Finite Group Databasebeta

← #28401558

Subgroups — #28401558

Order 14464.

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

normal subgroups only

This group has 444 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#20299143C211yesmaximal, characteristic, complemented
2C2×#16813609C211yesmaximal, characteristic, complemented
3#20298986C212yesmaximal, complemented
4#20298956C212yesmaximal, complemented
5#20298812C212yesmaximal, complemented
6#20298811C212yesmaximal, complemented
7#20298739C211yesmaximal, characteristic, complemented
8#20298736C211yesmaximal, characteristic, complemented
9#20298732C211yesmaximal, characteristic, complemented
10#20298652C211yesmaximal, characteristic, complemented
11#447×C113C211yesmaximal, characteristic, complemented
12C2×#14268646—21no—
13C22×Dic226C2211yescharacteristic
14C2×#14268636C2212yescomplemented
15C2×#14268635C2212yescomplemented
16C2×#14268632C2212yes—
17#16813621C2211yescharacteristic, complemented
18#16813618C2211yescharacteristic, complemented
19#16813609—21no—
20#16813609—21no—
21#16813609C2212yes—
22#16813609C2212yes—
23#16813608—21no—
24#16813596C2211yescharacteristic
25#16813594—21no—
26D4×Dic113C2211yescharacteristic, complemented
27#16813584C2211yescharacteristic, complemented
28#16813582—21no—
29C2×C22⋊Dic113—21no—
30C2×C22⋊Dic113—21no—
31C2×C4×Dic113C2211yescharacteristic
32#16813551C2212yescomplemented
33#16813547C2212yescomplemented
34#16813545C2212yescomplemented
35#16813543C2212yes—
36C22⋊#11744751C2211yescharacteristic
37#16813532C2212yescomplemented
38C22×D4×C113C2211yescharacteristic
39C2×D8×C113C2212yes—
40#121×C113C2211yescharacteristic
41#102×C113C2212yes—
42C22⋊C8×C113C2211yescharacteristic
43#14268646—44no—
44C2×Dic226—21no—
45C2×Dic226—21no—
46C2×Dic226—42no—
47C2×Dic226C2312yes—
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—21no—
50C2×C22⋊D113—21no—
51C2×C22⋊D113—21no—
52C22×Dic113—21no—
53C22×Dic113—21no—
54C22×Dic113D411yescharacteristic
55C22×Dic113D411yescharacteristic
56C2×C4×D113—21no—
57#14268636—42no—
58#14268635—42no—
59#14268632—42no—
60C2×#11744751C2312yes—
61C4⋊Dic113C2311yescharacteristic
62#14268626—21no—
63C22⋊Dic113—22no—
64C22⋊Dic113—22no—
65C22⋊Dic113—22no—
66C22⋊Dic113—22no—
67C22⋊Dic113—21no—
68#14268624—21no—
69#14268624—21no—
70C4×Dic113D411yescharacteristic
71C4×Dic113D411yescharacteristic
72C4×Dic113C2311yescharacteristic
73C4×Dic113C2311yescharacteristic
74C24×C113—21no—
75C2×D4×C113—21no—
76C2×D4×C113—21no—
77C2×D4×C113—42no—
78C2×D4×C113C2311yescharacteristic
79C2×D4×C113C2312yes—
80C22×C4×C113C2311yescharacteristic
81D8×C113—42no—
82C2×C8×C113C2312yes—
83C4⋊C4×C113C2311yescharacteristic
84C22⋊C4×C113—21no—
85C23×C113—21no—
86C23×C113—22no—
87C23×C113—42no—
88C23×C113—42no—
89C23×C113—42no—
90C23×C113C2×D411yescharacteristic
91C22×D113—21no—
92D4×C113—22no—
93D4×C113—22no—
94D4×C113—22no—
95D4×C113—42no—
96D4×C113—42no—
97C2×C4×C113—22no—
98C2×C4×C113—21no—
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2411yescharacteristic
101C22⋊D113—42no—
102C22⋊D113—42no—
103C22⋊D113—42no—
104C2×Dic113—22no—
105C2×Dic113—21no—
106C2×Dic113—22no—
107C2×Dic113—41no—
108C2×Dic113—42no—
109C2×Dic113—42no—
110C2×Dic113C2×D411yescharacteristic
111C2×Dic113C2×D411yescharacteristic
112C2×Dic113C2×D411yescharacteristic
113C2×Dic113C2×D411yescharacteristic
114D452—22no—
115C4×D113—42no—
116Dic226—22no—
117Dic226—22no—
118Dic226—42no—
119Dic226—42no—
120C8×C113—22no—
121#11744751—22no—
122C22×C113—21no—
123C22×C113—21no—
124C22×C113—42no—
125C22×C113—41no—
126C22×C113—41no—
127C22×C113—42no—
128C22×C113—41no—
129C22×C113—42no—
130C22×C113—84no—
131C22×C113AGL(1,ℤ/8)12yes—
132C22×C113C22×D411yescharacteristic
133C2×D113—41no—
134C2×D113—41no—
135C2×D113—41no—
136C4×C113—21no—
137C4×C113—41no—
138C4×C113H(5,𝔽2)12yes—
139Dic113—21no—
140Dic113—21no—
141Dic113—21no—
142Dic113—21no—
143Dic113—42no—
144Dic113—41no—
145C2×C113—22no—
146C2×C113—81no—
147C2×C113—82no—
148C2×C113#53511yescharacteristic
149C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
150C2×C113#57511yescharacteristic
151D113—81no—
152#3213—1131nomaximal, Sylow
153C113#321311yescharacteristic, complemented, Sylow
154#532—1131no—
155C2×#124—1131no—
156#496—1132no—
157#489—1132no—
158#463—1132no—
159#463—1132no—
160#448—1131no—
161#448—1131no—
162#447—1131no—
163#447D11311yescharacteristic, complemented
164#432—1131no—
165C2×#41—2261no—
166C22×Q8—1131no—
167C22×D4C2×D11311yescharacteristic
168C2×SD16—1132no—
169C2×SD16—1132no—
170C2×D8—1132no—
171C2×D8C2×D11312yes—
172C4⋊Q8—1131no—
173#127—1131no—
174#124—1132no—
175#124—1132no—
176#124—2261no—
177#124—2261no—
178#124—2261no—
179#121—1131no—
180#121—2261no—
181#121C2×D11311yescharacteristic
182C4×D4—1131no—
183C4×D4—1131no—
184C4×D4—2261no—
185C2×C22⋊C4—2261no—
186C2×C22⋊C4—2261no—
187C2×C42—1131no—
188C4⋊C8—1132no—
189#103—1132no—
190#103—1132no—
191#102—1132no—
192#102C2×D11312yes—
193C22⋊C8—1131no—
194C22⋊C8C2×D11311yescharacteristic
195#97—1132no—
196C24—21no—
197#41—4524no—
198C2×Q8—1132no—
199C2×Q8—4522no—
200C2×Q8—2261no—
201C2×Q8—2261no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—42no—
205C2×D4—1131no—
206C2×D4—2261no—
207C2×D4—2261no—
208C2×D4—2261no—
209C2×D4C22×D11312yes—
210C2×D4C22×D11311yescharacteristic
211C22×C4—1131no—
212C22×C4—1131no—
213C22×C4—2261no—
214C22×C4—2261no—
215C22×C4—2261no—
216C22×C4C22×D11311yescharacteristic
217SD16—4522no—
218SD16—4522no—
219D8—42no—
220D8—4522no—
221C2×C8—1132no—
222C2×C8C22×D11312yes—
223C4⋊C4—1131no—
224C4⋊C4—2261no—
225C4⋊C4C22×D11311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2261no—
228C22⋊C4—2262no—
229C22⋊C4—2262no—
230C22⋊C4—2262no—
231C22⋊C4—2262no—
232C22⋊C4—2261no—
233C22⋊C4—2261no—
234C42—1131no—
235C42—1131no—
236C42—1131no—
237C42—1131no—
238C23—21no—
239C23—22no—
240C23—42no—
241C23—42no—
242C23—42no—
243C23—2261no—
244C23D4×D11311yescharacteristic
245Q8—4522no—
246Q8—4522no—
247Q8—2262no—
248Q8—2262no—
249D4—22no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—42no—
254D4—4522no—
255D4—4522no—
256D4—4522no—
257D4—2262no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—1131no—
261C2×C4—1131no—
262C2×C4—1131no—
263C2×C4—1131no—
264C2×C4—4522no—
265C2×C4—4522no—
266C2×C4—4522no—
267C2×C4—4521no—
268C2×C4—2262no—
269C2×C4—2261no—
270C2×C4—2262no—
271C2×C4D4×D11311yescharacteristic
272C2×C4C23×D11311yescharacteristic
273C8—22no—
274C8—2262no—
275C22—21no—
276C22—21no—
277C22—41no—
278C22—42no—
279C22—41no—
280C22—42no—
281C22—42no—
282C22—41no—
283C22—84no—
284C22—4521no—
285C22—4521no—
286C22—4521no—
287C22#1681364612yes—
288C22C2×D4×D11311yescharacteristic
289C4—21no—
290C4—41no—
291C4—4521no—
292C4—4522no—
293C4—2261no—
294C4—2261no—
295C4—2261no—
296C4—2261no—
297C4#1681366712yes—
298C2—22no—
299C2—82no—
300C2—81no—
301C2—9041no—
302C2#2029916311yescharacteristic
303C2C2×#1681364611yescharacteristic
304C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113#3213
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20299143C2semidirect
2. C2×#16813609C2semidirect
3. #20298986C2semidirect
4. #20298956C2semidirect
5. #20298812C2semidirect
6. #20298811C2semidirect
7. #20298739C2semidirect
8. #20298736C2semidirect
9. #20298732C2semidirect
10. #20298652C2semidirect
11. #447×C113C2semidirect
14. C2×#14268636C22semidirect
15. C2×#14268635C22semidirect
17. #16813621C22semidirect
18. #16813618C22semidirect
26. D4×Dic113C22semidirect
27. #16813584C22semidirect
32. #16813551C22semidirect
33. #16813547C22semidirect
34. #16813545C22semidirect
37. #16813532C22semidirect
153. C113#3213semidirect
163. #447D113semidirect

Maximal subgroups

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

subgroupindex
#202991432
C2×#168136092
#202989862
#202989562
#202988122
#202988112
#202987392
#202987362
#202987322
#202986522
#447×C1132
#3213113