Finite Group Databasebeta

← #28401412

Subgroups — #28401412

Order 14464.

418 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#20299108C211yesmaximal, characteristic, complemented
3#20298941C211yesmaximal, characteristic, complemented
4#20298938C211yesmaximal, characteristic, complemented
5#20298925C211yesmaximal, characteristic, complemented
6#20298920C211yesmaximal, characteristic, complemented
7#20298854C211yesmaximal, characteristic, complemented
8#20298849C211yesmaximal, characteristic, complemented
9#20298844C211yesmaximal, characteristic, complemented
10#20298763C211yesmaximal, characteristic, complemented
11#20298757C211yesmaximal, characteristic, complemented
12#20298744C211yesmaximal, characteristic, complemented
13#20298742C211yesmaximal, characteristic, complemented
14#20298561C211yesmaximal, characteristic, complemented
15#468×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C2×#14268637C2211yescharacteristic, complemented
20C2×#14268636C2211yescharacteristic, complemented
21C2×#14268632C2211yescharacteristic, complemented
22C2×#14268631C2211yescharacteristic
23#16813607—21no—
24#16813604—21no—
25#16813602C2211yescharacteristic
26#16813601C2211yescharacteristic
27#16813598C2211yescharacteristic
28#16813597C2211yescharacteristic
29#16813596C2211yescharacteristic
30#16813593C2211yescharacteristic
31#16813592—21no—
32#16813590—21no—
33D4×Dic113—21no—
34#16813584—21no—
35#16813582—21no—
36#16813582—21no—
37#16813580C2211yescharacteristic
38#16813580C2211yescharacteristic
39#16813556C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813553C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813545C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic, complemented
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic, complemented
53C2×M16×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59C23×D113D411yescharacteristic
60#14268648—41no—
61#14268648—41no—
62#14268646—41no—
63#14268646—41no—
64C2×Dic226C2311yescharacteristic
65C2×D452—21no—
66C2×D452—21no—
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C22×Dic113—21no—
72C22×Dic113D411yescharacteristic
73C2×C4×D113—21no—
74C2×C4×D113—41no—
75C2×C4×D113—41no—
76C2×C4×D113D411yescharacteristic
77C2×C4×D113D411yescharacteristic
78C2×C4×D113C2311yescharacteristic
79C2×C4×D113C2311yescharacteristic
80#14268637—41no—
81#14268636—41no—
82#14268632—41no—
83#14268631—41no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C4⋊Dic113—21no—
87C4⋊Dic113C2311yescharacteristic
88C4⋊Dic113C2311yescharacteristic
89#14268626—21no—
90#14268626—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99C4×Dic113—21no—
100C4×Dic113—21no—
101C2×Q8×C113C2311yescharacteristic
102C2×D4×C113—21no—
103C2×D4×C113C2311yescharacteristic
104C22×C4×C113C2311yescharacteristic
105SD16×C113—41no—
106M16×C113—41no—
107C2×C8×C113C2311yescharacteristic
108C2×C8×C113C2311yescharacteristic
109C4⋊C4×C113—21no—
110C4⋊C4×C113C2311yescharacteristic
111C4⋊C4×C113C2311yescharacteristic
112C22⋊C4×C113—21no—
113C22⋊C4×C113—21no—
114C23×C113—21no—
115C23×C113C2×D411yescharacteristic
116C22×D113—21no—
117C22×D113—41no—
118C22×D113—41no—
119C22×D113—41no—
120C22×D113C2×D411yescharacteristic
121C22×D113C2×D411yescharacteristic
122Q8×C113—21no—
123Q8×C113—21no—
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—42no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2411yescharacteristic
134C22⋊D113—42no—
135C22⋊D113—42no—
136C22⋊D113—42no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—41no—
141C2×Dic113—42no—
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144D452—21no—
145D452—21no—
146D452—42no—
147D452—42no—
148C4×D113—21no—
149C4×D113—21no—
150C4×D113—21no—
151C4×D113—21no—
152C4×D113—41no—
153C4×D113—41no—
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×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113C22×D411yescharacteristic
168C2×D113—21no—
169C2×D113—21no—
170C2×D113—21no—
171C2×D113—21no—
172C2×D113—21no—
173C2×D113—21no—
174C2×D113—44no—
175C2×D113—41no—
176C2×D113—41no—
177C2×D113—41no—
178C4×C113—21no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113—41no—
182C4×C113H(5,𝔽2)11yescharacteristic
183C4×C113H(5,𝔽2)11yescharacteristic
184Dic113—21no—
185Dic113—21no—
186Dic113—41no—
187Dic113—41no—
188Dic113—41no—
189C2×C113—41no—
190C2×C113—81no—
191C2×C113#53411yescharacteristic
192C2×C113#57511yescharacteristic
193C2×C113#57511yescharacteristic
194D113—41no—
195D113—41no—
196D113—81no—
197#3197—1131nomaximal, Sylow
198C113#319711yescharacteristic, complemented, Sylow
199#525—1131no—
200#525—1131no—
201#485—1131no—
202#485—1131no—
203#482—1131no—
204#482—1131no—
205#470—1131no—
206#469—1131no—
207#468—1131no—
208#468D11311yescharacteristic, complemented
209#452—1131no—
210#452—1131no—
211#449—1131no—
212#449—1131no—
213#407—1131no—
214C2×#41—1131no—
215C2×#41—1131no—
216C23×C4—1131no—
217C2×Q16—1131no—
218C2×SD16—1131no—
219C2×SD16C2×D11311yescharacteristic, complemented
220C2×D8—1131no—
221C2×M16—1131no—
222C2×M16C2×D11311yescharacteristic
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#121C2×D11311yescharacteristic
233#120—2261no—
234#120—2261no—
235C4×D4—2261no—
236C4×D4—2261no—
237C4×D4—2261no—
238C4×D4—2261no—
239#117—1131no—
240#117—1131no—
241#107—1131no—
242#107C2×D11311yescharacteristic, complemented
243#106—1131no—
244#106—1131no—
245#103—1131no—
246#103—1131no—
247#103—1131no—
248#103C2×D11311yescharacteristic, complemented
249#102—1131no—
250#102—1131no—
251#102—1131no—
252#102C2×D11311yescharacteristic, complemented
253C22⋊C8—1131no—
254C22⋊C8—1131no—
255C22⋊C8—1131no—
256C22⋊C8—1131no—
257C24—1131no—
258#41—4521no—
259#41—4521no—
260#41—4521no—
261#41—4521no—
262C2×Q8—1131no—
263C2×Q8C22×D11311yescharacteristic
264C2×D4—21no—
265C2×D4—1131no—
266C2×D4—2261no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4C22×D11311yescharacteristic
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—41no—
284SD16—4521no—
285D8—4521no—
286M16—41no—
287M16—4521no—
288C2×C8—1131no—
289C2×C8—1131no—
290C2×C8C22×D11311yescharacteristic
291C2×C8C22×D11311yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—1131no—
294C4⋊C4—1131no—
295C4⋊C4—2261no—
296C4⋊C4—2261no—
297C4⋊C4—2261no—
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—2261no—
311C42—2261no—
312C23—21no—
313C23—1131no—
314C23—1131no—
315C23—4521no—
316C23—4521no—
317C23—4521no—
318C23—2261no—
319C23D4×D11311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—2261no—
323Q8—2261no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—4522no—
328D4—4522no—
329D4—4522no—
330D4—4522no—
331D4—4522no—
332D4—2261no—
333D4—2261no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—1131no—
340C2×C4—1131no—
341C2×C4—4521no—
342C2×C4—4521no—
343C2×C4—4522no—
344C2×C4—4522no—
345C2×C4—4521no—
346C2×C4—2261no—
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—41no—
363C22—41no—
364C22—41no—
365C22—4524no—
366C22—4521no—
367C22—4521no—
368C22—4521no—
369C22—2261no—
370C22—2261no—
371C22—2261no—
372C22—2261no—
373C22—2261no—
374C22—2261no—
375C22C2×D4×D11311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—4521no—
381C4—4521no—
382C4—4521no—
383C4—2261no—
384C4—2261no—
385C4#1681366711yescharacteristic
386C4#1681366811yescharacteristic
387C2—41no—
388C2—81no—
389C2—9041no—
390C2—4521no—
391C2—4521no—
392C2#2029915611yescharacteristic
393C2#2029939411yescharacteristic
394C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#468×C113C2
socleC22×C113C22×D4
hypercenter#468D113
hypocenterC113#3197
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #20299111C2semidirect
2. #20299108C2semidirect
3. #20298941C2semidirect
4. #20298938C2semidirect
5. #20298925C2semidirect
6. #20298920C2semidirect
7. #20298854C2semidirect
8. #20298849C2semidirect
9. #20298844C2semidirect
10. #20298763C2semidirect
11. #20298757C2semidirect
12. #20298744C2semidirect
13. #20298742C2semidirect
14. #20298561C2semidirect
15. #468×C113C2semidirect
19. C2×#14268637C22semidirect
20. C2×#14268636C22semidirect
21. C2×#14268632C22semidirect
39. #16813556C22semidirect
40. #16813553C22semidirect
41. #16813553C22semidirect
42. #16813547C22semidirect
43. #16813546C22semidirect
44. #16813545C22semidirect
45. #16813544C22semidirect
46. #16813543C22semidirect
47. #16813542C22semidirect
52. C2×SD16×C113C22semidirect
56. #107×C113C22semidirect
57. #103×C113C22semidirect
58. #102×C113C22semidirect
198. C113#3197semidirect
208. #468D113semidirect
219. C2×SD16C2×D113semidirect
242. #107C2×D113semidirect
248. #103C2×D113semidirect
252. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991112
#202991082
#202989412
#202989382
#202989252
#202989202
#202988542
#202988492
#202988442
#202987632
#202987572
#202987442
#202987422
#202985612
#468×C1132
#3197113