Finite Group Databasebeta

← #15683780

Subgroups — #15683780

Order 2944.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#13092973C211yesmaximal, characteristic, complemented
2#124×D23C211yesmaximal, characteristic
3#13092778C212yesmaximal, complemented
4#13092775C212yesmaximal, complemented
5#13092774C211yesmaximal, characteristic, complemented
6#13092772C211yesmaximal, characteristic, complemented
7#13092771C211yesmaximal, characteristic, complemented
8#13092424C212yesmaximal, complemented
9#13092420C212yesmaximal
10C4×#67262C211yesmaximal, characteristic, complemented
11C23×#488C211yesmaximal, characteristic, complemented
12C2×Q8×D23C2211yescharacteristic
13C2×D4×D23C2211yescharacteristic
14C23×#125C2211yescharacteristic, complemented
15C23×#124C2211yescharacteristic
16#10625118C2211yescharacteristic
17#10625107C2211yescharacteristic
18C2×#67262C2212yes—
19#10625067—22no—
20#10625063C2212yes—
21#10625059C2212yescomplemented
22#10625058—22no—
23#10625056—22no—
24C22⋊C4×D23—22no—
25#10625046C2211yescharacteristic
26C42×D23C2211yescharacteristic
27#10625041C2211yescharacteristic, complemented
28C23×#103C2212yescomplemented
29C23×#102C2212yes—
30C4×C8×C23C2211yescharacteristic, complemented
31#10625017C2212yescomplemented
32#10625014C2212yes—
33#10625003C2212yes—
34#10624998C2212yescomplemented
35#10624997C2212yescomplemented
36#10624992C2212yescomplemented
37#10624991C2212yes—
38C4×C23⋊C8C2211yescharacteristic, complemented
39C23×D23—21no—
40C2×Q8×C23C2311yescharacteristic
41C2×D4×C23C2311yescharacteristic
42C2×C22⋊D23—21no—
43Q8×D23—24no—
44D4×D23—24no—
45C2×D92C2311yescharacteristic
46C2×C4×D23—21no—
47C2×C4×D23D412yes—
48C2×C4×D23C2311yescharacteristic
49C2×Dic46—21no—
50C2×Dic46—22no—
51C2×Dic46C2311yescharacteristic
52C2×C8×C23C2312yes—
53C4⋊C4×C23—22no—
54C4⋊C4×C23C2312yes—
55C22⋊C4×C23—22no—
56C42×C23C2311yescharacteristic
57C22⋊Dic23—22no—
58(C2×D23)⋊C4—22no—
59(C2×D23)⋊C4—22no—
60(C2×D23)⋊C4—22no—
61C4⋊Dic23C2312yes—
62Dic23⋊C4—22no—
63Dic23⋊C4—22no—
64C4×Dic23—22no—
65C4×Dic23D412yes—
66C4×Dic23C2311yescharacteristic
67C2×C23⋊C8C2312yes—
68#67262—24no—
69C23×C23—21no—
70C22×D23—21no—
71C22×D23—44no—
72C22×D23—42no—
73C22×D23C2×D411yescharacteristic
74Q8×C23—22no—
75D4×C23—22no—
76C2×C4×C23—22no—
77C2×C4×C23—21no—
78C2×C4×C23C2×D412yes—
79C2×C4×C23C2411yescharacteristic
80C22⋊D23—42no—
81C2×Dic23—22no—
82C2×Dic23—21no—
83C2×Dic23C2×D412yes—
84C2×Dic23C2×D411yescharacteristic
85D92—22no—
86C4×D23—42no—
87C4×D23—42no—
88C4×D23#4114yes—
89Dic46—22no—
90Dic46—44no—
91Dic46—42no—
92C8×C23—22no—
93C23⋊C8—22no—
94#3140—231nomaximal, Sylow
95C22×C23—41no—
96C22×C23—42no—
97C22×C23C22×D411yescharacteristic
98C2×D23—22no—
99C2×D23—41no—
100C2×D23—42no—
101C2×D23—84no—
102C2×D23#12412yes—
103C4×C23—22no—
104C4×C23—41no—
105C4×C23—42no—
106C4×C23C2×#4112yes—
107Dic23—22no—
108Dic23—41no—
109Dic23—42no—
110Dic23#12412yes—
111#533—231no—
112C2×#124—231no—
113#489—232no—
114#489—232no—
115#488—231no—
116#488—231no—
117#488—231no—
118#488D2311yescharacteristic, complemented
119#419—232no—
120#418—232no—
121C4×M16—231no—
122C2×C23—81no—
123C2×C23C2×#12411yescharacteristic
124C2×C23#57512yes—
125D23—22no—
126D23—81no—
127C22×Q8—231no—
128C22×D4—231no—
129C2×M16—232no—
130C4⋊Q8—232no—
131#125—231no—
132#125C2×D2311yescharacteristic, complemented
133#124—231no—
134#124—231no—
135#124—231no—
136#124—462no—
137#124C2×D2311yescharacteristic
138C22⋊Q8—462no—
139C4×Q8—462no—
140#117—232no—
141C2×C22⋊C4—462no—
142C2×C42—231no—
143#103—232no—
144#103—232no—
145#103—232no—
146#103C2×D2312yescomplemented
147#102—232no—
148#102—232no—
149#102—232no—
150#102C2×D2312yes—
151#97—232no—
152C4×C8—231no—
153C4×C8C2×D2311yescharacteristic, complemented
154C23#314011yescharacteristic, complemented, Sylow
155C24—461no—
156C2×Q8—231no—
157C2×Q8—462no—
158C2×Q8—461no—
159C2×Q8—464no—
160C2×Q8C22×D2311yescharacteristic
161C2×D4—231no—
162C2×D4—464no—
163C2×D4—461no—
164C2×D4C22×D2311yescharacteristic
165C22×C4—231no—
166C22×C4—232no—
167C22×C4—461no—
168M16—464no—
169C2×C8—232no—
170C2×C8C22×D2312yes—
171C4⋊C4—22no—
172C4⋊C4—232no—
173C4⋊C4—462no—
174C4⋊C4—462no—
175C4⋊C4C22×D2312yes—
176C22⋊C4—22no—
177C22⋊C4—462no—
178C22⋊C4—462no—
179C22⋊C4—462no—
180C22⋊C4—462no—
181C42—232no—
182C42—231no—
183C42—462no—
184C42C22×D2311yescharacteristic
185C23—21no—
186C23—231no—
187C23—461no—
188C23—922no—
189C23—924no—
190Q8—22no—
191Q8—462no—
192Q8—922no—
193Q8—924no—
194D4—22no—
195D4—462no—
196D4—922no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—231no—
200C2×C4—234no—
201C2×C4—232no—
202C2×C4—462no—
203C2×C4—461no—
204C2×C4—922no—
205C2×C4—922no—
206C2×C4D4×D2312yes—
207C2×C4C23×D2311yescharacteristic
208C8—22no—
209C8—462no—
210C22—41no—
211C22—42no—
212C22—232no—
213C22—462no—
214C22—921no—
215C22—922no—
216C22—1844no—
217C22C2×D4×D2311yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—232no—
222C4—462no—
223C4—921no—
224C4—922no—
225C4#41×D2312yes—
226C2—81no—
227C2—462no—
228C2—1841no—
229C2#124×D2311yescharacteristic
230C2#1309321412yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#488C2
socleC22×C23C22×D4
prime radicalC2×D4×D23C22
hypercenter#488D23
hypocenterC23#3140
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #13092973C2semidirect
3. #13092778C2semidirect
4. #13092775C2semidirect
5. #13092774C2semidirect
6. #13092772C2semidirect
7. #13092771C2semidirect
8. #13092424C2semidirect
10. C4×#67262C2semidirect
11. C23×#488C2semidirect
14. C23×#125C22semidirect
21. #10625059C22semidirect
27. #10625041C22semidirect
28. C23×#103C22semidirect
30. C4×C8×C23C22semidirect
31. #10625017C22semidirect
34. #10624998C22semidirect
35. #10624997C22semidirect
36. #10624992C22semidirect
38. C4×C23⋊C8C22semidirect
118. #488D23semidirect
132. #125C2×D23semidirect
146. #103C2×D23semidirect
153. C4×C8C2×D23semidirect
154. C23#3140semidirect

Maximal subgroups

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

subgroupindex
#130929732
#124×D232
#130927782
#130927752
#130927742
#130927722
#130927712
#130924242
#130924202
C4×#672622
C23×#4882
#314023