Finite Group Databasebeta

← #28402402

Subgroups — #28402402

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#20299282C211yesmaximal, characteristic, complemented
2#20299236C211yesmaximal, characteristic
3#20298954C211yesmaximal, characteristic, complemented
4#20298927C211yesmaximal, characteristic, complemented
5#20298923C211yesmaximal, characteristic, complemented
6#20298896C211yesmaximal, characteristic, complemented
7#20298836C211yesmaximal, characteristic, complemented
8#20298829C211yesmaximal, characteristic, complemented
9#20298822C211yesmaximal, characteristic, complemented
10#20298747C211yesmaximal, characteristic, complemented
11SD16×Dic113C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13#20298594C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#452×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C22×#11744751C2211yescharacteristic, complemented
19C2×C8×D113C2211yescharacteristic
20#16813615—21no—
21#16813613C2211yescharacteristic, complemented
22#16813612—21no—
23#16813611C2211yescharacteristic
24#16813605—21no—
25#16813604—21no—
26#16813598C2211yescharacteristic
27#16813598C2211yescharacteristic
28#16813596C2211yescharacteristic
29#16813594—21no—
30#16813590—21no—
31Q8×Dic113C2211yescharacteristic, complemented
32D4×Dic113C2211yescharacteristic
33C4×C22⋊D113C2211yescharacteristic
34#16813581C2211yescharacteristic, complemented
35#16813580—21no—
36C4⋊C4×D113C2211yescharacteristic
37C2×#14268624—21no—
38#16813556C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813546C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic, complemented
52C2×#41×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
62C2×C22⋊D113—21no—
63C2×C22⋊D113D411yescharacteristic
64D4×D113—22no—
65D4×D113—41no—
66C22×Dic113—21no—
67C2×C4×D113—21no—
68C2×C4×D113C2311yescharacteristic
69#14268634—41no—
70C2×#11744751—41no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C8×D113—41no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113D411yescharacteristic
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96#41×C113—22no—
97#41×C113—41no—
98C2×Q8×C113C2311yescharacteristic
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104Q16×C113—41no—
105SD16×C113—22no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113—42no—
115C22×D113—42no—
116C22×D113—81no—
117C22×D113C2×D411yescharacteristic
118Q8×C113—21no—
119Q8×C113—21no—
120Q8×C113—21no—
121Q8×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×C113—21no—
130C2×C4×C113—42no—
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2411yescharacteristic
133C22⋊D113—22no—
134C22⋊D113—42no—
135C22⋊D113—81no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—81no—
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142C2×Dic113C2×D411yescharacteristic
143D452—21no—
144D452—21no—
145C4×D113—21no—
146C4×D113—21no—
147C4×D113—42no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—22no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—41no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—84no—
165C2×D113#13512yes—
166C4×C113—21no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113—41no—
170C4×C113C2×#4111yescharacteristic
171C4×C113H(5,𝔽2)11yescharacteristic
172Dic113—21no—
173Dic113—21no—
174Dic113—21no—
175Dic113—41no—
176Dic113—41no—
177Dic113—41no—
178C2×C113—42no—
179C2×C113—41no—
180C2×C113#54611yescharacteristic
181C2×C113C2×#13511yescharacteristic
182C2×C113#57711yescharacteristic
183D113—22no—
184D113—81no—
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#452D11311yescharacteristic, complemented
197#450—1131no—
198C4×SD16—1131no—
199C8×D4—1131no—
200#416—1131no—
201C2×#102—1131no—
202C2×#41C2×D11311yescharacteristic
203C22×D4—1131no—
204C2×Q16C2×D11311yescharacteristic, complemented
205C2×SD16—1131no—
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, complemented
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#103C2×D11311yescharacteristic, complemented
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241#102C2×D11311yescharacteristic
242C22⋊C8—1131no—
243C22⋊C8C2×D11311yescharacteristic, complemented
244C4×C8—1131no—
245C24—2261no—
246#41—22no—
247#41—41no—
248C2×Q8C22×D11311yescharacteristic
249C2×Q8C22×D11311yescharacteristic
250C2×D4—21no—
251C2×D4—1131no—
252C2×D4—1131no—
253C2×D4—4521no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4—2262no—
257C2×D4C22×D11311yescharacteristic
258C22×C4—21no—
259C22×C4—1131no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4C22×D11311yescharacteristic
263Q16—41no—
264SD16—22no—
265SD16—4521no—
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—1131no—
299C23—9041no—
300C23—4522no—
301C23—4522no—
302C23—2261no—
303C23D4×D11311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—42no—
310D4—9041no—
311D4—4522no—
312D4—2262no—
313D4—2261no—
314D4—2261no—
315D4#1426864612yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—1131no—
323C2×C4—1131no—
324C2×C4—1131no—
325C2×C4—9041no—
326C2×C4—4522no—
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—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—1132no—
345C22—9044no—
346C22—4521no—
347C22—4521no—
348C22—4521no—
349C22—2261no—
350C22—2261no—
351C22C2×D4×D11311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—4521no—
357C4—4521no—
358C4—4521no—
359C4—2261no—
360C4—2261no—
361C4—2261no—
362C4C2×#1426864611yescharacteristic
363C4#1681366711yescharacteristic
364C2—41no—
365C2—42no—
366C2—9041no—
367C2—2262no—
368C2#2029923511yescharacteristic
369C2#135×D11311yescharacteristic
370C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#452×C113C2
socleC22×C113C22×D4
prime radical#20299236C2
hypercenter#452D113
hypocenterC113#3296
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #20299282C2semidirect
3. #20298954C2semidirect
4. #20298927C2semidirect
5. #20298923C2semidirect
6. #20298896C2semidirect
7. #20298836C2semidirect
8. #20298829C2semidirect
9. #20298822C2semidirect
10. #20298747C2semidirect
11. SD16×Dic113C2semidirect
12. #20298661C2semidirect
13. #20298594C2semidirect
14. #102×D113C2semidirect
15. #452×C113C2semidirect
18. C22×#11744751C22semidirect
21. #16813613C22semidirect
31. Q8×Dic113C22semidirect
34. #16813581C22semidirect
38. #16813556C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813546C22semidirect
43. #16813546C22semidirect
44. #16813546C22semidirect
51. C8×Dic113C22semidirect
53. C2×Q16×C113C22semidirect
55. C22⋊Q8×C113C22semidirect
56. #103×C113C22semidirect
58. C22⋊C8×C113C22semidirect
186. C113#3296semidirect
196. #452D113semidirect
204. C2×Q16C2×D113semidirect
217. C22⋊Q8C2×D113semidirect
235. #103C2×D113semidirect
243. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992822
#202992362
#202989542
#202989272
#202989232
#202988962
#202988362
#202988292
#202988222
#202987472
SD16×Dic1132
#202986612
#202985942
#102×D1132
#452×C1132
#3296113