Finite Group Databasebeta

← #15683313

Subgroups — #15683313

Order 2944.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#13092930C211yesmaximal, characteristic
2C2×#10625063C211yesmaximal, characteristic, complemented
3#13092757C212yesmaximal, complemented
4#13092745C211yesmaximal, characteristic, complemented
5#13092744C212yesmaximal, complemented
6#13092735C211yesmaximal, characteristic, complemented
7#13092731C211yesmaximal, characteristic, complemented
8#13092454C212yesmaximal, complemented
9#13092412C212yesmaximal, complemented
10C22⋊C8×D23C211yesmaximal, characteristic, complemented
11C23×#484C211yesmaximal, characteristic, complemented
12C2×#67292C2211yescharacteristic
13C22×C4×D23C2211yescharacteristic
14C23×C22⋊Q8C2211yescharacteristic
15C2×C4⋊C4×C23C2211yescharacteristic
16#10625117C2211yescharacteristic
17#10625101C2211yescharacteristic
18C2×(C2×D23)⋊C4—21no—
19C2×C4⋊Dic23C2211yescharacteristic
20C2×C4×Dic23—21no—
21C2×C8×D23C2212yes—
22#10625066C2211yescharacteristic
23#10625065—21no—
24#10625064—21no—
25#10625063—21no—
26#10625063—21no—
27#10625063C2212yes—
28#10625063C2212yes—
29#10625063C2211yescharacteristic
30#10625053—21no—
31(C22⋊D23)⋊C4—21no—
32C23×#107C2212yescomplemented
33C23×#103C2212yescomplemented
34C23×C22⋊C8C2211yescharacteristic
35#10625017C2212yescomplemented
36C22⋊(C23⋊C8)C2211yescharacteristic
37#10625003C2212yescomplemented
38(C2×D23)⋊C8C2212yes—
39#10625000C2212yescomplemented
40#10624991C2212yescomplemented
41#10624990C2212yescomplemented
42#10624990C2212yescomplemented
43C23×D23D411yescharacteristic
44C2×Q8×C23C2311yescharacteristic
45C22×C4×C23—21no—
46C22×C4×C23C2311yescharacteristic
47C2×C22⋊D23—21no—
48C22×Dic23—21no—
49C22×Dic23D411yescharacteristic
50#67292—24no—
51C2×D92—21no—
52C2×D92—21no—
53C2×D92C2311yescharacteristic
54C2×C4×D23—24no—
55C2×C4×D23—21no—
56C2×C4×D23D411yescharacteristic
57C2×C4×D23D411yescharacteristic
58C2×C4×D23C2311yescharacteristic
59C2×C4×D23C2311yescharacteristic
60C2×C8×C23C2312yes—
61C4⋊C4×C23—21no—
62C4⋊C4×C23—21no—
63C4⋊C4×C23C2312yes—
64C4⋊C4×C23C2311yescharacteristic
65C22⋊C4×C23—21no—
66(C2×D23)⋊C4—21no—
67(C2×D23)⋊C4—21no—
68(C2×D23)⋊C4—22no—
69(C2×D23)⋊C4—22no—
70(C2×D23)⋊C4—21no—
71(C2×D23)⋊C4—21no—
72C4⋊Dic23—21no—
73C4⋊Dic23C2312yes—
74C4⋊Dic23C2311yescharacteristic
75Dic23⋊C4—21no—
76C4×Dic23—21no—
77C4×Dic23—22no—
78C4×Dic23—22no—
79C2×C23⋊C8C2312yes—
80C8×D23—24no—
81C23×C23C2×D411yescharacteristic
82C22×D23—22no—
83C22×D23—22no—
84C22×D23—21no—
85C22×D23—41no—
86C22×D23C2×D411yescharacteristic
87C22×D23C2×D411yescharacteristic
88Q8×C23—22no—
89C2×C4×C23—22no—
90C2×C4×C23—22no—
91C2×C4×C23—21no—
92C2×C4×C23—21no—
93C2×C4×C23—42no—
94C2×C4×C23C2×D411yescharacteristic
95C2×C4×C23C2411yescharacteristic
96C22⋊D23—42no—
97C2×Dic23—22no—
98C2×Dic23—22no—
99C2×Dic23—21no—
100C2×Dic23—42no—
101C2×Dic23C2×D411yescharacteristic
102C2×Dic23C2×D411yescharacteristic
103D92—22no—
104D92—42no—
105D92—42no—
106C4×D23—22no—
107C4×D23—22no—
108C4×D23—22no—
109C4×D23—42no—
110C4×D23#4114yes—
111C8×C23—22no—
112C23⋊C8—22no—
113#3091—231nomaximal, Sylow
114C22×C23—21no—
115C22×C23—21no—
116C22×C23#13512yes—
117C22×C23C22×D411yescharacteristic
118C2×D23—21no—
119C2×D23—21no—
120C2×D23—21no—
121C2×D23—21no—
122C2×D23—21no—
123C2×D23—44no—
124C2×D23—41no—
125C2×D23—41no—
126C2×D23—41no—
127C2×D23#12312yes—
128C4×C23—21no—
129C4×C23—41no—
130C4×C23—41no—
131C4×C23—42no—
132C4×C23C2×#4112yes—
133Dic23—21no—
134Dic23—42no—
135Dic23—41no—
136Dic23#12312yes—
137#525—231no—
138C2×#117—231no—
139#485—232no—
140#484D2311yescharacteristic, complemented
141#483—231no—
142#482—232no—
143#481—231no—
144#480—231no—
145#427—232no—
146#416—232no—
147C2×C22⋊C8—231no—
148C2×C23—22no—
149C2×C23C2×#12311yescharacteristic
150C2×C23C2×#13511yescharacteristic
151C2×C23#57511yescharacteristic
152D23—22no—
153D23—41no—
154D23—81no—
155C2×#41—231no—
156C23×C4—231no—
157C22×C8—232no—
158#123—461no—
159C22⋊Q8—231no—
160C22⋊Q8C2×D2311yescharacteristic
161#121—231no—
162#121—231no—
163#120—461no—
164C4×D4—461no—
165C4×D4—461no—
166#117—232no—
167#117—232no—
168#117—231no—
169#117—461no—
170#117—461no—
171C2×C4⋊C4—231no—
172C2×C4⋊C4C2×D2311yescharacteristic
173C2×C22⋊C4—461no—
174C2×C42—461no—
175#107—232no—
176#107C2×D2312yescomplemented
177#106—232no—
178#106—232no—
179#103—232no—
180#103C2×D2312yescomplemented
181#102—232no—
182#102—232no—
183C22⋊C8—231no—
184C22⋊C8—232no—
185C22⋊C8C2×D2311yescharacteristic
186C23#309111yescharacteristic, complemented, Sylow
187C24—231no—
188#41—464no—
189C2×Q8C22×D2311yescharacteristic
190C2×D4—231no—
191C2×D4—461no—
192C2×D4—461no—
193C2×D4—461no—
194C22×C4—21no—
195C22×C4—231no—
196C22×C4—231no—
197C22×C4—231no—
198C22×C4—231no—
199C22×C4—231no—
200C22×C4—464no—
201C22×C4—461no—
202C22×C4—461no—
203C22×C4C22×D2311yescharacteristic
204C2×C8—232no—
205C2×C8—464no—
206C2×C8C22×D2312yes—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—232no—
210C4⋊C4—231no—
211C4⋊C4—461no—
212C4⋊C4—461no—
213C4⋊C4C22×D2312yes—
214C4⋊C4C22×D2311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—461no—
217C22⋊C4—462no—
218C22⋊C4—462no—
219C22⋊C4—461no—
220C22⋊C4—461no—
221C22⋊C4—461no—
222C42—462no—
223C42—462no—
224C42—461no—
225C23—231no—
226C23—231no—
227C23—462no—
228C23—462no—
229C23—461no—
230C23—921no—
231C23D4×D2311yescharacteristic
232Q8—22no—
233D4—462no—
234D4—922no—
235D4—922no—
236D4—922no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—231no—
243C2×C4—234no—
244C2×C4—231no—
245C2×C4—462no—
246C2×C4—462no—
247C2×C4—462no—
248C2×C4—462no—
249C2×C4—462no—
250C2×C4—461no—
251C2×C4—922no—
252C2×C4—922no—
253C2×C4D4×D2311yescharacteristic
254C2×C4C23×D2311yescharacteristic
255C8—22no—
256C8—462no—
257C22—21no—
258C22—21no—
259C22—232no—
260C22—461no—
261C22—461no—
262C22—461no—
263C22—461no—
264C22—461no—
265C22—924no—
266C22—921no—
267C22—921no—
268C22—921no—
269C22#1062509012yes—
270C22C2×D4×D2311yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—41no—
275C4—232no—
276C4—461no—
277C4—922no—
278C4—921no—
279C4#41×D2312yes—
280C2—22no—
281C2—462no—
282C2—921no—
283C2—1841no—
284C2#123×D2311yescharacteristic
285C2C2×#1062509011yescharacteristic
286C2#1309321311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#484C2
socleC22×C23C22×D4
prime radical#13092930C2
hypercenter#484D23
hypocenterC23#3091
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#10625063C2semidirect
3. #13092757C2semidirect
4. #13092745C2semidirect
5. #13092744C2semidirect
6. #13092735C2semidirect
7. #13092731C2semidirect
8. #13092454C2semidirect
9. #13092412C2semidirect
10. C22⋊C8×D23C2semidirect
11. C23×#484C2semidirect
32. C23×#107C22semidirect
33. C23×#103C22semidirect
35. #10625017C22semidirect
37. #10625003C22semidirect
39. #10625000C22semidirect
40. #10624991C22semidirect
41. #10624990C22semidirect
42. #10624990C22semidirect
140. #484D23semidirect
176. #107C2×D23semidirect
180. #103C2×D23semidirect
186. C23#3091semidirect

Maximal subgroups

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

subgroupindex
#130929302
C2×#106250632
#130927572
#130927452
#130927442
#130927352
#130927312
#130924542
#130924122
C22⋊C8×D232
C23×#4842
#309123