Finite Group Databasebeta

← #13081060

Subgroups — #13081060

Order 1408.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623142C211yesmaximal, characteristic
2#10623044C211yesmaximal, characteristic, complemented
3C11×#480C211yesmaximal, characteristic, complemented
4#10622654C211yesmaximal, characteristic, complemented
5C2×#66871C211yesmaximal, characteristic, complemented
6#10622497C211yesmaximal, characteristic, complemented
7#10622494C211yesmaximal, characteristic, complemented
8#10622489C211yesmaximal, characteristic, complemented
9#10622488C211yesmaximal, characteristic, complemented
10#10622393C211yesmaximal, characteristic, complemented
11#10622392C211yesmaximal, characteristic, complemented
12#10622376C211yesmaximal, characteristic, complemented
13#10622370C211yesmaximal, characteristic, complemented
14#10622343C211yesmaximal, characteristic, complemented
15#10622334C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C11×#121C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19#66991C2211yescharacteristic
20#66988—21no—
21D4×Dic11C2211yescharacteristic
22C2×#4324C2211yescharacteristic
23#66982—21no—
24C4×C22⋊D11C2211yescharacteristic
25#66979—21no—
26C2×C4⋊Dic11C2211yescharacteristic
27#66977C2211yescharacteristic
28C22×C11⋊C8C2211yescharacteristic
29C2×#4313C2211yescharacteristic
30#66951—21no—
31#66950C2211yescharacteristic
32#66945C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34#66943C2211yescharacteristic
35#66942—21no—
36#66941C2211yescharacteristic
37#66940C2211yescharacteristic
38#66936—21no—
39#66931—21no—
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66896C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47#66881C2211yescharacteristic
48#66881C2211yescharacteristic
49#66880C2211yescharacteristic
50#66880C2211yescharacteristic
51#66879C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53#66874C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11D411yescharacteristic
65C22×Dic11—21no—
66C22×Dic11—21no—
67#4341—44no—
68C2×C4×D11—21no—
69C2×C4×D11C2311yescharacteristic
70C2×Dic22—21no—
71C2×Dic22C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C22⋊C4—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11D411yescharacteristic
83#4324—22no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4D411yescharacteristic
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8—22no—
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#4313—22no—
106#3343—111nomaximal, Sylow
107C23×C11—21no—
108C23×C11C2×D411yescharacteristic
109C22×D11C2×D411yescharacteristic
110D4×C11—21no—
111D4×C11—21no—
112D4×C11—42no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—42no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C22⋊D11—22no—
122C22⋊D11—42no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C4×D11—21no—
133C4×D11—21no—
134C4×D11—42no—
135Dic22—21no—
136Dic22—21no—
137Dic22—42no—
138C8×C11—21no—
139C8×C11—21no—
140C11⋊C8—21no—
141C11⋊C8#4112yescomplemented
142#552—111no—
143#547—111no—
144#501—111no—
145#484—111no—
146#483—111no—
147#482—111no—
148#480D1111yescharacteristic, complemented
149#478—111no—
150#477—111no—
151#468—111no—
152#465—111no—
153#440—111no—
154#435—111no—
155#428—111no—
156C2×#107—111no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11AGL(1,ℤ/8)12yes—
163C22×C11C22×D411yescharacteristic
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11C2×#4111yescharacteristic
172C4×C112−1+411yescharacteristic
173Dic11—21no—
174Dic11—21no—
175Dic11—21no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180C2×#41—221no—
181C2×SD16—111no—
182C2×M16—111no—
183C22×C8—111no—
184C4⋊Q8—111no—
185#126—221no—
186#125—111no—
187#125—221no—
188#123—221no—
189#123—221no—
190#123—221no—
191C22⋊Q8—111no—
192C22⋊Q8—111no—
193C22⋊Q8—221no—
194#121—111no—
195#121C2×D1111yescharacteristic
196C4×Q8—111no—
197C4×D4—111no—
198C4×D4—111no—
199#117—111no—
200#117—221no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4C2×D1111yescharacteristic
204#107—111no—
205#107—111no—
206#107—111no—
207#107—111no—
208#107C2×D1111yescharacteristic
209#107C2×D1111yescharacteristic
210#106—111no—
211#106—111no—
212#106—111no—
213C4⋊C8—111no—
214#103—111no—
215#103—111no—
216#103—111no—
217#102—111no—
218#102C2×D1111yescharacteristic
219#102C2×D1111yescharacteristic
220C22⋊C8—111no—
221C22⋊C8C2×D1111yescharacteristic
222#97—111no—
223C2×C11—22no—
224C2×C11—81no—
225C2×C11#54711yescharacteristic
226C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C2×C11#57811yescharacteristic
228D11—41no—
229#41—444no—
230C2×Q8—111no—
231C2×Q8—221no—
232C2×D4—21no—
233C2×D4—111no—
234C2×D4—221no—
235C2×D4C22×D1111yescharacteristic
236C22×C4—21no—
237C22×C4—111no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4C22×D1111yescharacteristic
242SD16—222no—
243M16—222no—
244C2×C8—111no—
245C2×C8—111no—
246C2×C8—222no—
247C2×C8C22×D1111yescharacteristic
248C2×C8C22×D1111yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—111no—
253C4⋊C4—111no—
254C4⋊C4—221no—
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
264C4⋊C4C22×D1111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—111no—
267C22⋊C4—111no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C42—111no—
274C42—221no—
275C42—221no—
276C11#334311yescharacteristic, complemented, Sylow
277C23—21no—
278C23—111no—
279C23D4×D1111yescharacteristic
280Q8—221no—
281Q8—221no—
282Q8—442no—
283D4—21no—
284D4—21no—
285D4—42no—
286D4—222no—
287D4—442no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4D4×D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—112no—
311C8—221no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—221no—
318C22—221no—
319C22—221no—
320C22#6696412yes—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—221no—
327C4—221no—
328C4—221no—
329C4—441no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4#41×D1111yescharacteristic
334C4#6704311yescharacteristic
335C2—22no—
336C2—81no—
337C2—441no—
338C2#1062318611yescharacteristic
339C2C2×#6696411yescharacteristic
340C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#480C2
socleC22×C11C22×D4
prime radical#10623142C2
hypercenter#480D11
hypocenterC11#3343
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #10623044C2semidirect
3. C11×#480C2semidirect
4. #10622654C2semidirect
5. C2×#66871C2semidirect
6. #10622497C2semidirect
7. #10622494C2semidirect
8. #10622489C2semidirect
9. #10622488C2semidirect
10. #10622393C2semidirect
11. #10622392C2semidirect
12. #10622376C2semidirect
13. #10622370C2semidirect
14. #10622343C2semidirect
15. #10622334C2semidirect
141. C11⋊C8#41semidirect
148. #480D11semidirect
276. C11#3343semidirect

Maximal subgroups

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

subgroupindex
#106231422
#106230442
C11×#4802
#106226542
C2×#668712
#106224972
#106224942
#106224892
#106224882
#106223932
#106223922
#106223762
#106223702
#106223432
#106223342
#334311