Finite Group Databasebeta

← #28401543

Subgroups — #28401543

Order 14464.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299135C211yesmaximal, characteristic, complemented
2#124×D113C211yesmaximal, characteristic, complemented
3#20298983C211yesmaximal, characteristic, complemented
4#20298979C211yesmaximal, characteristic, complemented
5#20298954C211yesmaximal, characteristic, complemented
6#20298951C211yesmaximal, characteristic, complemented
7#20298820C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298810C211yesmaximal, characteristic, complemented
10#20298752C211yesmaximal, characteristic, complemented
11#20298747C211yesmaximal, characteristic, complemented
12#20298738C211yesmaximal, characteristic, complemented
13#20298733C211yesmaximal, characteristic
14#20298650C211yesmaximal, characteristic, complemented
15#464×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268637C2211yescharacteristic, complemented
19C2×#14268636C2211yescharacteristic, complemented
20C2×#14268634C2211yescharacteristic
21C2×#14268634C2211yescharacteristic, complemented
22C2×D904C2211yescharacteristic
23C2×#14268632C2211yescharacteristic
24#16813617—21no—
25#16813613C2211yescharacteristic, complemented
26#16813611C2211yescharacteristic
27#16813611C2211yescharacteristic, complemented
28#16813610C2211yescharacteristic
29#16813609C2211yescharacteristic
30#16813608—21no—
31#16813608—21no—
32#16813607—21no—
33#16813598C2211yescharacteristic
34#16813597C2211yescharacteristic
35C4×D452—21no—
36C4×D452C2211yescharacteristic, complemented
37#16813579—21no—
38C22⋊C4×D113—21no—
39C22⋊C4×D113—21no—
40C42×D113C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813545C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50C8×Dic113C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×Q16×C113C2211yescharacteristic, complemented
53C2×SD16×C113C2211yescharacteristic
54#124×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic
59C23×D113—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62Q8×D113—41no—
63Q8×D113—41no—
64C2×D452—21no—
65C2×D452C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68D4×D113—41no—
69D4×D113—41no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113D411yescharacteristic
73C2×C4×D113D411yescharacteristic
74C2×C4×D113C2311yescharacteristic
75#14268637—41no—
76#14268636—41no—
77#14268634—41no—
78#14268634—41no—
79D904—41no—
80#14268632—41no—
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2311yescharacteristic
83C4⋊Dic113—21no—
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98C4×Dic113D411yescharacteristic
99C4×Dic113D411yescharacteristic
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×Q8×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104Q16×C113—41no—
105SD16×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C22⋊C4×C113—21no—
112C42×C113—21no—
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C22×D113—21no—
116C22×D113—21no—
117C22×D113—42no—
118C22×D113—42no—
119C22×D113—42no—
120C22×D113C2×D411yescharacteristic
121Q8×C113—21no—
122Q8×C113—21no—
123Q8×C113—21no—
124Q8×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2411yescharacteristic
133C22⋊D113—42no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139D452—21no—
140D452—21no—
141D452—21no—
142D452—21no—
143D452—42no—
144C4×D113—22no—
145C4×D113—21no—
146C4×D113—21no—
147C4×D113—41no—
148C4×D113—42no—
149C4×D113—42no—
150Dic226—21no—
151Dic226—21no—
152Dic226—42no—
153C8×C113—21no—
154C8×C113—21no—
155#11744751—21no—
156#11744751—21no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113C22×D411yescharacteristic
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—84no—
170C2×D113#13512yes—
171C4×C113—21no—
172C4×C113—21no—
173C4×C113—41no—
174C4×C113—41no—
175C4×C113—41no—
176C4×C113H(5,𝔽2)11yescharacteristic
177C4×C113H(5,𝔽2)11yescharacteristic
178Dic113—21no—
179Dic113—21no—
180Dic113—21no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—81no—
184C2×C113#53511yescharacteristic
185C2×C113C2×#13511yescharacteristic
186C2×C113#57511yescharacteristic
187D113—22no—
188D113—81no—
189D113—81no—
190#3211—1131nomaximal, Sylow
191C113#321111yescharacteristic, complemented, Sylow
192#529—1131no—
193C2×#124—1131no—
194#495—1131no—
195#495—1131no—
196#488—1131no—
197#488—1131no—
198#464—1131no—
199#464D11311yescharacteristic, complemented
200#463—1131no—
201#463—1131no—
202#451—1131no—
203#450—1131no—
204#448—1131no—
205#447—1131no—
206#431—1131no—
207C22×Q8—1131no—
208C22×D4—1131no—
209C2×Q16—1131no—
210C2×Q16C2×D11311yescharacteristic, complemented
211C2×SD16—1131no—
212C2×SD16—1131no—
213C2×SD16—1131no—
214C2×SD16C2×D11311yescharacteristic
215C2×D8—1131no—
216C2×D8—1131no—
217#126—2261no—
218#125—1131no—
219#124—1131no—
220#124—1131no—
221#124—1131no—
222#124—1131no—
223#124—2261no—
224#124—2261no—
225#124C2×D11311yescharacteristic
226#123—2261no—
227C22⋊Q8—1131no—
228#121—1131no—
229C4×Q8C2×D11311yescharacteristic, complemented
230C4×D4—1131no—
231C4×D4—2261no—
232#117—2261no—
233C2×C22⋊C4—2261no—
234C2×C22⋊C4—2261no—
235C2×C42—1131no—
236C4⋊C8—1131no—
237C4⋊C8C2×D11311yescharacteristic, complemented
238#103—1131no—
239#103—1131no—
240#103—1131no—
241#103C2×D11311yescharacteristic, complemented
242#102—1131no—
243#102—1131no—
244#102—1131no—
245#102C2×D11311yescharacteristic
246C22⋊C8—1131no—
247C22⋊C8—1131no—
248C4×C8—1131no—
249C4×C8—1131no—
250C24—2261no—
251C2×Q8—1131no—
252C2×Q8—4521no—
253C2×Q8—4521no—
254C2×Q8—2261no—
255C2×Q8C22×D11311yescharacteristic
256C2×Q8C22×D11311yescharacteristic
257C2×D4—1131no—
258C2×D4—1131no—
259C2×D4—4521no—
260C2×D4—4521no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4C22×D11311yescharacteristic
264C22×C4—1131no—
265C22×C4—1131no—
266C22×C4—1131no—
267C22×C4—2261no—
268C22×C4—2261no—
269Q16—41no—
270Q16—4521no—
271SD16—41no—
272SD16—4521no—
273SD16—4521no—
274SD16—4521no—
275D8—4521no—
276D8—4521no—
277C2×C8—1131no—
278C2×C8—1131no—
279C2×C8C22×D11311yescharacteristic
280C2×C8C22×D11311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—1131no—
283C4⋊C4—2261no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4C22×D11311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C42—21no—
301C42—1131no—
302C42—1131no—
303C42—1131no—
304C42C22×D11311yescharacteristic
305C23—21no—
306C23—1131no—
307C23—4522no—
308C23—4522no—
309C23—4522no—
310C23—2261no—
311C23—2261no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—4522no—
317Q8—2261no—
318Q8—2261no—
319D4—21no—
320D4—21no—
321D4—4522no—
322D4—4522no—
323D4—2261no—
324D4—2261no—
325D4—2261no—
326D4—2261no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—1131no—
331C2×C4—1131no—
332C2×C4—1131no—
333C2×C4—4522no—
334C2×C4—4521no—
335C2×C4—4522no—
336C2×C4—2262no—
337C2×C4—2261no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4D4×D11311yescharacteristic
342C2×C4D4×D11311yescharacteristic
343C2×C4C23×D11311yescharacteristic
344C8—21no—
345C8—21no—
346C8—2261no—
347C8—2261no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—1132no—
352C22—9044no—
353C22—4521no—
354C22—4521no—
355C22—4521no—
356C22—4521no—
357C22—4521no—
358C22—4521no—
359C22—2261no—
360C22—2261no—
361C22C2×D4×D11311yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—4521no—
368C4—4521no—
369C4—2261no—
370C4—2261no—
371C4—2261no—
372C4#1681366711yescharacteristic
373C4#1681366811yescharacteristic
374C2—81no—
375C2—9041no—
376C2—9041no—
377C2—2262no—
378C2#2029916411yescharacteristic
379C2#135×D11311yescharacteristic
380C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radical#20298733C2
hypercenter#464D113
hypocenterC113#3211
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #20299135C2semidirect
2. #124×D113C2semidirect
3. #20298983C2semidirect
4. #20298979C2semidirect
5. #20298954C2semidirect
6. #20298951C2semidirect
7. #20298820C2semidirect
8. #20298814C2semidirect
9. #20298810C2semidirect
10. #20298752C2semidirect
11. #20298747C2semidirect
12. #20298738C2semidirect
14. #20298650C2semidirect
15. #464×C113C2semidirect
18. C2×#14268637C22semidirect
19. C2×#14268636C22semidirect
21. C2×#14268634C22semidirect
25. #16813613C22semidirect
27. #16813611C22semidirect
36. C4×D452C22semidirect
41. C4⋊#11744751C22semidirect
42. #16813547C22semidirect
43. #16813546C22semidirect
44. #16813545C22semidirect
50. C8×Dic113C22semidirect
51. C8×Dic113C22semidirect
52. C2×Q16×C113C22semidirect
55. C4×Q8×C113C22semidirect
56. C4⋊C8×C113C22semidirect
57. #103×C113C22semidirect
191. C113#3211semidirect
199. #464D113semidirect
210. C2×Q16C2×D113semidirect
229. C4×Q8C2×D113semidirect
237. C4⋊C8C2×D113semidirect
241. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991352
#124×D1132
#202989832
#202989792
#202989542
#202989512
#202988202
#202988142
#202988102
#202987522
#202987472
#202987382
#202987332
#202986502
#464×C1132
#3211113