Finite Group Databasebeta

← #13081140

Subgroups — #13081140

Order 1408.

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
1C11×#556C211yesmaximal, characteristic
2#10623072C211yesmaximal, characteristic
3#10622704C211yesmaximal, characteristic, complemented
4#10622693C211yesmaximal, characteristic, complemented
5#10622665C211yesmaximal, characteristic, complemented
6#10622664C211yesmaximal, characteristic, complemented
7#10622658C211yesmaximal, characteristic, complemented
8#10622657C211yesmaximal, characteristic, complemented
9#10622643C211yesmaximal, characteristic, complemented
10#10622635C211yesmaximal, characteristic, complemented
11#10622624C211yesmaximal, characteristic
12#10622611C211yesmaximal, characteristic, complemented
13#10622609C211yesmaximal, characteristic, complemented
14#10622609C211yesmaximal, characteristic, complemented
15#10622608C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#126—21no—
18C11×#126—21no—
19C11×#124—21no—
20C11×C22⋊Q8C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C4×Q8×C11—21no—
23C4×Q8×C11C2211yescharacteristic
24C4×D4×C11C2211yescharacteristic
25C11×#117C2211yescharacteristic
26C11×#117C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28#66988—21no—
29#66979C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31#66977C2211yescharacteristic
32#66977C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66942—21no—
36#66932—21no—
37#66930—21no—
38#66923C2211yescharacteristic
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#66871C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11D411yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×Dic11—21no—
65C2×Dic22C2311yescharacteristic
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4D411yescharacteristic
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C11×C22⋊C4—21no—
76C11×C22⋊C4—21no—
77C11×C22⋊C4—21no—
78C11×C22⋊C4D411yescharacteristic
79C11×C22⋊C4D411yescharacteristic
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11C2311yescharacteristic
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87#4326—22no—
88C4⋊Dic11—21no—
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99#4318—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3349—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C23×C11C2×D411yescharacteristic
108Q8×C11—21no—
109Q8×C11—21no—
110Q8×C11—42no—
111D4×C11—41no—
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—21no—
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—42no—
130Dic22—21no—
131Dic22—21no—
132C11⋊C8—21no—
133C11⋊C8—21no—
134C11⋊C8—21no—
135C11⋊C8#4112yes—
136#556D1111yescharacteristic
137#552—111no—
138#501—111no—
139#485—111no—
140#485—111no—
141#485—111no—
142#484—111no—
143#479—111no—
144#477—111no—
145#470—111no—
146#467—111no—
147#441—111no—
148#435—111no—
149#428—111no—
150#427—111no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11C22×D411yescharacteristic
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11C2×#4111yescharacteristic
167C4×C112−1+411yescharacteristic
168Dic11—41no—
169Dic11—41no—
170Dic11—41no—
171Dic11—41no—
172C2×Q16—111no—
173C2×M16—111no—
174C22×C8—111no—
175C4⋊Q8C2×D1111yescharacteristic
176#126—21no—
177#126—21no—
178#126—221no—
179#125—111no—
180#125—221no—
181#124—21no—
182#123—221no—
183C22⋊Q8—111no—
184C22⋊Q8—111no—
185C22⋊Q8C2×D1111yescharacteristic
186C22⋊Q8C2×D1111yescharacteristic
187C4×Q8—21no—
188C4×Q8—111no—
189C4×Q8C2×D1111yescharacteristic
190C4×D4C2×D1111yescharacteristic
191#117—111no—
192#117—221no—
193#117C2×D1111yescharacteristic
194#117C2×D1111yescharacteristic
195C2×C4⋊C4—111no—
196#107—111no—
197#107—111no—
198#107—111no—
199#107—111no—
200#107—111no—
201#106—111no—
202#106—111no—
203#106—111no—
204#106—111no—
205C4⋊C8—111no—
206#103—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212C22⋊C8—111no—
213C22⋊C8—111no—
214#97—111no—
215C2×C11—41no—
216C2×C11—41no—
217C2×C11#54711yescharacteristic
218C2×C11#57511yescharacteristic
219C2×C11#57811yescharacteristic
220C2×Q8—21no—
221C2×Q8—111no—
222C2×Q8C22×D1111yescharacteristic
223C2×D4C22⋊D1111yescharacteristic
224C22×C4—221no—
225C22×C4C22×D1111yescharacteristic
226C22×C4C22×D1111yescharacteristic
227Q16—222no—
228M16—222no—
229C2×C8—111no—
230C2×C8—111no—
231C2×C8—111no—
232C2×C8—111no—
233C2×C8—222no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—111no—
239C4⋊C4—111no—
240C4⋊C4—111no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4C22⋊D1111yescharacteristic
248C4⋊C4C22×D1111yescharacteristic
249C4⋊C4C22×D1111yescharacteristic
250C4⋊C4C22×D1111yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—221no—
256C22⋊C4—221no—
257C22⋊C4—221no—
258C22⋊C4C22⋊D1111yescharacteristic
259C22⋊C4C22⋊D1111yescharacteristic
260C42—21no—
261C42—21no—
262C42—21no—
263C42—221no—
264C42—221no—
265C42C22×D1111yescharacteristic
266C11#334911yescharacteristic, complemented, Sylow
267C23C2×C22⋊D1111yescharacteristic
268C23C2×C22⋊D1111yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—42no—
272Q8—221no—
273Q8—221no—
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—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—442no—
288C2×C4C2×C22⋊D1111yescharacteristic
289C2×C4C2×C22⋊D1111yescharacteristic
290C2×C4C2×C22⋊D1111yescharacteristic
291C2×C4C2×C22⋊D1111yescharacteristic
292C2×C4C23×D1111yescharacteristic
293C8—112no—
294C8—221no—
295C8—221no—
296C8—221no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22C22×C22⋊D1111yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—441no—
313C4—441no—
314C4—441no—
315C4—441no—
316C4#41×D1111yescharacteristic
317C4#6704311yescharacteristic
318C2—41no—
319C2—41no—
320C2#1062335311yescharacteristic
321C2#1062335511yescharacteristic
322C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#556C2
socleC22×C11C22×D4
prime radicalC2×D4×C11D4
hypercenter#556D11
hypocenterC11#3349
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
3. #10622704C2semidirect
4. #10622693C2semidirect
5. #10622665C2semidirect
6. #10622664C2semidirect
7. #10622658C2semidirect
8. #10622657C2semidirect
9. #10622643C2semidirect
10. #10622635C2semidirect
12. #10622611C2semidirect
13. #10622609C2semidirect
14. #10622609C2semidirect
15. #10622608C2semidirect
266. C11#3349semidirect

Maximal subgroups

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

subgroupindex
C11×#5562
#106230722
#106227042
#106226932
#106226652
#106226642
#106226582
#106226572
#106226432
#106226352
#106226242
#106226112
#106226092
#106226082
#334911