Finite Group Databasebeta

← #13082706

Subgroups — #13082706

Order 1408.

992 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#519C211yesmaximal, characteristic, complemented
2Q8×C22⋊D11C211yesmaximal, characteristic, complemented
3Q8×C22⋊D11C211yesmaximal, characteristic, complemented
4#10623114C213yesmaximal, complemented
5#10623112C213yesmaximal, complemented
6#10623109C213yesmaximal, complemented
7Q8×D44C211yesmaximal, characteristic, complemented
8#10623103C211yesmaximal, characteristic, complemented
9C4×Q8×D11C211yesmaximal, characteristic, complemented
10#10623100C211yesmaximal, characteristic, complemented
11#10623098C213yesmaximal, complemented
12#10623064C213yesmaximal, complemented
13#10623060C213yesmaximal, complemented
14#10623059C213yesmaximal
15#10623049C213yesmaximal, complemented
16C22×Q8×C11C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C4×Q8×C11C2213yes—
20C4×Q8×C11C2211yescharacteristic
21C4×Q8×C11C2211yescharacteristic
22C4×Q8×C11C2213yes—
23C11×#117C2213yes—
24C11×#117C2213yes—
25#66999C2213yes—
26#66999C2213yes—
27Q8×Dic11C2211yescharacteristic
28Q8×Dic11C2211yescharacteristic
29#66997C2213yes—
30#66997C2213yes—
31C4×C22⋊D11C2213yes—
32C4×C22⋊D11C2213yes—
33#66977C2213yes—
34#66977C2213yes—
35#66951C2213yes—
36#66950C2213yes—
37#66950C2213yes—
38#66949C2213yes—
39#66947C2213yes—
40#66945C2213yes—
41C4⋊C4×D11C2213yes—
42#66943C2213yes—
43#66942C2216yes—
44#66942C2216yes—
45#66942C2213yes—
46#66941C2213yes—
47#66940C2213yes—
48#66940C2213yes—
49#66938C2213yes—
50#66937C2211yescharacteristic
51#66936C2213yes—
52#66932C2213yes—
53#66932C2216yes—
54#66929C2216yes—
55C4×D44C2213yes—
56#66925C2213yes—
57#66925C2216yes—
58C42×D11C2213yes—
59#66923C2213yes—
60#66923C2216yes—
61#66922C2213yes—
62C4×Dic22C2213yes—
63C4×Dic22C2213yes—
64C4×Dic22C2213yes—
65C4×Dic22C2216yes—
66C2×Q8×C11—24no—
67C2×Q8×C11C2313yes—
68C2×Q8×C11C2311yescharacteristic
69C22×C4×C11C2313yes—
70C2×C22⋊D11C2311yescharacteristic
71C2×C22⋊D11C2311yescharacteristic
72Q8×D11—24no—
73Q8×D11—24no—
74C2×D44C2311yescharacteristic
75C2×C4×D11C2311yescharacteristic
76C2×C4×D11C2313yes—
77C2×C4×D11C2313yes—
78C2×C4×D11C2313yes—
79C2×Dic22C2313yes—
80C2×Dic22C2313yes—
81C2×Dic22C2313yes—
82C11×C4⋊C4C2313yes—
83C11×C4⋊C4C2313yes—
84C11×C4⋊C4C2313yes—
85C11×C4⋊C4C2313yes—
86C11×C22⋊C4C2311yescharacteristic
87C11×C22⋊C4C2313yes—
88C42×C11C2313yes—
89C42×C11C2313yes—
90C42×C11C2316yes—
91C22⋊Dic11C2313yes—
92C22⋊Dic11C2313yes—
93(C2×D11)⋊C4C2311yescharacteristic
94(C2×D11)⋊C4C2313yes—
95(C2×D11)⋊C4C2313yes—
96(C2×D11)⋊C4C2313yes—
97(C2×D11)⋊C4C2313yes—
98(C2×D11)⋊C4C2313yes—
99C4⋊Dic11C2316yes—
100C4⋊Dic11C2313yes—
101C4⋊Dic11C2313yes—
102C4⋊Dic11C2313yes—
103C4⋊Dic11C2313yes—
104Dic11⋊C4C2311yescharacteristic
105Dic11⋊C4C2313yes—
106Dic11⋊C4C2313yes—
107Dic11⋊C4C2313yes—
108Dic11⋊C4C2316yes—
109Dic11⋊C4C2316yes—
110Dic11⋊C4C2313yes—
111Dic11⋊C4C2313yes—
112Dic11⋊C4C2316yes—
113Dic11⋊C4C2316yes—
114C4×Dic11C2313yes—
115C4×Dic11C2313yes—
116C4×Dic11C2316yes—
117C4×Dic11C2313yes—
118C4×Dic11C2313yes—
119#3523—111nomaximal, Sylow
120C23×C11C2411yescharacteristic
121C22×D11C2411yescharacteristic
122C22×D11C2411yescharacteristic
123Q8×C11—26no—
124Q8×C11#4114yes—
125C2×C4×C11—26no—
126C2×C4×C11C2411yescharacteristic
127C2×C4×C11C2413yes—
128C2×C4×C11C2413yes—
129C2×C4×C11C2411yescharacteristic
130C2×C4×C11C2413yes—
131C2×C4×C11C2413yes—
132C22⋊D11—22no—
133C22⋊D11—22no—
134C2×Dic11C2411yescharacteristic
135C2×Dic11C2413yes—
136C2×Dic11C2413yes—
137C2×Dic11C2413yes—
138C2×Dic11C2413yes—
139C2×Dic11C2411yescharacteristic
140D44—22no—
141C4×D11—26no—
142C4×D11—26no—
143C4×D11—26no—
144C4×D11—22no—
145Dic22—26no—
146Dic22—26no—
147Dic22—26no—
148#557—113no—
149#557—111no—
150#556—113no—
151#552—113no—
152#552—113no—
153D4×Q8—111no—
154D4×Q8—111no—
155D4×Q8—111no—
156#541—113no—
157#541—113no—
158#533—113no—
159#529—113no—
160#519—111no—
161#519D1111yescharacteristic, complemented
162C2×C4×Q8—111no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11C2511yescharacteristic
167C2×D11—21no—
168C2×D11—21no—
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—21no—
172C2×D112−1+412yes—
173C4×C11—23no—
174C4×C11—23no—
175C4×C11—23no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11C2×#4116yes—
179Dic11—23no—
180Dic11—23no—
181Dic11—23no—
182Dic11—23no—
183Dic11—21no—
184Dic112−1+412yes—
185C22×Q8—111no—
186C22×Q8—111no—
187C22×Q8C2×D1111yescharacteristic
188C4⋊Q8—113no—
189C4⋊Q8—113no—
190C4⋊Q8—113no—
191C4⋊Q8—113no—
192#126—113no—
193#126—113no—
194#126—116no—
195#126—116no—
196#125—113no—
197#125—116no—
198#125—116no—
199#125—113no—
200#125—116no—
201#125—113no—
202#124—113no—
203#123—113no—
204#123—113no—
205C22⋊Q8—113no—
206C22⋊Q8—113no—
207C22⋊Q8—113no—
208C22⋊Q8—113no—
209C22⋊Q8—113no—
210C22⋊Q8—113no—
211C22⋊Q8—113no—
212#121—111no—
213C4×Q8—111no—
214C4×Q8—111no—
215C4×Q8—113no—
216C4×Q8—113no—
217C4×Q8—113no—
218C4×Q8—113no—
219C4×Q8—113no—
220C4×Q8—116no—
221C4×Q8C2×D1111yescharacteristic
222C4×Q8C2×D1113yes—
223C4×Q8C2×D1111yescharacteristic
224C4×Q8C2×D1113yes—
225C4×D4—113no—
226C4×D4—113no—
227C4×D4—113no—
228#117—113no—
229#117—113no—
230#117—116no—
231#117C2×D1113yes—
232#117C2×D1113yes—
233C2×C4⋊C4—113no—
234C2×C42—113no—
235C2×C11—41no—
236C2×C11C22×#4111yescharacteristic
237C2×C11C2×2−1+411yescharacteristic
238C2×C11C2×2−1+411yescharacteristic
239D11—22no—
240D11—41no—
241C2×Q8—24no—
242C2×Q8—113no—
243C2×Q8—113no—
244C2×Q8—113no—
245C2×Q8—224no—
246C2×Q8—224no—
247C2×Q8C22×D1113yes—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—111no—
250C2×D4—111no—
251C2×D4—111no—
252C22×C4—111no—
253C22×C4—113no—
254C22×C4—113no—
255C22×C4—113no—
256C22×C4C22×D1113yes—
257C4⋊C4—113no—
258C4⋊C4—116no—
259C4⋊C4—113no—
260C4⋊C4—113no—
261C4⋊C4—113no—
262C4⋊C4—116no—
263C4⋊C4—116no—
264C4⋊C4—113no—
265C4⋊C4—113no—
266C4⋊C4—113no—
267C4⋊C4—111no—
268C4⋊C4—116no—
269C4⋊C4—116no—
270C4⋊C4—113no—
271C4⋊C4—113no—
272C4⋊C4C22×D1113yes—
273C4⋊C4C22×D1113yes—
274C4⋊C4C22×D1113yes—
275C4⋊C4C22×D1113yes—
276C22⋊C4—113no—
277C22⋊C4—113no—
278C22⋊C4—111no—
279C22⋊C4—113no—
280C22⋊C4—113no—
281C22⋊C4—113no—
282C22⋊C4—113no—
283C22⋊C4—113no—
284C22⋊C4C22×D1111yescharacteristic
285C22⋊C4C22×D1113yes—
286C42—113no—
287C42—113no—
288C42—113no—
289C42—116no—
290C42—113no—
291C42C22×D1113yes—
292C42C22×D1116yes—
293C42C22×D1113yes—
294C11#352311yescharacteristic, complemented, Sylow
295C23—111no—
296C23—111no—
297C23C23×D1111yescharacteristic
298Q8—26no—
299Q8—226no—
300Q8—226no—
301Q8—226no—
302Q8#433914yes—
303D4—222no—
304D4—222no—
305D4—222no—
306C2×C4—26no—
307C2×C4—111no—
308C2×C4—113no—
309C2×C4—111no—
310C2×C4—113no—
311C2×C4—113no—
312C2×C4—113no—
313C2×C4—222no—
314C2×C4—226no—
315C2×C4—226no—
316C2×C4—226no—
317C2×C4C23×D1113yes—
318C2×C4C23×D1111yescharacteristic
319C2×C4C23×D1113yes—
320C2×C4C23×D1111yescharacteristic
321C2×C4C23×D1113yes—
322C2×C4C23×D1113yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—112no—
327C22—221no—
328C22—221no—
329C22—221no—
330C22—221no—
331C22—221no—
332C22C24×D1111yescharacteristic
333C4—23no—
334C4—21no—
335C4—23no—
336C4—21no—
337C4—23no—
338C4—112no—
339C4—223no—
340C4—223no—
341C4—223no—
342C4—221no—
343C4—223no—
344C4C2×#433916yes—
345C2—41no—
346C2—222no—
347C2—441no—
348C2C22×#433911yescharacteristic
349C2D11×2−1+411yescharacteristic
350C2D11×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#519C2
prime radical#66937C22
hypercenter#519D11
hypocenterC11#3523
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C11×#519C2semidirect
2. Q8×C22⋊D11C2semidirect
3. Q8×C22⋊D11C2semidirect
4. #10623114C2semidirect
5. #10623112C2semidirect
6. #10623109C2semidirect
7. Q8×D44C2semidirect
8. #10623103C2semidirect
9. C4×Q8×D11C2semidirect
10. #10623100C2semidirect
11. #10623098C2semidirect
12. #10623064C2semidirect
13. #10623060C2semidirect
15. #10623049C2semidirect
161. #519D11semidirect
294. C11#3523semidirect

Maximal subgroups

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

subgroupindex
C11×#5192
Q8×C22⋊D112
#106231142
#106231122
#106231092
Q8×D442
#106231032
C4×Q8×D112
#106231002
#106230982
#106230642
#106230602
#106230592
#106230492
#352311