Finite Group Databasebeta

← #13082602

Subgroups — #13082602

Order 1408.

1012 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#548C211yesmaximal, characteristic, complemented
2#10623362C211yesmaximal, characteristic, complemented
3#10623358C211yesmaximal, characteristic, complemented
4Q8×C22⋊D11C211yesmaximal, characteristic, complemented
5#10623343C211yesmaximal, characteristic, complemented
6#10623211C213yesmaximal, complemented
7#10623202C213yesmaximal, complemented
8#10623166C213yesmaximal, complemented
9#10623156C213yesmaximal, complemented
10#10623145C213yesmaximal, complemented
11#10623134C213yesmaximal, complemented
12C4×Q8×D11C211yesmaximal, characteristic, complemented
13#10623100C211yesmaximal, characteristic, complemented
14#10623088C213yesmaximal, complemented
15#10623072C213yesmaximal, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C11×#124C2213yes—
20C11×C22⋊Q8C2213yes—
21C11×#121C2213yes—
22C4×Q8×C11C2211yescharacteristic
23C4×D4×C11C2213yes—
24#66999C2213yes—
25Q8×Dic11C2211yescharacteristic
26Q8×Dic11C2211yescharacteristic
27Q8×Dic11C2213yes—
28Q8×Dic11C2213yes—
29Q8×Dic11C2211yescharacteristic
30#66997C2213yes—
31#66991C2213yes—
32#66991C2213yes—
33#66989C2213yes—
34#66989C2213yes—
35#66988C2216yes—
36D4×Dic11C2213yes—
37D4×Dic11C2213yes—
38C4×C22⋊D11C2213yes—
39C4×C22⋊D11C2213yes—
40#66979C2213yes—
41#66979C2213yes—
42#66979C2213yes—
43C2×C4⋊Dic11C2213yes—
44#66977C2213yes—
45#66977C2213yes—
46#66950C2213yes—
47C4⋊C4×D11C2213yes—
48#66943C2213yes—
49#66943C2213yes—
50#66942C2216yes—
51#66941C2213yes—
52#66940C2213yes—
53#66936C2211yescharacteristic
54#66936C2213yes—
55(C22⋊D11)⋊C4C2216yes—
56#66932C2213yes—
57#66932C2213yes—
58#66932C2216yes—
59#66932C2216yes—
60#66931C2216yes—
61#66930C2216yes—
62C42×D11C2213yes—
63#66923C2213yes—
64C4×Dic22C2213yes—
65C4×Dic22C2213yes—
66C11×#41—24no—
67C2×Q8×C11—24no—
68C2×Q8×C11C2313yes—
69C2×Q8×C11C2311yescharacteristic
70C2×D4×C11C2313yes—
71C2×D4×C11C2313yes—
72C22×C4×C11C2313yes—
73C22×C4×C11C2313yes—
74C2×C22⋊D11C2313yes—
75C2×C22⋊D11C2311yescharacteristic
76C22×Dic11C2316yes—
77Q8×D11—24no—
78C2×C4×D11C2311yescharacteristic
79C2×C4×D11C2313yes—
80C2×C4×D11C2313yes—
81C2×Dic22C2313yes—
82C2×Dic22C2313yes—
83C11×C4⋊C4C2313yes—
84C11×C4⋊C4C2313yes—
85C11×C22⋊C4C2313yes—
86C11×C22⋊C4C2316yes—
87C11×C22⋊C4C2311yescharacteristic
88C42×C11C2313yes—
89C22⋊Dic11C2316yes—
90C22⋊Dic11C2313yes—
91C22⋊Dic11C2313yes—
92C22⋊Dic11C2313yes—
93C22⋊Dic11C2313yes—
94C22⋊Dic11C2313yes—
95C22⋊Dic11C2311yescharacteristic
96(C2×D11)⋊C4C2313yes—
97(C2×D11)⋊C4C2311yescharacteristic
98C4⋊Dic11C2313yes—
99C4⋊Dic11C2313yes—
100C4⋊Dic11C2313yes—
101C4⋊Dic11C2313yes—
102C4⋊Dic11C2313yes—
103C4⋊Dic11C2313yes—
104C4⋊Dic11C2313yes—
105C4⋊Dic11C2311yescharacteristic
106Dic11⋊C4C2311yescharacteristic
107Dic11⋊C4C2313yes—
108Dic11⋊C4C2316yes—
109Dic11⋊C4C2316yes—
110Dic11⋊C4C2316yes—
111Dic11⋊C4C2313yes—
112Dic11⋊C4C2313yes—
113C4×Dic11C2313yes—
114C4×Dic11C2313yes—
115C4×Dic11C2313yes—
116C4×Dic11C2313yes—
117C4×Dic11C2313yes—
118C4×Dic11C2316yes—
119#3516—111nomaximal, Sylow
120C23×C11C2411yescharacteristic
121C23×C11C2413yes—
122C22×D11C2411yescharacteristic
123Q8×C11—26no—
124Q8×C11#4114yes—
125D4×C11—26no—
126D4×C11—43no—
127C2×C4×C11—26no—
128C2×C4×C11—26no—
129C2×C4×C11C2411yescharacteristic
130C2×C4×C11C2413yes—
131C2×C4×C11C2413yes—
132C2×C4×C11C2411yescharacteristic
133C2×C4×C11C2413yes—
134C22⋊D11—26no—
135C22⋊D11—22no—
136C2×Dic11—46no—
137C2×Dic11C2411yescharacteristic
138C2×Dic11C2413yes—
139C2×Dic11C2413yes—
140C2×Dic11C2411yescharacteristic
141C2×Dic11C2411yescharacteristic
142C2×Dic11C2413yes—
143C2×Dic11C2413yes—
144C4×D11—22no—
145C4×D11—26no—
146C4×D11—43no—
147Dic22—26no—
148Dic22—43no—
149#557—111no—
150#556—113no—
151#554—113no—
152#553—113no—
153#552—113no—
154D4×Q8—111no—
155#548—111no—
156#548D1111yescharacteristic, complemented
157#542—113no—
158#541—113no—
159#529—113no—
160#529—113no—
161#520—111no—
162#519—111no—
163C2×C4×Q8—111no—
164C22×C11—21no—
165C22×C11—23no—
166C22×C11—21no—
167C22×C11—23no—
168C22×C11—21no—
169C22×C11—23no—
170C22×C11C2511yescharacteristic
171C2×D11—21no—
172C2×D11—21no—
173C2×D112−1+412yes—
174C4×C11—21no—
175C4×C11—23no—
176C4×C11—21no—
177C4×C11—23no—
178C4×C11C2×#4116yes—
179Dic11—23no—
180Dic11—21no—
181Dic11—23no—
182Dic11—21no—
183Dic11—21no—
184Dic11—23no—
185Dic11—23no—
186C2×#41C2×D1111yescharacteristic
187C22×Q8—111no—
188C22×Q8C2×D1111yescharacteristic
189C4⋊Q8—113no—
190C4⋊Q8—113no—
191#126—116no—
192#126—113no—
193#126—113no—
194#126—116no—
195#125—113no—
196#125—116no—
197#125—113no—
198#125—113no—
199#124—113no—
200#124—113no—
201#124C2×D1113yes—
202#123—116no—
203#123—111no—
204#123—113no—
205C22⋊Q8—113no—
206C22⋊Q8—113no—
207C22⋊Q8—113no—
208C22⋊Q8—113no—
209C22⋊Q8—116no—
210C22⋊Q8C2×D1113yes—
211#121—113no—
212#121—113no—
213#121C2×D1113yes—
214C4×Q8—111no—
215C4×Q8—113no—
216C4×Q8—111no—
217C4×Q8—113no—
218C4×Q8—111no—
219C4×Q8—113no—
220C4×Q8—113no—
221C4×Q8—113no—
222C4×Q8C2×D1111yescharacteristic
223C4×D4—113no—
224C4×D4—113no—
225C4×D4—113no—
226C4×D4—113no—
227C4×D4—116no—
228C4×D4C2×D1113yes—
229#117—113no—
230#117—113no—
231#117—113no—
232#117—116no—
233C2×C4⋊C4—113no—
234C2×C4⋊C4—113no—
235C2×C42—113no—
236C2×C11—41no—
237C2×C11—43no—
238C2×C11C22×#4111yescharacteristic
239C2×C11C2×2−1+411yescharacteristic
240C2×C11#58511yescharacteristic
241D11—22no—
242#41—24no—
243C2×Q8—24no—
244C2×Q8—113no—
245C2×Q8—113no—
246C2×Q8—224no—
247C2×Q8C22×D1113yes—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—111no—
250C2×D4—113no—
251C2×D4C22×D1113yes—
252C2×D4C22×D1113yes—
253C22×C4—116no—
254C22×C4—111no—
255C22×C4—113no—
256C22×C4—113no—
257C22×C4C22×D1113yes—
258C22×C4C22×D1113yes—
259C4⋊C4—113no—
260C4⋊C4—113no—
261C4⋊C4—113no—
262C4⋊C4—116no—
263C4⋊C4—111no—
264C4⋊C4—113no—
265C4⋊C4—113no—
266C4⋊C4—113no—
267C4⋊C4—113no—
268C4⋊C4—116no—
269C4⋊C4—113no—
270C4⋊C4—116no—
271C4⋊C4—113no—
272C4⋊C4—111no—
273C4⋊C4—113no—
274C4⋊C4C22×D1113yes—
275C4⋊C4C22×D1113yes—
276C22⋊C4—113no—
277C22⋊C4—111no—
278C22⋊C4—113no—
279C22⋊C4—113no—
280C22⋊C4—116no—
281C22⋊C4—113no—
282C22⋊C4—113no—
283C22⋊C4—111no—
284C22⋊C4—113no—
285C22⋊C4C22×D1113yes—
286C22⋊C4C22×D1116yes—
287C22⋊C4C22×D1111yescharacteristic
288C42—113no—
289C42—113no—
290C42—113no—
291C42—116no—
292C42—113no—
293C42—113no—
294C42C22×D1113yes—
295C11#351611yescharacteristic, complemented, Sylow
296C23—111no—
297C23C23×D1111yescharacteristic
298C23C23×D1113yes—
299Q8—26no—
300Q8—226no—
301Q8—443no—
302Q8#434114yes—
303D4—26no—
304D4—43no—
305D4—222no—
306D4—226no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—111no—
310C2×C4—113no—
311C2×C4—111no—
312C2×C4—113no—
313C2×C4—111no—
314C2×C4—113no—
315C2×C4—113no—
316C2×C4—222no—
317C2×C4—226no—
318C2×C4—443no—
319C2×C4—446no—
320C2×C4C23×D1111yescharacteristic
321C2×C4C23×D1113yes—
322C2×C4C23×D1113yes—
323C2×C4C23×D1111yescharacteristic
324C2×C4C23×D1113yes—
325C22—21no—
326C22—23no—
327C22—23no—
328C22—21no—
329C22—21no—
330C22—23no—
331C22—112no—
332C22—221no—
333C22—221no—
334C22C24×D1111yescharacteristic
335C4—21no—
336C4—23no—
337C4—23no—
338C4—21no—
339C4—223no—
340C4—223no—
341C4—223no—
342C4—221no—
343C4—221no—
344C4—223no—
345C4—221no—
346C4C2×#434116yes—
347C2—41no—
348C2—43no—
349C2—222no—
350C2C22×#434111yescharacteristic
351C2#1062345311yescharacteristic
352C2D11×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#548C2
hypercenter#548D11
hypocenterC11#3516
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C11×#548C2semidirect
2. #10623362C2semidirect
3. #10623358C2semidirect
4. Q8×C22⋊D11C2semidirect
5. #10623343C2semidirect
6. #10623211C2semidirect
7. #10623202C2semidirect
8. #10623166C2semidirect
9. #10623156C2semidirect
10. #10623145C2semidirect
11. #10623134C2semidirect
12. C4×Q8×D11C2semidirect
13. #10623100C2semidirect
14. #10623088C2semidirect
15. #10623072C2semidirect
156. #548D11semidirect
295. C11#3516semidirect

Maximal subgroups

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

subgroupindex
C11×#5482
#106233622
#106233582
Q8×C22⋊D112
#106233432
#106232112
#106232022
#106231662
#106231562
#106231452
#106231342
C4×Q8×D112
#106231002
#106230882
#106230722
#351611