Finite Group Databasebeta

← #15682788

Subgroups — #15682788

Order 2944.

766 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 145 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#13093253C211yesmaximal, characteristic, complemented
2#13092928C212yesmaximal, complemented
3#13092606C214yesmaximal, complemented
4#13092603C214yesmaximal, complemented
5#13092391C211yesmaximal, characteristic, complemented
6#13092390C212yesmaximal, complemented
7C23×#525C211yesmaximal, characteristic, complemented
8C2×#41×C23C2211yescharacteristic
9C23×C4×C23C2211yescharacteristic, complemented
10#10625161—22no—
11#10625160—22no—
12#41×D23—24no—
13#10625158—21no—
14#10625155—21no—
15#10625155C2214yes—
16C2×#67288—22no—
17C2×#67288C2212yes—
18C23×#123C2212yescomplemented
19C23×C22⋊Q8—21no—
20C23×#121—21no—
21C23×#120C2212yescomplemented
22C4×D4×C23—22no—
23C23×#117C2211yescharacteristic, complemented
24#10625124C2214yescomplemented
25#10625101—22no—
26#10625100C2214yescomplemented
27C4×C22⋊D23—24no—
28#10625097C2212yescomplemented
29#10625095—22no—
30#10625016C2214yescomplemented
31#10624988C2218yescomplemented
32C24×C23C2311yescharacteristic
33#41×C23—22no—
34#41×C23—22no—
35C2×Q8×C23D411yescharacteristic, complemented
36C2×D4×C23—22no—
37C2×D4×C23D411yescharacteristic, complemented
38C2×D4×C23C2312yes—
39C22×C4×C23—22no—
40C22×C4×C23—22no—
41C22×C4×C23—21no—
42C22×C4×C23—21no—
43C22×C4×C23D412yescomplemented
44C22×C4×C23C2311yescharacteristic
45C22×C4×C23C2311yescharacteristic
46C2×C22⋊D23—24no—
47C2×C22⋊D23—24no—
48C2×C22⋊D23C2314yes—
49#67292—24no—
50Q8×D23—24no—
51#67290—24no—
52#67290—28no—
53D4×D23—24no—
54D4×D23—28no—
55#67288—24no—
56#67288—24no—
57#67288—22no—
58#67288—24no—
59#67288—22no—
60#67288—22no—
61#67288—22no—
62C2×D92—22no—
63C2×D92D412yescomplemented
64C2×C4×D23—24no—
65C2×C4×D23D414yescomplemented
66C2×Dic46—22no—
67C2×Dic46D412yescomplemented
68C4⋊C4×C23—21no—
69C4⋊C4×C23—22no—
70C22⋊C4×C23—22no—
71C22⋊C4×C23—22no—
72C22⋊C4×C23C2312yes—
73C42×C23—21no—
74C22⋊Dic23—24no—
75C22⋊Dic23C2314yes—
76(C2×D23)⋊C4—24no—
77C4⋊Dic23—22no—
78Dic23⋊C4—24no—
79C4×Dic23—22no—
80C23×C23—22no—
81C23×C23—21no—
82C23×C23—42no—
83C23×C23C2×D412yes—
84C23×C23C2411yescharacteristic
85C22×D23—24no—
86C22×D23C2×D414yes—
87Q8×C23—22no—
88D4×C23—24no—
89D4×C23—22no—
90D4×C23—44no—
91C2×C4×C23—22no—
92C2×C4×C23—22no—
93C2×C4×C23—22no—
94C2×C4×C23—22no—
95C2×C4×C23—21no—
96C2×C4×C23—41no—
97C2×C4×C23—42no—
98C2×C4×C23—41no—
99C2×C4×C23C2×D412yes—
100C2×C4×C23C2×D412yes—
101C2×C4×C23C2×D412yes—
102C2×C4×C23C2×D411yescharacteristic
103C2×C4×C23C2×D411yescharacteristic
104C22⋊D23—28no—
105C22⋊D23—24no—
106C22⋊D23—24no—
107C22⋊D23—48no—
108C2×Dic23—24no—
109C2×Dic23—24no—
110C2×Dic23C2×D414yes—
111D92—24no—
112D92—22no—
113D92—22no—
114C4×D23—28no—
115C4×D23—24no—
116C4×D23—24no—
117Dic46—24no—
118Dic46—22no—
119Dic46—22no—
120#3025—231nomaximal, Sylow
121C22×C23—24no—
122C22×C23—22no—
123C22×C23—22no—
124C22×C23—41no—
125C22×C23—42no—
126C22×C23—42no—
127C22×C23—41no—
128C22×C23—41no—
129C22×C23C22×D412yes—
130C22×C23C22×D411yescharacteristic
131C2×D23—24no—
132C2×D23—44no—
133C2×D23—84no—
134C4×C23—22no—
135C4×C23—42no—
136C4×C23—41no—
137C4×C23#12011yescharacteristic
138C4×C23#12012yes—
139C4×C23#12011yescharacteristic
140Dic23—24no—
141Dic23—44no—
142#585—231no—
143#525—232no—
144#525D2311yescharacteristic, complemented
145#458—234no—
146B(4,𝔽2)—234no—
147#410—231no—
148#410—232no—
149C2×C23—22no—
150C2×C23—21no—
151C2×C23—42no—
152C2×C23—42no—
153C2×C23C2×#12011yescharacteristic
154D23—44no—
1552−1+4—462no—
1562−1+4—461no—
157H(5,𝔽2)—234no—
158H(5,𝔽2)—462no—
159H(5,𝔽2)—461no—
160C2×#41—232no—
161C2×#41—464no—
162C2×#41—462no—
163C2×#41C2×D2311yescharacteristic
164C23×C4C2×D2311yescharacteristic, complemented
165#123—234no—
166#123C2×D2312yescomplemented
167C22⋊Q8—21no—
168C22⋊Q8—462no—
169#121—21no—
170#121—462no—
171#120—234no—
172#120C2×D2312yescomplemented
173C4×D4—22no—
174C4×D4—464no—
175#117—232no—
176#117C2×D2311yescharacteristic, complemented
177#99—234no—
178#99—238no—
179C23#302511yescharacteristic, complemented, Sylow
180C24C22×D2311yescharacteristic
181#41—22no—
182#41—22no—
183#41—464no—
184#41—464no—
185#41—468no—
186#41—464no—
187#41—464no—
188#41—462no—
189#41—462no—
190#41—462no—
191#41—462no—
192#41—464no—
193C2×Q8—232no—
194C2×Q8—462no—
195C2×Q8—464no—
196C2×Q8C22⋊D2311yescharacteristic, complemented
197C2×D4—22no—
198C2×D4—234no—
199C2×D4—232no—
200C2×D4—462no—
201C2×D4—468no—
202C2×D4—464no—
203C2×D4—464no—
204C2×D4—464no—
205C2×D4C22⋊D2311yescharacteristic, complemented
206C2×D4C22×D2312yes—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—234no—
212C22×C4—464no—
213C22×C4C22⋊D2312yescomplemented
214C22×C4C22×D2311yescharacteristic
215C22×C4C22×D2311yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—22no—
218C4⋊C4—464no—
219C4⋊C4—462no—
220C22⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—234no—
223C22⋊C4—464no—
224C22⋊C4—464no—
225C22⋊C4C22×D2312yes—
226C42—21no—
227C42—462no—
228C23—22no—
229C23—21no—
230C23—42no—
231C23—234no—
232C23—464no—
233C23C2×C22⋊D2312yes—
234C23C23×D2311yescharacteristic
235Q8—22no—
236Q8—464no—
237Q8—462no—
238Q8—462no—
239D4—24no—
240D4—22no—
241D4—44no—
242D4—464no—
243D4—468no—
244D4—464no—
245D4—464no—
246D4—462no—
247D4—462no—
248D4—928no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—234no—
258C2×C4—468no—
259C2×C4—464no—
260C2×C4—464no—
261C2×C4—464no—
262C2×C4—464no—
263C2×C4D4×D2312yes—
264C2×C4D4×D2312yes—
265C2×C4C2×C22⋊D2312yes—
266C2×C4C2×C22⋊D2311yescharacteristic
267C2×C4C2×C22⋊D2311yescharacteristic
268C22—22no—
269C22—24no—
270C22—22no—
271C22—41no—
272C22—42no—
273C22—41no—
274C22—42no—
275C22—41no—
276C22—464no—
277C22—924no—
278C22—1844no—
279C22C2×D4×D2312yes—
280C22C22×C22⋊D2311yescharacteristic
281C4—22no—
282C4—42no—
283C4—41no—
284C4—464no—
285C4—924no—
286C4#1062510811yescharacteristic
287C4#1062510812yes—
288C4#1062510811yescharacteristic
289C2—21no—
290C2—22no—
291C2—42no—
292C2—42no—
293C2—924no—
294C2C2×#1062510811yescharacteristic
subgroupG/H
centerC4#10625108
commutator, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC23×#525C2
socleC2×C23C2×#120
hypercenter#525D23
hypocenterC23#3025
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #13093253C2semidirect
2. #13092928C2semidirect
3. #13092606C2semidirect
4. #13092603C2semidirect
5. #13092391C2semidirect
6. #13092390C2semidirect
7. C23×#525C2semidirect
9. C23×C4×C23C22semidirect
18. C23×#123C22semidirect
21. C23×#120C22semidirect
23. C23×#117C22semidirect
24. #10625124C22semidirect
26. #10625100C22semidirect
28. #10625097C22semidirect
30. #10625016C22semidirect
31. #10624988C22semidirect
35. C2×Q8×C23D4semidirect
37. C2×D4×C23D4semidirect
43. C22×C4×C23D4semidirect
63. C2×D92D4semidirect
65. C2×C4×D23D4semidirect
67. C2×Dic46D4semidirect
144. #525D23semidirect
164. C23×C4C2×D23semidirect
166. #123C2×D23semidirect
172. #120C2×D23semidirect
176. #117C2×D23semidirect
179. C23#3025semidirect
196. C2×Q8C22⋊D23semidirect
205. C2×D4C22⋊D23semidirect
213. C22×C4C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130932532
#130929282
#130926062
#130926032
#130923912
#130923902
C23×#5252
#302523