Finite Group Databasebeta

← #28401350

Subgroups — #28401350

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299108C211yesmaximal, characteristic
2C22⋊Q8×D113C211yesmaximal, characteristic, complemented
3#20298942C211yesmaximal, characteristic, complemented
4#20298938C211yesmaximal, characteristic, complemented
5#20298930C211yesmaximal, characteristic, complemented
6#20298910C211yesmaximal, characteristic, complemented
7#20298839C211yesmaximal, characteristic, complemented
8#20298837C211yesmaximal, characteristic, complemented
9#20298825C211yesmaximal, characteristic, complemented
10#20298761C211yesmaximal, characteristic, complemented
11#20298757C211yesmaximal, characteristic, complemented
12#20298755C211yesmaximal, characteristic, complemented
13#20298735C211yesmaximal, characteristic, complemented
14C2×#16813534C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C2×Dic452C2211yescharacteristic, complemented
20C2×#14268637C2211yescharacteristic, complemented
21C2×#14268635C2211yescharacteristic, complemented
22C22×#11744751C2211yescharacteristic
23#16813604—21no—
24#16813602C2211yescharacteristic
25#16813602C2211yescharacteristic
26#16813601C2211yescharacteristic
27#16813601C2211yescharacteristic
28#16813600—21no—
29#16813599—21no—
30#16813598C2211yescharacteristic
31#16813593C2211yescharacteristic
32#16813590—21no—
33D4×Dic113—21no—
34#16813582—21no—
35#16813580C2211yescharacteristic
36C4⋊C4×D113—21no—
37C4⋊C4×D113C2211yescharacteristic
38C22⋊C4×D113—21no—
39#16813556C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813553C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813546C2211yescharacteristic, complemented
45#16813545C2211yescharacteristic, complemented
46#16813545C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic, complemented
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic, complemented
53C22×C8×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59C23×D113D411yescharacteristic
60#14268646—41no—
61#14268646—41no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64C2×Dic226C2311yescharacteristic
65Q8×D113—41no—
66Q8×D113—41no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C22×Dic113—21no—
70C22×Dic113D411yescharacteristic
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—41no—
74C2×C4×D113—41no—
75C2×C4×D113D411yescharacteristic
76C2×C4×D113D411yescharacteristic
77C2×C4×D113C2311yescharacteristic
78C2×C4×D113C2311yescharacteristic
79Dic452—41no—
80#14268637—41no—
81#14268635—41no—
82C2×#11744751—41no—
83C2×#11744751C2311yescharacteristic
84C2×#11744751C2311yescharacteristic
85C4⋊Dic113—21no—
86C4⋊Dic113—21no—
87C4⋊Dic113C2311yescharacteristic
88C4⋊Dic113C2311yescharacteristic
89#14268626—21no—
90#14268626—21no—
91#14268626—21no—
92#14268626—21no—
93C22⋊Dic113—21no—
94C22⋊Dic113—21no—
95C22⋊Dic113—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99#14268624—21no—
100C4×Dic113—21no—
101C2×Q8×C113C2311yescharacteristic
102C2×D4×C113—21no—
103C2×D4×C113C2311yescharacteristic
104C22×C4×C113C2311yescharacteristic
105SD16×C113—41no—
106C2×C8×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—22no—
117C22×D113—22no—
118C22×D113—41no—
119C22×D113C2×D411yescharacteristic
120C22×D113C2×D411yescharacteristic
121Q8×C113—21no—
122Q8×C113—21no—
123D4×C113—21no—
124D4×C113—21no—
125D4×C113—42no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2411yescharacteristic
133C22⋊D113—42no—
134C22⋊D113—42no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—41no—
140C2×Dic113—42no—
141C2×Dic113C2×D411yescharacteristic
142C2×Dic113C2×D411yescharacteristic
143C4×D113—21no—
144C4×D113—21no—
145C4×D113—21no—
146C4×D113—21no—
147C4×D113—41no—
148C4×D113—41no—
149C4×D113—42no—
150C4×D113—42no—
151Dic226—21no—
152Dic226—21no—
153Dic226—21no—
154Dic226—21no—
155Dic226—42no—
156C8×C113—21no—
157C8×C113—21no—
158#11744751—21no—
159#11744751—21no—
160C22×C113—21no—
161C22×C113—21no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113#13712yes—
166C22×C113C22×D411yescharacteristic
167C2×D113—21no—
168C2×D113—21no—
169C2×D113—21no—
170C2×D113—21no—
171C2×D113—21no—
172C2×D113—44no—
173C2×D113#13512yes—
174C4×C113—21no—
175C4×C113—41no—
176C4×C113—41no—
177C4×C113—41no—
178C4×C113H(5,𝔽2)11yescharacteristic
179C4×C113H(5,𝔽2)11yescharacteristic
180Dic113—21no—
181Dic113—21no—
182Dic113—41no—
183Dic113—41no—
184Dic113—41no—
185Dic113—41no—
186C2×C113—22no—
187C2×C113—81no—
188C2×C113#53411yescharacteristic
189C2×C113C2×#13511yescharacteristic
190C2×C113C2×#13711yescharacteristic
191D113—22no—
192D113—41no—
193#3190—1131nomaximal, Sylow
194C113#319011yescharacteristic, complemented, Sylow
195#525—1131no—
196C2×C22⋊Q8—1131no—
197#485—1131no—
198#485—1131no—
199#483—1131no—
200#480—1131no—
201#467—1131no—
202#467—1131no—
203#465—1131no—
204#465D11311yescharacteristic, complemented
205#452—1131no—
206#452—1131no—
207#451—1131no—
208#448—1131no—
209C2×C22⋊C8—1131no—
210C2×#41—1131no—
211C22×Q8—1131no—
212C23×C4—1131no—
213C2×Q16—1131no—
214C2×Q16—1131no—
215C2×SD16—1131no—
216C2×SD16C2×D11311yescharacteristic, complemented
217C22×C8—1131no—
218C22×C8C2×D11311yescharacteristic
219#123—2261no—
220C22⋊Q8—1131no—
221C22⋊Q8—1131no—
222C22⋊Q8—1131no—
223C22⋊Q8—1131no—
224C22⋊Q8—1131no—
225C22⋊Q8—2261no—
226C22⋊Q8—2261no—
227C22⋊Q8C2×D11311yescharacteristic
228#121—1131no—
229#121C2×D11311yescharacteristic
230#120—2261no—
231C4×D4—2261no—
232C4×D4—2261no—
233#117—1131no—
234C2×C4⋊C4—1131no—
235C2×C4⋊C4—2261no—
236C2×C22⋊C4—2261no—
237#107—1131no—
238#107—1131no—
239#106—1131no—
240#106C2×D11311yescharacteristic, complemented
241#103—1131no—
242#103—1131no—
243#103—1131no—
244#103—1131no—
245#103—1131no—
246#103C2×D11311yescharacteristic, complemented
247#102—1131no—
248#102C2×D11311yescharacteristic, complemented
249C22⋊C8—1131no—
250C22⋊C8—1131no—
251C22⋊C8—1131no—
252C22⋊C8—1131no—
253C24—1131no—
254#41—4521no—
255#41—4521no—
256C2×Q8—1131no—
257C2×Q8—1131no—
258C2×Q8—4521no—
259C2×Q8—4521no—
260C2×Q8—2261no—
261C2×Q8C22×D11311yescharacteristic
262C2×D4—21no—
263C2×D4—2261no—
264C2×D4—2261no—
265C2×D4C22×D11311yescharacteristic
266C22×C4—1131no—
267C22×C4—1131no—
268C22×C4—1131no—
269C22×C4—1131no—
270C22×C4—1131no—
271C22×C4—4521no—
272C22×C4—4521no—
273C22×C4—2261no—
274C22×C4—2261no—
275C22×C4—2261no—
276C22×C4C22×D11311yescharacteristic
277Q16—4521no—
278Q16—4521no—
279SD16—41no—
280SD16—4521no—
281C2×C8—41no—
282C2×C8—1131no—
283C2×C8—1131no—
284C2×C8—4521no—
285C2×C8C22×D11311yescharacteristic
286C2×C8C22×D11311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—1131no—
289C4⋊C4—1131no—
290C4⋊C4—2261no—
291C4⋊C4—2261no—
292C4⋊C4—2261no—
293C4⋊C4—2261no—
294C4⋊C4—2261no—
295C4⋊C4—2261no—
296C4⋊C4C22×D11311yescharacteristic
297C4⋊C4C22×D11311yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—2261no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C42—2261no—
308C23—21no—
309C23—1131no—
310C23—1131no—
311C23—4521no—
312C23—2262no—
313C23—2262no—
314C23D4×D11311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—4522no—
318Q8—2261no—
319Q8—2261no—
320Q8—2261no—
321Q8—2261no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—4522no—
326D4—4522no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—1131no—
333C2×C4—1131no—
334C2×C4—4521no—
335C2×C4—4521no—
336C2×C4—4522no—
337C2×C4—4522no—
338C2×C4—4522no—
339C2×C4—4521no—
340C2×C4—2261no—
341C2×C4—2261no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4—2261no—
345C2×C4—2261no—
346C2×C4—2261no—
347C2×C4—2261no—
348C2×C4D4×D11311yescharacteristic
349C2×C4C23×D11311yescharacteristic
350C8—21no—
351C8—21no—
352C8—2261no—
353C8—2261no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—1132no—
360C22—4524no—
361C22—2261no—
362C22—2261no—
363C22—2261no—
364C22—2261no—
365C22—2261no—
366C22#1681365112yes—
367C22C2×D4×D11311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—4521no—
373C4—4521no—
374C4—4521no—
375C4—4521no—
376C4—2261no—
377C4—2261no—
378C4#1681366711yescharacteristic
379C4#1681366811yescharacteristic
380C2—22no—
381C2—81no—
382C2—4521no—
383C2—2262no—
384C2#2029915611yescharacteristic
385C2#135×D11311yescharacteristic
386C2C2×#1681365111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
prime radical#20299108C2
hypercenter#465D113
hypocenterC113#3190
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D113C2semidirect
3. #20298942C2semidirect
4. #20298938C2semidirect
5. #20298930C2semidirect
6. #20298910C2semidirect
7. #20298839C2semidirect
8. #20298837C2semidirect
9. #20298825C2semidirect
10. #20298761C2semidirect
11. #20298757C2semidirect
12. #20298755C2semidirect
13. #20298735C2semidirect
14. C2×#16813534C2semidirect
15. #465×C113C2semidirect
19. C2×Dic452C22semidirect
20. C2×#14268637C22semidirect
21. C2×#14268635C22semidirect
39. #16813556C22semidirect
40. #16813555C22semidirect
41. #16813553C22semidirect
42. #16813547C22semidirect
43. #16813547C22semidirect
44. #16813546C22semidirect
45. #16813545C22semidirect
46. #16813545C22semidirect
47. #16813543C22semidirect
52. C2×SD16×C113C22semidirect
56. #106×C113C22semidirect
57. #103×C113C22semidirect
58. #102×C113C22semidirect
194. C113#3190semidirect
204. #465D113semidirect
216. C2×SD16C2×D113semidirect
240. #106C2×D113semidirect
246. #103C2×D113semidirect
248. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991082
C22⋊Q8×D1132
#202989422
#202989382
#202989302
#202989102
#202988392
#202988372
#202988252
#202987612
#202987572
#202987552
#202987352
C2×#168135342
#465×C1132
#3190113