Finite Group Databasebeta

← #13081186

Subgroups — #13081186

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#10623173C211yesmaximal, characteristic
2#10623170C211yesmaximal, characteristic
3C11×#470C211yesmaximal, characteristic, complemented
4#10622802C211yesmaximal, characteristic, complemented
5Q16×Dic11C211yesmaximal, characteristic, complemented
6#10622741C211yesmaximal, characteristic
7#10622734C211yesmaximal, characteristic, complemented
8#10622658C211yesmaximal, characteristic, complemented
9#10622657C211yesmaximal, characteristic, complemented
10#10622474C211yesmaximal, characteristic, complemented
11#10622471C211yesmaximal, characteristic, complemented
12#10622428C211yesmaximal, characteristic, complemented
13#10622422C211yesmaximal, characteristic, complemented
14#10622412C211yesmaximal, characteristic, complemented
15#10622409C211yesmaximal, characteristic, complemented
16C2×C11×Q16C2211yescharacteristic
17C2×C11×M16C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20#66999C2211yescharacteristic
21#66999C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24C4×C22⋊D11C2211yescharacteristic
25#66979C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×#4313C2211yescharacteristic
28#66951—21no—
29#66945—21no—
30#66945C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32#66943—21no—
33#66943C2211yescharacteristic
34#66943C2211yescharacteristic
35#66942—21no—
36#66939—21no—
37#66936—21no—
38#66932—21no—
39#66930—21no—
40C11×#106C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#103C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11D411yescharacteristic
63C22×Dic11—21no—
64C2×C4×D11—21no—
65C2×C4×D11C2311yescharacteristic
66C11×Q16—22no—
67C11×M16—22no—
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C11×C22⋊C4—21no—
76C22⋊Dic11—21no—
77C22⋊Dic11D411yescharacteristic
78(C2×D11)⋊C4—21no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4D411yescharacteristic
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4313—22no—
105#3352—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—41no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—42no—
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C4×D11—21no—
130C4×D11—21no—
131C4×D11—42no—
132C8×C11—21no—
133C8×C11#4112yes—
134C11⋊C8—21no—
135C11⋊C8—21no—
136#552—111no—
137#552—111no—
138#499—111no—
139#485—111no—
140#485—111no—
141#484—111no—
142#484—111no—
143#479—111no—
144#479—111no—
145#470—111no—
146#470D1111yescharacteristic, complemented
147C4×Q16—111no—
148#436—111no—
149#428—111no—
150#428—111no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11C22×D411yescharacteristic
155C2×D11—21no—
156C2×D11—21no—
157C2×D11—21no—
158C4×C11—21no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11C2×#4111yescharacteristic
164C4×C112−1+411yescharacteristic
165Dic11—21no—
166Dic11—21no—
167Dic11—21no—
168Dic11—41no—
169Dic11—41no—
170Dic11—41no—
171Dic11—41no—
172C2×Q16C2×D1111yescharacteristic
173C2×M16—111no—
174C2×M16C2×D1111yescharacteristic
175#126—221no—
176#126—221no—
177#125—111no—
178#125—111no—
179#125—221no—
180#125—221no—
181#123—221no—
182#123—221no—
183C22⋊Q8—111no—
184C22⋊Q8—111no—
185C22⋊Q8C2×D1111yescharacteristic
186C22⋊Q8C2×D1111yescharacteristic
187C4×Q8—111no—
188C4×Q8—111no—
189C4×D4—111no—
190#117—111no—
191#117—111no—
192#117—221no—
193#117—221no—
194C2×C4⋊C4—111no—
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—
214C4×C8—111no—
215C2×C11—41no—
216C2×C11#54711yescharacteristic
217C2×C11#57511yescharacteristic
218C2×C11#57811yescharacteristic
219D11—41no—
220C2×Q8C22×D1111yescharacteristic
221C2×Q8C22×D1111yescharacteristic
222C2×D4—111no—
223C22×C4—111no—
224C22×C4—221no—
225C22×C4—221no—
226C22×C4C22×D1111yescharacteristic
227Q16—22no—
228M16—22no—
229M16—222no—
230C2×C8—111no—
231C2×C8—111no—
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⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4C22×D1111yescharacteristic
252C4⋊C4C22×D1111yescharacteristic
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—111no—
256C22⋊C4—111no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C42—111no—
262C42—221no—
263C42—221no—
264C42—221no—
265C42—221no—
266C11#335211yescharacteristic, complemented, Sylow
267C23—111no—
268C23D4×D1111yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273D4—441no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—111no—
281C2×C4—111no—
282C2×C4—111no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4D4×D1111yescharacteristic
292C2×C4C23×D1111yescharacteristic
293C8—21no—
294C8—221no—
295C8—221no—
296C8#434112yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—221no—
301C22—221no—
302C22—221no—
303C22C2×D4×D1111yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—221no—
310C4—221no—
311C4—221no—
312C4—441no—
313C4—441no—
314C4—441no—
315C4—441no—
316C4C2×#434111yescharacteristic
317C4#6704311yescharacteristic
318C2—41no—
319C2—441no—
320C2#1062314211yescharacteristic
321C2#1062330811yescharacteristic
322C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#470C2
socleC22×C11C22×D4
prime radicalC2×C22⋊D11D4
hypercenter#470D11
hypocenterC11#3352
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
3. C11×#470C2semidirect
4. #10622802C2semidirect
5. Q16×Dic11C2semidirect
7. #10622734C2semidirect
8. #10622658C2semidirect
9. #10622657C2semidirect
10. #10622474C2semidirect
11. #10622471C2semidirect
12. #10622428C2semidirect
13. #10622422C2semidirect
14. #10622412C2semidirect
15. #10622409C2semidirect
146. #470D11semidirect
266. C11#3352semidirect

Maximal subgroups

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

subgroupindex
#106231732
#106231702
C11×#4702
#106228022
Q16×Dic112
#106227412
#106227342
#106226582
#106226572
#106224742
#106224712
#106224282
#106224222
#106224122
#106224092
#335211