Finite Group Databasebeta

← #28402404

Subgroups — #28402404

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#20299245C211yesmaximal, characteristic
3#20298951C211yesmaximal, characteristic, complemented
4#20298930C211yesmaximal, characteristic, complemented
5#20298919C211yesmaximal, characteristic, complemented
6#20298897C211yesmaximal, characteristic, complemented
7#20298838C211yesmaximal, characteristic, complemented
8#20298818C211yesmaximal, characteristic, complemented
9#20298758C211yesmaximal, characteristic, complemented
10#20298747C211yesmaximal, characteristic, complemented
11#20298683C211yesmaximal, characteristic, complemented
12C8×C22⋊D113C211yesmaximal, characteristic, complemented
13#20298595C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268637C2211yescharacteristic, complemented
19C2×#14268634C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813615—21no—
22#16813613C2211yescharacteristic, complemented
23#16813612—21no—
24#16813609C2211yescharacteristic
25#16813604—21no—
26#16813604—21no—
27#16813602C2211yescharacteristic
28#16813598C2211yescharacteristic
29#16813593—21no—
30#16813590—21no—
31Q8×Dic113C2211yescharacteristic, complemented
32#16813584C2211yescharacteristic
33C4×C22⋊D113C2211yescharacteristic
34#16813581C2211yescharacteristic, complemented
35#16813580—21no—
36C4⋊C4×D113C2211yescharacteristic
37C22⋊C4×D113—21no—
38#16813555C2211yescharacteristic, complemented
39#16813553C2211yescharacteristic, complemented
40#16813551C2211yescharacteristic, complemented
41#16813547C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813545C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic, complemented
54C22⋊Q8×C113C2211yescharacteristic, complemented
55#121×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic
59C23×D113—21no—
60#14268647—22no—
61#14268647—41no—
62C2×Dic226C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113D411yescharacteristic
67D4×D113—22no—
68D4×D113—41no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113C2311yescharacteristic
73#14268637—41no—
74#14268634—22no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C8×D113—41no—
78C4⋊Dic113—21no—
79C4⋊Dic113—21no—
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626D411yescharacteristic
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113D411yescharacteristic
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113—21no—
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102SD16×C113—41no—
103C2×C8×C113—41no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
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—
120D4×C113—21no—
121D4×C113—21no—
122D4×C113—81no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—22no—
131C22⋊D113—42no—
132C22⋊D113—42no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139D452—21no—
140D452#4112yes—
141C4×D113—21no—
142C4×D113—21no—
143C4×D113—42no—
144C4×D113—42no—
145C4×D113—81no—
146Dic226—21no—
147Dic226—21no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—22no—
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—41no—
179C2×C113—81no—
180C2×C113#54611yescharacteristic
181C2×C113C2×#13511yescharacteristic
182C2×C113#57711yescharacteristic
183D113—22no—
184D113—42no—
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#465D11311yescharacteristic, complemented
195#464—1131no—
196#452—1131no—
197#450—1131no—
198C4×SD16—1131no—
199C8×D4—1131no—
200#416—1131no—
201C2×#102—1131no—
202C2×#41—1131no—
203C22×D4—1131no—
204C2×Q16—1131no—
205C2×SD16—1131no—
206C2×SD16C2×D11311yescharacteristic
207C22×C8—1131no—
208C22×C8C2×D11311yescharacteristic, complemented
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—2261no—
219#121C2×D11311yescharacteristic
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#106C2×D11311yescharacteristic, complemented
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⋊C8—1131no—
244C4×C8—1131no—
245C24—2261no—
246#41—4521no—
247#41—2262no—
248C2×Q8—1131no—
249C2×Q8C22×D11311yescharacteristic
250C2×D4—21no—
251C2×D4—1131no—
252C2×D4—1131no—
253C2×D4—4521no—
254C2×D4—2261no—
255C2×D4—2262no—
256C2×D4—2261no—
257C2×D4C22×D11311yescharacteristic
258C22×C4—1131no—
259C22×C4—2261no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4C22×D11311yescharacteristic
263Q16—4521no—
264SD16—41no—
265SD16—2262no—
266C2×C8—41no—
267C2×C8—1131no—
268C2×C8—1131no—
269C2×C8—4521no—
270C2×C8C22×D11311yescharacteristic
271C2×C8C22×D11311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4C22×D11311yescharacteristic
283C4⋊C4C22×D11311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—1131no—
287C22⋊C4—1131no—
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—2261no—
307Q8—2261no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—1132no—
312D4—4522no—
313D4—4522no—
314D4—2262no—
315D4—2261no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—1131no—
322C2×C4—1131no—
323C2×C4—1131no—
324C2×C4—9041no—
325C2×C4—4522no—
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—41no—
342C22—41no—
343C22—41no—
344C22—1132no—
345C22—9044no—
346C22—4521no—
347C22—4521no—
348C22—2262no—
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—
362C4#41×D11311yescharacteristic
363C4#1681366711yescharacteristic
364C2—41no—
365C2—81no—
366C2—4522no—
367C2—2262no—
368C2#2029923711yescharacteristic
369C2#135×D11311yescharacteristic
370C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
prime radical#20299245C2
hypercenter#465D113
hypocenterC113#3296
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #20299282C2semidirect
3. #20298951C2semidirect
4. #20298930C2semidirect
5. #20298919C2semidirect
6. #20298897C2semidirect
7. #20298838C2semidirect
8. #20298818C2semidirect
9. #20298758C2semidirect
10. #20298747C2semidirect
11. #20298683C2semidirect
12. C8×C22⋊D113C2semidirect
13. #20298595C2semidirect
14. #102×D113C2semidirect
15. #465×C113C2semidirect
18. C2×#14268637C22semidirect
22. #16813613C22semidirect
31. Q8×Dic113C22semidirect
34. #16813581C22semidirect
38. #16813555C22semidirect
39. #16813553C22semidirect
40. #16813551C22semidirect
41. #16813547C22semidirect
42. #16813547C22semidirect
43. #16813545C22semidirect
49. C22⋊#11744751C22semidirect
51. C8×Dic113C22semidirect
53. C22×C8×C113C22semidirect
54. C22⋊Q8×C113C22semidirect
56. #106×C113C22semidirect
57. #103×C113C22semidirect
186. C113#3296semidirect
194. #465D113semidirect
208. C22×C8C2×D113semidirect
217. C22⋊Q8C2×D113semidirect
230. #106C2×D113semidirect
235. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992822
#202992452
#202989512
#202989302
#202989192
#202988972
#202988382
#202988182
#202987582
#202987472
#202986832
C8×C22⋊D1132
#202985952
#102×D1132
#465×C1132
#3296113