Finite Group Databasebeta

← #28401539

Subgroups — #28401539

Order 14464.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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#20299132C211yesmaximal, characteristic, complemented
2#20298980C212yesmaximal, complemented
3#20298952C212yesmaximal, complemented
4#20298817C212yesmaximal, complemented
5#20298810C212yesmaximal, complemented
6#20298754C211yesmaximal, characteristic, complemented
7#20298749C211yesmaximal, characteristic, complemented
8#20298737C211yesmaximal, characteristic, complemented
9#20298732C211yesmaximal, characteristic
10#20298651C211yesmaximal, characteristic, complemented
11C2×#124×C113C211yesmaximal, characteristic, complemented
12C2×#14268637C2212yescomplemented
13C2×#14268635C2212yes—
14C2×#14268634C2212yescomplemented
15C2×#14268632C2212yes—
16#16813616—21no—
17#16813614C2211yescharacteristic, complemented
18#16813610C2211yescharacteristic, complemented
19#16813605—21no—
20#16813601C2211yescharacteristic
21#16813596C2211yescharacteristic
22C4×Dic226C2211yescharacteristic, complemented
23C4×D452C2211yescharacteristic, complemented
24C4×C22⋊D113—21no—
25#16813579—21no—
26C4⋊#11744751C2212yescomplemented
27#16813546C2212yescomplemented
28#16813546C2212yescomplemented
29#16813543C2212yes—
30#16813543C2212yes—
31C22⋊#11744751C2211yescharacteristic
32C22⋊#11744751C2211yescharacteristic
33C4×#11744751C2212yescomplemented
34C22×Q8×C113C2211yescharacteristic
35C22×D4×C113C2211yescharacteristic
36#124×C113—21no—
37#124×C113—21no—
38#124×C113C2212yes—
39#124×C113C2212yes—
40C2×C22⋊C4×C113—21no—
41C2×C22⋊C4×C113—21no—
42C2×C42×C113C2211yescharacteristic
43C2×Dic226C2311yescharacteristic
44C2×D452C2311yescharacteristic
45C2×C22⋊D113—21no—
46C2×C4×D113—21no—
47#14268637—42no—
48#14268635—42no—
49#14268634—42no—
50#14268632—42no—
51C2×#11744751C2312yes—
52C2×#11744751C2312yes—
53C4⋊Dic113C2311yescharacteristic
54C4⋊Dic113C2311yescharacteristic
55#14268626—21no—
56#14268626—21no—
57#14268626—21no—
58#14268626—21no—
59C22⋊Dic113—21no—
60#14268624—21no—
61#14268624—21no—
62#14268624—21no—
63#14268624—21no—
64C4×Dic113—21no—
65C24×C113—21no—
66C2×Q8×C113—21no—
67C2×Q8×C113—42no—
68C2×Q8×C113C2312yes—
69C2×D4×C113—21no—
70C2×D4×C113—42no—
71C2×D4×C113C2312yes—
72C22×C4×C113—21no—
73C22×C4×C113D411yescharacteristic
74C22×C4×C113D411yescharacteristic
75C22×C4×C113C2311yescharacteristic
76C22⋊C4×C113—22no—
77C22⋊C4×C113—22no—
78C22⋊C4×C113—22no—
79C22⋊C4×C113—22no—
80C42×C113D411yescharacteristic
81C42×C113D411yescharacteristic
82C42×C113C2311yescharacteristic
83C42×C113C2311yescharacteristic
84C23×C113—22no—
85C23×C113—42no—
86C23×C113—42no—
87C23×C113—42no—
88C23×C113C2×D411yescharacteristic
89C22×D113—21no—
90Q8×C113—22no—
91Q8×C113—22no—
92Q8×C113—42no—
93D4×C113—22no—
94D4×C113—22no—
95D4×C113—42no—
96C2×C4×C113—22no—
97C2×C4×C113—22no—
98C2×C4×C113—22no—
99C2×C4×C113—41no—
100C2×C4×C113—42no—
101C2×C4×C113C2×D411yescharacteristic
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113C2×D411yescharacteristic
104C2×C4×C113C2×D411yescharacteristic
105C2×C4×C113C2×D411yescharacteristic
106C2×C4×C113C2411yescharacteristic
107C22⋊D113—42no—
108C2×Dic113—21no—
109C2×Dic113—21no—
110C2×Dic113—21no—
111D452—22no—
112C4×D113—42no—
113Dic226—22no—
114#11744751—22no—
115#11744751—22no—
116C22×C113—21no—
117C22×C113—21no—
118C22×C113—42no—
119C22×C113—42no—
120C22×C113—42no—
121C22×C113—84no—
122C22×C113#13512yes—
123C22×C113C22×D411yescharacteristic
124C2×D113—41no—
125C2×D113—41no—
126C2×D113—41no—
127C4×C113—21no—
128C4×C113—21no—
129C4×C113—21no—
130C4×C113—21no—
131C4×C113—21no—
132C4×C113—42no—
133C4×C113H(5,𝔽2)12yes—
134Dic113—41no—
135Dic113—41no—
136Dic113—41no—
137C2×C113—22no—
138C2×C113—82no—
139C2×C113#53511yescharacteristic
140C2×C113C2×#13511yescharacteristic
141C2×C113#57511yescharacteristic
142D113—81no—
143#3211—1131nomaximal, Sylow
144C113#321111yescharacteristic, complemented, Sylow
145#529—1131no—
146C2×#124D11311yescharacteristic, complemented
147#495—1132no—
148#488—1132no—
149#464—1132no—
150#463—1132no—
151#451—1131no—
152#450—1131no—
153#448—1131no—
154#447—1131no—
155#431—1131no—
156C22×Q8C2×D11311yescharacteristic
157C22×D4C2×D11311yescharacteristic
158C2×Q16—1132no—
159C2×SD16—1132no—
160C2×SD16—1132no—
161C2×D8—1132no—
162#126—2261no—
163#125—1131no—
164#124—21no—
165#124—21no—
166#124—1131no—
167#124C2×D11312yes—
168#124C2×D11312yes—
169#123—2261no—
170C22⋊Q8—1131no—
171#121—1131no—
172C4×Q8—1131no—
173C4×D4—1131no—
174C4×D4—2261no—
175#117—2261no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C42C2×D11311yescharacteristic
179C4⋊C8—1132no—
180#103—1132no—
181#103—1132no—
182#102—1132no—
183#102—1132no—
184C22⋊C8—1131no—
185C22⋊C8—1131no—
186C4×C8—1132no—
187C24—21no—
188C2×Q8—21no—
189C2×Q8—42no—
190C2×Q8—1131no—
191C2×Q8C22×D11312yes—
192C2×D4—21no—
193C2×D4—42no—
194C2×D4—1131no—
195C2×D4—2261no—
196C2×D4C22×D11312yes—
197C22×C4—21no—
198C22×C4—2261no—
199C22×C4C22⋊D11311yescharacteristic
200C22×C4C22⋊D11311yescharacteristic
201C22×C4C22×D11311yescharacteristic
202Q16—4522no—
203SD16—4522no—
204SD16—4522no—
205D8—4522no—
206C2×C8—1132no—
207C2×C8—1132no—
208C4⋊C4—1131no—
209C4⋊C4—1131no—
210C4⋊C4—2261no—
211C4⋊C4—2261no—
212C4⋊C4—2261no—
213C4⋊C4—2261no—
214C22⋊C4—22no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—2261no—
219C22⋊C4—2261no—
220C22⋊C4—2261no—
221C22⋊C4—2261no—
222C22⋊C4—2261no—
223C42—2261no—
224C42C22⋊D11311yescharacteristic
225C42C22⋊D11311yescharacteristic
226C42C22×D11311yescharacteristic
227C42C22×D11311yescharacteristic
228C23—22no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—2261no—
233C23C2×C22⋊D11311yescharacteristic
234Q8—22no—
235Q8—22no—
236Q8—42no—
237Q8—2262no—
238D4—22no—
239D4—22no—
240D4—42no—
241D4—4522no—
242D4—2262no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—4522no—
249C2×C4—2261no—
250C2×C4—2261no—
251C2×C4—2261no—
252C2×C4C2×C22⋊D11311yescharacteristic
253C2×C4C2×C22⋊D11311yescharacteristic
254C2×C4C2×C22⋊D11311yescharacteristic
255C2×C4C2×C22⋊D11311yescharacteristic
256C2×C4C2×C22⋊D11311yescharacteristic
257C2×C4C23×D11311yescharacteristic
258C8—2262no—
259C8—2262no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—4521no—
267C22—4521no—
268C22—4521no—
269C22#1681364212yes—
270C22C22×C22⋊D11311yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—42no—
277C4—4521no—
278C4—4521no—
279C4—4521no—
280C4#1681366712yes—
281C2—22no—
282C2—82no—
283C2—9041no—
284C2#2029916511yescharacteristic
285C2C2×#1681364211yescharacteristic
286C2#2029939611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#124×C113C2
socleC22×C113C22×D4
prime radical#20298732C2
hypercenterC2×#124D113
hypocenterC113#3211
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #20299132C2semidirect
2. #20298980C2semidirect
3. #20298952C2semidirect
4. #20298817C2semidirect
5. #20298810C2semidirect
6. #20298754C2semidirect
7. #20298749C2semidirect
8. #20298737C2semidirect
10. #20298651C2semidirect
11. C2×#124×C113C2semidirect
12. C2×#14268637C22semidirect
14. C2×#14268634C22semidirect
17. #16813614C22semidirect
18. #16813610C22semidirect
22. C4×Dic226C22semidirect
23. C4×D452C22semidirect
26. C4⋊#11744751C22semidirect
27. #16813546C22semidirect
28. #16813546C22semidirect
33. C4×#11744751C22semidirect
144. C113#3211semidirect
146. C2×#124D113semidirect

Maximal subgroups

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

subgroupindex
#202991322
#202989802
#202989522
#202988172
#202988102
#202987542
#202987492
#202987372
#202987322
#202986512
C2×#124×C1132
#3211113