Finite Group Databasebeta

← #15682798

Subgroups — #15682798

Order 2944.

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

normal subgroups only

This group has 772 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#13092984C212yesmaximal, complemented
3#13092603C218yesmaximal, complemented
4#13092391C211yesmaximal, characteristic, complemented
5#13092390C212yesmaximal, complemented
6C23×#535C211yesmaximal, characteristic, complemented
7C2×#41×C23C2211yescharacteristic
8C22×D4×C23C2211yescharacteristic, complemented
9#10625161—22no—
10#10625160—22no—
11#41×D23—24no—
12#10625158—21no—
13#10625155—21no—
14#10625155C2214yes—
15C2×#67288—22no—
16C2×#67288C2212yes—
17C23×#127—21no—
18C23×#124—21no—
19C23×#121—22no—
20C23×#120C2214yescomplemented
21C23×#117C2211yescharacteristic, complemented
22#10625124C2218yescomplemented
23#10625111—22no—
24#10625109—24no—
25#10625107—22no—
26#10625097C2212yescomplemented
27#10625016C2214yescomplemented
28#10624988C2218yescomplemented
29C24×C23C2312yes—
30#41×C23—22no—
31#41×C23—22no—
32C2×Q8×C23D411yescharacteristic, complemented
33C2×D4×C23—24no—
34C2×D4×C23—22no—
35C2×D4×C23—22no—
36C2×D4×C23—21no—
37C2×D4×C23—21no—
38C2×D4×C23D411yescharacteristic, complemented
39C2×D4×C23C2312yes—
40C22×C4×C23D412yescomplemented
41C22×C4×C23C2311yescharacteristic
42C2×C22⋊D23—24no—
43C2×C22⋊D23—28no—
44C2×C22⋊D23C2314yes—
45#67292—24no—
46Q8×D23—24no—
47#67290—24no—
48#67290—28no—
49D4×D23—24no—
50D4×D23—28no—
51#67288—24no—
52#67288—24no—
53#67288—22no—
54#67288—24no—
55#67288—22no—
56#67288—22no—
57#67288—22no—
58C2×D92—22no—
59C2×D92D412yescomplemented
60C2×C4×D23—24no—
61C2×C4×D23D414yescomplemented
62C2×Dic46—22no—
63C2×Dic46D412yescomplemented
64C4⋊C4×C23—21no—
65C22⋊C4×C23—24no—
66C22⋊C4×C23C2312yes—
67C42×C23—21no—
68C22⋊Dic23—28no—
69C22⋊Dic23C2314yes—
70C4⋊Dic23—22no—
71C4×Dic23—22no—
72C23×C23—24no—
73C23×C23—22no—
74C23×C23—82no—
75C23×C23C2×D412yes—
76C23×C23C2411yescharacteristic
77C22×D23—24no—
78C22×D23C2×D414yes—
79Q8×C23—22no—
80D4×C23—24no—
81D4×C23—22no—
82D4×C23—41no—
83D4×C23—42no—
84D4×C23—41no—
85D4×C23—84no—
86C2×C4×C23—22no—
87C2×C4×C23—22no—
88C2×C4×C23—22no—
89C2×C4×C23C2×D412yes—
90C2×C4×C23C2×D412yes—
91C2×C4×C23C2×D412yes—
92C2×C4×C23C2×D411yescharacteristic
93C2×C4×C23C2×D411yescharacteristic
94C22⋊D23—28no—
95C22⋊D23—24no—
96C22⋊D23—24no—
97C22⋊D23—88no—
98C2×Dic23—24no—
99C2×Dic23—24no—
100C2×Dic23C2×D414yes—
101D92—24no—
102D92—22no—
103D92—22no—
104C4×D23—28no—
105C4×D23—24no—
106C4×D23—24no—
107Dic46—24no—
108Dic46—22no—
109Dic46—22no—
110#3027—231nomaximal, Sylow
111C22×C23—22no—
112C22×C23—41no—
113C22×C23—42no—
114C22×C23—48no—
115C22×C23—44no—
116C22×C23—42no—
117C22×C23C22×D412yes—
118C22×C23C22×D411yescharacteristic
119C2×D23—24no—
120C2×D23—44no—
121C2×D23—84no—
122C4×C23—22no—
123C4×C23—42no—
124C4×C23#12011yescharacteristic
125C4×C23#12012yes—
126C4×C23#12011yescharacteristic
127Dic23—24no—
128Dic23—44no—
129#585—231no—
130#535—232no—
131#535D2311yescharacteristic, complemented
132B(4,𝔽2)—238no—
133#410—231no—
134#410—232no—
135C2×C23—22no—
136C2×C23—21no—
137C2×C23—42no—
138C2×C23—82no—
139C2×C23C2×#12011yescharacteristic
140D23—44no—
1412−1+4—462no—
1422−1+4—461no—
143H(5,𝔽2)—234no—
144H(5,𝔽2)—462no—
145H(5,𝔽2)—461no—
146C2×#41—232no—
147C2×#41—464no—
148C2×#41—462no—
149C2×#41C2×D2311yescharacteristic
150C22×D4C2×D2311yescharacteristic, complemented
151#127—21no—
152#127—462no—
153#124—21no—
154#124—462no—
155#121—22no—
156#121—464no—
157#120—238no—
158#120C2×D2314yescomplemented
159#117—232no—
160#117C2×D2311yescharacteristic, complemented
161#99—234no—
162#99—238no—
163C23#302711yescharacteristic, complemented, Sylow
164C24C22×D2312yes—
165#41—22no—
166#41—22no—
167#41—464no—
168#41—464no—
169#41—468no—
170#41—464no—
171#41—464no—
172#41—462no—
173#41—462no—
174#41—462no—
175#41—462no—
176#41—464no—
177C2×Q8—232no—
178C2×Q8—462no—
179C2×Q8—464no—
180C2×Q8C22⋊D2311yescharacteristic, complemented
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—234no—
187C2×D4—232no—
188C2×D4—462no—
189C2×D4—468no—
190C2×D4—464no—
191C2×D4—464no—
192C2×D4—468no—
193C2×D4C22⋊D2311yescharacteristic, complemented
194C2×D4C22×D2312yes—
195C22×C4—234no—
196C22×C4—464no—
197C22×C4C22⋊D2312yescomplemented
198C22×C4C22×D2311yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—462no—
201C22⋊C4—24no—
202C22⋊C4—234no—
203C22⋊C4—468no—
204C22⋊C4C22×D2312yes—
205C42—21no—
206C42—462no—
207C23—24no—
208C23—22no—
209C23—82no—
210C23—234no—
211C23—464no—
212C23C2×C22⋊D2312yes—
213C23C23×D2311yescharacteristic
214Q8—22no—
215Q8—464no—
216Q8—462no—
217Q8—462no—
218D4—24no—
219D4—22no—
220D4—41no—
221D4—41no—
222D4—42no—
223D4—84no—
224D4—464no—
225D4—468no—
226D4—464no—
227D4—464no—
228D4—462no—
229D4—462no—
230D4—1848no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—234no—
235C2×C4—468no—
236C2×C4—464no—
237C2×C4—464no—
238C2×C4—464no—
239C2×C4—464no—
240C2×C4D4×D2312yes—
241C2×C4D4×D2312yes—
242C2×C4C2×C22⋊D2312yes—
243C2×C4C2×C22⋊D2311yescharacteristic
244C2×C4C2×C22⋊D2311yescharacteristic
245C22—22no—
246C22—41no—
247C22—42no—
248C22—44no—
249C22—48no—
250C22—42no—
251C22—464no—
252C22—924no—
253C22—1844no—
254C22C2×D4×D2312yes—
255C22C22×C22⋊D2311yescharacteristic
256C4—22no—
257C4—42no—
258C4—464no—
259C4—924no—
260C4#1062510811yescharacteristic
261C4#1062510811yescharacteristic
262C4#1062510812yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—82no—
267C2—924no—
268C2C2×#1062510811yescharacteristic
subgroupG/H
centerC2C2×#10625108
commutator, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC23×#535C2
socleC2×C23C2×#120
hypercenter#535D23
hypocenterC23#3027
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #13093253C2semidirect
2. #13092984C2semidirect
3. #13092603C2semidirect
4. #13092391C2semidirect
5. #13092390C2semidirect
6. C23×#535C2semidirect
8. C22×D4×C23C22semidirect
20. C23×#120C22semidirect
21. C23×#117C22semidirect
22. #10625124C22semidirect
26. #10625097C22semidirect
27. #10625016C22semidirect
28. #10624988C22semidirect
32. C2×Q8×C23D4semidirect
38. C2×D4×C23D4semidirect
40. C22×C4×C23D4semidirect
59. C2×D92D4semidirect
61. C2×C4×D23D4semidirect
63. C2×Dic46D4semidirect
131. #535D23semidirect
150. C22×D4C2×D23semidirect
158. #120C2×D23semidirect
160. #117C2×D23semidirect
163. C23#3027semidirect
180. C2×Q8C22⋊D23semidirect
193. C2×D4C22⋊D23semidirect
197. C22×C4C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130932532
#130929842
#130926032
#130923912
#130923902
C23×#5352
#302723