Finite Group Databasebeta

← #28402767

Subgroups — #28402767

Order 14464.

392 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#20299313C211yesmaximal, characteristic, complemented
2#20299256C211yesmaximal, characteristic, complemented
3#20298957C211yesmaximal, characteristic, complemented
4#20298937C211yesmaximal, characteristic, complemented
5#20298921C211yesmaximal, characteristic, complemented
6#20298884C211yesmaximal, characteristic, complemented
7#20298848C211yesmaximal, characteristic, complemented
8#20298824C211yesmaximal, characteristic, complemented
9#20298740C211yesmaximal, characteristic, complemented
10#20298735C211yesmaximal, characteristic, complemented
11#20298698C211yesmaximal, characteristic, complemented
12#20298668C211yesmaximal, characteristic, complemented
13#20298605C211yesmaximal, characteristic, complemented
14#20298591C211yesmaximal, characteristic, complemented
15#463×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268630C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813622C2211yescharacteristic
22#16813608—21no—
23#16813608—21no—
24#16813608—21no—
25#16813599—21no—
26#16813598C2211yescharacteristic
27#16813596—21no—
28#16813595—21no—
29#16813593C2211yescharacteristic
30#16813593C2211yescharacteristic
31#16813593C2211yescharacteristic
32C4×Dic226C2211yescharacteristic
33C4×D452C2211yescharacteristic
34#16813582—21no—
35#16813581—21no—
36#16813580C2211yescharacteristic
37#16813580C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813533C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C2×D8×C113C2211yescharacteristic
54#124×C113C2211yescharacteristic
55C4×D4×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—41no—
61C2×Dic226—21no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64Q8×D113—22no—
65Q8×D113—41no—
66C2×D452D411yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C22×Dic113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74C2×C4×D113C2311yescharacteristic
75#14268635—22no—
76#14268630—41no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C8×D113—41no—
80C4⋊Dic113—21no—
81C4⋊Dic113D411yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113—21no—
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113C2311yescharacteristic
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113—21no—
102SD16×C113—41no—
103D8×C113—41no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C22⋊C4×C113—21no—
109C22⋊C4×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C23×C113—21no—
113C22×D113C2×D411yescharacteristic
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113—21no—
120D4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—42no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—42no—
128C22⋊D113—42no—
129C22⋊D113—81no—
130C22⋊D113—81no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—42no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138D452—41no—
139C4×D113—21no—
140C4×D113—21no—
141C4×D113—21no—
142C4×D113—21no—
143C4×D113—42no—
144Dic226—21no—
145Dic226—42no—
146Dic226—81no—
147Dic226#4112yes—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—21no—
164C2×D113—21no—
165C4×C113—21no—
166C4×C113—21no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113H(5,𝔽2)11yescharacteristic
171Dic113—22no—
172Dic113—21no—
173Dic113—21no—
174Dic113—41no—
175Dic113—41no—
176Dic113—41no—
177C2×C113—81no—
178C2×C113—81no—
179C2×C113#54611yescharacteristic
180C2×C113#57511yescharacteristic
181C2×C113#57711yescharacteristic
182D113—41no—
183D113—41no—
184#3321—1131nomaximal, Sylow
185C113#332111yescharacteristic, complemented, Sylow
186#555—1131no—
187#548—1131no—
188#489—1131no—
189#485—1131no—
190#482—1131no—
191#475—1131no—
192#469—1131no—
193#465—1131no—
194#463D11311yescharacteristic, complemented
195#449—1131no—
196#448—1131no—
197#440—1131no—
198#435—1131no—
199#419—1131no—
200#416—1131no—
201C2×#41—1131no—
202C22×Q8—1131no—
203C2×SD16—1131no—
204C2×SD16C2×D11311yescharacteristic
205C2×D8C2×D11311yescharacteristic
206C2×M16—1131no—
207C22×C8—1131no—
208C4⋊Q8—1131no—
209#124—2261no—
210#124—2261no—
211#124—2261no—
212#124C2×D11311yescharacteristic
213C22⋊Q8—1131no—
214C22⋊Q8—2261no—
215#121—1131no—
216#121—1131no—
217#121—1131no—
218#121—2261no—
219#121—2261no—
220C4×Q8—1131no—
221C4×D4—1131no—
222C4×D4—2261no—
223C4×D4C2×D11311yescharacteristic
224#117—1131no—
225#117—1131no—
226#117—2261no—
227#107—1131no—
228#106—1131no—
229#106—1131no—
230C4⋊C8C2×D11311yescharacteristic
231#103—1131no—
232#103—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⋊C8—1131no—
243#97—1131no—
244#41—4521no—
245#41—2262no—
246C2×Q8—1131no—
247C2×Q8—4521no—
248C2×Q8—2261no—
249C2×Q8—2262no—
250C2×Q8—2261no—
251C2×Q8C22×D11311yescharacteristic
252C2×D4—1131no—
253C2×D4—2261no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4C22×D11311yescharacteristic
258C2×D4C22×D11311yescharacteristic
259C22×C4—21no—
260C22×C4—1131no—
261C22×C4—1131no—
262C22×C4—2261no—
263C22×C4—2261no—
264SD16—41no—
265SD16—2262no—
266D8—41no—
267M16—4521no—
268C2×C8—1131no—
269C2×C8—1131no—
270C2×C8—4521no—
271C2×C8C22×D11311yescharacteristic
272C2×C8C22×D11311yescharacteristic
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1131no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4C22×D11311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—1131no—
285C22⋊C4—1131no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C42—2261no—
293C42—2261no—
294C42—2261no—
295C42C22×D11311yescharacteristic
296C23—21no—
297C23—21no—
298C23—1131no—
299C23—1131no—
300Q8—21no—
301Q8—21no—
302Q8—1132no—
303Q8—9041no—
304Q8—4522no—
305Q8—2261no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—9041no—
311D4—9041no—
312D4—4521no—
313D4—4522no—
314D4—4522no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—42no—
318C2×C4—1131no—
319C2×C4—1131no—
320C2×C4—4522no—
321C2×C4—4522no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4D4×D11311yescharacteristic
331C2×C4D4×D11311yescharacteristic
332C2×C4C23×D11311yescharacteristic
333C8—21no—
334C8—21no—
335C8—2261no—
336C8—2261no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—2261no—
344C22—2261no—
345C22—2261no—
346C22—2261no—
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—2262no—
360C4#41×D11311yescharacteristic
361C4#1681366711yescharacteristic
362C2—81no—
363C2—81no—
364C2—4521no—
365C2—4521no—
366C2#2029924511yescharacteristic
367C2#2029939411yescharacteristic
368C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#463×C113C2
socleC22×C113C22×D4
hypercenter#463D113
hypocenterC113#3321
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. #20299313C2semidirect
2. #20299256C2semidirect
3. #20298957C2semidirect
4. #20298937C2semidirect
5. #20298921C2semidirect
6. #20298884C2semidirect
7. #20298848C2semidirect
8. #20298824C2semidirect
9. #20298740C2semidirect
10. #20298735C2semidirect
11. #20298698C2semidirect
12. #20298668C2semidirect
13. #20298605C2semidirect
14. #20298591C2semidirect
15. #463×C113C2semidirect
185. C113#3321semidirect
194. #463D113semidirect

Maximal subgroups

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

subgroupindex
#202993132
#202992562
#202989572
#202989372
#202989212
#202988842
#202988482
#202988242
#202987402
#202987352
#202986982
#202986682
#202986052
#202985912
#463×C1132
#3321113