Group #22611346 — subgroups

Subgroups — #22611346

Order 9344.

258 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 79 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×#14556513	C₂	1	2	yes	maximal
2	#17988489	C₂	1	1	yes	maximal, characteristic
3	#17988453	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988350	C₂	1	2	yes	maximal, complemented
5	#336×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₂₉₂	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
9	C₂×#11924005	—	2	2	no	—
10	#14556513	—	2	4	no	—
11	#14556498	—	2	2	no	—
12	C₂²×C₈×C₇₃	C₂²	1	2	yes	—
13	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
14	C₂³×D₇₃	—	2	1	no	—
15	C₂×D₂₉₂	—	2	2	no	—
16	C₂×D₂₉₂	—	2	2	no	—
17	C₂×D₂₉₂	—	2	1	no	—
18	C₂×D₂₉₂	D₄	1	2	yes	—
19	C₂²×Dic₇₃	—	2	2	no	—
20	C₂²×Dic₇₃	—	2	1	no	—
21	C₄⋊Dic₇₃	—	2	2	no	—
22	C₄⋊Dic₇₃	—	2	2	no	—
23	C₄⋊Dic₇₃	—	2	2	no	—
24	#11924005	—	4	4	no	—
25	C₂²×C₄×C₇₃	D₄	1	2	yes	—
26	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
27	C₂×C₈×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	—	2	2	no	—
29	C₂×C₈×C₇₃	—	2	2	no	—
30	C₄²×C₇₃	—	2	2	no	—
31	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
32	C₂²×D₇₃	—	2	2	no	—
33	C₂²×D₇₃	—	4	1	no	—
34	C₂²×D₇₃	—	4	1	no	—
35	C₂²×D₇₃	—	4	2	no	—
36	C₂²×D₇₃	—	4	2	no	—
37	C₂×C₄×C₇₃	—	2	2	no	—
38	C₂×C₄×C₇₃	—	2	2	no	—
39	C₂×C₄×C₇₃	—	2	2	no	—
40	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₇₃	#41	1	2	yes	—
42	C₂×C₄×C₇₃	#41	1	2	yes	—
43	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
44	C₂×Dic₇₃	—	4	2	no	—
45	C₂×Dic₇₃	—	4	1	no	—
46	C₂×Dic₇₃	—	4	2	no	—
47	C₂×Dic₇₃	—	4	2	no	—
48	C₂×Dic₇₃	—	4	2	no	—
49	D₂₉₂	—	2	4	no	—
50	D₂₉₂	—	4	2	no	—
51	C₈×C₇₃	—	4	2	no	—
52	C₂²×C₇₃	#121	1	1	yes	characteristic
53	C₂²×C₇₃	#123	1	1	yes	characteristic
54	C₂²×C₇₃	#124	1	1	yes	characteristic
55	C₂²×C₇₃	#135	1	2	yes	—
56	C₂²×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
57	C₂×D₇₃	—	4	2	no	—
58	C₂×D₇₃	—	4	4	no	—
59	C₂×D₇₃	—	8	2	no	—
60	C₂×D₇₃	—	8	1	no	—
61	C₂×D₇₃	—	8	1	no	—
62	C₄×C₇₃	—	4	2	no	—
63	C₄×C₇₃	#123	1	2	yes	—
64	C₄×C₇₃	#126	1	2	yes	—
65	Dic₇₃	—	8	2	no	—
66	Dic₇₃	—	8	1	no	—
67	C₂×C₇₃	#397	1	1	yes	characteristic
68	C₂×C₇₃	#463	1	2	yes	—
69	C₂×C₇₃	#482	1	2	yes	—
70	C₂×C₇₃	#488	1	1	yes	characteristic
71	C₂×C₇₃	#490	1	1	yes	characteristic
72	D₇₃	—	8	2	no	—
73	#2073	—	73	1	no	maximal, Sylow
74	C₇₃	#2073	1	1	yes	characteristic, complemented, Sylow
75	C₂×#102	—	73	2	no	—
76	#390	—	73	1	no	—
77	#382	—	73	1	no	—
78	#340	—	73	2	no	—
79	#336	D₇₃	1	1	yes	characteristic, complemented
80	C₂²×D₄	—	73	1	no	—
81	C₂²×C₈	C₂×D₇₃	1	2	yes	—
82	C₂×C₄⋊C₄	—	73	1	no	—
83	C₂×C₄⋊C₄	—	73	2	no	—
84	C₂×C₂²⋊C₄	—	146	2	no	—
85	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
86	#102	—	146	4	no	—
87	#95	—	146	2	no	—
88	C₂⁴	—	146	1	no	—
89	C₂×D₄	—	73	2	no	—
90	C₂×D₄	—	146	2	no	—
91	C₂×D₄	—	146	2	no	—
92	C₂×D₄	—	146	1	no	—
93	C₂²×C₄	—	146	2	no	—
94	C₂²×C₄	—	146	1	no	—
95	C₂²×C₄	D₂₉₂	1	2	yes	—
96	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	2	2	no	—
100	C₄⋊C₄	—	146	2	no	—
101	C₄⋊C₄	—	146	2	no	—
102	C₄⋊C₄	—	146	2	no	—
103	C₂²⋊C₄	—	292	4	no	—
104	C₄²	—	2	2	no	—
105	C₂³	—	292	1	no	—
106	C₂³	—	292	1	no	—
107	C₂³	—	292	2	no	—
108	C₂³	—	292	2	no	—
109	C₂³	—	146	2	no	—
110	C₂³	C₂×D₂₉₂	1	1	yes	characteristic
111	D₄	—	292	2	no	—
112	D₄	—	146	4	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	292	2	no	—
117	C₂×C₄	—	292	1	no	—
118	C₂×C₄	—	292	2	no	—
119	C₂×C₄	—	292	2	no	—
120	C₂×C₄	—	292	2	no	—
121	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
122	C₂×C₄	#11924027	1	2	yes	—
123	C₂×C₄	#11924028	1	2	yes	—
124	C₂×C₄	#11924029	1	1	yes	characteristic
125	C₈	—	4	2	no	—
126	C₂²	—	292	2	no	—
127	C₂²	—	292	4	no	—
128	C₂²	—	584	2	no	—
129	C₂²	—	584	1	no	—
130	C₂²	—	584	1	no	—
131	C₂²	#14556566	1	1	yes	characteristic
132	C₂²	#14556575	1	1	yes	characteristic
133	C₂²	#14556579	1	1	yes	characteristic
134	C₂²	#14556613	1	2	yes	—
135	C₂²	#14556619	1	2	yes	—
136	C₄	—	4	2	no	—
137	C₄	—	584	1	no	—
138	C₄	—	584	2	no	—
139	C₄	#14556573	1	2	yes	—
140	C₄	#14556586	1	2	yes	—
141	C₂	—	584	2	no	—
142	C₂	#17988514	1	1	yes	characteristic
143	C₂	#17988803	1	2	yes	—
144	C₂	#17988912	1	2	yes	—
145	C₂	#17988942	1	1	yes	characteristic
146	C₂	#17988952	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556513

C₂

yes

maximal

#17988489

C₂

yes

maximal, characteristic

#17988453

C₂

yes

maximal, characteristic, complemented

#17988350

C₂

yes

maximal, complemented

#336×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₂₉₂

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

—

—

C₂²×C₈×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂³×D₇₃

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

D₄

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924005

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

C₈×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₂²×C₇₃

AGL(1,ℤ/8)

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#123

yes

—

C₄×C₇₃

#126

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#397

yes

characteristic

C₂×C₇₃

#463

yes

—

C₂×C₇₃

#482

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#2073

—

maximal, Sylow

C₇₃

#2073

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₃

yes

characteristic, complemented

C₂²×D₄

—

C₂²×C₈

C₂×D₇₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

146

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

#102

—

146

—

#95

—

146

—

C₂⁴

—

146

—

C₂×D₄

—

C₂×D₄

—

146

—

C₂×D₄

—

146

—

C₂×D₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

D₂₉₂

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₄⋊C₄

—

146

—

101

C₄⋊C₄

—

146

—

102

C₄⋊C₄

—

146

—

103

C₂²⋊C₄

—

292

—

104

C₄²

—

105

C₂³

—

292

—

106

C₂³

—

292

—

107

C₂³

—

292

—

108

C₂³

—

292

—

109

C₂³

—

146

—

110

C₂³

C₂×D₂₉₂

yes

characteristic

111

D₄

—

292

—

112

D₄

—

146

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

292

—

117

C₂×C₄

—

292

—

118

C₂×C₄

—

292

—

119

C₂×C₄

—

292

—

120

C₂×C₄

—

292

—

121

C₂×C₄

D₄×D₇₃

yes

characteristic

122

C₂×C₄

#11924027

yes

—

123

C₂×C₄

#11924028

yes

—

124

C₂×C₄

#11924029

yes

characteristic

125

C₈

—

126

C₂²

—

292

—

127

C₂²

—

292

—

128

C₂²

—

584

—

129

C₂²

—

584

—

130

C₂²

—

584

—

131

C₂²

#14556566

yes

characteristic

132

C₂²

#14556575

yes

characteristic

133

C₂²

#14556579

yes

characteristic

134

C₂²

#14556613

yes

—

135

C₂²

#14556619

yes

—

136

C₄

—

137

C₄

—

584

—

138

C₄

—

584

—

139

C₄

#14556573

yes

—

140

C₄

#14556586

yes

—

141

C₂

—

584

—

142

C₂

#17988514

yes

characteristic

143

C₂

#17988803

yes

—

144

C₂

#17988912

yes

—

145

C₂

#17988942

yes

characteristic

146

C₂

#17988952

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₂₉₂
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#336×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	#336	D₇₃
hypocenter	C₇₃	#2073
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₂₉₂

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#336×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
3. #17988453	C₂	semidirect
4. #17988350	C₂	semidirect
5. #336×C₇₃	C₂	semidirect
74. C₇₃	#2073	semidirect
79. #336	D₇₃	semidirect

H ≅ G/N

type

3. #17988453

C₂

semidirect

4. #17988350

C₂

semidirect

5. #336×C₇₃

C₂

semidirect

74. C₇₃

#2073

semidirect

79. #336

D₇₃

semidirect

Subgroups — #22611346

Conjugacy classes of subgroups

Complements