Finite Group Databasebeta

← #28401642

Subgroups — #28401642

Order 14464.

396 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#20299208C211yesmaximal, characteristic, complemented
2#20299165C211yesmaximal, characteristic
3#20298989C211yesmaximal, characteristic, complemented
4#20298969C211yesmaximal, characteristic, complemented
5#20298961C211yesmaximal, characteristic, complemented
6#20298951C211yesmaximal, characteristic, complemented
7#20298819C211yesmaximal, characteristic, complemented
8#20298818C211yesmaximal, characteristic, complemented
9#20298797C211yesmaximal, characteristic, complemented
10#20298796C211yesmaximal, characteristic, complemented
11#20298762C211yesmaximal, characteristic, complemented
12#20298758C211yesmaximal, characteristic, complemented
13#20298749C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#450×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×Dic452C2211yescharacteristic, complemented
18C2×#14268637C2211yescharacteristic, complemented
19C2×#14268636C2211yescharacteristic, complemented
20C2×#14268635C2211yescharacteristic
21C2×#14268635C2211yescharacteristic
22C2×#14268634C2211yescharacteristic, complemented
23#16813620C2211yescharacteristic, complemented
24#16813618C2211yescharacteristic
25#16813618C2211yescharacteristic
26#16813615—21no—
27#16813615—21no—
28#16813613—21no—
29#16813613C2211yescharacteristic, complemented
30#16813612—21no—
31#16813609C2211yescharacteristic
32#16813609C2211yescharacteristic
33#16813601C2211yescharacteristic
34#16813593—21no—
35#16813593—21no—
36#16813591—21no—
37#16813591—21no—
38Q8×Dic113C2211yescharacteristic, complemented
39#16813587C2211yescharacteristic, complemented
40#16813581C2211yescharacteristic
41#16813551C2211yescharacteristic, complemented
42#16813551C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813545C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic, 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#14268647—41no—
60#14268647—41no—
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C4×D113—21no—
70Dic452—41no—
71#14268637—41no—
72#14268636—41no—
73#14268635—41no—
74#14268635—41no—
75#14268634—41no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C4⋊Dic113—21no—
79C4⋊Dic113—21no—
80C4⋊Dic113D411yescharacteristic
81C4⋊Dic113D411yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93C22⋊Dic113D411yescharacteristic
94C22⋊Dic113D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98C4×Dic113C2311yescharacteristic
99C24×C113—21no—
100C2×Q8×C113C2311yescharacteristic
101C2×D4×C113—21no—
102C2×D4×C113—41no—
103C2×D4×C113—41no—
104C2×D4×C113C2311yescharacteristic
105C2×D4×C113C2311yescharacteristic
106C22×C4×C113C2311yescharacteristic
107SD16×C113—41no—
108SD16×C113—41no—
109C2×C8×C113C2311yescharacteristic
110C2×C8×C113C2311yescharacteristic
111C4⋊C4×C113—21no—
112C4⋊C4×C113C2311yescharacteristic
113C22⋊C4×C113—21no—
114C23×C113—21no—
115C23×C113—21no—
116C23×C113—42no—
117C23×C113—81no—
118C23×C113—81no—
119C23×C113C2×D411yescharacteristic
120C22×D113—21no—
121Q8×C113—21no—
122Q8×C113—21no—
123D4×C113—21no—
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—42no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2411yescharacteristic
134C22⋊D113—42no—
135C22⋊D113—81no—
136C22⋊D113—81no—
137C22⋊D113—81no—
138C22⋊D113—81no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144C2×Dic113C2×D411yescharacteristic
145C2×Dic113C2×D411yescharacteristic
146D452—21no—
147D452—21no—
148C4×D113—42no—
149Dic226—21no—
150Dic226—21no—
151Dic226—21no—
152Dic226—21no—
153C8×C113—21no—
154C8×C113—21no—
155#11744751—21no—
156#11744751—21no—
157C22×C113—21no—
158C22×C113—21no—
159C22×C113—21no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—84no—
167C22×C113C22×D411yescharacteristic
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C4×C113—21no—
172C4×C113—41no—
173C4×C113—41no—
174C4×C113H(5,𝔽2)11yescharacteristic
175C4×C113H(5,𝔽2)11yescharacteristic
176Dic113—21no—
177Dic113—21no—
178Dic113—21no—
179Dic113—21no—
180Dic113—41no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—41no—
184C2×C113—81no—
185C2×C113—81no—
186C2×C113#53511yescharacteristic
187C2×C113#57711yescharacteristic
188C2×C113#57711yescharacteristic
189D113—81no—
190#3222—1131nomaximal, Sylow
191C113#322211yescharacteristic, complemented, Sylow
192#541—1131no—
193#535—1131no—
194#497—1131no—
195#492—1131no—
196#490—1131no—
197#488—1131no—
198#464—1131no—
199#464—1131no—
200#460—1131no—
201#460—1131no—
202#452—1131no—
203#452—1131no—
204#450—1131no—
205#450D11311yescharacteristic, complemented
206#433—1131no—
207C2×#41—1131no—
208C22×D4C2×D11311yescharacteristic
209C2×Q16—1131no—
210C2×Q16—1131no—
211C2×SD16—1131no—
212C2×SD16—1131no—
213C2×SD16—1131no—
214C2×SD16—1131no—
215C2×SD16C2×D11311yescharacteristic
216C2×SD16C2×D11311yescharacteristic
217C4⋊Q8—1131no—
218#127—1131no—
219#127—1131no—
220#126—2261no—
221#126—2261no—
222#125—1131no—
223#125—2261no—
224#125—2261no—
225#124—1131no—
226#124—1131no—
227C22⋊Q8—1131no—
228C22⋊Q8C2×D11311yescharacteristic
229#121—2261no—
230#121—2261no—
231#120—2261no—
232#120—2261no—
233C4×Q8—1131no—
234C4×Q8—1131no—
235#117—1131no—
236C4⋊C8—1131no—
237C4⋊C8—1131no—
238#103—1131no—
239#103—1131no—
240#102—1131no—
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102C2×D11311yescharacteristic
245#102C2×D11311yescharacteristic
246C22⋊C8—1131no—
247C22⋊C8C2×D11311yescharacteristic
248#97—1131no—
249C4×C8—1131no—
250C24—21no—
251#41—4521no—
252#41—4521no—
253C2×Q8—1131no—
254C2×Q8—1131no—
255C2×Q8C22×D11311yescharacteristic
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—1131no—
260C2×D4—2261no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4—2261no—
264C2×D4—2261no—
265C2×D4C22×D11311yescharacteristic
266C2×D4C22×D11311yescharacteristic
267C22×C4—2261no—
268C22×C4C22×D11311yescharacteristic
269Q16—4521no—
270Q16—4521no—
271SD16—41no—
272SD16—41no—
273SD16—4521no—
274SD16—4521no—
275SD16—4521no—
276SD16—4521no—
277C2×C8—1131no—
278C2×C8—1131no—
279C2×C8C22×D11311yescharacteristic
280C2×C8C22×D11311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—1131no—
283C4⋊C4—1131no—
284C4⋊C4—1131no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4—2261no—
288C4⋊C4—2261no—
289C4⋊C4—2261no—
290C4⋊C4—2261no—
291C4⋊C4—2261no—
292C4⋊C4C22×D11311yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—1131no—
295C22⋊C4—1131no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C42—1131no—
302C42—1131no—
303C42—2261no—
304C42—2261no—
305C23—21no—
306C23—21no—
307C23—42no—
308C23—81no—
309C23—81no—
310C23—2261no—
311C23D4×D11311yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—2261no—
315Q8—2261no—
316Q8—2261no—
317Q8—2261no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—9041no—
324D4—9041no—
325D4—9041no—
326D4—9041no—
327D4—4522no—
328D4—2261no—
329D4—2261no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—1131no—
335C2×C4—1131no—
336C2×C4—1131no—
337C2×C4—1131no—
338C2×C4—4522no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4—2261no—
342C2×C4D4×D11311yescharacteristic
343C2×C4C23×D11311yescharacteristic
344C8—21no—
345C8—21no—
346C8—2261no—
347C8—2261no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—84no—
358C22—4521no—
359C22—4521no—
360C22—4521no—
361C22C2×D4×D11311yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—4521no—
366C4—4521no—
367C4—4521no—
368C4—2261no—
369C4—2261no—
370C4—2261no—
371C4—2261no—
372C4#1681366711yescharacteristic
373C4#1681366711yescharacteristic
374C2—41no—
375C2—81no—
376C2—81no—
377C2—9041no—
378C2#2029916311yescharacteristic
379C2#2029940411yescharacteristic
380C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
prime radical#20299165C2
hypercenter#450D113
hypocenterC113#3222
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. #20299208C2semidirect
3. #20298989C2semidirect
4. #20298969C2semidirect
5. #20298961C2semidirect
6. #20298951C2semidirect
7. #20298819C2semidirect
8. #20298818C2semidirect
9. #20298797C2semidirect
10. #20298796C2semidirect
11. #20298762C2semidirect
12. #20298758C2semidirect
13. #20298749C2semidirect
14. #20298656C2semidirect
15. #450×C113C2semidirect
17. C2×Dic452C22semidirect
18. C2×#14268637C22semidirect
19. C2×#14268636C22semidirect
22. C2×#14268634C22semidirect
23. #16813620C22semidirect
29. #16813613C22semidirect
38. Q8×Dic113C22semidirect
39. #16813587C22semidirect
41. #16813551C22semidirect
42. #16813551C22semidirect
43. #16813547C22semidirect
44. #16813545C22semidirect
45. #16813544C22semidirect
48. #16813542C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
191. C113#3222semidirect
205. #450D113semidirect

Maximal subgroups

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

subgroupindex
#202992082
#202991652
#202989892
#202989692
#202989612
#202989512
#202988192
#202988182
#202987972
#202987962
#202987622
#202987582
#202987492
#202986562
#450×C1132
#3222113