Finite Group Databasebeta

← #13081161

Subgroups — #13081161

Order 1408.

348 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
1C11×#556C211yesmaximal, characteristic, complemented
2#10623096C211yesmaximal, characteristic
3#10622697C211yesmaximal, characteristic, complemented
4#10622693C211yesmaximal, characteristic, complemented
5#10622662C211yesmaximal, characteristic, complemented
6#10622661C211yesmaximal, characteristic, complemented
7#10622658C211yesmaximal, characteristic, complemented
8#10622656C211yesmaximal, characteristic, complemented
9#10622639C211yesmaximal, characteristic, complemented
10#10622635C211yesmaximal, characteristic, complemented
11#10622624C211yesmaximal, characteristic, complemented
12#10622616C211yesmaximal, characteristic, complemented
13#10622616C211yesmaximal, characteristic, complemented
14#10622611C211yesmaximal, characteristic, complemented
15#10622608C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#126—21no—
18C11×#126—21no—
19C11×#124—21no—
20C11×C22⋊Q8C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C4×Q8×C11—21no—
23C4×Q8×C11C2211yescharacteristic
24C4×D4×C11C2211yescharacteristic
25C11×#117C2211yescharacteristic
26C11×#117C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28#66992—21no—
29#66983C2211yescharacteristic
30#66983C2211yescharacteristic
31#66979C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66951—21no—
36#66936—21no—
37(C22⋊D11)⋊C4—21no—
38C4×D44C2211yescharacteristic
39#66923C2211yescharacteristic
40#66899C2211yescharacteristic
41#66899C2211yescharacteristic
42#66899C2211yescharacteristic
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66873C2211yescharacteristic
46#66873C2211yescharacteristic
47#66873C2211yescharacteristic
48#66872C2211yescharacteristic
49#66872C2211yescharacteristic
50#66872C2211yescharacteristic
51#66872C2211yescharacteristic
52#66872C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11D411yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4D411yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C11×C22⋊C4D411yescharacteristic
82C11×C22⋊C4D411yescharacteristic
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88#4325—22no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99#4318—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3350—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C23×C11C2×D411yescharacteristic
108C22×D11—21no—
109Q8×C11—21no—
110Q8×C11—21no—
111Q8×C11—42no—
112D4×C11—41no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C22⋊D11—42no—
127C22⋊D11—81no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—81no—
132D44—21no—
133D44—21no—
134C4×D11—81no—
135C11⋊C8—21no—
136C11⋊C8—21no—
137C11⋊C8—21no—
138C11⋊C8#4112yes—
139#556D1111yescharacteristic, complemented
140#553—111no—
141#501—111no—
142#485—111no—
143#483—111no—
144#482—111no—
145#482—111no—
146#479—111no—
147#476—111no—
148#468—111no—
149#465—111no—
150#440—111no—
151#435—111no—
152#428—111no—
153#427—111no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11C22×D411yescharacteristic
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11C2×#4111yescharacteristic
173C4×C112−1+411yescharacteristic
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×SD16—111no—
178C2×M16—111no—
179C22×C8—111no—
180C4⋊Q8C2×D1111yescharacteristic
181#126—21no—
182#126—21no—
183#126—221no—
184#125—111no—
185#124—21no—
186#123—221no—
187C22⋊Q8C2×D1111yescharacteristic
188C22⋊Q8C2×D1111yescharacteristic
189#121—111no—
190#121—111no—
191#121—221no—
192C4×Q8—21no—
193C4×Q8C2×D1111yescharacteristic
194C4×D4—111no—
195C4×D4—221no—
196C4×D4C2×D1111yescharacteristic
197#117—111no—
198#117C2×D1111yescharacteristic
199#117C2×D1111yescharacteristic
200C2×C4⋊C4—111no—
201#107—111no—
202#107—111no—
203#107—111no—
204#107—111no—
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#102—111no—
216#102—111no—
217C22⋊C8—111no—
218C22⋊C8—111no—
219#97—111no—
220C2×C11—41no—
221C2×C11—41no—
222C2×C11#54711yescharacteristic
223C2×C11#57511yescharacteristic
224C2×C11#57711yescharacteristic
225D11—81no—
226C2×Q8—21no—
227C2×Q8C22×D1111yescharacteristic
228C2×D4—111no—
229C2×D4—221no—
230C2×D4—221no—
231C2×D4C22⋊D1111yescharacteristic
232C22×C4—221no—
233C22×C4—221no—
234C22×C4C22×D1111yescharacteristic
235C22×C4C22×D1111yescharacteristic
236SD16—222no—
237M16—222no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—111no—
241C2×C8—111no—
242C2×C8—222no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4C22⋊D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C4⋊C4C22×D1111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4C22⋊D1111yescharacteristic
266C22⋊C4C22⋊D1111yescharacteristic
267C42—21no—
268C42—21no—
269C42—21no—
270C42—221no—
271C42C22×D1111yescharacteristic
272C11#335011yescharacteristic, complemented, Sylow
273C23—221no—
274C23C2×C22⋊D1111yescharacteristic
275C23C2×C22⋊D1111yescharacteristic
276Q8—21no—
277Q8—21no—
278Q8—42no—
279D4—41no—
280D4—221no—
281D4—221no—
282D4—442no—
283D4—881no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—881no—
296C2×C4—881no—
297C2×C4C2×C22⋊D1111yescharacteristic
298C2×C4C2×C22⋊D1111yescharacteristic
299C2×C4C2×C22⋊D1111yescharacteristic
300C2×C4C2×C22⋊D1111yescharacteristic
301C2×C4C23×D1111yescharacteristic
302C8—112no—
303C8—221no—
304C8—221no—
305C8—221no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—441no—
313C22—441no—
314C22—441no—
315C22C22×C22⋊D1111yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—441no—
325C4—441no—
326C4—441no—
327C4#41×D1111yescharacteristic
328C4#6704311yescharacteristic
329C2—41no—
330C2—41no—
331C2—881no—
332C2#1062335311yescharacteristic
333C2#1062335511yescharacteristic
334C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#556C2
socleC22×C11C22×D4
prime radical#10623096C2
hypercenter#556D11
hypocenterC11#3350
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C11×#556C2semidirect
3. #10622697C2semidirect
4. #10622693C2semidirect
5. #10622662C2semidirect
6. #10622661C2semidirect
7. #10622658C2semidirect
8. #10622656C2semidirect
9. #10622639C2semidirect
10. #10622635C2semidirect
11. #10622624C2semidirect
12. #10622616C2semidirect
13. #10622616C2semidirect
14. #10622611C2semidirect
15. #10622608C2semidirect
139. #556D11semidirect
272. C11#3350semidirect

Maximal subgroups

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

subgroupindex
C11×#5562
#106230962
#106226972
#106226932
#106226622
#106226612
#106226582
#106226562
#106226392
#106226352
#106226242
#106226162
#106226112
#106226082
#335011