Finite Group Databasebeta

← #13081077

Subgroups — #13081077

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
1#10623173C211yesmaximal, characteristic
2#10623166C211yesmaximal, characteristic
3C11×#467C211yesmaximal, characteristic, complemented
4#10622802C211yesmaximal, characteristic, complemented
5#10622797C211yesmaximal, characteristic, complemented
6#10622724C211yesmaximal, characteristic
7C2×#66881C211yesmaximal, characteristic, complemented
8#10622657C211yesmaximal, characteristic, complemented
9#10622656C211yesmaximal, characteristic, complemented
10#10622494C211yesmaximal, characteristic, complemented
11#10622489C211yesmaximal, characteristic, complemented
12#10622428C211yesmaximal, characteristic, complemented
13#10622418C211yesmaximal, characteristic, complemented
14#10622412C211yesmaximal, characteristic, complemented
15#10622404C211yesmaximal, characteristic, complemented
16C2×C11×Q16C2211yescharacteristic
17C22×C8×C11C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20#66999C2211yescharacteristic
21#66999C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24C4×C22⋊D11C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×#4313C2211yescharacteristic
28#66951—21no—
29#66950—21no—
30#66945C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32#66943—21no—
33#66943C2211yescharacteristic
34#66942—21no—
35#66941C2211yescharacteristic
36#66939—21no—
37(C22⋊D11)⋊C4—21no—
38#66931—21no—
39#66930—21no—
40C11×#107C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#103C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66881C2211yescharacteristic
50#66881C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11D411yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—21no—
65C2×C4×D11—21no—
66C2×C4×D11C2311yescharacteristic
67C2×Dic22—21no—
68C11×Q16—22no—
69C2×C8×C11—22no—
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C22⋊C4—21no—
77C11×C22⋊C4—21no—
78C22⋊Dic11D411yescharacteristic
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4D411yescharacteristic
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4313—22no—
105#3344—111nomaximal, Sylow
106C23×C11C2×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×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—22no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—42no—
126C2×Dic11—81no—
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—81no—
133Dic22—81no—
134C8×C11—21no—
135C8×C11#4112yes—
136C11⋊C8—21no—
137C11⋊C8—21no—
138#554—111no—
139#552—111no—
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#467D1111yescharacteristic, complemented
149#441—111no—
150#435—111no—
151#428—111no—
152C2×#106—111no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11#13712yes—
156C22×C11C22×D411yescharacteristic
157C2×D11—21no—
158C2×D11—21no—
159C2×D11—21no—
160C4×C11—21no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11C2×#4111yescharacteristic
166C4×C112−1+411yescharacteristic
167Dic11—21no—
168Dic11—21no—
169Dic11—21no—
170Dic11—41no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174C2×Q16C2×D1111yescharacteristic
175C2×M16—111no—
176C22×C8C2×D1111yescharacteristic
177C4⋊Q8—111no—
178#126—221no—
179#125—111no—
180#125—221no—
181#125—221no—
182#123—221no—
183C22⋊Q8—111no—
184C22⋊Q8—111no—
185C22⋊Q8—221no—
186C22⋊Q8—221no—
187C22⋊Q8C2×D1111yescharacteristic
188C22⋊Q8C2×D1111yescharacteristic
189C4×Q8—111no—
190C4×Q8—111no—
191C4×D4—111no—
192C4×D4—221no—
193#117—111no—
194#117—221no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198#107—111no—
199#107—111no—
200#107C2×D1111yescharacteristic
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#103C2×D1111yescharacteristic
213#103C2×D1111yescharacteristic
214C22⋊C8—111no—
215C22⋊C8—111no—
216#97—111no—
217C2×C11—22no—
218C2×C11#54711yescharacteristic
219C2×C11C2×#13711yescharacteristic
220C2×C11#57711yescharacteristic
221D11—41no—
222C2×Q8—221no—
223C2×Q8C22×D1111yescharacteristic
224C2×Q8C22×D1111yescharacteristic
225C2×D4—111no—
226C22×C4—111no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4C22×D1111yescharacteristic
231Q16—22no—
232M16—222no—
233C2×C8—22no—
234C2×C8—111no—
235C2×C8—111no—
236C2×C8C22×D1111yescharacteristic
237C2×C8C22×D1111yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—111no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—111no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4C22×D1111yescharacteristic
256C4⋊C4C22×D1111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—111no—
260C22⋊C4—111no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C42—111no—
265C42—221no—
266C42—221no—
267C42—221no—
268C11#334411yescharacteristic, complemented, Sylow
269C23—111no—
270C23D4×D1111yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—881no—
276D4—222no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—111no—
284C2×C4—111no—
285C2×C4—111no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—442no—
293C2×C4—881no—
294C2×C4—881no—
295C2×C4D4×D1111yescharacteristic
296C2×C4C23×D1111yescharacteristic
297C8—21no—
298C8—221no—
299C8—221no—
300C8#434112yes—
301C22—21no—
302C22—21no—
303C22—221no—
304C22—221no—
305C22—221no—
306C22#6697112yes—
307C22C2×D4×D1111yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—221no—
314C4—221no—
315C4—221no—
316C4—441no—
317C4—441no—
318C4—441no—
319C4—441no—
320C4C2×#434111yescharacteristic
321C4#6704311yescharacteristic
322C2—22no—
323C2—441no—
324C2#1062314211yescharacteristic
325C2C2×#6697111yescharacteristic
326C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#467C2
socleC22×C11C22×D4
prime radicalC2×C22⋊D11D4
hypercenter#467D11
hypocenterC11#3344
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. C11×#467C2semidirect
4. #10622802C2semidirect
5. #10622797C2semidirect
7. C2×#66881C2semidirect
8. #10622657C2semidirect
9. #10622656C2semidirect
10. #10622494C2semidirect
11. #10622489C2semidirect
12. #10622428C2semidirect
13. #10622418C2semidirect
14. #10622412C2semidirect
15. #10622404C2semidirect
148. #467D11semidirect
268. C11#3344semidirect

Maximal subgroups

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

subgroupindex
#106231732
#106231662
C11×#4672
#106228022
#106227972
#106227242
C2×#668812
#106226572
#106226562
#106224942
#106224892
#106224282
#106224182
#106224122
#106224042
#334411