Finite Group Databasebeta

← #28400710

Subgroups — #28400710

Order 14464.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299130C211yesmaximal, characteristic, complemented
2C4×D4×D113C211yesmaximal, characteristic, complemented
3#20298930C211yesmaximal, characteristic, complemented
4#20298910C211yesmaximal, characteristic, complemented
5#20298897C211yesmaximal, characteristic, complemented
6#20298896C211yesmaximal, characteristic, complemented
7#20298812C211yesmaximal, characteristic, complemented
8#20298811C211yesmaximal, characteristic, complemented
9#20298750C211yesmaximal, characteristic, complemented
10#20298730C211yesmaximal, characteristic
11#20298708C211yesmaximal, characteristic, complemented
12#20298700C211yesmaximal, characteristic, complemented
13#20298698C211yesmaximal, characteristic, complemented
14#20298653C211yesmaximal, characteristic, complemented
15#442×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C22×C4×D113—21no—
18C2×#14268636C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21#16813615—21no—
22#16813613C2211yescharacteristic, complemented
23#16813609C2211yescharacteristic, complemented
24#16813604—21no—
25#16813602C2211yescharacteristic
26#16813593C2211yescharacteristic
27C4×Dic226C2211yescharacteristic, complemented
28C4×D452C2211yescharacteristic
29D4×Dic113C2211yescharacteristic
30#16813584C2211yescharacteristic
31C4×C22⋊D113—21no—
32C4×C22⋊D113—21no—
33#16813582—21no—
34#16813581—21no—
35C4⋊C4×D113C2211yescharacteristic
36C22⋊C4×D113—21no—
37C42×D113C2211yescharacteristic
38#16813556C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813551C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813545C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic, complemented
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813533C2211yescharacteristic, complemented
52C2×D8×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic, complemented
58#97×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64D4×D113—22no—
65D4×D113—22no—
66C22×Dic113—21no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—44no—
71C2×C4×D113D411yescharacteristic
72C2×C4×D113D411yescharacteristic
73C2×C4×D113C2311yescharacteristic
74#14268636—22no—
75#14268635—22no—
76#14268632—22no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113—21no—
94C4×Dic113D411yescharacteristic
95C4×Dic113D411yescharacteristic
96C4×Dic113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100C22×C4×C113—21no—
101D8×C113—22no—
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C22⋊C4×C113—21no—
108C42×C113C2311yescharacteristic
109C23×C113—21no—
110C23×C113—21no—
111C22×D113—24no—
112C22×D113—21no—
113C22×D113—42no—
114C22×D113—42no—
115C22×D113C2×D411yescharacteristic
116D4×C113—21no—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113#4112yes—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—42no—
123C2×C4×C113—42no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—24no—
128C22⋊D113—42no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—42no—
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136D452—21no—
137D452#4112yes—
138C4×D113—22no—
139C4×D113—21no—
140C4×D113—21no—
141C4×D113—41no—
142C4×D113—42no—
143C4×D113—42no—
144C4×D113—42no—
145Dic226—21no—
146Dic226—21no—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—22no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113C22×D411yescharacteristic
158C2×D113—21no—
159C2×D113—21no—
160C2×D113—22no—
161C2×D113—48no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113AGL(1,ℤ/8)12yes—
165C4×C113—21no—
166C4×C113—21no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113C2×#4111yescharacteristic
171Dic113—21no—
172Dic113—21no—
173Dic113—21no—
174Dic113—41no—
175Dic113—41no—
176Dic113—41no—
177C2×C113—42no—
178C2×C113—81no—
179C2×C113#52511yescharacteristic
180C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C113#57511yescharacteristic
182D113—22no—
183D113—42no—
184#3114—1131nomaximal, Sylow
185C113#311411yescharacteristic, complemented, Sylow
186#529—1131no—
187C2×C4×D4—1131no—
188#483—1131no—
189#480—1131no—
190#478—1131no—
191#478—1131no—
192#463—1131no—
193#463—1131no—
194#450—1131no—
195#447—1131no—
196#442—1131no—
197#442D11311yescharacteristic, complemented
198#440—1131no—
199#440—1131no—
200#432—1131no—
201C22×D4—1131no—
202C23×C4—2261no—
203C2×SD16—1131no—
204C2×SD16—1131no—
205C2×D8—1131no—
206C2×D8C2×D11311yescharacteristic
207#126—2261no—
208#125—1131no—
209#124—1131no—
210#123—2261no—
211C22⋊Q8—1131no—
212#121—1131no—
213C4×Q8—1131no—
214C4×D4—1131no—
215C4×D4—1131no—
216C4×D4—1131no—
217C4×D4—2261no—
218C4×D4—2261no—
219C4×D4—2261no—
220C4×D4C2×D11311yescharacteristic
221C4×D4C2×D11311yescharacteristic, complemented
222#117—2261no—
223C2×C4⋊C4—1131no—
224C2×C22⋊C4—2261no—
225C2×C42—1131no—
226#107—1131no—
227#107—1131no—
228#106—1131no—
229#106C2×D11311yescharacteristic, complemented
230C4⋊C8—1131no—
231C4⋊C8—1131no—
232#103—1131no—
233#103—1131no—
234#102—1131no—
235#102—1131no—
236#102—1131no—
237#102—1131no—
238#102C2×D11311yescharacteristic
239#102C2×D11311yescharacteristic, complemented
240C22⋊C8—1131no—
241C22⋊C8—1131no—
242#97—1131no—
243#97C2×D11311yescharacteristic, complemented
244C24—2261no—
245C2×Q8—1131no—
246C2×D4—1131no—
247C2×D4—2261no—
248C2×D4—2262no—
249C2×D4—2261no—
250C2×D4—2262no—
251C2×D4C22×D11311yescharacteristic
252C2×D4C22×D11311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1131no—
256C22×C4—1131no—
257C22×C4—1131no—
258C22×C4—4524no—
259C22×C4—2261no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4—2261no—
263SD16—2262no—
264SD16—2262no—
265D8—22no—
266D8—2262no—
267C2×C8—1131no—
268C2×C8—1131no—
269C2×C8C22×D11311yescharacteristic
270C2×C8C22×D11311yescharacteristic
271C4⋊C4—1131no—
272C4⋊C4—1131no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4C22×D11311yescharacteristic
279C4⋊C4C22×D11311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C42—1131no—
290C42—1131no—
291C42—1131no—
292C42—2261no—
293C42C22×D11311yescharacteristic
294C23—21no—
295C23—21no—
296C23—1131no—
297C23—4522no—
298C23—4522no—
299C23—2264no—
300C23—2261no—
301Q8—2261no—
302Q8—2261no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—1132no—
307D4—4522no—
308D4—2264no—
309D4—2261no—
310D4#1426864712yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—1131no—
316C2×C4—1131no—
317C2×C4—1131no—
318C2×C4—4522no—
319C2×C4—4521no—
320C2×C4—4522no—
321C2×C4—4522no—
322C2×C4—4522no—
323C2×C4—2262no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4D4×D11311yescharacteristic
330C2×C4D4×D11311yescharacteristic
331C2×C4C23×D11311yescharacteristic
332C8—21no—
333C8—21no—
334C8—2261no—
335C8—2261no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—1132no—
343C22—4528no—
344C22—4521no—
345C22—4521no—
346C22—2262no—
347C22—2261no—
348C22—2261no—
349C22C2×D4×D11311yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—4521no—
355C4—4521no—
356C4—4521no—
357C4—2261no—
358C4—2261no—
359C4—2261no—
360C4#41×D11311yescharacteristic
361C4C2×#1426864711yescharacteristic
362C2—42no—
363C2—81no—
364C2—4522no—
365C2—2262no—
366C2#2029910711yescharacteristic
367C2AGL(1,ℤ/8)×D11311yescharacteristic
368C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#442×C113C2
socleC22×C113C22×D4
prime radical#20298730C2
hypercenter#442D113
hypocenterC113#3114
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #20299130C2semidirect
2. C4×D4×D113C2semidirect
3. #20298930C2semidirect
4. #20298910C2semidirect
5. #20298897C2semidirect
6. #20298896C2semidirect
7. #20298812C2semidirect
8. #20298811C2semidirect
9. #20298750C2semidirect
11. #20298708C2semidirect
12. #20298700C2semidirect
13. #20298698C2semidirect
14. #20298653C2semidirect
15. #442×C113C2semidirect
22. #16813613C22semidirect
23. #16813609C22semidirect
27. C4×Dic226C22semidirect
38. #16813556C22semidirect
39. #16813555C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813551C22semidirect
43. #16813547C22semidirect
44. #16813545C22semidirect
47. #16813543C22semidirect
51. #16813533C22semidirect
54. C4×D4×C113C22semidirect
55. #106×C113C22semidirect
57. #102×C113C22semidirect
58. #97×C113C22semidirect
185. C113#3114semidirect
197. #442D113semidirect
221. C4×D4C2×D113semidirect
229. #106C2×D113semidirect
239. #102C2×D113semidirect
243. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991302
C4×D4×D1132
#202989302
#202989102
#202988972
#202988962
#202988122
#202988112
#202987502
#202987302
#202987082
#202987002
#202986982
#202986532
#442×C1132
#3114113