Finite Group Databasebeta

← #13081073

Subgroups — #13081073

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#10623074C211yesmaximal, characteristic
2#10623072C211yesmaximal, characteristic
3C11×#435C211yesmaximal, characteristic
4#10622750C211yesmaximal, characteristic, complemented
5#10622734C211yesmaximal, characteristic, complemented
6#10622729C211yesmaximal, characteristic, complemented
7C2×#66881C211yesmaximal, characteristic, complemented
8#10622464C211yesmaximal, characteristic, complemented
9#10622442C211yesmaximal, characteristic, complemented
10#10622336C211yesmaximal, characteristic, complemented
11#10622335C211yesmaximal, characteristic, complemented
12#10622334C211yesmaximal, characteristic, complemented
13#10622334C211yesmaximal, characteristic, complemented
14#10622329C211yesmaximal, characteristic, complemented
15#10622315C211yesmaximal, characteristic, complemented
16C2×C11×M16C2211yescharacteristic
17C22×C8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66988—21no—
20D4×Dic11—21no—
21#66979C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25#66977C2211yescharacteristic
26#66977C2211yescharacteristic
27#66977C2211yescharacteristic
28#66977C2211yescharacteristic
29C2×Dic44C2211yescharacteristic
30#66943—21no—
31#66942—21no—
32#66932—21no—
33#66931—21no—
34#66931—21no—
35#66930—21no—
36#66923C2211yescharacteristic
37#66922C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×C22⋊C8C2211yescharacteristic
42C11×C22⋊C8C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66882C2211yescharacteristic
45#66882C2211yescharacteristic
46#66882C2211yescharacteristic
47#66881C2211yescharacteristic
48#66881C2211yescharacteristic
49#66881C2211yescharacteristic
50#66881C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C2×D4×C11D411yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×Dic11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65C2×Dic22—21no—
66C2×Dic22C2311yescharacteristic
67C2×Dic22C2311yescharacteristic
68C11×M16—22no—
69C2×C8×C11—22no—
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4D411yescharacteristic
75C11×C22⋊C4D411yescharacteristic
76C11×C22⋊C4D411yescharacteristic
77C42×C11C2311yescharacteristic
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104Dic44—22no—
105#3344—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C23×C11C2×D411yescharacteristic
108D4×C11—22no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2411yescharacteristic
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—42no—
127C2×Dic11—81no—
128C2×Dic11—81no—
129Dic22—21no—
130Dic22—21no—
131Dic22—21no—
132Dic22—21no—
133Dic22—81no—
134C8×C11—21no—
135C8×C11—21no—
136C8×C11—21no—
137C8×C11#4112yes—
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#467—111no—
149#441—111no—
150#435D1111yescharacteristic
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×C11C2×#4111yescharacteristic
165C4×C112−1+411yescharacteristic
166Dic11—41no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170Dic11—41no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174C2×Q16—111no—
175C2×M16C2×D1111yescharacteristic
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—111no—
186C22⋊Q8—111no—
187C22⋊Q8—221no—
188C22⋊Q8—221no—
189C4×Q8—111no—
190C4×Q8—111no—
191C4×D4—221no—
192C4×D4C2×D1111yescharacteristic
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#107—111no—
201#106—111no—
202#106—111no—
203#106—111no—
204#106—111no—
205#106—111no—
206#106—111no—
207C4⋊C8C2×D1111yescharacteristic
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214C22⋊C8C2×D1111yescharacteristic
215C22⋊C8C2×D1111yescharacteristic
216#97C2×D1111yescharacteristic
217C2×C11—22no—
218C2×C11—41no—
219C2×C11#54711yescharacteristic
220C2×C11C2×#13711yescharacteristic
221C2×C11#57711yescharacteristic
222C2×Q8—111no—
223C2×Q8—111no—
224C2×Q8—221no—
225C2×D4D4411yescharacteristic
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4C22×D1111yescharacteristic
230C22×C4C22×D1111yescharacteristic
231Q16—222no—
232M16—22no—
233C2×C8—22no—
234C2×C8C22×D1111yescharacteristic
235C2×C8C22×D1111yescharacteristic
236C2×C8C22×D1111yescharacteristic
237C2×C8C22×D1111yescharacteristic
238C4⋊C4—111no—
239C4⋊C4—111no—
240C4⋊C4—111no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—221no—
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⋊C4—221no—
256C4⋊C4D4411yescharacteristic
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4D4411yescharacteristic
263C22⋊C4D4411yescharacteristic
264C42—221no—
265C42—221no—
266C42—221no—
267C42C22×D1111yescharacteristic
268C11#334411yescharacteristic, complemented, Sylow
269C23C2×D4411yescharacteristic
270C23C2×D4411yescharacteristic
271Q8—221no—
272Q8—221no—
273Q8—221no—
274Q8—221no—
275Q8—881no—
276D4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
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×C4—881no—
291C2×C4—881no—
292C2×C4C2×D4411yescharacteristic
293C2×C4C2×D4411yescharacteristic
294C2×C4C2×D4411yescharacteristic
295C2×C4C2×D4411yescharacteristic
296C2×C4C23×D1111yescharacteristic
297C8—21no—
298C8—21no—
299C8—21no—
300C8#434112yes—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#6696212yes—
307C22C22×D4411yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—441no—
313C4—441no—
314C4—441no—
315C4—441no—
316C4—441no—
317C4—441no—
318C4—441no—
319C4—441no—
320C4C2×#434111yescharacteristic
321C4#6704311yescharacteristic
322C2—22no—
323C2—41no—
324C2#1062308611yescharacteristic
325C2C2×#6696211yescharacteristic
326C2#1062328211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#435C2
socleC22×C11C22×D4
prime radicalC2×D4×C11D4
hypercenter#435D11
hypocenterC11#3344
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
4. #10622750C2semidirect
5. #10622734C2semidirect
6. #10622729C2semidirect
7. C2×#66881C2semidirect
8. #10622464C2semidirect
9. #10622442C2semidirect
10. #10622336C2semidirect
11. #10622335C2semidirect
12. #10622334C2semidirect
13. #10622334C2semidirect
14. #10622329C2semidirect
15. #10622315C2semidirect
268. C11#3344semidirect

Maximal subgroups

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

subgroupindex
#106230742
#106230722
C11×#4352
#106227502
#106227342
#106227292
C2×#668812
#106224642
#106224422
#106223362
#106223352
#106223342
#106223292
#106223152
#334411