Finite Group Databasebeta

← #28401534

Subgroups — #28401534

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#20299127C211yesmaximal, characteristic, complemented
2#124×D113C211yesmaximal, characteristic, complemented
3#20298980C211yesmaximal, characteristic, complemented
4#20298953C211yesmaximal, characteristic, complemented
5#20298952C211yesmaximal, characteristic, complemented
6#20298822C211yesmaximal, characteristic, complemented
7#20298818C211yesmaximal, characteristic, complemented
8#20298815C211yesmaximal, characteristic, complemented
9#20298811C211yesmaximal, characteristic, complemented
10#20298752C211yesmaximal, characteristic, complemented
11#20298747C211yesmaximal, characteristic, complemented
12#20298735C211yesmaximal, characteristic, complemented
13#20298730C211yesmaximal, characteristic
14#20298649C211yesmaximal, characteristic, complemented
15#495×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268637C2211yescharacteristic, complemented
19C2×#14268635C2211yescharacteristic, complemented
20C2×#14268634C2211yescharacteristic
21C2×#14268632C2211yescharacteristic
22#16813615—21no—
23#16813614C2211yescharacteristic, complemented
24#16813611C2211yescharacteristic
25#16813610C2211yescharacteristic
26#16813609C2211yescharacteristic
27#16813608—21no—
28#16813608—21no—
29#16813604—21no—
30#16813598C2211yescharacteristic
31#16813593C2211yescharacteristic
32Q8×Dic113C2211yescharacteristic, complemented
33D4×Dic113C2211yescharacteristic, complemented
34#16813582—21no—
35#16813578—21no—
36C22⋊C4×D113—21no—
37C22⋊C4×D113—21no—
38C42×D113C2211yescharacteristic
39#16813551C2211yescharacteristic, complemented
40#16813551C2211yescharacteristic, complemented
41#16813547C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813546C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51C4×#11744751C2211yescharacteristic, complemented
52C2×Q16×C113C2211yescharacteristic, complemented
53C2×SD16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic, complemented
55C2×D8×C113C2211yescharacteristic
56#124×C113C2211yescharacteristic
57#124×C113C2211yescharacteristic, complemented
58C4×C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62Q8×D113—41no—
63Q8×D113—41no—
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67D4×D113—41no—
68D4×D113—41no—
69C22×Dic113—21no—
70C2×C4×D113—21no—
71C2×C4×D113D411yescharacteristic
72C2×C4×D113D411yescharacteristic
73C2×C4×D113C2311yescharacteristic
74#14268637—41no—
75#14268635—41no—
76#14268634—41no—
77#14268632—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95C4×Dic113—21no—
96C4×Dic113D411yescharacteristic
97C4×Dic113D411yescharacteristic
98C4×Dic113C2311yescharacteristic
99C2×Q8×C113C2311yescharacteristic
100C2×Q8×C113C2311yescharacteristic
101C2×D4×C113C2311yescharacteristic
102C2×D4×C113C2311yescharacteristic
103Q16×C113—41no—
104SD16×C113—41no—
105SD16×C113—41no—
106D8×C113—41no—
107C2×C8×C113C2311yescharacteristic
108C2×C8×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C22⋊C4×C113—21no—
111C22⋊C4×C113—21no—
112C22⋊C4×C113—21no—
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C23×C113—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—
127D4×C113—21no—
128D4×C113—21no—
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—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—42no—
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142C2×Dic113C2×D411yescharacteristic
143D452—21no—
144D452—21no—
145C4×D113—22no—
146C4×D113—21no—
147C4×D113—21no—
148C4×D113—41no—
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×C113—41no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113C22×D411yescharacteristic
164C2×D113—21no—
165C2×D113—21no—
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×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×C113C2×#13511yescharacteristic
187C2×C113#57511yescharacteristic
188D113—22no—
189D113—81no—
190#3211—1131nomaximal, Sylow
191C113#321111yescharacteristic, complemented, Sylow
192#529—1131no—
193C2×#124—1131no—
194#495—1131no—
195#495D11311yescharacteristic, complemented
196#488—1131no—
197#488—1131no—
198#464—1131no—
199#464—1131no—
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×SD16C2×D11311yescharacteristic
214C2×SD16C2×D11311yescharacteristic, complemented
215C2×D8—1131no—
216C2×D8C2×D11311yescharacteristic
217#126—2261no—
218#125—1131no—
219#124—1131no—
220#124—1131no—
221#124—1131no—
222#124—2261no—
223#124—2261no—
224#124C2×D11311yescharacteristic
225#124C2×D11311yescharacteristic, complemented
226#123—2261no—
227C22⋊Q8—1131no—
228#121—1131no—
229C4×Q8—1131no—
230C4×D4—1131no—
231C4×D4—2261no—
232#117—2261no—
233C2×C22⋊C4—2261no—
234C2×C22⋊C4—2261no—
235C2×C42—1131no—
236C4⋊C8—1131no—
237C4⋊C8—1131no—
238#103—1131no—
239#103—1131no—
240#103—1131no—
241#103—1131no—
242#102—1131no—
243#102—1131no—
244#102—1131no—
245#102—1131no—
246C22⋊C8—1131no—
247C22⋊C8—1131no—
248C4×C8—1131no—
249C4×C8C2×D11311yescharacteristic, complemented
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—4521no—
259C2×D4—4521no—
260C2×D4—2261no—
261C2×D4—2261no—
262C2×D4C22×D11311yescharacteristic
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—41no—
273SD16—4521no—
274SD16—4521no—
275D8—41no—
276D8—4521no—
277C2×C8—1131no—
278C2×C8—1131no—
279C2×C8C22×D11311yescharacteristic
280C2×C8C22×D11311yescharacteristic
281C4⋊C4—1131no—
282C4⋊C4—1131no—
283C4⋊C4—2261no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
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—1131no—
301C42—1131no—
302C42—1131no—
303C42—2261no—
304C42C22×D11311yescharacteristic
305C23—21no—
306C23—21no—
307C23—1131no—
308C23—4522no—
309C23—4522no—
310C23—4522no—
311C23—2261no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—4522no—
317Q8—2261no—
318Q8—2261no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—4522no—
324D4—4522no—
325D4—2261no—
326D4—2261no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—1131no—
330C2×C4—1131no—
331C2×C4—1131no—
332C2×C4—4521no—
333C2×C4—4522no—
334C2×C4—4522no—
335C2×C4—2262no—
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—1132no—
355C22—9044no—
356C22—4521no—
357C22—4521no—
358C22—4521no—
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#1681366711yescharacteristic
374C2—81no—
375C2—81no—
376C2—9041no—
377C2—2262no—
378C2#2029916111yescharacteristic
379C2#135×D11311yescharacteristic
380C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#495×C113C2
socleC22×C113C22×D4
prime radical#20298730C2
hypercenter#495D113
hypocenterC113#3211
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #20299127C2semidirect
2. #124×D113C2semidirect
3. #20298980C2semidirect
4. #20298953C2semidirect
5. #20298952C2semidirect
6. #20298822C2semidirect
7. #20298818C2semidirect
8. #20298815C2semidirect
9. #20298811C2semidirect
10. #20298752C2semidirect
11. #20298747C2semidirect
12. #20298735C2semidirect
14. #20298649C2semidirect
15. #495×C113C2semidirect
18. C2×#14268637C22semidirect
19. C2×#14268635C22semidirect
23. #16813614C22semidirect
32. Q8×Dic113C22semidirect
33. D4×Dic113C22semidirect
39. #16813551C22semidirect
40. #16813551C22semidirect
41. #16813547C22semidirect
42. #16813547C22semidirect
43. #16813546C22semidirect
44. #16813546C22semidirect
51. C4×#11744751C22semidirect
52. C2×Q16×C113C22semidirect
54. C2×SD16×C113C22semidirect
57. #124×C113C22semidirect
58. C4×C8×C113C22semidirect
191. C113#3211semidirect
195. #495D113semidirect
210. C2×Q16C2×D113semidirect
214. C2×SD16C2×D113semidirect
225. #124C2×D113semidirect
249. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991272
#124×D1132
#202989802
#202989532
#202989522
#202988222
#202988182
#202988152
#202988112
#202987522
#202987472
#202987352
#202987302
#202986492
#495×C1132
#3211113