Finite Group Databasebeta

← #13082441

Subgroups — #13082441

Order 1408.

988 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#557C211yesmaximal, characteristic, complemented
2#10623261C213yesmaximal, complemented
3#10623260C213yesmaximal, complemented
4#10623221C213yesmaximal, complemented
5#10623221C213yesmaximal, complemented
6#10623220C213yesmaximal, complemented
7D11×#125C213yesmaximal, complemented
8#10623110C213yesmaximal, complemented
9#10623109C213yesmaximal, complemented
10#10623105C211yesmaximal, characteristic
11#10623105C211yesmaximal, characteristic
12C4×#4343C211yesmaximal, characteristic
13#10623101C211yesmaximal, characteristic, complemented
14#10623100C211yesmaximal, characteristic, complemented
15#10623100C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C11×C4⋊Q8C2213yes—
18C11×#125C2213yes—
19C11×#125C2213yes—
20C4×Q8×C11C2211yescharacteristic
21C4×Q8×C11C2211yescharacteristic
22C4×Q8×C11C2211yescharacteristic
23C4×Q8×C11C2213yes—
24#66999C2216yes—
25#66999C2213yes—
26Q8×Dic11C2211yescharacteristic
27Q8×Dic11C2211yescharacteristic
28Q8×Dic11C2211yescharacteristic
29#66997C2213yes—
30#66950C2216yes—
31#66950C2213yes—
32#66949C2216yes—
33#66949C2213yes—
34#66949C2213yes—
35#66949C2216yes—
36#66946C2213yes—
37#66946C2213yes—
38#66946C2213yes—
39#66945C2213yes—
40C4⋊C4×D11C2213yes—
41C4⋊C4×D11C2216yes—
42C4⋊C4×D11C2213yes—
43C4⋊C4×D11C2216yes—
44#66943C2213yes—
45#66943C2213yes—
46#66943C2213yes—
47#66943C2213yes—
48#66942C2216yes—
49#66942C2211yescharacteristic
50#66942C2213yes—
51#66941C2213yes—
52#66941C2213yes—
53#66941C2213yes—
54C4×D44C2213yes—
55C4×D44C2213yes—
56C4×D44C2213yes—
57#66925C2213yes—
58#66925C2213yes—
59C42×D11C2213yes—
60#66923C2213yes—
61#66923C2213yes—
62#66922C2213yes—
63C4×Dic22C2213yes—
64C4×Dic22C2213yes—
65C4×Dic22C2213yes—
66C2×Q8×C11C2313yes—
67C2×Q8×C11C2311yescharacteristic
68#4343Q818yescomplemented
69C2×D44C2313yes—
70C2×C4×D11C2313yes—
71C2×C4×D11C2313yes—
72C2×C4×D11C2316yes—
73C2×C4×D11C2316yes—
74C2×C4×D11C2313yes—
75C2×Dic22C2313yes—
76C2×Dic22C2313yes—
77C2×Dic22C2313yes—
78C11×C4⋊C4C2313yes—
79C11×C4⋊C4C2313yes—
80C11×C4⋊C4C2313yes—
81C11×C4⋊C4C2313yes—
82C11×C4⋊C4C2316yes—
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2313yes—
85C42×C11C2313yes—
86C42×C11C2313yes—
87C42×C11C2313yes—
88(C2×D11)⋊C4C2313yes—
89(C2×D11)⋊C4C2313yes—
90(C2×D11)⋊C4C2313yes—
91(C2×D11)⋊C4C2313yes—
92(C2×D11)⋊C4C2316yes—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2313yes—
95C4⋊Dic11C2313yes—
96C4⋊Dic11C2313yes—
97C4⋊Dic11C2313yes—
98C4⋊Dic11C2316yes—
99C4⋊Dic11C2313yes—
100Dic11⋊C4C2311yescharacteristic
101Dic11⋊C4C2311yescharacteristic
102Dic11⋊C4C2313yes—
103Dic11⋊C4C2313yes—
104Dic11⋊C4C2313yes—
105Dic11⋊C4C2313yes—
106Dic11⋊C4C2316yes—
107Dic11⋊C4C2316yes—
108Dic11⋊C4C2311yescharacteristic
109Dic11⋊C4C2311yescharacteristic
110Dic11⋊C4C2313yes—
111Dic11⋊C4C2313yes—
112C4×Dic11C2313yes—
113C4×Dic11C2313yes—
114C4×Dic11C2313yes—
115C4×Dic11C2311yescharacteristic
116C4×Dic11C2313yes—
117#3504—111nomaximal, Sylow
118C22×D11C2413yes—
119Q8×C11—43no—
120Q8×C11C2×Q814yes—
121C2×C4×C11C2411yescharacteristic
122C2×C4×C11C2413yes—
123C2×C4×C11C2411yescharacteristic
124C2×C4×C11C2413yes—
125C2×C4×C11C2413yes—
126C2×C4×C11C2411yescharacteristic
127C2×C4×C11C2413yes—
128C2×Dic11C2411yescharacteristic
129C2×Dic11C2411yescharacteristic
130C2×Dic11C2411yescharacteristic
131C2×Dic11C2413yes—
132C2×Dic11C2413yes—
133C2×Dic11C2413yes—
134C2×Dic11C2411yescharacteristic
135D44C2×Q8112yes—
136C4×D11—43no—
137C4×D11—46no—
138C4×D11—46no—
139C4×D11—43no—
140C4×D11C2×Q8112yes—
141Dic22—43no—
142Dic22—43no—
143Dic22—43no—
144#557—111no—
145#557—111no—
146#557—111no—
147#557D1111yescharacteristic, complemented
148#554—113no—
149#554—113no—
150#554—113no—
151#554—113no—
152#544—113no—
153#544—113no—
154#533—113no—
155C2×#125—113no—
156#520—111no—
157#520—111no—
158C4×#41—111no—
159C22×C11C2511yescharacteristic
160C2×D11—23no—
161C2×D11—23no—
162C2×D11C22×Q816yes—
163C4×C11—21no—
164C4×C11—23no—
165C4×C11—23no—
166C4×C11—21no—
167C4×C11—23no—
168C4×C11—21no—
169C4×C11C22×Q816yes—
170Dic11—21no—
171Dic11—21no—
172Dic11—23no—
173Dic11—23no—
174Dic11—23no—
175Dic11—21no—
176Dic11C22×Q812yes—
177C2×#41—111no—
178C4⋊Q8—113no—
179C4⋊Q8—113no—
180C4⋊Q8—113no—
181C4⋊Q8—113no—
182C4⋊Q8—113no—
183C4⋊Q8C2×D1113yes—
184#125—113no—
185#125—116no—
186#125—113no—
187#125—113no—
188#125—111no—
189#125—113no—
190#125—113no—
191#125—113no—
192#125—113no—
193#125C2×D1113yes—
194#125C2×D1113yes—
195C22⋊Q8—113no—
196C22⋊Q8—116no—
197C22⋊Q8—113no—
198C22⋊Q8—113no—
199C22⋊Q8—113no—
200C22⋊Q8—116no—
201C22⋊Q8—116no—
202C22⋊Q8—116no—
203C4×Q8—111no—
204C4×Q8—111no—
205C4×Q8—111no—
206C4×Q8—113no—
207C4×Q8—113no—
208C4×Q8—113no—
209C4×Q8C2×D1111yescharacteristic
210C4×Q8C2×D1111yescharacteristic
211C4×Q8C2×D1111yescharacteristic
212C4×Q8C2×D1113yes—
213C4×D4—113no—
214C4×D4—113no—
215C4×D4—113no—
216C4×D4—113no—
217C4×D4—113no—
218C4×D4—113no—
219#117—113no—
220#117—113no—
221#117—113no—
222C2×C4⋊C4—113no—
223C2×C4⋊C4—113no—
224C2×C4⋊C4—116no—
225C2×C4⋊C4—116no—
226C2×C42—113no—
227C2×C11C23×Q811yescharacteristic
228C2×C11#58511yescharacteristic
229C2×C11#58511yescharacteristic
230D11—26no—
231#41—118no—
232C2×Q8—113no—
233C2×Q8—113no—
234C2×Q8—113no—
235C2×Q8C22×D1113yes—
236C2×Q8C22×D1111yescharacteristic
237C2×D4—113no—
238C22×C4—113no—
239C22×C4—113no—
240C22×C4—113no—
241C22×C4—116no—
242C22×C4—116no—
243C4⋊C4—113no—
244C4⋊C4—113no—
245C4⋊C4—113no—
246C4⋊C4—113no—
247C4⋊C4—113no—
248C4⋊C4—113no—
249C4⋊C4—113no—
250C4⋊C4—116no—
251C4⋊C4—116no—
252C4⋊C4—116no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—113no—
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—113no—
260C4⋊C4—113no—
261C4⋊C4—113no—
262C4⋊C4C22×D1113yes—
263C4⋊C4C22×D1113yes—
264C4⋊C4C22×D1113yes—
265C4⋊C4C22×D1116yes—
266C4⋊C4C22×D1113yes—
267C4⋊C4C22×D1111yescharacteristic
268C4⋊C4C22×D1113yes—
269C22⋊C4—113no—
270C22⋊C4—113no—
271C22⋊C4—116no—
272C22⋊C4—113no—
273C22⋊C4—113no—
274C42—111no—
275C42—113no—
276C42—113no—
277C42—113no—
278C42—113no—
279C42C22×D1113yes—
280C42C22×D1113yes—
281C42C22×D1113yes—
282C11#350411yescharacteristic, complemented, Sylow
283C23—113no—
284Q8—43no—
285Q8—443no—
286Q8—443no—
287Q8—443no—
288Q8Q8×D1114yes—
289D4—1112no—
290C2×C4—111no—
291C2×C4—1112no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—113no—
296C2×C4—113no—
297C2×C4—113no—
298C2×C4—446no—
299C2×C4—443no—
300C2×C4—443no—
301C2×C4—446no—
302C2×C4C23×D1111yescharacteristic
303C2×C4C23×D1113yes—
304C2×C4C23×D1111yescharacteristic
305C2×C4C23×D1111yescharacteristic
306C2×C4C23×D1113yes—
307C2×C4C23×D1113yes—
308C2×C4C23×D1113yes—
309C22—116no—
310C22—223no—
311C22—223no—
312C22C24×D1111yescharacteristic
313C4—23no—
314C4—23no—
315C4—21no—
316C4—21no—
317C4—23no—
318C4—21no—
319C4—112no—
320C4—221no—
321C4—223no—
322C4—221no—
323C4—223no—
324C4—223no—
325C4—221no—
326C4C2×Q8×D1116yes—
327C2—226no—
328C2C22×Q8×D1111yescharacteristic
329C2#1062345311yescharacteristic
330C2#1062345711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#557C2
prime radicalC2×#4343C22
hypercenter#557D11
hypocenterC11#3504
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. #10623261C2semidirect
3. #10623260C2semidirect
4. #10623221C2semidirect
5. #10623221C2semidirect
6. #10623220C2semidirect
7. D11×#125C2semidirect
8. #10623110C2semidirect
9. #10623109C2semidirect
13. #10623101C2semidirect
14. #10623100C2semidirect
15. #10623100C2semidirect
68. #4343Q8semidirect
147. #557D11semidirect
282. C11#3504semidirect

Maximal subgroups

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

subgroupindex
C11×#5572
#106232612
#106232602
#106232212
#106232202
D11×#1252
#106231102
#106231092
#106231052
C4×#43432
#106231012
#106231002
#350411