Finite Group Databasebeta

← #28401542

Subgroups — #28401542

Order 14464.

410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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#20299134C211yesmaximal, characteristic, complemented
2C2×#16813609C211yesmaximal, characteristic, complemented
3#20298979C212yesmaximal, complemented
4#20298951C212yesmaximal, complemented
5#20298818C212yesmaximal, complemented
6#20298812C212yesmaximal, complemented
7#20298753C211yesmaximal, characteristic, complemented
8#20298739C211yesmaximal, characteristic, complemented
9#20298732C211yesmaximal, characteristic
10#20298648C211yesmaximal, characteristic, complemented
11#450×C113C211yesmaximal, characteristic, complemented
12C22×Dic226C2211yescharacteristic
13C2×#14268637C2212yescomplemented
14C2×#14268636C2212yescomplemented
15C2×#14268632C2212yes—
16#16813617—21no—
17#16813613C2211yescharacteristic, complemented
18#16813611C2211yescharacteristic, complemented
19#16813609—21no—
20#16813609—21no—
21#16813609C2212yes—
22#16813609C2212yes—
23#16813606—21no—
24#16813596C2211yescharacteristic
25Q8×Dic113C2211yescharacteristic, complemented
26#16813584C2211yescharacteristic, complemented
27#16813582—21no—
28#16813580—21no—
29C2×C22⋊Dic113—21no—
30C2×C22⋊Dic113—21no—
31C2×C4×Dic113C2211yescharacteristic
32#16813551C2212yescomplemented
33#16813547C2212yescomplemented
34#16813545C2212yescomplemented
35#16813543C2212yes—
36C22⋊#11744751C2211yescharacteristic
37C8×Dic113C2212yescomplemented
38C22×D4×C113C2211yescharacteristic
39C2×SD16×C113C2212yes—
40C22⋊Q8×C113C2211yescharacteristic
41#102×C113C2212yes—
42C22⋊C8×C113C2211yescharacteristic
43C2×Dic226—21no—
44C2×Dic226—42no—
45C2×Dic226C2312yes—
46C2×D452C2311yescharacteristic
47C2×C22⋊D113—21no—
48C22×Dic113—21no—
49C22×Dic113D411yescharacteristic
50C22×Dic113D411yescharacteristic
51C2×C4×D113—21no—
52#14268637—42no—
53#14268636—42no—
54#14268632—42no—
55C2×#11744751C2312yes—
56C4⋊Dic113—21no—
57C4⋊Dic113—21no—
58C4⋊Dic113C2311yescharacteristic
59#14268626—21no—
60C22⋊Dic113—22no—
61C22⋊Dic113—22no—
62C22⋊Dic113—22no—
63C22⋊Dic113—22no—
64#14268624—21no—
65#14268624—21no—
66#14268624—21no—
67#14268624—21no—
68C4×Dic113—21no—
69C4×Dic113D411yescharacteristic
70C4×Dic113D411yescharacteristic
71C4×Dic113C2311yescharacteristic
72C4×Dic113C2311yescharacteristic
73C24×C113—21no—
74C2×Q8×C113C2311yescharacteristic
75C2×D4×C113—21no—
76C2×D4×C113—42no—
77C2×D4×C113C2312yes—
78C22×C4×C113C2311yescharacteristic
79SD16×C113—42no—
80C2×C8×C113C2312yes—
81C4⋊C4×C113—21no—
82C4⋊C4×C113C2311yescharacteristic
83C22⋊C4×C113—21no—
84C23×C113—22no—
85C23×C113—42no—
86C23×C113—42no—
87C23×C113—42no—
88C23×C113C2×D411yescharacteristic
89C22×D113—21no—
90Q8×C113—22no—
91D4×C113—22no—
92D4×C113—22no—
93D4×C113—42no—
94C2×C4×C113—22no—
95C2×C4×C113—21no—
96C2×C4×C113—21no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2411yescharacteristic
99C22⋊D113—42no—
100C2×Dic113—22no—
101C2×Dic113—21no—
102C2×Dic113—22no—
103C2×Dic113—41no—
104C2×Dic113—42no—
105C2×Dic113C2×D411yescharacteristic
106C2×Dic113C2×D411yescharacteristic
107C2×Dic113C2×D411yescharacteristic
108C2×Dic113C2×D411yescharacteristic
109D452—22no—
110C4×D113—42no—
111Dic226—22no—
112Dic226—22no—
113Dic226—42no—
114C8×C113—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—41no—
129C4×C113—41no—
130C4×C113H(5,𝔽2)12yes—
131Dic113—21no—
132Dic113—21no—
133Dic113—21no—
134Dic113—21no—
135Dic113—42no—
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×#124—1131no—
147#495—1132no—
148#488—1132no—
149#464—1132no—
150#463—1132no—
151#451—1131no—
152#450D11311yescharacteristic, complemented
153#448—1131no—
154#447—1131no—
155#431—1131no—
156C22×Q8—1131no—
157C22×D4C2×D11311yescharacteristic
158C2×Q16—1132no—
159C2×SD16—1132no—
160C2×SD16C2×D11312yes—
161C2×D8—1132no—
162#126—2261no—
163#125—1131no—
164#124—1131no—
165#124—1132no—
166#124—1132no—
167#124—2261no—
168#124—2261no—
169#123—2261no—
170C22⋊Q8C2×D11311yescharacteristic
171#121—1131no—
172C4×Q8—1131no—
173C4×D4—1131no—
174C4×D4—2261no—
175#117—2261no—
176C2×C22⋊C4—2261no—
177C2×C22⋊C4—2261no—
178C2×C42—1131no—
179C4⋊C8—1132no—
180#103—1132no—
181#103—1132no—
182#102—1132no—
183#102C2×D11312yes—
184C22⋊C8—1131no—
185C22⋊C8C2×D11311yescharacteristic
186C4×C8—1132no—
187C24—21no—
188C2×Q8—1132no—
189C2×Q8—4522no—
190C2×Q8—2261no—
191C2×Q8C22×D11311yescharacteristic
192C2×D4—21no—
193C2×D4—42no—
194C2×D4—1131no—
195C2×D4—2261no—
196C2×D4C22×D11312yes—
197C22×C4—1131no—
198C22×C4—1131no—
199C22×C4—2261no—
200C22×C4—2261no—
201C22×C4C22×D11311yescharacteristic
202Q16—4522no—
203SD16—42no—
204SD16—4522no—
205D8—4522no—
206C2×C8—1132no—
207C2×C8C22×D11312yes—
208C4⋊C4—21no—
209C4⋊C4—1131no—
210C4⋊C4—2261no—
211C4⋊C4—2261no—
212C4⋊C4—2261no—
213C4⋊C4C22×D11311yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—2261no—
216C22⋊C4—2261no—
217C22⋊C4—2261no—
218C22⋊C4—2262no—
219C22⋊C4—2262no—
220C22⋊C4—2262no—
221C22⋊C4—2262no—
222C22⋊C4—2261no—
223C42—1131no—
224C42—1131no—
225C42—1131no—
226C42—1131no—
227C42—2261no—
228C23—22no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—2261no—
233C23D4×D11311yescharacteristic
234Q8—22no—
235Q8—4522no—
236Q8—2262no—
237Q8—2262no—
238D4—22no—
239D4—22no—
240D4—42no—
241D4—4522no—
242D4—2262no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—1131no—
247C2×C4—1131no—
248C2×C4—1131no—
249C2×C4—1131no—
250C2×C4—4522no—
251C2×C4—4522no—
252C2×C4—4521no—
253C2×C4—2261no—
254C2×C4—2262no—
255C2×C4—2262no—
256C2×C4D4×D11311yescharacteristic
257C2×C4C23×D11311yescharacteristic
258C8—22no—
259C8—2262no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—4521no—
267C22—4521no—
268C22—4521no—
269C22#1681364312yes—
270C22C2×D4×D11311yescharacteristic
271C4—21no—
272C4—41no—
273C4—41no—
274C4—4521no—
275C4—4522no—
276C4—2261no—
277C4—2261no—
278C4—2261no—
279C4—2261no—
280C4#1681366712yes—
281C2—22no—
282C2—82no—
283C2—9041no—
284C2#2029916311yescharacteristic
285C2C2×#1681364311yescharacteristic
286C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
prime radical#20298732C2
hypercenter#450D113
hypocenterC113#3211
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #20299134C2semidirect
2. C2×#16813609C2semidirect
3. #20298979C2semidirect
4. #20298951C2semidirect
5. #20298818C2semidirect
6. #20298812C2semidirect
7. #20298753C2semidirect
8. #20298739C2semidirect
10. #20298648C2semidirect
11. #450×C113C2semidirect
13. C2×#14268637C22semidirect
14. C2×#14268636C22semidirect
17. #16813613C22semidirect
18. #16813611C22semidirect
25. Q8×Dic113C22semidirect
26. #16813584C22semidirect
32. #16813551C22semidirect
33. #16813547C22semidirect
34. #16813545C22semidirect
37. C8×Dic113C22semidirect
144. C113#3211semidirect
152. #450D113semidirect

Maximal subgroups

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

subgroupindex
#202991342
C2×#168136092
#202989792
#202989512
#202988182
#202988122
#202987532
#202987392
#202987322
#202986482
#450×C1132
#3211113