Finite Group Databasebeta

← #14644179

Subgroups — #14644179

Order 2816.

524 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077246C211yesmaximal, characteristic
2D11×#432C211yesmaximal, characteristic
3D11×#432C211yesmaximal, characteristic
4C11⋊#1308C211yesmaximal, characteristic, complemented
5C11⋊#1308C211yesmaximal, characteristic, complemented
6C11⋊#1308C211yesmaximal, characteristic, complemented
7C11×#1308C211yesmaximal, characteristic, complemented
8C2×C42×D11C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12#10622539C2211yescharacteristic
13#10622539C2211yescharacteristic
14#10622539C2211yescharacteristic
15#10622450—21no—
16#10622448—21no—
17#10622448—21no—
18#10622446—21no—
19D11×C4⋊C8—21no—
20D11×C4⋊C8—21no—
21#10622339C412yes—
22D11×C22⋊C8C412yes—
23D11×C22⋊C8C412yes—
24#10622332C412yes—
25#10622332C412yes—
26#10622331C412yes—
27#10622320—21no—
28#10622318—21no—
29#10622318—21no—
30#10622318—21no—
31D11×#97—21no—
32D11×#97—21no—
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11C2×C411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×C4×Dic11C2×C411yescharacteristic
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11C2×C411yescharacteristic
40C2×#4313—22no—
41C2×C8×D11—22no—
42C2×C8×D11—22no—
43C42×D11D411yescharacteristic
44C42×D11D411yescharacteristic
45C42×D11D411yescharacteristic
46C42×D11D411yescharacteristic
47C42×D11D411yescharacteristic
48C42×D11D411yescharacteristic
49C42×D11Q811yescharacteristic
50C42×D11Q811yescharacteristic
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8C2×C412yes—
55C11×C22⋊C8C2×C412yes—
56C11×C22⋊C8C2×C412yes—
57C11×#97—21no—
58C11×#97—21no—
59C11×#97—21no—
60C22⋊(C11⋊C8)C2×C412yes—
61C22⋊(C11⋊C8)C2×C412yes—
62C22⋊(C11⋊C8)C2×C412yes—
63(C2×D11)⋊C8—22no—
64(C2×D11)⋊C8—22no—
65(C2×D11)⋊C8—22no—
66#66879—22no—
67#66879—22no—
68Dic11⋊C8—22no—
69Dic11⋊C8—22no—
70Dic11⋊C8—22no—
71C8×Dic11—22no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75#66867—21no—
76#66867—21no—
77#66867—21no—
78#8125—111nomaximal, Sylow
79C23×D11C4211yescharacteristic
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×Dic11C4211yescharacteristic
84C22×Dic11C4211yescharacteristic
85C22×Dic11C4211yescharacteristic
86C2×C4×D11—42no—
87C2×C4×D11—42no—
88C2×C4×D11—42no—
89C2×C4×D11C22⋊C411yescharacteristic
90C2×C4×D11C22⋊C411yescharacteristic
91C2×C4×D11C22⋊C411yescharacteristic
92C2×C4×D11C22⋊C411yescharacteristic
93C2×C4×D11C22⋊C411yescharacteristic
94C2×C4×D11C22⋊C411yescharacteristic
95C2×C4×D11C4⋊C411yescharacteristic
96C2×C4×D11C4⋊C411yescharacteristic
97C2×C4×D11C4⋊C411yescharacteristic
98C2×C4×D11C4⋊C411yescharacteristic
99C2×C4×D11C4⋊C411yescharacteristic
100C2×C4×D11C4⋊C411yescharacteristic
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×Q811yescharacteristic
108C4×Dic11C22⋊C411yescharacteristic
109C4×Dic11C22⋊C411yescharacteristic
110C4×Dic11C22⋊C411yescharacteristic
111C4×Dic11C22⋊C411yescharacteristic
112C4×Dic11C22⋊C411yescharacteristic
113C4×Dic11C22⋊C411yescharacteristic
114C4×Dic11C4⋊C411yescharacteristic
115C4×Dic11C4⋊C411yescharacteristic
116C4×Dic11C4⋊C411yescharacteristic
117C4×Dic11C4⋊C411yescharacteristic
118C4×Dic11C4⋊C411yescharacteristic
119C4×Dic11C4⋊C411yescharacteristic
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123#4313—44no—
124C8×D11—44no—
125C8×D11—44no—
126#2920—111no—
127C2×#432—111no—
128C2×#432—111no—
129#1308—111no—
130#1308—111no—
131#1308—111no—
132#1308D1111yescharacteristic, complemented
133C23×C11C2×C4211yescharacteristic
134C22×D11—22no—
135C22×D11—22no—
136C22×D11—41no—
137C22×D11#9511yescharacteristic
138C22×D11#9511yescharacteristic
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11C2×C22⋊C411yescharacteristic
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C2×C22⋊C411yescharacteristic
145C2×C4×C11C2×C4⋊C411yescharacteristic
146C2×C4×C11C2×C4⋊C411yescharacteristic
147C2×C4×C11C2×C4⋊C411yescharacteristic
148C2×Dic11—22no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11#9511yescharacteristic
152C2×Dic11#9511yescharacteristic
153C2×Dic11#9511yescharacteristic
154C2×Dic11#9511yescharacteristic
155C2×Dic11#9511yescharacteristic
156C2×Dic11#9511yescharacteristic
157C4×D11—22no—
158C4×D11—22no—
159C4×D11—22no—
160C4×D11—22no—
161C4×D11—22no—
162C4×D11—22no—
163C4×D11—41no—
164C4×D11—41no—
165C4×D11—41no—
166C4×D11—41no—
167C4×D11—41no—
168C4×D11—41no—
169C8×C11—42no—
170C8×C11—42no—
171C8×C11—42no—
172C11⋊C8—42no—
173C11⋊C8—42no—
174C11⋊C8—42no—
175C22×C42—111no—
176#432—111no—
177#432—111no—
178#432—111no—
179#432—112no—
180#432—112no—
181#432—221no—
182#432—221no—
183#432—221no—
184#432—221no—
185#432—221no—
186#432C2×D1111yescharacteristic
187#432C2×D1111yescharacteristic
188#432C2×D1111yescharacteristic
189#431—112no—
190#431—221no—
191#423—221no—
192C2×C4⋊C8—221no—
193C2×C4⋊C8—221no—
194#407—112no—
195C2×C22⋊C8—112no—
196C2×C22⋊C8—112no—
197C4×M16—221no—
198C2×#97—221no—
199C2×#97—221no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11C2×#9511yescharacteristic
204C2×D11—21no—
205C2×D11—21no—
206C2×D11—21no—
207C2×D11—21no—
208C2×D11—44no—
209C2×D11#34412yes—
210C2×D11#34412yes—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217Dic11—21no—
218Dic11—21no—
219Dic11—21no—
220Dic11—21no—
221Dic11—21no—
222Dic11#34412yes—
223C23×C4—111no—
224C23×C4—111no—
225C23×C4—111no—
226C2×M16—222no—
227C22×C8—222no—
228C22×C8—222no—
229C2×C42—111no—
230C2×C42—111no—
231C2×C42—111no—
232C2×C42—111no—
233C2×C42—111no—
234C2×C42—111no—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42—111no—
238C2×C42—111no—
239C2×C42—111no—
240C2×C42C22×D1111yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—222no—
245C4⋊C8—222no—
246C4⋊C8—222no—
247C4⋊C8—221no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250C22⋊C8—112no—
251C22⋊C8—112no—
252C22⋊C8—112no—
253C22⋊C8—222no—
254C22⋊C8—222no—
255C22⋊C8—222no—
256C22⋊C8C4×D1112yes—
257C22⋊C8C4×D1112yes—
258C22⋊C8C4×D1112yes—
259#97—21no—
260#97—21no—
261#97—21no—
262#97—222no—
263#97—222no—
264#97—221no—
265#97—221no—
266#97—221no—
267C4×C8—222no—
268C2×C11—41no—
269C2×C11C2×#34411yescharacteristic
270C2×C11C2×#34411yescharacteristic
271C2×C11C2×#34411yescharacteristic
272D11—22no—
273D11—22no—
274C24—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—111no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—111no—
283C22×C4—111no—
284C22×C4—111no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—442no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4C2×C4×D1111yescharacteristic
294C22×C4C2×C4×D1111yescharacteristic
295C22×C4C2×C4×D1111yescharacteristic
296M16—444no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—222no—
301C2×C8—222no—
302C2×C8—222no—
303C2×C8—444no—
304C2×C8—444no—
305C42—111no—
306C42—111no—
307C42—111no—
308C42—111no—
309C42—111no—
310C42—111no—
311C42—111no—
312C42—111no—
313C42—111no—
314C42—111no—
315C42—111no—
316C42—111no—
317C42D4×D1111yescharacteristic
318C42D4×D1111yescharacteristic
319C42D4×D1111yescharacteristic
320C42Q8×D1111yescharacteristic
321C11#812511yescharacteristic, complemented, Sylow
322C23—111no—
323C23—111no—
324C23—222no—
325C23—222no—
326C23—441no—
327C23C42×D1111yescharacteristic
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—111no—
332C2×C4—111no—
333C2×C4—111no—
334C2×C4—111no—
335C2×C4—111no—
336C2×C4—111no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4—222no—
340C2×C4—222no—
341C2×C4—222no—
342C2×C4—222no—
343C2×C4—222no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4C22⋊C4×D1111yescharacteristic
353C2×C4C22⋊C4×D1111yescharacteristic
354C2×C4C22⋊C4×D1111yescharacteristic
355C2×C4C4⋊C4×D1111yescharacteristic
356C2×C4C4⋊C4×D1111yescharacteristic
357C2×C4C4⋊C4×D1111yescharacteristic
358C8—42no—
359C8—42no—
360C8—42no—
361C8—442no—
362C8—442no—
363C8—442no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—112no—
368C22—112no—
369C22—221no—
370C22—221no—
371C22—221no—
372C22—221no—
373C22—444no—
374C22D11×#9511yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—112no—
382C4—221no—
383C4—221no—
384C4—221no—
385C4—221no—
386C4—221no—
387C2—41no—
388C2—222no—
389C2—222no—
390C2D11×#34411yescharacteristic
391C2D11×#34411yescharacteristic
392C2D11×#34411yescharacteristic
subgroupG/H
centerC22D11×#95
commutatorC23×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#1308C2
socleC22×C11C2×#95
prime radicalC23×D11C42
cosocleC2×C42×C11C23
hypercenter#1308D11
hypocenterC11#8125
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1308

Complements

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

NH ≅ G/Ntype
4. C11⋊#1308C2semidirect
5. C11⋊#1308C2semidirect
6. C11⋊#1308C2semidirect
7. C11×#1308C2semidirect
132. #1308D11semidirect
321. C11#8125semidirect

Maximal subgroups

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

subgroupindex
#130772462
D11×#4322
C11⋊#13082
C11×#13082
#812511