Finite Group Databasebeta

← #28403104

Subgroups — #28403104

Order 14464.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299318C211yesmaximal, characteristic
2#20299008C211yesmaximal, characteristic, complemented
3#20298939C211yesmaximal, characteristic, complemented
4#20298936C211yesmaximal, characteristic, complemented
5#20298936C211yesmaximal, characteristic, complemented
6#20298933C211yesmaximal, characteristic, complemented
7#20298902C211yesmaximal, characteristic, complemented
8#20298893C211yesmaximal, characteristic, complemented
9#20298854C211yesmaximal, characteristic, complemented
10#20298837C211yesmaximal, characteristic, complemented
11#20298703C211yesmaximal, characteristic, complemented
12#20298670C211yesmaximal, characteristic
13#20298638C211yesmaximal, characteristic, complemented
14#20298634C211yesmaximal, characteristic, complemented
15#552×C113C211yesmaximal, characteristic
16C2×#14268637C2211yescharacteristic
17C2×#14268631C2211yescharacteristic
18C22×#11744751C2211yescharacteristic
19#16813622C2211yescharacteristic
20#16813615—21no—
21#16813615—21no—
22#16813609—21no—
23#16813601C2211yescharacteristic
24#16813601C2211yescharacteristic
25C4×Dic226C2211yescharacteristic
26#16813587—21no—
27#16813581C2211yescharacteristic
28#16813581C2211yescharacteristic
29#16813555C2211yescharacteristic
30#16813555C2211yescharacteristic
31#16813555C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813555C2211yescharacteristic
34#16813553C2211yescharacteristic
35#16813553C2211yescharacteristic
36#16813553C2211yescharacteristic
37#16813553C2211yescharacteristic
38C4⋊#11744751C2211yescharacteristic
39#16813546C2211yescharacteristic
40#16813546C2211yescharacteristic
41#16813546C2211yescharacteristic
42#16813545C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813545C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47#16813533C2211yescharacteristic
48#126×C113—21no—
49#125×C113—21no—
50#125×C113C2211yescharacteristic
51#123×C113—21no—
52C22⋊Q8×C113C2211yescharacteristic
53C22⋊Q8×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55C4×D4×C113C2211yescharacteristic
56#117×C113—21no—
57#117×C113C2211yescharacteristic
58C2×C4⋊C4×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61#14268637—22no—
62#14268631—22no—
63C2×#11744751—22no—
64C2×#11744751C2311yescharacteristic
65C2×#11744751C2311yescharacteristic
66C2×#11744751C2311yescharacteristic
67C2×#11744751C2311yescharacteristic
68C4⋊Dic113—21no—
69C4⋊Dic113C2311yescharacteristic
70C4⋊Dic113C2311yescharacteristic
71C4⋊Dic113C2311yescharacteristic
72#14268626—21no—
73#14268626—21no—
74#14268626—21no—
75C22⋊Dic113—21no—
76C22⋊Dic113—21no—
77C22⋊Dic113—21no—
78C22⋊Dic113—21no—
79C4×Dic113—21no—
80C4×Dic113—21no—
81C4×Dic113—21no—
82C2×Q8×C113C2311yescharacteristic
83C2×D4×C113D411yescharacteristic
84C22×C4×C113—21no—
85C22×C4×C113C2311yescharacteristic
86C22×C4×C113C2311yescharacteristic
87C4⋊C4×C113—21no—
88C4⋊C4×C113—21no—
89C4⋊C4×C113—21no—
90C4⋊C4×C113—21no—
91C4⋊C4×C113—21no—
92C4⋊C4×C113—21no—
93C4⋊C4×C113D411yescharacteristic
94C4⋊C4×C113C2311yescharacteristic
95C4⋊C4×C113C2311yescharacteristic
96C4⋊C4×C113C2311yescharacteristic
97C22⋊C4×C113—21no—
98C22⋊C4×C113—21no—
99C22⋊C4×C113—21no—
100C22⋊C4×C113D411yescharacteristic
101C22⋊C4×C113D411yescharacteristic
102C42×C113—21no—
103C42×C113—21no—
104C42×C113C2311yescharacteristic
105C23×C113C2×D411yescharacteristic
106C23×C113C2×D411yescharacteristic
107Q8×C113—21no—
108Q8×C113—21no—
109D4×C113—41no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—42no—
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2411yescharacteristic
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128Dic226—21no—
129Dic226—21no—
130Dic226—42no—
131#11744751—21no—
132#11744751—21no—
133#11744751—21no—
134#11744751#4112yes—
135C22×C113—21no—
136C22×C113—21no—
137C22×C113—21no—
138C22×C113—21no—
139C22×C113—21no—
140C22×C113—21no—
141C22×C113C22×D411yescharacteristic
142C4×C113—21no—
143C4×C113—21no—
144C4×C113—21no—
145C4×C113—21no—
146C4×C113—41no—
147C4×C113—41no—
148C4×C113—41no—
149C4×C113—41no—
150C4×C113C2×#4111yescharacteristic
151C4×C1132−1+411yescharacteristic
152Dic113—41no—
153Dic113—41no—
154Dic113—41no—
155Dic113—41no—
156C2×C113—41no—
157C2×C113—41no—
158C2×C113#54711yescharacteristic
159C2×C113#57511yescharacteristic
160C2×C113#57811yescharacteristic
161#3349—1131nomaximal, Sylow
162C113#334911yescharacteristic, complemented, Sylow
163#556—1131no—
164#552D11311yescharacteristic
165#501—1131no—
166#485—1131no—
167#485—1131no—
168#485—1131no—
169#484—1131no—
170#479—1131no—
171#477—1131no—
172#470—1131no—
173#467—1131no—
174#441—1131no—
175#435—1131no—
176#428—1131no—
177#427—1131no—
178C2×Q16—1131no—
179C2×M16—1131no—
180C22×C8—1131no—
181C4⋊Q8—1131no—
182#126—21no—
183#126—2261no—
184#126—2261no—
185#125—21no—
186#125C2×D11311yescharacteristic
187#124—2261no—
188#123—21no—
189C22⋊Q8—1131no—
190C22⋊Q8—1131no—
191C22⋊Q8C2×D11311yescharacteristic
192C22⋊Q8C2×D11311yescharacteristic
193C4×Q8—1131no—
194C4×Q8—2261no—
195C4×Q8C2×D11311yescharacteristic
196C4×D4C2×D11311yescharacteristic
197#117—21no—
198#117—1131no—
199#117—1131no—
200#117C2×D11311yescharacteristic
201C2×C4⋊C4C2×D11311yescharacteristic
202#107—1131no—
203#107—1131no—
204#107—1131no—
205#107—1131no—
206#107—1131no—
207#106—1131no—
208#106—1131no—
209#106—1131no—
210#106—1131no—
211C4⋊C8—1131no—
212#103—1131no—
213#103—1131no—
214#103—1131no—
215#103—1131no—
216#103—1131no—
217#103—1131no—
218C22⋊C8—1131no—
219C22⋊C8—1131no—
220#97—1131no—
221C2×Q8—1131no—
222C2×Q8—2261no—
223C2×Q8C22×D11311yescharacteristic
224C2×D4C22⋊D11311yescharacteristic
225C22×C4—21no—
226C22×C4C22×D11311yescharacteristic
227C22×C4C22×D11311yescharacteristic
228Q16—2262no—
229M16—2262no—
230C2×C8—1131no—
231C2×C8—1131no—
232C2×C8—1131no—
233C2×C8—1131no—
234C2×C8—2262no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—1131no—
242C4⋊C4—1131no—
243C4⋊C4—1131no—
244C4⋊C4—2261no—
245C4⋊C4—2261no—
246C4⋊C4—2261no—
247C4⋊C4—2261no—
248C4⋊C4C22⋊D11311yescharacteristic
249C4⋊C4C22×D11311yescharacteristic
250C4⋊C4C22×D11311yescharacteristic
251C4⋊C4C22×D11311yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—2261no—
256C22⋊C4—2261no—
257C22⋊C4—2261no—
258C22⋊C4—2261no—
259C22⋊C4C22⋊D11311yescharacteristic
260C22⋊C4C22⋊D11311yescharacteristic
261C42—21no—
262C42—21no—
263C42—2261no—
264C42—2261no—
265C42—2261no—
266C42C22×D11311yescharacteristic
267C23C2×C22⋊D11311yescharacteristic
268C23C2×C22⋊D11311yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—4522no—
272Q8—2261no—
273Q8—2261no—
274D4—41no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—2261no—
285C2×C4—2261no—
286C2×C4—2261no—
287C2×C4—2261no—
288C2×C4C2×C22⋊D11311yescharacteristic
289C2×C4C2×C22⋊D11311yescharacteristic
290C2×C4C2×C22⋊D11311yescharacteristic
291C2×C4C2×C22⋊D11311yescharacteristic
292C2×C4C23×D11311yescharacteristic
293C8—1132no—
294C8—2261no—
295C8—2261no—
296C8—2261no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22C22×C22⋊D11311yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—4521no—
313C4—4521no—
314C4—4521no—
315C4—4521no—
316C4#41×D11311yescharacteristic
317C4#1681366911yescharacteristic
318C2—41no—
319C2—41no—
320C2#2029924711yescharacteristic
321C2#2029939611yescharacteristic
322C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#552×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×C113D4
hypercenter#552D113
hypocenterC113#3349
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #20299008C2semidirect
3. #20298939C2semidirect
4. #20298936C2semidirect
5. #20298936C2semidirect
6. #20298933C2semidirect
7. #20298902C2semidirect
8. #20298893C2semidirect
9. #20298854C2semidirect
10. #20298837C2semidirect
11. #20298703C2semidirect
13. #20298638C2semidirect
14. #20298634C2semidirect
162. C113#3349semidirect

Maximal subgroups

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

subgroupindex
#202993182
#202990082
#202989392
#202989362
#202989332
#202989022
#202988932
#202988542
#202988372
#202987032
#202986702
#202986382
#202986342
#552×C1132
#3349113