Finite Group Databasebeta

← #13080969

Subgroups — #13080969

Order 1408.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623042C211yesmaximal, characteristic, complemented
2#10623038C211yesmaximal, characteristic
3C2×C11×#106C211yesmaximal, characteristic, complemented
4#10622727C211yesmaximal, characteristic, complemented
5C8×C22⋊D11C211yesmaximal, characteristic, complemented
6#10622584C211yesmaximal, characteristic, complemented
7#10622581C211yesmaximal, characteristic, complemented
8#10622483C211yesmaximal, characteristic, complemented
9#10622477C211yesmaximal, characteristic, complemented
10#10622476C211yesmaximal, characteristic, complemented
11#10622475C211yesmaximal, characteristic, complemented
12D11×#106C211yesmaximal, characteristic, complemented
13#10622468C211yesmaximal, characteristic, complemented
14#10622467C211yesmaximal, characteristic, complemented
15#10622465C211yesmaximal, characteristic, complemented
16C2×#4339—21no—
17C22×C8×C11C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20#66983C2211yescharacteristic
21#66982—21no—
22C4×C22⋊D11—21no—
23C4×C22⋊D11C2211yescharacteristic
24#66977—21no—
25#66977C2211yescharacteristic
26C2×#4314C2211yescharacteristic
27C2×C8×D11C2211yescharacteristic
28#66950C2211yescharacteristic
29#66949—21no—
30#66949—21no—
31#66948C2211yescharacteristic
32#66947—21no—
33#66946C2211yescharacteristic
34C4⋊C4×D11C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic
36#66942—21no—
37#66941C2211yescharacteristic
38#66941C2211yescharacteristic
39#66940C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66885C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47#66881C2211yescharacteristic
48#66880C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50C8×Dic11C2211yescharacteristic
51#66874C2211yescharacteristic
52#66874C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58#66872C2211yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64#4339—44no—
65C2×D44—21no—
66C2×D44C2311yescharacteristic
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11C2311yescharacteristic
71C2×Dic22—21no—
72C2×Dic22—21no—
73C2×Dic22C2311yescharacteristic
74C2×C8×C11—22no—
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C22⋊Dic11—21no—
84C22⋊Dic11D411yescharacteristic
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4D411yescharacteristic
90C4⋊Dic11—21no—
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4314—22no—
105C8×D11—22no—
106#3335—111nomaximal, Sylow
107C23×C11C2×D411yescharacteristic
108C22×D11—21no—
109C22×D11C2×D411yescharacteristic
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—42no—
117C2×C4×C11—81no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—42no—
121C22⋊D11SD1614yescomplemented
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128D44—21no—
129D44—21no—
130D44—42no—
131C4×D11—21no—
132C4×D11—21no—
133C4×D11—42no—
134C4×D11—42no—
135C4×D11—81no—
136Dic22—21no—
137Dic22—21no—
138Dic22—42no—
139Dic22—81no—
140C8×C11—21no—
141C8×C11#4112yescomplemented
142C11⋊C8—21no—
143C11⋊C8—21no—
144#554—111no—
145#547—111no—
146#498—111no—
147#483—111no—
148#483—111no—
149#481—111no—
150#481—111no—
151#476—111no—
152#475—111no—
153#465—111no—
154#465—111no—
155C4×SD16—111no—
156C8×D4—111no—
157C2×#106—111no—
158C2×#106D1111yescharacteristic, complemented
159C22×C11—21no—
160C22×C11—21no—
161C22×C11C2×SD1612yes—
162C22×C11C22×D411yescharacteristic
163C2×D11—21no—
164C2×D11—21no—
165C2×D11—41no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11C2×SD1612yes—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11C2×#4111yescharacteristic
175C4×C112−1+411yescharacteristic
176Dic11—21no—
177Dic11—21no—
178Dic11—41no—
179Dic11—41no—
180Dic11—41no—
181Dic11C2×SD1612yes—
182C2×#41—221no—
183C2×SD16—111no—
184C22×C8—111no—
185C22×C8C2×D1111yescharacteristic
186C4⋊Q8—111no—
187C4⋊Q8—111no—
188#125—221no—
189#123—221no—
190#123—221no—
191C22⋊Q8—111no—
192C22⋊Q8—111no—
193C22⋊Q8—221no—
194C22⋊Q8—221no—
195C22⋊Q8—221no—
196#121—111no—
197#121—111no—
198C4×Q8—111no—
199C4×D4—111no—
200C4×D4—111no—
201C4×D4—221no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4C2×D1111yescharacteristic
205C2×C4⋊C4C2×D1111yescharacteristic
206#106—111no—
207#106—111no—
208#106—111no—
209#106—111no—
210#106—111no—
211#106C2×D1111yescharacteristic
212#106C2×D1111yescharacteristic
213#106C2×D1111yescharacteristic
214#106C2×D1111yescharacteristic
215C4⋊C8—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#102—111no—
220#102—111no—
221#102—111no—
222C22⋊C8—111no—
223C22⋊C8—111no—
224C4×C8—111no—
225C2×C11—22no—
226C2×C11#54711yescharacteristic
227C2×C11C22×SD1611yescharacteristic
228C2×C11#57711yescharacteristic
229D11—22no—
230D11—81no—
231#41—444no—
232C2×Q8—111no—
233C2×Q8—221no—
234C2×Q8—221no—
235C2×D4—111no—
236C2×D4—111no—
237C2×D4—221no—
238C2×D4—221no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—111no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4C22×D1111yescharacteristic
246SD16—222no—
247C2×C8—22no—
248C2×C8—111no—
249C2×C8—111no—
250C2×C8—222no—
251C2×C8C22×D1111yescharacteristic
252C2×C8C22×D1111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4C22×D1111yescharacteristic
266C4⋊C4C22×D1111yescharacteristic
267C4⋊C4C22×D1111yescharacteristic
268C4⋊C4C22×D1111yescharacteristic
269C22⋊C4—111no—
270C22⋊C4—111no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C42—111no—
277C42—221no—
278C11#333511yescharacteristic, complemented, Sylow
279C23—111no—
280C23—221no—
281C23D4×D1111yescharacteristic
282Q8—221no—
283Q8—221no—
284Q8—442no—
285Q8—881no—
286D4—114no—
287D4—221no—
288D4—221no—
289D4—442no—
290D4—442no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—81no—
299C2×C4—111no—
300C2×C4—111no—
301C2×C4—111no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—881no—
310C2×C4D4×D1111yescharacteristic
311C2×C4C23×D1111yescharacteristic
312C8—21no—
313C8—221no—
314C8—221no—
315C8#433912yescomplemented
316C22—21no—
317C22—21no—
318C22—112no—
319C22—221no—
320C22—221no—
321C22—441no—
322C22—441no—
323C22—441no—
324C22SD16×D1112yes—
325C22C2×D4×D1111yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—112no—
332C4—221no—
333C4—221no—
334C4—441no—
335C4—441no—
336C4—441no—
337C4C2×#433911yescharacteristic
338C4#6704011yescharacteristic
339C2—22no—
340C2—222no—
341C2—881no—
342C2#1062303811yescharacteristic
343C2C2×SD16×D1111yescharacteristic
344C2#1062329311yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#106C2
socleC22×C11C22×D4
prime radical#10623038C2
hypercenterC2×#106D11
hypocenterC11#3335
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. #10623042C2semidirect
3. C2×C11×#106C2semidirect
4. #10622727C2semidirect
5. C8×C22⋊D11C2semidirect
6. #10622584C2semidirect
7. #10622581C2semidirect
8. #10622483C2semidirect
9. #10622477C2semidirect
10. #10622476C2semidirect
11. #10622475C2semidirect
12. D11×#106C2semidirect
13. #10622468C2semidirect
14. #10622467C2semidirect
15. #10622465C2semidirect
121. C22⋊D11SD16semidirect
141. C8×C11#41semidirect
158. C2×#106D11semidirect
278. C11#3335semidirect
315. C8#4339semidirect

Maximal subgroups

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

subgroupindex
#106230422
#106230382
C2×C11×#1062
#106227272
C8×C22⋊D112
#106225842
#106225812
#106224832
#106224772
#106224762
#106224752
D11×#1062
#106224682
#106224672
#106224652
#333511