Finite Group Databasebeta

← #13081378

Subgroups — #13081378

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×#559C211yesmaximal, characteristic
2#10623098C211yesmaximal, characteristic, complemented
3#10622688C211yesmaximal, characteristic
4#10622684C211yesmaximal, characteristic
5#10622669C211yesmaximal, characteristic, complemented
6#10622668C211yesmaximal, characteristic, complemented
7#10622667C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622643C211yesmaximal, characteristic, complemented
10#10622637C211yesmaximal, characteristic, complemented
11#10622635C211yesmaximal, characteristic, complemented
12#10622631C211yesmaximal, characteristic, complemented
13C4×#4324C211yesmaximal, characteristic, complemented
14#10622622C211yesmaximal, characteristic, complemented
15#10622621C211yesmaximal, characteristic, complemented
16C11×#127C2211yescharacteristic
17C11×#124—21no—
18C11×#124C2211yescharacteristic
19C11×#124C2211yescharacteristic
20C11×#123—21no—
21C11×#123—21no—
22C4×Q8×C11C2211yescharacteristic
23C4×Q8×C11C2211yescharacteristic
24C4×D4×C11—21no—
25C4×D4×C11C2211yescharacteristic
26C4×D4×C11C2211yescharacteristic
27#66997—21no—
28C2×#4326C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31#66942—21no—
32#66942—21no—
33#66940—21no—
34#66923C2211yescharacteristic
35#66923C2211yescharacteristic
36#66922C2211yescharacteristic
37C4×Dic22C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40#66899C2211yescharacteristic
41#66899C2211yescharacteristic
42#66899C2211yescharacteristic
43#66896C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66874C2211yescharacteristic
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×C11D411yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C2×Dic22—21no—
68C2×Dic22C2311yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4D411yescharacteristic
71C11×C4⋊C4D411yescharacteristic
72C11×C4⋊C4D411yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C11×C22⋊C4—21no—
76C11×C22⋊C4—21no—
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C11×C22⋊C4—21no—
80C42×C11—21no—
81C42×C11C2311yescharacteristic
82C42×C11C2311yescharacteristic
83C42×C11C2311yescharacteristic
84#4326—22no—
85#4324—22no—
86#4324—22no—
87C4⋊Dic11—21no—
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3371—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11—21no—
108Q8×C11—21no—
109Q8×C11—21no—
110Q8×C11—41no—
111D4×C11—21no—
112D4×C11—21no—
113D4×C11—21no—
114D4×C11—21no—
115D4×C11—42no—
116D4×C11—81no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132Dic22—21no—
133Dic22—42no—
134Dic22#4112yes—
135C11⋊C8—21no—
136C11⋊C8—21no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139#559D1111yescharacteristic
140#557—111no—
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×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C22×D411yescharacteristic
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11C2×#4111yescharacteristic
170C4×C112−1+411yescharacteristic
171Dic11—22no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175C2×Q16—111no—
176C2×SD16—111no—
177C2×SD16—111no—
178C4⋊Q8—111no—
179C4⋊Q8—221no—
180#127C2×D1111yescharacteristic
181#125—111no—
182#125—111no—
183#125—221no—
184#125—221no—
185#124—21no—
186#124C2×D1111yescharacteristic
187#124C2×D1111yescharacteristic
188#123—21no—
189#123—21no—
190C4×Q8—111no—
191C4×Q8—111no—
192C4×Q8—111no—
193C4×Q8—221no—
194C4×Q8C2×D1111yescharacteristic
195C4×Q8C2×D1111yescharacteristic
196C4×D4—21no—
197C4×D4C2×D1111yescharacteristic
198C4×D4C2×D1111yescharacteristic
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—81no—
219C2×C11—81no—
220C2×C11#54811yescharacteristic
221C2×C11#57511yescharacteristic
222C2×C11#57711yescharacteristic
223C2×Q8—111no—
224C2×Q8—221no—
225C2×Q8C22⋊D1111yescharacteristic
226C2×Q8C22×D1111yescharacteristic
227C2×D4—21no—
228C2×D4—21no—
229C2×D4C22×D1111yescharacteristic
230C2×D4C22×D1111yescharacteristic
231C22×C4—21no—
232C22×C4—21no—
233Q16—222no—
234SD16—222no—
235SD16—222no—
236C2×C8—111no—
237C2×C8—111no—
238C2×C8—111no—
239C2×C8—111no—
240C4⋊C4—21no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4C22⋊D1111yescharacteristic
253C4⋊C4C22⋊D1111yescharacteristic
254C4⋊C4C22⋊D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C42—21no—
263C42—221no—
264C42—221no—
265C42—221no—
266C42C22×D1111yescharacteristic
267C42C22×D1111yescharacteristic
268C42C22×D1111yescharacteristic
269C11#337111yescharacteristic, complemented, Sylow
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—21no—
274Q8—41no—
275Q8—112no—
276Q8—221no—
277Q8—442no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4—21no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
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—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C22×C22⋊D1111yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—222no—
319C4—441no—
320C4—441no—
321C4—441no—
322C4#41×D1111yescharacteristic
323C4#6704311yescharacteristic
324C2—81no—
325C2—81no—
326C2#1062335311yescharacteristic
327C2#1062336211yescharacteristic
328C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#559C2
socleC22×C11C22×D4
prime radicalC11×#127C22
hypercenter#559D11
hypocenterC11#3371
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
2. #10623098C2semidirect
5. #10622669C2semidirect
6. #10622668C2semidirect
7. #10622667C2semidirect
8. #10622667C2semidirect
9. #10622643C2semidirect
10. #10622637C2semidirect
11. #10622635C2semidirect
12. #10622631C2semidirect
13. C4×#4324C2semidirect
14. #10622622C2semidirect
15. #10622621C2semidirect
269. C11#3371semidirect

Maximal subgroups

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

subgroupindex
C11×#5592
#106230982
#106226882
#106226842
#106226692
#106226682
#106226672
#106226432
#106226372
#106226352
#106226312
C4×#43242
#106226222
#106226212
#337111