Finite Group Databasebeta

← #13079869

Subgroups — #13079869

Order 1408.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#544C211yesmaximal, characteristic, complemented
2#10623066C211yesmaximal, characteristic
3#10622701C211yesmaximal, characteristic, complemented
4#10622700C211yesmaximal, characteristic, complemented
5#10622697C211yesmaximal, characteristic, complemented
6#10622693C211yesmaximal, characteristic, complemented
7#10622680C211yesmaximal, characteristic, complemented
8#10622679C211yesmaximal, characteristic, complemented
9#10622679C211yesmaximal, characteristic, complemented
10#10622677C211yesmaximal, characteristic, complemented
11#10622616C211yesmaximal, characteristic, complemented
12#10622616C211yesmaximal, characteristic, complemented
13#10622613C211yesmaximal, characteristic, complemented
14#10622581C211yesmaximal, characteristic, complemented
15#10622580C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8—21no—
17C11×C4⋊Q8C2211yescharacteristic
18C11×C4⋊Q8C2211yescharacteristic
19C11×#125—21no—
20C11×#125C2211yescharacteristic
21C11×#125C2211yescharacteristic
22C11×C22⋊Q8—21no—
23C11×C22⋊Q8—21no—
24C11×#117C2211yescharacteristic
25C11×#117C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27#66983C2211yescharacteristic
28#66983C2211yescharacteristic
29#66947—21no—
30#66947—21no—
31#66937—21no—
32#66937—21no—
33#66927C2211yescharacteristic
34C4×D44C2211yescharacteristic
35C4×D44C2211yescharacteristic
36#66923C2211yescharacteristic
37C22⋊(C11⋊C8)C2211yescharacteristic
38C22⋊(C11⋊C8)C2211yescharacteristic
39#66873C2211yescharacteristic
40#66873C2211yescharacteristic
41#66873C2211yescharacteristic
42#66873C2211yescharacteristic
43#66873C2211yescharacteristic
44#66873C2211yescharacteristic
45#66873C2211yescharacteristic
46#66873C2211yescharacteristic
47#66872C2211yescharacteristic
48#66872C2211yescharacteristic
49#66872C2211yescharacteristic
50#66872C2211yescharacteristic
51#66871C2211yescharacteristic
52#66871C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55C4⋊(C11⋊C8)C2211yescharacteristic
56C4⋊(C11⋊C8)C2211yescharacteristic
57#66867C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44C2311yescharacteristic
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—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⋊C4—21no—
78C11×C4⋊C4D411yescharacteristic
79C11×C4⋊C4D411yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C22⋊C4—21no—
85C11×C22⋊C4D411yescharacteristic
86C11×C22⋊C4D411yescharacteristic
87C42×C11—21no—
88C42×C11C2311yescharacteristic
89C42×C11C2311yescharacteristic
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C2×C11⋊C8C2311yescharacteristic
99C2×C11⋊C8C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3241—111nomaximal, Sylow
103C23×C11C2×D411yescharacteristic
104C22×D11—21no—
105C22×D11—21no—
106Q8×C11—81no—
107Q8×C11—81no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—81no—
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C22⋊D11—81no—
122C22⋊D11—81no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125D44—21no—
126D44—21no—
127D44—21no—
128D44—21no—
129D44—81no—
130D44—81no—
131C4×D11—81no—
132C4×D11—81no—
133C11⋊C8—21no—
134C11⋊C8—21no—
135C11⋊C8—21no—
136C11⋊C8—21no—
137#544D1111yescharacteristic, complemented
138#540—111no—
139#501—111no—
140#499—111no—
141#490—111no—
142#486—111no—
143#482—111no—
144#482—111no—
145#481—111no—
146#480—111no—
147#478—111no—
148#478—111no—
149#476—111no—
150#474—111no—
151#433—111no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11C22×D411yescharacteristic
156C2×D11—41no—
157C2×D11—41no—
158C2×D11—41no—
159C2×D11—41no—
160C2×D11—41no—
161C2×D11—41no—
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×C11—41no—
171C4×C112−1+411yescharacteristic
172C4×C112−1+411yescharacteristic
173Dic11—41no—
174Dic11—41no—
175C4⋊Q8—21no—
176C4⋊Q8C2×D1111yescharacteristic
177C4⋊Q8C2×D1111yescharacteristic
178#127—111no—
179#125—21no—
180#125—111no—
181#125C2×D1111yescharacteristic
182#125C2×D1111yescharacteristic
183#123—221no—
184#123—221no—
185C22⋊Q8—21no—
186C22⋊Q8—21no—
187#121—111no—
188#121—111no—
189#121—221no—
190#121—221no—
191C4×D4—111no—
192C4×D4—111no—
193#117C2×D1111yescharacteristic
194#117C2×D1111yescharacteristic
195C2×C4⋊C4C2×D1111yescharacteristic
196#107—111no—
197#107—111no—
198#107—111no—
199#107—111no—
200#106—111no—
201#106—111no—
202#106—111no—
203#106—111no—
204C4⋊C8—111no—
205C4⋊C8—111no—
206#102—111no—
207#102—111no—
208#102—111no—
209#102—111no—
210#102—111no—
211#102—111no—
212#102—111no—
213#102—111no—
214C22⋊C8—111no—
215C22⋊C8—111no—
216#97—111no—
217C4×C8—111no—
218C2×C11—41no—
219C2×C11#53611yescharacteristic
220C2×C11#57611yescharacteristic
221C2×C11#57711yescharacteristic
222D11—81no—
223D11—81no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×D4—111no—
227C2×D4—111no—
228C2×D4—221no—
229C2×D4—221no—
230C2×D4—221no—
231C2×D4—221no—
232C22×C4—21no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4C22×D1111yescharacteristic
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—111no—
248C4⋊C4—111no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4C22⋊D1111yescharacteristic
252C4⋊C4C22⋊D1111yescharacteristic
253C4⋊C4C22×D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C4⋊C4C22×D1111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4C22⋊D1111yescharacteristic
263C22⋊C4C22⋊D1111yescharacteristic
264C42—21no—
265C42C22×D1111yescharacteristic
266C42C22×D1111yescharacteristic
267C11#324111yescharacteristic, complemented, Sylow
268C23—221no—
269C23—221no—
270C23C2×C22⋊D1111yescharacteristic
271Q8—81no—
272Q8—81no—
273D4—221no—
274D4—221no—
275D4—221no—
276D4—221no—
277D4—881no—
278D4—881no—
279D4—881no—
280D4—881no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—81no—
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×C4C23×D1111yescharacteristic
298C8—221no—
299C8—221no—
300C8—221no—
301C8—221no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—441no—
306C22—441no—
307C22—441no—
308C22—441no—
309C22—441no—
310C22—441no—
311C22C22×C22⋊D1111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—441no—
322C4—441no—
323C4#6704011yescharacteristic
324C4#6704011yescharacteristic
325C2—41no—
326C2—881no—
327C2—881no—
328C2#1062334711yescharacteristic
329C2#1062336611yescharacteristic
330C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#544C2
socleC22×C11C22×D4
prime radical#10623066C2
hypercenter#544D11
hypocenterC11#3241
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
1. C11×#544C2semidirect
3. #10622701C2semidirect
4. #10622700C2semidirect
5. #10622697C2semidirect
6. #10622693C2semidirect
7. #10622680C2semidirect
8. #10622679C2semidirect
9. #10622679C2semidirect
10. #10622677C2semidirect
11. #10622616C2semidirect
12. #10622616C2semidirect
13. #10622613C2semidirect
14. #10622581C2semidirect
15. #10622580C2semidirect
137. #544D11semidirect
267. C11#3241semidirect

Maximal subgroups

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

subgroupindex
C11×#5442
#106230662
#106227012
#106227002
#106226972
#106226932
#106226802
#106226792
#106226772
#106226162
#106226132
#106225812
#106225802
#324111