Finite Group Databasebeta

← #28401645

Subgroups — #28401645

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#20299206C211yesmaximal, characteristic, complemented
2#20299161C211yesmaximal, characteristic
3#20298989C211yesmaximal, characteristic, complemented
4#20298969C211yesmaximal, characteristic, complemented
5#20298961C211yesmaximal, characteristic, complemented
6#20298951C211yesmaximal, characteristic, complemented
7#20298821C211yesmaximal, characteristic, complemented
8#20298820C211yesmaximal, characteristic, complemented
9#20298795C211yesmaximal, characteristic, complemented
10#20298761C211yesmaximal, characteristic, complemented
11#20298757C211yesmaximal, characteristic, complemented
12#20298750C211yesmaximal, characteristic, complemented
13#20298747C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#460×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×Dic452C2211yescharacteristic, complemented
19C2×#14268637C2211yescharacteristic, complemented
20C2×#14268636C2211yescharacteristic
21C2×#14268635C2211yescharacteristic
22C2×#14268635C2211yescharacteristic, complemented
23C2×#14268634C2211yescharacteristic
24#16813620C2211yescharacteristic, complemented
25#16813618C2211yescharacteristic
26#16813617—21no—
27#16813616—21no—
28#16813614—21no—
29#16813613C2211yescharacteristic, complemented
30#16813612—21no—
31#16813610C2211yescharacteristic
32#16813609C2211yescharacteristic
33#16813602C2211yescharacteristic
34#16813598C2211yescharacteristic
35#16813594—21no—
36#16813594—21no—
37#16813590—21no—
38#16813590—21no—
39C4×Dic226C2211yescharacteristic, complemented
40#16813579C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813545C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic, complemented
54#127×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268646—41no—
61#14268646—41no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69D4×D113—41no—
70D4×D113—41no—
71C22×Dic113—21no—
72C2×C4×D113C2311yescharacteristic
73Dic452—41no—
74#14268637—41no—
75#14268636—41no—
76#14268635—41no—
77#14268635—41no—
78#14268634—41no—
79C2×#11744751C2311yescharacteristic
80C2×#11744751C2311yescharacteristic
81C4⋊Dic113—21no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626D411yescharacteristic
90#14268626D411yescharacteristic
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624D411yescharacteristic
98#14268624D411yescharacteristic
99C4×Dic113—21no—
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×D4×C113—21no—
103C2×D4×C113—21no—
104C2×D4×C113C2311yescharacteristic
105C2×D4×C113C2311yescharacteristic
106SD16×C113—41no—
107SD16×C113—41no—
108C2×C8×C113C2311yescharacteristic
109C2×C8×C113C2311yescharacteristic
110C4⋊C4×C113—21no—
111C4⋊C4×C113C2311yescharacteristic
112C42×C113—21no—
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C23×C113—21no—
116C22×D113—21no—
117C22×D113—42no—
118C22×D113—81no—
119C22×D113—81no—
120C22×D113C2×D411yescharacteristic
121Q8×C113—21no—
122Q8×C113—21no—
123D4×C113—21no—
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—81no—
128D4×C113—81no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2411yescharacteristic
134C22⋊D113—42no—
135C22⋊D113—42no—
136C22⋊D113—81no—
137C22⋊D113—81no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—42no—
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144C2×Dic113C2×D411yescharacteristic
145D452—21no—
146D452—21no—
147C4×D113—21no—
148C4×D113—21no—
149Dic226—21no—
150Dic226—21no—
151Dic226—21no—
152Dic226—21no—
153C8×C113—21no—
154C8×C113—21no—
155#11744751—21no—
156#11744751—21no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113C22×D411yescharacteristic
164C2×D113—21no—
165C2×D113—21no—
166C2×D113—21no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—84no—
171C4×C113—21no—
172C4×C113—21no—
173C4×C113—41no—
174C4×C113—41no—
175C4×C113H(5,𝔽2)11yescharacteristic
176C4×C113H(5,𝔽2)11yescharacteristic
177Dic113—21no—
178Dic113—21no—
179Dic113—21no—
180Dic113—41no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—81no—
184C2×C113—81no—
185C2×C113#53511yescharacteristic
186C2×C113#57711yescharacteristic
187C2×C113#57711yescharacteristic
188D113—41no—
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#460D11311yescharacteristic, complemented
202#452—1131no—
203#452—1131no—
204#450—1131no—
205#450—1131no—
206#433—1131no—
207C2×#41—1131no—
208C22×D4—1131no—
209C2×Q16—1131no—
210C2×Q16—1131no—
211C2×SD16—1131no—
212C2×SD16—1131no—
213C2×SD16—1131no—
214C2×SD16—1131no—
215C2×SD16C2×D11311yescharacteristic
216C2×SD16C2×D11311yescharacteristic, complemented
217C4⋊Q8—1131no—
218#127—1131no—
219#127C2×D11311yescharacteristic
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⋊Q8—1131no—
229#121—2261no—
230#121—2261no—
231#120—2261no—
232#120—2261no—
233C4×Q8—1131no—
234C4×Q8C2×D11311yescharacteristic, complemented
235#117—1131no—
236C4⋊C8—1131no—
237C4⋊C8C2×D11311yescharacteristic, complemented
238#103—1131no—
239#103—1131no—
240#102—1131no—
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102C2×D11311yescharacteristic
245#102C2×D11311yescharacteristic, complemented
246C22⋊C8—1131no—
247C22⋊C8—1131no—
248#97—1131no—
249C4×C8—1131no—
250C24—2261no—
251#41—4521no—
252#41—4521no—
253C2×Q8—1131no—
254C2×Q8—1131no—
255C2×Q8C22×D11311yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—1131no—
259C2×D4—4521no—
260C2×D4—4521no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4—2261no—
264C2×D4—2261no—
265C2×D4C22×D11311yescharacteristic
266C2×D4C22×D11311yescharacteristic
267C22×C4—1131no—
268C22×C4—2261no—
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—1131no—
294C22⋊C4—1131no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C42—21no—
302C42—1131no—
303C42—2261no—
304C42C22×D11311yescharacteristic
305C23—21no—
306C23—21no—
307C23—1131no—
308C23—9041no—
309C23—9041no—
310C23—4522no—
311C23—2261no—
312Q8—21no—
313Q8—21no—
314Q8—2261no—
315Q8—2261no—
316Q8—2261no—
317Q8—2261no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—81no—
323D4—81no—
324D4—9041no—
325D4—9041no—
326D4—4522no—
327D4—4522no—
328D4—2261no—
329D4—2261no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—1131no—
333C2×C4—1131no—
334C2×C4—1131no—
335C2×C4—4522no—
336C2×C4—2261no—
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—41no—
352C22—41no—
353C22—41no—
354C22—9044no—
355C22—4521no—
356C22—4521no—
357C22—4521no—
358C22—2261no—
359C22—2261no—
360C22—2261no—
361C22C2×D4×D11311yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—4521no—
367C4—4521no—
368C4—4521no—
369C4—2261no—
370C4—2261no—
371C4—2261no—
372C4#1681366711yescharacteristic
373C4#1681366811yescharacteristic
374C2—81no—
375C2—81no—
376C2—9041no—
377C2—4521no—
378C2#2029916411yescharacteristic
379C2#2029940411yescharacteristic
380C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#460×C113C2
socleC22×C113C22×D4
prime radical#20299161C2
hypercenter#460D113
hypocenterC113#3222
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #20299206C2semidirect
3. #20298989C2semidirect
4. #20298969C2semidirect
5. #20298961C2semidirect
6. #20298951C2semidirect
7. #20298821C2semidirect
8. #20298820C2semidirect
9. #20298795C2semidirect
10. #20298761C2semidirect
11. #20298757C2semidirect
12. #20298750C2semidirect
13. #20298747C2semidirect
14. #20298658C2semidirect
15. #460×C113C2semidirect
18. C2×Dic452C22semidirect
19. C2×#14268637C22semidirect
22. C2×#14268635C22semidirect
24. #16813620C22semidirect
29. #16813613C22semidirect
39. C4×Dic226C22semidirect
41. C4⋊#11744751C22semidirect
42. #16813547C22semidirect
43. #16813545C22semidirect
46. #16813543C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
53. C2×SD16×C113C22semidirect
55. C4×Q8×C113C22semidirect
56. C4⋊C8×C113C22semidirect
58. #102×C113C22semidirect
191. C113#3222semidirect
201. #460D113semidirect
216. C2×SD16C2×D113semidirect
234. C4×Q8C2×D113semidirect
237. C4⋊C8C2×D113semidirect
245. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992062
#202991612
#202989892
#202989692
#202989612
#202989512
#202988212
#202988202
#202987952
#202987612
#202987572
#202987502
#202987472
#202986582
#460×C1132
#3222113