Finite Group Databasebeta

← #28400761

Subgroups — #28400761

Order 14464.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299221C211yesmaximal, characteristic, complemented
2#20299072C211yesmaximal, characteristic, complemented
3#20298922C211yesmaximal, characteristic, complemented
4#20298887C211yesmaximal, characteristic, complemented
5#20298877C211yesmaximal, characteristic, complemented
6#20298816C211yesmaximal, characteristic, complemented
7#20298816C211yesmaximal, characteristic, complemented
8#20298748C211yesmaximal, characteristic, complemented
9#20298734C211yesmaximal, characteristic
10#20298709C211yesmaximal, characteristic, complemented
11#20298701C211yesmaximal, characteristic, complemented
12#20298683C211yesmaximal, characteristic, complemented
13#20298680C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#485×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×D904C2211yescharacteristic
20C2×D904C2211yescharacteristic
21#16813621C2211yescharacteristic, complemented
22#16813617—21no—
23#16813611C2211yescharacteristic, complemented
24#16813608—21no—
25#16813604—21no—
26#16813602—21no—
27#16813596C2211yescharacteristic
28Q8×Dic113C2211yescharacteristic, complemented
29C4×D452—21no—
30C4×D452—21no—
31#16813584C2211yescharacteristic
32#16813584C2211yescharacteristic
33#16813584C2211yescharacteristic
34#16813584C2211yescharacteristic
35#16813584C2211yescharacteristic, complemented
36#16813581C2211yescharacteristic
37C22⋊C4×D113—21no—
38C22⋊C4×D113—21no—
39#16813555C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813551C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813542C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic, complemented
48#16813542C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C22⋊Q8×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C23×D113—21no—
60C2×Dic226—21no—
61C2×D452—21no—
62C2×D452—22no—
63C2×D452—22no—
64C2×D452C2311yescharacteristic
65C2×D452C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73#14268634—22no—
74#14268634—22no—
75D904—22no—
76D904—22no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113D411yescharacteristic
81C4⋊Dic113D411yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84C22⋊Dic113D411yescharacteristic
85C22⋊Dic113D411yescharacteristic
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C22×C4×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C23×C113C2×D411yescharacteristic
109C22×D113—21no—
110C22×D113—21no—
111C22×D113—24no—
112C22×D113—21no—
113C22×D113—81no—
114C22×D113—81no—
115Q8×C113—21no—
116Q8×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2411yescharacteristic
125C22⋊D113—81no—
126C2×Dic113—21no—
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131D452—24no—
132D452—21no—
133D452—21no—
134D452—21no—
135D452—21no—
136D452#4112yes—
137D452#4112yes—
138C4×D113—81no—
139C4×D113—81no—
140C4×D113—81no—
141C4×D113—81no—
142C4×D113—81no—
143Dic226—81no—
144C8×C113—21no—
145C8×C113—21no—
146#11744751—21no—
147#11744751—21no—
148C22×C113—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113C22×D411yescharacteristic
152C2×D113—22no—
153C2×D113—22no—
154C2×D113—41no—
155C2×D113—41no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—84no—
162C4×C113—21no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113—41no—
167C4×C113C2×#4111yescharacteristic
168C4×C113C2×#4111yescharacteristic
169Dic113—21no—
170Dic113—21no—
171Dic113—21no—
172Dic113—21no—
173Dic113—41no—
174C2×C113—41no—
175C2×C113#52511yescharacteristic
176C2×C113#57611yescharacteristic
177C2×C113#57711yescharacteristic
178D113—42no—
179D113—42no—
180D113—81no—
181#3118—1131nomaximal, Sylow
182C113#311811yescharacteristic, complemented, Sylow
183#542—1131no—
184#518—1131no—
185#485D11311yescharacteristic, complemented
186#482—1131no—
187#476—1131no—
188#474—1131no—
189#463—1131no—
190#463—1131no—
191#450—1131no—
192#447—1131no—
193#442—1131no—
194#440—1131no—
195C4×SD16—1131no—
196C4×D8—1131no—
197#433—1131no—
198C22×D4—1131no—
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×D8—1131no—
202C2×D8—1131no—
203C4⋊Q8—1131no—
204#126—2261no—
205#124—1131no—
206#124—2261no—
207#123—2261no—
208C22⋊Q8—2261no—
209C22⋊Q8C2×D11311yescharacteristic
210#121—1131no—
211C4×Q8—1131no—
212C4×D4—1131no—
213C4×D4—1131no—
214C4×D4—1131no—
215C4×D4—1131no—
216C4×D4—1131no—
217C4×D4—2261no—
218C4×D4—2261no—
219#117—1131no—
220#117C2×D11311yescharacteristic
221C2×C22⋊C4—2261no—
222C2×C22⋊C4—2261no—
223#107—1131no—
224#107C2×D11311yescharacteristic, complemented
225#106—1131no—
226#106C2×D11311yescharacteristic, complemented
227C4⋊C8—1131no—
228C4⋊C8—1131no—
229#103C2×D11311yescharacteristic, complemented
230#103C2×D11311yescharacteristic, complemented
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235#102—1131no—
236#102—1131no—
237C22⋊C8—1131no—
238C22⋊C8C2×D11311yescharacteristic
239#97—1131no—
240C4×C8—1131no—
241C24—2261no—
242C2×Q8—2261no—
243C2×Q8C22×D11311yescharacteristic
244C2×D4—1131no—
245C2×D4—1131no—
246C2×D4—1131no—
247C2×D4—2262no—
248C2×D4—2262no—
249C2×D4—2261no—
250C2×D4—2261no—
251C22×C4—2261no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4C22×D11311yescharacteristic
257SD16—2262no—
258SD16—2262no—
259D8—2262no—
260D8—2262no—
261C2×C8—1131no—
262C2×C8—1131no—
263C2×C8C22×D11311yescharacteristic
264C2×C8C22×D11311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4C22×D11311yescharacteristic
272C4⋊C4C22×D11311yescharacteristic
273C4⋊C4C22×D11311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—1131no—
277C22⋊C4—1131no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—21no—
287C42—1131no—
288C42—1131no—
289C42—2261no—
290C23—9041no—
291C23—9041no—
292C23—2264no—
293C23—2261no—
294C23—2261no—
295C23—2261no—
296C23D4×D11311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—9041no—
300D4—1132no—
301D4—1132no—
302D4—9041no—
303D4—2264no—
304D4—2261no—
305D4—2261no—
306D4—2261no—
307D4—2261no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—1131no—
315C2×C4—1131no—
316C2×C4—1131no—
317C2×C4—1131no—
318C2×C4—9041no—
319C2×C4—9041no—
320C2×C4—9041no—
321C2×C4—9041no—
322C2×C4—9041no—
323C2×C4—2261no—
324C2×C4D4×D11311yescharacteristic
325C2×C4C23×D11311yescharacteristic
326C8—21no—
327C8—21no—
328C8—2261no—
329C8—2261no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—9044no—
334C22—4521no—
335C22—4521no—
336C22—4521no—
337C22—4521no—
338C22—4521no—
339C22—4521no—
340C22—4521no—
341C22—2262no—
342C22—2262no—
343C22C2×D4×D11311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—4521no—
350C4—2261no—
351C4—2261no—
352C4—2261no—
353C4—2261no—
354C4#41×D11311yescharacteristic
355C4#41×D11311yescharacteristic
356C2—41no—
357C2—9041no—
358C2—4522no—
359C2—4522no—
360C2#2029910611yescharacteristic
361C2#2029940011yescharacteristic
362C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#485×C113C2
socleC22×C113C22×D4
prime radical#20298734C2
hypercenter#485D113
hypocenterC113#3118
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #20299221C2semidirect
2. #20299072C2semidirect
3. #20298922C2semidirect
4. #20298887C2semidirect
5. #20298877C2semidirect
6. #20298816C2semidirect
7. #20298816C2semidirect
8. #20298748C2semidirect
10. #20298709C2semidirect
11. #20298701C2semidirect
12. #20298683C2semidirect
13. #20298680C2semidirect
14. #20298656C2semidirect
15. #485×C113C2semidirect
21. #16813621C22semidirect
23. #16813611C22semidirect
28. Q8×Dic113C22semidirect
35. #16813584C22semidirect
39. #16813555C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813551C22semidirect
47. #16813542C22semidirect
48. #16813542C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
56. #103×C113C22semidirect
57. #103×C113C22semidirect
182. C113#3118semidirect
185. #485D113semidirect
224. #107C2×D113semidirect
226. #106C2×D113semidirect
229. #103C2×D113semidirect
230. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992212
#202990722
#202989222
#202988872
#202988772
#202988162
#202987482
#202987342
#202987092
#202987012
#202986832
#202986802
#202986562
#485×C1132
#3118113