Group #22608779 — subgroups

Subgroups — #22608779

Order 9344.

152 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 67 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	C₈×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic
2	C₄×#11924018	C₂	1	1	yes	maximal, characteristic
3	#17988339	C₂	1	1	yes	maximal, characteristic
4	Q₈⋊#10596831	C₂	1	1	yes	maximal, characteristic
5	#17988317	C₂	1	1	yes	maximal, characteristic
6	#17988308	C₂	1	1	yes	maximal, characteristic
7	#446×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#11924018	C₄	1	1	yes	characteristic
9	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
10	#14556524	C₄	1	1	yes	characteristic
11	C₄⋊#10596831	C₂²	1	1	yes	characteristic
12	#14556520	—	2	1	no	—
13	#14556515	C₄	1	1	yes	characteristic
14	#14556514	C₄	1	1	yes	characteristic
15	C₄×#10596831	C₂²	1	1	yes	characteristic
16	C₄×#10596831	C₂²	1	1	yes	characteristic
17	C₈×Dic₇₃	—	2	1	no	—
18	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₄⋊C₈×C₇₃	—	2	1	no	—
20	C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
21	#97×C₇₃	—	2	1	no	—
22	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
24	#11924018	—	2	2	no	—
25	C₂×#10596831	—	2	1	no	—
26	C₂×#10596831	—	2	1	no	—
27	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
28	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
29	C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
30	#11924007	—	2	1	no	—
31	C₄×Dic₇₃	—	2	1	no	—
32	C₂×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₈×C₇₃	—	2	1	no	—
34	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
35	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
36	C₄⋊C₄×C₇₃	—	2	1	no	—
37	C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₄²×C₇₃	—	2	1	no	—
39	C₄²×C₇₃	C₂³	1	1	yes	characteristic
40	Q₈×C₇₃	—	2	1	no	—
41	Q₈×C₇₃	—	2	1	no	—
42	C₂×C₄×C₇₃	—	2	1	no	—
43	C₂×C₄×C₇₃	—	2	1	no	—
44	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
47	C₂×Dic₇₃	—	2	1	no	—
48	C₂×Dic₇₃	—	2	1	no	—
49	Dic₁₄₆	—	2	1	no	—
50	Dic₁₄₆	M₁₆	1	2	yes	—
51	C₈×C₇₃	—	2	1	no	—
52	C₈×C₇₃	—	4	1	no	—
53	C₈×C₇₃	Q₁₆	1	2	yes	complemented
54	#10596831	—	2	1	no	—
55	#10596831	—	2	1	no	—
56	#10596831	—	4	1	no	—
57	#10596831	—	4	1	no	—
58	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
59	C₄×C₇₃	—	2	1	no	—
60	C₄×C₇₃	—	4	1	no	—
61	C₄×C₇₃	—	4	1	no	—
62	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
63	C₄×C₇₃	#131	1	1	yes	characteristic
64	C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
65	C₄×C₇₃	#135	1	1	yes	characteristic
66	Dic₇₃	—	2	2	no	—
67	Dic₇₃	—	4	1	no	—
68	C₂×C₇₃	#435	1	1	yes	characteristic
69	C₂×C₇₃	C₄×Q₁₆	1	1	yes	characteristic
70	C₂×C₇₃	#444	1	1	yes	characteristic
71	#1584	—	73	1	no	maximal, Sylow
72	C₇₃	#1584	1	1	yes	characteristic, complemented, Sylow
73	#446	D₇₃	1	1	yes	characteristic
74	C₈×Q₈	—	73	1	no	—
75	C₄×Q₁₆	—	73	1	no	—
76	#335	—	73	1	no	—
77	Q₈⋊C₈	—	73	1	no	—
78	Q₈⋊C₈	—	73	1	no	—
79	#322	—	73	1	no	—
80	C₂×Q₁₆	—	73	1	no	—
81	C₄×Q₈	—	73	1	no	—
82	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
83	#107	—	73	1	no	—
84	C₄⋊C₈	—	2	1	no	—
85	C₄⋊C₈	—	73	1	no	—
86	C₄⋊C₈	—	146	1	no	—
87	C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
88	#103	—	73	1	no	—
89	#103	—	73	1	no	—
90	#97	—	2	1	no	—
91	C₄×C₈	—	73	1	no	—
92	C₄×C₈	—	73	1	no	—
93	C₄×C₈	—	146	1	no	—
94	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
95	C₂×Q₈	—	73	1	no	—
96	C₂×Q₈	C₄×D₇₃	1	1	yes	characteristic
97	Q₁₆	—	146	2	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	73	1	no	—
100	C₂×C₈	—	73	1	no	—
101	C₂×C₈	—	146	1	no	—
102	C₂×C₈	—	146	1	no	—
103	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
104	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
105	C₄⋊C₄	—	2	1	no	—
106	C₄⋊C₄	—	73	1	no	—
107	C₄⋊C₄	—	146	1	no	—
108	C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
109	C₄²	—	2	1	no	—
110	C₄²	—	146	1	no	—
111	C₄²	C₂²×D₇₃	1	1	yes	characteristic
112	Q₈	—	2	1	no	—
113	Q₈	—	2	1	no	—
114	Q₈	—	73	2	no	—
115	Q₈	—	146	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	146	1	no	—
119	C₂×C₄	—	146	1	no	—
120	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
121	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
122	C₂×C₄	#11924028	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	4	1	no	—
125	C₈	—	292	1	no	—
126	C₈	—	292	1	no	—
127	C₈	—	146	1	no	—
128	C₈	—	146	1	no	—
129	C₈	#11924018	1	2	yes	complemented
130	C₂²	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	4	1	no	—
133	C₄	—	4	1	no	—
134	C₄	—	292	1	no	—
135	C₄	—	146	2	no	—
136	C₄	M₁₆×D₇₃	1	1	yes	characteristic
137	C₄	#14556599	1	1	yes	characteristic
138	C₄	C₂×#11924018	1	1	yes	characteristic
139	C₄	#14556611	1	1	yes	characteristic
140	C₂	#17988656	1	1	yes	characteristic
141	C₂	C₄×#11924018	1	1	yes	characteristic
142	C₂	#17988707	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₁₄₆

C₂

yes

maximal, characteristic

C₄×#11924018

C₂

yes

maximal, characteristic

#17988339

C₂

yes

maximal, characteristic

Q₈⋊#10596831

C₂

yes

maximal, characteristic

#17988317

C₂

yes

maximal, characteristic

#17988308

C₂

yes

maximal, characteristic

#446×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924018

C₄

yes

characteristic

C₄×Dic₁₄₆

C₂²

yes

characteristic

#14556524

C₄

yes

characteristic

C₄⋊#10596831

C₂²

yes

characteristic

#14556520

—

#14556515

C₄

yes

characteristic

#14556514

C₄

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

C₈×Dic₇₃

—

C₄×Q₈×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

C₂²

yes

characteristic

#97×C₇₃

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

C₂×C₄

yes

—

—

—

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₄⋊Dic₇₃

C₂×C₄

yes

characteristic

#11924007

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

M₁₆

yes

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

Q₁₆

yes

—

—

—

—

C₂²×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

#131

yes

characteristic

C₄×C₇₃

C₂×Q₁₆

yes

characteristic

C₄×C₇₃

#135

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#435

yes

characteristic

C₂×C₇₃

C₄×Q₁₆

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#446

D₇₃

yes

characteristic

C₈×Q₈

—

C₄×Q₁₆

—

#335

—

Q₈⋊C₈

—

Q₈⋊C₈

—

#322

—

C₂×Q₁₆

—

C₄×Q₈

—

C₄×Q₈

C₂×D₇₃

yes

characteristic

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

146

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

C₄×D₇₃

yes

characteristic

Q₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

146

—

102

C₂×C₈

—

146

—

103

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

104

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

146

—

108

C₄⋊C₄

C₄×D₇₃

yes

characteristic

109

C₄²

—

110

C₄²

—

146

—

111

C₄²

C₂²×D₇₃

yes

characteristic

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

146

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

146

—

119

C₂×C₄

—

146

—

120

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

121

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

122

C₂×C₄

#11924028

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

292

—

126

C₈

—

292

—

127

C₈

—

146

—

128

C₈

—

146

—

129

C₈

#11924018

yes

complemented

130

C₂²

C₄×C₂²⋊D₇₃

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

292

—

135

C₄

—

146

—

136

C₄

M₁₆×D₇₃

yes

characteristic

137

C₄

#14556599

yes

characteristic

138

C₄

C₂×#11924018

yes

characteristic

139

C₄

#14556611

yes

characteristic

140

C₂

#17988656

yes

characteristic

141

C₂

C₄×#11924018

yes

characteristic

142

C₂

#17988707

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₄²	C₂²×D₇₃
Fitting	#446×C₇₃	C₂
socle	C₂²×C₇₃	C₄×D₄
hypercenter	#446	D₇₃
hypocenter	C₇₃	#1584
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #446

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₄²

C₂²×D₇₃

Fitting

#446×C₇₃

C₂

socle

C₂²×C₇₃

C₄×D₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #446

N	H ≅ G/N	type
53. C₈×C₇₃	Q₁₆	semidirect
72. C₇₃	#1584	semidirect
129. C₈	#11924018	semidirect

H ≅ G/N

type

53. C₈×C₇₃

Q₁₆

semidirect

72. C₇₃

#1584

semidirect

129. C₈

#11924018

semidirect

Subgroups — #22608779

Conjugacy classes of subgroups

Complements