Finite Group Databasebeta

← #13082616

Subgroups — #13082616

Order 1408.

1122 conjugacy classes of subgroups.

The subgroup lattice has 364 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#10623365C211yesmaximal, characteristic, complemented
4#10623108C211yesmaximal, characteristic, complemented
5#10623105C211yesmaximal, characteristic, complemented
6C4×#4343C211yesmaximal, characteristic, complemented
7#10623100C211yesmaximal, characteristic, complemented
8#10623093C213yesmaximal, complemented
9#10623089C213yesmaximal, complemented
10#10623084C213yesmaximal, complemented
11#10623079C213yesmaximal, complemented
12#10623066C213yesmaximal, complemented
13#10623059C213yesmaximal, complemented
14#10623045C213yesmaximal, complemented
15#10623038C213yesmaximal, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×#4343C2211yescharacteristic
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#66993C2213yes—
30#66991C2213yes—
31#66991C2213yes—
32#66983C2213yes—
33#66983C2213yes—
34#66983C2216yes—
35#66982C2216yes—
36C4×C22⋊D11C2213yes—
37C4×C22⋊D11C2213yes—
38C4×C22⋊D11C2216yes—
39#66951C2213yes—
40#66949C2213yes—
41#66948C2213yes—
42#66948C2213yes—
43#66947C2216yes—
44#66947C2213yes—
45#66946C2213yes—
46#66946C2213yes—
47#66945C2213yes—
48C4⋊C4×D11C2213yes—
49#66943C2213yes—
50#66942C2211yescharacteristic
51#66941C2213yes—
52#66938C2213yes—
53#66937C2213yes—
54#66937C2216yes—
55#66937C2216yes—
56#66936C2213yes—
57#66932C2213yes—
58#66927C2213yes—
59C4×D44C2213yes—
60C4×D44C2213yes—
61C4×D44C2213yes—
62#66925C2213yes—
63C42×D11C2213yes—
64#66923C2213yes—
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—
74C2×C22⋊D11C2316yes—
75#4343—24no—
76#4343—24no—
77#4339—412no—
78C2×D44C2313yes—
79C2×D44C2313yes—
80C2×D44C2313yes—
81C2×D44C2316yes—
82C2×C4×D11C2313yes—
83C2×C4×D11C2313yes—
84C2×C4×D11C2313yes—
85C2×C4×D11C2313yes—
86C2×C4×D11C2316yes—
87C2×Dic22C2313yes—
88C11×C4⋊C4C2313yes—
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2313yes—
91C11×C4⋊C4C2313yes—
92C11×C22⋊C4C2313yes—
93C11×C22⋊C4C2313yes—
94C42×C11C2313yes—
95C42×C11C2313yes—
96C22⋊Dic11C2313yes—
97C22⋊Dic11C2313yes—
98(C2×D11)⋊C4C2313yes—
99(C2×D11)⋊C4C2313yes—
100(C2×D11)⋊C4C2313yes—
101(C2×D11)⋊C4C2316yes—
102(C2×D11)⋊C4C2313yes—
103(C2×D11)⋊C4C2313yes—
104(C2×D11)⋊C4C2313yes—
105C4⋊Dic11C2313yes—
106C4⋊Dic11C2313yes—
107C4⋊Dic11C2313yes—
108C4⋊Dic11C2311yescharacteristic
109Dic11⋊C4C2311yescharacteristic
110Dic11⋊C4C2313yes—
111Dic11⋊C4C2316yes—
112Dic11⋊C4C2311yescharacteristic
113Dic11⋊C4C2313yes—
114Dic11⋊C4C2311yescharacteristic
115Dic11⋊C4C2311yescharacteristic
116C4×Dic11C2313yes—
117C4×Dic11C2313yes—
118C4×Dic11C2311yescharacteristic
119C4×Dic11C2313yes—
120#3517—111nomaximal, Sylow
121C23×C11C2413yes—
122C22×D11C2413yes—
123C22×D11C2413yes—
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—46no—
136C22⋊D11—46no—
137C22⋊D11—43no—
138C2×Dic11C2411yescharacteristic
139C2×Dic11C2411yescharacteristic
140C2×Dic11C2413yes—
141C2×Dic11C2413yes—
142C2×Dic11C2411yescharacteristic
143C2×Dic11C2411yescharacteristic
144D44—26no—
145D44—26no—
146D44—43no—
147D44—46no—
148C4×D11—26no—
149C4×D11—26no—
150C4×D11—26no—
151C4×D11—43no—
152C4×D11—46no—
153Dic22—26no—
154#557—111no—
155#553—113no—
156#553—113no—
157#550—111no—
158#550—111no—
159#550—111no—
160#550—113no—
161#547—113no—
162#540—113no—
163#540—113no—
164#532—113no—
165#529—113no—
166#520—111no—
167#520D1111yescharacteristic, complemented
168C4×#41—111no—
169C22×C11—23no—
170C22×C11—23no—
171C22×C11—23no—
172C22×C11C2511yescharacteristic
173C2×D11—23no—
174C2×D11—23no—
175C2×D11—23no—
176C2×D11—23no—
177C2×D11—23no—
178C2×D11—23no—
179C4×C11—21no—
180C4×C11—23no—
181C4×C11—23no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11C2×#4116yes—
185Dic11—21no—
186Dic11—21no—
187Dic11—23no—
188Dic11—23no—
189Dic11—21no—
190Dic11H(5,𝔽2)12yes—
191C2×#41—111no—
192C2×#41—111no—
193C2×#41—116no—
194C2×#41C2×D1111yescharacteristic
195C4⋊Q8—113no—
196#127—113no—
197#127—113no—
198#127—113no—
199#126—113no—
200#126—113no—
201#125—111no—
202#125—113no—
203#125—113no—
204#124—113no—
205#123—116no—
206#123—113no—
207#123—116no—
208#123—113no—
209C22⋊Q8—113no—
210#121—113no—
211#121—113no—
212#121—113no—
213#121—116no—
214#121—113no—
215#121—113no—
216#121—113no—
217#121—113no—
218#121—116no—
219#121—116no—
220C4×Q8—111no—
221C4×Q8—111no—
222C4×Q8—113no—
223C4×Q8C2×D1111yescharacteristic
224C4×Q8C2×D1111yescharacteristic
225C4×D4—113no—
226C4×D4—113no—
227C4×D4—116no—
228C4×D4—113no—
229C4×D4—113no—
230C4×D4—113no—
231C4×D4—113no—
232C4×D4—113no—
233C4×D4C2×D1113yes—
234C4×D4C2×D1113yes—
235#117—113no—
236#117—113no—
237#117C2×D1113yes—
238C2×C4⋊C4—113no—
239C2×C4⋊C4C2×D1113yes—
240C2×C42—113no—
241C2×C11—43no—
242C2×C11C22×#4111yescharacteristic
243C2×C11C2×H(5,𝔽2)11yescharacteristic
244C2×C11#58511yescharacteristic
245D11—43no—
246D11—43no—
247#41—24no—
248#41—224no—
249#41—224no—
250#41—4412no—
251C2×Q8—113no—
252C2×Q8C22×D1111yescharacteristic
253C2×D4—113no—
254C2×D4—116no—
255C2×D4—113no—
256C2×D4—116no—
257C2×D4—113no—
258C2×D4—113no—
259C2×D4—113no—
260C2×D4—116no—
261C2×D4C22×D1113yes—
262C22×C4—113no—
263C22×C4—113no—
264C22×C4—113no—
265C22×C4—113no—
266C22×C4—116no—
267C22×C4C22×D1113yes—
268C22×C4C22×D1116yes—
269C4⋊C4—113no—
270C4⋊C4—113no—
271C4⋊C4—111no—
272C4⋊C4—113no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—116no—
277C4⋊C4—111no—
278C4⋊C4—113no—
279C4⋊C4—113no—
280C4⋊C4C22×D1113yes—
281C4⋊C4C22×D1113yes—
282C4⋊C4C22×D1113yes—
283C4⋊C4C22×D1111yescharacteristic
284C22⋊C4—113no—
285C22⋊C4—113no—
286C22⋊C4—113no—
287C22⋊C4—116no—
288C22⋊C4—113no—
289C22⋊C4—113no—
290C22⋊C4—113no—
291C22⋊C4—113no—
292C22⋊C4—113no—
293C22⋊C4C22×D1113yes—
294C22⋊C4C22×D1113yes—
295C42—111no—
296C42—113no—
297C42—113no—
298C42—113no—
299C42C22×D1113yes—
300C42C22×D1113yes—
301C11#351711yescharacteristic, complemented, Sylow
302C23—113no—
303C23—113no—
304C23C23×D1113yes—
305Q8—226no—
306Q8#433914yescomplemented
307D4—26no—
308D4—226no—
309D4—226no—
310D4—226no—
311D4—446no—
312D4—443no—
313D4—446no—
314D4—446no—
315D4—443no—
316C2×C4—26no—
317C2×C4—46no—
318C2×C4—111no—
319C2×C4—111no—
320C2×C4—111no—
321C2×C4—113no—
322C2×C4—113no—
323C2×C4—111no—
324C2×C4—226no—
325C2×C4—226no—
326C2×C4—226no—
327C2×C4—446no—
328C2×C4—443no—
329C2×C4C23×D1111yescharacteristic
330C2×C4C23×D1113yes—
331C2×C4C23×D1111yescharacteristic
332C2×C4C23×D1113yes—
333C2×C4C23×D1111yescharacteristic
334C2×C4C23×D1113yes—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—223no—
339C22—223no—
340C22—223no—
341C22—223no—
342C22—223no—
343C22—223no—
344C22C24×D1111yescharacteristic
345C4—21no—
346C4—23no—
347C4—23no—
348C4—21no—
349C4—21no—
350C4—112no—
351C4—221no—
352C4—221no—
353C4—223no—
354C4—223no—
355C4—221no—
356C4C2×#433916yes—
357C2—43no—
358C2—443no—
359C2—443no—
360C2C22×#433911yescharacteristic
361C2D11×H(5,𝔽2)11yescharacteristic
362C2#1062345711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#520C2
hypercenter#520D11
hypocenterC11#3517
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. #10623365C2semidirect
4. #10623108C2semidirect
5. #10623105C2semidirect
6. C4×#4343C2semidirect
7. #10623100C2semidirect
8. #10623093C2semidirect
9. #10623089C2semidirect
10. #10623084C2semidirect
11. #10623079C2semidirect
12. #10623066C2semidirect
13. #10623059C2semidirect
14. #10623045C2semidirect
15. #10623038C2semidirect
124. Q8×C11#41semidirect
167. #520D11semidirect
301. C11#3517semidirect
306. 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
#106231082
#106231052
C4×#43432
#106231002
#106230932
#106230892
#106230842
#106230792
#106230662
#106230592
#106230452
#106230382
#351711