Finite Group Databasebeta

← #15683342

Subgroups — #15683342

Order 2944.

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

normal subgroups only

This group has 410 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
1C22⋊Q8×D23C211yesmaximal, characteristic
2C2×#10625063C211yesmaximal, characteristic
3#13092760C212yesmaximal, complemented
4#13092756C212yesmaximal, complemented
5#13092752C211yesmaximal, characteristic, complemented
6#13092748C211yesmaximal, characteristic, complemented
7#13092745C211yesmaximal, characteristic, complemented
8#13092458C212yesmaximal, complemented
9#13092424C212yesmaximal, complemented
10#13092379C211yesmaximal, characteristic
11C23×#484C211yesmaximal, characteristic, complemented
12C2×Q8×D23C2211yescharacteristic
13C22×C4×D23C2211yescharacteristic
14C23×C22⋊Q8C2211yescharacteristic
15C2×C4⋊C4×C23C2211yescharacteristic
16#10625117C2211yescharacteristic
17C2×(C2×D23)⋊C4—21no—
18C2×C4⋊Dic23C2211yescharacteristic
19#10625095C2211yescharacteristic
20C2×C4×Dic23—21no—
21C2×#67262C2212yes—
22#10625068C2211yescharacteristic
23#10625067—21no—
24#10625063—21no—
25#10625063—21no—
26#10625063C2212yes—
27#10625063C2212yes—
28C4⋊C4×D23—21no—
29C4⋊C4×D23C2211yescharacteristic
30C22⋊C4×D23—21no—
31#10625049—21no—
32C23×#107C2212yescomplemented
33C23×#103C2212yescomplemented
34C23×C22⋊C8C2211yescharacteristic
35#10625017C2212yescomplemented
36C22⋊(C23⋊C8)C2211yescharacteristic
37(C2×D23)⋊C8C2212yes—
38#10624999C2212yescomplemented
39#10624998C2212yescomplemented
40#10624992C2212yescomplemented
41#10624990C2212yescomplemented
42#10624989C2212yescomplemented
43C23×D23D411yescharacteristic
44C2×Q8×C23C2311yescharacteristic
45C22×C4×C23—21no—
46C22×C4×C23C2311yescharacteristic
47C22×Dic23—21no—
48C22×Dic23D411yescharacteristic
49Q8×D23—24no—
50C2×C4×D23—24no—
51C2×C4×D23—21no—
52C2×C4×D23—21no—
53C2×C4×D23D411yescharacteristic
54C2×C4×D23D411yescharacteristic
55C2×C4×D23C2311yescharacteristic
56C2×C4×D23C2311yescharacteristic
57C2×Dic46—21no—
58C2×Dic46C2311yescharacteristic
59C2×C8×C23C2312yes—
60C4⋊C4×C23—21no—
61C4⋊C4×C23—21no—
62C4⋊C4×C23C2312yes—
63C4⋊C4×C23C2311yescharacteristic
64C22⋊C4×C23—21no—
65C22⋊Dic23—21no—
66(C2×D23)⋊C4—21no—
67(C2×D23)⋊C4—21no—
68(C2×D23)⋊C4—22no—
69(C2×D23)⋊C4—22no—
70C4⋊Dic23—21no—
71C4⋊Dic23—21no—
72C4⋊Dic23C2311yescharacteristic
73C4⋊Dic23C2312yes—
74Dic23⋊C4—21no—
75Dic23⋊C4—21no—
76Dic23⋊C4—21no—
77C4×Dic23—22no—
78C4×Dic23—22no—
79C2×C23⋊C8C2312yes—
80#67262—24no—
81C23×C23C2×D411yescharacteristic
82C22×D23—22no—
83C22×D23—22no—
84C22×D23—41no—
85C22×D23C2×D411yescharacteristic
86C22×D23C2×D411yescharacteristic
87Q8×C23—22no—
88C2×C4×C23—22no—
89C2×C4×C23—22no—
90C2×C4×C23—21no—
91C2×C4×C23—21no—
92C2×C4×C23—42no—
93C2×C4×C23C2×D411yescharacteristic
94C2×C4×C23C2411yescharacteristic
95C2×Dic23—22no—
96C2×Dic23—22no—
97C2×Dic23—21no—
98C2×Dic23—21no—
99C2×Dic23—42no—
100C2×Dic23C2×D411yescharacteristic
101C2×Dic23C2×D411yescharacteristic
102C4×D23—22no—
103C4×D23—22no—
104C4×D23—22no—
105C4×D23—42no—
106C4×D23—42no—
107C4×D23#4114yes—
108Dic46—22no—
109Dic46—42no—
110C8×C23—22no—
111C23⋊C8—22no—
112#3095—231nomaximal, Sylow
113C22×C23—21no—
114C22×C23—21no—
115C22×C23#13712yes—
116C22×C23C22×D411yescharacteristic
117C2×D23—21no—
118C2×D23—21no—
119C2×D23—21no—
120C2×D23—21no—
121C2×D23—21no—
122C2×D23—44no—
123C2×D23#12312yes—
124C4×C23—21no—
125C4×C23—41no—
126C4×C23—41no—
127C4×C23—42no—
128C4×C23C2×#4112yes—
129Dic23—21no—
130Dic23—41no—
131Dic23—42no—
132Dic23—41no—
133Dic23#12312yes—
134C2×C22⋊Q8—231no—
135C2×#117—231no—
136#485—232no—
137#485—232no—
138#484—231no—
139#484D2311yescharacteristic, complemented
140#483—231no—
141#483—231no—
142#428—232no—
143#419—232no—
144#407—231no—
145C2×C23—22no—
146C2×C23C2×#12311yescharacteristic
147C2×C23C2×#13711yescharacteristic
148C2×C23#57511yescharacteristic
149D23—22no—
150D23—41no—
151C22×Q8—231no—
152C23×C4—231no—
153C2×M16—232no—
154C22⋊Q8—231no—
155C22⋊Q8—231no—
156C22⋊Q8—231no—
157C22⋊Q8—461no—
158C22⋊Q8—461no—
159C22⋊Q8C2×D2311yescharacteristic
160#117—232no—
161#117—232no—
162#117—461no—
163#117—461no—
164C2×C4⋊C4—231no—
165C2×C4⋊C4—231no—
166C2×C4⋊C4—461no—
167C2×C4⋊C4C2×D2311yescharacteristic
168C2×C22⋊C4—461no—
169C2×C22⋊C4—461no—
170C2×C42—461no—
171#107—232no—
172#107C2×D2312yescomplemented
173#106—232no—
174#106—232no—
175#103—232no—
176#103—232no—
177#103—232no—
178#103C2×D2312yescomplemented
179C22⋊C8—231no—
180C22⋊C8—232no—
181C22⋊C8C2×D2311yescharacteristic
182C23#309511yescharacteristic, complemented, Sylow
183C24—231no—
184C2×Q8—231no—
185C2×Q8—461no—
186C2×Q8—464no—
187C2×Q8C22×D2311yescharacteristic
188C22×C4—21no—
189C22×C4—231no—
190C22×C4—231no—
191C22×C4—231no—
192C22×C4—231no—
193C22×C4—231no—
194C22×C4—464no—
195C22×C4—461no—
196C22×C4—461no—
197C22×C4—461no—
198C22×C4C22×D2311yescharacteristic
199M16—464no—
200C2×C8—232no—
201C2×C8C22×D2312yes—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—232no—
205C4⋊C4—231no—
206C4⋊C4—461no—
207C4⋊C4—461no—
208C4⋊C4—461no—
209C4⋊C4—461no—
210C4⋊C4—461no—
211C4⋊C4C22×D2312yes—
212C4⋊C4C22×D2311yescharacteristic
213C22⋊C4—21no—
214C22⋊C4—462no—
215C22⋊C4—462no—
216C22⋊C4—461no—
217C22⋊C4—461no—
218C22⋊C4—461no—
219C42—462no—
220C42—462no—
221C23—231no—
222C23—231no—
223C23—462no—
224C23—462no—
225C23—921no—
226C23D4×D2311yescharacteristic
227Q8—22no—
228Q8—462no—
229Q8—922no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—231no—
236C2×C4—234no—
237C2×C4—231no—
238C2×C4—462no—
239C2×C4—462no—
240C2×C4—462no—
241C2×C4—462no—
242C2×C4—462no—
243C2×C4—461no—
244C2×C4—461no—
245C2×C4—922no—
246C2×C4—922no—
247C2×C4—922no—
248C2×C4D4×D2311yescharacteristic
249C2×C4C23×D2311yescharacteristic
250C8—22no—
251C8—462no—
252C22—21no—
253C22—21no—
254C22—232no—
255C22—461no—
256C22—461no—
257C22—461no—
258C22—461no—
259C22—461no—
260C22—924no—
261C22#1062508912yes—
262C22C2×D4×D2311yescharacteristic
263C4—21no—
264C4—41no—
265C4—42no—
266C4—41no—
267C4—232no—
268C4—461no—
269C4—921no—
270C4—922no—
271C4—921no—
272C4#41×D2312yes—
273C2—22no—
274C2—462no—
275C2—921no—
276C2#123×D2311yescharacteristic
277C2C2×#1062508911yescharacteristic
278C2#1309321311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#484C2
socleC22×C23C22×D4
prime radicalC23×D23D4
hypercenter#484D23
hypocenterC23#3095
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
3. #13092760C2semidirect
4. #13092756C2semidirect
5. #13092752C2semidirect
6. #13092748C2semidirect
7. #13092745C2semidirect
8. #13092458C2semidirect
9. #13092424C2semidirect
11. C23×#484C2semidirect
32. C23×#107C22semidirect
33. C23×#103C22semidirect
35. #10625017C22semidirect
38. #10624999C22semidirect
39. #10624998C22semidirect
40. #10624992C22semidirect
41. #10624990C22semidirect
42. #10624989C22semidirect
139. #484D23semidirect
172. #107C2×D23semidirect
178. #103C2×D23semidirect
182. C23#3095semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D232
C2×#106250632
#130927602
#130927562
#130927522
#130927482
#130927452
#130924582
#130924242
#130923792
C23×#4842
#309523