Finite Group Databasebeta

← #28402437

Subgroups — #28402437

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299261C211yesmaximal, characteristic, complemented
2#20299249C211yesmaximal, characteristic
3#20298947C211yesmaximal, characteristic, complemented
4#20298930C211yesmaximal, characteristic, complemented
5#20298882C211yesmaximal, characteristic, complemented
6#20298829C211yesmaximal, characteristic, complemented
7#20298828C211yesmaximal, characteristic, complemented
8#20298802C211yesmaximal, characteristic, complemented
9#20298739C211yesmaximal, characteristic, complemented
10#20298738C211yesmaximal, characteristic, complemented
11#20298685C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13C2×#16813545C211yesmaximal, characteristic, complemented
14#103×D113C211yesmaximal, characteristic, complemented
15#483×C113C211yesmaximal, characteristic, complemented
16C2×#14268647—21no—
17C22×Dic226C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C2×#14268634C2211yescharacteristic
22C22×#11744751C2211yescharacteristic
23C2×C8×D113C2211yescharacteristic
24#16813621—21no—
25#16813621C2211yescharacteristic
26#16813620C2211yescharacteristic
27#16813607—21no—
28#16813605—21no—
29#16813602C2211yescharacteristic
30#16813600—21no—
31#16813600—21no—
32#16813599—21no—
33#16813597C2211yescharacteristic
34#16813596C2211yescharacteristic
35#16813587C2211yescharacteristic
36#16813584C2211yescharacteristic
37C4×C22⋊D113C2211yescharacteristic
38#16813582—21no—
39C4⋊C4×D113C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22⋊Q8×C113C2211yescharacteristic
53C2×C4⋊C4×C113C2211yescharacteristic
54#106×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268647—44no—
60C2×Dic226—22no—
61C2×Dic226—21no—
62C2×Dic226—21no—
63C2×Dic226—21no—
64C2×Dic226—41no—
65C2×Dic226C2311yescharacteristic
66C2×Dic226C2311yescharacteristic
67Q8×D113—22no—
68Q8×D113—41no—
69C2×D452—21no—
70C2×D452C2311yescharacteristic
71C2×C22⋊D113—21no—
72C2×C22⋊D113D411yescharacteristic
73C22×Dic113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113—21no—
77C2×C4×D113C2311yescharacteristic
78#14268636—22no—
79#14268636—41no—
80#14268634—41no—
81C2×#11744751—41no—
82C2×#11744751C2311yescharacteristic
83C2×#11744751C2311yescharacteristic
84C8×D113—41no—
85C4⋊Dic113—21no—
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268626—21no—
91#14268626—21no—
92#14268626D411yescharacteristic
93C22⋊Dic113D411yescharacteristic
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624D411yescharacteristic
99C4×Dic113—21no—
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—42no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C22⋊D113—42no—
127C22⋊D113SD1614yescomplemented
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—42no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135D452—21no—
136D452—21no—
137D452—42no—
138C4×D113—21no—
139C4×D113—21no—
140C4×D113—42no—
141C4×D113—42no—
142C4×D113—42no—
143Dic226—21no—
144Dic226—21no—
145Dic226—21no—
146Dic226—42no—
147Dic226—42no—
148Dic226—42no—
149Dic226#4112yescomplemented
150C8×C113—21no—
151C8×C113—21no—
152#11744751—21no—
153#11744751—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113C2×SD1612yes—
157C22×C113C22×D411yescharacteristic
158C2×D113—21no—
159C2×D113—21no—
160C2×D113—41no—
161C2×D113—41no—
162C2×D113—41no—
163C2×D113C2×SD1612yes—
164C4×C113—21no—
165C4×C113—41no—
166C4×C113—41no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113H(5,𝔽2)11yescharacteristic
171Dic113—22no—
172Dic113—21no—
173Dic113—21no—
174Dic113—41no—
175Dic113—41no—
176Dic113C2×SD1612yes—
177C2×C113—22no—
178C2×C113#54611yescharacteristic
179C2×C113C22×SD1611yescharacteristic
180C2×C113#57811yescharacteristic
181D113—22no—
182D113—81no—
183#3298—1131nomaximal, Sylow
184C113#329811yescharacteristic, complemented, Sylow
185D4×Q8—1131no—
186#547—1131no—
187#487—1131no—
188#483—1131no—
189#483D11311yescharacteristic, complemented
190#475—1131no—
191#465—1131no—
192#465—1131no—
193#461—1131no—
194#448—1131no—
195#448—1131no—
196C4×SD16—1131no—
197C8×D4—1131no—
198C2×#103—1131no—
199C2×#103—1131no—
200C2×#41—2261no—
201C22×Q8—1131no—
202C22×Q8—1131no—
203C2×SD16—1131no—
204C2×SD16—1131no—
205C2×SD16—1131no—
206C22×C8—1131no—
207C22×C8—1131no—
208C4⋊Q8—1131no—
209C4⋊Q8—1131no—
210C4⋊Q8—2261no—
211#123—2261no—
212#123—2261no—
213C22⋊Q8—1131no—
214C22⋊Q8—2261no—
215C22⋊Q8—2261no—
216C22⋊Q8—2261no—
217C22⋊Q8C2×D11311yescharacteristic
218#121—1131no—
219#121—1131no—
220C4×Q8—1131no—
221C4×D4—1131no—
222C4×D4—1131no—
223C4×D4—2261no—
224C2×C4⋊C4—1131no—
225C2×C4⋊C4C2×D11311yescharacteristic
226#106—1131no—
227#106C2×D11311yescharacteristic
228#106C2×D11311yescharacteristic
229C4⋊C8—1131no—
230#103—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#103—1131no—
237#103C2×D11311yescharacteristic
238#103C2×D11311yescharacteristic
239#102—1131no—
240C22⋊C8—1131no—
241C22⋊C8C2×D11311yescharacteristic
242C4×C8—1131no—
243#41—4524no—
244C2×Q8—1131no—
245C2×Q8—1131no—
246C2×Q8—4521no—
247C2×Q8—4521no—
248C2×Q8—2261no—
249C2×Q8—2261no—
250C2×Q8—2262no—
251C2×Q8—2262no—
252C2×Q8—2261no—
253C2×Q8C22×D11311yescharacteristic
254C2×D4—1131no—
255C2×D4—1131no—
256C2×D4—2261no—
257C2×D4—2261no—
258C22×C4—21no—
259C22×C4—1131no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4—2261no—
263C22×C4—2261no—
264C22×C4C22×D11311yescharacteristic
265SD16—4521no—
266SD16—4521no—
267SD16—2262no—
268C2×C8—1131no—
269C2×C8—1131no—
270C2×C8—4521no—
271C2×C8—4521no—
272C2×C8C22×D11311yescharacteristic
273C2×C8C22×D11311yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—1131no—
277C4⋊C4—1131no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4—2261no—
283C4⋊C4—2261no—
284C4⋊C4C22×D11311yescharacteristic
285C4⋊C4C22×D11311yescharacteristic
286C4⋊C4C22×D11311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—1131no—
289C22⋊C4—1131no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C42—1131no—
295C42—2261no—
296C23—1131no—
297C23—2261no—
298C23D4×D11311yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—1132no—
302Q8—4522no—
303Q8—4522no—
304Q8—4522no—
305Q8—2261no—
306Q8—2261no—
307Q8—2261no—
308D4—1134no—
309D4—4522no—
310D4—4522no—
311D4—2261no—
312D4—2261no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—1131no—
321C2×C4—1131no—
322C2×C4—1131no—
323C2×C4—4522no—
324C2×C4—4522no—
325C2×C4—4522no—
326C2×C4—4522no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4D4×D11311yescharacteristic
333C2×C4C23×D11311yescharacteristic
334C8—21no—
335C8—21no—
336C8—2261no—
337C8—2261no—
338C22—21no—
339C22—21no—
340C22—1132no—
341C22—4521no—
342C22—4521no—
343C22—4521no—
344C22—2261no—
345C22—2261no—
346C22SD16×D11312yes—
347C22C2×D4×D11311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—1132no—
354C4—4521no—
355C4—4521no—
356C4—2261no—
357C4—2261no—
358C4—2262no—
359C4#41×D11311yescharacteristic
360C4#1681366811yescharacteristic
361C2—22no—
362C2—9041no—
363C2—2262no—
364C2#2029924011yescharacteristic
365C2C2×SD16×D11311yescharacteristic
366C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#483×C113C2
socleC22×C113C22×D4
prime radical#20299249C2
hypercenter#483D113
hypocenterC113#3298
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #20299261C2semidirect
3. #20298947C2semidirect
4. #20298930C2semidirect
5. #20298882C2semidirect
6. #20298829C2semidirect
7. #20298828C2semidirect
8. #20298802C2semidirect
9. #20298739C2semidirect
10. #20298738C2semidirect
11. #20298685C2semidirect
12. #20298661C2semidirect
13. C2×#16813545C2semidirect
14. #103×D113C2semidirect
15. #483×C113C2semidirect
127. C22⋊D113SD16semidirect
149. Dic226#41semidirect
184. C113#3298semidirect
189. #483D113semidirect

Maximal subgroups

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

subgroupindex
#202992612
#202992492
#202989472
#202989302
#202988822
#202988292
#202988282
#202988022
#202987392
#202987382
#202986852
#202986612
C2×#168135452
#103×D1132
#483×C1132
#3298113