Finite Group Databasebeta

← #13082423

Subgroups — #13082423

Order 1408.

964 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#557C211yesmaximal, characteristic, complemented
2#10623260C213yesmaximal
3#10623253C213yesmaximal, complemented
4#10623220C213yesmaximal
5#10623219C213yesmaximal
6#10623216C213yesmaximal, complemented
7#10623216C213yesmaximal, complemented
8#10623109C213yesmaximal
9#10623103C211yesmaximal, characteristic
10#10623103C211yesmaximal, characteristic
11C4×Q8×D11C211yesmaximal, characteristic
12#10623100C211yesmaximal, characteristic, complemented
13#10623100C211yesmaximal, characteristic, complemented
14#10623098C213yesmaximal, complemented
15Q8×Dic22C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C11×C4⋊Q8C2213yes—
18C11×#125C2213yes—
19C11×#125C2213yes—
20C4×Q8×C11C2211yescharacteristic
21C4×Q8×C11C2213yes—
22C4×Q8×C11C2211yescharacteristic
23C4×Q8×C11C2211yescharacteristic
24#66999C2213yes—
25Q8×Dic11C2211yescharacteristic
26Q8×Dic11C2211yescharacteristic
27Q8×Dic11C2211yescharacteristic
28#66997C2213yes—
29#66997C2216yes—
30#66950C2213yes—
31#66949C2216yes—
32#66949C2211yescharacteristic
33#66949C2213yes—
34#66945C2213yes—
35#66945C2213yes—
36C4⋊C4×D11C2213yes—
37#66943C2213yes—
38#66943C2213yes—
39#66942C2216yes—
40#66942C2213yes—
41#66942C2216yes—
42#66942C2213yes—
43#66941C2213yes—
44#66941C2213yes—
45#66941C2216yes—
46#66941C2213yes—
47#66941C2213yes—
48#66941C2213yes—
49#66940C2213yes—
50#66940C2213yes—
51#66940C2216yes—
52#66940C2216yes—
53#66940C2213yes—
54#66925C2213yes—
55#66925C2213yes—
56C42×D11C2213yes—
57#66923C2213yes—
58#66923C2213yes—
59#66922C2213yes—
60C4×Dic22C2213yes—
61C4×Dic22C2213yes—
62C4×Dic22C2213yes—
63C4×Dic22C2213yes—
64C4×Dic22C2213yes—
65C4×Dic22C2213yes—
66C2×Q8×C11C2313yes—
67C2×Q8×C11C2311yescharacteristic
68Q8×D11Q818yescomplemented
69C2×C4×D11C2311yescharacteristic
70C2×C4×D11C2313yes—
71C2×C4×D11C2313yes—
72C2×Dic22C2311yescharacteristic
73C2×Dic22C2313yes—
74C2×Dic22C2313yes—
75C2×Dic22C2316yes—
76C2×Dic22C2313yes—
77C11×C4⋊C4C2313yes—
78C11×C4⋊C4C2313yes—
79C11×C4⋊C4C2316yes—
80C11×C4⋊C4C2313yes—
81C11×C4⋊C4C2313yes—
82C11×C4⋊C4C2313yes—
83C11×C4⋊C4C2311yescharacteristic
84C42×C11C2313yes—
85C42×C11C2313yes—
86C42×C11C2313yes—
87(C2×D11)⋊C4C2311yescharacteristic
88(C2×D11)⋊C4C2311yescharacteristic
89(C2×D11)⋊C4C2313yes—
90(C2×D11)⋊C4C2313yes—
91C4⋊Dic11C2313yes—
92C4⋊Dic11C2313yes—
93C4⋊Dic11C2313yes—
94C4⋊Dic11C2313yes—
95C4⋊Dic11C2313yes—
96C4⋊Dic11C2313yes—
97Dic11⋊C4C2311yescharacteristic
98Dic11⋊C4C2311yescharacteristic
99Dic11⋊C4C2313yes—
100Dic11⋊C4C2313yes—
101Dic11⋊C4C2313yes—
102Dic11⋊C4C2313yes—
103Dic11⋊C4C2313yes—
104Dic11⋊C4C2316yes—
105Dic11⋊C4C2313yes—
106Dic11⋊C4C2316yes—
107Dic11⋊C4C2316yes—
108Dic11⋊C4C2313yes—
109Dic11⋊C4C2313yes—
110C4×Dic11C2313yes—
111C4×Dic11C2313yes—
112C4×Dic11C2313yes—
113C4×Dic11C2313yes—
114C4×Dic11C2316yes—
115C4×Dic11C2316yes—
116C4×Dic11C2313yes—
117#3502—111nomaximal, Sylow
118C22×D11C2411yescharacteristic
119Q8×C11—43no—
120Q8×C11C2×Q814yes—
121C2×C4×C11C2411yescharacteristic
122C2×C4×C11C2413yes—
123C2×C4×C11C2413yes—
124C2×C4×C11C2413yes—
125C2×C4×C11C2411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C2×C4×C11C2413yes—
128C2×Dic11C2411yescharacteristic
129C2×Dic11C2413yes—
130C2×Dic11C2411yescharacteristic
131C2×Dic11C2413yes—
132C2×Dic11C2413yes—
133C2×Dic11C2413yes—
134C2×Dic11C2411yescharacteristic
135C4×D11—22no—
136C4×D11—43no—
137C4×D11C2×Q8112yes—
138Dic22—22no—
139Dic22—26no—
140Dic22—43no—
141Dic22—46no—
142Dic22C2×Q8112yes—
143Q82—113no—
144Q82—111no—
145#557—113no—
146#557—113no—
147#557—113no—
148#557—111no—
149#557—111no—
150#557D1111yescharacteristic, complemented
151#544—113no—
152#544—113no—
153#533—113no—
154#533—113no—
155#519—111no—
156#519—111no—
157C2×C4×Q8—111no—
158C22×C11C2511yescharacteristic
159C2×D11—21no—
160C2×D11—21no—
161C2×D11C22×Q812yes—
162C4×C11—23no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—23no—
167C4×C11—23no—
168C4×C11C22×Q816yes—
169Dic11—21no—
170Dic11—23no—
171Dic11—21no—
172Dic11—23no—
173Dic11—23no—
174Dic11C22×Q816yes—
175Dic112−1+412yes—
176C22×Q8—111no—
177C4⋊Q8—113no—
178C4⋊Q8—116no—
179C4⋊Q8—113no—
180C4⋊Q8—113no—
181C4⋊Q8—113no—
182C4⋊Q8—116no—
183C4⋊Q8—113no—
184C4⋊Q8—113no—
185C4⋊Q8—113no—
186C4⋊Q8C2×D1113yes—
187#125—113no—
188#125—113no—
189#125—116no—
190#125—116no—
191#125—113no—
192#125—113no—
193#125—113no—
194#125—113no—
195#125C2×D1113yes—
196#125C2×D1113yes—
197C22⋊Q8—113no—
198C22⋊Q8—113no—
199C22⋊Q8—111no—
200C22⋊Q8—116no—
201C22⋊Q8—113no—
202C4×Q8—111no—
203C4×Q8—111no—
204C4×Q8—111no—
205C4×Q8—113no—
206C4×Q8—113no—
207C4×Q8—113no—
208C4×Q8—116no—
209C4×Q8—116no—
210C4×Q8—113no—
211C4×Q8—113no—
212C4×Q8—113no—
213C4×Q8—113no—
214C4×Q8—113no—
215C4×Q8—113no—
216C4×Q8C2×D1111yescharacteristic
217C4×Q8C2×D1111yescharacteristic
218C4×Q8C2×D1111yescharacteristic
219C4×Q8C2×D1113yes—
220#117—113no—
221#117—113no—
222#117—113no—
223#117—113no—
224C2×C4⋊C4—113no—
225C2×C42—113no—
226C2×C11C23×Q811yescharacteristic
227C2×C11C2×2−1+411yescharacteristic
228C2×C11#58511yescharacteristic
229D11—22no—
230C2×Q8—118no—
231C2×Q8—113no—
232C2×Q8—113no—
233C2×Q8—111no—
234C2×Q8—113no—
235C2×Q8—116no—
236C2×Q8C22×D1113yes—
237C2×Q8C22×D1111yescharacteristic
238C22×C4—113no—
239C22×C4—111no—
240C22×C4—113no—
241C4⋊C4—116no—
242C4⋊C4—113no—
243C4⋊C4—113no—
244C4⋊C4—113no—
245C4⋊C4—113no—
246C4⋊C4—113no—
247C4⋊C4—113no—
248C4⋊C4—113no—
249C4⋊C4—113no—
250C4⋊C4—111no—
251C4⋊C4—113no—
252C4⋊C4—111no—
253C4⋊C4—116no—
254C4⋊C4—113no—
255C4⋊C4—116no—
256C4⋊C4—113no—
257C4⋊C4—113no—
258C4⋊C4—113no—
259C4⋊C4—113no—
260C4⋊C4C22×D1113yes—
261C4⋊C4C22×D1113yes—
262C4⋊C4C22×D1113yes—
263C4⋊C4C22×D1113yes—
264C4⋊C4C22×D1116yes—
265C4⋊C4C22×D1111yescharacteristic
266C4⋊C4C22×D1113yes—
267C22⋊C4—113no—
268C22⋊C4—111no—
269C22⋊C4—113no—
270C22⋊C4—111no—
271C42—113no—
272C42—113no—
273C42—113no—
274C42—116no—
275C42—116no—
276C42—113no—
277C42—113no—
278C42C22×D1113yes—
279C42C22×D1113yes—
280C42C22×D1113yes—
281C11#350211yescharacteristic, complemented, Sylow
282C23—111no—
283Q8—43no—
284Q8—1112no—
285Q8—226no—
286Q8—222no—
287Q8—443no—
288Q8—446no—
289Q8Q8×D1114yes—
290C2×C4—113no—
291C2×C4—111no—
292C2×C4—1112no—
293C2×C4—111no—
294C2×C4—113no—
295C2×C4—111no—
296C2×C4—113no—
297C2×C4—113no—
298C2×C4—222no—
299C2×C4—443no—
300C2×C4C23×D1111yescharacteristic
301C2×C4C23×D1113yes—
302C2×C4C23×D1113yes—
303C2×C4C23×D1113yes—
304C2×C4C23×D1111yescharacteristic
305C2×C4C23×D1111yescharacteristic
306C2×C4C23×D1113yes—
307C22—112no—
308C22—221no—
309C22—221no—
310C22C24×D1111yescharacteristic
311C4—23no—
312C4—21no—
313C4—23no—
314C4—21no—
315C4—23no—
316C4—21no—
317C4—116no—
318C4—112no—
319C4—223no—
320C4—221no—
321C4—223no—
322C4—221no—
323C4—223no—
324C4C2×Q8×D1116yes—
325C2—222no—
326C2C22×Q8×D1111yescharacteristic
327C2#1062345311yescharacteristic
328C2D11×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#557C2
prime radicalC22×D11C24
hypercenter#557D11
hypocenterC11#3502
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C11×#557C2semidirect
3. #10623253C2semidirect
6. #10623216C2semidirect
7. #10623216C2semidirect
12. #10623100C2semidirect
13. #10623100C2semidirect
14. #10623098C2semidirect
15. Q8×Dic22C2semidirect
68. Q8×D11Q8semidirect
150. #557D11semidirect
281. C11#3502semidirect

Maximal subgroups

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

subgroupindex
C11×#5572
#106232602
#106232532
#106232202
#106232192
#106232162
#106231092
#106231032
C4×Q8×D112
#106231002
#106230982
Q8×Dic222
#350211