Finite Group Databasebeta

← #28401364

Subgroups — #28401364

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#20299108C211yesmaximal, characteristic, complemented
2#20299105C211yesmaximal, characteristic, complemented
3#20298940C211yesmaximal, characteristic, complemented
4#20298938C211yesmaximal, characteristic, complemented
5#20298921C211yesmaximal, characteristic, complemented
6#20298919C211yesmaximal, characteristic, complemented
7#20298838C211yesmaximal, characteristic, complemented
8#20298831C211yesmaximal, characteristic, complemented
9#20298826C211yesmaximal, characteristic, complemented
10#20298824C211yesmaximal, characteristic, complemented
11#20298760C211yesmaximal, characteristic, complemented
12#20298757C211yesmaximal, characteristic, complemented
13#20298740C211yesmaximal, characteristic, complemented
14C22⋊C8×D113C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C22×C4×D113C2211yescharacteristic
18C2×#14268637C2211yescharacteristic, complemented
19C2×#14268635C2211yescharacteristic, complemented
20C2×C8×D113C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813604—21no—
23#16813603—21no—
24#16813602C2211yescharacteristic
25#16813601C2211yescharacteristic
26#16813598C2211yescharacteristic
27#16813598C2211yescharacteristic
28#16813593C2211yescharacteristic
29#16813593C2211yescharacteristic
30#16813593C2211yescharacteristic
31#16813590—21no—
32#16813590—21no—
33D4×Dic113—21no—
34C4×C22⋊D113—21no—
35C4×C22⋊D113—21no—
36#16813582—21no—
37#16813581C2211yescharacteristic
38#16813580C2211yescharacteristic
39#16813556C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic, complemented
48#16813543C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic, complemented
54C2×D8×C113C2211yescharacteristic, complemented
55#121×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C23×D113D411yescharacteristic
60#14268646—41no—
61#14268646—41no—
62C2×Dic226C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C22×Dic113—21no—
68C22×Dic113D411yescharacteristic
69C2×C4×D113—41no—
70C2×C4×D113—41no—
71C2×C4×D113D411yescharacteristic
72C2×C4×D113D411yescharacteristic
73C2×C4×D113C2311yescharacteristic
74C2×C4×D113C2311yescharacteristic
75#14268637—41no—
76#14268635—41no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C8×D113—41no—
80C8×D113—41no—
81C4⋊Dic113—21no—
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97C4×Dic113—21no—
98C4×Dic113—21no—
99#41×C113—41no—
100#41×C113—41no—
101C2×Q8×C113C2311yescharacteristic
102C2×D4×C113—21no—
103C2×D4×C113—21no—
104C2×D4×C113C2311yescharacteristic
105C2×D4×C113C2311yescharacteristic
106C22×C4×C113—21no—
107C22×C4×C113C2311yescharacteristic
108SD16×C113—41no—
109D8×C113—41no—
110C2×C8×C113C2311yescharacteristic
111C2×C8×C113C2311yescharacteristic
112C4⋊C4×C113C2311yescharacteristic
113C22⋊C4×C113—21no—
114C23×C113—21no—
115C23×C113—21no—
116C23×C113C2×D411yescharacteristic
117C22×D113—22no—
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—21no—
127D4×C113—21no—
128D4×C113—42no—
129D4×C113—42no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—42no—
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2411yescharacteristic
137C22⋊D113—42no—
138C22⋊D113—42no—
139C22⋊D113—42no—
140C22⋊D113—42no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—41no—
146C2×Dic113—42no—
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149C4×D113—21no—
150C4×D113—21no—
151C4×D113—21no—
152C4×D113—21no—
153C4×D113—41no—
154C4×D113—41no—
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×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113C22×D411yescharacteristic
171C2×D113—21no—
172C2×D113—21no—
173C2×D113—21no—
174C2×D113—21no—
175C2×D113—21no—
176C2×D113—44no—
177C2×D113#13512yes—
178C4×C113—21no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113H(5,𝔽2)11yescharacteristic
182C4×C113H(5,𝔽2)11yescharacteristic
183Dic113—21no—
184Dic113—21no—
185Dic113—41no—
186Dic113—41no—
187Dic113—41no—
188Dic113—41no—
189C2×C113—41no—
190C2×C113—81no—
191C2×C113—81no—
192C2×C113#53411yescharacteristic
193C2×C113C2×#13511yescharacteristic
194C2×C113#57511yescharacteristic
195D113—22no—
196D113—41no—
197#3191—1131nomaximal, Sylow
198C113#319111yescharacteristic, complemented, Sylow
199#525—1131no—
200#525—1131no—
201#485—1131no—
202#485—1131no—
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#449D11311yescharacteristic, complemented
213C2×C22⋊C8—1131no—
214C2×#41—1131no—
215C2×#41C2×D11311yescharacteristic
216C23×C4—1131no—
217C2×Q16—1131no—
218C2×SD16—1131no—
219C2×SD16C2×D11311yescharacteristic, complemented
220C2×D8C2×D11311yescharacteristic, complemented
221C22×C8—1131no—
222C22×C8—1131no—
223#123—2261no—
224#123—2261no—
225C22⋊Q8—1131no—
226C22⋊Q8—1131no—
227C22⋊Q8—1131no—
228C22⋊Q8—1131no—
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#107—1131no—
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⋊C8C2×D11311yescharacteristic
257C24—1131no—
258#41—41no—
259#41—41no—
260#41—4521no—
261#41—4521no—
262C2×Q8—1131no—
263C2×Q8C22×D11311yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—2261no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4C22×D11311yescharacteristic
271C2×D4C22×D11311yescharacteristic
272C22×C4—21no—
273C22×C4—1131no—
274C22×C4—1131no—
275C22×C4—1131no—
276C22×C4—1131no—
277C22×C4—1131no—
278C22×C4—4521no—
279C22×C4—4521no—
280C22×C4—2261no—
281C22×C4C22×D11311yescharacteristic
282Q16—4521no—
283SD16—41no—
284SD16—4521no—
285D8—41no—
286C2×C8—1131no—
287C2×C8—1131no—
288C2×C8—4521no—
289C2×C8—4521no—
290C2×C8C22×D11311yescharacteristic
291C2×C8C22×D11311yescharacteristic
292C4⋊C4—1131no—
293C4⋊C4—1131no—
294C4⋊C4—1131no—
295C4⋊C4—2261no—
296C4⋊C4—2261no—
297C4⋊C4—2261no—
298C4⋊C4—2261no—
299C4⋊C4C22×D11311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—2261no—
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—21no—
314C23—1131no—
315C23—1131no—
316C23—4521no—
317C23—4521no—
318C23—2262no—
319C23D4×D11311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—2261no—
323Q8—2261no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—4522no—
331D4—4522no—
332D4—4522no—
333D4—4522no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—1131no—
340C2×C4—1131no—
341C2×C4—4521no—
342C2×C4—4521no—
343C2×C4—4522no—
344C2×C4—4521no—
345C2×C4—2261no—
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—41no—
366C22—41no—
367C22—41no—
368C22—1132no—
369C22—4524no—
370C22—2261no—
371C22—2261no—
372C22—2261no—
373C22—2261no—
374C22—2261no—
375C22C2×D4×D11311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—4521no—
380C4—4521no—
381C4—4521no—
382C4—4521no—
383C4—2261no—
384C4—2261no—
385C4#1681366711yescharacteristic
386C4#1681366711yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—4521no—
391C2—2262no—
392C2#2029915811yescharacteristic
393C2#135×D11311yescharacteristic
394C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3191
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. #20299108C2semidirect
2. #20299105C2semidirect
3. #20298940C2semidirect
4. #20298938C2semidirect
5. #20298921C2semidirect
6. #20298919C2semidirect
7. #20298838C2semidirect
8. #20298831C2semidirect
9. #20298826C2semidirect
10. #20298824C2semidirect
11. #20298760C2semidirect
12. #20298757C2semidirect
13. #20298740C2semidirect
14. C22⋊C8×D113C2semidirect
15. #449×C113C2semidirect
18. C2×#14268637C22semidirect
19. C2×#14268635C22semidirect
39. #16813556C22semidirect
40. #16813555C22semidirect
41. #16813554C22semidirect
42. #16813553C22semidirect
43. #16813547C22semidirect
44. #16813547C22semidirect
45. #16813546C22semidirect
46. #16813543C22semidirect
47. #16813543C22semidirect
48. #16813543C22semidirect
53. C2×SD16×C113C22semidirect
54. C2×D8×C113C22semidirect
56. #103×C113C22semidirect
57. #102×C113C22semidirect
198. C113#3191semidirect
212. #449D113semidirect
219. C2×SD16C2×D113semidirect
220. C2×D8C2×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
#202991082
#202991052
#202989402
#202989382
#202989212
#202989192
#202988382
#202988312
#202988262
#202988242
#202987602
#202987572
#202987402
C22⋊C8×D1132
#449×C1132
#3191113