Finite Group Databasebeta

← #28401369

Subgroups — #28401369

Order 14464.

424 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#20299111C211yesmaximal, characteristic, complemented
2#20299110C211yesmaximal, characteristic, complemented
3#20298941C211yesmaximal, characteristic, complemented
4#20298924C211yesmaximal, characteristic, complemented
5#20298922C211yesmaximal, characteristic, complemented
6#20298838C211yesmaximal, characteristic, complemented
7#20298835C211yesmaximal, characteristic, complemented
8#20298830C211yesmaximal, characteristic, complemented
9#20298828C211yesmaximal, characteristic, complemented
10#20298763C211yesmaximal, characteristic, complemented
11#20298758C211yesmaximal, characteristic, complemented
12#20298746C211yesmaximal, characteristic, complemented
13#20298745C211yesmaximal, characteristic, complemented
14C22⋊C8×D113C211yesmaximal, characteristic, complemented
15#485×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C2×#14268637C2211yescharacteristic, complemented
20C2×#14268636C2211yescharacteristic, complemented
21C2×#14268634C2211yescharacteristic, complemented
22C2×D904C2211yescharacteristic, complemented
23C2×C8×D113C2211yescharacteristic
24C2×C8×D113C2211yescharacteristic
25#16813607—21no—
26#16813606—21no—
27#16813602C2211yescharacteristic
28#16813602C2211yescharacteristic
29#16813598C2211yescharacteristic
30#16813597C2211yescharacteristic
31#16813597C2211yescharacteristic
32#16813597C2211yescharacteristic
33#16813596C2211yescharacteristic
34#16813592—21no—
35#16813592—21no—
36C4×D452—21no—
37C4×D452—21no—
38#16813584—21no—
39#16813582—21no—
40#16813580C2211yescharacteristic
41#16813555C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813545C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic, complemented
46#16813542C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic, complemented
48#16813542C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C22⋊Q8×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C23×D113D411yescharacteristic
60#14268648—41no—
61#14268648—41no—
62#14268647—41no—
63#14268647—41no—
64C2×Dic226C2311yescharacteristic
65C2×D452—21no—
66C2×D452—21no—
67C2×D452—21no—
68C2×D452—21no—
69C2×D452C2311yescharacteristic
70C2×D452C2311yescharacteristic
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C22×Dic113D411yescharacteristic
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113—41no—
77C2×C4×D113—41no—
78C2×C4×D113D411yescharacteristic
79C2×C4×D113D411yescharacteristic
80C2×C4×D113C2311yescharacteristic
81C2×C4×D113C2311yescharacteristic
82#14268637—41no—
83#14268636—41no—
84#14268634—41no—
85D904—41no—
86C2×#11744751C2311yescharacteristic
87C2×#11744751C2311yescharacteristic
88C8×D113—41no—
89C8×D113—41no—
90C4⋊Dic113—21no—
91C4⋊Dic113—21no—
92C4⋊Dic113C2311yescharacteristic
93#14268626—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99#14268624—21no—
100#14268624—21no—
101#14268624—21no—
102C4×Dic113—21no—
103C2×Q8×C113C2311yescharacteristic
104C22×C4×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C22⋊C4×C113—21no—
113C42×C113—21no—
114C23×C113C2×D411yescharacteristic
115C22×D113—22no—
116C22×D113—21no—
117C22×D113—21no—
118C22×D113—41no—
119C22×D113—41no—
120C22×D113C2×D411yescharacteristic
121C22×D113C2×D411yescharacteristic
122Q8×C113—21no—
123Q8×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2411yescharacteristic
132C22⋊D113—42no—
133C22⋊D113—42no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—41no—
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139D452—21no—
140D452—21no—
141D452—21no—
142D452—21no—
143D452—42no—
144D452—42no—
145D452—42no—
146D452—42no—
147C4×D113—21no—
148C4×D113—21no—
149C4×D113—21no—
150C4×D113—21no—
151C4×D113—41no—
152C4×D113—41no—
153C4×D113—42no—
154C4×D113—42no—
155Dic226—21no—
156Dic226—21no—
157C8×C113—21no—
158C8×C113—21no—
159#11744751—21no—
160#11744751—21no—
161C22×C113—21no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113C22×D411yescharacteristic
165C2×D113—21no—
166C2×D113—21no—
167C2×D113—21no—
168C2×D113—21no—
169C2×D113—21no—
170C2×D113—44no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C2×D113#13512yes—
178C4×C113—21no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113—41no—
182C4×C113—41no—
183C4×C113H(5,𝔽2)11yescharacteristic
184C4×C113H(5,𝔽2)11yescharacteristic
185Dic113—21no—
186Dic113—21no—
187Dic113—41no—
188Dic113—41no—
189C2×C113—41no—
190C2×C113#53411yescharacteristic
191C2×C113C2×#13511yescharacteristic
192C2×C113#57511yescharacteristic
193D113—22no—
194D113—41no—
195D113—81no—
196D113—81no—
197#3191—1131nomaximal, Sylow
198C113#319111yescharacteristic, complemented, Sylow
199#525—1131no—
200#525—1131no—
201#485—1131no—
202#485D11311yescharacteristic, complemented
203#482—1131no—
204#482—1131no—
205#467—1131no—
206#466—1131no—
207#465—1131no—
208#465—1131no—
209#452—1131no—
210#452—1131no—
211#449—1131no—
212#449—1131no—
213C2×C22⋊C8—1131no—
214C2×#41—1131no—
215C2×#41—1131no—
216C23×C4—1131no—
217C2×Q16—1131no—
218C2×SD16—1131no—
219C2×SD16—1131no—
220C2×D8—1131no—
221C22×C8—1131no—
222C22×C8—1131no—
223#123—2261no—
224#123—2261no—
225C22⋊Q8—1131no—
226C22⋊Q8—1131no—
227C22⋊Q8—1131no—
228C22⋊Q8C2×D11311yescharacteristic
229#121—1131no—
230#121—1131no—
231#121—1131no—
232#121—1131no—
233#120—2261no—
234#120—2261no—
235C4×D4—2261no—
236C4×D4—2261no—
237C4×D4—2261no—
238C4×D4—2261no—
239#117—1131no—
240#117C2×D11311yescharacteristic
241#107—1131no—
242#107C2×D11311yescharacteristic, complemented
243#106—1131no—
244#106C2×D11311yescharacteristic, complemented
245#103—1131no—
246#103—1131no—
247#103C2×D11311yescharacteristic, complemented
248#103C2×D11311yescharacteristic, complemented
249#102—1131no—
250#102—1131no—
251#102—1131no—
252#102—1131no—
253C22⋊C8—1131no—
254C22⋊C8—1131no—
255C22⋊C8—1131no—
256C22⋊C8C2×D11311yescharacteristic
257C24—1131no—
258#41—4521no—
259#41—4521no—
260#41—4521no—
261#41—4521no—
262C2×Q8—1131no—
263C2×Q8C22×D11311yescharacteristic
264C2×D4—1131no—
265C2×D4—1131no—
266C2×D4—2261no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4—2261no—
272C22×C4—1131no—
273C22×C4—1131no—
274C22×C4—1131no—
275C22×C4—1131no—
276C22×C4—1131no—
277C22×C4—4521no—
278C22×C4—4521no—
279C22×C4—2261no—
280C22×C4—2261no—
281C22×C4C22×D11311yescharacteristic
282Q16—4521no—
283SD16—4521no—
284SD16—4521no—
285D8—4521no—
286C2×C8—1131no—
287C2×C8—1131no—
288C2×C8—4521no—
289C2×C8—4521no—
290C2×C8C22×D11311yescharacteristic
291C2×C8C22×D11311yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—1131no—
294C4⋊C4—2261no—
295C4⋊C4—2261no—
296C4⋊C4—2261no—
297C4⋊C4C22×D11311yescharacteristic
298C4⋊C4C22×D11311yescharacteristic
299C4⋊C4C22×D11311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C42—21no—
311C42—2261no—
312C23—1131no—
313C23—1131no—
314C23—4521no—
315C23—4521no—
316C23—2262no—
317C23—2261no—
318C23—2261no—
319C23D4×D11311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—2261no—
323Q8—2261no—
324D4—4522no—
325D4—4522no—
326D4—4522no—
327D4—4522no—
328D4—4522no—
329D4—4522no—
330D4—2261no—
331D4—2261no—
332D4—2261no—
333D4—2261no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—1131no—
341C2×C4—1131no—
342C2×C4—4522no—
343C2×C4—4521no—
344C2×C4—4521no—
345C2×C4—4522no—
346C2×C4—4521no—
347C2×C4—2261no—
348C2×C4—2261no—
349C2×C4—2261no—
350C2×C4—2261no—
351C2×C4—2261no—
352C2×C4—2261no—
353C2×C4D4×D11311yescharacteristic
354C2×C4C23×D11311yescharacteristic
355C8—21no—
356C8—21no—
357C8—2261no—
358C8—2261no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—1132no—
363C22—4524no—
364C22—4521no—
365C22—4521no—
366C22—4521no—
367C22—4521no—
368C22—4521no—
369C22—4521no—
370C22—2261no—
371C22—2261no—
372C22—2261no—
373C22—2261no—
374C22—2261no—
375C22C2×D4×D11311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—4521no—
382C4—4521no—
383C4—2261no—
384C4—2261no—
385C4#1681366811yescharacteristic
386C4#1681366811yescharacteristic
387C2—41no—
388C2—9041no—
389C2—9041no—
390C2—4521no—
391C2—2262no—
392C2#2029915911yescharacteristic
393C2#135×D11311yescharacteristic
394C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#485×C113C2
socleC22×C113C22×D4
hypercenter#485D113
hypocenterC113#3191
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #20299111C2semidirect
2. #20299110C2semidirect
3. #20298941C2semidirect
4. #20298924C2semidirect
5. #20298922C2semidirect
6. #20298838C2semidirect
7. #20298835C2semidirect
8. #20298830C2semidirect
9. #20298828C2semidirect
10. #20298763C2semidirect
11. #20298758C2semidirect
12. #20298746C2semidirect
13. #20298745C2semidirect
14. C22⋊C8×D113C2semidirect
15. #485×C113C2semidirect
19. C2×#14268637C22semidirect
20. C2×#14268636C22semidirect
21. C2×#14268634C22semidirect
22. C2×D904C22semidirect
41. #16813555C22semidirect
42. #16813553C22semidirect
43. #16813547C22semidirect
44. #16813545C22semidirect
45. #16813544C22semidirect
46. #16813542C22semidirect
47. #16813542C22semidirect
48. #16813542C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
56. #103×C113C22semidirect
57. #103×C113C22semidirect
198. C113#3191semidirect
202. #485D113semidirect
242. #107C2×D113semidirect
244. #106C2×D113semidirect
247. #103C2×D113semidirect
248. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991112
#202991102
#202989412
#202989242
#202989222
#202988382
#202988352
#202988302
#202988282
#202987632
#202987582
#202987462
#202987452
C22⋊C8×D1132
#485×C1132
#3191113