Finite Group Databasebeta

← #37543973

Subgroups — #37543973

Order 23168.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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#26041891C211yesmaximal, characteristic, complemented
2#26041620C212yesmaximal, complemented
3#26041579C212yesmaximal, complemented
4#26041484C212yesmaximal, complemented
5#26041430C212yesmaximal
6#26041379C212yesmaximal, complemented
7C4×#15668437C212yesmaximal, complemented
8#26041340C211yesmaximal, characteristic, complemented
9#518×C181C211yesmaximal, characteristic
10C2×#15668437C2212yes—
11C2×#15668437C2212yes—
12#19153816C2211yescharacteristic, complemented
13#19153809—22no—
14#19153808C2211yescharacteristic, complemented
15#19153806—22no—
16#19153795C2212yes—
17C4×Dic362C2212yescomplemented
18#19153749C2212yescomplemented
19#19153747C2212yescomplemented
20C4⋊#13089678C2212yescomplemented
21#19153739C2212yescomplemented
22#19153739C2212yescomplemented
23#19153737C2212yes—
24#19153737C2212yes—
25C22⋊#13089678C2212yes—
26#19153727C2211yescharacteristic, complemented
27C4×#13089678C2211yescharacteristic, complemented
28C22×D4×C181C2211yescharacteristic
29C4×D4×C181—22no—
30C4×D4×C181C2212yes—
31C4×D4×C181C2212yes—
32#117×C181C2211yescharacteristic
33#117×C181C2211yescharacteristic
34C2×C22⋊C4×C181—22no—
35C2×Dic362C2312yes—
36#15668437—24no—
37#15668437—24no—
38C2×#13089678C2312yes—
39C2×#13089678C2312yes—
40C4⋊Dic181—22no—
41C4⋊Dic181C2312yes—
42#15668428—22no—
43#15668428—22no—
44#15668428—22no—
45C22⋊Dic181—22no—
46C4×Dic181—22no—
47C24×C181—21no—
48C2×D4×C181—24no—
49C2×D4×C181—21no—
50C2×D4×C181C2312yes—
51C22×C4×C181—22no—
52C22×C4×C181—22no—
53C22×C4×C181C2311yescharacteristic
54C4⋊C4×C181D412yes—
55C4⋊C4×C181C2312yes—
56C22⋊C4×C181—21no—
57C22⋊C4×C181—22no—
58C22⋊C4×C181—22no—
59C22⋊C4×C181D412yes—
60C42×C181—21no—
61C42×C181C2311yescharacteristic
62C42×C181C2311yescharacteristic
63Dic362—22no—
64Dic362—22no—
65C2×Dic181—22no—
66C2×Dic181—22no—
67#13089678—22no—
68#13089678—22no—
69C23×C181—24no—
70C23×C181—22no—
71C23×C181—82no—
72C23×C181C2×D411yescharacteristic
73D4×C181—24no—
74D4×C181—22no—
75D4×C181#4114yes—
76C2×C4×C181—22no—
77C2×C4×C181—22no—
78C2×C4×C181—82no—
79C2×C4×C181—82no—
80C2×C4×C181C2×D411yescharacteristic
81C2×C4×C181C2×D412yes—
82C2×C4×C181C2×D412yes—
83C2×C4×C181C2411yescharacteristic
84C22×C181—21no—
85C22×C181—24no—
86C22×C181—22no—
87C22×C181—42no—
88C22×C181—42no—
89C22×C181—84no—
90C22×C181C22×D411yescharacteristic
91C4×C181—21no—
92C4×C181—22no—
93C4×C181—22no—
94C4×C181—42no—
95C4×C181C2×#4112yes—
96Dic181—42no—
97Dic181—42no—
98C2×C181—41no—
99C2×C181—44no—
100C2×C181#52511yescharacteristic
101C2×C181#57712yes—
102C181#312311yescharacteristic, complemented, Sylow
103#3123—1811nomaximal, Sylow
104#541—1811no—
105#518D18111yescharacteristic
106#485—1812no—
107#478—1812no—
108#461—1812no—
109#450—1812no—
110#440—1812no—
111C4×SD16—1812no—
112#433—1811no—
113C22×D4C2×D18111yescharacteristic
114C2×SD16—1812no—
115C2×SD16—1812no—
116C4⋊Q8—1811no—
117#126—3622no—
118#125—3622no—
119#125—1811no—
120C22⋊Q8—1812no—
121C4×Q8—1812no—
122C4×D4—22no—
123C4×D4C2×D18112yes—
124C4×D4C2×D18112yes—
125#117C2×D18111yescharacteristic
126#117C2×D18111yescharacteristic
127C2×C22⋊C4—22no—
128#107—1812no—
129#106—1812no—
130C4⋊C8—1812no—
131#103—1812no—
132#103—1812no—
133#102—1812no—
134#102—1812no—
135C22⋊C8—1812no—
136#97—1811no—
137C4×C8—1811no—
138C24—21no—
139C2×Q8—1812no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D18112yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D18111yescharacteristic
146SD16—3624no—
147SD16—3624no—
148C2×C8—1812no—
149C2×C8—1812no—
150C4⋊C4—3622no—
151C4⋊C4—3622no—
152C4⋊C4—3622no—
153C4⋊C4—3622no—
154C4⋊C4—1812no—
155C4⋊C4C22⋊D18112yes—
156C4⋊C4C22×D18112yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—3622no—
161C22⋊C4C22⋊D18112yes—
162C42—21no—
163C42—3622no—
164C42C22×D18111yescharacteristic
165C42C22×D18111yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D18111yescharacteristic
170Q8—3622no—
171Q8—3622no—
172D4—24no—
173D4—22no—
174D4#1566844914yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—3622no—
180C2×C4—3622no—
181C2×C4C2×C22⋊D18111yescharacteristic
182C2×C4C2×C22⋊D18112yes—
183C2×C4C2×C22⋊D18112yes—
184C2×C4C23×D18111yescharacteristic
185C8—3622no—
186C8—3622no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D18111yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—7242no—
199C4—7242no—
200C4C2×#1566844912yes—
201C2—41no—
202C2—44no—
203C2#2604179011yescharacteristic
204C2#2604209012yes—
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#518×C181C2
socleC22×C181C22×D4
prime radicalC22×D4×C181C22
hypercenter#518D181
hypocenterC181#3123
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #26041891C2semidirect
2. #26041620C2semidirect
3. #26041579C2semidirect
4. #26041484C2semidirect
6. #26041379C2semidirect
7. C4×#15668437C2semidirect
8. #26041340C2semidirect
12. #19153816C22semidirect
14. #19153808C22semidirect
17. C4×Dic362C22semidirect
18. #19153749C22semidirect
19. #19153747C22semidirect
20. C4⋊#13089678C22semidirect
21. #19153739C22semidirect
22. #19153739C22semidirect
26. #19153727C22semidirect
27. C4×#13089678C22semidirect
102. C181#3123semidirect

Maximal subgroups

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

subgroupindex
#260418912
#260416202
#260415792
#260414842
#260414302
#260413792
C4×#156684372
#260413402
#518×C1812
#3123181