Finite Group Databasebeta

← #28400489

Subgroups — #28400489

Order 14464.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16813581C211yesmaximal, characteristic, complemented
3#20298940C212yesmaximal, complemented
4#20298934C211yesmaximal, characteristic, complemented
5#20298929C211yesmaximal, characteristic, complemented
6#20298923C212yesmaximal, complemented
7#20298917C211yesmaximal, characteristic, complemented
8#20298912C211yesmaximal, characteristic, complemented
9#20298636C212yesmaximal, complemented
10#20298595C212yesmaximal, complemented
11C2×C22⋊C8×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13#16813605—21no—
14#16813601C2211yescharacteristic
15#16813601C2211yescharacteristic
16#16813596C2211yescharacteristic
17#16813596C2211yescharacteristic
18#16813591—21no—
19C4×C22⋊D113—21no—
20C4×C22⋊D113—21no—
21#16813581—21no—
22#16813581—21no—
23#16813581C2212yes—
24#16813581C2212yes—
25#16813581C2211yescharacteristic
26C2×C4⋊Dic113C2211yescharacteristic
27C2×C4⋊Dic113C2211yescharacteristic
28C2×C22⋊Dic113—21no—
29C2×C4×Dic113—21no—
30#16813556C2212yescomplemented
31#16813556C2212yescomplemented
32#16813554C2212yescomplemented
33#16813554C2212yescomplemented
34#16813547C2212yescomplemented
35#16813547C2212yescomplemented
36#16813544C2212yescomplemented
37#16813544C2212yescomplemented
38C23×C4×C113C2211yescharacteristic
39C22×C8×C113C2212yes—
40C22⋊C8×C113C2211yescharacteristic
41C22⋊C8×C113C2211yescharacteristic
42C22⋊C8×C113C2212yes—
43#14268647—24no—
44C2×Dic226C2311yescharacteristic
45C2×D452C2311yescharacteristic
46C2×C22⋊D113—21no—
47C2×C22⋊D113—21no—
48C2×C22⋊D113—21no—
49C22×Dic113—21no—
50C22×Dic113—21no—
51C2×C4×D113—21no—
52C4⋊Dic113—21no—
53C4⋊Dic113—21no—
54C4⋊Dic113C2312yes—
55C4⋊Dic113C2312yes—
56C4⋊Dic113C2311yescharacteristic
57C4⋊Dic113C2311yescharacteristic
58#14268626—21no—
59#14268626—21no—
60C22⋊Dic113—22no—
61C22⋊Dic113—22no—
62C22⋊Dic113—21no—
63C22⋊Dic113—21no—
64C22⋊Dic113—21no—
65#14268624—21no—
66#14268624—21no—
67C4×Dic113—22no—
68C4×Dic113—22no—
69C4×Dic113—21no—
70C24×C113D411yescharacteristic
71C22×C4×C113—24no—
72C22×C4×C113D411yescharacteristic
73C22×C4×C113D411yescharacteristic
74C22×C4×C113D411yescharacteristic
75C22×C4×C113C2311yescharacteristic
76C22×C4×C113C2311yescharacteristic
77C22×C4×C113C2311yescharacteristic
78C2×C8×C113—24no—
79C2×C8×C113C2312yes—
80C2×C8×C113C2312yes—
81C23×C113—22no—
82C23×C113—22no—
83C23×C113—41no—
84C23×C113C2×D411yescharacteristic
85C23×C113C2×D411yescharacteristic
86C23×C113C2×D411yescharacteristic
87C22×D113—21no—
88C2×C4×C113—22no—
89C2×C4×C113—22no—
90C2×C4×C113—22no—
91C2×C4×C113—22no—
92C2×C4×C113—22no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113#4114yes—
97C2×C4×C113C2411yescharacteristic
98C22⋊D113—42no—
99C22⋊D113—42no—
100C22⋊D113—42no—
101C2×Dic113—22no—
102C2×Dic113—22no—
103C2×Dic113—21no—
104C2×Dic113—21no—
105C2×Dic113—21no—
106C2×Dic113—42no—
107C2×Dic113—42no—
108D452—22no—
109C4×D113—42no—
110Dic226—22no—
111C8×C113—22no—
112C8×C113—22no—
113C22×C113—21no—
114C22×C113—21no—
115C22×C113—21no—
116C22×C113—21no—
117C22×C113—21no—
118C22×C113—21no—
119C22×C113—21no—
120C22×C113—44no—
121C22×C113#12312yes—
122C22×C113#13512yes—
123C22×C113C22×D411yescharacteristic
124C2×D113—41no—
125C2×D113—41no—
126C2×D113—41no—
127C4×C113—21no—
128C4×C113—21no—
129C4×C113#12312yes—
130C4×C113C2×#4112yes—
131Dic113—41no—
132Dic113—42no—
133Dic113—41no—
134Dic113—42no—
135Dic113—41no—
136C2×C113—22no—
137C2×C113—22no—
138C2×C113—41no—
139C2×C113C2×#12311yescharacteristic
140C2×C113C2×#13511yescharacteristic
141C2×C113#57511yescharacteristic
142D113—81no—
143#3091—1131nomaximal, Sylow
144C113#309111yescharacteristic, complemented, Sylow
145#525—1131no—
146C2×#117—1131no—
147#485—1132no—
148#484—1131no—
149#483—1131no—
150#482—1132no—
151#481—1131no—
152#480—1131no—
153#427—1132no—
154#416—1132no—
155C2×C22⋊C8D11311yescharacteristic, complemented
156C2×#41—1131no—
157C23×C4C2×D11311yescharacteristic
158C22×C8C2×D11312yes—
159#123—2261no—
160C22⋊Q8—1131no—
161C22⋊Q8—1131no—
162#121—1131no—
163#121—1131no—
164#120—2261no—
165C4×D4—2261no—
166C4×D4—2261no—
167#117—1132no—
168#117—1132no—
169#117—1131no—
170#117—2261no—
171#117—2261no—
172C2×C4⋊C4—1131no—
173C2×C4⋊C4—1131no—
174C2×C22⋊C4—2261no—
175C2×C42—2261no—
176#107—1132no—
177#107—1132no—
178#106—1132no—
179#106—1132no—
180#103—1132no—
181#103—1132no—
182#102—1132no—
183#102—1132no—
184C22⋊C8C2×D11311yescharacteristic
185C22⋊C8C2×D11311yescharacteristic
186C22⋊C8C2×D11312yes—
187C24D45211yescharacteristic
188#41—2264no—
189C2×Q8—1131no—
190C2×D4—1131no—
191C2×D4—2261no—
192C2×D4—2261no—
193C2×D4—2261no—
194C22×C4—24no—
195C22×C4—2261no—
196C22×C4—2261no—
197C22×C4—2261no—
198C22×C4D45211yescharacteristic
199C22×C4D45211yescharacteristic
200C22×C4D45211yescharacteristic
201C22×C4C22×D11311yescharacteristic
202C22×C4C22×D11311yescharacteristic
203C22×C4C22×D11311yescharacteristic
204C2×C8—24no—
205C2×C8C22×D11312yes—
206C2×C8C22×D11312yes—
207C4⋊C4—1132no—
208C4⋊C4—1132no—
209C4⋊C4—1131no—
210C4⋊C4—1131no—
211C4⋊C4—2261no—
212C4⋊C4—2261no—
213C4⋊C4—2261no—
214C4⋊C4—2261no—
215C22⋊C4—2262no—
216C22⋊C4—2262no—
217C22⋊C4—2261no—
218C22⋊C4—2261no—
219C22⋊C4—2261no—
220C22⋊C4—2261no—
221C22⋊C4—2261no—
222C42—2262no—
223C42—2262no—
224C42—2261no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—2261no—
229C23C2×D45211yescharacteristic
230C23C2×D45211yescharacteristic
231C23C2×D45211yescharacteristic
232Q8—2262no—
233D4—4522no—
234D4—4522no—
235D4—4522no—
236D4—2262no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—4522no—
243C2×C4—4522no—
244C2×C4—4522no—
245C2×C4—2262no—
246C2×C4—2262no—
247C2×C4—2261no—
248C2×C4—2261no—
249C2×C4—2261no—
250C2×C4C2×D45211yescharacteristic
251C2×C4C2×D45211yescharacteristic
252C2×C4C2×D45211yescharacteristic
253C2×C4#1426864614yes—
254C2×C4C23×D11311yescharacteristic
255C8—22no—
256C8—22no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—4521no—
266C22—4521no—
267C22—4521no—
268C22#1681360612yes—
269C22#1681364412yes—
270C22C22×D45211yescharacteristic
271C4—21no—
272C4—21no—
273C4—4521no—
274C4—4522no—
275C4—4521no—
276C4—4522no—
277C4—4521no—
278C4#1681360612yes—
279C4C2×#1426864612yes—
280C2—22no—
281C2—22no—
282C2—41no—
283C2—9041no—
284C2C2×#1681360611yescharacteristic
285C2C2×#1681364411yescharacteristic
286C2#2029939811yescharacteristic
subgroupG/H
centerC2×C4C2×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C22⋊C8×C113C2
socleC22×C113C22×D4
prime radical#20299109C2
hypercenterC2×C22⋊C8D113
hypocenterC113#3091
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16813581C2semidirect
3. #20298940C2semidirect
4. #20298934C2semidirect
5. #20298929C2semidirect
6. #20298923C2semidirect
7. #20298917C2semidirect
8. #20298912C2semidirect
9. #20298636C2semidirect
10. #20298595C2semidirect
11. C2×C22⋊C8×C113C2semidirect
30. #16813556C22semidirect
31. #16813556C22semidirect
32. #16813554C22semidirect
33. #16813554C22semidirect
34. #16813547C22semidirect
35. #16813547C22semidirect
36. #16813544C22semidirect
37. #16813544C22semidirect
144. C113#3091semidirect
155. 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×#168135812
#202989402
#202989342
#202989292
#202989232
#202989172
#202989122
#202986362
#202985952
C2×C22⋊C8×C1132
#3091113