Finite Group Databasebeta

← #15683873

Subgroups — #15683873

Order 2944.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#10625080C211yesmaximal, characteristic, complemented
2C2×#10625079C211yesmaximal, characteristic, complemented
3C2×#10625075C211yesmaximal, characteristic, complemented
4C22×#67263C211yesmaximal, characteristic, complemented
5#13092993C211yesmaximal, characteristic, complemented
6#13092986C211yesmaximal, characteristic, complemented
7#13092811C212yesmaximal, complemented
8#13092806C212yesmaximal, complemented
9#13092801C212yesmaximal, complemented
10#13092790C212yesmaximal, complemented
11C23×#405C211yesmaximal, characteristic, complemented
12C2×#67288C2211yescharacteristic
13C2×#67288C2211yescharacteristic
14C22×D92C2211yescharacteristic
15C22×Dic46C2211yescharacteristic
16C2×M16×C23C2211yescharacteristic
17C22×C8×C23C2211yescharacteristic
18C23×#117C2211yescharacteristic
19#10625080—24no—
20#10625079—24no—
21C2×Dic92C2211yescharacteristic, complemented
22C2×Dic92C2212yescomplemented
23#10625075—24no—
24C2×D184C2212yes—
25C2×D184C2211yescharacteristic, complemented
26C2×#67263—24no—
27C2×#67263C2212yes—
28C2×#67263C2212yes—
29C2×#67263C2212yes—
30C2×#67263C2211yescharacteristic, complemented
31C2×#67263C2211yescharacteristic, complemented
32C2×#67263C2212yescomplemented
33#10625068—22no—
34#10625066—22no—
35#10625057—22no—
36#10625053—22no—
37#10625046C2212yes—
38#10625046C2212yescomplemented
39#10625045C2212yes—
40#10625040C2212yescomplemented
41C23×#97C2212yescomplemented
42C4×C8×C23C2212yescomplemented
43C23×D23—21no—
44C22×C4×C23C2311yescharacteristic
45C2×C22⋊D23—21no—
46C2×C22⋊D23—21no—
47C22×Dic23—21no—
48#67288—22no—
49#67288—22no—
50#67288—22no—
51#67288—22no—
52C2×D92—22no—
53C2×D92—22no—
54C2×D92—21no—
55C2×D92—24no—
56C2×D92C2311yescharacteristic
57C2×D92C2312yes—
58C2×D92C2311yescharacteristic
59C2×C4×D23—21no—
60C2×C4×D23—21no—
61C2×Dic46—22no—
62C2×Dic46—22no—
63C2×Dic46—21no—
64C2×Dic46C2311yescharacteristic
65C2×Dic46C2312yes—
66C2×Dic46C2311yescharacteristic
67M16×C23D414yescomplemented
68C2×C8×C23D414yescomplemented
69C2×C8×C23C2311yescharacteristic
70C2×C8×C23C2311yescharacteristic
71C2×C8×C23C2312yes—
72C4⋊C4×C23D412yes—
73C22⋊C4×C23D412yes—
74C42×C23C2312yes—
75(C2×D23)⋊C4—24no—
76(C2×D23)⋊C4—24no—
77C4⋊Dic23—24no—
78Dic92—22no—
79Dic92—24no—
80D184—24no—
81D184—22no—
82#67263—24no—
83#67263—24no—
84#67263—24no—
85#67263—22no—
86#67263—22no—
87#67263—24no—
88C23×C23C2×D411yescharacteristic
89C22×D23—21no—
90C22×D23—22no—
91C22×D23—21no—
92C22×D23—42no—
93C22×D23—82no—
94C2×C4×C23C2×D414yes—
95C2×C4×C23C2×D411yescharacteristic
96C2×C4×C23C2×D412yes—
97C2×C4×C23C2×D412yes—
98C2×C4×C23C2411yescharacteristic
99C22⋊D23—42no—
100C22⋊D23—42no—
101C2×Dic23—21no—
102C2×Dic23—22no—
103C2×Dic23—21no—
104C2×Dic23—42no—
105D92—22no—
106D92—21no—
107D92—22no—
108D92—21no—
109D92—21no—
110D92—21no—
111D92—42no—
112D92—84no—
113C4×D23—42no—
114C4×D23—42no—
115Dic46—22no—
116Dic46—21no—
117Dic46—22no—
118Dic46—21no—
119Dic46—21no—
120Dic46—21no—
121Dic46—42no—
122C8×C23C2×D412yes—
123C8×C23C2×D412yes—
124C8×C23C2×D414yes—
125#3154—231nomaximal, Sylow
126C22×C23—22no—
127C22×C23#12712yes—
128C22×C23C22×D411yescharacteristic
129C2×D23—41no—
130C2×D23—41no—
131C2×D23—42no—
132C2×D23—42no—
133C2×D23—44no—
134C2×D23—42no—
135C2×D23—84no—
136C4×C23—24no—
137C4×C23#12712yes—
138C4×C23C22×D411yescharacteristic
139C4×C23C22×D411yescharacteristic
140Dic23—42no—
141Dic23—41no—
142Dic23—41no—
143C2×#137—231no—
144C2×AGL(1,ℤ/8)—231no—
145C2×#135—231no—
146C22×SD16—231no—
147#536—231no—
148#535—231no—
149#497—232no—
150#496—232no—
151#495—232no—
152#492—232no—
153#405D2311yescharacteristic, complemented
154C2×C23—22no—
155C2×C23C2×#12711yescharacteristic
156C2×C23#57712yes—
157D23—81no—
158D23—81no—
159D23—82no—
160C2×#41—231no—
161C2×#41—231no—
162C22×Q8—231no—
163C22×D4—231no—
164#137—464no—
165AGL(1,ℤ/8)—464no—
166#135—464no—
167C2×Q16—231no—
168C2×Q16—232no—
169C2×SD16—232no—
170C2×SD16—232no—
171C2×SD16—232no—
172C2×SD16—231no—
173C2×SD16—231no—
174C2×SD16—232no—
175C2×SD16—464no—
176C2×D8—232no—
177C2×D8—231no—
178C2×M16C2×D2311yescharacteristic
179C22×C8C2×D2311yescharacteristic
180C4⋊Q8—232no—
181#127—232no—
182#124—232no—
183#124—232no—
184#123—462no—
185C22⋊Q8—462no—
186#121—462no—
187#120—462no—
188#117C2×D2311yescharacteristic
189#97C2×D2312yescomplemented
190C4×C8C2×D2312yescomplemented
191C23#315411yescharacteristic, complemented, Sylow
192C24—461no—
193#41—462no—
194#41—462no—
195#41—462no—
196#41—462no—
197C2×Q8—231no—
198C2×Q8—232no—
199C2×Q8—231no—
200C2×Q8—461no—
201C2×Q8—462no—
202C2×Q8—462no—
203C2×D4—231no—
204C2×D4—232no—
205C2×D4—231no—
206C2×D4—461no—
207C2×D4—461no—
208C2×D4—462no—
209C2×D4—462no—
210C2×D4—461no—
211C2×D4—464no—
212C22×C4—461no—
213C22×C4—461no—
214C22×C4—461no—
215C22×C4C22×D2311yescharacteristic
216Q16—462no—
217Q16—464no—
218SD16—464no—
219SD16—464no—
220SD16—462no—
221SD16—462no—
222SD16—464no—
223SD16—464no—
224D8—462no—
225D8—464no—
226M16D9214yescomplemented
227C2×C8D9214yescomplemented
228C2×C8C22×D2311yescharacteristic
229C2×C8C22×D2312yes—
230C2×C8C22×D2311yescharacteristic
231C4⋊C4—464no—
232C4⋊C4D9212yes—
233C22⋊C4—464no—
234C22⋊C4—464no—
235C22⋊C4D9212yes—
236C42C22×D2312yes—
237C23—461no—
238C23—462no—
239C23—461no—
240C23—922no—
241C23—1842no—
242C23C2×D9211yescharacteristic
243Q8—462no—
244Q8—461no—
245Q8—462no—
246Q8—461no—
247Q8—461no—
248Q8—461no—
249Q8—922no—
250D4—461no—
251D4—462no—
252D4—461no—
253D4—461no—
254D4—462no—
255D4—461no—
256D4—922no—
257D4—922no—
258D4—922no—
259D4—1844no—
260C2×C4—461no—
261C2×C4—462no—
262C2×C4—461no—
263C2×C4—922no—
264C2×C4—922no—
265C2×C4—922no—
266C2×C4C2×D9214yes—
267C2×C4C2×D9211yescharacteristic
268C2×C4C2×D9212yes—
269C2×C4C2×D9212yes—
270C2×C4C23×D2311yescharacteristic
271C8C2×D9212yes—
272C8C2×D9212yes—
273C8C2×D9214yes—
274C22—22no—
275C22—921no—
276C22—921no—
277C22—922no—
278C22—922no—
279C22—924no—
280C22—922no—
281C22—1844no—
282C22#1062504512yes—
283C22C22×D9211yescharacteristic
284C4—24no—
285C4—921no—
286C4—921no—
287C4—922no—
288C4#1062504512yes—
289C4C22×D9211yescharacteristic
290C4C22×D9211yescharacteristic
291C2—22no—
292C2—1842no—
293C2—1841no—
294C2—1841no—
295C2C2×#1062504511yescharacteristic
296C2#1309322912yes—
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#405C2
socleC22×C23C22×D4
hypercenter#405D23
hypocenterC23#3154
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. C2×#10625080C2semidirect
2. C2×#10625079C2semidirect
3. C2×#10625075C2semidirect
4. C22×#67263C2semidirect
5. #13092993C2semidirect
6. #13092986C2semidirect
7. #13092811C2semidirect
8. #13092806C2semidirect
9. #13092801C2semidirect
10. #13092790C2semidirect
11. C23×#405C2semidirect
21. C2×Dic92C22semidirect
22. C2×Dic92C22semidirect
25. C2×D184C22semidirect
30. C2×#67263C22semidirect
31. C2×#67263C22semidirect
32. C2×#67263C22semidirect
38. #10625046C22semidirect
40. #10625040C22semidirect
41. C23×#97C22semidirect
42. C4×C8×C23C22semidirect
67. M16×C23D4semidirect
68. C2×C8×C23D4semidirect
153. #405D23semidirect
189. #97C2×D23semidirect
190. C4×C8C2×D23semidirect
191. C23#3154semidirect
226. M16D92semidirect
227. C2×C8D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250802
C2×#106250792
C2×#106250752
C22×#672632
#130929932
#130929862
#130928112
#130928062
#130928012
#130927902
C23×#4052
#315423