Finite Group Databasebeta

← #13081369

Subgroups — #13081369

Order 1408.

358 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
1C11×#554C211yesmaximal, characteristic, complemented
2#10623116C211yesmaximal, characteristic, complemented
3#10622702C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic, complemented
5#10622681C211yesmaximal, characteristic, complemented
6#10622680C211yesmaximal, characteristic, complemented
7#10622679C211yesmaximal, characteristic, complemented
8#10622676C211yesmaximal, characteristic, complemented
9#10622637C211yesmaximal, characteristic, complemented
10#10622631C211yesmaximal, characteristic, complemented
11#10622629C211yesmaximal, characteristic, complemented
12#10622629C211yesmaximal, characteristic, complemented
13#10622628C211yesmaximal, characteristic
14#10622627C211yesmaximal, characteristic, complemented
15C4×#4323C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#125C2211yescharacteristic
18C11×#125C2211yescharacteristic
19C11×C22⋊Q8—21no—
20C11×C22⋊Q8—21no—
21C11×C22⋊Q8—21no—
22C4×Q8×C11C2211yescharacteristic
23C4×D4×C11C2211yescharacteristic
24C4×D4×C11C2211yescharacteristic
25C4×D4×C11C2211yescharacteristic
26C2×C11×C4⋊C4—21no—
27#67000—21no—
28C2×#4324C2211yescharacteristic
29C2×#4323C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66947—21no—
32#66947—21no—
33#66946—21no—
34#66928C2211yescharacteristic
35#66928C2211yescharacteristic
36#66927C2211yescharacteristic
37C4×D44C2211yescharacteristic
38C4×D44C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40#66896C2211yescharacteristic
41#66874C2211yescharacteristic
42#66874C2211yescharacteristic
43#66874C2211yescharacteristic
44#66873C2211yescharacteristic
45#66873C2211yescharacteristic
46#66873C2211yescharacteristic
47#66873C2211yescharacteristic
48#66873C2211yescharacteristic
49#66873C2211yescharacteristic
50#66872C2211yescharacteristic
51#66871C2211yescharacteristic
52#66871C2211yescharacteristic
53C4⋊(C11⋊C8)C2211yescharacteristic
54C4⋊(C11⋊C8)C2211yescharacteristic
55C4⋊(C11⋊C8)C2211yescharacteristic
56#66867C2211yescharacteristic
57#66867C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11D411yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44C2311yescharacteristic
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×Dic22C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4D411yescharacteristic
78C11×C4⋊C4D411yescharacteristic
79C11×C4⋊C4D411yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4—21no—
86C42×C11C2311yescharacteristic
87C42×C11C2311yescharacteristic
88C42×C11C2311yescharacteristic
89#4324—22no—
90#4323—22no—
91#4323—22no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100C4×Dic11—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3370—111nomaximal, Sylow
106C23×C11—21no—
107C22×D11—21no—
108C22×D11—21no—
109Q8×C11—41no—
110Q8×C11—81no—
111D4×C11—21no—
112D4×C11#4112yes—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—42no—
117C2×C4×C11—81no—
118C2×C4×C11—81no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C2×Dic11—21no—
127C2×Dic11—21no—
128D44—21no—
129D44—21no—
130D44—21no—
131D44—21no—
132D44—42no—
133D44—81no—
134C4×D11—81no—
135C4×D11—81no—
136Dic22—21no—
137Dic22—21no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140C11⋊C8—21no—
141C11⋊C8—21no—
142#559—111no—
143#554D1111yescharacteristic, complemented
144#490—111no—
145#489—111no—
146#488—111no—
147#479—111no—
148#478—111no—
149#474—111no—
150#463—111no—
151#463—111no—
152#459—111no—
153#446—111no—
154#442—111no—
155#440—111no—
156C4×D8—111no—
157C22×C11—22no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C22×D411yescharacteristic
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11C2×#4111yescharacteristic
177C4×C112−1+411yescharacteristic
178Dic11—41no—
179Dic11—41no—
180C2×SD16—111no—
181C2×D8—111no—
182C2×D8—111no—
183C4⋊Q8C2×D1111yescharacteristic
184#127—111no—
185#125C2×D1111yescharacteristic
186#125C2×D1111yescharacteristic
187#124—111no—
188#124—111no—
189#124—221no—
190#123—221no—
191#123—221no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194C22⋊Q8—21no—
195C4×Q8—111no—
196C4×Q8C2×D1111yescharacteristic
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—221no—
200C4×D4C2×D1111yescharacteristic
201C4×D4C2×D1111yescharacteristic
202C4×D4C2×D1111yescharacteristic
203C2×C4⋊C4—21no—
204#107—111no—
205#107—111no—
206#106—111no—
207C4⋊C8—111no—
208C4⋊C8—111no—
209C4⋊C8—111no—
210#103—111no—
211#103—111no—
212#103—111no—
213#102—111no—
214#102—111no—
215#102—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220#97—111no—
221#97—111no—
222C4×C8—111no—
223C2×C11—42no—
224C2×C11#54811yescharacteristic
225C2×C11#57511yescharacteristic
226C2×C11#57611yescharacteristic
227D11—81no—
228D11—81no—
229C2×Q8—21no—
230C2×Q8—111no—
231C2×Q8C22⋊D1111yescharacteristic
232C2×D4—111no—
233C2×D4—111no—
234C2×D4—221no—
235C2×D4—221no—
236C2×D4C22×D1111yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—221no—
241C22×C4—221no—
242SD16—222no—
243D8—222no—
244D8—222no—
245C2×C8—111no—
246C2×C8—111no—
247C2×C8—111no—
248C2×C8—111no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—111no—
255C4⋊C4—221no—
256C4⋊C4C22⋊D1111yescharacteristic
257C4⋊C4C22⋊D1111yescharacteristic
258C4⋊C4C22⋊D1111yescharacteristic
259C4⋊C4C22×D1111yescharacteristic
260C4⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C42—221no—
272C42C22×D1111yescharacteristic
273C42C22×D1111yescharacteristic
274C42C22×D1111yescharacteristic
275C11#337011yescharacteristic, complemented, Sylow
276C23—21no—
277C23—221no—
278C23—221no—
279Q8—41no—
280Q8—81no—
281Q8—221no—
282Q8—221no—
283D4—21no—
284D4—221no—
285D4—221no—
286D4—221no—
287D4—221no—
288D4—442no—
289D4—881no—
290D4#434312yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4C2×C22⋊D1111yescharacteristic
302C2×C4C2×C22⋊D1111yescharacteristic
303C2×C4C2×C22⋊D1111yescharacteristic
304C2×C4C2×C22⋊D1111yescharacteristic
305C2×C4C2×C22⋊D1111yescharacteristic
306C2×C4C2×C22⋊D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—221no—
309C8—221no—
310C8—221no—
311C8—221no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—441no—
316C22—441no—
317C22—441no—
318C22—441no—
319C22—441no—
320C22—441no—
321C22C22×C22⋊D1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—441no—
332C4—441no—
333C4C2×#434311yescharacteristic
334C4#6704011yescharacteristic
335C2—42no—
336C2—881no—
337C2—881no—
338C2#1062334811yescharacteristic
339C2#1062335311yescharacteristic
340C2#1062336611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#554C2
socleC22×C11C22×D4
prime radical#10622628C2
hypercenter#554D11
hypocenterC11#3370
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C11×#554C2semidirect
2. #10623116C2semidirect
3. #10622702C2semidirect
4. #10622700C2semidirect
5. #10622681C2semidirect
6. #10622680C2semidirect
7. #10622679C2semidirect
8. #10622676C2semidirect
9. #10622637C2semidirect
10. #10622631C2semidirect
11. #10622629C2semidirect
12. #10622629C2semidirect
14. #10622627C2semidirect
15. C4×#4323C2semidirect
143. #554D11semidirect
275. C11#3370semidirect

Maximal subgroups

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

subgroupindex
C11×#5542
#106231162
#106227022
#106227002
#106226812
#106226802
#106226792
#106226762
#106226372
#106226312
#106226292
#106226282
#106226272
C4×#43232
#337011