Finite Group Databasebeta

← #37549181

Subgroups — #37549181

Order 23168.

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

normal subgroups only

This group has 264 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#26042302C211yesmaximal, characteristic, complemented
2C4×#15668459C211yesmaximal, characteristic, complemented
3#26042135C212yesmaximal, complemented
4#26042134C212yesmaximal, complemented
5#124×D181C211yesmaximal, characteristic
6C2×#15668459—21no—
7#19153883—21no—
8#19153873—21no—
9#19153871C2212yescomplemented
10#19153871C2212yescomplemented
11C4×#13089685—21no—
12C2×Q8×D181C411yescharacteristic
13C2×D4×D181C411yescharacteristic
14#19153805C2211yescharacteristic
15#19153804C411yescharacteristic
16#19153803C2211yescharacteristic
17#19153802—21no—
18#19153802—21no—
19C22⋊C4×D181—21no—
20C22⋊C4×D181—21no—
21C42×D181C2211yescharacteristic
22#124×C181C411yescharacteristic
23#15668459—24no—
24C2×#13089685—22no—
25C2×#13089685—22no—
26C23×D181—21no—
27C2×Dic362—21no—
28C2×Dic362C2×C411yescharacteristic
29Q8×D181—42no—
30C2×D724C2×C411yescharacteristic
31C2×C22⋊D181—21no—
32D4×D181—42no—
33C2×C4×D181—21no—
34C2×C4×D181C2×C411yescharacteristic
35C2×C4×D181D411yescharacteristic
36C2×C4×D181D411yescharacteristic
37C22⋊Dic181—21no—
38C22⋊Dic181—21no—
39#15668426—21no—
40#15668426—21no—
41#15668426—21no—
42#15668426—21no—
43C4×Dic181D411yescharacteristic
44C4×Dic181D411yescharacteristic
45C4×Dic181C2311yescharacteristic
46C2×Q8×C181C2×C411yescharacteristic
47C2×D4×C181C2×C411yescharacteristic
48C22⋊C4×C181—21no—
49C22⋊C4×C181—21no—
50C42×C181C2×C411yescharacteristic
51#13089685—24no—
52#13089685—42no—
53C22×D181—21no—
54C22×D181—42no—
55C22×D181—42no—
56C22×D181—42no—
57C22×D181C22⋊C411yescharacteristic
58Dic362—42no—
59Dic362—41no—
60D724—41no—
61C22⋊D181—42no—
62C2×Dic181—21no—
63C2×Dic181C22⋊C411yescharacteristic
64C2×Dic181C2×D411yescharacteristic
65C2×Dic181C2×D411yescharacteristic
66C4×D181—22no—
67C4×D181—22no—
68C4×D181—41no—
69C4×D181—42no—
70C23×C181—21no—
71Q8×C181—41no—
72D4×C181—41no—
73C2×C4×C181—21no—
74C2×C4×C181C22⋊C411yescharacteristic
75C2×C4×C181C22⋊C411yescharacteristic
76C2×C4×C181C22×C411yescharacteristic
77C22×C181—41no—
78C22×C181—41no—
79C22×C181—41no—
80C22×C181C2×C22⋊C411yescharacteristic
81C2×D181—21no—
82C2×D181—21no—
83C2×D181—41no—
84C2×D181—41no—
85C2×D181—41no—
86C2×D181—84no—
87C2×D181#10412yes—
88C4×C181—21no—
89C4×C181—21no—
90C4×C181—21no—
91C4×C181—41no—
92Dic181—21no—
93Dic181—21no—
94Dic181—41no—
95Dic181#10012yes—
96C2×C181—81no—
97C2×C181C2×#10011yescharacteristic
98C2×C181C2×#10411yescharacteristic
99C2×C181#42111yescharacteristic
100D181—22no—
101D181—81no—
102C181#152711yescharacteristic, complemented, Sylow
103#1527—1811nomaximal, Sylow
104C2×#124—1811no—
105#432—1811no—
106C4×M16—1811no—
107#329—1812no—
108#329—1812no—
109C22×Q8—1811no—
110C22×D4—1811no—
111C2×M16—3621no—
112#124—3621no—
113#124—3621no—
114#124—1811no—
115#124—1811no—
116#124—1811no—
117#124#1062438211yescharacteristic
118C2×C22⋊C4—3621no—
119C2×C22⋊C4—3621no—
120C2×C42—1811no—
121C4⋊C8—3621no—
122C22⋊C8—3621no—
123#97—1812no—
124#97—1812no—
125C4×C8—3621no—
126C24—3621no—
127C2×Q8—3621no—
128C2×Q8—1811no—
129C2×Q8—7242no—
130C2×Q8C2×#1062438211yescharacteristic
131C2×D4—3621no—
132C2×D4—1811no—
133C2×D4—7242no—
134C2×D4C2×#1062438211yescharacteristic
135C22×C4—3621no—
136C22×C4—1811no—
137C22×C4—1811no—
138C22×C4—1811no—
139M16—3624no—
140C2×C8—3622no—
141C2×C8—3622no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—3621no—
145C22⋊C4—3621no—
146C22⋊C4—3621no—
147C22⋊C4—3621no—
148C22⋊C4—3621no—
149C22⋊C4—3621no—
150C42—1811no—
151C42—1811no—
152C42—1811no—
153C42C2×#1062438211yescharacteristic
154C23—21no—
155C23—3621no—
156C23—1811no—
157C23—7242no—
158C23—7242no—
159C23—7242no—
160Q8—41no—
161Q8—7241no—
162Q8—7242no—
163D4—41no—
164D4—7241no—
165D4—7242no—
166C2×C4—21no—
167C2×C4—3622no—
168C2×C4—3622no—
169C2×C4—3621no—
170C2×C4—1811no—
171C2×C4—1811no—
172C2×C4—1811no—
173C2×C4—7241no—
174C2×C4—7242no—
175C2×C4C22⋊#1062438211yescharacteristic
176C2×C4C22⋊#1062438211yescharacteristic
177C2×C4C22×#1062438211yescharacteristic
178C8—3624no—
179C8—7242no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—3621no—
184C22—3621no—
185C22—14484no—
186C22—1812no—
187C22—7241no—
188C22—7241no—
189C22—7241no—
190C22C2×C22⋊#1062438211yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—41no—
195C4—3621no—
196C4—3621no—
197C4—1812no—
198C4—7241no—
199C2—81no—
200C2—3622no—
201C2—14481no—
202C2D181⋊#10011yescharacteristic
203C2D181⋊#10411yescharacteristic
204C2#2604227611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#124×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC2×D4×D181C4
cosocleC4×Dic181C23
hypercenter#124#10624382
hypocenterC181#1527
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #26042302C2semidirect
2. C4×#15668459C2semidirect
3. #26042135C2semidirect
4. #26042134C2semidirect
9. #19153871C22semidirect
10. #19153871C22semidirect
102. C181#1527semidirect

Maximal subgroups

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

subgroupindex
#260423022
C4×#156684592
#260421352
#260421342
#124×D1812
#1527181