Finite Group Databasebeta

← #14722342

Subgroups — #14722342

Order 2816.

1230 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623247C211yesmaximal, characteristic
2#13077246C212yesmaximal, complemented
3#13067348C214yesmaximal, complemented
4#13067341C212yesmaximal, complemented
5#13067330C211yesmaximal, characteristic, complemented
6#13067275C214yesmaximal, complemented
7C11×#1555C211yesmaximal, characteristic, complemented
8C22×#4341C412yes—
9C2×C11×#127C2211yescharacteristic
10C2×#66991—22no—
11C2×#66989C412yes—
12C2×D4×Dic11—22no—
13#10623247—22no—
14#10623247—22no—
15#10623247C412yes—
16#10623247C412yes—
17#10623247C2212yes—
18#10623247C2212yes—
19C2×C42×D11C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C11×#432C2212yes—
22#10622539C2212yes—
23#10622450C2214yescomplemented
24#10622446C2214yescomplemented
25#10622339—22no—
26#10622331—22no—
27#10622320—22no—
28#10622318—22no—
29C11×#331C2214yescomplemented
30#10622182C2214yescomplemented
31#10622119C2218yescomplemented
32C22×D4×C11—22no—
33C22×D4×C11C2×C412yes—
34C22×C22⋊D11—22no—
35C23×Dic11—22no—
36C2×#4341—22no—
37C2×#4341—22no—
38C2×#4341—48no—
39C2×#4341C2×C414yes—
40C2×#4341C2×C414yes—
41C22×C4×D11C2×C411yescharacteristic
42C22×C4×D11D412yes—
43C22×Dic22C2×C412yes—
44C11×#127—22no—
45C11×#127C2×C412yes—
46C11×#127C2312yes—
47C2×C42×C11C2311yescharacteristic
48C2×C22⋊Dic11—24no—
49#66991—24no—
50#66991—24no—
51#66991—24no—
52#66991—24no—
53#66989—24no—
54#66989C2×C414yes—
55#66989C2×C414yes—
56D4×Dic11—24no—
57D4×Dic11—24no—
58D4×Dic11—24no—
59D4×Dic11—24no—
60C2×C4⋊Dic11—22no—
61C2×C4×Dic11C2×C411yescharacteristic
62C2×C4×Dic11D412yes—
63C2×#4313—24no—
64C42×D11C2×C411yescharacteristic
65C42×D11C2×C411yescharacteristic
66C42×D11D412yes—
67C42×D11D412yes—
68C42×D11C2311yescharacteristic
69C42×D11C2311yescharacteristic
70#66922—22no—
71#66922C2×C412yes—
72#66922C2312yes—
73C11×C4⋊C8C2314yes—
74C11×C22⋊C8—22no—
75C11×#97—22no—
76C22⋊(C11⋊C8)—22no—
77(C2×D11)⋊C8—24no—
78Dic11⋊C8—24no—
79C8×Dic11—24no—
80C4⋊(C11⋊C8)C2314yes—
81#66867—22no—
82#17738—111nomaximal, Sylow
83C24×C11—22no—
84C23×D11C22⋊C411yescharacteristic
85C2×D4×C11—24no—
86C2×D4×C11—22no—
87C2×D4×C11—24no—
88C2×D4×C11—48no—
89C2×D4×C11—44no—
90C2×D4×C11C22×C414yes—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D412yes—
93C2×C22⋊D11—24no—
94C2×C22⋊D11—24no—
95C2×C22⋊D11—48no—
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11—22no—
99C22×Dic11—48no—
100C22×Dic11C22⋊C412yes—
101C22×Dic11C22⋊C411yescharacteristic
102#4341—48no—
103#4341—48no—
104#4341—48no—
105#4341—48no—
106C2×C4×D11—24no—
107C2×C4×D11—44no—
108C2×C4×D11C22⋊C411yescharacteristic
109C2×C4×D11C22⋊C411yescharacteristic
110C2×C4×D11C22⋊C412yes—
111C2×C4×D11C22⋊C412yes—
112C2×C4×D11C22×C411yescharacteristic
113C2×C4×D11C22×C411yescharacteristic
114C2×C4×D11C2×D412yes—
115C2×C4×D11C2×D412yes—
116C2×Dic22—22no—
117C2×Dic22—44no—
118C2×Dic22C22×C414yes—
119C2×C8×C11—24no—
120C42×C11C22×C411yescharacteristic
121C42×C11C2×D412yes—
122C42×C11C2411yescharacteristic
123C22⋊Dic11—28no—
124C22⋊Dic11—28no—
125C4⋊Dic11—24no—
126C4⋊Dic11—24no—
127C4×Dic11C22⋊C412yes—
128C4×Dic11C22⋊C412yes—
129C4×Dic11C22⋊C412yes—
130C4×Dic11C22×C411yescharacteristic
131C4×Dic11C22×C411yescharacteristic
132C4×Dic11C2×D412yes—
133C4×Dic11C2×D412yes—
134C2×C11⋊C8—24no—
135#4313—48no—
136C2×#532—111no—
137#2920—112no—
138#1560—114no—
139#1558—112no—
140#1555—111no—
141#1555D1111yescharacteristic, complemented
142#1543—114no—
143C23×C11—24no—
144C23×C11—48no—
145C23×C11—44no—
146C23×C11C2×C22⋊C411yescharacteristic
147C22×D11—22no—
148C22×D11—42no—
149C22×D11C2×C22⋊C411yescharacteristic
150C22×D11C2×C22⋊C411yescharacteristic
151D4×C11—44no—
152D4×C11—44no—
153D4×C11—48no—
154D4×C11—48no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11C2×C22⋊C412yes—
158C2×C4×C11C2×C22⋊C411yescharacteristic
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C22×D412yes—
161C22⋊D11—48no—
162C22⋊D11—48no—
163C2×Dic11—24no—
164C2×Dic11—42no—
165C2×Dic11—44no—
166C2×Dic11—48no—
167C2×Dic11—48no—
168C2×Dic11#10014yes—
169C2×Dic11C2×C22⋊C412yes—
170C2×Dic11C2×C22⋊C412yes—
171C2×Dic11C2×C22⋊C411yescharacteristic
172C2×Dic11C2×C22⋊C411yescharacteristic
173C4×D11—24no—
174C4×D11—24no—
175C4×D11—22no—
176C4×D11—22no—
177C4×D11—22no—
178C4×D11—22no—
179C4×D11—42no—
180C4×D11—42no—
181Dic22—44no—
182Dic22—44no—
183C8×C11—44no—
184C11⋊C8—44no—
185C22×#41—112no—
186#532—112no—
187#532—112no—
188#532—112no—
189#532—112no—
190#532—222no—
191#532—222no—
192C2×C4⋊Q8—111no—
193C2×#127C2×D1111yescharacteristic
194C2×#124—112no—
195C2×#121—222no—
196C2×C4×D4—222no—
197C22×C42—111no—
198#432—112no—
199#432—222no—
200#432C2×D1112yes—
201#431—114no—
202#431—222no—
203#423—114no—
204#407—222no—
205C4×M16—222no—
206#333—118no—
207#331—114no—
208#331C2×D1114yescomplemented
209C22×C11—22no—
210C22×C11—44no—
211C22×C11—48no—
212C22×C11—88no—
213C22×C11C2×#10012yes—
214C22×C11C22×C22⋊C411yescharacteristic
215C2×D11—21no—
216C2×D11—21no—
217C2×D11—22no—
218C2×D11—22no—
219C2×D11—44no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—22no—
223C4×C11#57514yes—
224Dic11—22no—
225Dic11—22no—
226Dic11—44no—
227Dic11C2×#10012yes—
228Dic11C2×#10012yes—
229C2×#41—114no—
230C2×#41—114no—
231C2×#41—222no—
232C2×#41—222no—
233C2×#41—448no—
234C22×Q8—112no—
235C22×D4—22no—
236C22×D4—222no—
237C22×D4C4×D1112yes—
238C23×C4—111no—
239C23×C4—112no—
240C23×C4—222no—
241C2×M16—224no—
242C4⋊Q8—112no—
243C4⋊Q8—112no—
244C4⋊Q8—222no—
245#127—22no—
246#127C4×D1112yes—
247#127C22×D1112yes—
248#124—114no—
249#124—114no—
250#124—224no—
251#121—224no—
252#121—224no—
253#121—224no—
254#121—224no—
255C4×D4—224no—
256C4×D4—224no—
257C4×D4—224no—
258C4×D4—224no—
259C2×C4⋊C4—222no—
260C2×C22⋊C4—224no—
261C2×C42—111no—
262C2×C42—112no—
263C2×C42—111no—
264C2×C42—111no—
265C2×C42—112no—
266C2×C42—112no—
267C2×C42—111no—
268C2×C42—111no—
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—114no—
271C4⋊C8—224no—
272C4⋊C8C22×D1114yes—
273C22⋊C8—22no—
274C22⋊C8—224no—
275C22⋊C8—222no—
276#97—22no—
277#97—222no—
278C4×C8—224no—
279C2×C11—22no—
280C2×C11—84no—
281C2×C11C22×#10011yescharacteristic
282C2×C11#289612yes—
283D11—41no—
284D11—41no—
285C24—22no—
286C24—111no—
287#41—448no—
288#41—448no—
289#41—448no—
290#41—448no—
291C2×Q8—114no—
292C2×Q8—222no—
293C2×Q8—444no—
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—24no—
297C2×D4—44no—
298C2×D4—48no—
299C2×D4—224no—
300C2×D4—224no—
301C2×D4—448no—
302C2×D4C2×C4×D1114yes—
303C22×C4—111no—
304C22×C4—112no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—112no—
310C22×C4—112no—
311C22×C4—112no—
312C22×C4—112no—
313C22×C4—224no—
314C22×C4—224no—
315C22×C4—224no—
316C22×C4—222no—
317C22×C4—444no—
318C22×C4—448no—
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4D4×D1112yes—
321M16—448no—
322C2×C8—24no—
323C2×C8—224no—
324C4⋊C4—224no—
325C4⋊C4—224no—
326C22⋊C4—228no—
327C22⋊C4—228no—
328C42—112no—
329C42—112no—
330C42—112no—
331C42—111no—
332C42—111no—
333C42—112no—
334C42—112no—
335C42C2×C4×D1111yescharacteristic
336C42D4×D1112yes—
337C42C23×D1111yescharacteristic
338C11#1773811yescharacteristic, complemented, Sylow
339C23—24no—
340C23—48no—
341C23—44no—
342C23—111no—
343C23—111no—
344C23—222no—
345C23—442no—
346C23C22⋊C4×D1111yescharacteristic
347Q8—444no—
348Q8—444no—
349D4—44no—
350D4—48no—
351D4—44no—
352D4—48no—
353D4—448no—
354D4—448no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—111no—
358C2×C4—111no—
359C2×C4—114no—
360C2×C4—112no—
361C2×C4—112no—
362C2×C4—222no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—224no—
367C2×C4—224no—
368C2×C4—224no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—448no—
372C2×C4—448no—
373C2×C4—442no—
374C2×C4—444no—
375C2×C4C22⋊C4×D1112yes—
376C2×C4C22⋊C4×D1111yescharacteristic
377C2×C4C22×C4×D1111yescharacteristic
378C2×C4C2×D4×D1112yes—
379C8—44no—
380C8—444no—
381C22—22no—
382C22—44no—
383C22—48no—
384C22—88no—
385C22—221no—
386C22—221no—
387C22—222no—
388C22—222no—
389C22—444no—
390C22D11×#10012yes—
391C22C2×C22⋊C4×D1111yescharacteristic
392C4—21no—
393C4—21no—
394C4—22no—
395C4—112no—
396C4—112no—
397C4—222no—
398C4—222no—
399C4—444no—
400C4#1062330414yes—
401C2—22no—
402C2—84no—
403C2—441no—
404C2—441no—
405C2C2×D11×#10011yescharacteristic
406C2#1307713012yes—
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1555C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623247C2
cosocleC42×C11C24
hypercenter#1555D11
hypocenterC11#17738
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
2. #13077246C2semidirect
3. #13067348C2semidirect
4. #13067341C2semidirect
5. #13067330C2semidirect
6. #13067275C2semidirect
7. C11×#1555C2semidirect
23. #10622450C22semidirect
24. #10622446C22semidirect
29. C11×#331C22semidirect
30. #10622182C22semidirect
31. #10622119C22semidirect
141. #1555D11semidirect
208. #331C2×D11semidirect
338. C11#17738semidirect

Maximal subgroups

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

subgroupindex
C2×#106232472
#130772462
#130673482
#130673412
#130673302
#130672752
C11×#15552
#1773811