Finite Group Databasebeta

← #13082725

Subgroups — #13082725

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
1C4×C11×#41C211yesmaximal, characteristic, complemented
2#10623365C211yesmaximal, characteristic, complemented
3#10623362C211yesmaximal, characteristic, complemented
4#10623107C211yesmaximal, characteristic, complemented
5#10623105C211yesmaximal, characteristic, complemented
6#10623103C211yesmaximal, characteristic, complemented
7#10623100C211yesmaximal, characteristic, complemented
8#10623093C213yesmaximal, complemented
9#10623092C213yesmaximal, complemented
10#10623090C213yesmaximal, complemented
11#10623089C213yesmaximal, complemented
12#10623063C213yesmaximal, complemented
13#10623060C213yesmaximal, complemented
14#10623010C213yesmaximal, complemented
15#10623010C213yesmaximal, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C4×Q8×C11C2211yescharacteristic
21C4×D4×C11C2213yes—
22C4×D4×C11C2213yes—
23C11×#117C2213yes—
24C2×C42×C11C2213yes—
25Q8×Dic11C2211yescharacteristic
26Q8×Dic11C2211yescharacteristic
27#66993C2213yes—
28#66991C2213yes—
29#66991C2213yes—
30#66989C2213yes—
31#66983C2213yes—
32#66983C2213yes—
33#66982C2213yes—
34#66982C2213yes—
35#66982C2216yes—
36C4×C22⋊D11C2213yes—
37C4×C22⋊D11C2213yes—
38C4×C22⋊D11C2216yes—
39#66977C2213yes—
40#66977C2213yes—
41#66950C2213yes—
42#66948C2213yes—
43#66946C2213yes—
44#66945C2213yes—
45C4⋊C4×D11C2213yes—
46#66943C2213yes—
47#66941C2213yes—
48#66940C2213yes—
49#66938C2216yes—
50#66937C2216yes—
51#66936C2216yes—
52#66932C2216yes—
53#66929C2211yescharacteristic
54#66929C2213yes—
55#66928C2213yes—
56#66928C2213yes—
57C4×D44C2213yes—
58C4×D44C2213yes—
59#66925C2216yes—
60#66925C2213yes—
61#66925C2213yes—
62#66923C2213yes—
63#66923C2213yes—
64C4×Dic22C2213yes—
65C4×Dic22C2213yes—
66C11×#41—24no—
67C2×Q8×C11C2311yescharacteristic
68C2×D4×C11C2313yes—
69C22×C4×C11C2313yes—
70C22×C4×C11C2313yes—
71C22×C4×C11C2313yes—
72C2×C22⋊D11C2313yes—
73C2×C22⋊D11C2313yes—
74C2×C22⋊D11C2316yes—
75#4343—24no—
76Q8×D11—24no—
77C2×D44C2313yes—
78C2×D44C2313yes—
79C2×C4×D11C2313yes—
80C2×C4×D11C2313yes—
81C2×C4×D11C2316yes—
82C2×Dic22C2313yes—
83C2×Dic22C2313yes—
84C11×C4⋊C4C2313yes—
85C11×C4⋊C4C2313yes—
86C11×C22⋊C4C2316yes—
87C42×C11C2313yes—
88C42×C11C2313yes—
89C42×C11C2313yes—
90C42×C11C2311yescharacteristic
91C22⋊Dic11C2313yes—
92C22⋊Dic11C2316yes—
93C22⋊Dic11C2313yes—
94(C2×D11)⋊C4C2311yescharacteristic
95(C2×D11)⋊C4C2313yes—
96(C2×D11)⋊C4C2313yes—
97(C2×D11)⋊C4C2316yes—
98(C2×D11)⋊C4C2313yes—
99(C2×D11)⋊C4C2313yes—
100(C2×D11)⋊C4C2311yescharacteristic
101(C2×D11)⋊C4C2313yes—
102(C2×D11)⋊C4C2311yescharacteristic
103C4⋊Dic11C2313yes—
104C4⋊Dic11C2313yes—
105C4⋊Dic11C2313yes—
106C4⋊Dic11C2313yes—
107Dic11⋊C4C2311yescharacteristic
108Dic11⋊C4C2313yes—
109Dic11⋊C4C2313yes—
110Dic11⋊C4C2311yescharacteristic
111Dic11⋊C4C2313yes—
112Dic11⋊C4C2313yes—
113Dic11⋊C4C2316yes—
114Dic11⋊C4C2313yes—
115Dic11⋊C4C2311yescharacteristic
116C4×Dic11C2316yes—
117C4×Dic11C2313yes—
118C4×Dic11C2313yes—
119#3524—111nomaximal, Sylow
120C23×C11C2413yes—
121C22×D11C2411yescharacteristic
122C22×D11C2413yes—
123Q8×C11#4114yes—
124D4×C11—26no—
125C2×C4×C11—26no—
126C2×C4×C11—43no—
127C2×C4×C11—43no—
128C2×C4×C11C2413yes—
129C2×C4×C11C2411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C2×C4×C11C2413yes—
133C2×C4×C11C2413yes—
134C22⋊D11—46no—
135C22⋊D11—43no—
136C22⋊D11—43no—
137C2×Dic11C2411yescharacteristic
138C2×Dic11C2413yes—
139C2×Dic11C2411yescharacteristic
140C2×Dic11C2413yes—
141C2×Dic11C2413yes—
142C2×Dic11C2411yescharacteristic
143D44—26no—
144D44—43no—
145C4×D11—26no—
146C4×D11—26no—
147C4×D11—46no—
148Dic22—26no—
149Dic22—43no—
150#559—113no—
151#557—111no—
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×#41D1111yescharacteristic, complemented
165C22×C11—23no—
166C22×C11—23no—
167C22×C11—23no—
168C22×C11C2511yescharacteristic
169C2×D11—21no—
170C2×D11—23no—
171C2×D11—23no—
172C2×D11—21no—
173C2×D11—23no—
174C2×D11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—23no—
179C4×C11—23no—
180C4×C11C2×#4116yes—
181Dic11—23no—
182Dic11—21no—
183Dic11—21no—
184Dic11—23no—
185Dic11—23no—
186Dic11—21no—
187C2×#41—111no—
188C2×#41C2×D1111yescharacteristic
189C22×Q8—111no—
190C4⋊Q8—113no—
191#127—113no—
192#126—116no—
193#126—111no—
194#126—113no—
195#125—113no—
196#125—113no—
197#125—113no—
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—113no—
214#121—116no—
215C4×Q8—111no—
216C4×Q8—111no—
217C4×Q8—113no—
218C4×Q8—113no—
219C4×Q8—113no—
220C4×Q8C2×D1111yescharacteristic
221C4×Q8C2×D1111yescharacteristic
222C4×D4—113no—
223C4×D4—113no—
224C4×D4—116no—
225C4×D4—113no—
226C4×D4—113no—
227C4×D4—113no—
228C4×D4C2×D1113yes—
229C4×D4C2×D1113yes—
230#117—113no—
231#117—113no—
232#117—113no—
233#117—116no—
234#117C2×D1113yes—
235C2×C4⋊C4—113no—
236C2×C42C2×D1113yes—
237C2×C11—43no—
238C2×C11C22×#4111yescharacteristic
239C2×C11#58511yescharacteristic
240C2×C11#58511yescharacteristic
241D11—41no—
242D11—43no—
243#41—24no—
244#41—224no—
245C2×Q8—113no—
246C2×Q8—113no—
247C2×Q8—224no—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—113no—
250C2×D4—116no—
251C2×D4—113no—
252C2×D4—113no—
253C2×D4—113no—
254C2×D4C22×D1113yes—
255C22×C4—113no—
256C22×C4—113no—
257C22×C4—116no—
258C22×C4C22×D1113yes—
259C22×C4C22×D1113yes—
260C22×C4C22×D1113yes—
261C4⋊C4—113no—
262C4⋊C4—113no—
263C4⋊C4—111no—
264C4⋊C4—113no—
265C4⋊C4—113no—
266C4⋊C4—113no—
267C4⋊C4—113no—
268C4⋊C4—116no—
269C4⋊C4—111no—
270C4⋊C4—113no—
271C4⋊C4—113no—
272C4⋊C4—111no—
273C4⋊C4—113no—
274C4⋊C4C22×D1113yes—
275C4⋊C4C22×D1113yes—
276C22⋊C4—113no—
277C22⋊C4—116no—
278C22⋊C4—113no—
279C22⋊C4—111no—
280C22⋊C4—113no—
281C22⋊C4—113no—
282C22⋊C4—113no—
283C22⋊C4—113no—
284C22⋊C4—116no—
285C22⋊C4—111no—
286C22⋊C4—113no—
287C22⋊C4—111no—
288C22⋊C4C22×D1116yes—
289C42—116no—
290C42—113no—
291C42—113no—
292C42C22×D1111yescharacteristic
293C42C22×D1113yes—
294C42C22×D1113yes—
295C42C22×D1113yes—
296C11#352411yescharacteristic, complemented, Sylow
297C23—111no—
298C23—113no—
299C23C23×D1113yes—
300Q8—226no—
301Q8—443no—
302Q8#433914yes—
303D4—26no—
304D4—226no—
305D4—443no—
306D4—443no—
307D4—443no—
308D4—446no—
309C2×C4—26no—
310C2×C4—43no—
311C2×C4—43no—
312C2×C4—111no—
313C2×C4—113no—
314C2×C4—111no—
315C2×C4—113no—
316C2×C4—113no—
317C2×C4—111no—
318C2×C4—226no—
319C2×C4—226no—
320C2×C4—446no—
321C2×C4C23×D1113yes—
322C2×C4C23×D1111yescharacteristic
323C2×C4C23×D1111yescharacteristic
324C2×C4C23×D1111yescharacteristic
325C2×C4C23×D1113yes—
326C2×C4C23×D1113yes—
327C22—23no—
328C22—23no—
329C22—23no—
330C22—221no—
331C22—223no—
332C22—223no—
333C22—221no—
334C22—223no—
335C22—221no—
336C22C24×D1111yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—23no—
341C4—23no—
342C4—221no—
343C4—223no—
344C4—223no—
345C4—221no—
346C4—223no—
347C4—221no—
348C4C2×#433916yes—
349C2—43no—
350C2—441no—
351C2—443no—
352C2C22×#433911yescharacteristic
353C2#1062345311yescharacteristic
354C2#1062345311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC4×C11×#41C2
hypercenterC4×#41D11
hypocenterC11#3524
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C4×C11×#41C2semidirect
2. #10623365C2semidirect
3. #10623362C2semidirect
4. #10623107C2semidirect
5. #10623105C2semidirect
6. #10623103C2semidirect
7. #10623100C2semidirect
8. #10623093C2semidirect
9. #10623092C2semidirect
10. #10623090C2semidirect
11. #10623089C2semidirect
12. #10623063C2semidirect
13. #10623060C2semidirect
14. #10623010C2semidirect
15. #10623010C2semidirect
164. C4×#41D11semidirect
296. C11#3524semidirect

Maximal subgroups

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

subgroupindex
C4×C11×#412
#106233652
#106233622
#106231072
#106231052
#106231032
#106231002
#106230932
#106230922
#106230902
#106230892
#106230632
#106230602
#106230102
#352411