Finite Group Databasebeta

← #28402528

Subgroups — #28402528

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#20299248C211yesmaximal, characteristic, complemented
2#20299236C211yesmaximal, characteristic, complemented
3#20298959C211yesmaximal, characteristic, complemented
4#20298927C211yesmaximal, characteristic, complemented
5#20298917C211yesmaximal, characteristic, complemented
6#20298886C211yesmaximal, characteristic, complemented
7#20298849C211yesmaximal, characteristic, complemented
8#20298824C211yesmaximal, characteristic, complemented
9#20298815C211yesmaximal, characteristic, complemented
10#20298730C211yesmaximal, characteristic, complemented
11#20298710C211yesmaximal, characteristic, complemented
12#20298672C211yesmaximal, characteristic, complemented
13#20298599C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×D4×D113C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19C2×#14268631C2211yescharacteristic, complemented
20C2×C8×D113C2211yescharacteristic
21#16813621C2211yescharacteristic, complemented
22#16813611C2211yescharacteristic
23#16813605—21no—
24#16813604—21no—
25#16813603—21no—
26#16813599—21no—
27#16813598C2211yescharacteristic
28#16813596C2211yescharacteristic
29#16813594—21no—
30#16813593C2211yescharacteristic
31#16813590—21no—
32D4×Dic113C2211yescharacteristic
33D4×Dic113C2211yescharacteristic, complemented
34C4×C22⋊D113C2211yescharacteristic
35C2×C4⋊Dic113C2211yescharacteristic, complemented
36C4⋊C4×D113C2211yescharacteristic
37C2×#14268624—21no—
38#16813554C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic, complemented
49#16813542C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813532C2211yescharacteristic, complemented
52C2×#41×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic, complemented
54C2×D8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268646—44no—
61C2×Dic226—21no—
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113D411yescharacteristic
67D4×D113—22no—
68D4×D113—41no—
69C22×Dic113—21no—
70C22×Dic113—21no—
71C22×Dic113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74#14268632—41no—
75#14268631—41no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C8×D113—41no—
79C4⋊Dic113—21no—
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626D411yescharacteristic
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113D411yescharacteristic
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624D411yescharacteristic
96C4×Dic113C2311yescharacteristic
97#41×C113—22no—
98#41×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113—21no—
102C2×D4×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104C22×C4×C113—21no—
105C22×C4×C113C2311yescharacteristic
106SD16×C113—41no—
107D8×C113—22no—
108C2×C8×C113C2311yescharacteristic
109C2×C8×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C23×C113—21no—
113C23×C113—21no—
114C23×C113C2×D411yescharacteristic
115C22×D113—21no—
116C22×D113—42no—
117C22×D113—42no—
118C22×D113—81no—
119C22×D113C2×D411yescharacteristic
120Q8×C113—21no—
121Q8×C113—21no—
122D4×C113—21no—
123D4×C113—21no—
124D4×C113—21no—
125D4×C113—42no—
126D4×C113—42no—
127D4×C113#4112yescomplemented
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—42no—
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2411yescharacteristic
135C22⋊D113—22no—
136C22⋊D113—42no—
137C22⋊D113—42no—
138C22⋊D113—81no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113—42no—
143C2×Dic113—42no—
144C2×Dic113—81no—
145C2×Dic113C2×D411yescharacteristic
146C2×Dic113C2×D411yescharacteristic
147C2×Dic113C2×D411yescharacteristic
148D452—21no—
149D452—21no—
150C4×D113—21no—
151C4×D113—21no—
152C4×D113—42no—
153Dic226—42no—
154C8×C113—21no—
155C8×C113—21no—
156#11744751—21no—
157#11744751—21no—
158C22×C113—22no—
159C22×C113—21no—
160C22×C113—21no—
161C22×C113—21no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113C22×D411yescharacteristic
168C2×D113—21no—
169C2×D113—21no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—84no—
174C2×D113AGL(1,ℤ/8)12yes—
175C4×C113—21no—
176C4×C113—41no—
177C4×C113—41no—
178C4×C113C2×#4111yescharacteristic
179C4×C113H(5,𝔽2)11yescharacteristic
180Dic113—21no—
181Dic113—21no—
182Dic113—21no—
183Dic113—41no—
184Dic113—41no—
185Dic113—41no—
186C2×C113—42no—
187C2×C113—41no—
188C2×C113—81no—
189C2×C113#54611yescharacteristic
190C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C113#57711yescharacteristic
192D113—22no—
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#449D11311yescharacteristic, complemented
206#447—1131no—
207#442—1131no—
208#435—1131no—
209#417—1131no—
210C2×#102—1131no—
211C2×#41—2261no—
212C2×#41C2×D11311yescharacteristic
213C22×D4—1131no—
214C2×SD16C2×D11311yescharacteristic, complemented
215C2×D8—1131no—
216C2×D8C2×D11311yescharacteristic
217C2×M16—1131no—
218C22×C8—1131no—
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—2261no—
229#121C2×D11311yescharacteristic, complemented
230#120—2261no—
231C4×D4—1131no—
232C4×D4—1131no—
233C4×D4—1131no—
234C2×C4⋊C4—1131no—
235C2×C4⋊C4—1131no—
236C2×C22⋊C4—2261no—
237#106—1131no—
238#106—1131no—
239#106—1131no—
240C4⋊C8—1131no—
241#103—1131no—
242#103—1131no—
243#103C2×D11311yescharacteristic, complemented
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102C2×D11311yescharacteristic
251C22⋊C8—1131no—
252C22⋊C8C2×D11311yescharacteristic, complemented
253#97—1131no—
254C24—2261no—
255#41—22no—
256#41—41no—
257#41—4524no—
258C2×Q8—2261no—
259C2×Q8C22×D11311yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—1131no—
263C2×D4—1131no—
264C2×D4—4521no—
265C2×D4—2261no—
266C2×D4—2261no—
267C2×D4—2261no—
268C2×D4—2262no—
269C2×D4C22×D11311yescharacteristic
270C2×D4C22×D11311yescharacteristic
271C22×C4—21no—
272C22×C4—1131no—
273C22×C4—2261no—
274C22×C4—2261no—
275C22×C4—2261no—
276C22×C4—2261no—
277C22×C4C22×D11311yescharacteristic
278SD16—41no—
279D8—22no—
280D8—4521no—
281M16—4521no—
282C2×C8—1131no—
283C2×C8—1131no—
284C2×C8—4521no—
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⋊C4C22×D11311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—1131no—
298C22⋊C4—1131no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C42—1131no—
307C23—21no—
308C23—21no—
309C23—1131no—
310C23—9041no—
311C23—4522no—
312C23—4522no—
313C23—2261no—
314C23D4×D11311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—4522no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—9041no—
324D4—4522no—
325D4—4522no—
326D4—2262no—
327D4—2261no—
328D4—2261no—
329D4#1426864612yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—1131no—
336C2×C4—1131no—
337C2×C4—1131no—
338C2×C4—9041no—
339C2×C4—4522no—
340C2×C4—4522no—
341C2×C4—4522no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4—2261no—
345C2×C4—2261no—
346C2×C4—2261no—
347C2×C4D4×D11311yescharacteristic
348C2×C4C23×D11311yescharacteristic
349C8—21no—
350C8—21no—
351C8—2261no—
352C8—2261no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—1132no—
363C22—9044no—
364C22—4521no—
365C22—4521no—
366C22—4521no—
367C22—2261no—
368C22—2261no—
369C22C2×D4×D11311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—4521no—
374C4—4521no—
375C4—4521no—
376C4—2261no—
377C4—2261no—
378C4—2261no—
379C4C2×#1426864611yescharacteristic
380C4#1681366711yescharacteristic
381C2—41no—
382C2—42no—
383C2—81no—
384C2—9041no—
385C2—2262no—
386C2#2029923511yescharacteristic
387C2AGL(1,ℤ/8)×D11311yescharacteristic
388C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3306
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #20299248C2semidirect
2. #20299236C2semidirect
3. #20298959C2semidirect
4. #20298927C2semidirect
5. #20298917C2semidirect
6. #20298886C2semidirect
7. #20298849C2semidirect
8. #20298824C2semidirect
9. #20298815C2semidirect
10. #20298730C2semidirect
11. #20298710C2semidirect
12. #20298672C2semidirect
13. #20298599C2semidirect
14. #102×D113C2semidirect
15. #449×C113C2semidirect
19. C2×#14268631C22semidirect
21. #16813621C22semidirect
33. D4×Dic113C22semidirect
35. C2×C4⋊Dic113C22semidirect
38. #16813554C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813546C22semidirect
43. #16813546C22semidirect
48. #16813543C22semidirect
51. #16813532C22semidirect
53. C2×SD16×C113C22semidirect
55. #121×C113C22semidirect
56. #103×C113C22semidirect
58. C22⋊C8×C113C22semidirect
127. D4×C113#41semidirect
195. C113#3306semidirect
205. #449D113semidirect
214. C2×SD16C2×D113semidirect
229. #121C2×D113semidirect
243. #103C2×D113semidirect
252. C22⋊C8C2×D113semidirect
329. D4#14268646semidirect

Maximal subgroups

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

subgroupindex
#202992482
#202992362
#202989592
#202989272
#202989172
#202988862
#202988492
#202988242
#202988152
#202987302
#202987102
#202986722
#202985992
#102×D1132
#449×C1132
#3306113