Finite Group Databasebeta

← #28401582

Subgroups — #28401582

Order 14464.

390 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#20299150C211yesmaximal, characteristic, complemented
2#20299144C211yesmaximal, characteristic
3#20298991C211yesmaximal, characteristic, complemented
4#20298989C211yesmaximal, characteristic, complemented
5#20298959C211yesmaximal, characteristic, complemented
6#20298956C211yesmaximal, characteristic, complemented
7#20298807C211yesmaximal, characteristic, complemented
8#20298806C211yesmaximal, characteristic, complemented
9#20298797C211yesmaximal, characteristic, complemented
10#20298796C211yesmaximal, characteristic, complemented
11#20298762C211yesmaximal, characteristic, complemented
12#20298760C211yesmaximal, characteristic, complemented
13#20298758C211yesmaximal, characteristic, complemented
14#20298652C211yesmaximal, characteristic, complemented
15#452×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C2×#14268635C2211yescharacteristic
22C2×#14268634C2211yescharacteristic
23#16813621C2211yescharacteristic
24#16813620C2211yescharacteristic
25#16813620C2211yescharacteristic
26#16813618C2211yescharacteristic
27#16813612—21no—
28#16813611C2211yescharacteristic
29#16813609C2211yescharacteristic
30#16813601C2211yescharacteristic
31#16813599—21no—
32#16813594—21no—
33#16813594—21no—
34Q8×Dic113C2211yescharacteristic
35#16813587—21no—
36#16813587C2211yescharacteristic
37C4×C22⋊D113—21no—
38C4×C22⋊D113—21no—
39#16813578—21no—
40C2×C4×Dic113C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic
51#16813532C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268647—41no—
60#14268647—41no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C22×Dic113D411yescharacteristic
69C22×Dic113D411yescharacteristic
70C2×C4×D113—21no—
71Dic452—41no—
72#14268637—41no—
73#14268637—41no—
74#14268636—41no—
75#14268635—41no—
76#14268634—41no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113D411yescharacteristic
96C4×Dic113D411yescharacteristic
97C4×Dic113C2311yescharacteristic
98C4×Dic113C2311yescharacteristic
99#41×C113—41no—
100#41×C113—41no—
101C2×Q8×C113C2311yescharacteristic
102C2×Q8×C113C2311yescharacteristic
103C2×D4×C113—21no—
104C2×D4×C113C2311yescharacteristic
105C22×C4×C113—21no—
106C22×C4×C113C2311yescharacteristic
107Q16×C113—41no—
108SD16×C113—41no—
109C2×C8×C113C2311yescharacteristic
110C2×C8×C113C2311yescharacteristic
111C4⋊C4×C113—21no—
112C4⋊C4×C113C2311yescharacteristic
113C22⋊C4×C113—21no—
114C23×C113—21no—
115C23×C113C2×D411yescharacteristic
116C22×D113—21no—
117Q8×C113—21no—
118Q8×C113—21no—
119Q8×C113—21no—
120Q8×C113—21no—
121D4×C113—21no—
122D4×C113—21no—
123D4×C113—42no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—42no—
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2411yescharacteristic
132C22⋊D113—42no—
133C22⋊D113—42no—
134C22⋊D113—42no—
135C2×Dic113—22no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—41no—
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144D452—21no—
145D452—21no—
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—21no—
157C22×C113—21no—
158C22×C113—21no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113C22×D411yescharacteristic
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—41no—
166C4×C113—21no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113—41no—
170C4×C113H(5,𝔽2)11yescharacteristic
171C4×C113H(5,𝔽2)11yescharacteristic
172Dic113—21no—
173Dic113—21no—
174Dic113—21no—
175Dic113—41no—
176Dic113—41no—
177Dic113—41no—
178Dic113#13712yes—
179C2×C113—41no—
180C2×C113—81no—
181C2×C113#53511yescharacteristic
182C2×C113C2×#13711yescharacteristic
183C2×C113#57511yescharacteristic
184D113—81no—
185#3216—1131nomaximal, Sylow
186C113#321611yescharacteristic, complemented, Sylow
187#533—1131no—
188#532—1131no—
189#497—1131no—
190#497—1131no—
191#489—1131no—
192#489—1131no—
193#462—1131no—
194#462—1131no—
195#460—1131no—
196#460—1131no—
197#452—1131no—
198#452—1131no—
199#452—1131no—
200#452D11311yescharacteristic, complemented
201#432—1131no—
202C2×#41—1131no—
203C2×#41C2×D11311yescharacteristic
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#124—1131no—
219C22⋊Q8—1131no—
220C22⋊Q8—2261no—
221C22⋊Q8C2×D11311yescharacteristic
222#121—2261no—
223#121—2261no—
224C4×Q8—1131no—
225C4×Q8—1131no—
226C4×Q8—2261no—
227C4×D4—2261no—
228C4×D4—2261no—
229#117—2261no—
230C2×C42—1131no—
231C4⋊C8—1131no—
232C4⋊C8—1131no—
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⋊C8C2×D11311yescharacteristic
243#97—1131no—
244#97—1131no—
245#41—41no—
246#41—41no—
247#41—4521no—
248#41—4521no—
249C2×Q8—1131no—
250C2×Q8—1131no—
251C2×Q8—2261no—
252C2×Q8C22×D11311yescharacteristic
253C2×Q8C22×D11311yescharacteristic
254C2×D4—21no—
255C2×D4—1131no—
256C2×D4—2261no—
257C2×D4—2261no—
258C2×D4—2261no—
259C2×D4C22×D11311yescharacteristic
260C22×C4—21no—
261C22×C4—1131no—
262C22×C4—1131no—
263C22×C4—2261no—
264C22×C4C22×D11311yescharacteristic
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—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C42—1131no—
295C42—1131no—
296C42—1131no—
297C42—1131no—
298C42—2261no—
299C42—2261no—
300C23—21no—
301C23—2261no—
302C23D4×D11311yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—4522no—
308Q8—2261no—
309Q8—2261no—
310Q8—2261no—
311Q8—2261no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—4522no—
316D4—4522no—
317D4—4522no—
318D4—2261no—
319D4—2261no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—1131no—
327C2×C4—1131no—
328C2×C4—1131no—
329C2×C4—1131no—
330C2×C4—4522no—
331C2×C4—4521no—
332C2×C4—2262no—
333C2×C4—2261no—
334C2×C4—2261no—
335C2×C4—2261no—
336C2×C4D4×D11311yescharacteristic
337C2×C4C23×D11311yescharacteristic
338C8—21no—
339C8—21no—
340C8—2261no—
341C8—2261no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—4521no—
349C22—4521no—
350C22—4521no—
351C22C2×D4×D11311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—1132no—
357C4—4521no—
358C4—4521no—
359C4—4521no—
360C4—2261no—
361C4—2261no—
362C4—2261no—
363C4#1681366711yescharacteristic
364C4#1681366711yescharacteristic
365C2—41no—
366C2—81no—
367C2—9041no—
368C2#2029916311yescharacteristic
369C2#137×D11311yescharacteristic
370C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#452×C113C2
socleC22×C113C22×D4
prime radical#20299144C2
hypercenter#452D113
hypocenterC113#3216
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #20299150C2semidirect
3. #20298991C2semidirect
4. #20298989C2semidirect
5. #20298959C2semidirect
6. #20298956C2semidirect
7. #20298807C2semidirect
8. #20298806C2semidirect
9. #20298797C2semidirect
10. #20298796C2semidirect
11. #20298762C2semidirect
12. #20298760C2semidirect
13. #20298758C2semidirect
14. #20298652C2semidirect
15. #452×C113C2semidirect
186. C113#3216semidirect
200. #452D113semidirect

Maximal subgroups

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

subgroupindex
#202991502
#202991442
#202989912
#202989892
#202989592
#202989562
#202988072
#202988062
#202987972
#202987962
#202987622
#202987602
#202987582
#202986522
#452×C1132
#3216113