Finite Group Databasebeta

← #28399965

Subgroups — #28399965

Order 14464.

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#20299434C211yesmaximal, characteristic, complemented
2#20299109C212yesmaximal, complemented
3#20298787C214yesmaximal, complemented
4#20298784C214yesmaximal, complemented
5#20298572C211yesmaximal, characteristic, complemented
6#20298571C212yesmaximal, complemented
7#525×C113C211yesmaximal, characteristic, complemented
8#16813670—21no—
9#16813669—22no—
10#16813668—22no—
11#16813667—21no—
12#16813667C2214yes—
13C2×#14268647—22no—
14C2×#14268647C2212yes—
15#41×D113—24no—
16#16813605C2214yescomplemented
17#16813601—22no—
18#16813596—22no—
19#16813591C2214yescomplemented
20C4×C22⋊D113—24no—
21#16813581C2212yescomplemented
22#16813537C2214yescomplemented
23#16813536C2218yescomplemented
24C2×#41×C113C2211yescharacteristic
25C23×C4×C113C2211yescharacteristic, complemented
26#123×C113C2212yescomplemented
27C22⋊Q8×C113—21no—
28#121×C113—21no—
29#120×C113C2212yescomplemented
30C4×D4×C113—22no—
31#117×C113C2211yescharacteristic, complemented
32#14268648—24no—
33#14268647—24no—
34#14268647—24no—
35#14268647—22no—
36#14268647—22no—
37#14268647—24no—
38#14268647—22no—
39#14268647—22no—
40#14268646—24no—
41#14268646—28no—
42C2×Dic226—22no—
43C2×Dic226D412yescomplemented
44Q8×D113—24no—
45C2×D452—22no—
46C2×D452D412yescomplemented
47C2×C22⋊D113—24no—
48C2×C22⋊D113—24no—
49C2×C22⋊D113C2314yes—
50D4×D113—24no—
51D4×D113—28no—
52C2×C4×D113—24no—
53C2×C4×D113D414yescomplemented
54C4⋊Dic113—22no—
55#14268626—24no—
56C22⋊Dic113—24no—
57C22⋊Dic113C2314yes—
58#14268624—24no—
59C4×Dic113—22no—
60C24×C113C2311yescharacteristic
61#41×C113—22no—
62#41×C113—22no—
63C2×Q8×C113D411yescharacteristic, complemented
64C2×D4×C113—22no—
65C2×D4×C113D411yescharacteristic, complemented
66C2×D4×C113C2312yes—
67C22×C4×C113—22no—
68C22×C4×C113—22no—
69C22×C4×C113—21no—
70C22×C4×C113—21no—
71C22×C4×C113D412yescomplemented
72C22×C4×C113C2311yescharacteristic
73C22×C4×C113C2311yescharacteristic
74C4⋊C4×C113—21no—
75C4⋊C4×C113—22no—
76C22⋊C4×C113—22no—
77C22⋊C4×C113—22no—
78C22⋊C4×C113C2312yes—
79C42×C113—21no—
80C23×C113—21no—
81C23×C113—22no—
82C23×C113—42no—
83C23×C113C2×D412yes—
84C23×C113C2411yescharacteristic
85C22×D113—24no—
86C22×D113C2×D414yes—
87Q8×C113—22no—
88D4×C113—24no—
89D4×C113—22no—
90D4×C113—44no—
91C2×C4×C113—22no—
92C2×C4×C113—22no—
93C2×C4×C113—22no—
94C2×C4×C113—21no—
95C2×C4×C113—22no—
96C2×C4×C113—41no—
97C2×C4×C113—42no—
98C2×C4×C113—41no—
99C2×C4×C113C2×D412yes—
100C2×C4×C113C2×D412yes—
101C2×C4×C113C2×D412yes—
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113C2×D411yescharacteristic
104C22⋊D113—28no—
105C22⋊D113—24no—
106C22⋊D113—24no—
107C22⋊D113—48no—
108C2×Dic113—24no—
109C2×Dic113—24no—
110C2×Dic113C2×D414yes—
111D452—24no—
112D452—22no—
113D452—22no—
114C4×D113—28no—
115C4×D113—24no—
116C4×D113—24no—
117Dic226—24no—
118Dic226—22no—
119Dic226—22no—
120C22×C113—24no—
121C22×C113—22no—
122C22×C113—22no—
123C22×C113—41no—
124C22×C113—42no—
125C22×C113—42no—
126C22×C113—41no—
127C22×C113—41no—
128C22×C113C22×D412yes—
129C22×C113C22×D411yescharacteristic
130C2×D113—24no—
131C2×D113—44no—
132C2×D113—84no—
133C4×C113—22no—
134C4×C113—42no—
135C4×C113—41no—
136C4×C113#12011yescharacteristic
137C4×C113#12012yes—
138C4×C113#12011yescharacteristic
139Dic113—24no—
140Dic113—44no—
141C2×C113—22no—
142C2×C113—21no—
143C2×C113—42no—
144C2×C113—42no—
145C2×C113C2×#12011yescharacteristic
146D113—44no—
147#3025—1131nomaximal, Sylow
148C113#302511yescharacteristic, complemented, Sylow
149#585—1131no—
150#525—1132no—
151#525D11311yescharacteristic, complemented
152#458—1134no—
153B(4,𝔽2)—1134no—
154#410—1131no—
155#410—1132no—
1562−1+4—2262no—
1572−1+4—2261no—
158H(5,𝔽2)—1134no—
159H(5,𝔽2)—2262no—
160H(5,𝔽2)—2261no—
161C2×#41—1132no—
162C2×#41—2264no—
163C2×#41—2262no—
164C2×#41C2×D11311yescharacteristic
165C23×C4C2×D11311yescharacteristic, complemented
166#123—1134no—
167#123C2×D11312yescomplemented
168C22⋊Q8—21no—
169C22⋊Q8—2262no—
170#121—21no—
171#121—2262no—
172#120—1134no—
173#120C2×D11312yescomplemented
174C4×D4—22no—
175C4×D4—2264no—
176#117—1132no—
177#117C2×D11311yescharacteristic, complemented
178#99—1134no—
179#99—1138no—
180C24C22×D11311yescharacteristic
181#41—22no—
182#41—22no—
183#41—2264no—
184#41—2264no—
185#41—2268no—
186#41—2264no—
187#41—2264no—
188#41—2262no—
189#41—2262no—
190#41—2262no—
191#41—2262no—
192#41—2264no—
193C2×Q8—1132no—
194C2×Q8—2262no—
195C2×Q8—2264no—
196C2×Q8C22⋊D11311yescharacteristic, complemented
197C2×D4—22no—
198C2×D4—1134no—
199C2×D4—1132no—
200C2×D4—2262no—
201C2×D4—2268no—
202C2×D4—2264no—
203C2×D4—2264no—
204C2×D4—2264no—
205C2×D4C22⋊D11311yescharacteristic, complemented
206C2×D4C22×D11312yes—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—1134no—
212C22×C4—2264no—
213C22×C4C22⋊D11312yescomplemented
214C22×C4C22×D11311yescharacteristic
215C22×C4C22×D11311yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—22no—
218C4⋊C4—2264no—
219C4⋊C4—2262no—
220C22⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—1134no—
223C22⋊C4—2264no—
224C22⋊C4—2264no—
225C22⋊C4C22×D11312yes—
226C42—21no—
227C42—2262no—
228C23—22no—
229C23—21no—
230C23—42no—
231C23—1134no—
232C23—2264no—
233C23C2×C22⋊D11312yes—
234C23C23×D11311yescharacteristic
235Q8—22no—
236Q8—2264no—
237Q8—2262no—
238Q8—2262no—
239D4—24no—
240D4—22no—
241D4—44no—
242D4—4528no—
243D4—2264no—
244D4—2268no—
245D4—2264no—
246D4—2264no—
247D4—2262no—
248D4—2262no—
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—1134no—
258C2×C4—2268no—
259C2×C4—2264no—
260C2×C4—2264no—
261C2×C4—2264no—
262C2×C4—2264no—
263C2×C4D4×D11312yes—
264C2×C4D4×D11312yes—
265C2×C4C2×C22⋊D11312yes—
266C2×C4C2×C22⋊D11311yescharacteristic
267C2×C4C2×C22⋊D11311yescharacteristic
268C22—22no—
269C22—24no—
270C22—22no—
271C22—41no—
272C22—42no—
273C22—41no—
274C22—42no—
275C22—41no—
276C22—9044no—
277C22—4524no—
278C22—2264no—
279C22C2×D4×D11312yes—
280C22C22×C22⋊D11311yescharacteristic
281C4—22no—
282C4—42no—
283C4—41no—
284C4—4524no—
285C4—2264no—
286C4#1681359011yescharacteristic
287C4#1681359012yes—
288C4#1681359011yescharacteristic
289C2—21no—
290C2—22no—
291C2—42no—
292C2—42no—
293C2—4524no—
294C2C2×#1681359011yescharacteristic
subgroupG/H
centerC4#16813590
commutator, cosocleC23×C113C24
FrattiniC23C23×D113
Fitting#525×C113C2
socleC2×C113C2×#120
hypercenter#525D113
hypocenterC113#3025
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #20299434C2semidirect
2. #20299109C2semidirect
3. #20298787C2semidirect
4. #20298784C2semidirect
5. #20298572C2semidirect
6. #20298571C2semidirect
7. #525×C113C2semidirect
16. #16813605C22semidirect
19. #16813591C22semidirect
21. #16813581C22semidirect
22. #16813537C22semidirect
23. #16813536C22semidirect
25. C23×C4×C113C22semidirect
26. #123×C113C22semidirect
29. #120×C113C22semidirect
31. #117×C113C22semidirect
43. C2×Dic226D4semidirect
46. C2×D452D4semidirect
53. C2×C4×D113D4semidirect
63. C2×Q8×C113D4semidirect
65. C2×D4×C113D4semidirect
71. C22×C4×C113D4semidirect
148. C113#3025semidirect
151. #525D113semidirect
165. C23×C4C2×D113semidirect
167. #123C2×D113semidirect
173. #120C2×D113semidirect
177. #117C2×D113semidirect
196. C2×Q8C22⋊D113semidirect
205. C2×D4C22⋊D113semidirect
213. C22×C4C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202994342
#202991092
#202987872
#202987842
#202985722
#202985712
#525×C1132
#3025113