Finite Group Databasebeta

← #13082695

Subgroups — #13082695

Order 1408.

1104 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#520C211yesmaximal, characteristic, complemented
2#10623365C211yesmaximal, characteristic, complemented
3#10623362C211yesmaximal, characteristic, complemented
4#10623107C211yesmaximal, characteristic, complemented
5#10623105C211yesmaximal, characteristic, complemented
6C4×Q8×D11C211yesmaximal, characteristic, complemented
7Q8×Dic22C211yesmaximal, characteristic, complemented
8#10623092C213yesmaximal, complemented
9#10623090C213yesmaximal, complemented
10#10623082C213yesmaximal, complemented
11#10623079C213yesmaximal, complemented
12#10623065C213yesmaximal, complemented
13#10623059C213yesmaximal, complemented
14#10623042C213yesmaximal, complemented
15#10623038C213yesmaximal, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C2×#4339C2216yes—
20C4×Q8×C11C2211yescharacteristic
21C4×Q8×C11C2211yescharacteristic
22C4×D4×C11C2213yes—
23C4×D4×C11C2213yes—
24C11×#117C2213yes—
25C2×C11×C4⋊C4C2213yes—
26Q8×Dic11C2211yescharacteristic
27Q8×Dic11C2211yescharacteristic
28#66993C2213yes—
29#66991C2213yes—
30#66991C2213yes—
31#66989C2213yes—
32#66983C2213yes—
33#66982C2216yes—
34C4×C22⋊D11C2213yes—
35C4×C22⋊D11C2213yes—
36C4×C22⋊D11C2216yes—
37#66977C2213yes—
38#66977C2216yes—
39#66951C2213yes—
40#66950C2213yes—
41#66949C2216yes—
42#66949C2211yescharacteristic
43#66948C2213yes—
44#66947C2213yes—
45#66946C2213yes—
46C4⋊C4×D11C2213yes—
47C4⋊C4×D11C2213yes—
48#66942C2213yes—
49#66941C2213yes—
50#66941C2213yes—
51#66940C2213yes—
52#66938C2213yes—
53#66938C2216yes—
54#66937C2213yes—
55#66936C2213yes—
56#66936C2216yes—
57#66932C2213yes—
58#66928C2213yes—
59C4×D44C2213yes—
60C4×D44C2213yes—
61#66925C2213yes—
62C42×D11C2213yes—
63#66922C2213yes—
64C4×Dic22C2213yes—
65C4×Dic22C2213yes—
66C11×#41—24no—
67C2×Q8×C11C2311yescharacteristic
68C2×D4×C11C2313yes—
69C22×C4×C11C2313yes—
70C22×C4×C11C2316yes—
71C2×C22⋊D11C2313yes—
72C2×C22⋊D11C2313yes—
73C2×C22⋊D11C2316yes—
74#4343—24no—
75Q8×D11—24no—
76#4339—412no—
77C2×D44C2313yes—
78C2×D44C2313yes—
79C2×C4×D11C2311yescharacteristic
80C2×C4×D11C2313yes—
81C2×C4×D11C2313yes—
82C2×C4×D11C2313yes—
83C2×C4×D11C2316yes—
84C2×Dic22C2311yescharacteristic
85C2×Dic22C2313yes—
86C2×Dic22C2316yes—
87C11×C4⋊C4C2313yes—
88C11×C4⋊C4C2313yes—
89C11×C4⋊C4C2313yes—
90C11×C4⋊C4C2311yescharacteristic
91C11×C22⋊C4C2313yes—
92C11×C22⋊C4C2313yes—
93C42×C11C2313yes—
94C42×C11C2313yes—
95C22⋊Dic11C2313yes—
96C22⋊Dic11C2313yes—
97C22⋊Dic11C2316yes—
98(C2×D11)⋊C4C2313yes—
99(C2×D11)⋊C4C2313yes—
100(C2×D11)⋊C4C2311yescharacteristic
101(C2×D11)⋊C4C2313yes—
102(C2×D11)⋊C4C2316yes—
103(C2×D11)⋊C4C2311yescharacteristic
104(C2×D11)⋊C4C2313yes—
105C4⋊Dic11C2313yes—
106C4⋊Dic11C2313yes—
107C4⋊Dic11C2313yes—
108C4⋊Dic11C2313yes—
109Dic11⋊C4C2313yes—
110Dic11⋊C4C2316yes—
111Dic11⋊C4C2313yes—
112Dic11⋊C4C2311yescharacteristic
113Dic11⋊C4C2313yes—
114Dic11⋊C4C2311yescharacteristic
115Dic11⋊C4C2313yes—
116C4×Dic11C2313yes—
117C4×Dic11C2313yes—
118C4×Dic11C2313yes—
119C4×Dic11C2313yes—
120#3522—111nomaximal, Sylow
121C23×C11C2413yes—
122C22×D11C2413yes—
123C22×D11C2411yescharacteristic
124Q8×C11#4114yescomplemented
125D4×C11—26no—
126C2×C4×C11—26no—
127C2×C4×C11—46no—
128C2×C4×C11C2411yescharacteristic
129C2×C4×C11C2413yes—
130C2×C4×C11C2411yescharacteristic
131C2×C4×C11C2413yes—
132C2×C4×C11C2411yescharacteristic
133C2×C4×C11C2413yes—
134C22⋊D11—26no—
135C22⋊D11—26no—
136C22⋊D11—46no—
137C2×Dic11C2411yescharacteristic
138C2×Dic11C2413yes—
139C2×Dic11C2413yes—
140C2×Dic11C2413yes—
141C2×Dic11C2411yescharacteristic
142C2×Dic11C2411yescharacteristic
143D44—26no—
144D44—26no—
145C4×D11—26no—
146C4×D11—26no—
147C4×D11—26no—
148C4×D11—22no—
149C4×D11—46no—
150Dic22—26no—
151Dic22—22no—
152Dic22—46no—
153#559—113no—
154Q82—111no—
155#554—113no—
156#550—111no—
157#548—111no—
158#548—111no—
159#547—113no—
160#547—113no—
161#542—113no—
162#542—113no—
163#532—113no—
164#529—113no—
165#520—111no—
166#520D1111yescharacteristic, complemented
167C2×C4×Q8—111no—
168C22×C11—23no—
169C22×C11—23no—
170C22×C11—23no—
171C22×C11C2511yescharacteristic
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—23no—
175C2×D11—23no—
176C2×D11—23no—
177C2×D11H(5,𝔽2)12yes—
178C4×C11—21no—
179C4×C11—23no—
180C4×C11—23no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11C2×#4116yes—
184Dic11—23no—
185Dic11—21no—
186Dic11—23no—
187Dic11—23no—
188Dic11—21no—
189Dic112−1+412yes—
190C2×#41—111no—
191C2×#41—116no—
192C2×#41C2×D1111yescharacteristic
193C22×Q8—111no—
194C4⋊Q8—113no—
195C4⋊Q8—113no—
196C4⋊Q8—113no—
197#127—113no—
198#126—113no—
199#126—113no—
200#125—113no—
201#124—113no—
202#124—113no—
203#124—116no—
204#124—113no—
205#123—116no—
206#123—113no—
207#123—113no—
208#123—116no—
209C22⋊Q8—116no—
210C22⋊Q8—113no—
211C22⋊Q8—111no—
212C22⋊Q8—116no—
213C22⋊Q8—113no—
214#121—113no—
215#121—113no—
216#121—113no—
217#121—113no—
218#121—113no—
219C4×Q8—111no—
220C4×Q8—111no—
221C4×Q8—113no—
222C4×Q8—113no—
223C4×Q8—113no—
224C4×Q8C2×D1111yescharacteristic
225C4×Q8C2×D1111yescharacteristic
226C4×D4—113no—
227C4×D4—113no—
228C4×D4—116no—
229C4×D4—113no—
230C4×D4—113no—
231C4×D4—113no—
232C4×D4C2×D1113yes—
233C4×D4C2×D1113yes—
234#117—113no—
235#117C2×D1113yes—
236C2×C4⋊C4—113no—
237C2×C4⋊C4—113no—
238C2×C4⋊C4C2×D1113yes—
239C2×C42—113no—
240C2×C11—43no—
241C2×C11C22×#4111yescharacteristic
242C2×C11C2×H(5,𝔽2)11yescharacteristic
243C2×C11C2×2−1+411yescharacteristic
244D11—22no—
245D11—43no—
246#41—24no—
247#41—224no—
248#41—4412no—
249C2×Q8—111no—
250C2×Q8—113no—
251C2×Q8—116no—
252C2×Q8—224no—
253C2×Q8C22×D1111yescharacteristic
254C2×D4—113no—
255C2×D4—113no—
256C2×D4—116no—
257C2×D4—113no—
258C2×D4—113no—
259C2×D4C22×D1113yes—
260C22×C4—111no—
261C22×C4—113no—
262C22×C4—113no—
263C22×C4—113no—
264C22×C4—116no—
265C22×C4C22×D1113yes—
266C22×C4C22×D1116yes—
267C4⋊C4—113no—
268C4⋊C4—113no—
269C4⋊C4—113no—
270C4⋊C4—116no—
271C4⋊C4—111no—
272C4⋊C4—111no—
273C4⋊C4—113no—
274C4⋊C4—113no—
275C4⋊C4—113no—
276C4⋊C4—113no—
277C4⋊C4—113no—
278C4⋊C4C22×D1113yes—
279C4⋊C4C22×D1113yes—
280C4⋊C4C22×D1113yes—
281C4⋊C4C22×D1111yescharacteristic
282C22⋊C4—113no—
283C22⋊C4—116no—
284C22⋊C4—113no—
285C22⋊C4—113no—
286C22⋊C4—113no—
287C22⋊C4—111no—
288C22⋊C4—111no—
289C22⋊C4—113no—
290C22⋊C4—116no—
291C22⋊C4—113no—
292C22⋊C4C22×D1113yes—
293C22⋊C4C22×D1113yes—
294C42—113no—
295C42—113no—
296C42—113no—
297C42—113no—
298C42C22×D1113yes—
299C42C22×D1113yes—
300C11#352211yescharacteristic, complemented, Sylow
301C23—111no—
302C23—113no—
303C23C23×D1113yes—
304Q8—222no—
305Q8—226no—
306Q8—446no—
307Q8#433914yescomplemented
308D4—26no—
309D4—226no—
310D4—226no—
311D4—226no—
312D4—226no—
313D4—446no—
314C2×C4—26no—
315C2×C4—46no—
316C2×C4—111no—
317C2×C4—111no—
318C2×C4—113no—
319C2×C4—113no—
320C2×C4—113no—
321C2×C4—111no—
322C2×C4—222no—
323C2×C4—226no—
324C2×C4—226no—
325C2×C4—226no—
326C2×C4—446no—
327C2×C4C23×D1111yescharacteristic
328C2×C4C23×D1113yes—
329C2×C4C23×D1111yescharacteristic
330C2×C4C23×D1113yes—
331C2×C4C23×D1111yescharacteristic
332C2×C4C23×D1113yes—
333C22—23no—
334C22—23no—
335C22—23no—
336C22—112no—
337C22—221no—
338C22—221no—
339C22—223no—
340C22—223no—
341C22—223no—
342C22C24×D1111yescharacteristic
343C4—21no—
344C4—23no—
345C4—23no—
346C4—21no—
347C4—21no—
348C4—112no—
349C4—221no—
350C4—223no—
351C4—223no—
352C4—223no—
353C4—221no—
354C4C2×#433916yes—
355C2—43no—
356C2—222no—
357C2—443no—
358C2C22×#433911yescharacteristic
359C2D11×H(5,𝔽2)11yescharacteristic
360C2D11×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#520C2
hypercenter#520D11
hypocenterC11#3522
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C11×#520C2semidirect
2. #10623365C2semidirect
3. #10623362C2semidirect
4. #10623107C2semidirect
5. #10623105C2semidirect
6. C4×Q8×D11C2semidirect
7. Q8×Dic22C2semidirect
8. #10623092C2semidirect
9. #10623090C2semidirect
10. #10623082C2semidirect
11. #10623079C2semidirect
12. #10623065C2semidirect
13. #10623059C2semidirect
14. #10623042C2semidirect
15. #10623038C2semidirect
124. Q8×C11#41semidirect
166. #520D11semidirect
300. C11#3522semidirect
307. Q8#4339semidirect

Maximal subgroups

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

subgroupindex
C11×#5202
#106233652
#106233622
#106231072
#106231052
C4×Q8×D112
Q8×Dic222
#106230922
#106230902
#106230822
#106230792
#106230652
#106230592
#106230422
#106230382
#352211