Finite Group Databasebeta

← #13081384

Subgroups — #13081384

Order 1408.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#557C211yesmaximal, characteristic, complemented
2#10623116C211yesmaximal, characteristic
3#10622702C211yesmaximal, characteristic, complemented
4#10622697C211yesmaximal, characteristic, complemented
5#10622681C211yesmaximal, characteristic, complemented
6#10622680C211yesmaximal, characteristic
7#10622679C211yesmaximal, characteristic, complemented
8#10622676C211yesmaximal, characteristic, complemented
9#10622643C211yesmaximal, characteristic, complemented
10#10622641C211yesmaximal, characteristic, complemented
11#10622641C211yesmaximal, characteristic, complemented
12#10622640C211yesmaximal, characteristic
13#10622639C211yesmaximal, characteristic, complemented
14C4×#4325C211yesmaximal, characteristic, complemented
15#10622637C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8—21no—
17C11×C4⋊Q8C2211yescharacteristic
18C11×#125—21no—
19C11×#125—21no—
20C11×#125C2211yescharacteristic
21C11×#125C2211yescharacteristic
22C4×Q8×C11—21no—
23C4×Q8×C11C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×Q8×C11C2211yescharacteristic
26C4×Q8×C11C2211yescharacteristic
27#67000—21no—
28C2×#4326C2211yescharacteristic
29C2×#4325C2211yescharacteristic
30C2×#4325C2211yescharacteristic
31#66947—21no—
32#66947—21no—
33#66946—21no—
34#66928C2211yescharacteristic
35#66928C2211yescharacteristic
36#66927C2211yescharacteristic
37C4×D44C2211yescharacteristic
38C4×D44C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40#66899C2211yescharacteristic
41#66874C2211yescharacteristic
42#66874C2211yescharacteristic
43#66874C2211yescharacteristic
44#66873C2211yescharacteristic
45#66873C2211yescharacteristic
46#66873C2211yescharacteristic
47#66873C2211yescharacteristic
48#66873C2211yescharacteristic
49#66873C2211yescharacteristic
50#66872C2211yescharacteristic
51#66872C2211yescharacteristic
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×Q8×C11C2311yescharacteristic
62C2×D44—21no—
63C2×D44—21no—
64C2×D44C2311yescharacteristic
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×Dic22C2311yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
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
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11C2311yescharacteristic
87C42×C11C2311yescharacteristic
88C42×C11C2311yescharacteristic
89#4326—22no—
90#4325—22no—
91#4325—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#3371—111nomaximal, Sylow
106C22×D11—21no—
107C22×D11—21no—
108Q8×C11—21no—
109Q8×C11—41no—
110Q8×C11—42no—
111Q8×C11#4112yes—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C2×Dic11—21no—
124C2×Dic11—21no—
125D44—21no—
126D44—21no—
127D44—21no—
128D44—21no—
129D44—42no—
130D44—81no—
131C4×D11—81no—
132C4×D11—81no—
133Dic22—21no—
134Dic22—21no—
135C11⋊C8—21no—
136C11⋊C8—21no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139#559—111no—
140#557D1111yescharacteristic, complemented
141#490—111no—
142#489—111no—
143#488—111no—
144#479—111no—
145#478—111no—
146#476—111no—
147#464—111no—
148#464—111no—
149#460—111no—
150#446—111no—
151#441—111no—
152#440—111no—
153C4×SD16—111no—
154C22×C11C22×D411yescharacteristic
155C2×D11—41no—
156C2×D11—41no—
157C2×D11—41no—
158C2×D11—41no—
159C2×D11—41no—
160C2×D11—41no—
161C4×C11—22no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11C2×#4111yescharacteristic
172C4×C112−1+411yescharacteristic
173Dic11—41no—
174Dic11—41no—
175C2×Q16—111no—
176C2×SD16—111no—
177C2×SD16—111no—
178C4⋊Q8—21no—
179C4⋊Q8C2×D1111yescharacteristic
180#127—111no—
181#125—21no—
182#125—21no—
183#125C2×D1111yescharacteristic
184#125C2×D1111yescharacteristic
185#124—111no—
186#124—111no—
187#124—221no—
188#123—221no—
189#123—221no—
190C4×Q8—21no—
191C4×Q8—111no—
192C4×Q8C2×D1111yescharacteristic
193C4×Q8C2×D1111yescharacteristic
194C4×Q8C2×D1111yescharacteristic
195C4×Q8C2×D1111yescharacteristic
196C4×D4—111no—
197C4×D4—111no—
198C4×D4—221no—
199#107—111no—
200#106—111no—
201#106—111no—
202C4⋊C8—111no—
203C4⋊C8—111no—
204C4⋊C8—111no—
205#103—111no—
206#103—111no—
207#103—111no—
208#103—111no—
209#102—111no—
210#102—111no—
211#102—111no—
212#102—111no—
213#102—111no—
214#102—111no—
215#97—111no—
216#97—111no—
217C4×C8—111no—
218C2×C11#54811yescharacteristic
219C2×C11#57511yescharacteristic
220C2×C11#57711yescharacteristic
221D11—81no—
222D11—81no—
223C2×Q8—21no—
224C2×Q8—111no—
225C2×Q8C22⋊D1111yescharacteristic
226C2×Q8C22×D1111yescharacteristic
227C2×D4—111no—
228C2×D4—111no—
229C2×D4—221no—
230C2×D4—221no—
231C22×C4—221no—
232C22×C4—221no—
233Q16—222no—
234SD16—222no—
235SD16—222no—
236C2×C8—111no—
237C2×C8—111no—
238C2×C8—111no—
239C2×C8—111no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—111no—
249C4⋊C4—221no—
250C4⋊C4C22⋊D1111yescharacteristic
251C4⋊C4C22⋊D1111yescharacteristic
252C4⋊C4C22⋊D1111yescharacteristic
253C4⋊C4C22×D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C22⋊C4—221no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—221no—
266C42C22×D1111yescharacteristic
267C42C22×D1111yescharacteristic
268C42C22×D1111yescharacteristic
269C11#337111yescharacteristic, complemented, Sylow
270C23—221no—
271C23—221no—
272Q8—21no—
273Q8—41no—
274Q8—42no—
275Q8—221no—
276Q8—221no—
277Q8#434312yes—
278D4—221no—
279D4—221no—
280D4—221no—
281D4—221no—
282D4—442no—
283D4—881no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4C2×C22⋊D1111yescharacteristic
293C2×C4C2×C22⋊D1111yescharacteristic
294C2×C4C2×C22⋊D1111yescharacteristic
295C2×C4C2×C22⋊D1111yescharacteristic
296C2×C4C2×C22⋊D1111yescharacteristic
297C2×C4C2×C22⋊D1111yescharacteristic
298C2×C4C23×D1111yescharacteristic
299C8—221no—
300C8—221no—
301C8—221no—
302C8—221no—
303C22—441no—
304C22—441no—
305C22—441no—
306C22—441no—
307C22—441no—
308C22—441no—
309C22C22×C22⋊D1111yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—441no—
321C4—441no—
322C4C2×#434311yescharacteristic
323C4#6704011yescharacteristic
324C2—881no—
325C2—881no—
326C2#1062334811yescharacteristic
327C2#1062335311yescharacteristic
328C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#557C2
socleC22×C11C22×D4
prime radical#66927C22
hypercenter#557D11
hypocenterC11#3371
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C11×#557C2semidirect
3. #10622702C2semidirect
4. #10622697C2semidirect
5. #10622681C2semidirect
7. #10622679C2semidirect
8. #10622676C2semidirect
9. #10622643C2semidirect
10. #10622641C2semidirect
11. #10622641C2semidirect
13. #10622639C2semidirect
14. C4×#4325C2semidirect
15. #10622637C2semidirect
140. #557D11semidirect
269. C11#3371semidirect

Maximal subgroups

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

subgroupindex
C11×#5572
#106231162
#106227022
#106226972
#106226812
#106226802
#106226792
#106226762
#106226432
#106226412
#106226402
#106226392
C4×#43252
#106226372
#337111