Group #36442150 — subgroups

Subgroups — #36442150

Order 22784.

162 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 91 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×#19151432	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151428	C₂	1	1	yes	maximal, characteristic
3	C₂×#368×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#15667948	—	2	1	no	—
5	#19151432	—	2	1	no	—
6	#19151432	C₄	1	2	yes	—
7	C₂×#15667918	—	2	1	no	—
8	#19151428	—	2	1	no	—
9	#19151428	C₄	1	2	yes	—
10	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×#108×C₈₉	—	2	1	no	—
12	#368×C₈₉	—	2	1	no	—
13	#368×C₈₉	C₄	1	2	yes	—
14	C₂×#13083558	—	4	1	no	—
15	#15667948	—	2	2	no	—
16	#15667948	—	4	1	no	—
17	#15667918	—	2	2	no	—
18	C₂×M₁₆×C₈₉	—	4	1	no	—
19	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
20	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
24	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
25	C₂×C₁₆×C₈₉	Q₈	1	1	yes	characteristic
26	#108×C₈₉	—	2	2	no	—
27	#108×C₈₉	—	4	1	no	—
28	#13083558	—	4	2	no	—
29	#13083558	—	8	1	no	—
30	C₂×#10623494	—	8	1	no	—
31	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
32	M₁₆×C₈₉	—	4	2	no	—
33	M₁₆×C₈₉	—	8	1	no	—
34	C₂×C₈×C₈₉	—	8	1	no	—
35	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₈₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₈₉	SD₁₆	1	1	yes	characteristic
39	C₂×C₈×C₈₉	SD₁₆	1	1	yes	characteristic
40	C₂×C₈×C₈₉	Q₁₆	1	1	yes	characteristic
41	C₁₆×C₈₉	C₄²	1	1	yes	characteristic
42	C₁₆×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₁₆×C₈₉	C₄⋊C₄	1	1	yes	characteristic
44	C₁₆×C₈₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂³×C₈₉	Q₃₂	1	1	yes	characteristic
46	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
47	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
48	C₂×C₄×C₈₉	#107	1	1	yes	characteristic
49	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
50	C₂×C₄×C₈₉	SD₃₂	1	1	yes	characteristic
51	C₂×C₄×C₈₉	SD₃₂	1	1	yes	characteristic
52	C₈×C₈₉	—	8	2	no	—
53	C₈×C₈₉	#95	1	1	yes	characteristic
54	C₈×C₈₉	#103	1	1	yes	characteristic
55	C₈×C₈₉	#103	1	1	yes	characteristic
56	C₈×C₈₉	#106	1	1	yes	characteristic
57	#10623494	—	8	2	no	—
58	C₂²×C₈₉	—	4	1	no	—
59	C₂²×C₈₉	#358	1	1	yes	characteristic
60	C₂²×C₈₉	#358	1	1	yes	characteristic
61	C₂²×C₈₉	#366	1	1	yes	characteristic
62	C₄×C₈₉	#340	1	1	yes	characteristic
63	C₄×C₈₉	#357	1	1	yes	characteristic
64	C₄×C₈₉	#357	1	1	yes	characteristic
65	C₄×C₈₉	#367	1	1	yes	characteristic
66	#7479	—	89	1	no	maximal, Sylow
67	C₂×C₈₉	—	2	1	no	—
68	C₂×C₈₉	—	2	1	no	—
69	C₂×C₈₉	—	2	1	no	—
70	C₂×C₈₉	#1380	1	1	yes	characteristic
71	C₂×M₆₄	—	89	1	no	—
72	C₂×#368	—	89	1	no	—
73	C₂×#368	D₈₉	1	1	yes	characteristic
74	C₈₉	#7479	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
76	C₂×#108	—	2	1	no	—
77	C₂×#108	—	178	1	no	—
78	M₆₄	—	89	2	no	—
79	M₆₄	—	178	1	no	—
80	C₂×C₃₂	—	178	1	no	—
81	#368	—	2	1	no	—
82	#368	—	89	2	no	—
83	#368	—	178	1	no	—
84	#368	Dic₈₉	1	2	yes	—
85	C₂×M₁₆	—	4	1	no	—
86	C₂×M₁₆	—	356	1	no	—
87	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
88	C₂×C₁₆	Dic₁₇₈	1	1	yes	characteristic
89	C₂×C₁₆	C₄×D₈₉	1	1	yes	characteristic
90	C₂×C₁₆	C₄×D₈₉	1	1	yes	characteristic
91	C₂×C₁₆	D₃₅₆	1	1	yes	characteristic
92	C₂×C₁₆	C₂×Dic₈₉	1	1	yes	characteristic
93	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
94	#108	—	2	2	no	—
95	#108	—	4	1	no	—
96	#108	—	356	1	no	—
97	#108	—	178	2	no	—
98	C₃₂	—	178	2	no	—
99	C₂²×C₄	#13083559	1	1	yes	characteristic
100	M₁₆	—	4	2	no	—
101	M₁₆	—	8	1	no	—
102	M₁₆	—	356	2	no	—
103	M₁₆	—	712	1	no	—
104	C₂×C₈	—	8	1	no	—
105	C₂×C₈	—	712	1	no	—
106	C₂×C₈	#13083551	1	1	yes	characteristic
107	C₂×C₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
108	C₂×C₈	#13083553	1	1	yes	characteristic
109	C₂×C₈	#13083561	1	1	yes	characteristic
110	C₂×C₈	#13083562	1	1	yes	characteristic
111	C₂×C₈	#13083564	1	1	yes	characteristic
112	C₁₆	C₄×Dic₈₉	1	1	yes	characteristic
113	C₁₆	#13083551	1	1	yes	characteristic
114	C₁₆	#13083553	1	1	yes	characteristic
115	C₁₆	C₄⋊Dic₈₉	1	1	yes	characteristic
116	C₂³	#15667958	1	1	yes	characteristic
117	C₂×C₄	#15667932	1	1	yes	characteristic
118	C₂×C₄	#15667933	1	1	yes	characteristic
119	C₂×C₄	#15667945	1	1	yes	characteristic
120	C₂×C₄	#15667953	1	1	yes	characteristic
121	C₂×C₄	#15667955	1	1	yes	characteristic
122	C₂×C₄	#15667956	1	1	yes	characteristic
123	C₈	—	8	2	no	—
124	C₈	—	712	2	no	—
125	C₈	#15667919	1	1	yes	characteristic
126	C₈	#15667935	1	1	yes	characteristic
127	C₈	#15667936	1	1	yes	characteristic
128	C₈	#15667943	1	1	yes	characteristic
129	C₂²	—	4	1	no	—
130	C₂²	#19151401	1	1	yes	characteristic
131	C₂²	#19151402	1	1	yes	characteristic
132	C₂²	#19151423	1	1	yes	characteristic
133	C₄	#19151360	1	1	yes	characteristic
134	C₄	#19151398	1	1	yes	characteristic
135	C₄	#19151399	1	1	yes	characteristic
136	C₄	#19151425	1	1	yes	characteristic
137	C₂	—	2	1	no	—
138	C₂	—	2	1	no	—
139	C₂	—	2	1	no	—
140	C₂	#26018343	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151432

C₂

yes

maximal, characteristic

C₂×#19151428

C₂

yes

maximal, characteristic

C₂×#368×C₈₉

C₂

yes

maximal, characteristic

C₂×#15667948

—

#19151432

—

#19151432

C₄

yes

—

C₂×#15667918

—

#19151428

—

#19151428

C₄

yes

—

C₂²×C₁₆×C₈₉

C₂²

yes

characteristic

C₂×#108×C₈₉

—

#368×C₈₉

—

#368×C₈₉

C₄

yes

—

—

—

—

—

C₂×M₁₆×C₈₉

—

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

Q₈

yes

characteristic

#108×C₈₉

—

#108×C₈₉

—

#13083558

—

#13083558

—

C₂×#10623494

—

C₂²×C₄×C₈₉

D₈

yes

characteristic

M₁₆×C₈₉

—

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₈₉

SD₁₆

yes

characteristic

C₂×C₈×C₈₉

SD₁₆

yes

characteristic

C₂×C₈×C₈₉

Q₁₆

yes

characteristic

C₁₆×C₈₉

C₄²

yes

characteristic

C₁₆×C₈₉

C₂²⋊C₄

yes

characteristic

C₁₆×C₈₉

C₄⋊C₄

yes

characteristic

C₁₆×C₈₉

C₄⋊C₄

yes

characteristic

C₂³×C₈₉

Q₃₂

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

D₁₆

yes

characteristic

C₂×C₄×C₈₉

SD₃₂

yes

characteristic

C₂×C₄×C₈₉

SD₃₂

yes

characteristic

C₈×C₈₉

—

C₈×C₈₉

yes

C₈×C₈₉

yes

C₈×C₈₉

yes

C₈×C₈₉

yes

—

C₂²×C₈₉

—

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

—

C₂×C₈₉

—

C₂×C₈₉

—

C₂×C₈₉

—

C₂×C₈₉

#1380

yes

characteristic

C₂×M₆₄

—

C₂×#368

—

C₂×#368

D₈₉

yes

characteristic

C₈₉

#7479

yes

characteristic, complemented, Sylow

C₂²×C₁₆

C₂×D₈₉

yes

characteristic

C₂×#108

—

C₂×#108

—

178

—

M₆₄

—

M₆₄

—

178

—

C₂×C₃₂

—

178

—

#368

—

#368

—

#368

—

178

—

#368

Dic₈₉

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

356

—

C₂²×C₈

C₂²⋊D₈₉

yes

characteristic

C₂×C₁₆

Dic₁₇₈

yes

characteristic

C₂×C₁₆

C₄×D₈₉

yes

characteristic

C₂×C₁₆

C₄×D₈₉

yes

characteristic

C₂×C₁₆

D₃₅₆

yes

characteristic

C₂×C₁₆

C₂×Dic₈₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₈₉

yes

—

—

—

356

—

#108

—

178

—

C₃₂

—

178

—

C₂²×C₄

#13083559

yes

characteristic

100

M₁₆

—

101

M₁₆

—

102

M₁₆

—

356

—

103

M₁₆

—

712

—

104

C₂×C₈

—

105

C₂×C₈

—

712

—

106

C₂×C₈

#13083551

yes

characteristic

107

C₂×C₈

C₂²⋊Dic₈₉

yes

characteristic

108

C₂×C₈

#13083553

yes

characteristic

109

C₂×C₈

#13083561

yes

characteristic

110

C₂×C₈

#13083562

yes

characteristic

111

C₂×C₈

#13083564

yes

characteristic

112

C₁₆

C₄×Dic₈₉

yes

characteristic

113

C₁₆

#13083551

yes

characteristic

114

C₁₆

#13083553

yes

characteristic

115

C₁₆

C₄⋊Dic₈₉

yes

characteristic

116

C₂³

#15667958

yes

characteristic

117

C₂×C₄

#15667932

yes

characteristic

118

C₂×C₄

#15667933

yes

characteristic

119

C₂×C₄

#15667945

yes

characteristic

120

C₂×C₄

#15667953

yes

characteristic

121

C₂×C₄

#15667955

yes

characteristic

122

C₂×C₄

#15667956

yes

characteristic

123

C₈

—

124

C₈

—

712

—

125

C₈

#15667919

yes

characteristic

126

C₈

#15667935

yes

characteristic

127

C₈

#15667936

yes

characteristic

128

C₈

#15667943

yes

characteristic

129

C₂²

—

130

C₂²

#19151401

yes

characteristic

131

C₂²

#19151402

yes

characteristic

132

C₂²

#19151423

yes

characteristic

133

C₄

#19151360

yes

characteristic

134

C₄

#19151398

yes

characteristic

135

C₄

#19151399

yes

characteristic

136

C₄

#19151425

yes

characteristic

137

C₂

—

138

C₂

—

139

C₂

—

140

C₂

#26018343

yes

characteristic

	subgroup	G/H
center	C₄	#19151398
commutator	C₁₆×C₈₉	C₄²
Frattini	C₂²×C₁₆	C₂×D₈₉
Fitting	C₂×#368×C₈₉	C₂
socle	C₂×C₈₉	#1380
prime radical	C₂³×C₈₉	Q₃₂
cosocle	C₂²×C₁₆×C₈₉	C₂²
hypercenter	C₂×#368	D₈₉
hypocenter	C₈₉	#7479
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×#368

subgroup

G/H

center

C₄

#19151398

commutator

C₁₆×C₈₉

C₄²

Frattini

C₂²×C₁₆

C₂×D₈₉

Fitting

C₂×#368×C₈₉

C₂

socle

C₂×C₈₉

#1380

prime radical

C₂³×C₈₉

Q₃₂

cosocle

C₂²×C₁₆×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×#368

N	H ≅ G/N	type
74. C₈₉	#7479	semidirect

H ≅ G/N

type

74. C₈₉

#7479

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#19151432	2
C₂×#19151428	2
C₂×#368×C₈₉	2
#7479	89

subgroup

index

C₂×#19151432

C₂×#19151428

C₂×#368×C₈₉

#7479

Subgroups — #36442150

Conjugacy classes of subgroups

Complements

Maximal subgroups