Group #22611092 — subgroups

Subgroups — #22611092

Order 9344.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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	#17989218	C₂	1	1	yes	maximal, characteristic
2	#17988596	C₂	1	2	yes	maximal
3	#17988356	C₂	1	1	yes	maximal, characteristic
4	#17988347	C₂	1	2	yes	maximal
5	#391×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	C₂²	1	2	yes	—
7	#14556590	—	2	2	no	—
8	#14556582	—	2	2	no	—
9	#14556570	—	2	2	no	—
10	#14556550	C₂²	1	2	yes	—
11	#14556515	—	2	2	no	—
12	#14556515	—	2	2	no	—
13	C₂²×Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
16	#95×C₇₃	—	2	2	no	—
17	C₂×Dic₁₄₆	—	2	2	no	—
18	#11924012	—	2	2	no	—
19	#11924012	—	2	2	no	—
20	C₂×#10596831	—	2	2	no	—
21	C₄⋊Dic₇₃	—	2	2	no	—
22	C₄⋊Dic₇₃	D₄	1	2	yes	—
23	C₄⋊Dic₇₃	D₄	1	2	yes	—
24	#11924007	—	2	4	no	—
25	C₂²⋊Dic₇₃	—	2	2	no	—
26	C₄×Dic₇₃	—	2	2	no	—
27	C₂×Q₈×C₇₃	—	2	1	no	—
28	C₂×Q₈×C₇₃	—	2	2	no	—
29	C₂×Q₈×C₇₃	—	2	2	no	—
30	C₂×Q₈×C₇₃	Q₈	1	2	yes	complemented
31	C₂²×C₄×C₇₃	—	2	1	no	—
32	C₂²×C₄×C₇₃	—	2	1	no	—
33	C₂²×C₄×C₇₃	D₄	1	2	yes	—
34	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
35	C₄⋊C₄×C₇₃	—	2	2	no	—
36	C₄²×C₇₃	—	2	2	no	—
37	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
38	Q₈×C₇₃	—	2	4	no	—
39	Q₈×C₇₃	—	4	2	no	—
40	C₂×C₄×C₇₃	—	2	2	no	—
41	C₂×C₄×C₇₃	—	2	2	no	—
42	C₂×C₄×C₇₃	—	2	2	no	—
43	C₂×C₄×C₇₃	—	4	1	no	—
44	C₂×C₄×C₇₃	—	4	1	no	—
45	C₂×C₄×C₇₃	—	4	1	no	—
46	C₂×C₄×C₇₃	—	4	1	no	—
47	C₂×C₄×C₇₃	—	4	2	no	—
48	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₄×C₇₃	#41	1	2	yes	—
51	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
52	C₂×Dic₇₃	—	2	2	no	—
53	C₂×Dic₇₃	—	2	2	no	—
54	Dic₁₄₆	—	8	2	no	—
55	#10596831	—	4	2	no	—
56	C₂²×C₇₃	—	2	1	no	—
57	C₂²×C₇₃	—	2	1	no	—
58	C₂²×C₇₃	#120	1	1	yes	characteristic
59	C₂²×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
60	C₂²×C₇₃	#124	1	1	yes	characteristic
61	C₄×C₇₃	—	4	2	no	—
62	C₄×C₇₃	—	4	2	no	—
63	C₄×C₇₃	—	4	2	no	—
64	C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
65	C₄×C₇₃	#124	1	2	yes	—
66	Dic₇₃	—	4	2	no	—
67	Dic₇₃	—	4	2	no	—
68	C₂×C₇₃	—	2	1	no	—
69	C₂×C₇₃	—	2	1	no	—
70	C₂×C₇₃	#393	1	1	yes	characteristic
71	C₂×C₇₃	#455	1	1	yes	characteristic
72	C₂×C₇₃	#456	1	1	yes	characteristic
73	#2028	—	73	1	no	maximal, Sylow
74	C₇₃	#2028	1	1	yes	characteristic, complemented, Sylow
75	#544	—	73	1	no	—
76	#419	—	73	2	no	—
77	#391	D₇₃	1	1	yes	characteristic
78	#343	—	73	1	no	—
79	#339	—	73	2	no	—
80	C₂²×Q₈	C₂×D₇₃	1	1	yes	characteristic
81	C₂×M₁₆	—	73	2	no	—
82	C₄⋊Q₈	—	146	2	no	—
83	#125	—	146	2	no	—
84	C₂²⋊Q₈	—	146	2	no	—
85	#117	—	73	2	no	—
86	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
87	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
88	#103	—	146	2	no	—
89	#103	—	146	2	no	—
90	#95	—	2	2	no	—
91	C₂×Q₈	—	2	1	no	—
92	C₂×Q₈	—	2	2	no	—
93	C₂×Q₈	—	2	2	no	—
94	C₂×Q₈	—	146	2	no	—
95	C₂×Q₈	Dic₁₄₆	1	2	yes	complemented
96	C₂²×C₄	—	2	1	no	—
97	C₂²×C₄	—	2	1	no	—
98	C₂²×C₄	C₂²⋊D₇₃	1	2	yes	—
99	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
100	M₁₆	—	146	2	no	—
101	M₁₆	—	146	2	no	—
102	C₂×C₈	—	146	2	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	73	2	no	—
105	C₄⋊C₄	—	73	2	no	—
106	C₄⋊C₄	—	146	4	no	—
107	C₄⋊C₄	—	146	2	no	—
108	C₂²⋊C₄	—	146	2	no	—
109	C₄²	—	2	2	no	—
110	C₄²	—	146	2	no	—
111	C₂³	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
112	Q₈	—	2	4	no	—
113	Q₈	—	4	2	no	—
114	Q₈	—	584	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	4	2	no	—
123	C₂×C₄	—	146	2	no	—
124	C₂×C₄	—	146	2	no	—
125	C₂×C₄	D₄×D₇₃	1	2	yes	—
126	C₂×C₄	C₂×Dic₁₄₆	1	1	yes	characteristic
127	C₂×C₄	#11924027	1	2	yes	—
128	C₂×C₄	#11924028	1	1	yes	characteristic
129	C₈	—	292	2	no	—
130	C₂²	—	2	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	#14556559	1	1	yes	characteristic
133	C₂²	#14556570	1	1	yes	characteristic
134	C₂²	#14556578	1	1	yes	characteristic
135	C₄	—	4	2	no	—
136	C₄	—	4	2	no	—
137	C₄	—	4	2	no	—
138	C₄	—	292	2	no	—
139	C₄	—	292	2	no	—
140	C₄	#14556568	1	2	yes	—
141	C₄	#14556577	1	2	yes	—
142	C₂	—	2	1	no	—
143	C₂	—	2	1	no	—
144	C₂	#17988499	1	1	yes	characteristic
145	C₂	#17988764	1	1	yes	characteristic
146	C₂	#17988769	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989218

C₂

yes

maximal, characteristic

#17988596

C₂

yes

maximal

#17988356

C₂

yes

maximal, characteristic

#17988347

C₂

yes

maximal

#391×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

—

—

—

C₂²

yes

—

#14556515

—

#14556515

—

C₂²×Q₈×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#95×C₇₃

—

C₂×Dic₁₄₆

—

#11924012

—

#11924012

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

D₄

yes

—

C₄⋊Dic₇₃

D₄

yes

—

#11924007

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

Q₈

yes

complemented

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

—

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

—

Dic₁₄₆

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#120

yes

characteristic

C₂²×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₇₃

#124

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

#124

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#544

—

#419

—

#391

D₇₃

yes

characteristic

#343

—

#339

—

C₂²×Q₈

C₂×D₇₃

yes

characteristic

C₂×M₁₆

—

C₄⋊Q₈

—

146

—

#125

—

146

—

C₂²⋊Q₈

—

146

—

#117

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

characteristic

C₂×C₄²

C₂×D₇₃

yes

characteristic

#103

—

146

—

#103

—

146

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

Dic₁₄₆

yes

complemented

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

100

M₁₆

—

146

—

101

M₁₆

—

146

—

102

C₂×C₈

—

146

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

146

—

107

C₄⋊C₄

—

146

—

108

C₂²⋊C₄

—

146

—

109

C₄²

—

110

C₄²

—

146

—

111

C₂³

C₂×C₂²⋊D₇₃

yes

characteristic

112

Q₈

—

113

Q₈

—

114

Q₈

—

584

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

146

—

124

C₂×C₄

—

146

—

125

C₂×C₄

D₄×D₇₃

yes

—

126

C₂×C₄

C₂×Dic₁₄₆

yes

characteristic

127

C₂×C₄

#11924027

yes

—

128

C₂×C₄

#11924028

yes

characteristic

129

C₈

—

292

—

130

C₂²

—

131

C₂²

—

132

C₂²

#14556559

yes

characteristic

133

C₂²

#14556570

yes

characteristic

134

C₂²

#14556578

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

292

—

139

C₄

—

292

—

140

C₄

#14556568

yes

—

141

C₄

#14556577

yes

—

142

C₂

—

143

C₂

—

144

C₂

#17988499

yes

characteristic

145

C₂

#17988764

yes

characteristic

146

C₂

#17988769

yes

characteristic

	subgroup	G/H
center	C₂²	#14556559
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#391×C₇₃	C₂
socle	C₂²×C₇₃	#120
hypercenter	#391	D₇₃
hypocenter	C₇₃	#2028
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #391

subgroup

G/H

center

C₂²

#14556559

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#391×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #391

N	H ≅ G/N	type
30. C₂×Q₈×C₇₃	Q₈	semidirect
74. C₇₃	#2028	semidirect
95. C₂×Q₈	Dic₁₄₆	semidirect

H ≅ G/N

type

30. C₂×Q₈×C₇₃

Q₈

semidirect

74. C₇₃

#2028

semidirect

95. C₂×Q₈

Dic₁₄₆

semidirect

Subgroups — #22611092

Conjugacy classes of subgroups

Complements