Group #22611641 — subgroups

Subgroups — #22611641

Order 9344.

232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14556613	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556531	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988390	C₂	1	2	yes	maximal, complemented
4	#17988387	C₂	1	2	yes	maximal, complemented
5	C₂×#107×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924028	—	2	1	no	—
7	#14556613	—	2	2	no	—
8	#14556613	C₄	1	4	yes	complemented
9	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
10	C₂×#11924017	—	2	1	no	—
11	C₂×D₅₈₄	C₂²	1	1	yes	characteristic
12	#14556531	—	2	2	no	—
13	C₂×#11924003	C₂²	1	2	yes	—
14	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
16	#107×C₇₃	—	2	1	no	—
17	#107×C₇₃	C₂²	1	2	yes	—
18	#11924028	—	2	4	no	—
19	#11924028	—	4	2	no	—
20	C₂×Dic₁₄₆	—	2	1	no	—
21	C₂×D₂₉₂	—	2	1	no	—
22	C₂×C₂²⋊D₇₃	—	4	1	no	—
23	C₂×C₄×D₇₃	—	4	1	no	—
24	Dic₂₉₂	—	2	1	no	—
25	Dic₂₉₂	C₂×C₄	1	2	yes	complemented
26	#11924017	—	2	4	no	—
27	D₅₈₄	—	2	1	no	—
28	D₅₈₄	C₂×C₄	1	2	yes	complemented
29	#11924003	—	2	2	no	—
30	C₂²×C₄×C₇₃	—	4	1	no	—
31	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
32	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
33	C₂×C₈×C₇₃	D₄	1	2	yes	—
34	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
35	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
36	C₄⋊C₄×C₇₃	—	2	2	no	—
37	C₄⋊C₄×C₇₃	—	4	1	no	—
38	C₂³×C₇₃	D₈	1	1	yes	characteristic
39	C₂²×D₇₃	—	4	1	no	—
40	C₂×C₄×C₇₃	—	4	2	no	—
41	C₂×C₄×C₇₃	—	8	2	no	—
42	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
43	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
44	C₂×C₄×C₇₃	SD₁₆	1	2	yes	—
45	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
46	C₂²⋊D₇₃	—	4	4	no	—
47	C₂×Dic₇₃	—	4	1	no	—
48	D₂₉₂	—	2	2	no	—
49	D₂₉₂	—	4	1	no	—
50	C₄×D₇₃	—	4	4	no	—
51	Dic₁₄₆	—	2	2	no	—
52	Dic₁₄₆	—	4	1	no	—
53	C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
54	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
55	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₇₃	—	2	1	no	—
57	C₂²×C₇₃	—	2	1	no	—
58	C₂²×C₇₃	#102	1	2	yes	—
59	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
60	C₂×D₇₃	—	4	2	no	—
61	C₂×D₇₃	—	8	1	no	—
62	C₂×D₇₃	—	8	1	no	—
63	C₄×C₇₃	—	8	2	no	—
64	C₄×C₇₃	#102	1	2	yes	—
65	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
67	Dic₇₃	—	4	2	no	—
68	C₂×C₇₃	—	2	2	no	—
69	C₂×C₇₃	C₂×#102	1	1	yes	characteristic
70	C₂×C₇₃	#509	1	1	yes	characteristic
71	C₂×C₇₃	#510	1	1	yes	characteristic
72	D₇₃	—	8	2	no	—
73	#2139	—	73	1	no	maximal, Sylow
74	C₇₃	#2139	1	1	yes	characteristic, complemented, Sylow
75	C₂×#135	—	73	1	no	—
76	C₂×M₃₂	—	73	1	no	—
77	C₂×#107	D₇₃	1	1	yes	characteristic, complemented
78	#358	—	73	2	no	—
79	#357	—	73	2	no	—
80	C₂×#41	—	146	1	no	—
81	#135	—	73	4	no	—
82	#135	—	146	2	no	—
83	C₂×Q₁₆	—	73	1	no	—
84	C₂×SD₁₆	—	146	1	no	—
85	C₂×D₈	—	73	1	no	—
86	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
87	C₂×C₄⋊C₄	—	2	1	no	—
88	M₃₂	—	146	2	no	—
89	C₂×C₁₆	—	73	2	no	—
90	#107	—	2	1	no	—
91	#107	C₂×D₇₃	1	2	yes	—
92	#41	—	292	2	no	—
93	#41	—	146	4	no	—
94	C₂×Q₈	—	146	1	no	—
95	C₂×D₄	—	292	1	no	—
96	C₂×D₄	—	146	1	no	—
97	C₂²×C₄	—	4	1	no	—
98	C₂²×C₄	—	292	1	no	—
99	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
100	Q₁₆	—	73	2	no	—
101	Q₁₆	—	146	1	no	—
102	SD₁₆	—	146	4	no	—
103	D₈	—	73	2	no	—
104	D₈	—	146	1	no	—
105	C₂×C₈	C₄×D₇₃	1	2	yes	—
106	C₂×C₈	D₂₉₂	1	2	yes	—
107	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
108	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	4	1	no	—
111	C₁₆	—	146	2	no	—
112	C₂³	—	292	1	no	—
113	C₂³	#11924013	1	1	yes	characteristic
114	Q₈	—	292	1	no	—
115	Q₈	—	146	2	no	—
116	D₄	—	292	4	no	—
117	D₄	—	292	1	no	—
118	D₄	—	146	2	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	8	2	no	—
121	C₂×C₄	—	292	1	no	—
122	C₂×C₄	—	292	4	no	—
123	C₂×C₄	#11924005	1	2	yes	—
124	C₂×C₄	#11924013	1	1	yes	characteristic
125	C₂×C₄	#11924015	1	2	yes	—
126	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
127	C₈	#11924005	1	2	yes	—
128	C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
129	C₈	C₂×D₂₉₂	1	1	yes	characteristic
130	C₂²	—	2	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	—	292	2	no	—
133	C₂²	—	584	1	no	—
134	C₂²	—	584	1	no	—
135	C₂²	#14556511	1	2	yes	—
136	C₂²	C₂×#11924013	1	1	yes	characteristic
137	C₄	—	8	2	no	—
138	C₄	—	292	2	no	—
139	C₄	#14556511	1	2	yes	—
140	C₄	C₂×#11924005	1	1	yes	characteristic
141	C₄	C₂×#11924015	1	1	yes	characteristic
142	C₂	—	2	2	no	—
143	C₂	—	584	2	no	—
144	C₂	C₂×#14556511	1	1	yes	characteristic
145	C₂	#17989023	1	1	yes	characteristic
146	C₂	#17989028	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556613

C₂

yes

maximal, characteristic

C₂×#14556531

C₂

yes

maximal, characteristic, complemented

#17988390

C₂

yes

maximal, complemented

#17988387

C₂

yes

maximal, complemented

C₂×#107×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924028

—

#14556613

—

#14556613

C₄

yes

complemented

C₂×Dic₂₉₂

C₂²

yes

characteristic

C₂×#11924017

—

C₂×D₅₈₄

C₂²

yes

characteristic

#14556531

—

C₂×#11924003

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

—

#107×C₇₃

—

#107×C₇₃

C₂²

yes

—

#11924028

—

#11924028

—

C₂×Dic₁₄₆

—

C₂×D₂₉₂

—

C₂×C₂²⋊D₇₃

—

C₂×C₄×D₇₃

—

Dic₂₉₂

—

Dic₂₉₂

C₂×C₄

yes

complemented

#11924017

—

D₅₈₄

—

D₅₈₄

C₂×C₄

yes

complemented

#11924003

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

D₄

yes

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂³×C₇₃

D₈

yes

characteristic

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

SD₁₆

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂²⋊C₄

yes

—

C₈×C₇₃

C₂²×C₄

yes

characteristic

C₈×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#102

yes

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#102

yes

—

C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

C₂×SD₁₆

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#2139

—

maximal, Sylow

C₇₃

#2139

yes

characteristic, complemented, Sylow

C₂×#135

—

C₂×M₃₂

—

C₂×#107

D₇₃

yes

characteristic, complemented

#358

—

#357

—

C₂×#41

—

146

—

#135

—

#135

—

146

—

C₂×Q₁₆

—

C₂×SD₁₆

—

146

—

C₂×D₈

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

M₃₂

—

146

—

C₂×C₁₆

—

#107

—

#107

C₂×D₇₃

yes

—

#41

—

292

—

#41

—

146

—

C₂×Q₈

—

146

—

C₂×D₄

—

292

—

C₂×D₄

—

146

—

C₂²×C₄

—

C₂²×C₄

—

292

—

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

100

Q₁₆

—

101

Q₁₆

—

146

—

102

SD₁₆

—

146

—

103

D₈

—

104

D₈

—

146

—

105

C₂×C₈

C₄×D₇₃

yes

—

106

C₂×C₈

D₂₉₂

yes

—

107

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

108

C₂×C₈

C₂²×D₇₃

yes

characteristic

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₁₆

—

146

—

112

C₂³

—

292

—

113

C₂³

#11924013

yes

characteristic

114

Q₈

—

292

—

115

Q₈

—

146

—

116

D₄

—

292

—

117

D₄

—

292

—

118

D₄

—

146

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

292

—

122

C₂×C₄

—

292

—

123

C₂×C₄

#11924005

yes

—

124

C₂×C₄

#11924013

yes

characteristic

125

C₂×C₄

#11924015

yes

—

126

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

127

C₈

#11924005

yes

—

128

C₈

C₂×C₄×D₇₃

yes

characteristic

129

C₈

C₂×D₂₉₂

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

292

—

133

C₂²

—

584

—

134

C₂²

—

584

—

135

C₂²

#14556511

yes

—

136

C₂²

C₂×#11924013

yes

characteristic

137

C₄

—

138

C₄

—

292

—

139

C₄

#14556511

yes

—

140

C₄

C₂×#11924005

yes

characteristic

141

C₄

C₂×#11924015

yes

characteristic

142

C₂

—

143

C₂

—

584

—

144

C₂

C₂×#14556511

yes

characteristic

145

C₂

#17989023

yes

characteristic

146

C₂

#17989028

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#11924013
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₂×#107×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	C₂×#107	D₇₃
hypocenter	C₇₃	#2139
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#107

subgroup

G/H

center

C₂²

C₂×#11924013

commutator

C₈×C₇₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₂×#107×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

D₇₃

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#107

N	H ≅ G/N	type
2. C₂×#14556531	C₂	semidirect
3. #17988390	C₂	semidirect
4. #17988387	C₂	semidirect
5. C₂×#107×C₇₃	C₂	semidirect
8. #14556613	C₄	semidirect
25. Dic₂₉₂	C₂×C₄	semidirect
28. D₅₈₄	C₂×C₄	semidirect
74. C₇₃	#2139	semidirect
77. C₂×#107	D₇₃	semidirect

H ≅ G/N

type

2. C₂×#14556531

C₂

semidirect

3. #17988390

C₂

semidirect

4. #17988387

C₂

semidirect

5. C₂×#107×C₇₃

C₂

semidirect

8. #14556613

C₄

semidirect

25. Dic₂₉₂

C₂×C₄

semidirect

28. D₅₈₄

C₂×C₄

semidirect

74. C₇₃

#2139

semidirect

77. C₂×#107

D₇₃

semidirect

Subgroups — #22611641

Conjugacy classes of subgroups

Complements