Finite Group Databasebeta

← #14781157

Subgroups — #14781157

Order 2816.

1306 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic, complemented
2C2×#10622828C211yesmaximal, characteristic
3#13071198C211yesmaximal, characteristic
4#13069770C218yesmaximal, complemented
5#13068354C211yesmaximal, characteristic, complemented
6#13068327C211yesmaximal, characteristic, complemented
7#13068325C211yesmaximal, characteristic, complemented
8C2×C11×#418C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16#10623050—22no—
17#10623050C2214yescomplemented
18#10623048—22no—
19#10623048—22no—
20#10623031—22no—
21#10623014—22no—
22#10623001—22no—
23C11×#418—22no—
24C11×#418C2214yes—
25C2×C11×#102—22no—
26#10622860—22no—
27#10622834—22no—
28#10622834C2214yes—
29#10622828—22no—
30#10622828C2214yes—
31C2×#66896—22no—
32#10622193C2214yescomplemented
33#10622192C2214yescomplemented
34#10622170C2214yescomplemented
35C25×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11Q814yescomplemented
45C22×D4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C2×C11×M16—21no—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16C2312yes—
51C22×C8×C11—21no—
52C11×#117—21no—
53C11×#117—21no—
54C11×#117D412yes—
55C11×#117C2312yes—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C22⋊C4—21no—
58C2×C42×C11—21no—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11—28no—
62C2×C22⋊Dic11D412yes—
63#66979—21no—
64#66979—21no—
65#66979—21no—
66#66979—21no—
67#66979—21no—
68#66979—21no—
69#66979—22no—
70#66979—22no—
71#66979D412yes—
72#66979C2312yes—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11D412yes—
75C2×C4⋊Dic11C2312yes—
76#66977—28no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11D412yes—
79C2×C4×Dic11C2312yes—
80C2×#4318—21no—
81C2×#4318—22no—
82C2×#4318—22no—
83C2×#4318C2312yes—
84C22×C11⋊C8—21no—
85#66943—24no—
86#66943—24no—
87#66941—24no—
88#66941—24no—
89#66931—28no—
90#66931—28no—
91#66923—24no—
92#66922—24no—
93C4×Dic22—28no—
94C11×#102—28no—
95#66896—28no—
96#23463—111nomaximal, Sylow
97C24×C11—22no—
98C24×C11—24no—
99C24×C11—41no—
100C24×C11—41no—
101C24×C11—42no—
102C24×C11—84no—
103C24×C11C2×D411yescharacteristic
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—24no—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—41no—
115C2×D4×C11—41no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11C2×Q814yes—
122C22×C4×C11—22no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×Q812yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11C2×D414yes—
136C2×Dic22—28no—
137C11×M16—22no—
138C11×M16—22no—
139C11×M16—42no—
140C2×C8×C11—22no—
141C2×C8×C11—42no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4C2×D414yes—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C42×C11—22no—
147C42×C11—22no—
148C22⋊Dic11—22no—
149C22⋊Dic11—22no—
150C22⋊Dic11—22no—
151C22⋊Dic11—22no—
152C22⋊Dic11—42no—
153C22⋊Dic11—88no—
154C4⋊Dic11—28no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11—22no—
158C4⋊Dic11—42no—
159C4⋊Dic11C2×D414yes—
160Dic11⋊C4—28no—
161Dic11⋊C4—28no—
162C4×Dic11—22no—
163C4×Dic11—22no—
164C4×Dic11—22no—
165C4×Dic11—22no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168#4318—22no—
169#4318—22no—
170#4318—42no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—42no—
173#3458—111no—
174C2×#418—111no—
175C2×#418D1111yescharacteristic
176#2309—111no—
177#2027—118no—
178#1742—111no—
179#1733—111no—
180#1733—111no—
181C23×C11—24no—
182C23×C11—42no—
183C23×C11—48no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11—84no—
189C23×C11—84no—
190C23×C11—88no—
191C23×C11—88no—
192C23×C11#12011yescharacteristic
193C23×C11#12011yescharacteristic
194C23×C11C22⋊Q812yes—
195C23×C11#12412yes—
196C23×C11C22×D411yescharacteristic
197D4×C11—24no—
198D4×C11—24no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—44no—
202D4×C11—44no—
203C2×C4×C11—24no—
204C2×C4×C11—82no—
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11C22⋊Q812yes—
208C2×C4×C11C22⋊Q812yes—
209C2×C4×C11C22⋊Q812yes—
210C2×C4×C11C22⋊Q812yes—
211C2×C4×C11C22⋊Q812yes—
212C2×C4×C11#12412yes—
213C2×C4×C11#12412yes—
214C2×C4×C11#12412yes—
215C2×C4×C11#12412yes—
216C2×C4×C11#12412yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×Q811yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—44no—
226C2×Dic11—44no—
227C2×Dic11—42no—
228C2×Dic11—82no—
229Dic22—88no—
230C8×C11—42no—
231C11⋊C8—42no—
232C23×D4C2×D1111yescharacteristic
233C22×M16—111no—
234C22×M16C2×D1111yescharacteristic
235#544—114no—
236#544—222no—
237#544—222no—
238#543—222no—
239#533—222no—
240#533—222no—
241#533—222no—
242C2×#117—111no—
243C2×#117—111no—
244C2×#117—111no—
245C2×#117C2×D1111yescharacteristic
246#418—22no—
247#418—114no—
248#418—222no—
249#418C2×D1114yes—
250C2×#102—22no—
251C2×#102—222no—
252#390—114no—
253#390—222no—
254#379—222no—
255#343—114no—
256#339—114no—
257#339—114no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—48no—
264C22×C11—44no—
265C22×C11—84no—
266C22×C11—88no—
267C22×C11—88no—
268C22×C11—84no—
269C22×C11#39312yes—
270C22×C11#39312yes—
271C22×C11C2×#12011yescharacteristic
272C22×C11C2×C22⋊Q811yescharacteristic
273C22×C11C2×#12411yescharacteristic
274C4×C11—44no—
275C4×C11#39312yes—
276C4×C11#39312yes—
277C4×C11C2×C22⋊Q811yescharacteristic
278C4×C11C2×C22⋊Q811yescharacteristic
279C4×C11C2×#12411yescharacteristic
280C4×C11C2×#12411yescharacteristic
281Dic11—44no—
282Dic11—44no—
283Dic11—82no—
284C25—21no—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4Dic2214yescomplemented
294C22×D4C22×D1112yes—
295C23×C4C22×D1111yescharacteristic
296C2×M16—21no—
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—112no—
300C2×M16—221no—
301C2×M16—222no—
302C2×M16—222no—
303C2×M16C22×D1112yes—
304C22×C8—21no—
305C22×C8—221no—
306C4⋊Q8—224no—
307C4⋊Q8—224no—
308C4⋊Q8—224no—
309#125—224no—
310#125—224no—
311#125—224no—
312C22⋊Q8—228no—
313C22⋊Q8—228no—
314C22⋊Q8—228no—
315C4×Q8—228no—
316#117—21no—
317#117—21no—
318#117—112no—
319#117—112no—
320#117—221no—
321#117—221no—
322#117—221no—
323#117—221no—
324#117—221no—
325#117—221no—
326#117—222no—
327#117—222no—
328#117C22⋊D1112yes—
329#117C22×D1112yes—
330C2×C4⋊C4—112no—
331C2×C4⋊C4—112no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4C22⋊D1112yes—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—112no—
336C2×C22⋊C4—221no—
337C2×C22⋊C4—221no—
338C2×C22⋊C4—228no—
339C2×C42—21no—
340C2×C42—112no—
341C2×C42—112no—
342C2×C42—221no—
343#102—28no—
344#102—228no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—22no—
348C2×C11—22no—
349C2×C11—84no—
350C2×C11C2×#39311yescharacteristic
351C2×C11#302112yes—
352C24—22no—
353C24—24no—
354C24—42no—
355C24—41no—
356C24—41no—
357C24—84no—
358C24D4×D1111yescharacteristic
359C2×Q8—228no—
360C2×D4—24no—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—24no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4C2×Dic2214yes—
378C22×C4—22no—
379C22×C4—114no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4C2×Dic2212yes—
383C22×C4#433912yes—
384C22×C4D4×D1111yescharacteristic
385C22×C4D4×D1111yescharacteristic
386C22×C4D4×D1111yescharacteristic
387C22×C4#434112yes—
388C22×C4#434112yes—
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392M16—22no—
393M16—22no—
394M16—42no—
395M16—222no—
396M16—222no—
397M16—442no—
398C2×C8—22no—
399C2×C8—42no—
400C2×C8—222no—
401C2×C8—442no—
402C4⋊C4—22no—
403C4⋊C4—114no—
404C4⋊C4—228no—
405C4⋊C4—228no—
406C4⋊C4—228no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C4⋊C4—222no—
410C4⋊C4—442no—
411C4⋊C4C2×C22⋊D1114yes—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—222no—
415C22⋊C4—222no—
416C22⋊C4—222no—
417C22⋊C4—222no—
418C22⋊C4—442no—
419C22⋊C4—888no—
420C42—22no—
421C42—22no—
422C42—222no—
423C42—222no—
424C42—222no—
425C42—222no—
426C42—222no—
427C42—222no—
428C11#2346311yescharacteristic, complemented, Sylow
429C23—24no—
430C23—42no—
431C23—48no—
432C23—42no—
433C23—44no—
434C23—44no—
435C23—42no—
436C23—84no—
437C23—84no—
438C23—88no—
439C23—88no—
440C23#6693112yes—
441C23#6693812yes—
442C23#6699011yescharacteristic
443C23#6699011yescharacteristic
444C23C2×D4×D1111yescharacteristic
445Q8—888no—
446D4—24no—
447D4—24no—
448D4—42no—
449D4—44no—
450D4—44no—
451D4—42no—
452C2×C4—24no—
453C2×C4—82no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—444no—
457C2×C4—444no—
458C2×C4—442no—
459C2×C4—882no—
460C2×C4#6693112yes—
461C2×C4#6693112yes—
462C2×C4#6693112yes—
463C2×C4#6693812yes—
464C2×C4#6693812yes—
465C2×C4#6693812yes—
466C2×C4#6697712yes—
467C2×C4#6697712yes—
468C2×C4#6698912yes—
469C2×C4#6698912yes—
470C2×C4#6699011yescharacteristic
471C2×C4#6699011yescharacteristic
472C2×C4C22×Dic2211yescharacteristic
473C2×C4C2×#433911yescharacteristic
474C2×C4C2×D4×D1111yescharacteristic
475C2×C4C2×#434111yescharacteristic
476C2×C4C2×#434111yescharacteristic
477C2×C4C22×C22⋊D1111yescharacteristic
478C8—42no—
479C8—442no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—42no—
484C22—42no—
485C22—48no—
486C22—44no—
487C22—84no—
488C22—88no—
489C22—88no—
490C22—84no—
491C22#1062256012yes—
492C22#1062256012yes—
493C22C2×#6693111yescharacteristic
494C22C2×#6693811yescharacteristic
495C22C2×#6699011yescharacteristic
496C4—44no—
497C4—444no—
498C4—444no—
499C4—882no—
500C4#1062256012yes—
501C4#1062256012yes—
502C4C2×#6693111yescharacteristic
503C4C2×#6693811yescharacteristic
504C4C2×#6697711yescharacteristic
505C4C2×#6698911yescharacteristic
506C2—21no—
507C2—21no—
508C2—22no—
509C2—22no—
510C2—84no—
511C2C2×#1062256011yescharacteristic
512C2#1307798512yes—
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#418C2
socleC22×C11C2×#120
prime radicalC23×D4×C11C22
hypercenterC2×#418D11
hypocenterC11#23463
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. #13082021C2semidirect
4. #13069770C2semidirect
5. #13068354C2semidirect
6. #13068327C2semidirect
7. #13068325C2semidirect
17. #10623050C22semidirect
32. #10622193C22semidirect
33. #10622192C22semidirect
34. #10622170C22semidirect
44. C22×D4×C11Q8semidirect
293. C22×D4Dic22semidirect
428. C11#23463semidirect

Maximal subgroups

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

subgroupindex
#130820212
C2×#106228282
#130711982
#130697702
#130683542
#130683272
#130683252
C2×C11×#4182
#2346311