Finite Group Databasebeta

← #14758304

Subgroups — #14758304

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic
2C2×#10622450C211yesmaximal, characteristic
3C4×#66945C211yesmaximal, characteristic
4#13069574C211yesmaximal, characteristic, complemented
5#13069573C211yesmaximal, characteristic, complemented
6#13069572C212yesmaximal, complemented
7#13069571C211yesmaximal, characteristic, complemented
8#13069570C212yesmaximal, complemented
9#13068334C212yesmaximal
10#13068334C212yesmaximal
11C11×#1989C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13C22×#4313C2212yes—
14D11×#125—24no—
15D11×#125C418yescomplemented
16C2×#66945C2212yes—
17C2×C4⋊C4×D11—21no—
18C2×C4⋊C4×D11—21no—
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×#66943C2211yescharacteristic
23C2×#66942—21no—
24C2×#66942—21no—
25C2×C42×D11C2211yescharacteristic
26C2×#66923C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×Dic11⋊C8C2212yes—
30C4⋊C4×Dic11C2212yes—
31C4×(C2×D11)⋊C4—21no—
32C4×C4⋊Dic11C2211yescharacteristic
33C42×Dic11—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622450—24no—
36#10622279—21no—
37#10622261—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⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2312yes—
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—22no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80C2×#4313—24no—
81C2×#4313—28no—
82#66945—24no—
83#66945Q818yes—
84C4⋊C4×D11—28no—
85C4⋊C4×D11—28no—
86C4⋊C4×D11—22no—
87C4⋊C4×D11—22no—
88C4⋊C4×D11C2×C414yes—
89C4⋊C4×D11C2×C414yes—
90#66943—22no—
91#66943—22no—
92#66943C2×C414yes—
93#66943C2×C414yes—
94#66942—28no—
95#66942—28no—
96C42×D11C2×C414yes—
97C42×D11D414yes—
98#66923—22no—
99#66923C2×C414yes—
100C11×C4⋊C8—22no—
101C11×#95—21no—
102C11⋊#95—21no—
103C11⋊#95—22no—
104Dic11⋊C8—24no—
105C4⋊(C11⋊C8)—22no—
106#21314—111nomaximal, Sylow
107C23×D11C2×D411yescharacteristic
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—22no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11C2×D411yescharacteristic
118C22×Dic11C2×D411yescharacteristic
119C22×Dic11C2×D411yescharacteristic
120C2×C4×D11—24no—
121C2×C4×D11—24no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×C4×D11—42no—
125C2×C4×D11—44no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×C4×D11C22⋊C414yes—
129C2×C4×D11C22⋊C414yes—
130C2×C4×D11C22×C412yes—
131C2×C4×D11C2×D412yes—
132C2×C4×D11C2×Q814yes—
133C2×C4×D11#4114yes—
134C2×C8×C11—22no—
135C2×C8×C11—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4C22×C412yes—
142C11×C4⋊C4C22×C412yes—
143C11×C4⋊C4C2×Q814yes—
144C42×C11—42no—
145C42×C11C22×C412yes—
146C42×C11C2×D412yes—
147(C2×D11)⋊C4—28no—
148C4⋊Dic11—24no—
149C4⋊Dic11—24no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—22no—
153C4⋊Dic11C22×C412yes—
154C4⋊Dic11C22×C412yes—
155C4⋊Dic11C2×Q814yes—
156Dic11⋊C4—24no—
157Dic11⋊C4—24no—
158Dic11⋊C4—24no—
159Dic11⋊C4—24no—
160Dic11⋊C4—24no—
161Dic11⋊C4—24no—
162C4×Dic11—28no—
163C4×Dic11—42no—
164C4×Dic11—44no—
165C4×Dic11C22⋊C414yes—
166C4×Dic11C22⋊C414yes—
167C4×Dic11C22×C412yes—
168C4×Dic11C2×D412yes—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—24no—
171#4313—48no—
172C22×#125—111no—
173C2×#423—111no—
174C4×#117—111no—
175#1989—111no—
176#1989—111no—
177#1989—112no—
178#1989—112no—
179#1989—111no—
180#1989D1111yescharacteristic, complemented
181#1736—112no—
182#1736—112no—
183C23×C11C22×D411yescharacteristic
184C22×D11—22no—
185C22×D11—21no—
186C22×D11—21no—
187C22×D11C2×C22⋊C412yes—
188C22×D11C22⋊Q814yes—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11C2×C22⋊C412yes—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×Q812yes—
205C2×C4×C11C2×#4112yes—
206C2×Dic11—22no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—24no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11C2×C22⋊C412yes—
218C2×Dic11C2×C22⋊C412yes—
219C2×Dic11C2×C22⋊C412yes—
220C2×Dic11C22⋊Q814yes—
221C4×D11—44no—
222C4×D11—44no—
223C4×D11—48no—
224C4×D11—48no—
225C4×D11C4×Q818yes—
226C4×D11#12414yes—
227C4×D11C4⋊Q814yes—
228C8×C11—42no—
229C11⋊C8—42no—
230C22×M16—112no—
231C2×#125—118no—
232C2×#125—111no—
233C2×#125—111no—
234C2×#125—111no—
235C2×#125—221no—
236C2×#125—221no—
237C2×#125—224no—
238C2×#125C2×D1111yescharacteristic
239C2×#117—112no—
240C22×C4⋊C4—111no—
241C22×C4⋊C4—111no—
242C22×C4⋊C4—221no—
243C22×C4⋊C4—221no—
244C22×C42—111no—
245#423—224no—
246C2×C4⋊C8—112no—
247C2×C4⋊C8—111no—
248C2×C4⋊C8C2×D1111yescharacteristic
249C4×C4⋊C4—112no—
250C4×C4⋊C4—111no—
251C4×C4⋊C4C2×D1111yescharacteristic
252C4×C22⋊C4—221no—
253C4×C22⋊C4—221no—
254#376—221no—
255C43—221no—
256#340—112no—
257#340—112no—
258#340—112no—
259#340—112no—
260#340—112no—
261#340—112no—
262#340C2×D1112yes—
263#340C2×D1112yes—
264C22×C11C22×C22⋊C411yescharacteristic
265C22×C11C2×C22⋊Q812yes—
266C22×C11#57512yes—
267C22×C11#57511yescharacteristic
268C22×C11#57511yescharacteristic
269C2×D11—24no—
270C2×D11—24no—
271C2×D11—22no—
272C2×D11—22no—
273C2×D11#39114yes—
274C4×C11—22no—
275C4×C11—22no—
276C4×C11—44no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11C2×C4×Q812yes—
280C4×C11C2×#12411yescharacteristic
281C4×C11C2×C4⋊Q811yescharacteristic
282Dic11—22no—
283Dic11—22no—
284Dic11—44no—
285Dic11—42no—
286Dic11—42no—
287Dic11#39114yes—
288C23×C4—111no—
289C23×C4—111no—
290C23×C4—111no—
291C23×C4—221no—
292C23×C4—221no—
293C2×M16—228no—
294C2×M16—224no—
295C22×C8—112no—
296C22×C8C22×D1112yes—
297#125—22no—
298#125—114no—
299#125—114no—
300#125—114no—
301#125—228no—
302#125—228no—
303#125—222no—
304#125—222no—
305#125—222no—
306#125C4×D1114yes—
307#117—118no—
308#117—224no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—114no—
315C2×C4⋊C4—114no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—228no—
319C2×C4⋊C4—228no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C4⋊C4C22×D1111yescharacteristic
330C2×C4⋊C4C22×D1112yes—
331C2×C22⋊C4—222no—
332C2×C42—21no—
333C2×C42—111no—
334C2×C42—111no—
335C2×C42—111no—
336C2×C42—114no—
337C2×C42—114no—
338C2×C42—222no—
339C2×C42—222no—
340C2×C42—221no—
341C2×C42C22×D1111yescharacteristic
342C4⋊C8—22no—
343C4⋊C8—224no—
344C4⋊C8—222no—
345#95—21no—
346#95—222no—
347#95—221no—
348C2×C11C2×#39111yescharacteristic
349C2×C11#289611yescharacteristic
350C2×C11#289611yescharacteristic
351C2×C11#308012yes—
352C2×C11#308012yes—
353D11—24no—
354C24—111no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—111no—
359C22×C4—112no—
360C22×C4—112no—
361C22×C4—114no—
362C22×C4—114no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—114no—
366C22×C4—114no—
367C22×C4—224no—
368C22×C4—224no—
369C22×C4—222no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—442no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4—444no—
376C22×C4—442no—
377C22×C4—442no—
378C22×C4D4×D1111yescharacteristic
379C22×C4D4×D1111yescharacteristic
380C22×C4C23×D1111yescharacteristic
381M16—448no—
382C2×C8—22no—
383C2×C8—24no—
384C2×C8—222no—
385C2×C8—224no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—112no—
392C4⋊C4—112no—
393C4⋊C4—114no—
394C4⋊C4—224no—
395C4⋊C4—224no—
396C4⋊C4—224no—
397C4⋊C4—224no—
398C4⋊C4—224no—
399C4⋊C4—224no—
400C4⋊C4—224no—
401C4⋊C4—224no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—222no—
405C4⋊C4C2×C4×D1112yes—
406C4⋊C4C2×C4×D1112yes—
407C4⋊C4Q8×D1114yes—
408C22⋊C4—228no—
409C42—42no—
410C42—114no—
411C42—114no—
412C42—112no—
413C42—112no—
414C42—228no—
415C42—442no—
416C42—444no—
417C42C2×C4×D1112yes—
418C42D4×D1112yes—
419C11#2131411yescharacteristic, complemented, Sylow
420C23—112no—
421C23—114no—
422C23—222no—
423C23—221no—
424C23—221no—
425C23C2×D4×D1111yescharacteristic
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—112no—
438C2×C4—114no—
439C2×C4—114no—
440C2×C4—118no—
441C2×C4—114no—
442C2×C4—112no—
443C2×C4—112no—
444C2×C4—222no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—224no—
450C2×C4—444no—
451C2×C4—444no—
452C2×C4—448no—
453C2×C4—448no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—441no—
457C2×C4—442no—
458C2×C4—441no—
459C2×C4C22⋊C4×D1112yes—
460C2×C4C22⋊C4×D1112yes—
461C2×C4C22×C4×D1111yescharacteristic
462C2×C4C2×D4×D1111yescharacteristic
463C2×C4C2×Q8×D1112yes—
464C2×C4#41×D1112yes—
465C8—42no—
466C8—442no—
467C22—114no—
468C22—222no—
469C22—222no—
470C22—224no—
471C22—224no—
472C22C2×C22⋊C4×D1111yescharacteristic
473C22D11×C22⋊Q812yes—
474C22#1062329912yes—
475C22#1062330411yescharacteristic
476C22#1062330811yescharacteristic
477C4—22no—
478C4—22no—
479C4—42no—
480C4—42no—
481C4—44no—
482C4—114no—
483C4—222no—
484C4—222no—
485C4—442no—
486C4—442no—
487C4—444no—
488C4C4×Q8×D1112yes—
489C4D11×#12411yescharacteristic
490C4D11×C4⋊Q811yescharacteristic
491C2—224no—
492C2D11×#39111yescharacteristic
493C2#1307713111yescharacteristic
494C2#1307713211yescharacteristic
495C2#1307843312yes—
496C2#1307843512yes—
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#21314
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. #13069574C2semidirect
5. #13069573C2semidirect
6. #13069572C2semidirect
7. #13069571C2semidirect
8. #13069570C2semidirect
11. C11×#1989C2semidirect
15. D11×#125C4semidirect
180. #1989D11semidirect
419. C11#21314semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×#106224502
C4×#669452
#130695742
#130695732
#130695722
#130695712
#130695702
#130683342
C11×#19892
#2131411