes	characteristic
53	C₂²×C₇₃	C₂×Q₁₆	1	2	yes	—
54	C₂²×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
55	C₄×C₇₃	—	2	4	no	—
56	C₄×C₇₃	—	4	2	no	—
57	C₄×C₇₃	—	8	1	no	—
58	C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
59	C₄×C₇₃	#123	1	2	yes	—
60	Dic₇₃	—	8	2	no	—
61	C₂×C₇₃	#399	1	1	yes	characteristic
62	C₂×C₇₃	#477	1	2	yes	—
63	C₂×C₇₃	#484	1	2	yes	—
64	C₂×C₇₃	#494	1	1	yes	characteristic
65	C₂×C₇₃	#496	1	1	yes	characteristic
66	#2095	—	73	1	no	maximal, Sylow
67	C₇₃	#2095	1	1	yes	characteristic, complemented, Sylow
68	C₂×#107	—	73	2	no	—
69	C₂×#103	—	73	2	no	—
70	#391	D₇₃	1	1	yes	characteristic
71	#384	—	73	1	no	—
72	#336	—	73	1	no	—
73	C₂²×Q₈	C₂×D₇₃	1	1	yes	characteristic
74	C₂²×C₈	—	73	2	no	—
75	C₂×C₄⋊C₄	—	73	2	no	—
76	C₂×C₄⋊C₄	—	146	2	no	—
77	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
78	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
79	#107	—	146	4	no	—
80	#103	—	146	4	no	—
81	#95	—	2	2	no	—
82	C₂×Q₈	—	2	1	no	—
83	C₂×Q₈	—	2	2	no	—
84	C₂×Q₈	—	2	2	no	—
85	C₂×Q₈	Dic₁₄₆	1	2	yes	—
86	C₂²×C₄	—	2	1	no	—
87	C₂²×C₄	—	2	1	no	—
88	C₂²×C₄	—	146	2	no	—
89	C₂²×C₄	C₂²⋊D₇₃	1	2	yes	—
90	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
91	C₂×C₈	—	73	4	no	—
92	C₂×C₈	—	146	2	no	—
93	C₂×C₈	—	146	2	no	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄⋊C₄	—	292	4	no	—
96	C₄⋊C₄	—	146	2	no	—
97	C₄⋊C₄	—	146	2	no	—
98	C₄²	—	2	2	no	—
99	C₂³	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
100	Q₈	—	2	4	no	—
101	Q₈	—	4	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	292	2	no	—
110	C₂×C₄	—	292	4	no	—
111	C₂×C₄	#11924018	1	4	yes	—
112	C₂×C₄	D₄×D₇₃	1	2	yes	—
113	C₂×C₄	C₂×Dic₁₄₆	1	1	yes	characteristic
114	C₂×C₄	#11924027	1	2	yes	—
115	C₂×C₄	#11924028	1	1	yes	characteristic
116	C₈	—	146	4	no	—
117	C₂²	#14556570	1	1	yes	characteristic
118	C₂²	#14556572	1	1	yes	characteristic
119	C₂²	#14556587	1	1	yes	characteristic
120	C₂²	C₂×#11924018	1	2	yes	—
121	C₂²	#14556616	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	4	2	no	—
124	C₄	—	8	1	no	—
125	C₄	—	584	2	no	—
126	C₄	#14556568	1	2	yes	—
127	C₄	#14556573	1	2	yes	—
128	C₂	#17988523	1	1	yes	characteristic
129	C₂	#17988882	1	2	yes	—
130	C₂	#17988920	1	2	yes	—
131	C₂	#17988966	1	1	yes	characteristic
132	C₂	#17988977	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556524

C₂

yes

maximal

C₂×#14556515

C₂

yes

maximal

#17988457

C₂

yes

maximal, characteristic

#17988342

C₂

yes

maximal, characteristic

#391×C₇₃

C₂

yes

maximal, characteristic

C₂²×#10596831

C₂²

yes

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

#14556524

—

#14556515

—

C₂²×Q₈×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#95×C₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

D₄

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

Q₈

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

Q₁₆

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

#10596831

—

C₂²×C₇₃

C₂²⋊Q₈

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

C₂×Q₁₆

yes

—

C₂²×C₇₃

AGL(1,ℤ/8)

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

#123

yes

—

Dic₇₃

—

C₂×C₇₃

#399

yes

characteristic

C₂×C₇₃

#477

yes

—

C₂×C₇₃

#484

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×#107

—

C₂×#103

—

#391

D₇₃

yes

characteristic

#384

—

#336

—

C₂²×Q₈

C₂×D₇₃

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

characteristic

C₂×C₄²

C₂×D₇₃

yes

characteristic

#107

—

146

—

#103

—

146

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₁₄₆

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²⋊D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

C₂³

C₂×C₂²⋊D₇₃

yes

characteristic

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

292

—

110

C₂×C₄

—

292

—

111

C₂×C₄

#11924018

yes

—

112

C₂×C₄

D₄×D₇₃

yes

—

113

C₂×C₄

C₂×Dic₁₄₆

yes

characteristic

114

C₂×C₄

#11924027

yes

—

115

C₂×C₄

#11924028

yes

characteristic

116

C₈

—

146

—

117

C₂²

#14556570

yes

characteristic

118

C₂²

#14556572

yes

characteristic

119

C₂²

#14556587

yes

characteristic

120

C₂²

C₂×#11924018

yes

—

121

C₂²

#14556616

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

584

—

126

C₄

#14556568

yes

—

127

C₄

#14556573

yes

—

128

C₂

#17988523

yes

characteristic

129

C₂

#17988882

yes

—

130

C₂

#17988920

yes

—

131

C₂

#17988966

yes

characteristic

132

C₂

#17988977

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₃
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#391×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	#391	D₇₃
hypocenter	C₇₃	#2095
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₃

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#391×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
67. C₇₃	#2095	semidirect

H ≅ G/N

type

67. C₇₃

#2095

semidirect

Subgroups — #22611469

Conjugacy classes of subgroups

Complements