Finite Group Databasebeta

← #28402533

Subgroups — #28402533

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#20299249C211yesmaximal, characteristic, complemented
2#20299239C211yesmaximal, characteristic, complemented
3#20298959C211yesmaximal, characteristic, complemented
4#20298918C211yesmaximal, characteristic, complemented
5#20298887C211yesmaximal, characteristic, complemented
6#20298852C211yesmaximal, characteristic, complemented
7#20298829C211yesmaximal, characteristic, complemented
8#20298816C211yesmaximal, characteristic, complemented
9#20298746C211yesmaximal, characteristic, complemented
10#20298734C211yesmaximal, characteristic, complemented
11#20298709C211yesmaximal, characteristic, complemented
12#20298666C211yesmaximal, characteristic, complemented
13#20298598C211yesmaximal, characteristic, complemented
14C2×#16813542C211yesmaximal, characteristic, complemented
15#483×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647—21no—
18C22×D452C2211yescharacteristic
19C2×#14268634C2211yescharacteristic, complemented
20C2×D904C2211yescharacteristic
21C2×D904C2211yescharacteristic
22C2×#14268630C2211yescharacteristic, complemented
23C22×#11744751C2211yescharacteristic
24#16813621C2211yescharacteristic, complemented
25#16813611C2211yescharacteristic
26#16813607—21no—
27#16813607—21no—
28#16813605—21no—
29#16813600—21no—
30#16813597—21no—
31#16813597C2211yescharacteristic
32#16813597C2211yescharacteristic, complemented
33#16813596C2211yescharacteristic
34#16813592—21no—
35#16813584C2211yescharacteristic
36#16813584C2211yescharacteristic, complemented
37C4×C22⋊D113C2211yescharacteristic
38C4⋊C4×D113C2211yescharacteristic, complemented
39C22⋊C4×D113—21no—
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813542C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813542C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51#16813532C2211yescharacteristic, complemented
52C22⋊Q8×C113C2211yescharacteristic
53C2×C4⋊C4×C113C2211yescharacteristic
54#106×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C23×D113—21no—
60#14268648—22no—
61#14268648—41no—
62#14268647—44no—
63C2×Dic226—21no—
64C2×D452—22no—
65C2×D452—21no—
66C2×D452—21no—
67C2×D452—21no—
68C2×D452—21no—
69C2×D452—41no—
70C2×D452C2311yescharacteristic
71C2×D452C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×C22⋊D113—21no—
74C2×C22⋊D113D411yescharacteristic
75C2×C4×D113—21no—
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113—21no—
79C2×C4×D113C2311yescharacteristic
80#14268634—41no—
81D904—22no—
82D904—41no—
83#14268630—41no—
84C2×#11744751—41no—
85C2×#11744751C2311yescharacteristic
86C2×#11744751C2311yescharacteristic
87C4⋊Dic113C2311yescharacteristic
88#14268626—21no—
89#14268626—21no—
90#14268626D411yescharacteristic
91C22⋊Dic113D411yescharacteristic
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99#14268624D411yescharacteristic
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113—21no—
115C22×D113—21no—
116C22×D113—42no—
117C22×D113—42no—
118C22×D113—81no—
119C22×D113C2×D411yescharacteristic
120Q8×C113—21no—
121Q8×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—42no—
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C22⋊D113—22no—
132C22⋊D113—42no—
133C2×Dic113—21no—
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137D452—21no—
138D452—21no—
139D452—21no—
140D452—21no—
141D452—21no—
142D452—42no—
143D452—42no—
144D452—42no—
145D452—81no—
146D452#4112yescomplemented
147C4×D113—21no—
148C4×D113—21no—
149C4×D113—42no—
150C4×D113—42no—
151C4×D113—42no—
152C4×D113—81no—
153Dic226—42no—
154C8×C113—21no—
155C8×C113—21no—
156#11744751—21no—
157#11744751—21no—
158C22×C113—21no—
159C22×C113—21no—
160C22×C113AGL(1,ℤ/8)12yes—
161C22×C113C22×D411yescharacteristic
162C2×D113—21no—
163C2×D113—22no—
164C2×D113—21no—
165C2×D113—21no—
166C2×D113—41no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—84no—
175C4×C113—21no—
176C4×C113—41no—
177C4×C113—41no—
178C4×C113—41no—
179C4×C113—41no—
180C4×C113C2×#4111yescharacteristic
181C4×C113H(5,𝔽2)11yescharacteristic
182Dic113—21no—
183Dic113—21no—
184Dic113—21no—
185Dic113—41no—
186C2×C113—22no—
187C2×C113#54611yescharacteristic
188C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C113#57711yescharacteristic
190D113—41no—
191D113—42no—
192D113—81no—
193D113—81no—
194#3306—1131nomaximal, Sylow
195C113#330611yescharacteristic, complemented, Sylow
196#547—1131no—
197#546—1131no—
198#489—1131no—
199#483D11311yescharacteristic, complemented
200#481—1131no—
201#476—1131no—
202#469—1131no—
203#465—1131no—
204#463—1131no—
205#449—1131no—
206#447—1131no—
207#442—1131no—
208#435—1131no—
209#417—1131no—
210C2×#102—1131no—
211C2×#41—1131no—
212C2×#41—2261no—
213C22×D4—1131no—
214C2×SD16—1131no—
215C2×D8—1131no—
216C2×D8—1131no—
217C2×M16—1131no—
218C22×C8—1131no—
219C4⋊Q8—1131no—
220#124—1131no—
221#123—2261no—
222#123—2261no—
223#123—2261no—
224C22⋊Q8—2261no—
225C22⋊Q8C2×D11311yescharacteristic
226#121—1131no—
227#121—1131no—
228#121—1131no—
229#121—2261no—
230#120—2261no—
231C4×D4—1131no—
232C4×D4—1131no—
233C4×D4—1131no—
234C2×C4⋊C4—1131no—
235C2×C4⋊C4C2×D11311yescharacteristic
236C2×C22⋊C4—2261no—
237#106—1131no—
238#106C2×D11311yescharacteristic, complemented
239#106C2×D11311yescharacteristic, complemented
240C4⋊C8—1131no—
241#103—1131no—
242#103C2×D11311yescharacteristic, complemented
243#103C2×D11311yescharacteristic, complemented
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251C22⋊C8—1131no—
252C22⋊C8C2×D11311yescharacteristic
253#97—1131no—
254C24—2261no—
255#41—4524no—
256#41—4521no—
257#41—2262no—
258C2×Q8—2261no—
259C2×Q8C22×D11311yescharacteristic
260C2×D4—1131no—
261C2×D4—1131no—
262C2×D4—1131no—
263C2×D4—1131no—
264C2×D4—4521no—
265C2×D4—2262no—
266C2×D4—2261no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4—2261no—
271C22×C4—21no—
272C22×C4—1131no—
273C22×C4—2261no—
274C22×C4—2261no—
275C22×C4—2261no—
276C22×C4—2261no—
277C22×C4C22×D11311yescharacteristic
278SD16—4521no—
279D8—4521no—
280D8—2262no—
281M16—4521no—
282C2×C8—1131no—
283C2×C8—1131no—
284C2×C8—4521no—
285C2×C8C22×D11311yescharacteristic
286C2×C8C22×D11311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—1131no—
290C4⋊C4—1131no—
291C4⋊C4—2261no—
292C4⋊C4—2261no—
293C4⋊C4C22×D11311yescharacteristic
294C4⋊C4C22×D11311yescharacteristic
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—1131no—
308C23—9041no—
309C23—4522no—
310C23—4522no—
311C23—2261no—
312C23—2261no—
313C23—2261no—
314C23D4×D11311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—4522no—
318D4—1132no—
319D4—9041no—
320D4—4522no—
321D4—4522no—
322D4—4522no—
323D4—4522no—
324D4—2262no—
325D4—2261no—
326D4—2261no—
327D4—2261no—
328D4—2261no—
329D4—2261no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—1131no—
338C2×C4—1131no—
339C2×C4—1131no—
340C2×C4—9041no—
341C2×C4—4522no—
342C2×C4—4522no—
343C2×C4—4522no—
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—9044no—
356C22—4521no—
357C22—4521no—
358C22—4521no—
359C22—4521no—
360C22—4521no—
361C22—4521no—
362C22—4521no—
363C22—4521no—
364C22—2261no—
365C22—2261no—
366C22—2262no—
367C22—2261no—
368C22#1681364912yes—
369C22C2×D4×D11311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—4521no—
376C4—2261no—
377C4—2261no—
378C4—2261no—
379C4#41×D11311yescharacteristic
380C4#1681366811yescharacteristic
381C2—22no—
382C2—9041no—
383C2—9041no—
384C2—4522no—
385C2—4521no—
386C2#2029924011yescharacteristic
387C2C2×#1681364911yescharacteristic
388C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#483×C113C2
socleC22×C113C22×D4
hypercenter#483D113
hypocenterC113#3306
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #20299249C2semidirect
2. #20299239C2semidirect
3. #20298959C2semidirect
4. #20298918C2semidirect
5. #20298887C2semidirect
6. #20298852C2semidirect
7. #20298829C2semidirect
8. #20298816C2semidirect
9. #20298746C2semidirect
10. #20298734C2semidirect
11. #20298709C2semidirect
12. #20298666C2semidirect
13. #20298598C2semidirect
14. C2×#16813542C2semidirect
15. #483×C113C2semidirect
19. C2×#14268634C22semidirect
22. C2×#14268630C22semidirect
24. #16813621C22semidirect
32. #16813597C22semidirect
36. #16813584C22semidirect
38. C4⋊C4×D113C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813546C22semidirect
49. #16813542C22semidirect
50. #16813534C22semidirect
51. #16813532C22semidirect
54. #106×C113C22semidirect
55. #106×C113C22semidirect
56. #103×C113C22semidirect
57. #103×C113C22semidirect
146. D452#41semidirect
195. C113#3306semidirect
199. #483D113semidirect
238. #106C2×D113semidirect
239. #106C2×D113semidirect
242. #103C2×D113semidirect
243. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992492
#202992392
#202989592
#202989182
#202988872
#202988522
#202988292
#202988162
#202987462
#202987342
#202987092
#202986662
#202985982
C2×#168135422
#483×C1132
#3306113