Finite Group Databasebeta

← #37549002

Subgroups — #37549002

Order 23168.

214 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042300C211yesmaximal, characteristic, complemented
2#26042296C211yesmaximal, characteristic, complemented
3#26042124C212yesmaximal, complemented
4#26042122C212yesmaximal
5C2×#19153809C211yesmaximal, characteristic
6#19153883—21no—
7C4⋊#13089685—21no—
8C22⋊#13089685C2212yes—
9C22⋊#13089685C2212yes—
10#19153871—21no—
11C4×#13089685—21no—
12#19153809—21no—
13#19153809—21no—
14#19153809—21no—
15#19153809—21no—
16C2×C4⋊Dic181C2211yescharacteristic
17C2×#15668428C411yescharacteristic
18C2×#15668428C411yescharacteristic
19C2×C22⋊Dic181C411yescharacteristic
20C2×C22⋊Dic181C2211yescharacteristic
21C2×C4×Dic181C2211yescharacteristic
22C2×C22⋊C4×C181C411yescharacteristic
23C2×#13089685—22no—
24C2×#13089685—22no—
25C22×Dic181C2×C411yescharacteristic
26C22×Dic181C2×C411yescharacteristic
27C22×Dic181C2×C411yescharacteristic
28C22×Dic181C2311yescharacteristic
29C4⋊Dic181—21no—
30C4⋊Dic181—21no—
31#15668428—21no—
32#15668428—21no—
33#15668428—21no—
34#15668428—21no—
35C22⋊Dic181—21no—
36C22⋊Dic181—21no—
37C22⋊Dic181—21no—
38C22⋊Dic181—21no—
39C4×Dic181D411yescharacteristic
40C4×Dic181D411yescharacteristic
41C4×Dic181D411yescharacteristic
42C4×Dic181D411yescharacteristic
43C24×C181C2×C411yescharacteristic
44C22×C4×C181C2×C411yescharacteristic
45C22×C4×C181C2×C411yescharacteristic
46C22⋊C4×C181—21no—
47C22⋊C4×C181—21no—
48#13089685—42no—
49#13089685—42no—
50C2×Dic181—22no—
51C2×Dic181—21no—
52C2×Dic181—21no—
53C2×Dic181—41no—
54C2×Dic181—41no—
55C2×Dic181—41no—
56C2×Dic181C22⋊C411yescharacteristic
57C2×Dic181C22⋊C411yescharacteristic
58C2×Dic181C2×D411yescharacteristic
59C2×Dic181C2×D411yescharacteristic
60C23×C181—21no—
61C23×C181—22no—
62C23×C181—41no—
63C23×C181—41no—
64C23×C181C22×C411yescharacteristic
65C2×C4×C181—21no—
66C2×C4×C181—22no—
67C2×C4×C181—41no—
68C2×C4×C181C22⋊C411yescharacteristic
69C2×C4×C181C22⋊C411yescharacteristic
70C22×C181—21no—
71C22×C181—21no—
72C22×C181—41no—
73C22×C181—41no—
74C22×C181—41no—
75C22×C181—82no—
76C22×C181C2×C22⋊C411yescharacteristic
77C22×C181#13112yes—
78C4×C181—21no—
79C4×C181—21no—
80C4×C181—41no—
81Dic181—21no—
82Dic181—21no—
83Dic181—21no—
84Dic181—21no—
85Dic181—41no—
86Dic181—41no—
87C2×C181—22no—
88C2×C181—81no—
89C2×C181#40811yescharacteristic
90C2×C181#41011yescharacteristic
91C2×C181#41311yescharacteristic
92C181#147311yescharacteristic, complemented, Sylow
93#1473—1811nomaximal, Sylow
94C2×#126—1811no—
95#432—1811no—
96#431—1811no—
97#324—1812no—
98#323—1812no—
99#126—3621no—
100#126—3621no—
101#126—3621no—
102#126—3621no—
103C2×C4⋊C4—1811no—
104C2×C4⋊C4—1811no—
105C2×C4⋊C4—1811no—
106C2×C22⋊C4—1811no—
107C2×C22⋊C4—1811no—
108C2×C22⋊C4#1062438211yescharacteristic
109C2×C42—1811no—
110C4⋊C8—3621no—
111C4⋊C8—3621no—
112C22⋊C8—1812no—
113C22⋊C8—1812no—
114#97—3621no—
115C4×C8—3621no—
116C24C2×#1062438211yescharacteristic
117C22×C4—1811no—
118C22×C4—1811no—
119C22×C4—1811no—
120C22×C4—1811no—
121C22×C4C2×#1062438211yescharacteristic
122C22×C4C2×#1062438211yescharacteristic
123C2×C8—3622no—
124C2×C8—3622no—
125C4⋊C4—3621no—
126C4⋊C4—3621no—
127C4⋊C4—3621no—
128C4⋊C4—3621no—
129C4⋊C4—3621no—
130C4⋊C4—3621no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—3621no—
134C22⋊C4—3621no—
135C22⋊C4—3621no—
136C22⋊C4—3621no—
137C42—1811no—
138C42—1811no—
139C42—1811no—
140C42—1811no—
141C23—21no—
142C23—22no—
143C23—41no—
144C23—41no—
145C23C22×#1062438211yescharacteristic
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—3622no—
150C2×C4—3621no—
151C2×C4—3621no—
152C2×C4—1811no—
153C2×C4—1811no—
154C2×C4—1811no—
155C2×C4—1811no—
156C2×C4—7241no—
157C2×C4—7241no—
158C2×C4—7241no—
159C2×C4C22⋊#1062438211yescharacteristic
160C2×C4C22⋊#1062438211yescharacteristic
161C8—7242no—
162C8—7242no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—82no—
169C22C2×C22⋊#1062438211yescharacteristic
170C22#1915390312yes—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—3621no—
175C4—3621no—
176C4—3621no—
177C4—3621no—
178C4—7241no—
179C4—7241no—
180C2—22no—
181C2—81no—
182C2#2604225311yescharacteristic
183C2#2604225811yescharacteristic
184C2#2604226611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC23×C181C22×C4
FrattiniC23C22×#10624382
FittingC2×C22⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC24×C181C2×C4
cosocleC22×Dic181C23
hypercenterC2×C22⋊C4#10624382
hypocenterC181#1473
LCSG ▷ C23×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #26042300C2semidirect
2. #26042296C2semidirect
3. #26042124C2semidirect
92. C181#1473semidirect

Maximal subgroups

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

subgroupindex
#260423002
#260422962
#260421242
#260421222
C2×#191538092
#1473181