Finite Group Databasebeta

← #28402803

Subgroups — #28402803

Order 14464.

448 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299316C211yesmaximal, characteristic, complemented
2#20299232C211yesmaximal, characteristic
3#20298943C211yesmaximal, characteristic, complemented
4#20298924C211yesmaximal, characteristic, complemented
5#20298877C211yesmaximal, characteristic, complemented
6#20298845C211yesmaximal, characteristic, complemented
7#20298842C211yesmaximal, characteristic, complemented
8#20298797C211yesmaximal, characteristic, complemented
9#20298751C211yesmaximal, characteristic, complemented
10#20298750C211yesmaximal, characteristic, complemented
11#20298685C211yesmaximal, characteristic, complemented
12#20298673C211yesmaximal, characteristic, complemented
13#20298602C211yesmaximal, characteristic, complemented
14#20298601C211yesmaximal, characteristic, complemented
15#482×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic
17C2×D4×D113—21no—
18C2×D4×D113C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268636C2211yescharacteristic, complemented
21C2×#14268635C2211yescharacteristic, complemented
22C2×#14268631C2211yescharacteristic, complemented
23C2×#14268630C2211yescharacteristic, complemented
24#16813621C2211yescharacteristic, complemented
25#16813618C2211yescharacteristic
26#16813616—21no—
27#16813615—21no—
28#16813608—21no—
29#16813602C2211yescharacteristic, complemented
30#16813601C2211yescharacteristic, complemented
31#16813597C2211yescharacteristic
32#16813595—21no—
33#16813592—21no—
34#16813590—21no—
35C4×Dic226—21no—
36#16813587C2211yescharacteristic, complemented
37#16813584C2211yescharacteristic
38C4×C22⋊D113C2211yescharacteristic
39#16813580C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813545C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic, complemented
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic, complemented
49#16813542C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52#121×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic, complemented
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C23×D113—21no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×D452—22no—
64C2×D452—21no—
65C2×D452—21no—
66C2×D452—41no—
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113D411yescharacteristic
73D4×D113—22no—
74D4×D113—41no—
75D4×D113—44no—
76C2×C4×D113—21no—
77C2×C4×D113C2311yescharacteristic
78#14268636—22no—
79#14268636—41no—
80#14268635—41no—
81#14268631—41no—
82#14268630—41no—
83C2×#11744751C2311yescharacteristic
84C2×#11744751C2311yescharacteristic
85C4⋊Dic113—21no—
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268626D411yescharacteristic
91C22⋊Dic113—21no—
92C22⋊Dic113D411yescharacteristic
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624D411yescharacteristic
98C4×Dic113—21no—
99C4×Dic113—21no—
100C4×Dic113C2311yescharacteristic
101C2×D4×C113—21no—
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C22⋊C4×C113—21no—
111C42×C113—21no—
112C23×C113—21no—
113C23×C113C2×D411yescharacteristic
114C22×D113—21no—
115C22×D113—21no—
116C22×D113—42no—
117C22×D113—42no—
118C22×D113—42no—
119C22×D113—42no—
120C22×D113—81no—
121C22×D113—81no—
122C22×D113C2×D411yescharacteristic
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—22no—
134C22⋊D113—42no—
135C22⋊D113—42no—
136C22⋊D113—81no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113C2×D411yescharacteristic
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142D452—21no—
143D452—21no—
144D452—21no—
145D452—42no—
146D452—42no—
147D452#4112yes—
148C4×D113—21no—
149C4×D113—21no—
150C4×D113—42no—
151Dic226—21no—
152Dic226—21no—
153Dic226—42no—
154C8×C113—21no—
155C8×C113—21no—
156#11744751—21no—
157#11744751—21no—
158C22×C113—21no—
159C22×C113—21no—
160C22×C113—21no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113C22×D411yescharacteristic
165C2×D113—21no—
166C2×D113—22no—
167C2×D113—21no—
168C2×D113—21no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—84no—
175C2×D113—84no—
176C4×C113—21no—
177C4×C113—41no—
178C4×C113—41no—
179C4×C113—41no—
180C4×C113C2×#4111yescharacteristic
181C4×C113H(5,𝔽2)11yescharacteristic
182Dic113—21no—
183Dic113—21no—
184Dic113—41no—
185Dic113—41no—
186Dic113AGL(1,ℤ/8)12yes—
187C2×C113—41no—
188C2×C113—81no—
189C2×C113#54611yescharacteristic
190C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C113#57711yescharacteristic
192D113—41no—
193D113—42no—
194D113—81no—
195#3324—1131nomaximal, Sylow
196C113#332411yescharacteristic, complemented, Sylow
197#556—1131no—
198D42—1131no—
199#486—1131no—
200#482—1131no—
201#482D11311yescharacteristic, complemented
202#474—1131no—
203#468—1131no—
204#468—1131no—
205#460—1131no—
206#450—1131no—
207#450—1131no—
208C4×SD16—1131no—
209#436—1131no—
210#418—1131no—
211#418—1131no—
212C22×D4—1131no—
213C22×D4—1131no—
214C22×D4—2261no—
215C2×SD16—1131no—
216C2×SD16—1131no—
217C2×SD16—1131no—
218C2×M16—1131no—
219C2×M16—1131no—
220C4⋊Q8—1131no—
221#127—1131no—
222#126—2261no—
223#126—2261no—
224#124—2261no—
225C22⋊Q8—1131no—
226C22⋊Q8—1131no—
227#121—1131no—
228#121—2261no—
229#121C2×D11311yescharacteristic
230#120—2261no—
231#120—2261no—
232C4×Q8—1131no—
233C4×Q8—2261no—
234C4×D4—1131no—
235C4×D4—1131no—
236#117—1131no—
237#117C2×D11311yescharacteristic, complemented
238#107—1131no—
239#107C2×D11311yescharacteristic, complemented
240#106C2×D11311yescharacteristic, complemented
241C4⋊C8—1131no—
242#103—1131no—
243#102—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102C2×D11311yescharacteristic, complemented
251#102C2×D11311yescharacteristic, complemented
252C22⋊C8—1131no—
253C22⋊C8C2×D11311yescharacteristic, complemented
254C4×C8—1131no—
255C24—2261no—
256C24—2261no—
257C2×Q8—1131no—
258C2×Q8—2261no—
259C2×D4—21no—
260C2×D4—1131no—
261C2×D4—1131no—
262C2×D4—1131no—
263C2×D4—4521no—
264C2×D4—4524no—
265C2×D4—4521no—
266C2×D4—2262no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4—2262no—
272C2×D4—2261no—
273C2×D4C22×D11311yescharacteristic
274C22×C4—1131no—
275C22×C4—2261no—
276C22×C4C22×D11311yescharacteristic
277SD16—4521no—
278SD16—4521no—
279SD16—2262no—
280M16—4521no—
281M16—4521no—
282C2×C8—1131no—
283C2×C8—1131no—
284C2×C8C22×D11311yescharacteristic
285C2×C8C22×D11311yescharacteristic
286C4⋊C4—1131no—
287C4⋊C4—1131no—
288C4⋊C4—2261no—
289C4⋊C4—2261no—
290C4⋊C4—2261no—
291C4⋊C4—2261no—
292C4⋊C4C22×D11311yescharacteristic
293C4⋊C4C22×D11311yescharacteristic
294C4⋊C4C22×D11311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—1131no—
298C22⋊C4—1131no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C42—21no—
305C42—1131no—
306C42—2261no—
307C42—2261no—
308C23—21no—
309C23—1131no—
310C23—9041no—
311C23—9041no—
312C23—4522no—
313C23—4522no—
314C23—4522no—
315C23—4522no—
316C23—2261no—
317C23—2261no—
318C23D4×D11311yescharacteristic
319Q8—4522no—
320Q8—2261no—
321Q8—2261no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—1132no—
326D4—9041no—
327D4—4522no—
328D4—4522no—
329D4—4522no—
330D4—4522no—
331D4—2262no—
332D4—2261no—
333D4—2261no—
334D4—2261no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—1131no—
341C2×C4—1131no—
342C2×C4—1131no—
343C2×C4—4522no—
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—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—9044no—
361C22—9044no—
362C22—4521no—
363C22—4521no—
364C22—4521no—
365C22—4521no—
366C22—4521no—
367C22—2261no—
368C22—2261no—
369C22—2261no—
370C22—2262no—
371C22C2×D4×D11311yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—1132no—
377C4—4521no—
378C4—4521no—
379C4—2261no—
380C4—2261no—
381C4#41×D11311yescharacteristic
382C4#1681366811yescharacteristic
383C2—41no—
384C2—81no—
385C2—9041no—
386C2—4522no—
387C2—4521no—
388C2#2029924011yescharacteristic
389C2AGL(1,ℤ/8)×D11311yescharacteristic
390C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#482×C113C2
socleC22×C113C22×D4
prime radical#20299232C2
hypercenter#482D113
hypocenterC113#3324
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #20299316C2semidirect
3. #20298943C2semidirect
4. #20298924C2semidirect
5. #20298877C2semidirect
6. #20298845C2semidirect
7. #20298842C2semidirect
8. #20298797C2semidirect
9. #20298751C2semidirect
10. #20298750C2semidirect
11. #20298685C2semidirect
12. #20298673C2semidirect
13. #20298602C2semidirect
14. #20298601C2semidirect
15. #482×C113C2semidirect
20. C2×#14268636C22semidirect
21. C2×#14268635C22semidirect
22. C2×#14268631C22semidirect
23. C2×#14268630C22semidirect
24. #16813621C22semidirect
29. #16813602C22semidirect
30. #16813601C22semidirect
36. #16813587C22semidirect
39. #16813580C22semidirect
40. #16813555C22semidirect
41. #16813551C22semidirect
42. #16813545C22semidirect
44. #16813544C22semidirect
45. #16813543C22semidirect
48. #16813542C22semidirect
49. #16813542C22semidirect
50. #16813534C22semidirect
51. C8×Dic113C22semidirect
53. #117×C113C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
56. #102×C113C22semidirect
57. #102×C113C22semidirect
58. C22⋊C8×C113C22semidirect
196. C113#3324semidirect
201. #482D113semidirect
237. #117C2×D113semidirect
239. #107C2×D113semidirect
240. #106C2×D113semidirect
250. #102C2×D113semidirect
251. #102C2×D113semidirect
253. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993162
#202992322
#202989432
#202989242
#202988772
#202988452
#202988422
#202987972
#202987512
#202987502
#202986852
#202986732
#202986022
#202986012
#482×C1132
#3324113