Finite Group Databasebeta

← #28400712

Subgroups — #28400712

Order 14464.

450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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#20299132C211yesmaximal, characteristic, complemented
2#20298928C211yesmaximal, characteristic, complemented
3#20298911C211yesmaximal, characteristic, complemented
4#20298898C212yesmaximal, complemented
5#20298813C212yesmaximal, complemented
6#20298749C211yesmaximal, characteristic, complemented
7#20298732C211yesmaximal, characteristic
8#20298708C212yesmaximal, complemented
9#20298698C212yesmaximal, complemented
10#20298655C211yesmaximal, characteristic, complemented
11C2×C4×D4×C113C211yesmaximal, characteristic, complemented
12C2×#14268635C2212yes—
13C2×#14268632C2212yes—
14#16813616—21no—
15#16813614C2211yescharacteristic, complemented
16#16813610C2211yescharacteristic, complemented
17#16813605—21no—
18#16813601C2211yescharacteristic
19#16813596C2211yescharacteristic
20C4×Dic226C2211yescharacteristic, complemented
21C4×D452C2211yescharacteristic, complemented
22C4×C22⋊D113—21no—
23#16813579—21no—
24#16813555C2212yescomplemented
25#16813553C2212yescomplemented
26C4⋊#11744751C2212yescomplemented
27#16813545C2212yescomplemented
28#16813543C2212yes—
29#16813543C2212yes—
30#16813542C2212yescomplemented
31C22⋊#11744751C2211yescharacteristic
32C22⋊#11744751C2211yescharacteristic
33#16813533C2212yescomplemented
34C22×D4×C113C2211yescharacteristic
35C23×C4×C113—21no—
36C4×D4×C113—21no—
37C4×D4×C113—21no—
38C4×D4×C113C2212yes—
39C4×D4×C113C2212yes—
40C2×C4⋊C4×C113C2211yescharacteristic
41C2×C22⋊C4×C113—21no—
42C2×C42×C113C2211yescharacteristic
43C2×Dic226C2311yescharacteristic
44C2×D452C2311yescharacteristic
45C2×C22⋊D113—21no—
46C2×C4×D113—21no—
47#14268635—24no—
48#14268632—24no—
49C2×#11744751C2312yes—
50C2×#11744751C2312yes—
51C4⋊Dic113C2311yescharacteristic
52C4⋊Dic113C2311yescharacteristic
53#14268626—21no—
54#14268626—21no—
55#14268626—21no—
56#14268626—21no—
57C22⋊Dic113—21no—
58#14268624—21no—
59#14268624—21no—
60#14268624—21no—
61#14268624—21no—
62C4×Dic113—21no—
63C24×C113—21no—
64C2×D4×C113—24no—
65C2×D4×C113—21no—
66C2×D4×C113C2312yes—
67C22×C4×C113—21no—
68C22×C4×C113—22no—
69C22×C4×C113—22no—
70C22×C4×C113—44no—
71C22×C4×C113D411yescharacteristic
72C22×C4×C113D411yescharacteristic
73C22×C4×C113C2311yescharacteristic
74C4⋊C4×C113—21no—
75C4⋊C4×C113C2312yes—
76C22⋊C4×C113—22no—
77C22⋊C4×C113—22no—
78C42×C113D411yescharacteristic
79C42×C113D411yescharacteristic
80C42×C113C2311yescharacteristic
81C42×C113C2311yescharacteristic
82C23×C113—24no—
83C23×C113—22no—
84C23×C113—42no—
85C23×C113—42no—
86C23×C113C2×D411yescharacteristic
87C22×D113—21no—
88D4×C113—24no—
89D4×C113—22no—
90D4×C113#4114yes—
91C2×C4×C113—22no—
92C2×C4×C113—22no—
93C2×C4×C113—22no—
94C2×C4×C113—41no—
95C2×C4×C113—44no—
96C2×C4×C113—44no—
97C2×C4×C113—42no—
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2×D411yescharacteristic
101C2×C4×C113C2×D411yescharacteristic
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113C2411yescharacteristic
104C22⋊D113—42no—
105C2×Dic113—21no—
106C2×Dic113—21no—
107C2×Dic113—21no—
108D452—22no—
109C4×D113—42no—
110Dic226—22no—
111#11744751—22no—
112#11744751—22no—
113C22×C113—21no—
114C22×C113—21no—
115C22×C113—24no—
116C22×C113—48no—
117C22×C113—42no—
118C22×C113—42no—
119C22×C113AGL(1,ℤ/8)12yes—
120C22×C113C22×D411yescharacteristic
121C2×D113—41no—
122C2×D113—41no—
123C2×D113—41no—
124C4×C113—21no—
125C4×C113—21no—
126C4×C113—21no—
127C4×C113—21no—
128C4×C113—21no—
129C4×C113—42no—
130C4×C113C2×#4112yes—
131Dic113—41no—
132Dic113—41no—
133Dic113—41no—
134C2×C113—22no—
135C2×C113—44no—
136C2×C113#52511yescharacteristic
137C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C113#57511yescharacteristic
139D113—81no—
140#3114—1131nomaximal, Sylow
141C113#311411yescharacteristic, complemented, Sylow
142#529—1131no—
143C2×C4×D4D11311yescharacteristic, complemented
144#483—1131no—
145#480—1131no—
146#478—1132no—
147#463—1132no—
148#450—1131no—
149#447—1131no—
150#442—1132no—
151#440—1132no—
152#432—1131no—
153C22×D4C2×D11311yescharacteristic
154C23×C4—21no—
155C2×SD16—1132no—
156C2×D8—1132no—
157#126—2261no—
158#125—1131no—
159#124—1131no—
160#123—2261no—
161C22⋊Q8—1131no—
162#121—1131no—
163C4×Q8—1131no—
164C4×D4—21no—
165C4×D4—21no—
166C4×D4—1131no—
167C4×D4—2261no—
168C4×D4C2×D11312yes—
169C4×D4C2×D11312yes—
170#117—2261no—
171C2×C4⋊C4C2×D11311yescharacteristic
172C2×C22⋊C4—21no—
173C2×C42C2×D11311yescharacteristic
174#107—1132no—
175#106—1132no—
176C4⋊C8—1132no—
177#103—1132no—
178#102—1132no—
179#102—1132no—
180#102—1132no—
181C22⋊C8—1131no—
182C22⋊C8—1131no—
183#97—1132no—
184C24—21no—
185C2×Q8—1131no—
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—1131no—
189C2×D4—2261no—
190C2×D4C22×D11312yes—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4—2261no—
196C22×C4C22⋊D11311yescharacteristic
197C22×C4C22⋊D11311yescharacteristic
198C22×C4C22×D11311yescharacteristic
199SD16—2264no—
200D8—2264no—
201C2×C8—1132no—
202C2×C8—1132no—
203C4⋊C4—21no—
204C4⋊C4—1131no—
205C4⋊C4—1131no—
206C4⋊C4—2261no—
207C4⋊C4—2261no—
208C4⋊C4—2261no—
209C4⋊C4—2261no—
210C4⋊C4C22×D11312yes—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—2261no—
214C22⋊C4—2261no—
215C22⋊C4—2261no—
216C22⋊C4—2261no—
217C22⋊C4—2261no—
218C42—2261no—
219C42C22⋊D11311yescharacteristic
220C42C22⋊D11311yescharacteristic
221C42C22×D11311yescharacteristic
222C42C22×D11311yescharacteristic
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—2261no—
228C23C2×C22⋊D11311yescharacteristic
229Q8—2262no—
230D4—24no—
231D4—22no—
232D4—4522no—
233D4—2262no—
234D4#1426864714yes—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—4522no—
243C2×C4—2261no—
244C2×C4—2261no—
245C2×C4—2261no—
246C2×C4C2×C22⋊D11311yescharacteristic
247C2×C4C2×C22⋊D11311yescharacteristic
248C2×C4C2×C22⋊D11311yescharacteristic
249C2×C4C2×C22⋊D11311yescharacteristic
250C2×C4C2×C22⋊D11311yescharacteristic
251C2×C4C23×D11311yescharacteristic
252C8—2262no—
253C8—2262no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—4521no—
261C22—4521no—
262C22—4521no—
263C22#1681364812yes—
264C22C22×C22⋊D11311yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—4521no—
272C4—4521no—
273C4—4521no—
274C4C2×#1426864712yes—
275C2—22no—
276C2—44no—
277C2—9041no—
278C2#2029910911yescharacteristic
279C2C2×#1681364811yescharacteristic
280C2#2029939611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C4×D4×C113C2
socleC22×C113C22×D4
prime radical#20298732C2
hypercenterC2×C4×D4D113
hypocenterC113#3114
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #20299132C2semidirect
2. #20298928C2semidirect
3. #20298911C2semidirect
4. #20298898C2semidirect
5. #20298813C2semidirect
6. #20298749C2semidirect
8. #20298708C2semidirect
9. #20298698C2semidirect
10. #20298655C2semidirect
11. C2×C4×D4×C113C2semidirect
15. #16813614C22semidirect
16. #16813610C22semidirect
20. C4×Dic226C22semidirect
21. C4×D452C22semidirect
24. #16813555C22semidirect
25. #16813553C22semidirect
26. C4⋊#11744751C22semidirect
27. #16813545C22semidirect
30. #16813542C22semidirect
33. #16813533C22semidirect
141. C113#3114semidirect
143. C2×C4×D4D113semidirect

Maximal subgroups

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

subgroupindex
#202991322
#202989282
#202989112
#202988982
#202988132
#202987492
#202987322
#202987082
#202986982
#202986552
C2×C4×D4×C1132
#3114113