Finite Group Databasebeta

← #15683318

Subgroups — #15683318

Order 2944.

458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 129 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#13092924C211yesmaximal, characteristic
2C2×C4⋊C4×D23C211yesmaximal, characteristic, complemented
3#13092751C212yesmaximal, complemented
4#13092746C212yesmaximal, complemented
5#13092734C212yesmaximal, complemented
6#13092729C212yesmaximal, complemented
7#13092459C211yesmaximal, characteristic, complemented
8#13092457C211yesmaximal, characteristic, complemented
9#13092418C211yesmaximal, characteristic, complemented
10#13092380C211yesmaximal, characteristic, complemented
11C23×#417C211yesmaximal, characteristic, complemented
12C2×#41×C23C2211yescharacteristic
13C22×C4×D23—21no—
14C22×C4×D23C2211yescharacteristic
15C2×M16×C23C2211yescharacteristic
16C2×C4⋊C4×C23C2211yescharacteristic
17#10625117C2211yescharacteristic
18#10625117C2211yescharacteristic
19#10625109C2211yescharacteristic
20#10625109C2211yescharacteristic
21#10625108—21no—
22#10625106—21no—
23C4×C22⋊D23—21no—
24C4×C22⋊D23—21no—
25#10625097C2211yescharacteristic
26C2×C4⋊Dic23C2211yescharacteristic
27C2×Dic23⋊C4—21no—
28C2×#67267C2211yescharacteristic
29C4⋊C4×D23—21no—
30C4⋊C4×D23—21no—
31C4⋊C4×D23C2212yes—
32C4⋊C4×D23C2212yes—
33C23×#103C2212yescomplemented
34C23×#102C2212yescomplemented
35#10625017C2212yescomplemented
36#10625014C2212yescomplemented
37(C2×D23)⋊C8C2212yes—
38(C2×D23)⋊C8C2212yes—
39#10625000C2212yescomplemented
40#10624999C2212yescomplemented
41#10624990C2212yescomplemented
42#10624989C2212yescomplemented
43C23×D23D411yescharacteristic
44#41×C23—22no—
45#41×C23—22no—
46C2×Q8×C23C2311yescharacteristic
47C2×D4×C23—21no—
48C2×D4×C23C2311yescharacteristic
49C22×C4×C23—21no—
50C22×C4×C23—21no—
51C22×C4×C23C2311yescharacteristic
52C2×C22⋊D23—21no—
53C2×C22⋊D23—21no—
54C22×Dic23—21no—
55C22×Dic23D411yescharacteristic
56C2×C4×D23—22no—
57C2×C4×D23—22no—
58C2×C4×D23—22no—
59C2×C4×D23—22no—
60C2×C4×D23—44no—
61C2×C4×D23D411yescharacteristic
62C2×C4×D23D411yescharacteristic
63C2×C4×D23C2311yescharacteristic
64C2×C4×D23C2311yescharacteristic
65M16×C23—22no—
66C2×C8×C23C2312yes—
67C4⋊C4×C23—21no—
68C4⋊C4×C23C2312yes—
69C22⋊Dic23—21no—
70C22⋊Dic23—21no—
71C22⋊Dic23—21no—
72(C2×D23)⋊C4—21no—
73(C2×D23)⋊C4—21no—
74C4⋊Dic23—21no—
75C4⋊Dic23C2312yes—
76C4⋊Dic23C2311yescharacteristic
77C4⋊Dic23C2311yescharacteristic
78Dic23⋊C4—22no—
79Dic23⋊C4—22no—
80Dic23⋊C4—21no—
81Dic23⋊C4—21no—
82C4×Dic23—21no—
83#67267—22no—
84C2×C23⋊C8C2312yes—
85C23×C23—21no—
86C23×C23C2×D411yescharacteristic
87C22×D23—22no—
88C22×D23—22no—
89C22×D23—22no—
90C22×D23C2×D411yescharacteristic
91C22×D23C2×D411yescharacteristic
92Q8×C23—21no—
93Q8×C23—21no—
94D4×C23—21no—
95D4×C23—21no—
96D4×C23—42no—
97C2×C4×C23—21no—
98C2×C4×C23—22no—
99C2×C4×C23—42no—
100C2×C4×C23—42no—
101C2×C4×C23C2×D411yescharacteristic
102C2×C4×C23#4112yes—
103C2×C4×C23#4112yes—
104C2×C4×C23C2411yescharacteristic
105C22⋊D23—42no—
106C22⋊D23—42no—
107C2×Dic23—22no—
108C2×Dic23—21no—
109C2×Dic23—21no—
110C2×Dic23—22no—
111C2×Dic23—42no—
112C2×Dic23C2×D411yescharacteristic
113C2×Dic23C2×D411yescharacteristic
114C4×D23—22no—
115C4×D23—22no—
116C4×D23—21no—
117C4×D23—21no—
118C4×D23—21no—
119C4×D23—21no—
120C4×D23—44no—
121C4×D23—44no—
122C8×C23—22no—
123C23⋊C8—22no—
124#3092—231nomaximal, Sylow
125C22×C23—21no—
126C22×C23—21no—
127C22×C23—41no—
128C22×C23—41no—
129C22×C23—41no—
130C22×C23#12312yes—
131C22×C23C22×D411yescharacteristic
132C2×D23—28no—
133C2×D23—21no—
134C2×D23—21no—
135C2×D23—21no—
136C2×D23—21no—
137C2×D23AGL(1,ℤ/8)12yes—
138C2×D23#13712yes—
139C4×C23—41no—
140C4×C23—42no—
141C4×C23#12312yes—
142C4×C23C2×#4111yescharacteristic
143C4×C23C2×#4111yescharacteristic
144Dic23—21no—
145Dic23—21no—
146Dic23—42no—
147Dic23—41no—
148Dic23—41no—
149#525—231no—
150C22×C4⋊C4—231no—
151#484—232no—
152#483—232no—
153#481—232no—
154#480—232no—
155#428—231no—
156#428—231no—
157#417—231no—
158#417D2311yescharacteristic, complemented
159#407—231no—
160C2×C23—22no—
161C2×C23—81no—
162C2×C23C2×#12311yescharacteristic
163C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
164C2×C23C2×#13711yescharacteristic
165D23—22no—
166D23—22no—
167C2×#41C2×D2311yescharacteristic
168C23×C4—231no—
169C23×C4—461no—
170C2×M16—231no—
171C2×M16C2×D2311yescharacteristic
172#123—461no—
173C22⋊Q8—231no—
174C22⋊Q8—231no—
175#121—231no—
176#121—231no—
177#120—461no—
178C4×D4—461no—
179C4×D4—461no—
180#117—231no—
181C2×C4⋊C4—231no—
182C2×C4⋊C4—232no—
183C2×C4⋊C4—232no—
184C2×C4⋊C4—461no—
185C2×C4⋊C4—461no—
186C2×C4⋊C4—461no—
187C2×C4⋊C4C2×D2311yescharacteristic
188#107—232no—
189#107—232no—
190#106—232no—
191#106—232no—
192#103—232no—
193#103C2×D2312yescomplemented
194#102—232no—
195#102C2×D2312yescomplemented
196C22⋊C8—232no—
197C22⋊C8—232no—
198C23#309211yescharacteristic, complemented, Sylow
199C24—231no—
200#41—22no—
201#41—22no—
202C2×Q8C22×D2311yescharacteristic
203C2×D4—21no—
204C2×D4—461no—
205C2×D4—461no—
206C2×D4C22×D2311yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—231no—
210C22×C4—231no—
211C22×C4—231no—
212C22×C4—231no—
213C22×C4—231no—
214C22×C4—462no—
215C22×C4—462no—
216C22×C4—462no—
217C22×C4—462no—
218C22×C4—461no—
219C22×C4—924no—
220C22×C4C22×D2311yescharacteristic
221M16—22no—
222M16—462no—
223C2×C8—232no—
224C2×C8C22×D2312yes—
225C4⋊C4—21no—
226C4⋊C4—232no—
227C4⋊C4—231no—
228C4⋊C4—231no—
229C4⋊C4—462no—
230C4⋊C4—462no—
231C4⋊C4—461no—
232C4⋊C4—461no—
233C4⋊C4—461no—
234C4⋊C4C22×D2312yes—
235C22⋊C4—461no—
236C22⋊C4—461no—
237C22⋊C4—461no—
238C22⋊C4—461no—
239C22⋊C4—461no—
240C42—461no—
241C23—21no—
242C23—231no—
243C23—231no—
244C23—462no—
245C23—462no—
246C23—462no—
247C23D4×D2311yescharacteristic
248Q8—21no—
249Q8—21no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—922no—
254D4—922no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—231no—
260C2×C4—231no—
261C2×C4—462no—
262C2×C4—462no—
263C2×C4—462no—
264C2×C4—461no—
265C2×C4—461no—
266C2×C4—461no—
267C2×C4—461no—
268C2×C4—461no—
269C2×C4—461no—
270C2×C4—462no—
271C2×C4—924no—
272C2×C4—924no—
273C2×C4—922no—
274C2×C4#6728812yes—
275C2×C4D4×D2311yescharacteristic
276C2×C4#6729012yes—
277C2×C4C23×D2311yescharacteristic
278C8—22no—
279C8—462no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—232no—
286C22—232no—
287C22—468no—
288C22—461no—
289C22—461no—
290C22—461no—
291C22—461no—
292C22#1062505412yes—
293C22C2×D4×D2311yescharacteristic
294C4—41no—
295C4—42no—
296C4—461no—
297C4—461no—
298C4—922no—
299C4—921no—
300C4—921no—
301C4#1062505412yes—
302C4C2×#6728811yescharacteristic
303C4C2×#6729011yescharacteristic
304C2—22no—
305C2—81no—
306C2—462no—
307C2—462no—
308C2C2×#1062505411yescharacteristic
309C2AGL(1,ℤ/8)×D2311yescharacteristic
310C2#137×D2311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#417C2
socleC22×C23C22×D4
prime radical#13092924C2
hypercenter#417D23
hypocenterC23#3092
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D23C2semidirect
3. #13092751C2semidirect
4. #13092746C2semidirect
5. #13092734C2semidirect
6. #13092729C2semidirect
7. #13092459C2semidirect
8. #13092457C2semidirect
9. #13092418C2semidirect
10. #13092380C2semidirect
11. C23×#417C2semidirect
33. C23×#103C22semidirect
34. C23×#102C22semidirect
35. #10625017C22semidirect
36. #10625014C22semidirect
39. #10625000C22semidirect
40. #10624999C22semidirect
41. #10624990C22semidirect
42. #10624989C22semidirect
158. #417D23semidirect
193. #103C2×D23semidirect
195. #102C2×D23semidirect
198. C23#3092semidirect

Maximal subgroups

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

subgroupindex
#130929242
C2×C4⋊C4×D232
#130927512
#130927462
#130927342
#130927292
#130924592
#130924572
#130924182
#130923802
C23×#4172
#309223