Finite Group Databasebeta

← #13080999

Subgroups — #13080999

Order 1408.

354 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623149C211yesmaximal, characteristic
2#10623044C211yesmaximal, characteristic, complemented
3C11×#480C211yesmaximal, characteristic, complemented
4#10622654C211yesmaximal, characteristic, complemented
5C2×#66872C211yesmaximal, characteristic, complemented
6#10622501C211yesmaximal, characteristic, complemented
7#10622493C211yesmaximal, characteristic, complemented
8#10622491C211yesmaximal, characteristic, complemented
9#10622490C211yesmaximal, characteristic, complemented
10#10622397C211yesmaximal, characteristic, complemented
11#10622391C211yesmaximal, characteristic, complemented
12#10622379C211yesmaximal, characteristic, complemented
13#10622371C211yesmaximal, characteristic, complemented
14(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
15#10622335C211yesmaximal, characteristic, complemented
16C11×#121C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18#66992—21no—
19#66991C2211yescharacteristic
20D4×Dic11—21no—
21D4×Dic11C2211yescharacteristic
22C2×#4324C2211yescharacteristic
23#66982—21no—
24C4×C22⋊D11C2211yescharacteristic
25#66979—21no—
26C2×C4⋊Dic11C2211yescharacteristic
27#66977C2211yescharacteristic
28C22×C11⋊C8C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66951—21no—
31#66950C2211yescharacteristic
32#66945C2211yescharacteristic
33#66945C2211yescharacteristic
34#66943C2211yescharacteristic
35#66943C2211yescharacteristic
36#66942—21no—
37#66940C2211yescharacteristic
38#66939—21no—
39#66932—21no—
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66896C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47#66882C2211yescharacteristic
48#66882C2211yescharacteristic
49#66880C2211yescharacteristic
50#66880C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66874C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58#66872C2211yescharacteristic
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—
67C2×C4×D11C2311yescharacteristic
68C2×Dic22C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C22⋊C4—21no—
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11D411yescharacteristic
80#4324—22no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4D411yescharacteristic
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8—22no—
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C8×D11—22no—
105#3337—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11C2×D411yescharacteristic
108C22×D11C2×D411yescharacteristic
109D4×C11—21no—
110D4×C11—21no—
111D4×C11—42no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—22no—
121C22⋊D11—81no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—81no—
127C2×Dic11—81no—
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C4×D11—21no—
132C4×D11—21no—
133Dic22—21no—
134Dic22—21no—
135C8×C11—21no—
136C8×C11—21no—
137C11⋊C8—21no—
138C11⋊C8#4112yes—
139#553—111no—
140#552—111no—
141#499—111no—
142#485—111no—
143#484—111no—
144#482—111no—
145#480D1111yescharacteristic, complemented
146#479—111no—
147#478—111no—
148#465—111no—
149#465—111no—
150C4×SD16—111no—
151C8×D4—111no—
152#427—111no—
153C2×#106—111no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11#13512yes—
160C22×C11C22×D411yescharacteristic
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—21no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11C2×#4111yescharacteristic
169C4×C112−1+411yescharacteristic
170Dic11—21no—
171Dic11—21no—
172Dic11—21no—
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×SD16—111no—
178C22×C8—111no—
179C22×C8—111no—
180#126—221no—
181#126—221no—
182#125—111no—
183#125—111no—
184#125—221no—
185#123—221no—
186#123—221no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189#121—111no—
190#121—221no—
191#121C2×D1111yescharacteristic
192C4×Q8—111no—
193C4×D4—111no—
194C4×D4—111no—
195C4×D4—221no—
196#117—111no—
197#117—111no—
198#117—221no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4C2×D1111yescharacteristic
201#107—111no—
202#107—111no—
203#107C2×D1111yescharacteristic
204#107C2×D1111yescharacteristic
205#106—111no—
206#106—111no—
207#106—111no—
208#106—111no—
209#106—111no—
210C4⋊C8—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#102—111no—
215#102C2×D1111yescharacteristic
216#102C2×D1111yescharacteristic
217C22⋊C8—111no—
218C22⋊C8C2×D1111yescharacteristic
219C4×C8—111no—
220C2×C11—22no—
221C2×C11—81no—
222C2×C11#54711yescharacteristic
223C2×C11C2×#13511yescharacteristic
224C2×C11#57711yescharacteristic
225D11—41no—
226C2×Q8—111no—
227C2×D4—21no—
228C2×D4—111no—
229C2×D4—221no—
230C2×D4C22×D1111yescharacteristic
231C22×C4—21no—
232C22×C4—111no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4C22×D1111yescharacteristic
236SD16—222no—
237C2×C8—111no—
238C2×C8—111no—
239C2×C8—222no—
240C2×C8—222no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
257C4⋊C4C22×D1111yescharacteristic
258C4⋊C4C22×D1111yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—111no—
261C22⋊C4—111no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C42—111no—
269C42—221no—
270C42—221no—
271C42—221no—
272C11#333711yescharacteristic, complemented, Sylow
273C23—21no—
274C23—111no—
275C23D4×D1111yescharacteristic
276Q8—221no—
277Q8—221no—
278D4—21no—
279D4—21no—
280D4—42no—
281D4—222no—
282D4—881no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—111no—
290C2×C4—111no—
291C2×C4—111no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—881no—
299C2×C4—881no—
300C2×C4D4×D1111yescharacteristic
301C2×C4C23×D1111yescharacteristic
302C8—21no—
303C8—21no—
304C8—112no—
305C8—221no—
306C22—21no—
307C22—21no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—221no—
312C22—221no—
313C22—221no—
314C22#6696512yes—
315C22C2×D4×D1111yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—221no—
321C4—221no—
322C4—221no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4—441no—
327C4#41×D1111yescharacteristic
328C4#6704311yescharacteristic
329C2—22no—
330C2—81no—
331C2—441no—
332C2#1062318611yescharacteristic
333C2C2×#6696511yescharacteristic
334C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#480C2
socleC22×C11C22×D4
prime radical#10623149C2
hypercenter#480D11
hypocenterC11#3337
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×#66872C2semidirect
6. #10622501C2semidirect
7. #10622493C2semidirect
8. #10622491C2semidirect
9. #10622490C2semidirect
10. #10622397C2semidirect
11. #10622391C2semidirect
12. #10622379C2semidirect
13. #10622371C2semidirect
14. (C22⋊D11)⋊C8C2semidirect
15. #10622335C2semidirect
145. #480D11semidirect
272. C11#3337semidirect

Maximal subgroups

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

subgroupindex
#106231492
#106230442
C11×#4802
#106226542
C2×#668722
#106225012
#106224932
#106224912
#106224902
#106223972
#106223912
#106223792
#106223712
(C22⋊D11)⋊C82
#106223352
#333711