Finite Group Databasebeta

← #28401538

Subgroups — #28401538

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#20299129C211yesmaximal, characteristic, complemented
2C2×#16813611C211yesmaximal, characteristic, complemented
3#20298979C212yesmaximal, complemented
4#20298954C212yesmaximal, complemented
5#20298823C212yesmaximal, complemented
6#20298815C212yesmaximal, complemented
7#20298754C211yesmaximal, characteristic, complemented
8#20298751C211yesmaximal, characteristic, complemented
9#20298731C211yesmaximal, characteristic
10#20298648C211yesmaximal, characteristic, complemented
11#448×C113C211yesmaximal, characteristic, complemented
12C22×D452C2211yescharacteristic
13C2×#14268637C2212yescomplemented
14C2×#14268636C2212yes—
15C2×#14268632C2212yes—
16#16813615—21no—
17#16813613C2211yescharacteristic, complemented
18#16813611—21no—
19#16813611—21no—
20#16813611C2212yes—
21#16813611C2212yes—
22#16813609C2211yescharacteristic, complemented
23#16813603—21no—
24#16813601C2211yescharacteristic
25#16813587C2211yescharacteristic, complemented
26D4×Dic113—21no—
27D4×Dic113C2211yescharacteristic, complemented
28#16813578—21no—
29C2×#14268624—21no—
30C2×#14268624—21no—
31C2×C4×Dic113C2211yescharacteristic
32#16813551C2212yescomplemented
33#16813546C2212yescomplemented
34#16813544C2212yes—
35#16813542C2212yes—
36C22⋊#11744751C2211yescharacteristic
37C8×Dic113C2212yescomplemented
38C22×Q8×C113C2211yescharacteristic
39C2×SD16×C113C2212yescomplemented
40#121×C113C2211yescharacteristic
41#103×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113—21no—
44C2×Dic226C2311yescharacteristic
45C2×D452—21no—
46C2×D452—42no—
47C2×D452C2312yes—
48C22×Dic113—21no—
49C22×Dic113D411yescharacteristic
50C22×Dic113D411yescharacteristic
51#14268637—42no—
52#14268636—42no—
53#14268632—42no—
54C2×#11744751C2312yes—
55C4⋊Dic113—21no—
56C4⋊Dic113C2311yescharacteristic
57#14268626—21no—
58#14268626—21no—
59#14268626—21no—
60C22⋊Dic113—21no—
61C22⋊Dic113—21no—
62C22⋊Dic113—21no—
63C22⋊Dic113—21no—
64#14268624—22no—
65#14268624—22no—
66#14268624—22no—
67#14268624—22no—
68C4×Dic113—21no—
69C4×Dic113D411yescharacteristic
70C4×Dic113D411yescharacteristic
71C4×Dic113C2311yescharacteristic
72C4×Dic113C2311yescharacteristic
73C2×Q8×C113—21no—
74C2×Q8×C113—42no—
75C2×Q8×C113C2312yes—
76C2×D4×C113—21no—
77C2×D4×C113C2311yescharacteristic
78C22×C4×C113—21no—
79C22×C4×C113C2311yescharacteristic
80SD16×C113—42no—
81C2×C8×C113C2312yes—
82C4⋊C4×C113C2311yescharacteristic
83C22⋊C4×C113—21no—
84C23×C113—21no—
85C23×C113C2×D411yescharacteristic
86C22×D113—22no—
87C22×D113—42no—
88C22×D113—42no—
89C22×D113—42no—
90Q8×C113—22no—
91Q8×C113—22no—
92Q8×C113—42no—
93D4×C113—22no—
94D4×C113—42no—
95C2×C4×C113—22no—
96C2×C4×C113—21no—
97C2×C4×C113—22no—
98C2×C4×C113—42no—
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2411yescharacteristic
101C2×Dic113—22no—
102C2×Dic113—21no—
103C2×Dic113—21no—
104C2×Dic113—41no—
105C2×Dic113—42no—
106C2×Dic113C2×D411yescharacteristic
107C2×Dic113C2×D411yescharacteristic
108C2×Dic113C2×D411yescharacteristic
109C2×Dic113C2×D411yescharacteristic
110D452—22no—
111D452—22no—
112D452—42no—
113Dic226—22no—
114C8×C113—22no—
115#11744751—22no—
116C22×C113—21no—
117C22×C113—21no—
118C22×C113—41no—
119C22×C113—41no—
120C22×C113—41no—
121C22×C113#13512yes—
122C22×C113C22×D411yescharacteristic
123C2×D113—42no—
124C2×D113—42no—
125C2×D113—42no—
126C2×D113—84no—
127C4×C113—21no—
128C4×C113—42no—
129C4×C113—41no—
130C4×C113H(5,𝔽2)12yes—
131Dic113—21no—
132Dic113—21no—
133Dic113—21no—
134Dic113—21no—
135Dic113—41no—
136Dic113—41no—
137C2×C113—22no—
138C2×C113—81no—
139C2×C113#53511yescharacteristic
140C2×C113C2×#13511yescharacteristic
141C2×C113#57511yescharacteristic
142D113—82no—
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#450—1131no—
153#448D11311yescharacteristic, complemented
154#447—1131no—
155#431—1131no—
156C22×Q8C2×D11311yescharacteristic
157C22×D4—1131no—
158C2×Q16—1132no—
159C2×SD16—1132no—
160C2×SD16C2×D11312yescomplemented
161C2×D8—1132no—
162#126—2261no—
163#125—1131no—
164#124—1132no—
165#124—1132no—
166#124—1131no—
167#124—2261no—
168#124—2261no—
169#123—2261no—
170C22⋊Q8—1131no—
171#121C2×D11311yescharacteristic
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#103C2×D11312yescomplemented
182#102—1132no—
183#102—1132no—
184C22⋊C8—1131no—
185C22⋊C8C2×D11311yescharacteristic
186C4×C8—1132no—
187C24—2261no—
188C2×Q8—21no—
189C2×Q8—42no—
190C2×Q8—1131no—
191C2×Q8C22×D11312yes—
192C2×D4—21no—
193C2×D4—1132no—
194C2×D4—4522no—
195C2×D4—2261no—
196C2×D4C22×D11311yescharacteristic
197C22×C4—21no—
198C22×C4—1131no—
199C22×C4—1131no—
200C22×C4—2261no—
201C22×C4C22×D11311yescharacteristic
202Q16—4522no—
203SD16—42no—
204SD16—4522no—
205D8—4522no—
206C2×C8—1132no—
207C2×C8C22×D11312yes—
208C4⋊C4—1131no—
209C4⋊C4—2261no—
210C4⋊C4—2261no—
211C4⋊C4—2261no—
212C4⋊C4—2261no—
213C4⋊C4C22×D11311yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—2262no—
216C22⋊C4—2262no—
217C22⋊C4—2262no—
218C22⋊C4—2262no—
219C22⋊C4—2261no—
220C22⋊C4—2261no—
221C22⋊C4—2261no—
222C22⋊C4—2261no—
223C42—1131no—
224C42—1131no—
225C42—1131no—
226C42—1131no—
227C42—2261no—
228C23—21no—
229C23—4522no—
230C23—4522no—
231C23—4522no—
232C23—2262no—
233C23D4×D11311yescharacteristic
234Q8—22no—
235Q8—22no—
236Q8—42no—
237Q8—2262no—
238D4—22no—
239D4—42no—
240D4—4522no—
241D4—2262no—
242D4—2262no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—1131no—
248C2×C4—1131no—
249C2×C4—1131no—
250C2×C4—1131no—
251C2×C4—4522no—
252C2×C4—4521no—
253C2×C4—2261no—
254C2×C4—2261no—
255C2×C4—2262no—
256C2×C4D4×D11311yescharacteristic
257C2×C4C23×D11311yescharacteristic
258C8—22no—
259C8—2262no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—9044no—
266C22—4522no—
267C22—4522no—
268C22—4522no—
269C22#1681364312yes—
270C22C2×D4×D11311yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—4521no—
275C4—4521no—
276C4—2261no—
277C4—2261no—
278C4—2261no—
279C4—2261no—
280C4#1681366712yes—
281C2—22no—
282C2—81no—
283C2—9042no—
284C2#2029916311yescharacteristic
285C2C2×#1681364311yescharacteristic
286C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#448×C113C2
socleC22×C113C22×D4
prime radical#20298731C2
hypercenter#448D113
hypocenterC113#3211
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #20299129C2semidirect
2. C2×#16813611C2semidirect
3. #20298979C2semidirect
4. #20298954C2semidirect
5. #20298823C2semidirect
6. #20298815C2semidirect
7. #20298754C2semidirect
8. #20298751C2semidirect
10. #20298648C2semidirect
11. #448×C113C2semidirect
13. C2×#14268637C22semidirect
17. #16813613C22semidirect
22. #16813609C22semidirect
25. #16813587C22semidirect
27. D4×Dic113C22semidirect
32. #16813551C22semidirect
33. #16813546C22semidirect
37. C8×Dic113C22semidirect
39. C2×SD16×C113C22semidirect
41. #103×C113C22semidirect
144. C113#3211semidirect
153. #448D113semidirect
160. C2×SD16C2×D113semidirect
181. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991292
C2×#168136112
#202989792
#202989542
#202988232
#202988152
#202987542
#202987512
#202987312
#202986482
#448×C1132
#3211113