Finite Group Databasebeta

← #13079338

Subgroups — #13079338

Order 1408.

370 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#10623155C211yesmaximal, characteristic, complemented
2#10623131C211yesmaximal, characteristic, complemented
3C11×#468C211yesmaximal, characteristic, complemented
4#10622781C211yesmaximal, characteristic, complemented
5#10622777C211yesmaximal, characteristic, complemented
6#10622747C211yesmaximal, characteristic, complemented
7M16×Dic11C211yesmaximal, characteristic, complemented
8#10622665C211yesmaximal, characteristic, complemented
9#10622652C211yesmaximal, characteristic
10#10622502C211yesmaximal, characteristic, complemented
11#10622491C211yesmaximal, characteristic, complemented
12#10622413C211yesmaximal, characteristic, complemented
13#10622402C211yesmaximal, characteristic, complemented
14#10622398C211yesmaximal, characteristic, complemented
15#10622381C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×M16C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×#121C2211yescharacteristic
20#67000C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23#66989C2211yescharacteristic
24#66988—21no—
25D4×Dic11—21no—
26D4×Dic11C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28#66983C2211yescharacteristic
29#66977C2211yescharacteristic
30C2×C4×Dic11C2211yescharacteristic
31C2×#4318C2211yescharacteristic
32C2×#4314C2211yescharacteristic
33#66951—21no—
34#66946C2211yescharacteristic
35#66945—21no—
36#66943C2211yescharacteristic
37#66943C2211yescharacteristic
38#66940C2211yescharacteristic
39#66939—21no—
40(C22⋊D11)⋊C4—21no—
41#66932—21no—
42#66930—21no—
43C11×#107C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49#66882C2211yescharacteristic
50#66880C2211yescharacteristic
51#66879C2211yescharacteristic
52#66879C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66872C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65C22×Dic11D411yescharacteristic
66C22×Dic11D411yescharacteristic
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×Dic22C2311yescharacteristic
70C11×SD16—22no—
71C11×M16—22no—
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83#4326—22no—
84#4323—22no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11D411yescharacteristic
101C4×Dic11D411yescharacteristic
102C4×Dic11C2311yescharacteristic
103C4×Dic11C2311yescharacteristic
104#4318—22no—
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107#4314—22no—
108#3183—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111C22×D11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114D4×C11—21no—
115D4×C11—21no—
116D4×C11—42no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2411yescharacteristic
124C22⋊D11—42no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—42no—
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135D44—21no—
136D44—21no—
137C4×D11—42no—
138Dic22—21no—
139Dic22—21no—
140C8×C11—21no—
141C8×C11#4112yes—
142C11⋊C8—21no—
143C11⋊C8#4112yes—
144#529—111no—
145#529—111no—
146#499—111no—
147#495—111no—
148#488—111no—
149#488—111no—
150#470—111no—
151#469—111no—
152#468—111no—
153#468D1111yescharacteristic, complemented
154#442—111no—
155#441—111no—
156#440—111no—
157#440—111no—
158C4×M16—111no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11C22×D411yescharacteristic
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11C2×#4111yescharacteristic
174C4×C11C2×#4111yescharacteristic
175Dic11—21no—
176Dic11—21no—
177Dic11—21no—
178Dic11—21no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×Q16—111no—
183C2×SD16—111no—
184C2×SD16C2×D1111yescharacteristic
185C2×D8—111no—
186C2×M16—111no—
187C2×M16C2×D1111yescharacteristic
188#126—221no—
189#126—221no—
190#125—111no—
191#125—111no—
192#124—111no—
193#124—111no—
194#123—221no—
195#123—221no—
196C22⋊Q8—111no—
197C22⋊Q8C2×D1111yescharacteristic
198#121—111no—
199#121C2×D1111yescharacteristic
200C4×Q8—111no—
201C4×Q8—111no—
202C4×D4—111no—
203C4×D4—111no—
204C4×D4—221no—
205C4×D4—221no—
206#117—221no—
207#117—221no—
208C2×C42—111no—
209#107—111no—
210#107C2×D1111yescharacteristic
211#106—111no—
212#106—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#103C2×D1111yescharacteristic
217#102—111no—
218#102—111no—
219#102—111no—
220#102C2×D1111yescharacteristic
221#97—111no—
222#97—111no—
223C4×C8—111no—
224C4×C8—111no—
225C2×C11—41no—
226C2×C11—81no—
227C2×C11#53211yescharacteristic
228C2×C11#57511yescharacteristic
229C2×C11#57511yescharacteristic
230D11—81no—
231C2×Q8—111no—
232C2×Q8C22×D1111yescharacteristic
233C2×D4—21no—
234C2×D4—111no—
235C2×D4—221no—
236C2×D4C22×D1111yescharacteristic
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4C22×D1111yescharacteristic
242Q16—222no—
243SD16—22no—
244SD16—222no—
245D8—222no—
246M16—22no—
247M16—222no—
248C2×C8—111no—
249C2×C8—111no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C42—111no—
275C42—111no—
276C42—111no—
277C42—111no—
278C42—221no—
279C42—221no—
280C11#318311yescharacteristic, complemented, Sylow
281C23—21no—
282C23—221no—
283C23D4×D1111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—221no—
287Q8—221no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—221no—
292D4—221no—
293D4—442no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—111no—
300C2×C4—111no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—442no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—442no—
310C2×C4D4×D1111yescharacteristic
311C2×C4C23×D1111yescharacteristic
312C8—21no—
313C8—112no—
314C8—221no—
315C8#434112yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22C2×D4×D1111yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—221no—
331C4—221no—
332C4—221no—
333C4—221no—
334C4—441no—
335C4—441no—
336C4—441no—
337C4C2×#434111yescharacteristic
338C4#41×D1111yescharacteristic
339C2—41no—
340C2—81no—
341C2—881no—
342C2#1062312711yescharacteristic
343C2#1062330411yescharacteristic
344C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#468C2
socleC22×C11C22×D4
prime radical#10622652C2
hypercenter#468D11
hypocenterC11#3183
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #10623155C2semidirect
2. #10623131C2semidirect
3. C11×#468C2semidirect
4. #10622781C2semidirect
5. #10622777C2semidirect
6. #10622747C2semidirect
7. M16×Dic11C2semidirect
8. #10622665C2semidirect
10. #10622502C2semidirect
11. #10622491C2semidirect
12. #10622413C2semidirect
13. #10622402C2semidirect
14. #10622398C2semidirect
15. #10622381C2semidirect
153. #468D11semidirect
280. C11#3183semidirect

Maximal subgroups

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

subgroupindex
#106231552
#106231312
C11×#4682
#106227812
#106227772
#106227472
M16×Dic112
#106226652
#106226522
#106225022
#106224912
#106224132
#106224022
#106223982
#106223812
#318311