Group #22612010 — subgroups

Subgroups — #22612010

Order 9344.

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

normal subgroups only

This group has 150 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	#17989027	C₂	1	1	yes	maximal, characteristic
2	#17988965	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988704	C₂	1	1	yes	maximal, characteristic
4	#17988407	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988404	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988403	C₂	1	1	yes	maximal, characteristic, complemented
7	#510×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
9	C₂×#11924018	—	2	1	no	—
10	#14556598	—	2	1	no	—
11	#14556589	—	2	1	no	—
12	#14556537	—	2	1	no	—
13	#14556535	—	2	1	no	—
14	#14556531	C₂²	1	1	yes	characteristic
15	#14556527	C₂²	1	1	yes	characteristic
16	#14556518	—	2	1	no	—
17	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
18	#135×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
20	Q₃₂×C₇₃	—	2	1	no	—
21	SD₃₂×C₇₃	—	2	1	no	—
22	M₃₂×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₄₆	—	2	1	no	—
24	Dic₂₉₂	—	2	1	no	—
25	Dic₂₉₂	—	2	1	no	—
26	#11924018	—	4	1	no	—
27	#11924018	—	4	1	no	—
28	#11924012	—	2	1	no	—
29	#11924012	—	4	1	no	—
30	C₂×#10596831	—	4	1	no	—
31	C₂×#10596831	D₄	1	1	yes	characteristic
32	#11924007	—	4	2	no	—
33	C₄×Dic₇₃	D₄	1	1	yes	characteristic
34	#11924003	—	2	1	no	—
35	#41×C₇₃	—	2	1	no	—
36	C₂×Q₈×C₇₃	—	2	1	no	—
37	Q₁₆×C₇₃	—	2	1	no	—
38	Q₁₆×C₇₃	—	2	1	no	—
39	Q₁₆×C₇₃	D₄	1	1	yes	characteristic
40	SD₁₆×C₇₃	—	2	1	no	—
41	D₈×C₇₃	D₄	1	1	yes	characteristic
42	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
43	C₁₆×C₇₃	—	2	1	no	—
44	Q₈×C₇₃	—	2	1	no	—
45	Q₈×C₇₃	—	4	1	no	—
46	Q₈×C₇₃	—	4	1	no	—
47	D₄×C₇₃	—	2	1	no	—
48	D₄×C₇₃	—	4	1	no	—
49	C₂×C₄×C₇₃	—	4	1	no	—
50	C₂×C₄×C₇₃	—	4	1	no	—
51	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₇₃	—	2	1	no	—
53	C₂×Dic₇₃	—	4	1	no	—
54	Dic₁₄₆	—	4	1	no	—
55	Dic₁₄₆	—	4	1	no	—
56	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
57	C₈×C₇₃	#41	1	1	yes	characteristic
58	#10596831	—	4	1	no	—
59	#10596831	D₈	1	1	yes	characteristic
60	#10596831	D₈	1	1	yes	characteristic
61	C₂²×C₇₃	—	4	1	no	—
62	C₂²×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
63	C₄×C₇₃	—	4	1	no	—
64	C₄×C₇₃	—	8	1	no	—
65	C₄×C₇₃	#121	1	1	yes	characteristic
66	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
67	Dic₇₃	—	2	2	no	—
68	Dic₇₃	—	8	1	no	—
69	C₂×C₇₃	—	2	1	no	—
70	C₂×C₇₃	—	8	1	no	—
71	C₂×C₇₃	#459	1	1	yes	characteristic
72	#2214	—	73	1	no	maximal, Sylow
73	C₇₃	#2214	1	1	yes	characteristic, complemented, Sylow
74	#510	—	73	1	no	—
75	#510	D₇₃	1	1	yes	characteristic
76	#494	—	73	1	no	—
77	#443	—	73	1	no	—
78	#364	—	73	1	no	—
79	#362	—	73	1	no	—
80	#362	—	73	1	no	—
81	#135	C₂×D₇₃	1	1	yes	characteristic
82	C₂×Q₁₆	—	73	1	no	—
83	C₂×Q₁₆	—	146	1	no	—
84	C₂×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
85	#131	—	146	1	no	—
86	C₄⋊Q₈	—	146	1	no	—
87	Q₃₂	—	2	1	no	—
88	Q₃₂	—	146	1	no	—
89	SD₃₂	—	2	1	no	—
90	SD₃₂	—	146	1	no	—
91	M₃₂	—	73	1	no	—
92	M₃₂	C₂×D₇₃	1	1	yes	characteristic
93	#108	—	73	1	no	—
94	#104	—	146	1	no	—
95	C₄×C₈	—	73	1	no	—
96	#41	—	2	1	no	—
97	C₂×Q₈	—	2	1	no	—
98	C₂×Q₈	—	146	1	no	—
99	Q₁₆	—	2	1	no	—
100	Q₁₆	—	2	1	no	—
101	Q₁₆	—	292	1	no	—
102	Q₁₆	—	292	1	no	—
103	Q₁₆	—	146	1	no	—
104	Q₁₆	—	146	1	no	—
105	Q₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
106	SD₁₆	—	2	1	no	—
107	D₈	C₂²⋊D₇₃	1	1	yes	characteristic
108	M₁₆	—	292	1	no	—
109	M₁₆	—	146	1	no	—
110	C₂×C₈	—	292	1	no	—
111	C₂×C₈	—	73	1	no	—
112	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
113	C₄⋊C₄	—	292	2	no	—
114	C₄²	—	73	1	no	—
115	C₁₆	—	2	1	no	—
116	C₁₆	—	146	1	no	—
117	Q₈	—	2	1	no	—
118	Q₈	—	4	1	no	—
119	Q₈	—	4	1	no	—
120	Q₈	—	292	1	no	—
121	Q₈	—	292	1	no	—
122	D₄	—	2	1	no	—
123	D₄	—	4	1	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	292	1	no	—
127	C₂×C₄	—	146	1	no	—
128	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
129	C₈	—	292	1	no	—
130	C₈	—	73	1	no	—
131	C₈	—	73	1	no	—
132	C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
133	C₈	#11924027	1	1	yes	characteristic
134	C₂²	—	4	1	no	—
135	C₂²	#14556615	1	1	yes	characteristic
136	C₄	—	4	1	no	—
137	C₄	—	8	1	no	—
138	C₄	—	584	1	no	—
139	C₄	—	146	2	no	—
140	C₄	#14556563	1	1	yes	characteristic
141	C₄	D₈×D₇₃	1	1	yes	characteristic
142	C₂	—	2	1	no	—
143	C₂	—	8	1	no	—
144	C₂	#17988780	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989027

C₂

yes

maximal, characteristic

#17988965

C₂

yes

maximal, characteristic, complemented

#17988704

C₂

yes

maximal, characteristic

#17988407

C₂

yes

maximal, characteristic, complemented

#17988404

C₂

yes

maximal, characteristic, complemented

#17988403

C₂

yes

maximal, characteristic, complemented

#510×C₇₃

C₂

yes

maximal, characteristic

C₂×Dic₂₉₂

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

#14556527

C₂²

yes

characteristic

#14556518

—

C₈×Dic₇₃

C₂²

yes

characteristic

#135×C₇₃

C₂²

yes

characteristic

C₂×Q₁₆×C₇₃

C₂²

yes

characteristic

Q₃₂×C₇₃

—

SD₃₂×C₇₃

—

M₃₂×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

—

—

—

—

—

—

D₄

yes

characteristic

#11924007

—

C₄×Dic₇₃

D₄

yes

characteristic

#11924003

—

#41×C₇₃

—

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

D₄

yes

characteristic

SD₁₆×C₇₃

—

D₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₁₆×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂×D₄

yes

C₈×C₇₃

yes

—

D₈

yes

characteristic

#10596831

D₈

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

AGL(1,ℤ/8)

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#121

yes

characteristic

C₄×C₇₃

C₂×D₈

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#510

—

#510

D₇₃

yes

—

—

—

—

—

C₂×D₇₃

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

146

—

C₂×Q₁₆

C₂×D₇₃

yes

characteristic

#131

—

146

—

C₄⋊Q₈

—

146

—

Q₃₂

—

Q₃₂

—

146

—

SD₃₂

—

SD₃₂

—

146

—

M₃₂

—

M₃₂

C₂×D₇₃

yes

characteristic

#108

—

#104

—

146

—

C₄×C₈

—

#41

—

C₂×Q₈

—

C₂×Q₈

—

146

—

Q₁₆

—

100

Q₁₆

—

101

Q₁₆

—

292

—

102

Q₁₆

—

292

—

103

Q₁₆

—

146

—

104

Q₁₆

—

146

—

105

Q₁₆

C₂²⋊D₇₃

yes

characteristic

106

SD₁₆

—

107

D₈

C₂²⋊D₇₃

yes

characteristic

108

M₁₆

—

292

—

109

M₁₆

—

146

—

110

C₂×C₈

—

292

—

111

C₂×C₈

—

112

C₂×C₈

C₂²×D₇₃

yes

characteristic

113

C₄⋊C₄

—

292

—

114

C₄²

—

115

C₁₆

—

116

C₁₆

—

146

—

117

Q₈

—

118

Q₈

—

119

Q₈

—

120

Q₈

—

292

—

121

Q₈

—

292

—

122

D₄

—

123

D₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

292

—

127

C₂×C₄

—

146

—

128

C₂×C₄

D₄×D₇₃

yes

characteristic

129

C₈

—

292

—

130

C₈

—

131

C₈

—

132

C₈

C₂×C₂²⋊D₇₃

yes

characteristic

133

C₈

#11924027

yes

characteristic

134

C₂²

—

135

C₂²

#14556615

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

584

—

139

C₄

—

146

—

140

C₄

#14556563

yes

characteristic

141

C₄

D₈×D₇₃

yes

characteristic

142

C₂

—

143

C₂

—

144

C₂

#17988780

yes

characteristic

	subgroup	G/H
center	C₂	#17988780
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#510×C₇₃	C₂
socle	C₂×C₇₃	#459
hypercenter	#510	D₇₃
hypocenter	C₇₃	#2214
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #510

subgroup

G/H

center

C₂

#17988780

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#510×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #510

N	H ≅ G/N	type
2. #17988965	C₂	semidirect
4. #17988407	C₂	semidirect
5. #17988404	C₂	semidirect
6. #17988403	C₂	semidirect
73. C₇₃	#2214	semidirect

H ≅ G/N

type

2. #17988965

C₂

semidirect

4. #17988407

C₂

semidirect

5. #17988404

C₂

semidirect

6. #17988403

C₂

semidirect

73. C₇₃

#2214

semidirect

Subgroups — #22612010

Conjugacy classes of subgroups

Complements