Finite Group Databasebeta

← #28400487

Subgroups — #28400487

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
2#20298939C212yesmaximal, complemented
3#20298933C211yesmaximal, characteristic, complemented
4#20298928C211yesmaximal, characteristic, complemented
5#20298922C212yesmaximal, complemented
6#20298916C211yesmaximal, characteristic, complemented
7#20298911C211yesmaximal, characteristic, complemented
8#20298634C212yesmaximal, complemented
9#20298592C212yesmaximal, complemented
10C2×C22⋊#11744751C211yesmaximal, characteristic, complemented
11C2×#117×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×#11744751C2212yes—
14#16813605—21no—
15#16813601C2211yescharacteristic
16#16813601C2211yescharacteristic
17#16813596C2211yescharacteristic
18#16813596C2211yescharacteristic
19#16813591—21no—
20C4×C22⋊D113—21no—
21C4×C22⋊D113—21no—
22#16813581C2211yescharacteristic
23#16813555C2212yescomplemented
24#16813555C2212yescomplemented
25#16813553C2212yescomplemented
26#16813553C2212yescomplemented
27#16813545C2212yescomplemented
28#16813545C2212yescomplemented
29#16813542C2212yescomplemented
30#16813542C2212yescomplemented
31C22⋊#11744751C2211yescharacteristic
32C22⋊#11744751C2211yescharacteristic
33C22⋊#11744751C2212yes—
34C23×C4×C113C2211yescharacteristic
35#117×C113—21no—
36#117×C113—21no—
37#117×C113C2212yes—
38#117×C113C2212yes—
39C2×C4⋊C4×C113C2211yescharacteristic
40C2×C4⋊C4×C113C2211yescharacteristic
41C2×C22⋊C4×C113—21no—
42C2×C42×C113—21no—
43#14268647—24no—
44C2×Dic226C2311yescharacteristic
45C2×D452C2311yescharacteristic
46C2×C22⋊D113—21no—
47C2×C22⋊D113—21no—
48C2×C22⋊D113—21no—
49C2×C4×D113—21no—
50C2×#11744751—24no—
51C2×#11744751C2312yes—
52C2×#11744751C2312yes—
53C4⋊Dic113C2311yescharacteristic
54C4⋊Dic113C2311yescharacteristic
55#14268626—21no—
56#14268626—21no—
57C22⋊Dic113—21no—
58C22⋊Dic113—21no—
59C22⋊Dic113—21no—
60#14268624—21no—
61#14268624—21no—
62C4×Dic113—21no—
63C24×C113D411yescharacteristic
64C22×C4×C113—24no—
65C22×C4×C113—21no—
66C22×C4×C113—21no—
67C22×C4×C113D411yescharacteristic
68C22×C4×C113D411yescharacteristic
69C22×C4×C113D411yescharacteristic
70C22×C4×C113C2311yescharacteristic
71C22×C4×C113C2311yescharacteristic
72C22×C4×C113C2311yescharacteristic
73C4⋊C4×C113—21no—
74C4⋊C4×C113—21no—
75C4⋊C4×C113C2312yes—
76C4⋊C4×C113C2312yes—
77C22⋊C4×C113—22no—
78C22⋊C4×C113—22no—
79C42×C113—22no—
80C42×C113—22no—
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×C113—22no—
94C2×C4×C113—22no—
95C2×C4×C113—42no—
96C2×C4×C113—42no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113#4114yes—
101C2×C4×C113C2411yescharacteristic
102C22⋊D113—42no—
103C22⋊D113—42no—
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—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—42no—
130C4×C113—42no—
131C4×C113#12312yes—
132C4×C113C2×#4112yes—
133Dic113—41no—
134Dic113—41no—
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×#117D11311yescharacteristic, complemented
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⋊C8—1131no—
156C2×#41—1131no—
157C23×C4C2×D11311yescharacteristic
158C22×C8—1132no—
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—21no—
168#117—21no—
169#117—1131no—
170#117C2×D11312yes—
171#117C2×D11312yes—
172C2×C4⋊C4C2×D11311yescharacteristic
173C2×C4⋊C4C2×D11311yescharacteristic
174C2×C22⋊C4—21no—
175C2×C42—21no—
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⋊C8—1131no—
185C22⋊C8—1131no—
186C22⋊C8—1132no—
187C24C22⋊D11311yescharacteristic
188#41—2264no—
189C2×Q8—1131no—
190C2×D4—1131no—
191C2×D4—2261no—
192C2×D4—2261no—
193C2×D4—2261no—
194C22×C4—24no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—2261no—
198C22×C4C22⋊D11311yescharacteristic
199C22×C4C22⋊D11311yescharacteristic
200C22×C4C22⋊D11311yescharacteristic
201C22×C4C22×D11311yescharacteristic
202C22×C4C22×D11311yescharacteristic
203C22×C4C22×D11311yescharacteristic
204C2×C8—1132no—
205C2×C8—1132no—
206C2×C8—2264no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—1131no—
210C4⋊C4—1131no—
211C4⋊C4—2261no—
212C4⋊C4—2261no—
213C4⋊C4C22×D11312yes—
214C4⋊C4C22×D11312yes—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—2261no—
218C22⋊C4—2261no—
219C22⋊C4—2261no—
220C22⋊C4—2261no—
221C22⋊C4—2261no—
222C42—22no—
223C42—22no—
224C42—2261no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—2261no—
229C23C2×C22⋊D11311yescharacteristic
230C23C2×C22⋊D11311yescharacteristic
231C23C2×C22⋊D11311yescharacteristic
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—22no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—4522no—
247C2×C4—2261no—
248C2×C4—2261no—
249C2×C4—2261no—
250C2×C4C2×C22⋊D11311yescharacteristic
251C2×C4C2×C22⋊D11311yescharacteristic
252C2×C4C2×C22⋊D11311yescharacteristic
253C2×C4#1426864714yes—
254C2×C4C23×D11311yescharacteristic
255C8—2262no—
256C8—2262no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—4521no—
266C22—4521no—
267C22—4521no—
268C22#1681360512yes—
269C22#1681364212yes—
270C22C22×C22⋊D11311yescharacteristic
271C4—21no—
272C4—21no—
273C4—42no—
274C4—42no—
275C4—4521no—
276C4—4521no—
277C4—4521no—
278C4#1681360512yes—
279C4C2×#1426864712yes—
280C2—22no—
281C2—22no—
282C2—41no—
283C2—9041no—
284C2C2×#1681360511yescharacteristic
285C2C2×#1681364211yescharacteristic
286C2#2029939611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#117×C113C2
socleC22×C113C22×D4
prime radical#20299109C2
hypercenterC2×#117D113
hypocenterC113#3091
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #20298939C2semidirect
3. #20298933C2semidirect
4. #20298928C2semidirect
5. #20298922C2semidirect
6. #20298916C2semidirect
7. #20298911C2semidirect
8. #20298634C2semidirect
9. #20298592C2semidirect
10. C2×C22⋊#11744751C2semidirect
11. C2×#117×C113C2semidirect
23. #16813555C22semidirect
24. #16813555C22semidirect
25. #16813553C22semidirect
26. #16813553C22semidirect
27. #16813545C22semidirect
28. #16813545C22semidirect
29. #16813542C22semidirect
30. #16813542C22semidirect
144. C113#3091semidirect
146. C2×#117D113semidirect

Maximal subgroups

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

subgroupindex
#202991092
#202989392
#202989332
#202989282
#202989222
#202989162
#202989112
#202986342
#202985922
C2×C22⋊#117447512
C2×#117×C1132
#3091113