Finite Group Databasebeta

← #14644313

Subgroups — #14644313

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic
2C4×#66870C211yesmaximal, characteristic
3#13068390C211yesmaximal, characteristic, complemented
4C22⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
5#13066932C211yesmaximal, characteristic
6#13066463C211yesmaximal, characteristic, complemented
7C11×#1282C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D11C2211yescharacteristic
9C23×C11⋊C8C2211yescharacteristic
10C22×C8×D11C411yescharacteristic, complemented
11C2×C11×C22⋊C8C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14C4×C22⋊Dic11C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16C2×(C2×D11)⋊C8C411yescharacteristic, complemented
17C2×Dic11⋊C8C411yescharacteristic, complemented
18C2×C8×Dic11—21no—
19C2×C8×Dic11C411yescharacteristic, complemented
20C2×#66870C412yes—
21C2×C4×C11⋊C8—21no—
22(C22⋊D11)⋊C8—21no—
23(C22⋊D11)⋊C8—21no—
24(C22⋊D11)⋊C8—21no—
25(C22⋊D11)⋊C8—21no—
26#10622188—21no—
27#10622165C412yes—
28#10622162—21no—
29#10622107C412yescomplemented
30#10622106C412yescomplemented
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11C2×C411yescharacteristic
33C22×C4×D11C2×C411yescharacteristic
34C22×C8×C11—21no—
35C22×C8×C11C2×C411yescharacteristic
36C22×C8×C11C2×C411yescharacteristic
37C2×C11×C22⋊C4C2×C412yes—
38C2×C42×C11—21no—
39C2×C22⋊Dic11C2×C411yescharacteristic
40C2×C22⋊Dic11C2×C412yes—
41C4×C22⋊D11—21no—
42C4×C22⋊D11—21no—
43C4×C22⋊D11—21no—
44C4×C22⋊D11—21no—
45C2×(C2×D11)⋊C4C2×C411yescharacteristic
46C2×Dic11⋊C4C2×C411yescharacteristic
47C2×C4×Dic11—21no—
48C2×C4×Dic11C2×C411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8—42no—
51C22×C11⋊C8C2×C411yescharacteristic
52C22×C11⋊C8C2×C411yescharacteristic
53C22×C11⋊C8D411yescharacteristic
54C22×C11⋊C8D411yescharacteristic
55C22×C11⋊C8D411yescharacteristic
56C22×C11⋊C8D411yescharacteristic
57C2×C8×D11—21no—
58C2×C8×D11—21no—
59C2×C8×D11—42no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8C2×C412yes—
64C11×#95—21no—
65C11⋊#95—21no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)C2×C412yes—
68(C2×D11)⋊C8—21no—
69(C2×D11)⋊C8—21no—
70Dic11⋊C8—21no—
71Dic11⋊C8—21no—
72C8×Dic11—21no—
73C8×Dic11—21no—
74C8×Dic11—42no—
75#66870C818yescomplemented
76C4×C11⋊C8—42no—
77C8×#99—111nomaximal, Sylow
78C24×C11C22×C411yescharacteristic
79C23×D11C4211yescharacteristic
80C22×C4×C11—22no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C2×C22⋊D11—21no—
90C2×C22⋊D11—21no—
91C2×C22⋊D11—22no—
92C2×C22⋊D11C2×C814yes—
93C22×Dic11—22no—
94C22×Dic11C4211yescharacteristic
95C22×Dic11C4211yescharacteristic
96C22×Dic11C4211yescharacteristic
97C2×C4×D11—21no—
98C2×C4×D11—21no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C8×C11—21no—
102C2×C8×C11—21no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C11×C22⋊C4—22no—
109C11×C22⋊C4C2×C814yescomplemented
110C42×C11—41no—
111C42×C11—41no—
112C22⋊Dic11—21no—
113C22⋊Dic11—21no—
114C22⋊Dic11—22no—
115C22⋊Dic11C2×C814yescomplemented
116(C2×D11)⋊C4—21no—
117(C2×D11)⋊C4—21no—
118Dic11⋊C4—21no—
119Dic11⋊C4—21no—
120C4×Dic11—21no—
121C4×Dic11—21no—
122C4×Dic11—41no—
123C4×Dic11—41no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8C22⋊C411yescharacteristic
134C2×C11⋊C8C22⋊C411yescharacteristic
135C2×C11⋊C8C22⋊C411yescharacteristic
136C2×C11⋊C8C22⋊C411yescharacteristic
137C8×D11—42no—
138C8×D11—42no—
139C2×C8×D4—111no—
140C4×#99—111no—
141C8×C22⋊C4—111no—
142C8×C22⋊C4—111no—
143#1459—111no—
144#1282—111no—
145#1282D1111yescharacteristic, complemented
146C23×C11—41no—
147C23×C11—41no—
148C23×C11C2×C4211yescharacteristic
149C23×C11C4×D411yescharacteristic
150C23×C11C4×D411yescharacteristic
151C23×C11C22×C812yes—
152C23×C11#13112yes—
153C22×D11—21no—
154C22×D11—21no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11C4×C812yescomplemented
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—24no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11C2×C22⋊C411yescharacteristic
171C2×C4×C11#11711yescharacteristic
172C2×C4×C11C4×D411yescharacteristic
173C2×C4×C11C4×D411yescharacteristic
174C22⋊D11—24no—
175C22⋊D11—24no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—24no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11C4×C812yescomplemented
186C4×D11—42no—
187C4×D11—41no—
188C4×D11—41no—
189C8×C11—42no—
190C8×C11—41no—
191C8×C11—41no—
192C11⋊C8—21no—
193C11⋊C8—21no—
194C11⋊C8—21no—
195C11⋊C8—42no—
196C11⋊C8#9912yescomplemented
197C23×C8—111no—
198C23×C8—111no—
199C2×C4×D4—111no—
200C8×D4—221no—
201C8×D4—221no—
202C8×D4—221no—
203C8×D4—221no—
204C2×C4⋊C8—111no—
205C2×#99—112no—
206C2×C22⋊C8—111no—
207C2×C22⋊C8—111no—
208C2×C22⋊C8C2×D1111yescharacteristic
209C2×C22⋊C8C2×D1111yescharacteristic
210C2×C4×C8—111no—
211C2×C4×C8—221no—
212C2×C4×C8—221no—
213C4×C22⋊C4—111no—
214C4×C22⋊C4C2×D1111yescharacteristic
215#342—112no—
216#336—221no—
217#336—221no—
218#324—112no—
219#323—112no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11C4×C22⋊C411yescharacteristic
229C22×C11C2×C4×C811yescharacteristic
230C22×C11#40511yescharacteristic
231C22×C11C8×D412yes—
232C22×C11C8×D412yes—
233C2×D11—22no—
234C2×D11—42no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—42no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—44no—
242C4×C11C2×#9911yescharacteristic
243C4×C11#41011yescharacteristic
244Dic11—22no—
245Dic11—44no—
246Dic11—41no—
247Dic11—41no—
248C22×D4—111no—
249C23×C4—111no—
250C23×C4C22×D1111yescharacteristic
251C22×C8—21no—
252C22×C8—111no—
253C22×C8—111no—
254C22×C8—111no—
255C22×C8—111no—
256C22×C8—111no—
257C22×C8—111no—
258C22×C8—221no—
259C22×C8—221no—
260C22×C8—221no—
261C22×C8—442no—
262C22×C8—442no—
263C22×C8C4×D1111yescharacteristic
264C22×C8C4×D1111yescharacteristic
265C4×D4—221no—
266C4×D4—221no—
267C4×D4—221no—
268C4×D4—221no—
269C2×C4⋊C4—111no—
270C2×C22⋊C4—112no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—111no—
273C2×C22⋊C4C4×D1112yes—
274C2×C42—21no—
275C2×C42—111no—
276C2×C42—221no—
277C4⋊C8—221no—
278C4⋊C8—221no—
279#99—118no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—112no—
284C22⋊C8—221no—
285C22⋊C8—221no—
286C22⋊C8—221no—
287C22⋊C8C4×D1112yes—
288C4×C8—221no—
289C4×C8—221no—
290C4×C8—442no—
291C4×C8—442no—
292#95—21no—
293#95—221no—
294C2×C11—22no—
295C2×C11—22no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11C8×C22⋊C411yescharacteristic
299C2×C11C4×#9911yescharacteristic
300C2×C11#175711yescharacteristic
301D11—42no—
302C24—111no—
303C24C2×C4×D1111yescharacteristic
304C2×D4—114no—
305C2×D4—221no—
306C2×D4—221no—
307C2×D4—222no—
308C22×C4—22no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—222no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—441no—
318C22×C4—441no—
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4C2×C4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4#434111yescharacteristic
324C22×C4#434311yescharacteristic
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—111no—
333C2×C8—111no—
334C2×C8—111no—
335C2×C8—111no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—442no—
341C2×C8—442no—
342C2×C8—441no—
343C2×C8—441no—
344C2×C8—441no—
345C2×C8—441no—
346C2×C8—441no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C22⋊C4—22no—
350C22⋊C4—114no—
351C22⋊C4—221no—
352C22⋊C4—221no—
353C22⋊C4—222no—
354C22⋊C4—221no—
355C22⋊C4—221no—
356C22⋊C4C8×D1114yescomplemented
357C42—41no—
358C42—41no—
359C42—221no—
360C42—221no—
361C42—441no—
362C42—441no—
363C11C8×#9911yescharacteristic, complemented, Sylow
364C23—41no—
365C23—41no—
366C23—112no—
367C23—221no—
368C23—221no—
369C23—441no—
370C23—441no—
371C23C42×D1111yescharacteristic
372C23(C22⋊D11)⋊C411yescharacteristic
373C23#6694611yescharacteristic
374C23C2×C8×D1112yes—
375C23#6696012yes—
376D4—224no—
377D4—224no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—24no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—112no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—224no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4C22⋊C4×D1111yescharacteristic
404C2×C4(C22⋊D11)⋊C411yescharacteristic
405C2×C4#6694511yescharacteristic
406C2×C4#6694611yescharacteristic
407C8—42no—
408C8—41no—
409C8—41no—
410C8—112no—
411C8—221no—
412C8—221no—
413C8—221no—
414C8—442no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22—222no—
424C22—442no—
425C22—442no—
426C22—441no—
427C22—441no—
428C22#1062227911yescharacteristic
429C22C4×C8×D1111yescharacteristic
430C22#1062232111yescharacteristic
431C22(C22⋊D11)⋊C812yes—
432C22#1062244712yes—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—44no—
437C4—222no—
438C4—444no—
439C4—441no—
440C4—441no—
441C4#1062235311yescharacteristic
442C4D11×#9911yescharacteristic
443C2—22no—
444C2—22no—
445C2—21no—
446C2—21no—
447C2—442no—
448C2#1306838611yescharacteristic
449C2#1306840311yescharacteristic
450C2#1306841511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC22×C11C2×C4×C8
FrattiniC23×C4C22×D11
FittingC11×#1282C2
socleC22×C11C4×C22⋊C4
prime radicalC22×C22⋊D11C2×C4
cosocleC23×C4×C11C23
hypercenter#1282D11
hypocenterC11C8×#99
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
3. #13068390C2semidirect
4. C22⋊C4×C11⋊C8C2semidirect
6. #13066463C2semidirect
7. C11×#1282C2semidirect
10. C22×C8×D11C4semidirect
16. C2×(C2×D11)⋊C8C4semidirect
17. C2×Dic11⋊C8C4semidirect
19. C2×C8×Dic11C4semidirect
29. #10622107C4semidirect
30. #10622106C4semidirect
75. #66870C8semidirect
109. C11×C22⋊C4C2×C8semidirect
115. C22⋊Dic11C2×C8semidirect
145. #1282D11semidirect
157. C22×D11C4×C8semidirect
185. C2×Dic11C4×C8semidirect
196. C11⋊C8#99semidirect
356. C22⋊C4C8×D11semidirect
363. C11C8×#99semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D11)⋊C82
C4×#668702
#130683902
C22⋊C4×C11⋊C82
#130669322
#130664632
C11×#12822
C8×#9911