Finite Group Databasebeta

← #13082728

Subgroups — #13082728

Order 1408.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#557C211yesmaximal, characteristic, complemented
2#10623265C213yesmaximal, complemented
3#10623264C213yesmaximal, complemented
4#10623229C213yesmaximal, complemented
5#10623226C213yesmaximal, complemented
6#10623225C213yesmaximal, complemented
7#10623222C213yesmaximal, complemented
8#10623116C213yesmaximal, complemented
9#10623111C213yesmaximal, complemented
10#10623108C211yesmaximal, characteristic, complemented
11#10623107C211yesmaximal, characteristic, complemented
12#10623107C211yesmaximal, characteristic, complemented
13#10623105C211yesmaximal, characteristic, complemented
14C4×#4343C211yesmaximal, characteristic, complemented
15#10623103C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C11×C4⋊Q8C2213yes—
20C11×#125C2213yes—
21C11×#125C2213yes—
22C4×Q8×C11C2211yescharacteristic
23C4×Q8×C11C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×Q8×C11C2213yes—
26#67000C2216yes—
27#67000C2213yes—
28#66999C2213yes—
29Q8×Dic11C2211yescharacteristic
30#66951C2216yes—
31#66951C2211yescharacteristic
32#66951C2213yes—
33#66950C2213yes—
34#66950C2213yes—
35#66948C2213yes—
36#66948C2213yes—
37#66948C2213yes—
38#66948C2216yes—
39#66948C2213yes—
40#66948C2213yes—
41#66947C2216yes—
42#66947C2213yes—
43#66947C2213yes—
44#66947C2216yes—
45#66946C2213yes—
46#66946C2213yes—
47#66946C2216yes—
48#66945C2213yes—
49#66945C2213yes—
50#66945C2216yes—
51C4⋊C4×D11C2213yes—
52#66943C2213yes—
53#66940C2213yes—
54#66928C2213yes—
55#66928C2213yes—
56#66927C2213yes—
57C4×D44C2213yes—
58C4×D44C2213yes—
59C4×D44C2213yes—
60C4×D44C2213yes—
61C4×D44C2213yes—
62#66925C2213yes—
63#66925C2213yes—
64C42×D11C2213yes—
65C4×Dic22C2213yes—
66C2×Q8×C11C2313yes—
67C2×Q8×C11C2311yescharacteristic
68#4343—24no—
69#4343—24no—
70Q8×D11—24no—
71C2×D44C2313yes—
72C2×D44C2313yes—
73C2×D44C2313yes—
74C2×D44C2313yes—
75C2×D44C2313yes—
76C2×D44C2316yes—
77C2×C4×D11C2313yes—
78C2×C4×D11C2313yes—
79C2×C4×D11C2313yes—
80C2×C4×D11C2313yes—
81C2×C4×D11C2313yes—
82C2×C4×D11C2316yes—
83C2×Dic22C2313yes—
84C11×C4⋊C4C2313yes—
85C11×C4⋊C4C2313yes—
86C11×C4⋊C4C2313yes—
87C11×C4⋊C4C2313yes—
88C11×C4⋊C4C2316yes—
89C11×C4⋊C4C2313yes—
90C11×C4⋊C4C2311yescharacteristic
91C42×C11C2313yes—
92C42×C11C2313yes—
93C42×C11C2313yes—
94(C2×D11)⋊C4C2311yescharacteristic
95(C2×D11)⋊C4C2313yes—
96(C2×D11)⋊C4C2313yes—
97(C2×D11)⋊C4C2313yes—
98(C2×D11)⋊C4C2311yescharacteristic
99(C2×D11)⋊C4C2311yescharacteristic
100(C2×D11)⋊C4C2313yes—
101(C2×D11)⋊C4C2313yes—
102(C2×D11)⋊C4C2313yes—
103(C2×D11)⋊C4C2316yes—
104(C2×D11)⋊C4C2313yes—
105(C2×D11)⋊C4C2316yes—
106(C2×D11)⋊C4C2316yes—
107C4⋊Dic11C2313yes—
108C4⋊Dic11C2311yescharacteristic
109C4⋊Dic11C2313yes—
110C4⋊Dic11C2313yes—
111Dic11⋊C4C2313yes—
112Dic11⋊C4C2311yescharacteristic
113Dic11⋊C4C2313yes—
114Dic11⋊C4C2313yes—
115C4×Dic11C2316yes—
116C4×Dic11C2311yescharacteristic
117C4×Dic11C2313yes—
118C4×Dic11C2313yes—
119#3524—111nomaximal, Sylow
120C22×D11C2411yescharacteristic
121C22×D11C2413yes—
122C22×D11C2413yes—
123Q8×C11—43no—
124Q8×C11#4114yes—
125C2×C4×C11C2413yes—
126C2×C4×C11C2413yes—
127C2×C4×C11C2411yescharacteristic
128C2×C4×C11C2411yescharacteristic
129C2×C4×C11C2413yes—
130C2×C4×C11C2411yescharacteristic
131C2×C4×C11C2413yes—
132C2×Dic11C2411yescharacteristic
133C2×Dic11C2413yes—
134C2×Dic11C2411yescharacteristic
135C2×Dic11C2413yes—
136C2×Dic11C2411yescharacteristic
137D44—26no—
138D44—26no—
139D44—43no—
140D44—46no—
141D44—43no—
142D44—43no—
143C4×D11—26no—
144C4×D11—26no—
145C4×D11—26no—
146C4×D11—43no—
147C4×D11—43no—
148C4×D11—46no—
149Dic22—26no—
150#559—113no—
151#557D1111yescharacteristic, complemented
152#555—113no—
153#553—113no—
154#552—113no—
155#550—111no—
156#548—111no—
157#548—111no—
158#542—113no—
159#540—113no—
160#529—113no—
161#529—113no—
162#520—111no—
163#519—111no—
164C4×#41—111no—
165C22×C11C2511yescharacteristic
166C2×D11—21no—
167C2×D11—23no—
168C2×D11—23no—
169C2×D11—23no—
170C2×D11—23no—
171C2×D11—23no—
172C2×D11—21no—
173C2×D11—23no—
174C2×D11—21no—
175C4×C11—21no—
176C4×C11—23no—
177C4×C11—23no—
178C4×C11—21no—
179C4×C11—23no—
180C4×C11—21no—
181C4×C11C2×#4116yes—
182Dic11—23no—
183Dic11—21no—
184Dic11—21no—
185Dic11—21no—
186Dic11—23no—
187C2×#41—111no—
188C2×#41—111no—
189C22×Q8—111no—
190C4⋊Q8C2×D1113yes—
191#127—113no—
192#126—111no—
193#126—113no—
194#126—116no—
195#125—113no—
196#125C2×D1113yes—
197#125C2×D1113yes—
198#124—113no—
199#124—116no—
200#124—113no—
201#124—113no—
202#123—116no—
203#123—113no—
204#123—113no—
205#123—116no—
206C22⋊Q8—113no—
207C22⋊Q8—113no—
208C22⋊Q8—113no—
209#121—113no—
210#121—113no—
211#121—113no—
212#121—113no—
213#121—116no—
214#121—113no—
215C4×Q8—111no—
216C4×Q8—113no—
217C4×Q8—113no—
218C4×Q8C2×D1111yescharacteristic
219C4×Q8C2×D1111yescharacteristic
220C4×Q8C2×D1111yescharacteristic
221C4×Q8C2×D1113yes—
222C4×D4—113no—
223C4×D4—113no—
224C4×D4—116no—
225C4×D4—113no—
226C4×D4—113no—
227C4×D4—113no—
228C4×D4—113no—
229C4×D4—113no—
230#117—113no—
231#117—113no—
232#117—116no—
233#117—113no—
234#117—113no—
235C2×C4⋊C4—113no—
236C2×C42—113no—
237C2×C11C22×#4111yescharacteristic
238C2×C11#58511yescharacteristic
239C2×C11#58511yescharacteristic
240D11—41no—
241D11—43no—
242D11—43no—
243#41—224no—
244#41—224no—
245C2×Q8—113no—
246C2×Q8—224no—
247C2×Q8C22×D1113yes—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—113no—
250C2×D4—113no—
251C2×D4—113no—
252C2×D4—113no—
253C2×D4—116no—
254C2×D4—113no—
255C22×C4—113no—
256C22×C4—113no—
257C22×C4—113no—
258C22×C4—113no—
259C22×C4—113no—
260C22×C4—116no—
261C4⋊C4—113no—
262C4⋊C4—113no—
263C4⋊C4—111no—
264C4⋊C4—113no—
265C4⋊C4—113no—
266C4⋊C4—113no—
267C4⋊C4—111no—
268C4⋊C4—113no—
269C4⋊C4C22×D1113yes—
270C4⋊C4C22×D1113yes—
271C4⋊C4C22×D1113yes—
272C4⋊C4C22×D1116yes—
273C4⋊C4C22×D1113yes—
274C4⋊C4C22×D1111yescharacteristic
275C4⋊C4C22×D1113yes—
276C22⋊C4—111no—
277C22⋊C4—113no—
278C22⋊C4—113no—
279C22⋊C4—113no—
280C22⋊C4—116no—
281C22⋊C4—113no—
282C22⋊C4—116no—
283C22⋊C4—111no—
284C22⋊C4—113no—
285C22⋊C4—111no—
286C22⋊C4—113no—
287C22⋊C4—116no—
288C22⋊C4—113no—
289C42—111no—
290C42—113no—
291C42—113no—
292C42—116no—
293C42C22×D1113yes—
294C42C22×D1113yes—
295C42C22×D1113yes—
296C11#352411yescharacteristic, complemented, Sylow
297C23—111no—
298C23—113no—
299C23—113no—
300Q8—43no—
301Q8—226no—
302Q8#434314yes—
303D4—226no—
304D4—226no—
305D4—443no—
306D4—446no—
307D4—443no—
308D4—443no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—113no—
312C2×C4—113no—
313C2×C4—111no—
314C2×C4—226no—
315C2×C4—226no—
316C2×C4—226no—
317C2×C4—443no—
318C2×C4—443no—
319C2×C4—446no—
320C2×C4C23×D1113yes—
321C2×C4C23×D1111yescharacteristic
322C2×C4C23×D1113yes—
323C2×C4C23×D1111yescharacteristic
324C2×C4C23×D1111yescharacteristic
325C2×C4C23×D1113yes—
326C2×C4C23×D1113yes—
327C22—221no—
328C22—223no—
329C22—223no—
330C22—223no—
331C22—221no—
332C22—223no—
333C22—223no—
334C22—223no—
335C22—221no—
336C22C24×D1111yescharacteristic
337C4—23no—
338C4—23no—
339C4—21no—
340C4—21no—
341C4—23no—
342C4—21no—
343C4—221no—
344C4—221no—
345C4—223no—
346C4—221no—
347C4—223no—
348C4C2×#434316yes—
349C2—441no—
350C2—443no—
351C2—443no—
352C2C22×#434311yescharacteristic
353C2#1062345311yescharacteristic
354C2#1062345711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#557C2
hypercenter#557D11
hypocenterC11#3524
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C11×#557C2semidirect
2. #10623265C2semidirect
3. #10623264C2semidirect
4. #10623229C2semidirect
5. #10623226C2semidirect
6. #10623225C2semidirect
7. #10623222C2semidirect
8. #10623116C2semidirect
9. #10623111C2semidirect
10. #10623108C2semidirect
11. #10623107C2semidirect
12. #10623107C2semidirect
13. #10623105C2semidirect
14. C4×#4343C2semidirect
15. #10623103C2semidirect
151. #557D11semidirect
296. C11#3524semidirect

Maximal subgroups

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

subgroupindex
C11×#5572
#106232652
#106232642
#106232292
#106232262
#106232252
#106232222
#106231162
#106231112
#106231082
#106231072
#106231052
C4×#43432
#106231032
#352411