Finite Group Databasebeta

← #28402413

Subgroups — #28402413

Order 14464.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299290C211yesmaximal, characteristic, complemented
2#20299242C211yesmaximal, characteristic
3#20298951C211yesmaximal, characteristic, complemented
4#20298929C211yesmaximal, characteristic, complemented
5#20298921C211yesmaximal, characteristic, complemented
6#20298900C211yesmaximal, characteristic, complemented
7#20298837C211yesmaximal, characteristic, complemented
8#20298824C211yesmaximal, characteristic, complemented
9#20298818C211yesmaximal, characteristic, complemented
10#20298757C211yesmaximal, characteristic, complemented
11SD16×Dic113C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13#20298591C211yesmaximal, characteristic, complemented
14C2×#16813543C211yesmaximal, characteristic, complemented
15#450×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×#14268637C2211yescharacteristic, complemented
18C22×#11744751C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic, complemented
20#16813617—21no—
21#16813613—21no—
22#16813613C2211yescharacteristic, complemented
23#16813609C2211yescharacteristic
24#16813606—21no—
25#16813603—21no—
26#16813601C2211yescharacteristic
27#16813598C2211yescharacteristic, complemented
28#16813594—21no—
29#16813593C2211yescharacteristic
30#16813591—21no—
31Q8×Dic113C2211yescharacteristic, complemented
32D4×Dic113C2211yescharacteristic
33C4×C22⋊D113C2211yescharacteristic
34#16813580C2211yescharacteristic, complemented
35#16813578—21no—
36C2×C4⋊Dic113C2211yescharacteristic
37C2×C22⋊Dic113—21no—
38#16813555C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813546C2211yescharacteristic, complemented
45#16813545C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813534C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—41no—
61C2×Dic226C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C2×C22⋊D113D411yescharacteristic
65C22×Dic113—21no—
66C22×Dic113—21no—
67C22×Dic113—21no—
68C2×C4×D113C2311yescharacteristic
69#14268637—41no—
70C2×#11744751—41no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C8×D113—41no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113D411yescharacteristic
90#14268624—21no—
91#14268624—21no—
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96C24×C113—21no—
97C2×Q8×C113C2311yescharacteristic
98C2×D4×C113—22no—
99C2×D4×C113—21no—
100C2×D4×C113—41no—
101C2×D4×C113C2311yescharacteristic
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113C2311yescharacteristic
104SD16×C113—22no—
105SD16×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C23×C113—21no—
112C23×C113—21no—
113C23×C113—42no—
114C23×C113—42no—
115C23×C113—81no—
116C23×C113C2×D411yescharacteristic
117C22×D113C2×D411yescharacteristic
118Q8×C113—21no—
119Q8×C113—21no—
120D4×C113—21no—
121D4×C113—21no—
122D4×C113—21no—
123D4×C113—42no—
124D4×C113#4112yes—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C22⋊D113—22no—
132C22⋊D113—42no—
133C22⋊D113—81no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—42no—
139C2×Dic113—42no—
140C2×Dic113—81no—
141C2×Dic113C2×D411yescharacteristic
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144C4×D113—21no—
145C4×D113—21no—
146Dic226—21no—
147Dic226—21no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—22no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113—84no—
161C22×C113#13512yes—
162C22×C113C22×D411yescharacteristic
163C2×D113—21no—
164C2×D113—21no—
165C2×D113—21no—
166C4×C113—21no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113H(5,𝔽2)11yescharacteristic
171Dic113—21no—
172Dic113—21no—
173Dic113—21no—
174Dic113—41no—
175Dic113—41no—
176Dic113—41no—
177Dic113—41no—
178C2×C113—22no—
179C2×C113—42no—
180C2×C113—81no—
181C2×C113#54611yescharacteristic
182C2×C113C2×#13511yescharacteristic
183C2×C113#57711yescharacteristic
184D113—41no—
185#3296—1131nomaximal, Sylow
186C113#329611yescharacteristic, complemented, Sylow
187#552—1131no—
188#546—1131no—
189#488—1131no—
190#483—1131no—
191#482—1131no—
192#478—1131no—
193#467—1131no—
194#465—1131no—
195#464—1131no—
196#452—1131no—
197#450D11311yescharacteristic, complemented
198C4×SD16—1131no—
199C8×D4—1131no—
200#416—1131no—
201C2×#102—1131no—
202C2×#41—1131no—
203C22×D4C2×D11311yescharacteristic
204C2×Q16—1131no—
205C2×SD16C2×D11311yescharacteristic
206C2×SD16C2×D11311yescharacteristic
207C22×C8—1131no—
208C22×C8—1131no—
209#126—2261no—
210#125—1131no—
211#125—2261no—
212#124—1131no—
213#123—2261no—
214#123—2261no—
215C22⋊Q8—1131no—
216C22⋊Q8—1131no—
217C22⋊Q8C2×D11311yescharacteristic
218#121—1131no—
219#121—2261no—
220#120—2261no—
221C4×Q8—1131no—
222C4×D4—1131no—
223C4×D4—1131no—
224#117—1131no—
225#117—2261no—
226C2×C4⋊C4—1131no—
227C2×C22⋊C4—2261no—
228#107—1131no—
229#106—1131no—
230#106—1131no—
231C4⋊C8—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102C2×D11311yescharacteristic
241#102C2×D11311yescharacteristic
242C22⋊C8—1131no—
243C22⋊C8C2×D11311yescharacteristic
244C4×C8—1131no—
245C24—21no—
246#41—4521no—
247#41—2262no—
248C2×Q8—1131no—
249C2×Q8C22×D11311yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—1131no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4C22×D11311yescharacteristic
257C2×D4C22×D11311yescharacteristic
258C22×C4—1131no—
259C22×C4—2261no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4C22×D11311yescharacteristic
263Q16—4521no—
264SD16—22no—
265SD16—41no—
266C2×C8—1131no—
267C2×C8—1131no—
268C2×C8—4521no—
269C2×C8—4521no—
270C2×C8C22×D11311yescharacteristic
271C2×C8C22×D11311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1131no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4—2261no—
283C4⋊C4C22×D11311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—1131no—
286C22⋊C4—1131no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C42—1131no—
295C42—2261no—
296C42—2261no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—1131no—
303C23D4×D11311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2261no—
307Q8—2261no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—9041no—
313D4—4522no—
314D4—2262no—
315D4#1426864612yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—1131no—
321C2×C4—1131no—
322C2×C4—1131no—
323C2×C4—9041no—
324C2×C4—4522no—
325C2×C4—4522no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4D4×D11311yescharacteristic
333C2×C4C23×D11311yescharacteristic
334C8—21no—
335C8—21no—
336C8—2261no—
337C8—2261no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—2261no—
348C22—2261no—
349C22—2261no—
350C22#1681364312yes—
351C22C2×D4×D11311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—4521no—
356C4—4521no—
357C4—4521no—
358C4—4521no—
359C4—2261no—
360C4—2261no—
361C4—2261no—
362C4C2×#1426864611yescharacteristic
363C4#1681366711yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—4521no—
368C2#2029923511yescharacteristic
369C2C2×#1681364311yescharacteristic
370C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
prime radical#20299242C2
hypercenter#450D113
hypocenterC113#3296
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #20299290C2semidirect
3. #20298951C2semidirect
4. #20298929C2semidirect
5. #20298921C2semidirect
6. #20298900C2semidirect
7. #20298837C2semidirect
8. #20298824C2semidirect
9. #20298818C2semidirect
10. #20298757C2semidirect
11. SD16×Dic113C2semidirect
12. #20298661C2semidirect
13. #20298591C2semidirect
14. C2×#16813543C2semidirect
15. #450×C113C2semidirect
17. C2×#14268637C22semidirect
19. C2×C8×D113C22semidirect
22. #16813613C22semidirect
27. #16813598C22semidirect
31. Q8×Dic113C22semidirect
34. #16813580C22semidirect
38. #16813555C22semidirect
39. #16813554C22semidirect
40. #16813554C22semidirect
41. #16813551C22semidirect
42. #16813547C22semidirect
43. #16813547C22semidirect
44. #16813546C22semidirect
45. #16813545C22semidirect
50. #16813534C22semidirect
51. C8×Dic113C22semidirect
186. C113#3296semidirect
197. #450D113semidirect

Maximal subgroups

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

subgroupindex
#202992902
#202992422
#202989512
#202989292
#202989212
#202989002
#202988372
#202988242
#202988182
#202987572
SD16×Dic1132
#202986612
#202985912
C2×#168135432
#450×C1132
#3296113