Finite Group Databasebeta

← #15682791

Subgroups — #15682791

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#13092929C212yesmaximal, complemented
3#13092924C211yesmaximal, characteristic, complemented
4#13092608C214yesmaximal, complemented
5#13092605C214yesmaximal, complemented
6#13092390C212yesmaximal, complemented
7C23×#410C211yesmaximal, characteristic, complemented
8C2×#41×C23C2211yescharacteristic
9#10625161—22no—
10#10625160—22no—
11#41×D23—24no—
12#10625158—21no—
13#10625155—21no—
14#10625155C2214yes—
15C2×#67288—22no—
16C2×#67288C2212yes—
17C22×C4×D23C2211yescharacteristic, complemented
18C23×#117C2212yescomplemented
19#10625117—21no—
20#10625109—21no—
21#10625108C2212yescomplemented
22#10625106C2212yescomplemented
23C4×C22⋊D23—22no—
24#10625097C2211yescharacteristic, complemented
25#10625068—22no—
26#10625066—22no—
27#10625057C2214yescomplemented
28#10625053C2214yescomplemented
29C4×D92—24no—
30C23×#99C2214yescomplemented
31#10624988C2218yescomplemented
32C23×D23C2311yescharacteristic
33#41×C23—22no—
34#41×C23—22no—
35C2×Q8×C23D411yescharacteristic, complemented
36C2×D4×C23D411yescharacteristic, complemented
37C2×D4×C23C2312yes—
38C22×C4×C23D412yescomplemented
39C22×C4×C23C2311yescharacteristic
40C2×C22⋊D23—24no—
41C2×C22⋊D23—22no—
42C2×C22⋊D23C2314yes—
43C22×Dic23C2311yescharacteristic
44#67292—24no—
45Q8×D23—24no—
46#67290—24no—
47#67290—28no—
48D4×D23—24no—
49D4×D23—28no—
50#67288—24no—
51#67288—24no—
52#67288—22no—
53#67288—24no—
54#67288—22no—
55#67288—22no—
56#67288—22no—
57C2×D92—22no—
58C2×D92—24no—
59C2×D92D412yescomplemented
60C2×C4×D23—24no—
61C2×C4×D23—22no—
62C2×C4×D23—22no—
63C2×C4×D23—21no—
64C2×C4×D23—21no—
65C2×C4×D23D414yescomplemented
66C2×Dic46—22no—
67C2×Dic46D412yescomplemented
68C4⋊C4×C23—22no—
69C22⋊C4×C23C2314yes—
70C42×C23—22no—
71C22⋊Dic23—22no—
72C22⋊Dic23C2312yes—
73(C2×D23)⋊C4—24no—
74(C2×D23)⋊C4—22no—
75(C2×D23)⋊C4—24no—
76C4⋊Dic23—21no—
77C4⋊Dic23—24no—
78Dic23⋊C4—22no—
79C4×Dic23—21no—
80C23×C23C2×D412yes—
81C23×C23C2411yescharacteristic
82C22×D23—22no—
83C22×D23—21no—
84C22×D23—24no—
85C22×D23—42no—
86C22×D23C2×D414yes—
87Q8×C23—22no—
88D4×C23—24no—
89D4×C23—22no—
90C2×C4×C23—22no—
91C2×C4×C23—22no—
92C2×C4×C23—24no—
93C2×C4×C23C2×D412yes—
94C2×C4×C23C2×D411yescharacteristic
95C2×C4×C23C2×D411yescharacteristic
96C2×C4×C23C2×D412yes—
97C2×C4×C23C2×D412yes—
98C22⋊D23—28no—
99C22⋊D23—24no—
100C22⋊D23—24no—
101C22⋊D23—44no—
102C2×Dic23—24no—
103C2×Dic23—22no—
104C2×Dic23—21no—
105C2×Dic23—22no—
106C2×Dic23C2×D414yes—
107D92—24no—
108D92—22no—
109D92—22no—
110D92—48no—
111C4×D23—28no—
112C4×D23—24no—
113C4×D23—24no—
114C4×D23—41no—
115C4×D23—42no—
116C4×D23—41no—
117Dic46—24no—
118Dic46—22no—
119Dic46—22no—
120#3025—231nomaximal, Sylow
121C22×C23—22no—
122C22×C23—41no—
123C22×C23—42no—
124C22×C23C22×D411yescharacteristic
125C22×C23C22×D412yes—
126C2×D23—24no—
127C2×D23—22no—
128C2×D23—24no—
129C2×D23—41no—
130C2×D23—42no—
131C2×D23—41no—
132C2×D23—44no—
133C2×D23—84no—
134C4×C23—22no—
135C4×C23—44no—
136C4×C23#12011yescharacteristic
137C4×C23#12012yes—
138C4×C23#12011yescharacteristic
139Dic23—24no—
140Dic23—42no—
141Dic23—41no—
142#585—231no—
143#525—231no—
144#525—232no—
145#458—234no—
146B(4,𝔽2)—234no—
147#410—232no—
148#410D2311yescharacteristic, complemented
149C2×C23—21no—
150C2×C23—22no—
151C2×C23—42no—
152C2×C23C2×#12011yescharacteristic
153D23—42no—
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×C4—231no—
165#123—232no—
166#123—234no—
167C22⋊Q8—462no—
168C22⋊Q8—461no—
169#121—462no—
170#121—461no—
171#120—232no—
172#120—234no—
173C4×D4—464no—
174C4×D4—462no—
175#117—231no—
176#117C2×D2312yescomplemented
177#99—238no—
178#99C2×D2314yescomplemented
179C23#302511yescharacteristic, complemented, Sylow
180C24—231no—
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—464no—
191#41—462no—
192#41—462no—
193C2×Q8—232no—
194C2×Q8—462no—
195C2×Q8—464no—
196C2×Q8D9211yescharacteristic, complemented
197C2×D4—234no—
198C2×D4—232no—
199C2×D4—462no—
200C2×D4—464no—
201C2×D4—468no—
202C2×D4—464no—
203C2×D4—464no—
204C2×D4—462no—
205C2×D4D9211yescharacteristic, complemented
206C2×D4C22×D2312yes—
207C22×C4—234no—
208C22×C4—231no—
209C22×C4—464no—
210C22×C4—461no—
211C22×C4—461no—
212C22×C4—462no—
213C22×C4—462no—
214C22×C4D9212yescomplemented
215C22×C4C22×D2311yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—464no—
218C4⋊C4—461no—
219C4⋊C4—462no—
220C22⋊C4—232no—
221C22⋊C4—464no—
222C22⋊C4—464no—
223C22⋊C4—462no—
224C22⋊C4—462no—
225C22⋊C4C22×D2314yes—
226C42—22no—
227C42—461no—
228C23—234no—
229C23—464no—
230C23—461no—
231C23—462no—
232C23—922no—
233C23C2×D9212yes—
234C23C23×D2311yescharacteristic
235Q8—22no—
236Q8—464no—
237Q8—462no—
238Q8—462no—
239D4—24no—
240D4—22no—
241D4—464no—
242D4—468no—
243D4—464no—
244D4—464no—
245D4—462no—
246D4—462no—
247D4—928no—
248D4—924no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—234no—
253C2×C4—468no—
254C2×C4—464no—
255C2×C4—464no—
256C2×C4—464no—
257C2×C4—462no—
258C2×C4—461no—
259C2×C4—462no—
260C2×C4—921no—
261C2×C4—922no—
262C2×C4—921no—
263C2×C4C2×D9212yes—
264C2×C4C2×D9211yescharacteristic
265C2×C4C2×D9211yescharacteristic
266C2×C4D4×D2312yes—
267C2×C4D4×D2312yes—
268C22—22no—
269C22—41no—
270C22—42no—
271C22—464no—
272C22—462no—
273C22—464no—
274C22—924no—
275C22—922no—
276C22—921no—
277C22—921no—
278C22—1844no—
279C22C22×D9211yescharacteristic
280C22C2×D4×D2312yes—
281C4—22no—
282C4—44no—
283C4—464no—
284C4—922no—
285C4—921no—
286C4#1062505311yescharacteristic
287C4#1062505312yes—
288C4#1062505311yescharacteristic
289C2—22no—
290C2—21no—
291C2—42no—
292C2—922no—
293C2—924no—
294C2C2×#1062505311yescharacteristic
subgroupG/H
centerC4#10625053
commutator, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC23×#410C2
socleC2×C23C2×#120
hypercenter#410D23
hypocenterC23#3025
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #13093253C2semidirect
2. #13092929C2semidirect
3. #13092924C2semidirect
4. #13092608C2semidirect
5. #13092605C2semidirect
6. #13092390C2semidirect
7. C23×#410C2semidirect
17. C22×C4×D23C22semidirect
18. C23×#117C22semidirect
21. #10625108C22semidirect
22. #10625106C22semidirect
24. #10625097C22semidirect
27. #10625057C22semidirect
28. #10625053C22semidirect
30. C23×#99C22semidirect
31. #10624988C22semidirect
35. C2×Q8×C23D4semidirect
36. C2×D4×C23D4semidirect
38. C22×C4×C23D4semidirect
59. C2×D92D4semidirect
65. C2×C4×D23D4semidirect
67. C2×Dic46D4semidirect
148. #410D23semidirect
176. #117C2×D23semidirect
178. #99C2×D23semidirect
179. C23#3025semidirect
196. C2×Q8D92semidirect
205. C2×D4D92semidirect
214. C22×C4D92semidirect

Maximal subgroups

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

subgroupindex
#130932532
#130929292
#130929242
#130926082
#130926052
#130923902
C23×#4102
#302523