Finite Group Databasebeta

← #28401357

Subgroups — #28401357

Order 14464.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299109C211yesmaximal, characteristic
2C2×#16813601C211yesmaximal, characteristic, complemented
3#20298940C212yesmaximal, complemented
4#20298929C211yesmaximal, characteristic, complemented
5#20298912C211yesmaximal, characteristic, complemented
6#20298839C212yesmaximal, complemented
7#20298827C212yesmaximal, complemented
8#20298762C212yesmaximal, complemented
9#20298756C211yesmaximal, characteristic, complemented
10#20298739C211yesmaximal, characteristic, complemented
11C2×C22⋊C8×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×Dic226C2211yescharacteristic
14C2×Dic452C2212yescomplemented
15C2×#14268636C2212yescomplemented
16#16813605—21no—
17#16813601—21no—
18#16813601—21no—
19#16813601C2211yescharacteristic
20#16813601C2212yes—
21#16813601C2212yes—
22#16813601C2211yescharacteristic
23#16813596C2211yescharacteristic
24#16813596C2211yescharacteristic
25#16813591—21no—
26C4×C22⋊D113—21no—
27C4×C22⋊D113—21no—
28#16813581C2211yescharacteristic
29C2×C4⋊Dic113C2211yescharacteristic
30C2×#14268626—21no—
31C2×C22⋊Dic113—21no—
32#16813556C2212yescomplemented
33#16813554C2212yescomplemented
34#16813547C2212yescomplemented
35#16813547C2212yescomplemented
36#16813547C2212yescomplemented
37#16813544C2212yescomplemented
38C23×C4×C113C2211yescharacteristic
39C22×C8×C113C2212yes—
40C22⋊C8×C113C2211yescharacteristic
41C22⋊C8×C113C2212yes—
42C22⋊C8×C113C2211yescharacteristic
43#14268647—42no—
44C2×Dic226—21no—
45C2×Dic226—42no—
46C2×Dic226C2312yes—
47C2×Dic226C2311yescharacteristic
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—21no—
50C2×C22⋊D113—21no—
51C2×C22⋊D113—21no—
52C22×Dic113—21no—
53C22×Dic113—21no—
54C2×C4×D113—21no—
55Dic452—42no—
56#14268636—42no—
57C4⋊Dic113—21no—
58C4⋊Dic113C2312yes—
59C4⋊Dic113C2311yescharacteristic
60C4⋊Dic113C2311yescharacteristic
61#14268626—22no—
62#14268626—22no—
63#14268626—21no—
64#14268626—21no—
65C22⋊Dic113—22no—
66C22⋊Dic113—22no—
67C22⋊Dic113—21no—
68C22⋊Dic113—21no—
69C22⋊Dic113—21no—
70#14268624—21no—
71#14268624—21no—
72C4×Dic113—21no—
73C24×C113D411yescharacteristic
74C22×C4×C113—42no—
75C22×C4×C113D411yescharacteristic
76C22×C4×C113D411yescharacteristic
77C22×C4×C113D411yescharacteristic
78C22×C4×C113C2311yescharacteristic
79C22×C4×C113C2311yescharacteristic
80C22×C4×C113C2311yescharacteristic
81C2×C8×C113—42no—
82C2×C8×C113C2312yes—
83C2×C8×C113C2312yes—
84C23×C113—22no—
85C23×C113—22no—
86C23×C113—41no—
87C23×C113C2×D411yescharacteristic
88C23×C113C2×D411yescharacteristic
89C23×C113C2×D411yescharacteristic
90C22×D113—21no—
91C2×C4×C113—22no—
92C2×C4×C113—22no—
93C2×C4×C113—22no—
94C2×C4×C113—41no—
95C2×C4×C113—41no—
96C2×C4×C113—41no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2411yescharacteristic
101C22⋊D113—42no—
102C22⋊D113—42no—
103C22⋊D113—42no—
104C2×Dic113—21no—
105C2×Dic113—21no—
106C2×Dic113—22no—
107C2×Dic113—21no—
108C2×Dic113—22no—
109C2×Dic113—42no—
110C2×Dic113—42no—
111D452—22no—
112C4×D113—42no—
113Dic226—22no—
114Dic226—22no—
115Dic226—22no—
116Dic226—42no—
117C8×C113—22no—
118C8×C113—22no—
119C22×C113—21no—
120C22×C113—21no—
121C22×C113—21no—
122C22×C113—21no—
123C22×C113—21no—
124C22×C113—21no—
125C22×C113—21no—
126C22×C113—44no—
127C22×C113#13512yes—
128C22×C113#13712yes—
129C22×C113C22×D411yescharacteristic
130C2×D113—41no—
131C2×D113—41no—
132C2×D113—41no—
133C4×C113—21no—
134C4×C113—21no—
135C4×C113—21no—
136C4×C113H(5,𝔽2)12yes—
137Dic113—42no—
138Dic113—41no—
139Dic113—42no—
140Dic113—41no—
141Dic113—41no—
142C2×C113—22no—
143C2×C113—22no—
144C2×C113—41no—
145C2×C113#53411yescharacteristic
146C2×C113C2×#13511yescharacteristic
147C2×C113C2×#13711yescharacteristic
148D113—81no—
149#3190—1131nomaximal, Sylow
150C113#319011yescharacteristic, complemented, Sylow
151#525—1131no—
152C2×C22⋊Q8—1131no—
153#485—1132no—
154#483—1131no—
155#480—1131no—
156#467—1132no—
157#465—1132no—
158#452—1132no—
159#451—1131no—
160#448—1131no—
161C2×C22⋊C8D11311yescharacteristic, complemented
162C2×#41—1131no—
163C22×Q8—1131no—
164C23×C4C2×D11311yescharacteristic
165C2×Q16—1132no—
166C2×SD16—1132no—
167C22×C8C2×D11312yes—
168#123—2261no—
169C22⋊Q8—1132no—
170C22⋊Q8—1132no—
171C22⋊Q8—1131no—
172C22⋊Q8—1131no—
173C22⋊Q8—2261no—
174C22⋊Q8—2261no—
175#121—1131no—
176#121—1131no—
177#120—2261no—
178C4×D4—2261no—
179C4×D4—2261no—
180#117—1131no—
181C2×C4⋊C4—1131no—
182C2×C4⋊C4—2261no—
183C2×C22⋊C4—2261no—
184#107—1132no—
185#106—1132no—
186#103—1132no—
187#103—1132no—
188#103—1132no—
189#102—1132no—
190C22⋊C8C2×D11311yescharacteristic
191C22⋊C8C2×D11311yescharacteristic
192C22⋊C8C2×D11312yes—
193C24D45211yescharacteristic
194#41—4522no—
195C2×Q8—1132no—
196C2×Q8—1131no—
197C2×Q8—4522no—
198C2×Q8—2261no—
199C2×D4—1131no—
200C2×D4—2261no—
201C2×D4—2261no—
202C2×D4—2261no—
203C22×C4—42no—
204C22×C4—2261no—
205C22×C4—2261no—
206C22×C4—2261no—
207C22×C4D45211yescharacteristic
208C22×C4D45211yescharacteristic
209C22×C4D45211yescharacteristic
210C22×C4C22×D11311yescharacteristic
211C22×C4C22×D11311yescharacteristic
212C22×C4C22×D11311yescharacteristic
213Q16—4522no—
214SD16—4522no—
215C2×C8—42no—
216C2×C8C22×D11312yes—
217C2×C8C22×D11312yes—
218C4⋊C4—1132no—
219C4⋊C4—1131no—
220C4⋊C4—1131no—
221C4⋊C4—2261no—
222C4⋊C4—2262no—
223C4⋊C4—2262no—
224C4⋊C4—2261no—
225C4⋊C4—2261no—
226C22⋊C4—2262no—
227C22⋊C4—2262no—
228C22⋊C4—2261no—
229C22⋊C4—2261no—
230C22⋊C4—2261no—
231C22⋊C4—2261no—
232C22⋊C4—2261no—
233C42—2261no—
234C23—22no—
235C23—22no—
236C23—41no—
237C23—2261no—
238C23C2×D45211yescharacteristic
239C23C2×D45211yescharacteristic
240C23C2×D45211yescharacteristic
241Q8—4522no—
242Q8—2262no—
243Q8—2262no—
244Q8—2262no—
245D4—4522no—
246D4—4522no—
247D4—4522no—
248D4—2262no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—4522no—
256C2×C4—4522no—
257C2×C4—4522no—
258C2×C4—2261no—
259C2×C4—2261no—
260C2×C4—2262no—
261C2×C4—2261no—
262C2×C4—2262no—
263C2×C4C2×D45211yescharacteristic
264C2×C4C2×D45211yescharacteristic
265C2×C4C2×D45211yescharacteristic
266C2×C4C23×D11311yescharacteristic
267C8—22no—
268C8—22no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—44no—
277C22—4521no—
278C22—4521no—
279C22—4521no—
280C22#1681364412yes—
281C22#1681365512yes—
282C22C22×D45211yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—4522no—
287C4—4521no—
288C4—4521no—
289C4—4521no—
290C4—4522no—
291C4#1681366712yes—
292C2—22no—
293C2—22no—
294C2—41no—
295C2—9041no—
296C2#2029916011yescharacteristic
297C2C2×#1681364411yescharacteristic
298C2C2×#1681365511yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C22⋊C8×C113C2
socleC22×C113C22×D4
prime radical#20299109C2
hypercenterC2×C22⋊C8D113
hypocenterC113#3190
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16813601C2semidirect
3. #20298940C2semidirect
4. #20298929C2semidirect
5. #20298912C2semidirect
6. #20298839C2semidirect
7. #20298827C2semidirect
8. #20298762C2semidirect
9. #20298756C2semidirect
10. #20298739C2semidirect
11. C2×C22⋊C8×C113C2semidirect
14. C2×Dic452C22semidirect
15. C2×#14268636C22semidirect
32. #16813556C22semidirect
33. #16813554C22semidirect
34. #16813547C22semidirect
35. #16813547C22semidirect
36. #16813547C22semidirect
37. #16813544C22semidirect
150. C113#3190semidirect
161. C2×C22⋊C8D113semidirect

Maximal subgroups

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

subgroupindex
#202991092
C2×#168136012
#202989402
#202989292
#202989122
#202988392
#202988272
#202987622
#202987562
#202987392
C2×C22⋊C8×C1132
#3190113