Finite Group Databasebeta

← #28407448

Subgroups — #28407448

Order 14464.

422 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 148 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#20299630C212yesmaximal, complemented
2#20299628C212yesmaximal, complemented
3#20299626C212yesmaximal, complemented
4#20299625C212yesmaximal, complemented
5#20299622C212yesmaximal, complemented
6#20299572C211yesmaximal, characteristic, complemented
7#20299571C211yesmaximal, characteristic, complemented
8#20299566C212yesmaximal, complemented
9#20299106C211yesmaximal, characteristic
10C2×#14268657C2211yescharacteristic, complemented
11C2×#14268656C2211yescharacteristic, complemented
12C2×#14268655C2212yes—
13C2×#14268655C2212yes—
14C2×#14268655C2211yescharacteristic, complemented
15C22×#11744753C2211yescharacteristic, complemented
16#16813689C2212yescomplemented
17C4⋊#11744753C2212yescomplemented
18#16813679C2212yes—
19#16813679C2212yes—
20#16813679C2212yescomplemented
21C22⋊#11744753C2212yes—
22C22⋊#11744753C2212yes—
23C22⋊#11744753C2212yescomplemented
24#16813677C2212yescomplemented
25C4×#11744753C2212yescomplemented
26C2×#14268646C2211yescharacteristic
27C22×C4×D113C2211yescharacteristic
28#16813605C411yescharacteristic
29#16813600C412yes—
30#16813595C412yes—
31#16813592C411yescharacteristic
32#16813590C411yescharacteristic
33#16813584C2212yes—
34#16813582C2212yes—
35#16813578C2211yescharacteristic
36#123×C113C411yescharacteristic
37#14268657—41no—
38#14268656—41no—
39#14268655—42no—
40#14268655—42no—
41#14268655—41no—
42C2×#11744753—41no—
43C2×#11744753C2312yes—
44C2×#11744753C2312yes—
45C2×#11744753C2312yes—
46C2×#11744753C2312yes—
47C23×D113C2×C411yescharacteristic
48#14268646—41no—
49#14268646—41no—
50C2×Dic226C2×C411yescharacteristic
51C2×D452C2×C412yes—
52C2×C22⋊D113C2×C412yes—
53C2×C22⋊D113C2×C411yescharacteristic
54C2×C22⋊D113C2×C411yescharacteristic
55C22×Dic113C2311yescharacteristic
56C22×Dic113C2311yescharacteristic
57C2×C4×D113—41no—
58C2×C4×D113—41no—
59C2×C4×D113C2×C412yes—
60C2×C4×D113C2312yes—
61C2×C4×D113C2311yescharacteristic
62#14268626C2×C412yes—
63#14268626C2×C412yes—
64C22⋊Dic113C2×C411yescharacteristic
65#14268624C2×C412yes—
66#14268624C2×C412yes—
67#14268624C2×C412yes—
68C4×Dic113C2312yes—
69C2×D4×C113C2×C411yescharacteristic
70C22×C4×C113C2×C411yescharacteristic
71C4⋊C4×C113C2×C412yes—
72C22⋊C4×C113C2×C411yescharacteristic
73C22⋊C4×C113C2×C412yes—
74C23×C113C22×C411yescharacteristic
75C23×C113C22×C411yescharacteristic
76C22×D113—24no—
77C22×D113—41no—
78C22×D113C22×C411yescharacteristic
79C22×D113C22×C412yes—
80D4×C113—41no—
81C2×C4×C113—41no—
82C2×C4×C113C22×C412yes—
83C2×C4×C113C22×C412yes—
84C2×C4×C113C22×C411yescharacteristic
85C22⋊D113—24no—
86C22⋊D113—41no—
87C22⋊D113—41no—
88C2×Dic113—21no—
89C2×Dic113—21no—
90C2×Dic113—21no—
91C2×Dic113—21no—
92C2×Dic113C22×C412yes—
93C2×Dic113C22×C411yescharacteristic
94C2×Dic113C22×C411yescharacteristic
95C2×Dic113C2411yescharacteristic
96D452—24no—
97C4×D113—22no—
98C4×D113—22no—
99C4×D113—21no—
100C4×D113—21no—
101C4×D113—42no—
102Dic226—41no—
103#11744753—22no—
104#11744753—22no—
105#11744753—22no—
106#11744753—22no—
107C22×C113—21no—
108C22×C113—21no—
109C22×C113—22no—
110C22×C113—22no—
111C22×C113C23×C411yescharacteristic
112C2×D113—22no—
113C2×D113—22no—
114C2×D113—21no—
115C2×D113—22no—
116C2×D113—44no—
117C2×D113#13114yes—
118C4×C113—21no—
119C4×C113—22no—
120C4×C113—22no—
121Dic113—21no—
122Dic113—21no—
123Dic113—22no—
124Dic113H(5,𝔽2)11yescharacteristic
125Dic113H(5,𝔽2)11yescharacteristic
126C2×C113—41no—
127C2×C113—41no—
128C2×C113#51811yescharacteristic
129C2×C113C2×#13112yes—
130D113—24no—
131D113—41no—
132#2977—1131nomaximal, Sylow
133C113#297711yescharacteristic, complemented, Sylow
134#525—1131no—
135#435—1132no—
136#435—1132no—
137C8×D4—1132no—
138C8×D4—1132no—
139#433—1132no—
140#408—1131no—
141#408—1131no—
142C2×C22⋊C8—1132no—
143C2×#41—1131no—
144C23×C4—1131no—
145C2×M16—1131no—
146C2×M16—1131no—
147C22×C8—1131no—
148C22×C8—1132no—
149C22×C8—1132no—
150C22×C8—1131no—
151#123—1131no—
152#123#9067311yescharacteristic
153C22⋊Q8—1132no—
154#121—1132no—
155#120—1131no—
156#120—1131no—
157C4×D4—1132no—
158C4×D4—1132no—
159#117—1131no—
160C4⋊C8—1132no—
161C4⋊C8—1132no—
162C22⋊C8—1132no—
163C22⋊C8—1132no—
164C22⋊C8—1132no—
165C22⋊C8—1132no—
166C22⋊C8—1132no—
167C22⋊C8—1132no—
168#97—1132no—
169C4×C8—1132no—
170C24—1131no—
171#41—4521no—
172#41—4521no—
173C2×Q8—1131no—
174C2×D4—1131no—
175C2×D4—1131no—
176C2×D4—1132no—
177C2×D4—1132no—
178C2×D4C2×#9067311yescharacteristic
179C22×C4—1131no—
180C22×C4—1131no—
181C22×C4—1132no—
182C22×C4—1132no—
183C22×C4—1131no—
184C22×C4—4521no—
185C22×C4—4521no—
186C22×C4C2×#9067311yescharacteristic
187M16—4521no—
188M16—4521no—
189C2×C8—1132no—
190C2×C8—1132no—
191C2×C8—1132no—
192C2×C8—1132no—
193C2×C8—4521no—
194C2×C8—4521no—
195C2×C8—4522no—
196C2×C8—4522no—
197C4⋊C4—1132no—
198C4⋊C4—1132no—
199C4⋊C4C2×#9067312yes—
200C22⋊C4—1131no—
201C22⋊C4—1132no—
202C22⋊C4—1132no—
203C22⋊C4—1132no—
204C22⋊C4C2×#9067311yescharacteristic
205C22⋊C4C2×#9067312yes—
206C42—1132no—
207C23—1132no—
208C23—1131no—
209C23—4521no—
210C23—2264no—
211C23C22×#9067311yescharacteristic
212C23C22×#9067311yescharacteristic
213Q8—4521no—
214D4—41no—
215D4—4521no—
216D4—4521no—
217D4—2264no—
218D4—2264no—
219C2×C4—41no—
220C2×C4—1131no—
221C2×C4—1132no—
222C2×C4—1131no—
223C2×C4—1131no—
224C2×C4—4522no—
225C2×C4—2262no—
226C2×C4—2262no—
227C2×C4—2261no—
228C2×C4—2261no—
229C2×C4—2261no—
230C2×C4—2261no—
231C2×C4—2261no—
232C2×C4—2261no—
233C2×C4C22×#9067312yes—
234C2×C4C22×#9067311yescharacteristic
235C2×C4C22×#9067312yes—
236C8—2262no—
237C8—2262no—
238C8—2262no—
239C8—2262no—
240C22—21no—
241C22—21no—
242C22—22no—
243C22—22no—
244C22—1134no—
245C22—4524no—
246C22—2261no—
247C22—2262no—
248C22—2262no—
249C22—2262no—
250C22C23×#9067311yescharacteristic
251C4—22no—
252C4—21no—
253C4—22no—
254C4—1131no—
255C4—1131no—
256C4—2261no—
257C4—2261no—
258C4—2262no—
259C2—41no—
260C2—41no—
261C2—4521no—
262C2—2264no—
263C2#2029966511yescharacteristic
264C2D113⋊#13112yes—
subgroupG/H
center, FrattiniC22C23×#90673
commutator, socleC22×C113C23×C4
Fitting#123×C113C4
prime radical#20299106C2
cosocleC2×Dic113C24
hypercenter#123#90673
hypocenterC113#2977
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #20299630C2semidirect
2. #20299628C2semidirect
3. #20299626C2semidirect
4. #20299625C2semidirect
5. #20299622C2semidirect
6. #20299572C2semidirect
7. #20299571C2semidirect
8. #20299566C2semidirect
10. C2×#14268657C22semidirect
11. C2×#14268656C22semidirect
14. C2×#14268655C22semidirect
15. C22×#11744753C22semidirect
16. #16813689C22semidirect
17. C4⋊#11744753C22semidirect
20. #16813679C22semidirect
23. C22⋊#11744753C22semidirect
24. #16813677C22semidirect
25. C4×#11744753C22semidirect
133. C113#2977semidirect

Maximal subgroups

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

subgroupindex
#202996302
#202996282
#202996262
#202996252
#202996222
#202995722
#202995712
#202995662
#202991062
#2977113