Finite Group Databasebeta

← #13081437

Subgroups — #13081437

Order 1408.

346 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×#556C211yesmaximal, characteristic, complemented
2#10623110C211yesmaximal, characteristic, complemented
3#10622696C211yesmaximal, characteristic, complemented
4#10622695C211yesmaximal, characteristic, complemented
5#10622670C211yesmaximal, characteristic
6#10622670C211yesmaximal, characteristic
7#10622669C211yesmaximal, characteristic, complemented
8#10622668C211yesmaximal, characteristic, complemented
9#10622639C211yesmaximal, characteristic, complemented
10C4×#4325C211yesmaximal, characteristic, complemented
11#10622637C211yesmaximal, characteristic, complemented
12#10622635C211yesmaximal, characteristic, complemented
13#10622633C211yesmaximal, characteristic, complemented
14#10622627C211yesmaximal, characteristic
15#10622622C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#126—21no—
18C11×#126—21no—
19C11×#124C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C11×C22⋊Q8—21no—
22C4×Q8×C11C2211yescharacteristic
23C4×Q8×C11C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×D4×C11C2211yescharacteristic
26C11×#117—21no—
27#66999—21no—
28C2×#4325C2211yescharacteristic
29C2×#4325C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66949—21no—
32#66949—21no—
33C4⋊C4×D11—21no—
34C4×D44C2211yescharacteristic
35C4×D44C2211yescharacteristic
36C4×D44C2211yescharacteristic
37#66923C2211yescharacteristic
38#66923C2211yescharacteristic
39#66922C2211yescharacteristic
40#66899C2211yescharacteristic
41#66899C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
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×C11D411yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×Dic22—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4D411yescharacteristic
74C11×C4⋊C4D411yescharacteristic
75C11×C4⋊C4D411yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11C2311yescharacteristic
85C42×C11C2311yescharacteristic
86C42×C11C2311yescharacteristic
87#4325—22no—
88#4325—22no—
89#4323—22no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3376—111nomaximal, Sylow
106C23×C11—21no—
107C22×D11—21no—
108Q8×C11—21no—
109Q8×C11—21no—
110Q8×C11—21no—
111Q8×C11—21no—
112Q8×C11—41no—
113D4×C11—21no—
114D4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—42no—
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—
128C2×Dic11—21no—
129D44—21no—
130D44#4112yes—
131C4×D11—42no—
132C4×D11—81no—
133C4×D11—81no—
134Dic22—81no—
135C11⋊C8—21no—
136C11⋊C8—21no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139#556D1111yescharacteristic, complemented
140#554—111no—
141#491—111no—
142#489—111no—
143#488—111no—
144#479—111no—
145#478—111no—
146#475—111no—
147#463—111no—
148#463—111no—
149#461—111no—
150#446—111no—
151#442—111no—
152#440—111no—
153C4×SD16—111no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11C22×D411yescharacteristic
158C2×D11—22no—
159C2×D11—41no—
160C2×D11—41no—
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×C11—41no—
170C4×C11C2×#4111yescharacteristic
171C4×C112−1+411yescharacteristic
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175C2×SD16—111no—
176C2×SD16—111no—
177C2×D8—111no—
178C4⋊Q8—111no—
179C4⋊Q8C2×D1111yescharacteristic
180#126—21no—
181#126—21no—
182#125—111no—
183#125—111no—
184#124C2×D1111yescharacteristic
185#124C2×D1111yescharacteristic
186C22⋊Q8—21no—
187C22⋊Q8—221no—
188C22⋊Q8—221no—
189C22⋊Q8—221no—
190C4×Q8C2×D1111yescharacteristic
191C4×Q8C2×D1111yescharacteristic
192C4×Q8C2×D1111yescharacteristic
193C4×D4—111no—
194C4×D4—111no—
195C4×D4—111no—
196C4×D4C2×D1111yescharacteristic
197#117—21no—
198C2×C4⋊C4—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#103—111no—
210#103—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#54811yescharacteristic
220C2×C11#57511yescharacteristic
221C2×C11#57711yescharacteristic
222D11—42no—
223C2×Q8—221no—
224C2×Q8C22⋊D1111yescharacteristic
225C2×Q8C22×D1111yescharacteristic
226C2×Q8C22×D1111yescharacteristic
227C2×D4—111no—
228C2×D4C22×D1111yescharacteristic
229C22×C4—21no—
230C22×C4—221no—
231C22×C4—221no—
232C22×C4—221no—
233SD16—222no—
234SD16—222no—
235D8—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—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
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—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C42—21no—
265C42—21no—
266C42C22×D1111yescharacteristic
267C42C22×D1111yescharacteristic
268C42C22×D1111yescharacteristic
269C11#337611yescharacteristic, complemented, Sylow
270C23—21no—
271C23—221no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—41no—
277Q8—881no—
278D4—21no—
279D4—21no—
280D4—112no—
281D4—221no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—442no—
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—41no—
304C22—41no—
305C22—41no—
306C22—222no—
307C22—441no—
308C22—441no—
309C22C22×C22⋊D1111yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—441no—
320C4—441no—
321C4—441no—
322C4#41×D1111yescharacteristic
323C4#6704311yescharacteristic
324C2—81no—
325C2—442no—
326C2#1062335311yescharacteristic
327C2#1062336211yescharacteristic
328C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#556C2
socleC22×C11C22×D4
prime radicalC2×#4323C22
hypercenter#556D11
hypocenterC11#3376
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C11×#556C2semidirect
2. #10623110C2semidirect
3. #10622696C2semidirect
4. #10622695C2semidirect
7. #10622669C2semidirect
8. #10622668C2semidirect
9. #10622639C2semidirect
10. C4×#4325C2semidirect
11. #10622637C2semidirect
12. #10622635C2semidirect
13. #10622633C2semidirect
15. #10622622C2semidirect
139. #556D11semidirect
269. C11#3376semidirect

Maximal subgroups

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

subgroupindex
C11×#5562
#106231102
#106226962
#106226952
#106226702
#106226692
#106226682
#106226392
C4×#43252
#106226372
#106226352
#106226332
#106226272
#106226222
#337611