Finite Group Databasebeta

← #13081151

Subgroups — #13081151

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
1#10623115C211yesmaximal, characteristic
2#10623112C211yesmaximal, characteristic
3C11×#441C211yesmaximal, characteristic, complemented
4#10622802C211yesmaximal, characteristic, complemented
5#10622801C211yesmaximal, characteristic, complemented
6#10622635C211yesmaximal, characteristic, complemented
7#10622634C211yesmaximal, characteristic, complemented
8#10622474C211yesmaximal, characteristic, complemented
9#10622473C211yesmaximal, characteristic, complemented
10#10622428C211yesmaximal, characteristic, complemented
11#10622428C211yesmaximal, characteristic, complemented
12#10622427C211yesmaximal, characteristic, complemented
13#10622422C211yesmaximal, characteristic, complemented
14#10622319C211yesmaximal, characteristic
15#10622315C211yesmaximal, characteristic, complemented
16C2×C11×Q16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19#66999C2211yescharacteristic
20#66999C2211yescharacteristic
21#66999C2211yescharacteristic
22#66999C2211yescharacteristic
23C2×#4313C2211yescharacteristic
24C2×C8×D11C2211yescharacteristic
25#66951—21no—
26#66951—21no—
27#66947—21no—
28#66945C2211yescharacteristic
29#66945C2211yescharacteristic
30#66945C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32#66942—21no—
33#66929—21no—
34#66928—21no—
35C4×D44C2211yescharacteristic
36#66925—21no—
37#66923C2211yescharacteristic
38#66922C2211yescharacteristic
39C4×Dic22—21no—
40C11×#106C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic
51#66882C2211yescharacteristic
52#66881C2211yescharacteristic
53#66881C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D44D411yescharacteristic
62C2×C4×D11—21no—
63C2×C4×D11C2311yescharacteristic
64C2×C4×D11C2311yescharacteristic
65C2×Dic22—21no—
66C11×Q16—22no—
67C2×C8×C11C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C42×C11—21no—
74C42×C11—21no—
75C42×C11C2311yescharacteristic
76(C2×D11)⋊C4—21no—
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—21no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4D411yescharacteristic
84(C2×D11)⋊C4D411yescharacteristic
85C4⋊Dic11—21no—
86C4⋊Dic11D411yescharacteristic
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#4313—22no—
104C8×D11—22no—
105#3349—111nomaximal, Sylow
106C22×D11C2×D411yescharacteristic
107C22×D11C2×D411yescharacteristic
108Q8×C11—21no—
109Q8×C11—21no—
110Q8×C11—21no—
111Q8×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125D44—41no—
126C4×D11—21no—
127C4×D11—21no—
128C4×D11—21no—
129C4×D11—21no—
130C4×D11—42no—
131Dic22—42no—
132C8×C11—21no—
133C8×C11#4112yes—
134C11⋊C8—21no—
135C11⋊C8—21no—
136#556—111no—
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#441D1111yescharacteristic, complemented
148#435—111no—
149#428—111no—
150#427—111no—
151C22×C11C22×D411yescharacteristic
152C2×D11—21no—
153C2×D11—21no—
154C2×D11—21no—
155C2×D11—21no—
156C2×D11—21no—
157C2×D11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11C2×#4111yescharacteristic
165C4×C112−1+411yescharacteristic
166Dic11—21no—
167Dic11—21no—
168Dic11—41no—
169Dic11—41no—
170Dic11—41no—
171Dic11—41no—
172C2×Q16C2×D1111yescharacteristic
173C2×M16—111no—
174C22×C8—111no—
175C4⋊Q8—111no—
176#126—221no—
177#126—221no—
178#126—221no—
179#125—111no—
180#125—221no—
181#124—221no—
182#123—221no—
183C22⋊Q8—111no—
184C22⋊Q8—111no—
185C22⋊Q8—111no—
186C22⋊Q8—111no—
187C4×Q8—221no—
188C4×Q8C2×D1111yescharacteristic
189C4×Q8C2×D1111yescharacteristic
190C4×D4—111no—
191#117—111no—
192#117—111no—
193#117—111no—
194#117—221no—
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#106C2×D1111yescharacteristic
205C4⋊C8—111no—
206#103—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103C2×D1111yescharacteristic
211#103C2×D1111yescharacteristic
212C22⋊C8—111no—
213C22⋊C8—111no—
214#97C2×D1111yescharacteristic
215C2×C11#54711yescharacteristic
216C2×C11#57511yescharacteristic
217C2×C11#57811yescharacteristic
218D11—41no—
219D11—41no—
220C2×Q8—221no—
221C2×Q8C22×D1111yescharacteristic
222C2×Q8C22×D1111yescharacteristic
223C2×D4—111no—
224C22×C4—111no—
225C22×C4—111no—
226C22×C4—221no—
227Q16—22no—
228M16—222no—
229C2×C8—111no—
230C2×C8—111no—
231C2×C8—222no—
232C2×C8C22×D1111yescharacteristic
233C2×C8C22×D1111yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—111no—
237C4⋊C4—111no—
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⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4C22×D1111yescharacteristic
250C4⋊C4C22×D1111yescharacteristic
251C22⋊C4—111no—
252C22⋊C4—111no—
253C22⋊C4—221no—
254C22⋊C4—221no—
255C22⋊C4—221no—
256C22⋊C4—221no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C42—21no—
261C42—21no—
262C42—221no—
263C42—221no—
264C42—221no—
265C42C22×D1111yescharacteristic
266C11#334911yescharacteristic, complemented, Sylow
267C23—111no—
268C23—111no—
269Q8—21no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—442no—
274D4—441no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—111no—
280C2×C4—111no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—442no—
290C2×C4D4×D1111yescharacteristic
291C2×C4D4×D1111yescharacteristic
292C2×C4C23×D1111yescharacteristic
293C8—21no—
294C8—221no—
295C8—221no—
296C8#433912yes—
297C22—221no—
298C22—221no—
299C22—221no—
300C22—221no—
301C22—221no—
302C22—221no—
303C22C2×D4×D1111yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—221no—
311C4—221no—
312C4—441no—
313C4—441no—
314C4—441no—
315C4—441no—
316C4C2×#433911yescharacteristic
317C4#6704311yescharacteristic
318C2—441no—
319C2—441no—
320C2#1062308211yescharacteristic
321C2#1062330811yescharacteristic
322C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#441C2
socleC22×C11C22×D4
prime radicalC2×D44D4
hypercenter#441D11
hypocenterC11#3349
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. C11×#441C2semidirect
4. #10622802C2semidirect
5. #10622801C2semidirect
6. #10622635C2semidirect
7. #10622634C2semidirect
8. #10622474C2semidirect
9. #10622473C2semidirect
10. #10622428C2semidirect
11. #10622428C2semidirect
12. #10622427C2semidirect
13. #10622422C2semidirect
15. #10622315C2semidirect
147. #441D11semidirect
266. C11#3349semidirect

Maximal subgroups

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

subgroupindex
#106231152
#106231122
C11×#4412
#106228022
#106228012
#106226352
#106226342
#106224742
#106224732
#106224282
#106224272
#106224222
#106223192
#106223152
#334911