Finite Group Databasebeta

← #14763273

Subgroups — #14763273

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic
3#13071012C211yesmaximal, characteristic
4#13069579C212yesmaximal, complemented
5#13069579C212yesmaximal, complemented
6#13069574C211yesmaximal, characteristic, complemented
7#13069573C211yesmaximal, characteristic, complemented
8#13069571C211yesmaximal, characteristic, complemented
9#13068705C212yesmaximal
10#13068701C212yesmaximal
11C11×#1989C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13D11×#125—24no—
14D11×#125C418yescomplemented
15C2×C4⋊C4×D11—21no—
16C2×C4⋊C4×D11—21no—
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×#66943C2211yescharacteristic
20C2×#66943C2211yescharacteristic
21C2×#66942—21no—
22C2×#66942—21no—
23C2×C42×D11C2211yescharacteristic
24C2×#66923C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C8C2212yes—
28C2×C8×Dic11C2212yes—
29#10622600C2212yes—
30#10622590C2212yes—
31C4×(C2×D11)⋊C4—21no—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622545—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622446—24no—
36#10622277—21no—
37#10622264—21no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×C4×D11—21no—
47C22×C4×D11—21no—
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C11×#125—22no—
53C11×#125C2×C414yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78C4⋊C4×D11—28no—
79C4⋊C4×D11—28no—
80C4⋊C4×D11—22no—
81C4⋊C4×D11—22no—
82C4⋊C4×D11C2×C414yes—
83C4⋊C4×D11C2×C414yes—
84#66943—22no—
85#66943—22no—
86#66943C2×C414yes—
87#66943C2×C414yes—
88#66942—28no—
89#66942—28no—
90C42×D11C2×C414yes—
91C42×D11D414yes—
92#66923—22no—
93#66923C2×C414yes—
94C11×C4⋊C8—22no—
95C11×#95—21no—
96C11⋊#95—21no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100(C2×D11)⋊C8—24no—
101C8×Dic11—24no—
102C4⋊(C11⋊C8)—22no—
103#21836—111nomaximal, Sylow
104C23×D11C2×D411yescharacteristic
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11C2×D411yescharacteristic
115C22×Dic11C2×D411yescharacteristic
116C22×Dic11C2×D411yescharacteristic
117C2×C4×D11—24no—
118C2×C4×D11—24no—
119C2×C4×D11—24no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×C4×D11—42no—
125C2×C4×D11—42no—
126C2×C4×D11—44no—
127C2×C4×D11C22⋊C414yes—
128C2×C4×D11C22⋊C414yes—
129C2×C4×D11C22×C412yes—
130C2×C4×D11C2×D412yes—
131C2×C8×C11—22no—
132C2×C8×C11—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4C22×C412yes—
140C11×C4⋊C4C22×C412yes—
141C42×C11—42no—
142C42×C11C22×C412yes—
143C42×C11C2×D412yes—
144(C2×D11)⋊C4—44no—
145C4⋊Dic11—24no—
146C4⋊Dic11—24no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11C22×C412yes—
152C4⋊Dic11C22×C412yes—
153Dic11⋊C4—24no—
154Dic11⋊C4—24no—
155Dic11⋊C4—24no—
156Dic11⋊C4—24no—
157Dic11⋊C4—24no—
158Dic11⋊C4—24no—
159C4×Dic11—42no—
160C4×Dic11C22⋊C414yes—
161C4×Dic11C22⋊C414yes—
162C4×Dic11C22×C412yes—
163C4×Dic11C2×D412yes—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—24no—
166C22×#125—111no—
167C2×#431—111no—
168#2283—111no—
169#1991—112no—
170#1991—112no—
171#1989—111no—
172#1989—111no—
173#1989—111no—
174#1989D1111yescharacteristic, complemented
175#1824—112no—
176#1823—112no—
177C23×C11C22×D411yescharacteristic
178C22×D11—22no—
179C22×D11—21no—
180C22×D11—21no—
181C22×D11C2×C22⋊C412yes—
182C22×D11#13514yes—
183C2×C4×C11—22no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C2×C22⋊C412yes—
196C2×C4×C11C23×C411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C112−1+412yes—
199C2×C4×C112−1+412yes—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11C2×C22⋊C412yes—
213C2×Dic11C2×C22⋊C412yes—
214C2×Dic11C2×C22⋊C412yes—
215C4×D11—28no—
216C4×D11—24no—
217C4×D11—22no—
218C4×D11—22no—
219C4×D11—44no—
220C4×D11—48no—
221C4×D11—48no—
222C8×C11—42no—
223C11⋊C8—42no—
224C2×#125—118no—
225C2×#125—111no—
226C2×#125—111no—
227C2×#125—111no—
228C2×#125—221no—
229C2×#125—221no—
230C2×#125—224no—
231C2×#125C2×D1111yescharacteristic
232C22×C4⋊C4—111no—
233C22×C4⋊C4—111no—
234C22×C4⋊C4—221no—
235C22×C4⋊C4—221no—
236C22×C42—111no—
237#431—224no—
238C2×C4⋊C8—111no—
239C2×C4⋊C8C2×D1111yescharacteristic
240C2×C22⋊C8—112no—
241C2×C4×C8—112no—
242#383—221no—
243#382—112no—
244#381—221no—
245#380—112no—
246C4×C4⋊C4—111no—
247C4×C4⋊C4C2×D1111yescharacteristic
248C4×C22⋊C4—221no—
249#376—221no—
250#340—112no—
251#340—112no—
252#340—112no—
253#340—112no—
254#340—112no—
255#340—112no—
256#340C2×D1112yes—
257#340C2×D1112yes—
258C22×C11C22×C22⋊C411yescharacteristic
259C22×C11#53612yes—
260C22×C11C2×#13512yes—
261C22×C11#57511yescharacteristic
262C22×C11#57511yescharacteristic
263C2×D11—22no—
264C2×D11—22no—
265C2×D11—24no—
266C2×D11—24no—
267C2×D11#41614yes—
268C4×C11—22no—
269C4×C11—22no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—82no—
273C4×C11#51912yes—
274C4×C11#53611yescharacteristic
275C4×C11#53611yescharacteristic
276Dic11—22no—
277Dic11—22no—
278Dic11—22no—
279Dic11—42no—
280Dic11—42no—
281Dic11—82no—
282C23×C4—111no—
283C23×C4—111no—
284C23×C4—111no—
285C23×C4—221no—
286C23×C4—221no—
287C22×C8—112no—
288C22×C8C22×D1112yes—
289#125—22no—
290#125—114no—
291#125—114no—
292#125—114no—
293#125—228no—
294#125—228no—
295#125—222no—
296#125—222no—
297#125—222no—
298#125C4×D1114yes—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—114no—
304C2×C4⋊C4—114no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—228no—
309C2×C4⋊C4—228no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4C22×D1112yes—
319C2×C4⋊C4C22×D1111yescharacteristic
320C2×C4⋊C4C22×D1111yescharacteristic
321C2×C22⋊C4—222no—
322C2×C42—21no—
323C2×C42—111no—
324C2×C42—111no—
325C2×C42—111no—
326C2×C42—114no—
327C2×C42—114no—
328C2×C42—221no—
329C2×C42C22×D1111yescharacteristic
330C4⋊C8—22no—
331C4⋊C8—222no—
332C22⋊C8—224no—
333C4×C8—224no—
334#95—21no—
335#95—222no—
336#95—222no—
337#95—222no—
338#95—221no—
339C2×C11#231011yescharacteristic
340C2×C11C2×#41611yescharacteristic
341C2×C11#289611yescharacteristic
342C2×C11#323212yes—
343C2×C11#323212yes—
344D11—24no—
345C24—111no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—111no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—114no—
353C22×C4—112no—
354C22×C4—112no—
355C22×C4—114no—
356C22×C4—224no—
357C22×C4—224no—
358C22×C4—224no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—222no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4—444no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4D4×D1111yescharacteristic
370C22×C4D4×D1111yescharacteristic
371C22×C4C23×D1111yescharacteristic
372C2×C8—22no—
373C2×C8—24no—
374C2×C8—222no—
375C2×C8—224no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—112no—
383C4⋊C4—112no—
384C4⋊C4—224no—
385C4⋊C4—224no—
386C4⋊C4—224no—
387C4⋊C4—224no—
388C4⋊C4—224no—
389C4⋊C4—224no—
390C4⋊C4—224no—
391C4⋊C4—224no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—222no—
395C4⋊C4—222no—
396C4⋊C4C2×C4×D1112yes—
397C4⋊C4C2×C4×D1112yes—
398C22⋊C4—444no—
399C42—42no—
400C42—114no—
401C42—114no—
402C42—112no—
403C42—112no—
404C42—442no—
405C42C2×C4×D1112yes—
406C42D4×D1112yes—
407C11#2183611yescharacteristic, complemented, Sylow
408C23—112no—
409C23—114no—
410C23—221no—
411C23—221no—
412C23—222no—
413C23C2×D4×D1111yescharacteristic
414C2×C4—22no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—112no—
426C2×C4—112no—
427C2×C4—112no—
428C2×C4—228no—
429C2×C4—222no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—224no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—444no—
439C2×C4—448no—
440C2×C4—448no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4C22⋊C4×D1112yes—
448C2×C4C22⋊C4×D1112yes—
449C2×C4C22×C4×D1111yescharacteristic
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4#6704012yes—
452C2×C4#6704312yes—
453C8—42no—
454C8—442no—
455C22—114no—
456C22—222no—
457C22—222no—
458C22—224no—
459C22—224no—
460C22C2×C22⋊C4×D1111yescharacteristic
461C22#1062315912yes—
462C22D11×#13512yes—
463C22#1062330411yescharacteristic
464C22#1062330811yescharacteristic
465C4—22no—
466C4—22no—
467C4—42no—
468C4—42no—
469C4—82no—
470C4—222no—
471C4—222no—
472C4—222no—
473C4—442no—
474C4—442no—
475C4—882no—
476C4#1062310312yes—
477C4#1062320611yescharacteristic
478C4#1062325511yescharacteristic
479C2—224no—
480C2#1307119911yescharacteristic
481C2D11×#41611yescharacteristic
482C2#1307713211yescharacteristic
483C2#1307978212yes—
484C2#1307978812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1989C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1989D11
hypocenterC11#21836
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
4. #13069579C2semidirect
5. #13069579C2semidirect
6. #13069574C2semidirect
7. #13069573C2semidirect
8. #13069571C2semidirect
11. C11×#1989C2semidirect
14. D11×#125C4semidirect
174. #1989D11semidirect
407. C11#21836semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×#106224462
#130710122
#130695792
#130695742
#130695732
#130695712
#130687052
#130687012
C11×#19892
#2183611