Finite Group Databasebeta

← #15683312

Subgroups — #15683312

Order 2944.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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#13092928C211yesmaximal, characteristic
2C2×#10625097C211yesmaximal, characteristic, complemented
3#13092759C212yesmaximal, complemented
4#13092753C211yesmaximal, characteristic, complemented
5#13092748C211yesmaximal, characteristic, complemented
6#13092742C212yesmaximal, complemented
7#13092736C211yesmaximal, characteristic, complemented
8#13092731C211yesmaximal, characteristic, complemented
9#13092455C212yesmaximal, complemented
10#13092414C212yesmaximal, complemented
11C2×C23×C22⋊C8C211yesmaximal, characteristic, complemented
12C23×C4×C23C2211yescharacteristic
13C2×#67288C2211yescharacteristic
14C22×C8×C23C2212yes—
15#10625124—21no—
16C2×C22⋊Dic23—21no—
17#10625101C2211yescharacteristic
18#10625101C2211yescharacteristic
19#10625100—21no—
20C4×C22⋊D23—21no—
21C4×C22⋊D23—21no—
22#10625097—21no—
23#10625097—21no—
24#10625097C2212yes—
25#10625097C2212yes—
26#10625097C2211yescharacteristic
27C2×C4⋊Dic23C2211yescharacteristic
28C2×C4⋊Dic23C2211yescharacteristic
29#10625095C2211yescharacteristic
30#10625095C2211yescharacteristic
31C2×C4×Dic23—21no—
32C23×C22⋊C8C2211yescharacteristic
33C23×C22⋊C8C2211yescharacteristic
34C23×C22⋊C8C2212yes—
35#10625003C2212yescomplemented
36#10625003C2212yescomplemented
37#10625000C2212yescomplemented
38#10625000C2212yescomplemented
39#10624999C2212yescomplemented
40#10624999C2212yescomplemented
41#10624998C2212yescomplemented
42#10624998C2212yescomplemented
43C24×C23D411yescharacteristic
44C22×C4×C23—24no—
45C22×C4×C23D411yescharacteristic
46C22×C4×C23D411yescharacteristic
47C22×C4×C23D411yescharacteristic
48C22×C4×C23C2311yescharacteristic
49C22×C4×C23C2311yescharacteristic
50C22×C4×C23C2311yescharacteristic
51C2×C22⋊D23—21no—
52C2×C22⋊D23—21no—
53C2×C22⋊D23—21no—
54C22×Dic23—21no—
55C22×Dic23—21no—
56#67288—24no—
57C2×D92C2311yescharacteristic
58C2×C4×D23—21no—
59C2×Dic46C2311yescharacteristic
60C2×C8×C23—24no—
61C2×C8×C23C2312yes—
62C2×C8×C23C2312yes—
63C22⋊Dic23—21no—
64C22⋊Dic23—21no—
65C22⋊Dic23—22no—
66C22⋊Dic23—22no—
67C22⋊Dic23—21no—
68(C2×D23)⋊C4—21no—
69(C2×D23)⋊C4—21no—
70C4⋊Dic23—21no—
71C4⋊Dic23—21no—
72C4⋊Dic23C2311yescharacteristic
73C4⋊Dic23C2311yescharacteristic
74C4⋊Dic23C2312yes—
75C4⋊Dic23C2312yes—
76Dic23⋊C4—21no—
77Dic23⋊C4—21no—
78C4×Dic23—22no—
79C4×Dic23—22no—
80C4×Dic23—21no—
81C23×C23—22no—
82C23×C23—22no—
83C23×C23—41no—
84C23×C23C2×D411yescharacteristic
85C23×C23C2×D411yescharacteristic
86C23×C23C2×D411yescharacteristic
87C22×D23—21no—
88C2×C4×C23—22no—
89C2×C4×C23—22no—
90C2×C4×C23—22no—
91C2×C4×C23—22no—
92C2×C4×C23—22no—
93C2×C4×C23C2×D411yescharacteristic
94C2×C4×C23C2×D411yescharacteristic
95C2×C4×C23C2×D411yescharacteristic
96C2×C4×C23#4114yes—
97C2×C4×C23C2411yescharacteristic
98C22⋊D23—42no—
99C22⋊D23—42no—
100C22⋊D23—42no—
101C2×Dic23—22no—
102C2×Dic23—22no—
103C2×Dic23—21no—
104C2×Dic23—21no—
105C2×Dic23—21no—
106C2×Dic23—42no—
107C2×Dic23—42no—
108D92—22no—
109C4×D23—42no—
110Dic46—22no—
111C8×C23—22no—
112C8×C23—22no—
113#3091—231nomaximal, Sylow
114C22×C23—21no—
115C22×C23—21no—
116C22×C23—21no—
117C22×C23—21no—
118C22×C23—21no—
119C22×C23—21no—
120C22×C23—21no—
121C22×C23—44no—
122C22×C23#12312yes—
123C22×C23#13512yes—
124C22×C23C22×D411yescharacteristic
125C2×D23—41no—
126C2×D23—41no—
127C2×D23—41no—
128C4×C23—21no—
129C4×C23—21no—
130C4×C23#12312yes—
131C4×C23C2×#4112yes—
132Dic23—41no—
133Dic23—42no—
134Dic23—41no—
135Dic23—42no—
136Dic23—41no—
137#525—231no—
138C2×#117—231no—
139#485—232no—
140#484—231no—
141#483—231no—
142#482—232no—
143#481—231no—
144#480—231no—
145#427—232no—
146#416—232no—
147C2×C22⋊C8D2311yescharacteristic, complemented
148C2×C23—22no—
149C2×C23—22no—
150C2×C23—41no—
151C2×C23C2×#12311yescharacteristic
152C2×C23C2×#13511yescharacteristic
153C2×C23#57511yescharacteristic
154D23—81no—
155C2×#41—231no—
156C23×C4C2×D2311yescharacteristic
157C22×C8C2×D2312yes—
158#123—461no—
159C22⋊Q8—231no—
160C22⋊Q8—231no—
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⋊C4—231no—
173C2×C22⋊C4—461no—
174C2×C42—461no—
175#107—232no—
176#107—232no—
177#106—232no—
178#106—232no—
179#103—232no—
180#103—232no—
181#102—232no—
182#102—232no—
183C22⋊C8C2×D2311yescharacteristic
184C22⋊C8C2×D2311yescharacteristic
185C22⋊C8C2×D2312yes—
186C23#309111yescharacteristic, complemented, Sylow
187C24D9211yescharacteristic
188#41—464no—
189C2×Q8—231no—
190C2×D4—231no—
191C2×D4—461no—
192C2×D4—461no—
193C2×D4—461no—
194C22×C4—24no—
195C22×C4—461no—
196C22×C4—461no—
197C22×C4—461no—
198C22×C4D9211yescharacteristic
199C22×C4D9211yescharacteristic
200C22×C4D9211yescharacteristic
201C22×C4C22×D2311yescharacteristic
202C22×C4C22×D2311yescharacteristic
203C22×C4C22×D2311yescharacteristic
204C2×C8—24no—
205C2×C8C22×D2312yes—
206C2×C8C22×D2312yes—
207C4⋊C4—232no—
208C4⋊C4—232no—
209C4⋊C4—231no—
210C4⋊C4—231no—
211C4⋊C4—461no—
212C4⋊C4—461no—
213C4⋊C4—461no—
214C4⋊C4—461no—
215C22⋊C4—462no—
216C22⋊C4—462no—
217C22⋊C4—461no—
218C22⋊C4—461no—
219C22⋊C4—461no—
220C22⋊C4—461no—
221C22⋊C4—461no—
222C42—462no—
223C42—462no—
224C42—461no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—461no—
229C23C2×D9211yescharacteristic
230C23C2×D9211yescharacteristic
231C23C2×D9211yescharacteristic
232Q8—462no—
233D4—462no—
234D4—922no—
235D4—922no—
236D4—922no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—462no—
243C2×C4—462no—
244C2×C4—461no—
245C2×C4—461no—
246C2×C4—461no—
247C2×C4—922no—
248C2×C4—922no—
249C2×C4—922no—
250C2×C4C2×D9211yescharacteristic
251C2×C4C2×D9211yescharacteristic
252C2×C4C2×D9211yescharacteristic
253C2×C4#6729014yes—
254C2×C4C23×D2311yescharacteristic
255C8—22no—
256C8—22no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—921no—
266C22—921no—
267C22—921no—
268C22#1062505712yes—
269C22#1062507512yes—
270C22C22×D9211yescharacteristic
271C4—21no—
272C4—21no—
273C4—921no—
274C4—922no—
275C4—921no—
276C4—922no—
277C4—921no—
278C4#1062505712yes—
279C4C2×#6729012yes—
280C2—22no—
281C2—22no—
282C2—41no—
283C2—1841no—
284C2C2×#1062505711yescharacteristic
285C2C2×#1062507511yescharacteristic
286C2#1309321711yescharacteristic
subgroupG/H
centerC2×C4C2×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×C22⋊C8C2
socleC22×C23C22×D4
prime radical#13092928C2
hypercenterC2×C22⋊C8D23
hypocenterC23#3091
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10625097C2semidirect
3. #13092759C2semidirect
4. #13092753C2semidirect
5. #13092748C2semidirect
6. #13092742C2semidirect
7. #13092736C2semidirect
8. #13092731C2semidirect
9. #13092455C2semidirect
10. #13092414C2semidirect
11. C2×C23×C22⋊C8C2semidirect
35. #10625003C22semidirect
36. #10625003C22semidirect
37. #10625000C22semidirect
38. #10625000C22semidirect
39. #10624999C22semidirect
40. #10624999C22semidirect
41. #10624998C22semidirect
42. #10624998C22semidirect
147. C2×C22⋊C8D23semidirect
186. C23#3091semidirect

Maximal subgroups

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

subgroupindex
#130929282
C2×#106250972
#130927592
#130927532
#130927482
#130927422
#130927362
#130927312
#130924552
#130924142
C2×C23×C22⋊C82
#309123