Finite Group Databasebeta

← #28393153

Subgroups — #28393153

Order 14464.

1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C22×D4×D113C211yesmaximal, characteristic
2C2×#16813580C211yesmaximal, characteristic, complemented
3C2×#16813579C211yesmaximal, characteristic, complemented
4#20298501C211yesmaximal, characteristic, complemented
5#20298500C211yesmaximal, characteristic, complemented
6#20298499C211yesmaximal, characteristic, complemented
7#20298498C214yesmaximal, complemented
8#20298453C214yesmaximal, complemented
9#390×C113C211yesmaximal, characteristic, complemented
10C24×D113C2212yes—
11C22×D452C2211yescharacteristic
12C22×C22⋊D113C2212yes—
13C2×D4×D113—24no—
14C2×D4×D113—24no—
15C2×D4×D113C418yescomplemented
16C22×C4×D113C2211yescharacteristic
17#16813580—24no—
18#16813579—24no—
19C2×C4⋊Dic113C2211yescharacteristic, complemented
20C2×#14268626C2212yescomplemented
21C2×C22⋊Dic113C2214yescomplemented
22C2×#14268624C2212yes—
23C2×#14268624C2212yes—
24C2×#14268624C2214yescomplemented
25C2×#14268624C2214yescomplemented
26C2×C4×Dic113C2212yescomplemented
27C2×C4×Dic113C2211yescharacteristic, complemented
28C22×D4×C113C2211yescharacteristic
29C2×C4⋊C4×C113C2211yescharacteristic, complemented
30C2×C22⋊C4×C113C2214yescomplemented
31C2×C42×C113C2211yescharacteristic, complemented
32C23×D113—24no—
33C23×D113—24no—
34C23×D113—44no—
35C23×D113—44no—
36C23×D113C2×C418yes—
37C23×D113C2312yes—
38C23×D113C2311yescharacteristic
39C2×D452—22no—
40C2×D452—22no—
41C2×D452C2×C414yes—
42C2×C22⋊D113—24no—
43C2×C22⋊D113—24no—
44C2×C22⋊D113C2×C418yes—
45D4×D113—232no—
46C22×Dic113C2312yes—
47C22×Dic113C2312yes—
48C22×Dic113C2311yescharacteristic
49C2×C4×D113C2×C414yes—
50C2×C4×D113D414yes—
51C2×C4×D113D414yes—
52C4⋊Dic113—22no—
53#14268626—24no—
54C22⋊Dic113—44no—
55#14268624—24no—
56#14268624—24no—
57#14268624—44no—
58#14268624—44no—
59C4×Dic113—22no—
60C4×Dic113—24no—
61C24×C113C2312yes—
62C2×D4×C113—22no—
63C2×D4×C113—22no—
64C2×D4×C113C2×C414yes—
65C22×C4×C113C2312yes—
66C22×C4×C113C2312yes—
67C22×C4×C113C2311yescharacteristic
68C4⋊C4×C113—22no—
69C22⋊C4×C113—44no—
70C42×C113—22no—
71C23×C113—22no—
72C23×C113—22no—
73C23×C113—24no—
74C23×C113—24no—
75C23×C113C22×C414yes—
76C23×C113C2411yescharacteristic
77C22×D113—22no—
78C22×D113—22no—
79C22×D113—22no—
80C22×D113—22no—
81C22×D113—24no—
82C22×D113—24no—
83C22×D113—216no—
84C22×D113—416no—
85C22×D113—48no—
86C22×D113—416no—
87C22×D113—48no—
88C22×D113C22×C414yes—
89C22×D113C22×C412yes—
90C22×D113C2×D412yes—
91C22×D113C2×D412yes—
92D4×C113—28no—
93C2×C4×C113—22no—
94C2×C4×C113—22no—
95C2×C4×C113—22no—
96C2×C4×C113—24no—
97C2×C4×C113—22no—
98C2×C4×C113C22×C412yes—
99C2×C4×C113C2×D412yes—
100C2×C4×C113C2×D412yes—
101C22⋊D113—216no—
102C2×Dic113—22no—
103C2×Dic113—22no—
104C2×Dic113—22no—
105C2×Dic113—24no—
106C2×Dic113—22no—
107C2×Dic113C22×C412yes—
108C2×Dic113C2×D412yes—
109C2×Dic113C2×D412yes—
110D452—28no—
111C4×D113C22⋊C4116yescomplemented
112C22×C113—24no—
113C22×C113—28no—
114C22×C113—42no—
115C22×C113—44no—
116C22×C113—42no—
117C22×C113C23×C411yescharacteristic
118C22×C113C22×D411yescharacteristic
119C22×C113C22×D411yescharacteristic
120C22×C113H(5,𝔽2)12yes—
121C22×C113H(5,𝔽2)12yes—
122C2×D113—24no—
123C2×D113—22no—
124C2×D113—24no—
125C2×D113—22no—
126C2×D113—24no—
127C2×D113—28no—
128C2×D113—432no—
129C2×D113—42no—
130C2×D113—44no—
131C2×D113—42no—
132C2×D113C2×C22⋊C414yes—
133C4×C113—42no—
134C4×C113—42no—
135C4×C113C2×C22⋊C414yes—
136Dic113—42no—
137Dic113—42no—
138Dic113C2×C22⋊C414yes—
139C2×C113—44no—
140C2×C113C22×C22⋊C411yescharacteristic
141C2×C113#51812yes—
142C2×C113#53511yescharacteristic
143C2×C113#53512yes—
144C2×C113#53511yescharacteristic
145D113—24no—
146D113—44no—
147#2309—1131nomaximal, Sylow
148C113#230911yescharacteristic, complemented, Sylow
149C23×D4—1131no—
150C2×#117—1131no—
151C2×#117—1131no—
152#390—1131no—
153#390—1131no—
154#390—1134no—
155#390—1131no—
156#390D11311yescharacteristic, complemented
157#379—1134no—
158C25—1132no—
159C22×D4—1132no—
160C22×D4—1138no—
161C22×D4—1131no—
162C22×D4—2264no—
163C22×D4—2264no—
164C22×D4C2×D11311yescharacteristic
165C23×C4—1131no—
166#117—2264no—
167#117—2264no—
168C2×C4⋊C4—1132no—
169C2×C4⋊C4—1131no—
170C2×C4⋊C4C2×D11311yescharacteristic, complemented
171C2×C22⋊C4—1134no—
172C2×C22⋊C4—1134no—
173C2×C22⋊C4—1134no—
174C2×C22⋊C4—1132no—
175C2×C22⋊C4—1132no—
176C2×C22⋊C4C2×D11314yescomplemented
177C2×C42—1132no—
178C2×C42—1131no—
179C2×C42C2×D11311yescharacteristic, complemented
180C24—1131no—
181C24—1138no—
182C24—1132no—
183C24—4524no—
184C24—4524no—
185C24—2264no—
186C24—2264no—
187C24C22×D11312yes—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—1138no—
191C2×D4—1134no—
192C2×D4—22632no—
193C2×D4—2264no—
194C2×D4—2264no—
195C2×D4—2262no—
196C2×D4—2262no—
197C2×D4C4×D11314yes—
198C22×C4—1131no—
199C22×C4—1134no—
200C22×C4—1134no—
201C22×C4—1134no—
202C22×C4—1132no—
203C22×C4—1132no—
204C22×C4C22×D11312yes—
205C22×C4C22×D11312yes—
206C22×C4C22×D11311yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—2264no—
209C4⋊C4—2262no—
210C22⋊C4—44no—
211C22⋊C4—4524no—
212C22⋊C4—4524no—
213C22⋊C4—4524no—
214C22⋊C4—2264no—
215C22⋊C4—2264no—
216C42—22no—
217C42—2264no—
218C42—2262no—
219C23—22no—
220C23—22no—
221C23—24no—
222C23—24no—
223C23—1132no—
224C23—1132no—
225C23—1132no—
226C23—1134no—
227C23—45216no—
228C23—4528no—
229C23—45216no—
230C23—4528no—
231C23—22616no—
232C23—2262no—
233C23—2262no—
234C23—2264no—
235C23—2264no—
236C23—2262no—
237C23—2262no—
238C23C2×C4×D11314yes—
239C23C23×D11311yescharacteristic
240D4—28no—
241D4—22616no—
242D4—2268no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—22no—
248C2×C4—1132no—
249C2×C4—1132no—
250C2×C4—1132no—
251C2×C4—11316no—
252C2×C4—2262no—
253C2×C4—2262no—
254C2×C4—2262no—
255C2×C4—2262no—
256C2×C4—2264no—
257C2×C4C2×C4×D11312yes—
258C2×C4D4×D11312yes—
259C2×C4D4×D11312yes—
260C22—24no—
261C22—28no—
262C22—42no—
263C22—44no—
264C22—42no—
265C22—1134no—
266C22—45232no—
267C22—4522no—
268C22—4524no—
269C22—4522no—
270C22—2264no—
271C22—2268no—
272C22—2264no—
273C22—2262no—
274C22—2264no—
275C22—2262no—
276C22C22×C4×D11311yescharacteristic
277C22C2×D4×D11311yescharacteristic
278C22C2×D4×D11311yescharacteristic
279C22#1681366712yes—
280C22#1681366812yes—
281C4—42no—
282C4—42no—
283C4—1134no—
284C4—4522no—
285C4—4522no—
286C4C22⋊C4×D11314yes—
287C2—44no—
288C2—4524no—
289C2—2264no—
290C2C2×C22⋊C4×D11311yescharacteristic
291C2#2029907012yes—
292C2#2029916111yescharacteristic
293C2#2029916412yes—
294C2#2029916611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#390×C113C2
socle, cosocleC23×C113C24
prime radicalC22×D4×D113C2
hypercenter#390D113
hypocenterC113#2309
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#16813580C2semidirect
3. C2×#16813579C2semidirect
4. #20298501C2semidirect
5. #20298500C2semidirect
6. #20298499C2semidirect
7. #20298498C2semidirect
8. #20298453C2semidirect
9. #390×C113C2semidirect
15. C2×D4×D113C4semidirect
19. C2×C4⋊Dic113C22semidirect
20. C2×#14268626C22semidirect
21. C2×C22⋊Dic113C22semidirect
24. C2×#14268624C22semidirect
25. C2×#14268624C22semidirect
26. C2×C4×Dic113C22semidirect
27. C2×C4×Dic113C22semidirect
29. C2×C4⋊C4×C113C22semidirect
30. C2×C22⋊C4×C113C22semidirect
31. C2×C42×C113C22semidirect
111. C4×D113C22⋊C4semidirect
148. C113#2309semidirect
156. #390D113semidirect
170. C2×C4⋊C4C2×D113semidirect
176. C2×C22⋊C4C2×D113semidirect
179. C2×C42C2×D113semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1132
C2×#168135802
C2×#168135792
#202985012
#202985002
#202984992
#202984982
#202984532
#390×C1132
#2309113