Finite Group Databasebeta

← #14644156

Subgroups — #14644156

Order 2816.

522 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077248C211yesmaximal, characteristic
2#13077246C211yesmaximal, characteristic
3D11×#432C211yesmaximal, characteristic
4#13066527C211yesmaximal, characteristic, complemented
5#13066526C211yesmaximal, characteristic, complemented
6#13066526C211yesmaximal, characteristic, complemented
7C11×#1307C211yesmaximal, characteristic, complemented
8C2×C42×D11C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622739C412yes—
13M16×Dic11C412yes—
14#10622539C2211yescharacteristic
15#10622539C2211yescharacteristic
16#10622537C2211yescharacteristic
17#10622450—21no—
18#10622448—21no—
19#10622448—21no—
20#10622448—21no—
21#10622446—21no—
22#10622446—21no—
23#10622446—21no—
24D11×C4⋊C8—21no—
25#10622339C412yes—
26D11×C22⋊C8C412yes—
27#10622332C412yes—
28#10622331C412yes—
29#10622320—21no—
30#10622318—21no—
31#10622318—21no—
32D11×#97—21no—
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11C2×C411yescharacteristic
36C2×C11×M16C2×C412yes—
37C2×C42×C11C2311yescharacteristic
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11C2×C411yescharacteristic
41C2×#4318C2×C412yes—
42C2×#4313—22no—
43C2×C8×D11—22no—
44C42×D11D411yescharacteristic
45C42×D11D411yescharacteristic
46C42×D11D411yescharacteristic
47C42×D11D411yescharacteristic
48C42×D11D411yescharacteristic
49C42×D11D411yescharacteristic
50C42×D11Q811yescharacteristic
51C42×D11Q811yescharacteristic
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C22⋊C8C2×C412yes—
57C11×C22⋊C8C2×C412yes—
58C11×#97—21no—
59C11×#97—21no—
60C22⋊(C11⋊C8)C2×C412yes—
61C22⋊(C11⋊C8)C2×C412yes—
62(C2×D11)⋊C8—22no—
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—
70C8×Dic11—22no—
71C8×Dic11—22no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76#66867—21no—
77#66867—21no—
78#8118—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—41no—
87C2×C4×D11—41no—
88C2×C4×D11—42no—
89C2×C4×D11—42no—
90C2×C4×D11C22⋊C411yescharacteristic
91C2×C4×D11C22⋊C411yescharacteristic
92C2×C4×D11C22⋊C411yescharacteristic
93C2×C4×D11C22⋊C411yescharacteristic
94C2×C4×D11C22⋊C411yescharacteristic
95C2×C4×D11C22⋊C411yescharacteristic
96C2×C4×D11C4⋊C411yescharacteristic
97C2×C4×D11C4⋊C411yescharacteristic
98C2×C4×D11C4⋊C411yescharacteristic
99C2×C4×D11C4⋊C411yescharacteristic
100C2×C4×D11C4⋊C411yescharacteristic
101C2×C4×D11C4⋊C411yescharacteristic
102C11×M16—42no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×Q811yescharacteristic
110C4×Dic11C22⋊C411yescharacteristic
111C4×Dic11C22⋊C411yescharacteristic
112C4×Dic11C22⋊C411yescharacteristic
113C4×Dic11C22⋊C411yescharacteristic
114C4×Dic11C22⋊C411yescharacteristic
115C4×Dic11C22⋊C411yescharacteristic
116C4×Dic11C4⋊C411yescharacteristic
117C4×Dic11C4⋊C411yescharacteristic
118C4×Dic11C4⋊C411yescharacteristic
119C4×Dic11C4⋊C411yescharacteristic
120C4×Dic11C4⋊C411yescharacteristic
121C4×Dic11C4⋊C411yescharacteristic
122#4318—42no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126#4313—44no—
127C8×D11—44no—
128#2920—111no—
129#2920—111no—
130C2×#432—111no—
131#1307—111no—
132#1307—111no—
133#1307—111no—
134#1307D1111yescharacteristic, complemented
135C23×C11C2×C4211yescharacteristic
136C22×D11—22no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11#9511yescharacteristic
140C22×D11#9511yescharacteristic
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11C2×C22⋊C411yescharacteristic
146C2×C4×C11C2×C22⋊C411yescharacteristic
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11C2×C4⋊C411yescharacteristic
149C2×C4×C11C2×C4⋊C411yescharacteristic
150C2×C4×C11C2×C4⋊C411yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11#9511yescharacteristic
155C2×Dic11#9511yescharacteristic
156C2×Dic11#9511yescharacteristic
157C2×Dic11#9511yescharacteristic
158C2×Dic11#9511yescharacteristic
159C2×Dic11#9511yescharacteristic
160C4×D11—22no—
161C4×D11—22no—
162C4×D11—21no—
163C4×D11—21no—
164C4×D11—21no—
165C4×D11—21no—
166C4×D11—22no—
167C4×D11—22no—
168C4×D11—41no—
169C4×D11—41no—
170C4×D11—41no—
171C4×D11—41no—
172C4×D11—41no—
173C4×D11—41no—
174C8×C11—42no—
175C8×C11—42no—
176C8×C11—42no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180C22×C42—111no—
181#432—111no—
182#432—111no—
183#432—112no—
184#432—221no—
185#432—221no—
186#432—221no—
187#432—221no—
188#432—221no—
189#432C2×D1111yescharacteristic
190#432C2×D1111yescharacteristic
191#431—112no—
192#431—221no—
193#431—221no—
194#431—221no—
195#423—111no—
196#423—221no—
197#423C2×D1111yescharacteristic
198C2×C4⋊C8—221no—
199#407—112no—
200#407—112no—
201C2×C22⋊C8—112no—
202C4×M16—112no—
203C4×M16—221no—
204C2×#97—221no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11C2×#9511yescharacteristic
209C2×D11—21no—
210C2×D11—21no—
211C2×D11—21no—
212C2×D11—21no—
213C2×D11—21no—
214C2×D11—44no—
215C2×D11#34412yes—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11#41311yescharacteristic
222C4×C11#41311yescharacteristic
223Dic11—21no—
224Dic11—21no—
225Dic11—21no—
226Dic11—21no—
227Dic11—21no—
228Dic11#34412yes—
229C23×C4—111no—
230C23×C4—111no—
231C23×C4—111no—
232C2×M16—112no—
233C2×M16—222no—
234C2×M16C4×D1112yes—
235C22×C8—222no—
236C2×C42—111no—
237C2×C42—111no—
238C2×C42—111no—
239C2×C42—111no—
240C2×C42—111no—
241C2×C42—111no—
242C2×C42—111no—
243C2×C42—111no—
244C2×C42—111no—
245C2×C42—111no—
246C2×C42—111no—
247C2×C42C22×D1111yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—222no—
253C4⋊C8—222no—
254C4⋊C8—221no—
255C4⋊C8—221no—
256C4⋊C8—221no—
257C4⋊C8—221no—
258C22⋊C8—112no—
259C22⋊C8—112no—
260C22⋊C8—222no—
261C22⋊C8—222no—
262C22⋊C8—222no—
263C22⋊C8—222no—
264C22⋊C8C4×D1112yes—
265C22⋊C8C4×D1112yes—
266#97—21no—
267#97—21no—
268#97—222no—
269#97—222no—
270#97—221no—
271#97—221no—
272C4×C8—222no—
273C4×C8—222no—
274C2×C11—41no—
275C2×C11#174211yescharacteristic
276C2×C11C2×#34411yescharacteristic
277C2×C11C2×#34411yescharacteristic
278D11—22no—
279D11—41no—
280C24—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—111no—
291C22×C4—111no—
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—111no—
295C22×C4—111no—
296C22×C4—441no—
297C22×C4—441no—
298C22×C4—442no—
299C22×C4—442no—
300C22×C4C2×C4×D1111yescharacteristic
301C22×C4C2×C4×D1111yescharacteristic
302C22×C4C2×C4×D1111yescharacteristic
303M16—42no—
304M16—444no—
305M16—442no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—222no—
310C2×C8—222no—
311C2×C8—222no—
312C2×C8—444no—
313C42—111no—
314C42—111no—
315C42—111no—
316C42—111no—
317C42—111no—
318C42—111no—
319C42—111no—
320C42—111no—
321C42—111no—
322C42—111no—
323C42—111no—
324C42—111no—
325C42D4×D1111yescharacteristic
326C42D4×D1111yescharacteristic
327C42D4×D1111yescharacteristic
328C42Q8×D1111yescharacteristic
329C11#811811yescharacteristic, complemented, Sylow
330C23—111no—
331C23—111no—
332C23—222no—
333C23—441no—
334C23—441no—
335C23C42×D1111yescharacteristic
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—111no—
341C2×C4—111no—
342C2×C4—111no—
343C2×C4—111no—
344C2×C4—111no—
345C2×C4—111no—
346C2×C4—222no—
347C2×C4—222no—
348C2×C4—222no—
349C2×C4—222no—
350C2×C4—222no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4C22⋊C4×D1111yescharacteristic
364C2×C4C22⋊C4×D1111yescharacteristic
365C2×C4C22⋊C4×D1111yescharacteristic
366C2×C4C4⋊C4×D1111yescharacteristic
367C2×C4C4⋊C4×D1111yescharacteristic
368C2×C4C4⋊C4×D1111yescharacteristic
369C8—42no—
370C8—42no—
371C8—42no—
372C8—442no—
373C8—442no—
374C8—442no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—112no—
379C22—221no—
380C22—221no—
381C22—221no—
382C22—221no—
383C22—221no—
384C22—444no—
385C22D11×#9511yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—112no—
392C4—221no—
393C4—221no—
394C4—221no—
395C4—221no—
396C4—221no—
397C4#1062235811yescharacteristic
398C4#1062236411yescharacteristic
399C2—41no—
400C2—222no—
401C2—441no—
402C2#1306835311yescharacteristic
403C2D11×#34411yescharacteristic
404C2D11×#34411yescharacteristic
subgroupG/H
centerC22D11×#95
commutatorC23×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#1307C2
socleC22×C11C2×#95
prime radicalC23×D11C42
cosocleC2×C42×C11C23
hypercenter#1307D11
hypocenterC11#8118
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
4. #13066527C2semidirect
5. #13066526C2semidirect
6. #13066526C2semidirect
7. C11×#1307C2semidirect
134. #1307D11semidirect
329. C11#8118semidirect

Maximal subgroups

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

subgroupindex
#130772482
#130772462
D11×#4322
#130665272
#130665262
C11×#13072
#811811