Finite Group Databasebeta

← #28400711

Subgroups — #28400711

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#20299127C211yesmaximal, characteristic, complemented
2C4×D4×D113C211yesmaximal, characteristic, complemented
3#20298927C211yesmaximal, characteristic, complemented
4#20298910C211yesmaximal, characteristic, complemented
5#20298899C211yesmaximal, characteristic, complemented
6#20298898C211yesmaximal, characteristic, complemented
7#20298810C211yesmaximal, characteristic, complemented
8#20298747C211yesmaximal, characteristic, complemented
9#20298730C211yesmaximal, characteristic
10#20298710C211yesmaximal, characteristic, complemented
11#20298707C211yesmaximal, characteristic, complemented
12#20298701C211yesmaximal, characteristic, complemented
13#20298699C211yesmaximal, characteristic, complemented
14#20298654C211yesmaximal, characteristic, complemented
15#463×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C22×C4×D113—21no—
18C2×#14268634C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20#16813615—21no—
21#16813614C2211yescharacteristic, complemented
22#16813604—21no—
23#16813598C2211yescharacteristic
24#16813593C2211yescharacteristic
25Q8×Dic113C2211yescharacteristic, complemented
26C4×D452C2211yescharacteristic
27D4×Dic113C2211yescharacteristic
28D4×Dic113C2211yescharacteristic, complemented
29#16813584C2211yescharacteristic
30C4×C22⋊D113—21no—
31#16813582—21no—
32#16813582—21no—
33#16813578—21no—
34C4⋊C4×D113C2211yescharacteristic
35C22⋊C4×D113—21no—
36C42×D113C2211yescharacteristic
37#16813556C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41C4⋊#11744751C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic, complemented
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51#16813532C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic
53C2×D8×C113C2211yescharacteristic
54#124×C113C2211yescharacteristic, complemented
55C4×D4×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
62C2×C22⋊D113—21no—
63D4×D113—22no—
64D4×D113—22no—
65C22×Dic113—21no—
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#14268634—22no—
75#14268632—22no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92C4×Dic113—21no—
93C4×Dic113D411yescharacteristic
94C4×Dic113D411yescharacteristic
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100SD16×C113—22no—
101D8×C113—22no—
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
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
116Q8×C113—21no—
117Q8×C113—21no—
118D4×C113—21no—
119D4×C113—21no—
120D4×C113—21no—
121D4×C113#4112yes—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—42no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—24no—
129C22⋊D113—42no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—42no—
134C2×Dic113—42no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138D452—21no—
139D452#4112yes—
140C4×D113—22no—
141C4×D113—21no—
142C4×D113—21no—
143C4×D113—41no—
144C4×D113—42no—
145C4×D113—42no—
146C4×D113—42no—
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#463D11311yescharacteristic, complemented
194#450—1131no—
195#447—1131no—
196#442—1131no—
197#442—1131no—
198#440—1131no—
199#440—1131no—
200#432—1131no—
201C22×D4—1131no—
202C23×C4—2261no—
203C2×SD16—1131no—
204C2×SD16C2×D11311yescharacteristic
205C2×D8—1131no—
206C2×D8C2×D11311yescharacteristic
207#126—2261no—
208#125—1131no—
209#124C2×D11311yescharacteristic, complemented
210#123—2261no—
211C22⋊Q8—1131no—
212#121—1131no—
213C4×Q8—1131no—
214C4×D4—1131no—
215C4×D4—1131no—
216C4×D4—1131no—
217C4×D4—1131no—
218C4×D4—2261no—
219C4×D4—2261no—
220C4×D4—2261no—
221C4×D4C2×D11311yescharacteristic
222#117—2261no—
223C2×C4⋊C4—1131no—
224C2×C22⋊C4—2261no—
225C2×C42—1131no—
226#107—1131no—
227#107—1131no—
228#106—1131no—
229#106—1131no—
230C4⋊C8—1131no—
231C4⋊C8C2×D11311yescharacteristic, complemented
232#103—1131no—
233#103C2×D11311yescharacteristic, complemented
234#102—1131no—
235#102—1131no—
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102C2×D11311yescharacteristic, complemented
240C22⋊C8—1131no—
241C22⋊C8—1131no—
242#97—1131no—
243#97—1131no—
244C24—2261no—
245C2×Q8C22×D11311yescharacteristic
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—1131no—
255C22×C4—1131no—
256C22×C4—1131no—
257C22×C4—4524no—
258C22×C4—2261no—
259C22×C4—2261no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4—2261no—
263SD16—22no—
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—1131no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4C22×D11311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
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—21no—
302Q8—21no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—1132no—
307D4—4522no—
308D4—2264no—
309D4—2261no—
310D4#1426864612yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—1131no—
315C2×C4—1131no—
316C2×C4—1131no—
317C2×C4—4522no—
318C2×C4—4521no—
319C2×C4—4522no—
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×#1426864611yescharacteristic
362C2—42no—
363C2—81no—
364C2—4522no—
365C2—2262no—
366C2#2029910811yescharacteristic
367C2AGL(1,ℤ/8)×D11311yescharacteristic
368C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#463×C113C2
socleC22×C113C22×D4
prime radical#20298730C2
hypercenter#463D113
hypocenterC113#3114
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #20299127C2semidirect
2. C4×D4×D113C2semidirect
3. #20298927C2semidirect
4. #20298910C2semidirect
5. #20298899C2semidirect
6. #20298898C2semidirect
7. #20298810C2semidirect
8. #20298747C2semidirect
10. #20298710C2semidirect
11. #20298707C2semidirect
12. #20298701C2semidirect
13. #20298699C2semidirect
14. #20298654C2semidirect
15. #463×C113C2semidirect
21. #16813614C22semidirect
25. Q8×Dic113C22semidirect
28. D4×Dic113C22semidirect
37. #16813556C22semidirect
38. #16813555C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. C4⋊#11744751C22semidirect
42. #16813546C22semidirect
47. #16813543C22semidirect
50. #16813532C22semidirect
51. #16813532C22semidirect
54. #124×C113C22semidirect
56. C4⋊C8×C113C22semidirect
57. #103×C113C22semidirect
58. #102×C113C22semidirect
185. C113#3114semidirect
193. #463D113semidirect
209. #124C2×D113semidirect
231. C4⋊C8C2×D113semidirect
233. #103C2×D113semidirect
239. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991272
C4×D4×D1132
#202989272
#202989102
#202988992
#202988982
#202988102
#202987472
#202987302
#202987102
#202987072
#202987012
#202986992
#202986542
#463×C1132
#3114113