Finite Group Databasebeta

← #28402537

Subgroups — #28402537

Order 14464.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299252C211yesmaximal, characteristic, complemented
2#20299244C211yesmaximal, characteristic, complemented
3#20298958C211yesmaximal, characteristic, complemented
4#20298929C211yesmaximal, characteristic, complemented
5#20298917C211yesmaximal, characteristic, complemented
6#20298889C211yesmaximal, characteristic, complemented
7#20298851C211yesmaximal, characteristic, complemented
8#20298827C211yesmaximal, characteristic, complemented
9#20298814C211yesmaximal, characteristic, complemented
10#20298745C211yesmaximal, characteristic, complemented
11#20298734C211yesmaximal, characteristic, complemented
12#20298711C211yesmaximal, characteristic, complemented
13#20298600C211yesmaximal, characteristic, complemented
14C2×#16813544C211yesmaximal, characteristic, complemented
15#435×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268646—21no—
18C22×D452C2211yescharacteristic
19C2×#14268636C2211yescharacteristic, complemented
20C2×D904C2211yescharacteristic
21C2×D904C2211yescharacteristic
22#16813622C2211yescharacteristic, complemented
23#16813610C2211yescharacteristic
24#16813607—21no—
25#16813606—21no—
26#16813606—21no—
27#16813602—21no—
28#16813601C2211yescharacteristic
29#16813596C2211yescharacteristic
30#16813596C2211yescharacteristic
31#16813596C2211yescharacteristic, complemented
32#16813595—21no—
33#16813590—21no—
34C4×D452C2211yescharacteristic
35C4×D452C2211yescharacteristic, complemented
36C2×C4⋊Dic113C2211yescharacteristic
37C2×C4⋊Dic113C2211yescharacteristic, complemented
38C22⋊C4×D113—21no—
39#16813554C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic, complemented
52C2×M16×C113C2211yescharacteristic, complemented
53C22×C8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55C4⋊C8×C113C2211yescharacteristic, complemented
56C22⋊C8×C113C2211yescharacteristic
57C22⋊C8×C113C2211yescharacteristic, complemented
58#97×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268647—22no—
61#14268647—41no—
62#14268646—44no—
63C2×Dic226—21no—
64C2×Dic226C2311yescharacteristic
65C2×D452—22no—
66C2×D452—21no—
67C2×D452—41no—
68C2×D452C2311yescharacteristic
69C2×D452C2311yescharacteristic
70C2×D452C2311yescharacteristic
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C22×Dic113—21no—
76C22×Dic113—21no—
77C2×C4×D113—21no—
78C2×C4×D113—21no—
79C2×C4×D113—21no—
80#14268636—41no—
81D904—22no—
82D904—41no—
83C4⋊Dic113—21no—
84C4⋊Dic113—21no—
85C4⋊Dic113—21no—
86C4⋊Dic113C2311yescharacteristic
87C4⋊Dic113C2311yescharacteristic
88C4⋊Dic113C2311yescharacteristic
89C4⋊Dic113C2311yescharacteristic
90#14268626—21no—
91C22⋊Dic113—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99C2×D4×C113D411yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102M16×C113—41no—
103C2×C8×C113—41no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113D411yescharacteristic
109C22⋊C4×C113D411yescharacteristic
110C22⋊C4×C113D411yescharacteristic
111C42×C113C2311yescharacteristic
112C23×C113C2×D411yescharacteristic
113C23×C113C2×D411yescharacteristic
114C22×D113—21no—
115C22×D113—21no—
116C22×D113—21no—
117C22×D113—42no—
118C22×D113—42no—
119C22×D113—81no—
120D4×C113—22no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—42no—
131C22⋊D113—42no—
132C22⋊D113—42no—
133C22⋊D113—81no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—42no—
140C2×Dic113—42no—
141D452—21no—
142D452—21no—
143D452—21no—
144D452—21no—
145D452—21no—
146D452—42no—
147D452#4112yescomplemented
148C4×D113—42no—
149C4×D113—42no—
150C4×D113—81no—
151Dic226—21no—
152Dic226—21no—
153Dic226—42no—
154C8×C113—21no—
155C8×C113—21no—
156C8×C113—21no—
157C8×C113—21no—
158C22×C113—21no—
159C22×C113—21no—
160C22×C113—21no—
161C22×C113—21no—
162C22×C113—21no—
163C22×C113AGL(1,ℤ/8)12yes—
164C22×C113C22×D411yescharacteristic
165C2×D113—22no—
166C2×D113—41no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—84no—
175C4×C113—21no—
176C4×C113—21no—
177C4×C113—21no—
178C4×C113—21no—
179C4×C113C2×#4111yescharacteristic
180C4×C113H(5,𝔽2)11yescharacteristic
181Dic113—41no—
182Dic113—41no—
183Dic113—41no—
184Dic113—41no—
185Dic113—41no—
186C2×C113—22no—
187C2×C113—41no—
188C2×C113#54611yescharacteristic
189C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C113#57711yescharacteristic
191D113—42no—
192D113—81no—
193D113—81no—
194#3306—1131nomaximal, Sylow
195C113#330611yescharacteristic, complemented, Sylow
196#547—1131no—
197#546—1131no—
198#489—1131no—
199#483—1131no—
200#481—1131no—
201#476—1131no—
202#469—1131no—
203#465—1131no—
204#463—1131no—
205#449—1131no—
206#447—1131no—
207#442—1131no—
208#435D11311yescharacteristic, complemented
209#417—1131no—
210C2×#102—1131no—
211C2×#41—1131no—
212C2×#41—2261no—
213C22×D4—1131no—
214C2×SD16—1131no—
215C2×D8—1131no—
216C2×D8—1131no—
217C2×M16C2×D11311yescharacteristic, complemented
218C22×C8C2×D11311yescharacteristic
219C4⋊Q8—1131no—
220#124—1131no—
221#123—2261no—
222#123—2261no—
223#123—2261no—
224C22⋊Q8—1131no—
225C22⋊Q8—2261no—
226#121—1131no—
227#121—1131no—
228#121—1131no—
229#121—2261no—
230#120—2261no—
231C4×D4—1131no—
232C4×D4—1131no—
233C4×D4C2×D11311yescharacteristic
234C2×C4⋊C4—1131no—
235C2×C4⋊C4—1131no—
236C2×C22⋊C4—2261no—
237#106—1131no—
238#106—1131no—
239#106—1131no—
240C4⋊C8C2×D11311yescharacteristic, complemented
241#103—1131no—
242#103—1131no—
243#103—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251C22⋊C8C2×D11311yescharacteristic
252C22⋊C8C2×D11311yescharacteristic, complemented
253#97C2×D11311yescharacteristic, complemented
254C24—2261no—
255#41—4521no—
256#41—4524no—
257#41—2262no—
258C2×Q8—1131no—
259C2×Q8—2261no—
260C2×D4—1131no—
261C2×D4—1131no—
262C2×D4—1131no—
263C2×D4—4521no—
264C2×D4—2262no—
265C2×D4—2261no—
266C2×D4—2261no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4D45211yescharacteristic
271C22×C4—2261no—
272C22×C4—2261no—
273C22×C4—2261no—
274C22×C4—2261no—
275C22×C4—2261no—
276C22×C4C22×D11311yescharacteristic
277C22×C4C22×D11311yescharacteristic
278SD16—4521no—
279D8—4521no—
280D8—2262no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D11311yescharacteristic
284C2×C8C22×D11311yescharacteristic
285C2×C8C22×D11311yescharacteristic
286C2×C8C22×D11311yescharacteristic
287C4⋊C4—1131no—
288C4⋊C4—1131no—
289C4⋊C4—1131no—
290C4⋊C4—1131no—
291C4⋊C4—2261no—
292C4⋊C4—2261no—
293C4⋊C4—2261no—
294C4⋊C4—2261no—
295C4⋊C4D45211yescharacteristic
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C22⋊C4D45211yescharacteristic
305C22⋊C4D45211yescharacteristic
306C42C22×D11311yescharacteristic
307C23—9041no—
308C23—4522no—
309C23—4522no—
310C23—2261no—
311C23—2261no—
312C23—2261no—
313C23C2×D45211yescharacteristic
314C23C2×D45211yescharacteristic
315Q8—4522no—
316Q8—2261no—
317Q8—2261no—
318D4—22no—
319D4—1132no—
320D4—9041no—
321D4—4522no—
322D4—4522no—
323D4—4522no—
324D4—4522no—
325D4—2261no—
326D4—2261no—
327D4—2261no—
328D4—2261no—
329D4—2261no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—9041no—
335C2×C4—4522no—
336C2×C4—4522no—
337C2×C4—4522no—
338C2×C4—4522no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4—2261no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4C2×D45211yescharacteristic
345C2×C4C2×D45211yescharacteristic
346C2×C4C2×D45211yescharacteristic
347C2×C4C2×D45211yescharacteristic
348C2×C4C23×D11311yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—9044no—
359C22—4521no—
360C22—4521no—
361C22—4521no—
362C22—4521no—
363C22—4521no—
364C22—4521no—
365C22—4521no—
366C22—4521no—
367C22—2262no—
368C22#1681365012yes—
369C22C22×D45211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—4521no—
375C4—4521no—
376C4—4521no—
377C4—4521no—
378C4—4521no—
379C4#41×D11311yescharacteristic
380C4#1681366711yescharacteristic
381C2—22no—
382C2—41no—
383C2—9041no—
384C2—9041no—
385C2—4522no—
386C2#2029924311yescharacteristic
387C2C2×#1681365011yescharacteristic
388C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#435×C113C2
socleC22×C113C22×D4
hypercenter#435D113
hypocenterC113#3306
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #20299252C2semidirect
2. #20299244C2semidirect
3. #20298958C2semidirect
4. #20298929C2semidirect
5. #20298917C2semidirect
6. #20298889C2semidirect
7. #20298851C2semidirect
8. #20298827C2semidirect
9. #20298814C2semidirect
10. #20298745C2semidirect
11. #20298734C2semidirect
12. #20298711C2semidirect
13. #20298600C2semidirect
14. C2×#16813544C2semidirect
15. #435×C113C2semidirect
19. C2×#14268636C22semidirect
22. #16813622C22semidirect
31. #16813596C22semidirect
35. C4×D452C22semidirect
37. C2×C4⋊Dic113C22semidirect
39. #16813554C22semidirect
40. #16813554C22semidirect
41. #16813554C22semidirect
42. #16813547C22semidirect
43. #16813547C22semidirect
44. #16813547C22semidirect
51. #16813544C22semidirect
52. C2×M16×C113C22semidirect
55. C4⋊C8×C113C22semidirect
57. C22⋊C8×C113C22semidirect
58. #97×C113C22semidirect
147. D452#41semidirect
195. C113#3306semidirect
208. #435D113semidirect
217. C2×M16C2×D113semidirect
240. C4⋊C8C2×D113semidirect
252. C22⋊C8C2×D113semidirect
253. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992522
#202992442
#202989582
#202989292
#202989172
#202988892
#202988512
#202988272
#202988142
#202987452
#202987342
#202987112
#202986002
C2×#168135442
#435×C1132
#3306113