Finite Group Databasebeta

← #15683323

Subgroups — #15683323

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#13092929C211yesmaximal, characteristic
2C2×C4⋊C4×D23C211yesmaximal, characteristic, complemented
3#13092754C212yesmaximal, complemented
4#13092749C212yesmaximal, complemented
5#13092737C212yesmaximal, complemented
6#13092732C212yesmaximal, complemented
7#13092460C211yesmaximal, characteristic, complemented
8#13092419C211yesmaximal, characteristic, complemented
9#13092416C211yesmaximal, characteristic, complemented
10#13092380C211yesmaximal, characteristic, complemented
11C23×#428C211yesmaximal, characteristic, complemented
12C2×#67288C2211yescharacteristic
13C22×C4×D23—21no—
14C22×C4×D23C2211yescharacteristic
15C2×M16×C23C2211yescharacteristic
16C23×#117C2211yescharacteristic
17C2×C4⋊C4×C23C2211yescharacteristic
18C2×C4⋊Dic23C2211yescharacteristic
19C2×Dic23⋊C4—21no—
20C2×#67267C2211yescharacteristic
21#10625068C2211yescharacteristic
22#10625068C2211yescharacteristic
23#10625066C2211yescharacteristic
24#10625066C2211yescharacteristic
25C4⋊C4×D23—21no—
26C4⋊C4×D23—21no—
27C4⋊C4×D23C2212yes—
28C4⋊C4×D23C2212yes—
29#10625057—21no—
30#10625053—21no—
31C4×D92—21no—
32C4×D92—21no—
33C23×#107C2212yescomplemented
34C23×#106C2212yescomplemented
35#10625003C2212yescomplemented
36(C2×D23)⋊C8C2212yes—
37(C2×D23)⋊C8C2212yes—
38#10624998C2212yescomplemented
39#10624992C2212yescomplemented
40#10624991C2212yescomplemented
41#10624990C2212yescomplemented
42#10624989C2212yescomplemented
43C23×D23D411yescharacteristic
44C22×C4×C23—21no—
45C22×C4×C23C2311yescharacteristic
46C2×C22⋊D23—21no—
47C22×Dic23—21no—
48C22×Dic23D411yescharacteristic
49#67288—22no—
50#67288—22no—
51C2×D92—21no—
52C2×D92—21no—
53C2×D92C2311yescharacteristic
54C2×C4×D23—22no—
55C2×C4×D23—22no—
56C2×C4×D23—22no—
57C2×C4×D23—22no—
58C2×C4×D23—21no—
59C2×C4×D23—44no—
60C2×C4×D23D411yescharacteristic
61C2×C4×D23D411yescharacteristic
62C2×C4×D23C2311yescharacteristic
63C2×C4×D23C2311yescharacteristic
64C2×Dic46C2311yescharacteristic
65M16×C23—22no—
66C2×C8×C23C2312yes—
67C4⋊C4×C23—21no—
68C4⋊C4×C23C2311yescharacteristic
69C4⋊C4×C23C2312yes—
70C4⋊C4×C23C2311yescharacteristic
71C22⋊C4×C23—21no—
72C42×C23—21no—
73(C2×D23)⋊C4—21no—
74(C2×D23)⋊C4—21no—
75(C2×D23)⋊C4—21no—
76(C2×D23)⋊C4—21no—
77C4⋊Dic23—21no—
78C4⋊Dic23—21no—
79C4⋊Dic23—21no—
80C4⋊Dic23C2312yes—
81Dic23⋊C4—22no—
82Dic23⋊C4—22no—
83#67267—22no—
84C2×C23⋊C8C2312yes—
85C23×C23C2×D411yescharacteristic
86C22×D23—22no—
87C22×D23—22no—
88C22×D23—22no—
89C22×D23—21no—
90C22×D23C2×D411yescharacteristic
91C22×D23C2×D411yescharacteristic
92C2×C4×C23—22no—
93C2×C4×C23—21no—
94C2×C4×C23—21no—
95C2×C4×C23—42no—
96C2×C4×C23C2×D411yescharacteristic
97C2×C4×C23#4112yes—
98C2×C4×C23#4112yes—
99C2×C4×C23C2411yescharacteristic
100C22⋊D23—42no—
101C2×Dic23—22no—
102C2×Dic23—22no—
103C2×Dic23—21no—
104C2×Dic23—42no—
105C2×Dic23C2×D411yescharacteristic
106C2×Dic23C2×D411yescharacteristic
107D92—21no—
108D92—21no—
109D92—42no—
110D92—42no—
111C4×D23—22no—
112C4×D23—22no—
113C4×D23—21no—
114C4×D23—21no—
115C4×D23—21no—
116C4×D23—21no—
117C4×D23—44no—
118C4×D23—44no—
119C4×D23—42no—
120Dic46—21no—
121Dic46—21no—
122C8×C23—22no—
123C23⋊C8—22no—
124#3092—231nomaximal, Sylow
125C22×C23—21no—
126C22×C23—21no—
127C22×C23#12312yes—
128C22×C23C22×D411yescharacteristic
129C2×D23—28no—
130C2×D23—21no—
131C2×D23—21no—
132C2×D23—21no—
133C2×D23—21no—
134C2×D23—41no—
135C2×D23—41no—
136C2×D23—41no—
137C2×D23AGL(1,ℤ/8)12yes—
138C2×D23#13712yes—
139C4×C23—42no—
140C4×C23—41no—
141C4×C23—41no—
142C4×C23#12312yes—
143C4×C23C2×#4111yescharacteristic
144C4×C23C2×#4111yescharacteristic
145Dic23—21no—
146Dic23—21no—
147Dic23—41no—
148Dic23—42no—
149#525—231no—
150C22×C4⋊C4—231no—
151#484—232no—
152#483—232no—
153#481—232no—
154#480—232no—
155#428—231no—
156#428D2311yescharacteristic, complemented
157#417—231no—
158#417—231no—
159#407—231no—
160C2×C23—22no—
161C2×C23C2×#12311yescharacteristic
162C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
163C2×C23C2×#13711yescharacteristic
164D23—22no—
165D23—22no—
166D23—81no—
167C2×#41—231no—
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#117C2×D2311yescharacteristic
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#107C2×D2312yescomplemented
190#106—232no—
191#106C2×D2312yescomplemented
192#103—232no—
193#103—232no—
194#102—232no—
195#102—232no—
196C22⋊C8—232no—
197C22⋊C8—232no—
198C23#309211yescharacteristic, complemented, Sylow
199C24—231no—
200#41—462no—
201#41—462no—
202C2×Q8—231no—
203C2×D4—231no—
204C2×D4—461no—
205C2×D4—461no—
206C2×D4—461no—
207C22×C4—21no—
208C22×C4—231no—
209C22×C4—231no—
210C22×C4—231no—
211C22×C4—231no—
212C22×C4—231no—
213C22×C4—462no—
214C22×C4—462no—
215C22×C4—462no—
216C22×C4—462no—
217C22×C4—461no—
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—462no—
228C4⋊C4—462no—
229C4⋊C4—461no—
230C4⋊C4—461no—
231C4⋊C4—461no—
232C4⋊C4C22×D2312yes—
233C4⋊C4C22×D2311yescharacteristic
234C4⋊C4C22×D2311yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—461no—
237C22⋊C4—461no—
238C22⋊C4—461no—
239C22⋊C4—461no—
240C42—21no—
241C23—231no—
242C23—231no—
243C23—462no—
244C23—462no—
245C23—462no—
246C23—461no—
247C23D4×D2311yescharacteristic
248Q8—461no—
249Q8—461no—
250D4—461no—
251D4—461no—
252D4—922no—
253D4—922no—
254D4—922no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
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—462no—
270C2×C4—924no—
271C2×C4—924no—
272C2×C4—922no—
273C2×C4—922no—
274C2×C4#6728812yes—
275C2×C4D4×D2311yescharacteristic
276C2×C4#6729212yes—
277C2×C4C23×D2311yescharacteristic
278C8—22no—
279C8—462no—
280C22—21no—
281C22—21no—
282C22—232no—
283C22—232no—
284C22—468no—
285C22—461no—
286C22—461no—
287C22—461no—
288C22—461no—
289C22—921no—
290C22—921no—
291C22—921no—
292C22#1062506512yes—
293C22C2×D4×D2311yescharacteristic
294C4—42no—
295C4—41no—
296C4—41no—
297C4—461no—
298C4—461no—
299C4—921no—
300C4—922no—
301C4#1062506512yes—
302C4C2×#6728811yescharacteristic
303C4C2×#6729211yescharacteristic
304C2—22no—
305C2—462no—
306C2—462no—
307C2—1841no—
308C2C2×#1062506511yescharacteristic
309C2AGL(1,ℤ/8)×D2311yescharacteristic
310C2#137×D2311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#428C2
socleC22×C23C22×D4
prime radical#13092929C2
hypercenter#428D23
hypocenterC23#3092
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D23C2semidirect
3. #13092754C2semidirect
4. #13092749C2semidirect
5. #13092737C2semidirect
6. #13092732C2semidirect
7. #13092460C2semidirect
8. #13092419C2semidirect
9. #13092416C2semidirect
10. #13092380C2semidirect
11. C23×#428C2semidirect
33. C23×#107C22semidirect
34. C23×#106C22semidirect
35. #10625003C22semidirect
38. #10624998C22semidirect
39. #10624992C22semidirect
40. #10624991C22semidirect
41. #10624990C22semidirect
42. #10624989C22semidirect
156. #428D23semidirect
189. #107C2×D23semidirect
191. #106C2×D23semidirect
198. C23#3092semidirect

Maximal subgroups

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

subgroupindex
#130929292
C2×C4⋊C4×D232
#130927542
#130927492
#130927372
#130927322
#130924602
#130924192
#130924162
#130923802
C23×#4282
#309223