Finite Group Databasebeta

← #15683781

Subgroups — #15683781

Order 2944.

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

normal subgroups only

This group has 400 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#13092970C211yesmaximal, characteristic, complemented
2C2×#10625107C211yesmaximal, characteristic
3#13092775C214yesmaximal, complemented
4#13092770C214yesmaximal, complemented
5#13092427C211yesmaximal, characteristic, complemented
6#13092425C211yesmaximal, characteristic, complemented
7#13092422C211yesmaximal, characteristic
8M16×Dic23C211yesmaximal, characteristic, complemented
9C23×#418C211yesmaximal, characteristic
10C22×D4×C23C2211yescharacteristic
11C22×Dic46C2211yescharacteristic
12C2×M16×C23C2211yescharacteristic
13C23×#117C2211yescharacteristic
14C2×C22⋊Dic23—22no—
15#10625107—22no—
16#10625107C2212yes—
17#10625107C2212yes—
18#10625097C2211yescharacteristic
19C2×C4×Dic23C2211yescharacteristic
20C2×#67267C2211yescharacteristic
21#10625061C2212yescomplemented
22#10625059C2212yescomplemented
23#10625049—22no—
24C4×Dic46—22no—
25C23×#102C2214yes—
26#10625014C2214yes—
27#10624998C2214yescomplemented
28#10624997C2212yescomplemented
29C8×Dic23C2212yescomplemented
30#10624992C2214yescomplemented
31C24×C23—21no—
32C2×D4×C23—21no—
33C2×D4×C23—22no—
34C2×D4×C23—22no—
35C2×D4×C23C2312yes—
36C22×C4×C23C2311yescharacteristic
37C22×Dic23—21no—
38C22×Dic23D412yes—
39C2×Dic46—22no—
40C2×Dic46—22no—
41C2×Dic46—21no—
42C2×Dic46—22no—
43C2×Dic46C2312yes—
44M16×C23—22no—
45C2×C8×C23C2312yes—
46C4⋊C4×C23C2312yes—
47C22⋊C4×C23—21no—
48C42×C23—21no—
49C22⋊Dic23—21no—
50C22⋊Dic23—24no—
51C22⋊Dic23—24no—
52C4⋊Dic23—22no—
53C4⋊Dic23C2312yes—
54Dic23⋊C4—22no—
55Dic23⋊C4—22no—
56C4×Dic23—21no—
57C4×Dic23D412yes—
58C4×Dic23C2311yescharacteristic
59C4×Dic23C2311yescharacteristic
60#67267—22no—
61C2×C23⋊C8C2312yes—
62C23×C23—22no—
63C23×C23—44no—
64C23×C23—42no—
65C23×C23C2×D411yescharacteristic
66D4×C23—22no—
67D4×C23—22no—
68D4×C23—42no—
69C2×C4×C23—22no—
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23#4112yes—
72C2×C4×C23#4112yes—
73C2×C4×C23C2411yescharacteristic
74C2×Dic23—22no—
75C2×Dic23—22no—
76C2×Dic23—42no—
77C2×Dic23—42no—
78C2×Dic23C2×D412yes—
79C2×Dic23C2×D412yes—
80Dic46—22no—
81Dic46—22no—
82Dic46—44no—
83Dic46—42no—
84C8×C23—22no—
85C23⋊C8—22no—
86#3140—231nomaximal, Sylow
87C22×C23—22no—
88C22×C23—42no—
89C22×C23—44no—
90C22×C23—84no—
91C22×C23#12412yes—
92C22×C23C22×D411yescharacteristic
93C4×C23—42no—
94C4×C23#12412yes—
95C4×C23C2×#4111yescharacteristic
96C4×C23C2×#4111yescharacteristic
97Dic23—22no—
98Dic23—22no—
99Dic23—42no—
100Dic23—42no—
101#533—231no—
102C2×#124—231no—
103#489—234no—
104#488—234no—
105#419—231no—
106#419—231no—
107#418—231no—
108#418D2311yescharacteristic
109C4×M16—231no—
110C2×C23—22no—
111C2×C23—82no—
112C2×C23C2×#12411yescharacteristic
113C2×C23#57512yes—
114C22×Q8—231no—
115C22×D4C2×D2311yescharacteristic
116C2×M16—231no—
117C2×M16C2×D2311yescharacteristic
118C4⋊Q8—232no—
119#125—232no—
120#124—232no—
121#124—232no—
122#124—462no—
123C22⋊Q8—462no—
124C4×Q8—462no—
125#117—231no—
126#117C2×D2311yescharacteristic
127C2×C22⋊C4—462no—
128C2×C42—231no—
129#103—234no—
130#103—234no—
131#102—234no—
132#102C2×D2314yes—
133#97—232no—
134C4×C8—232no—
135C23#314011yescharacteristic, complemented, Sylow
136C24—21no—
137C2×Q8—232no—
138C2×Q8—462no—
139C2×Q8—461no—
140C2×Q8—462no—
141C2×Q8—462no—
142C2×D4—22no—
143C2×D4—21no—
144C2×D4—22no—
145C2×D4C22×D2312yes—
146C22×C4—232no—
147C22×C4—461no—
148C22×C4C22×D2311yescharacteristic
149M16—22no—
150M16—462no—
151C2×C8—232no—
152C2×C8C22×D2312yes—
153C4⋊C4—232no—
154C4⋊C4—462no—
155C4⋊C4—462no—
156C4⋊C4—462no—
157C4⋊C4C22×D2312yes—
158C22⋊C4—21no—
159C22⋊C4—464no—
160C22⋊C4—464no—
161C22⋊C4—461no—
162C42—21no—
163C42—232no—
164C42—231no—
165C42—231no—
166C42—461no—
167C23—22no—
168C23—44no—
169C23—42no—
170C23D4×D2311yescharacteristic
171Q8—462no—
172Q8—462no—
173Q8—924no—
174Q8—922no—
175D4—22no—
176D4—22no—
177D4—42no—
178C2×C4—22no—
179C2×C4—232no—
180C2×C4—232no—
181C2×C4—462no—
182C2×C4—462no—
183C2×C4—922no—
184C2×C4—922no—
185C2×C4#6728812yes—
186C2×C4D4×D2311yescharacteristic
187C2×C4#6729012yes—
188C2×C4C23×D2311yescharacteristic
189C8—22no—
190C8—462no—
191C22—22no—
192C22—42no—
193C22—44no—
194C22—84no—
195C22#1062505612yes—
196C22C2×D4×D2311yescharacteristic
197C4—42no—
198C4—462no—
199C4—462no—
200C4—922no—
201C4—922no—
202C4#1062505612yes—
203C4C2×#6728811yescharacteristic
204C4C2×#6729011yescharacteristic
205C2—22no—
206C2—82no—
207C2C2×#1062505611yescharacteristic
208C2#1309321312yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#418C2
socleC22×C23C22×D4
prime radicalC22×D4×C23C22
hypercenter#418D23
hypocenterC23#3140
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #13092970C2semidirect
3. #13092775C2semidirect
4. #13092770C2semidirect
5. #13092427C2semidirect
6. #13092425C2semidirect
8. M16×Dic23C2semidirect
21. #10625061C22semidirect
22. #10625059C22semidirect
27. #10624998C22semidirect
28. #10624997C22semidirect
29. C8×Dic23C22semidirect
30. #10624992C22semidirect
135. C23#3140semidirect

Maximal subgroups

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

subgroupindex
#130929702
C2×#106251072
#130927752
#130927702
#130924272
#130924252
#130924222
M16×Dic232
C23×#4182
#314023