Finite Group Databasebeta

← #28401529

Subgroups — #28401529

Order 14464.

394 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299152C211yesmaximal, characteristic, complemented
2#20299147C211yesmaximal, characteristic
3#20298976C211yesmaximal, characteristic, complemented
4#20298969C211yesmaximal, characteristic, complemented
5#20298947C211yesmaximal, characteristic, complemented
6#20298943C211yesmaximal, characteristic, complemented
7#20298821C211yesmaximal, characteristic, complemented
8#20298820C211yesmaximal, characteristic, complemented
9#20298817C211yesmaximal, characteristic, complemented
10#20298763C211yesmaximal, characteristic, complemented
11#20298761C211yesmaximal, characteristic, complemented
12#20298759C211yesmaximal, characteristic, complemented
13#20298757C211yesmaximal, characteristic, complemented
14#20298650C211yesmaximal, characteristic, complemented
15#464×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×Dic452C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268637C2211yescharacteristic
21C2×#14268636C2211yescharacteristic
22C2×#14268635C2211yescharacteristic
23C2×#14268634C2211yescharacteristic
24#16813621C2211yescharacteristic
25#16813620C2211yescharacteristic
26#16813620C2211yescharacteristic
27#16813618C2211yescharacteristic
28#16813612—21no—
29#16813610C2211yescharacteristic
30#16813602C2211yescharacteristic
31#16813600—21no—
32#16813598C2211yescharacteristic
33#16813595—21no—
34#16813595—21no—
35C4×Dic226—21no—
36C4×Dic226C2211yescharacteristic
37#16813582—21no—
38#16813582—21no—
39#16813579—21no—
40C42×D113C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50C8×Dic113C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54#124×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268648—41no—
60#14268648—41no—
61#14268646—41no—
62#14268646—41no—
63C2×Dic226—21no—
64C2×Dic226C2311yescharacteristic
65C2×Dic226C2311yescharacteristic
66C2×D452—21no—
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C22×Dic113—21no—
72C2×C4×D113—21no—
73C2×C4×D113D411yescharacteristic
74C2×C4×D113D411yescharacteristic
75C2×C4×D113C2311yescharacteristic
76Dic452—41no—
77#14268637—41no—
78#14268637—41no—
79#14268636—41no—
80#14268635—41no—
81#14268634—41no—
82C2×#11744751C2311yescharacteristic
83C2×#11744751C2311yescharacteristic
84C4⋊Dic113—21no—
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268626—21no—
91#14268626—21no—
92#14268626—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97C4×Dic113—21no—
98C4×Dic113D411yescharacteristic
99C4×Dic113D411yescharacteristic
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×Q8×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104Q16×C113—41no—
105SD16×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C22⋊C4×C113—21no—
112C42×C113—21no—
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C22×D113—21no—
116C22×D113C2×D411yescharacteristic
117Q8×C113—21no—
118Q8×C113—21no—
119Q8×C113—21no—
120Q8×C113—21no—
121D4×C113—21no—
122D4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—42no—
130C22⋊D113—42no—
131C22⋊D113—42no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—42no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139D452—21no—
140D452—21no—
141D452—42no—
142C4×D113—21no—
143C4×D113—21no—
144C4×D113—22no—
145C4×D113—22no—
146C4×D113—42no—
147Dic226—21no—
148Dic226—21no—
149Dic226—21no—
150Dic226—21no—
151Dic226—42no—
152C8×C113—21no—
153C8×C113—21no—
154#11744751—21no—
155#11744751—21no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113C22×D411yescharacteristic
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—41no—
166C4×C113—21no—
167C4×C113—21no—
168C4×C113—41no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113H(5,𝔽2)11yescharacteristic
172C4×C113H(5,𝔽2)11yescharacteristic
173Dic113—21no—
174Dic113—41no—
175Dic113—41no—
176Dic113—41no—
177Dic113#13512yes—
178Dic113#13712yes—
179C2×C113—81no—
180C2×C113#53511yescharacteristic
181C2×C113C2×#13511yescharacteristic
182C2×C113C2×#13711yescharacteristic
183D113—41no—
184D113—81no—
185#3210—1131nomaximal, Sylow
186C113#321011yescharacteristic, complemented, Sylow
187#533—1131no—
188#532—1131no—
189#494—1131no—
190#492—1131no—
191#487—1131no—
192#486—1131no—
193#464—1131no—
194#464—1131no—
195#464—1131no—
196#464D11311yescharacteristic, complemented
197#452—1131no—
198#452—1131no—
199#452—1131no—
200#452—1131no—
201#431—1131no—
202C2×#41—1131no—
203C2×#41—1131no—
204C2×Q16—1131no—
205C2×Q16—1131no—
206C2×Q16—1131no—
207C2×Q16C2×D11311yescharacteristic
208C2×SD16—1131no—
209C2×SD16—1131no—
210C2×SD16—1131no—
211C2×SD16C2×D11311yescharacteristic
212C4⋊Q8—1131no—
213C4⋊Q8—1131no—
214C4⋊Q8—1131no—
215#127—1131no—
216#125—2261no—
217#124—1131no—
218#124C2×D11311yescharacteristic
219C22⋊Q8—1131no—
220C22⋊Q8—1131no—
221C22⋊Q8—2261no—
222#121—2261no—
223#121—2261no—
224C4×Q8—1131no—
225C4×Q8—2261no—
226C4×Q8C2×D11311yescharacteristic
227C4×D4—2261no—
228C4×D4—2261no—
229#117—2261no—
230C2×C42—1131no—
231C4⋊C8—1131no—
232C4⋊C8C2×D11311yescharacteristic
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#103C2×D11311yescharacteristic
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102C2×D11311yescharacteristic
241C22⋊C8—1131no—
242C22⋊C8—1131no—
243C4×C8—1131no—
244C4×C8—1131no—
245#41—4521no—
246#41—4521no—
247#41—4521no—
248#41—4521no—
249C2×Q8—1131no—
250C2×Q8—1131no—
251C2×Q8—2261no—
252C2×Q8C22×D11311yescharacteristic
253C2×Q8C22×D11311yescharacteristic
254C2×D4—1131no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4—2261no—
258C2×D4—2261no—
259C2×D4C22×D11311yescharacteristic
260C22×C4—1131no—
261C22×C4—1131no—
262C22×C4—1131no—
263C22×C4—2261no—
264C22×C4—2261no—
265Q16—41no—
266Q16—4521no—
267Q16—4521no—
268Q16—4521no—
269SD16—41no—
270SD16—4521no—
271SD16—4521no—
272SD16—4521no—
273C2×C8—1131no—
274C2×C8—1131no—
275C2×C8C22×D11311yescharacteristic
276C2×C8C22×D11311yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—1131no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4—2261no—
283C4⋊C4—2261no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4C22×D11311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C42—21no—
295C42—1131no—
296C42—1131no—
297C42—1131no—
298C42—2261no—
299C42C22×D11311yescharacteristic
300C23—21no—
301C23—1131no—
302C23—2261no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—4522no—
308Q8—2261no—
309Q8—2261no—
310Q8—2261no—
311Q8—2261no—
312D4—21no—
313D4—21no—
314D4—4522no—
315D4—4522no—
316D4—4522no—
317D4—4522no—
318D4—2261no—
319D4—2261no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—1131no—
324C2×C4—1131no—
325C2×C4—1131no—
326C2×C4—4522no—
327C2×C4—4522no—
328C2×C4—2262no—
329C2×C4—2262no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4—2261no—
333C2×C4—2261no—
334C2×C4—2261no—
335C2×C4D4×D11311yescharacteristic
336C2×C4D4×D11311yescharacteristic
337C2×C4C23×D11311yescharacteristic
338C8—21no—
339C8—21no—
340C8—2261no—
341C8—2261no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—4521no—
346C22—4521no—
347C22—4521no—
348C22—2261no—
349C22—2261no—
350C22—2261no—
351C22C2×D4×D11311yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1132no—
358C4—1132no—
359C4—4521no—
360C4—4521no—
361C4—4521no—
362C4—2261no—
363C4#1681366711yescharacteristic
364C4#1681366811yescharacteristic
365C2—81no—
366C2—9041no—
367C2—4521no—
368C2#2029916411yescharacteristic
369C2#135×D11311yescharacteristic
370C2#137×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radical#20299147C2
hypercenter#464D113
hypocenterC113#3210
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #20299152C2semidirect
3. #20298976C2semidirect
4. #20298969C2semidirect
5. #20298947C2semidirect
6. #20298943C2semidirect
7. #20298821C2semidirect
8. #20298820C2semidirect
9. #20298817C2semidirect
10. #20298763C2semidirect
11. #20298761C2semidirect
12. #20298759C2semidirect
13. #20298757C2semidirect
14. #20298650C2semidirect
15. #464×C113C2semidirect
186. C113#3210semidirect
196. #464D113semidirect

Maximal subgroups

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

subgroupindex
#202991522
#202991472
#202989762
#202989692
#202989472
#202989432
#202988212
#202988202
#202988172
#202987632
#202987612
#202987592
#202987572
#202986502
#464×C1132
#3210113