Finite Group Databasebeta

← #13081071

Subgroups — #13081071

Order 1408.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#552C211yesmaximal, characteristic
2#10623074C211yesmaximal, characteristic
3#10622678C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622665C211yesmaximal, characteristic, complemented
6#10622664C211yesmaximal, characteristic, complemented
7#10622657C211yesmaximal, characteristic, complemented
8#10622656C211yesmaximal, characteristic, complemented
9#10622643C211yesmaximal, characteristic, complemented
10#10622633C211yesmaximal, characteristic, complemented
11#10622624C211yesmaximal, characteristic
12#10622609C211yesmaximal, characteristic, complemented
13#10622608C211yesmaximal, characteristic, complemented
14#10622584C211yesmaximal, characteristic, complemented
15C2×#66872C211yesmaximal, characteristic, complemented
16C11×#126—21no—
17C11×#125—21no—
18C11×#125C2211yescharacteristic
19C11×#123—21no—
20C11×C22⋊Q8C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C4×Q8×C11C2211yescharacteristic
23C4×D4×C11C2211yescharacteristic
24C11×#117—21no—
25C11×#117C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28D4×Dic11—21no—
29C2×C4⋊Dic11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31#66977C2211yescharacteristic
32#66977C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66943—21no—
36#66931—21no—
37#66931—21no—
38#66922C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40#66899C2211yescharacteristic
41#66899C2211yescharacteristic
42#66899C2211yescharacteristic
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66874C2211yescharacteristic
46#66874C2211yescharacteristic
47#66874C2211yescharacteristic
48#66872C2211yescharacteristic
49#66872C2211yescharacteristic
50#66872C2211yescharacteristic
51#66872C2211yescharacteristic
52#66872C2211yescharacteristic
53#66872C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11D411yescharacteristic
61C22×C4×C11—21no—
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4D411yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C22⋊C4—21no—
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C11×C22⋊C4D411yescharacteristic
82C11×C22⋊C4D411yescharacteristic
83C42×C11—21no—
84C42×C11—21no—
85C42×C11C2311yescharacteristic
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88#4326—22no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99#4318—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3344—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C23×C11C2×D411yescharacteristic
108Q8×C11—21no—
109Q8×C11—21no—
110D4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—42no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—81no—
130C2×Dic11—81no—
131Dic22—21no—
132Dic22—21no—
133Dic22—81no—
134C11⋊C8—21no—
135C11⋊C8—21no—
136C11⋊C8—21no—
137C11⋊C8#4112yes—
138#554—111no—
139#552D1111yescharacteristic
140#501—111no—
141#485—111no—
142#484—111no—
143#483—111no—
144#483—111no—
145#479—111no—
146#475—111no—
147#470—111no—
148#467—111no—
149#441—111no—
150#435—111no—
151#428—111no—
152C2×#106—111no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11#13712yes—
159C22×C11C22×D411yescharacteristic
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11C2×#4111yescharacteristic
169C4×C112−1+411yescharacteristic
170Dic11—41no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174C2×Q16—111no—
175C2×M16—111no—
176C22×C8—111no—
177C4⋊Q8—111no—
178#126—21no—
179#125—21no—
180#125—221no—
181#125C2×D1111yescharacteristic
182#123—21no—
183C22⋊Q8—111no—
184C22⋊Q8—111no—
185C22⋊Q8—221no—
186C22⋊Q8—221no—
187C22⋊Q8C2×D1111yescharacteristic
188C22⋊Q8C2×D1111yescharacteristic
189C4×Q8—111no—
190C4×Q8C2×D1111yescharacteristic
191C4×D4—221no—
192C4×D4C2×D1111yescharacteristic
193#117—21no—
194#117C2×D1111yescharacteristic
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4C2×D1111yescharacteristic
198#107—111no—
199#107—111no—
200#107—111no—
201#106—111no—
202#106—111no—
203#106—111no—
204#106—111no—
205#106—111no—
206#106—111no—
207C4⋊C8—111no—
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214C22⋊C8—111no—
215C22⋊C8—111no—
216#97—111no—
217C2×C11—22no—
218C2×C11—41no—
219C2×C11#54711yescharacteristic
220C2×C11C2×#13711yescharacteristic
221C2×C11#57711yescharacteristic
222C2×Q8—111no—
223C2×Q8—221no—
224C2×Q8C22×D1111yescharacteristic
225C2×D4C22⋊D1111yescharacteristic
226C22×C4—21no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4C22×D1111yescharacteristic
230C22×C4C22×D1111yescharacteristic
231Q16—222no—
232M16—222no—
233C2×C8—111no—
234C2×C8—111no—
235C2×C8—111no—
236C2×C8—111no—
237C2×C8—222no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4C22⋊D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C4⋊C4C22×D1111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4C22⋊D1111yescharacteristic
263C22⋊C4C22⋊D1111yescharacteristic
264C42—21no—
265C42—21no—
266C42—221no—
267C42C22×D1111yescharacteristic
268C11#334411yescharacteristic, complemented, Sylow
269C23C2×C22⋊D1111yescharacteristic
270C23C2×C22⋊D1111yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—221no—
274Q8—221no—
275Q8—881no—
276D4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4C2×C22⋊D1111yescharacteristic
293C2×C4C2×C22⋊D1111yescharacteristic
294C2×C4C2×C22⋊D1111yescharacteristic
295C2×C4C2×C22⋊D1111yescharacteristic
296C2×C4C23×D1111yescharacteristic
297C8—112no—
298C8—221no—
299C8—221no—
300C8—221no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#6700412yes—
307C22C22×C22⋊D1111yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—441no—
317C4—441no—
318C4—441no—
319C4—441no—
320C4#41×D1111yescharacteristic
321C4#6704311yescharacteristic
322C2—22no—
323C2—41no—
324C2C2×#6700411yescharacteristic
325C2#1062335511yescharacteristic
326C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#552C2
socleC22×C11C22×D4
prime radicalC2×D4×C11D4
hypercenter#552D11
hypocenterC11#3344
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
3. #10622678C2semidirect
4. #10622676C2semidirect
5. #10622665C2semidirect
6. #10622664C2semidirect
7. #10622657C2semidirect
8. #10622656C2semidirect
9. #10622643C2semidirect
10. #10622633C2semidirect
12. #10622609C2semidirect
13. #10622608C2semidirect
14. #10622584C2semidirect
15. C2×#66872C2semidirect
268. C11#3344semidirect

Maximal subgroups

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

subgroupindex
C11×#5522
#106230742
#106226782
#106226762
#106226652
#106226642
#106226572
#106226562
#106226432
#106226332
#106226242
#106226092
#106226082
#106225842
C2×#668722
#334411