Finite Group Databasebeta

← #28401339

Subgroups — #28401339

Order 14464.

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

normal subgroups only

This group has 472 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, complemented
2#20298933C211yesmaximal, characteristic, complemented
3#20298919C212yesmaximal, complemented
4#20298916C211yesmaximal, characteristic, complemented
5#20298832C212yesmaximal, complemented
6#20298825C212yesmaximal, complemented
7#20298749C211yesmaximal, characteristic, complemented
8#20298741C212yesmaximal, complemented
9#20298732C211yesmaximal, characteristic, complemented
10C2×C22⋊#11744751C211yesmaximal, characteristic, complemented
11C2×#121×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic, complemented
13C2×#14268635C2212yescomplemented
14C2×#14268632C2212yescomplemented
15C22×#11744751C2212yescomplemented
16#16813605—21no—
17#16813601C2211yescharacteristic
18#16813601C2211yescharacteristic, complemented
19#16813596C2211yescharacteristic
20#16813596C2211yescharacteristic, complemented
21#16813591—21no—
22C4×C22⋊D113—21no—
23C4×C22⋊D113—21no—
24#16813581C2211yescharacteristic, complemented
25#16813555C2212yescomplemented
26#16813553C2212yescomplemented
27#16813545C2212yescomplemented
28#16813543C2212yescomplemented
29#16813543C2212yescomplemented
30#16813542C2212yescomplemented
31C22⋊#11744751C2211yescharacteristic
32C22⋊#11744751C2211yescharacteristic
33C22⋊#11744751C2212yescomplemented
34C22×D4×C113—21no—
35C22×D4×C113C2211yescharacteristic
36C23×C4×C113C2211yescharacteristic
37#121×C113—21no—
38#121×C113—21no—
39#121×C113C2212yes—
40#121×C113C2212yes—
41C2×C4⋊C4×C113C2211yescharacteristic
42C2×C22⋊C4×C113—21no—
43#14268647—42no—
44C2×Dic226C2311yescharacteristic
45C2×D452C2311yescharacteristic
46C2×C22⋊D113—21no—
47C2×C22⋊D113—21no—
48C2×C22⋊D113—21no—
49C2×C4×D113—21no—
50#14268635—42no—
51#14268632—42no—
52C2×#11744751—42no—
53C2×#11744751C2312yes—
54C2×#11744751C2312yes—
55C4⋊Dic113C2311yescharacteristic
56C4⋊Dic113C2311yescharacteristic
57#14268626—21no—
58#14268626—21no—
59C22⋊Dic113—21no—
60C22⋊Dic113—21no—
61C22⋊Dic113—21no—
62#14268624—21no—
63#14268624—21no—
64C4×Dic113—21no—
65C24×C113—21no—
66C24×C113D411yescharacteristic
67C2×D4×C113—22no—
68C2×D4×C113—22no—
69C2×D4×C113—21no—
70C2×D4×C113—42no—
71C2×D4×C113—44no—
72C2×D4×C113C2312yes—
73C22×C4×C113—21no—
74C22×C4×C113—42no—
75C22×C4×C113D411yescharacteristic
76C22×C4×C113D411yescharacteristic
77C22×C4×C113D411yescharacteristic
78C22×C4×C113C2311yescharacteristic
79C22×C4×C113C2311yescharacteristic
80C22×C4×C113C2311yescharacteristic
81C4⋊C4×C113—21no—
82C4⋊C4×C113C2312yes—
83C22⋊C4×C113—22no—
84C22⋊C4×C113—22no—
85C23×C113—22no—
86C23×C113—22no—
87C23×C113—22no—
88C23×C113—41no—
89C23×C113—42no—
90C23×C113—42no—
91C23×C113—42no—
92C23×C113C2×D411yescharacteristic
93C23×C113C2×D411yescharacteristic
94C23×C113C2×D411yescharacteristic
95C22×D113—21no—
96D4×C113—22no—
97D4×C113—22no—
98D4×C113—42no—
99D4×C113—44no—
100D4×C113—44no—
101C2×C4×C113—22no—
102C2×C4×C113—22no—
103C2×C4×C113—22no—
104C2×C4×C113—22no—
105C2×C4×C113—41no—
106C2×C4×C113—41no—
107C2×C4×C113—41no—
108C2×C4×C113—42no—
109C2×C4×C113C2×D411yescharacteristic
110C2×C4×C113C2×D411yescharacteristic
111C2×C4×C113C2×D411yescharacteristic
112C2×C4×C113C2411yescharacteristic
113C22⋊D113—42no—
114C22⋊D113—42no—
115C22⋊D113—42no—
116C2×Dic113—21no—
117C2×Dic113—21no—
118C2×Dic113—21no—
119D452—22no—
120C4×D113—42no—
121Dic226—22no—
122#11744751—22no—
123#11744751—22no—
124C22×C113—21no—
125C22×C113—21no—
126C22×C113—21no—
127C22×C113—21no—
128C22×C113—21no—
129C22×C113—21no—
130C22×C113—21no—
131C22×C113—44no—
132C22×C113—42no—
133C22×C113—42no—
134C22×C113—42no—
135C22×C113—84no—
136C22×C113#13512yes—
137C22×C113AGL(1,ℤ/8)12yes—
138C22×C113C22×D411yescharacteristic
139C2×D113—41no—
140C2×D113—41no—
141C2×D113—41no—
142C4×C113—21no—
143C4×C113—21no—
144C4×C113—21no—
145C4×C113—42no—
146C4×C113H(5,𝔽2)12yes—
147Dic113—41no—
148Dic113—41no—
149Dic113—41no—
150C2×C113—22no—
151C2×C113—22no—
152C2×C113—41no—
153C2×C113—82no—
154C2×C113#53411yescharacteristic
155C2×C113C2×#13511yescharacteristic
156C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
157D113—81no—
158#3188—1131nomaximal, Sylow
159C113#318811yescharacteristic, complemented, Sylow
160#525—1131no—
161C2×#121D11311yescharacteristic, complemented
162#484—1131no—
163#482—1132no—
164#481—1131no—
165#466—1132no—
166#465—1132no—
167#450—1131no—
168#449—1132no—
169#447—1131no—
170C2×C22⋊C8—1131no—
171C2×#41—1131no—
172C22×D4—21no—
173C22×D4C2×D11311yescharacteristic
174C23×C4C2×D11311yescharacteristic
175C2×SD16—1132no—
176C2×D8—1132no—
177C22×C8—1132no—
178#123—2261no—
179C22⋊Q8—1131no—
180C22⋊Q8—1131no—
181#121—21no—
182#121—21no—
183#121—1131no—
184#121—1131no—
185#121C2×D11312yes—
186#121C2×D11312yes—
187#120—2261no—
188C4×D4—2261no—
189C4×D4—2261no—
190#117—1131no—
191C2×C4⋊C4C2×D11311yescharacteristic
192C2×C22⋊C4—21no—
193#107—1132no—
194#106—1132no—
195#103—1132no—
196#102—1132no—
197#102—1132no—
198#102—1132no—
199C22⋊C8—1131no—
200C22⋊C8—1132no—
201C22⋊C8—1131no—
202C24—21no—
203C24C22⋊D11311yescharacteristic
204#41—4522no—
205C2×Q8—1131no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—42no—
210C2×D4—44no—
211C2×D4—1131no—
212C2×D4—2261no—
213C2×D4—2261no—
214C2×D4—2261no—
215C2×D4C22×D11312yes—
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—2261no—
219C22×C4C22⋊D11311yescharacteristic
220C22×C4C22⋊D11311yescharacteristic
221C22×C4C22⋊D11311yescharacteristic
222C22×C4C22×D11311yescharacteristic
223C22×C4C22×D11311yescharacteristic
224C22×C4C22×D11311yescharacteristic
225SD16—4522no—
226D8—4522no—
227C2×C8—1132no—
228C2×C8—1132no—
229C2×C8—4522no—
230C4⋊C4—21no—
231C4⋊C4—1131no—
232C4⋊C4—1131no—
233C4⋊C4—2261no—
234C4⋊C4—2261no—
235C4⋊C4C22×D11312yes—
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—2261no—
239C22⋊C4—2261no—
240C22⋊C4—2261no—
241C22⋊C4—2261no—
242C22⋊C4—2261no—
243C42—2261no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—41no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—2261no—
252C23C2×C22⋊D11311yescharacteristic
253C23C2×C22⋊D11311yescharacteristic
254C23C2×C22⋊D11311yescharacteristic
255Q8—2262no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—44no—
260D4—44no—
261D4—4522no—
262D4—4522no—
263D4—4522no—
264D4—2262no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—4522no—
274C2×C4—2261no—
275C2×C4—2261no—
276C2×C4—2261no—
277C2×C4C2×C22⋊D11311yescharacteristic
278C2×C4C2×C22⋊D11311yescharacteristic
279C2×C4C2×C22⋊D11311yescharacteristic
280C2×C4C23×D11311yescharacteristic
281C8—2262no—
282C8—2262no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—44no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—84no—
295C22—4521no—
296C22—4521no—
297C22—4521no—
298C22#1681364212yes—
299C22#1681364812yes—
300C22C22×C22⋊D11311yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—42no—
305C4—4521no—
306C4—4521no—
307C4—4521no—
308C4#1681366712yes—
309C2—22no—
310C2—22no—
311C2—41no—
312C2—82no—
313C2—9041no—
314C2#2029915711yescharacteristic
315C2C2×#1681364211yescharacteristic
316C2C2×#1681364811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#121×C113C2
socleC22×C113C22×D4
hypercenterC2×#121D113
hypocenterC113#3188
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #20299109C2semidirect
2. #20298933C2semidirect
3. #20298919C2semidirect
4. #20298916C2semidirect
5. #20298832C2semidirect
6. #20298825C2semidirect
7. #20298749C2semidirect
8. #20298741C2semidirect
9. #20298732C2semidirect
10. C2×C22⋊#11744751C2semidirect
11. C2×#121×C113C2semidirect
12. C2×#14268647C22semidirect
13. C2×#14268635C22semidirect
14. C2×#14268632C22semidirect
15. C22×#11744751C22semidirect
18. #16813601C22semidirect
20. #16813596C22semidirect
24. #16813581C22semidirect
25. #16813555C22semidirect
26. #16813553C22semidirect
27. #16813545C22semidirect
28. #16813543C22semidirect
29. #16813543C22semidirect
30. #16813542C22semidirect
33. C22⋊#11744751C22semidirect
159. C113#3188semidirect
161. C2×#121D113semidirect

Maximal subgroups

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

subgroupindex
#202991092
#202989332
#202989192
#202989162
#202988322
#202988252
#202987492
#202987412
#202987322
C2×C22⋊#117447512
C2×#121×C1132
#3188113