Finite Group Databasebeta

← #28407440

Subgroups — #28407440

Order 14464.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299633C211yesmaximal, characteristic, complemented
2#20299631C211yesmaximal, characteristic, complemented
3#20299630C211yesmaximal, characteristic, complemented
4#20299629C211yesmaximal, characteristic, complemented
5#20299629C211yesmaximal, characteristic, complemented
6#20299627C211yesmaximal, characteristic, complemented
7#20299625C211yesmaximal, characteristic, complemented
8D4×#11744753C211yesmaximal, characteristic, complemented
9#20299622C211yesmaximal, characteristic, complemented
10#20299622C211yesmaximal, characteristic, complemented
11#20299572C211yesmaximal, characteristic, complemented
12#20299571C211yesmaximal, characteristic, complemented
13#20299568C211yesmaximal, characteristic, complemented
14C2×C22⋊#11744753C211yesmaximal, characteristic, complemented
15#20299104C211yesmaximal, characteristic
16C2×#14268657C2211yescharacteristic, complemented
17C2×#14268656C2211yescharacteristic
18C2×#14268656C2211yescharacteristic
19C2×#14268656C2211yescharacteristic, complemented
20C2×#14268655C2211yescharacteristic, complemented
21C22×#11744753C2211yescharacteristic
22C22×#11744753C2211yescharacteristic
23C22×#11744753C2211yescharacteristic, complemented
24#16813689C2211yescharacteristic, complemented
25#16813689C2211yescharacteristic, complemented
26C4⋊#11744753C2211yescharacteristic, complemented
27C4⋊#11744753C2211yescharacteristic, complemented
28#16813679C2211yescharacteristic, complemented
29#16813679C2211yescharacteristic, complemented
30C22⋊#11744753C2211yescharacteristic
31C22⋊#11744753C2211yescharacteristic
32C22⋊#11744753C2211yescharacteristic
33C22⋊#11744753C2211yescharacteristic
34C22⋊#11744753C2211yescharacteristic
35C22⋊#11744753C2211yescharacteristic
36C22⋊#11744753C2211yescharacteristic
37C22⋊#11744753C2211yescharacteristic
38C22⋊#11744753C2211yescharacteristic, complemented
39C22⋊#11744753C2211yescharacteristic, complemented
40#16813677C2211yescharacteristic, complemented
41#16813677C2211yescharacteristic, complemented
42C4×#11744753C2211yescharacteristic, complemented
43C4×#11744753C2211yescharacteristic, complemented
44C2×#14268646C2211yescharacteristic
45C23×Dic113C2211yescharacteristic
46#16813606C411yescharacteristic
47#16813603C411yescharacteristic
48#16813599C411yescharacteristic
49#16813599C411yescharacteristic
50#16813594C411yescharacteristic
51#16813594C411yescharacteristic
52#16813591C411yescharacteristic
53D4×Dic113C2211yescharacteristic
54D4×Dic113C2211yescharacteristic
55#16813582C2211yescharacteristic
56#16813582C2211yescharacteristic
57#16813578C2211yescharacteristic
58#120×C113C411yescharacteristic
59#14268657—41no—
60#14268656—41no—
61#14268656—41no—
62#14268656—41no—
63#14268655—41no—
64C2×#11744753—41no—
65C2×#11744753—41no—
66C2×#11744753—41no—
67C2×#11744753C2311yescharacteristic
68C2×#11744753C2311yescharacteristic
69C2×#11744753C2311yescharacteristic
70C2×#11744753C2311yescharacteristic
71C2×#11744753C2311yescharacteristic
72C2×#11744753C2311yescharacteristic
73C2×#11744753C2311yescharacteristic
74C2×#11744753C2311yescharacteristic
75#14268646—41no—
76#14268646—41no—
77C2×Dic226C2×C411yescharacteristic
78C2×C22⋊D113C2×C411yescharacteristic
79C2×C22⋊D113C2×C411yescharacteristic
80C2×C22⋊D113C2×C411yescharacteristic
81C2×C22⋊D113C2×C411yescharacteristic
82C22×Dic113—41no—
83C22×Dic113—41no—
84C22×Dic113C2×C411yescharacteristic
85C22×Dic113C2×C411yescharacteristic
86C22×Dic113C2×C411yescharacteristic
87C22×Dic113C2311yescharacteristic
88C22×Dic113C2311yescharacteristic
89C22×Dic113C2311yescharacteristic
90C22×Dic113C2311yescharacteristic
91C2×C4×D113C2311yescharacteristic
92C4⋊Dic113C2×C411yescharacteristic
93C4⋊Dic113C2×C411yescharacteristic
94#14268626C2×C411yescharacteristic
95#14268626C2×C411yescharacteristic
96#14268626C2×C411yescharacteristic
97#14268626C2×C411yescharacteristic
98C22⋊Dic113C2×C411yescharacteristic
99C22⋊Dic113C2×C411yescharacteristic
100C22⋊Dic113C2×C411yescharacteristic
101C22⋊Dic113C2×C411yescharacteristic
102C22⋊Dic113C2×C411yescharacteristic
103#14268624C2×C411yescharacteristic
104#14268624C2×C411yescharacteristic
105C4×Dic113C2311yescharacteristic
106C4×Dic113C2311yescharacteristic
107C24×C113C2×C411yescharacteristic
108C2×D4×C113C2×C411yescharacteristic
109C2×D4×C113C2×C411yescharacteristic
110C2×D4×C113C2×C411yescharacteristic
111C22⋊C4×C113C2×C411yescharacteristic
112C22⋊C4×C113C2×C411yescharacteristic
113C22⋊C4×C113C2×C411yescharacteristic
114C23×C113—22no—
115C23×C113—41no—
116C23×C113—41no—
117C23×C113C22×C411yescharacteristic
118C23×C113C22×C411yescharacteristic
119C23×C113C22×C411yescharacteristic
120C23×C113C22×C411yescharacteristic
121C22×D113C22×C411yescharacteristic
122D4×C113—22no—
123D4×C113—41no—
124D4×C113—41no—
125C2×C4×C113C22×C411yescharacteristic
126C2×C4×C113C22×C411yescharacteristic
127C2×C4×C113C22×C411yescharacteristic
128C22⋊D113—22no—
129C22⋊D113—41no—
130C22⋊D113—41no—
131C22⋊D113—41no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—41no—
141C2×Dic113—41no—
142C2×Dic113—41no—
143C2×Dic113C22×C411yescharacteristic
144C2×Dic113C22×C411yescharacteristic
145C2×Dic113C22×C411yescharacteristic
146C2×Dic113C22×C411yescharacteristic
147C2×Dic113C22×C411yescharacteristic
148C2×Dic113C22×C411yescharacteristic
149C2×Dic113C2411yescharacteristic
150C4×D113—21no—
151C4×D113—21no—
152Dic226—41no—
153#11744753—21no—
154#11744753—21no—
155#11744753—21no—
156#11744753—21no—
157#11744753—21no—
158#11744753—21no—
159#11744753—21no—
160#11744753—21no—
161C22×C113—21no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113—21no—
167C22×C113—21no—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—21no—
171C22×C113—21no—
172C22×C113—44no—
173C22×C113#13112yes—
174C22×C113C23×C411yescharacteristic
175C2×D113—21no—
176C2×D113—21no—
177C2×D113—21no—
178C4×C113—21no—
179C4×C113—21no—
180C4×C113—21no—
181Dic113—21no—
182Dic113—21no—
183Dic113—21no—
184Dic113—21no—
185Dic113—21no—
186Dic113—21no—
187Dic113H(5,𝔽2)11yescharacteristic
188Dic113H(5,𝔽2)11yescharacteristic
189C2×C113—22no—
190C2×C113—41no—
191C2×C113—41no—
192C2×C113—41no—
193C2×C113#51811yescharacteristic
194C2×C113C2×#13111yescharacteristic
195C2×C113#56811yescharacteristic
196D113—41no—
197#2976—1131nomaximal, Sylow
198C113#297611yescharacteristic, complemented, Sylow
199#525—1131no—
200#436—1131no—
201#436—1131no—
202#435—1131no—
203#435—1131no—
204#435—1131no—
205#435—1131no—
206C8×D4—1131no—
207C8×D4—1131no—
208#433—1131no—
209#433—1131no—
210#408—1131no—
211#408—1131no—
212#407—1131no—
213C2×C22⋊C8—1131no—
214C2×#41—1131no—
215C23×C4—1131no—
216C2×M16—1131no—
217C2×M16—1131no—
218C2×M16—1131no—
219C2×M16—1131no—
220C22×C8—1131no—
221C22×C8—1131no—
222C22×C8—1131no—
223C22×C8—1131no—
224#123—1131no—
225#123—1131no—
226C22⋊Q8—1131no—
227C22⋊Q8—1131no—
228#121—1131no—
229#121—1131no—
230#120—1131no—
231#120#9067311yescharacteristic
232C4×D4—1131no—
233C4×D4—1131no—
234C4×D4—1131no—
235C4×D4—1131no—
236#117—1131no—
237C4⋊C8—1131no—
238C4⋊C8—1131no—
239C4⋊C8—1131no—
240C4⋊C8—1131no—
241C22⋊C8—1131no—
242C22⋊C8—1131no—
243C22⋊C8—1131no—
244C22⋊C8—1131no—
245C22⋊C8—1131no—
246C22⋊C8—1131no—
247C22⋊C8—1131no—
248C22⋊C8—1131no—
249C22⋊C8—1131no—
250C22⋊C8—1131no—
251C22⋊C8—1131no—
252C22⋊C8—1131no—
253#97—1131no—
254#97—1131no—
255C4×C8—1131no—
256C4×C8—1131no—
257C24C2×#9067311yescharacteristic
258#41—4521no—
259#41—4521no—
260C2×Q8—1131no—
261C2×D4—1131no—
262C2×D4—1131no—
263C2×D4—1131no—
264C2×D4—1131no—
265C2×D4C2×#9067311yescharacteristic
266C2×D4C2×#9067311yescharacteristic
267C2×D4C2×#9067311yescharacteristic
268C22×C4—1131no—
269C22×C4—1131no—
270C22×C4—1131no—
271C22×C4—1131no—
272C22×C4—1131no—
273C22×C4—1131no—
274C22×C4—1131no—
275C22×C4—1131no—
276C22×C4—4521no—
277C22×C4—4521no—
278M16—4521no—
279M16—4521no—
280M16—4521no—
281M16—4521no—
282C2×C8—1131no—
283C2×C8—1131no—
284C2×C8—1131no—
285C2×C8—1131no—
286C2×C8—1131no—
287C2×C8—1131no—
288C2×C8—1131no—
289C2×C8—1131no—
290C2×C8—4521no—
291C2×C8—4521no—
292C2×C8—4521no—
293C2×C8—4521no—
294C4⋊C4—1131no—
295C4⋊C4—1131no—
296C4⋊C4—1131no—
297C4⋊C4—1131no—
298C4⋊C4—1131no—
299C4⋊C4—1131no—
300C22⋊C4—1131no—
301C22⋊C4—1131no—
302C22⋊C4—1131no—
303C22⋊C4—1131no—
304C22⋊C4—1131no—
305C22⋊C4—1131no—
306C22⋊C4—1131no—
307C22⋊C4C2×#9067311yescharacteristic
308C22⋊C4C2×#9067311yescharacteristic
309C22⋊C4C2×#9067311yescharacteristic
310C42—1131no—
311C42—1131no—
312C23—22no—
313C23—41no—
314C23—41no—
315C23—1131no—
316C23C22×#9067311yescharacteristic
317C23C22×#9067311yescharacteristic
318C23C22×#9067311yescharacteristic
319C23C22×#9067311yescharacteristic
320Q8—4521no—
321D4—22no—
322D4—41no—
323D4—41no—
324D4—4521no—
325D4—4521no—
326D4—4521no—
327D4—2262no—
328C2×C4—1131no—
329C2×C4—1131no—
330C2×C4—1131no—
331C2×C4—1131no—
332C2×C4—1131no—
333C2×C4—1131no—
334C2×C4—1131no—
335C2×C4—4521no—
336C2×C4—4521no—
337C2×C4—4521no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4—2261no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4—2261no—
345C2×C4—2261no—
346C2×C4—2261no—
347C2×C4—2261no—
348C2×C4C22×#9067311yescharacteristic
349C2×C4C22×#9067311yescharacteristic
350C2×C4C22×#9067311yescharacteristic
351C8—2261no—
352C8—2261no—
353C8—2261no—
354C8—2261no—
355C8—2261no—
356C8—2261no—
357C8—2261no—
358C8—2261no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—44no—
371C22—2261no—
372C22—2261no—
373C22—2261no—
374C22#1681370912yes—
375C22C23×#9067311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—1131no—
380C4—1131no—
381C4—2261no—
382C4—2261no—
383C4—2261no—
384C4—2261no—
385C4—2261no—
386C4—2261no—
387C2—22no—
388C2—41no—
389C2—41no—
390C2—41no—
391C2—4521no—
392C2#2029966511yescharacteristic
393C2C2×#1681370911yescharacteristic
394C2#2029967611yescharacteristic
subgroupG/H
center, FrattiniC22C23×#90673
commutator, socleC22×C113C23×C4
Fitting#120×C113C4
prime radical#20299104C2
cosocleC2×Dic113C24
hypercenter#120#90673
hypocenterC113#2976
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #20299633C2semidirect
2. #20299631C2semidirect
3. #20299630C2semidirect
4. #20299629C2semidirect
5. #20299629C2semidirect
6. #20299627C2semidirect
7. #20299625C2semidirect
8. D4×#11744753C2semidirect
9. #20299622C2semidirect
10. #20299622C2semidirect
11. #20299572C2semidirect
12. #20299571C2semidirect
13. #20299568C2semidirect
14. C2×C22⋊#11744753C2semidirect
16. C2×#14268657C22semidirect
19. C2×#14268656C22semidirect
20. C2×#14268655C22semidirect
23. C22×#11744753C22semidirect
24. #16813689C22semidirect
25. #16813689C22semidirect
26. C4⋊#11744753C22semidirect
27. C4⋊#11744753C22semidirect
28. #16813679C22semidirect
29. #16813679C22semidirect
38. C22⋊#11744753C22semidirect
39. C22⋊#11744753C22semidirect
40. #16813677C22semidirect
41. #16813677C22semidirect
42. C4×#11744753C22semidirect
43. C4×#11744753C22semidirect
198. C113#2976semidirect

Maximal subgroups

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

subgroupindex
#202996332
#202996312
#202996302
#202996292
#202996272
#202996252
D4×#117447532
#202996222
#202995722
#202995712
#202995682
C2×C22⋊#117447532
#202991042
#2976113