Finite Group Databasebeta

← #13079863

Subgroups — #13079863

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×#540C211yesmaximal, characteristic
2#10623050C211yesmaximal, characteristic, complemented
3#10622684C211yesmaximal, characteristic, complemented
4#10622683C211yesmaximal, characteristic, complemented
5#10622678C211yesmaximal, characteristic, complemented
6#10622677C211yesmaximal, characteristic, complemented
7#10622648C211yesmaximal, characteristic, complemented
8#10622648C211yesmaximal, characteristic, complemented
9#10622647C211yesmaximal, characteristic, complemented
10#10622646C211yesmaximal, characteristic, complemented
11#10622622C211yesmaximal, characteristic, complemented
12#10622622C211yesmaximal, characteristic, complemented
13#10622621C211yesmaximal, characteristic, complemented
14#10622620C211yesmaximal, characteristic, complemented
15#10622613C211yesmaximal, characteristic, complemented
16C11×#127C2211yescharacteristic
17C11×#125C2211yescharacteristic
18C11×#123—21no—
19C11×#123—21no—
20C11×#121—21no—
21C11×#121—21no—
22C11×#121C2211yescharacteristic
23C11×#121C2211yescharacteristic
24C4×D4×C11C2211yescharacteristic
25C4×D4×C11C2211yescharacteristic
26C11×#117C2211yescharacteristic
27#66979C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29#66943—21no—
30#66941—21no—
31#66931—21no—
32#66931—21no—
33#66923C2211yescharacteristic
34#66923C2211yescharacteristic
35#66922C2211yescharacteristic
36#66922C2211yescharacteristic
37#66896C2211yescharacteristic
38#66896C2211yescharacteristic
39#66896C2211yescharacteristic
40#66896C2211yescharacteristic
41#66896C2211yescharacteristic
42#66896C2211yescharacteristic
43#66896C2211yescharacteristic
44#66896C2211yescharacteristic
45C22⋊(C11⋊C8)C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic
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×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C2311yescharacteristic
68C22×Dic11—21no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4D411yescharacteristic
74C11×C4⋊C4D411yescharacteristic
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×C11C2311yescharacteristic
84C42×C11C2311yescharacteristic
85C22⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97C4×Dic11—21no—
98C2×C11⋊C8C2311yescharacteristic
99C2×C11⋊C8C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3241—111nomaximal, Sylow
103C23×C11—21no—
104C23×C11—21no—
105C23×C11C2×D411yescharacteristic
106D4×C11—21no—
107D4×C11—21no—
108D4×C11—21no—
109D4×C11—21no—
110D4×C11—81no—
111D4×C11—81no—
112D4×C11—81no—
113D4×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
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—
129C2×Dic11—21no—
130C2×Dic11—81no—
131Dic22—81no—
132Dic22—81no—
133C11⋊C8—21no—
134C11⋊C8—21no—
135C11⋊C8—21no—
136C11⋊C8—21no—
137#544—111no—
138#540D1111yescharacteristic
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×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11C22×D411yescharacteristic
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C112−1+411yescharacteristic
170C4×C112−1+411yescharacteristic
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175C4⋊Q8—111no—
176C4⋊Q8—111no—
177C4⋊Q8—221no—
178#127C2×D1111yescharacteristic
179#125—111no—
180#125—111no—
181#125—221no—
182#125C2×D1111yescharacteristic
183#123—21no—
184#123—21no—
185C22⋊Q8—221no—
186C22⋊Q8—221no—
187#121—21no—
188#121—21no—
189#121C2×D1111yescharacteristic
190#121C2×D1111yescharacteristic
191C4×D4C2×D1111yescharacteristic
192C4×D4C2×D1111yescharacteristic
193#117—111no—
194#117C2×D1111yescharacteristic
195C2×C4⋊C4—111no—
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—81no—
220C2×C11—81no—
221C2×C11#53611yescharacteristic
222C2×C11#57611yescharacteristic
223C2×C11#57711yescharacteristic
224C2×Q8—221no—
225C2×Q8—221no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C22×D1111yescharacteristic
231C2×D4C22×D1111yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
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—111no—
243C4⋊C4—111no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
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⋊C4C22⋊D1111yescharacteristic
263C22⋊C4C22⋊D1111yescharacteristic
264C42—221no—
265C42C22×D1111yescharacteristic
266C42C22×D1111yescharacteristic
267C11#324111yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23C2×C22⋊D1111yescharacteristic
271Q8—881no—
272Q8—881no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—81no—
280D4—81no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
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—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C22×C22⋊D1111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—441no—
320C4—441no—
321C4—441no—
322C4—441no—
323C4#6704311yescharacteristic
324C4#6704311yescharacteristic
325C2—41no—
326C2—81no—
327C2—81no—
328C2#1062335611yescharacteristic
329C2#1062336611yescharacteristic
330C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#540C2
socleC22×C11C22×D4
hypercenter#540D11
hypocenterC11#3241
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
2. #10623050C2semidirect
3. #10622684C2semidirect
4. #10622683C2semidirect
5. #10622678C2semidirect
6. #10622677C2semidirect
7. #10622648C2semidirect
8. #10622648C2semidirect
9. #10622647C2semidirect
10. #10622646C2semidirect
11. #10622622C2semidirect
12. #10622622C2semidirect
13. #10622621C2semidirect
14. #10622620C2semidirect
15. #10622613C2semidirect
267. C11#3241semidirect

Maximal subgroups

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

subgroupindex
C11×#5402
#106230502
#106226842
#106226832
#106226782
#106226772
#106226482
#106226472
#106226462
#106226222
#106226212
#106226202
#106226132
#324111