Finite Group Databasebeta

← #14781065

Subgroups — #14781065

Order 2816.

1294 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10622417C212yesmaximal
3#13071105C211yesmaximal, characteristic
4#13069765C212yesmaximal, complemented
5#13069761C212yesmaximal, complemented
6#13069757C211yesmaximal, characteristic, complemented
7#13069753C211yesmaximal, characteristic, complemented
8#13069749C211yesmaximal, characteristic, complemented
9#13068331C212yesmaximal, complemented
10D11×#336C211yesmaximal, characteristic, complemented
11C11×#2024C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999—21no—
15C2×Q8×Dic11—21no—
16C22×C8×D11C2212yes—
17#10623259—28no—
18C2×#66950—21no—
19C2×#66945C2211yescharacteristic
20C2×#66945C2212yes—
21C2×#66943C2212yes—
22C2×#66940—21no—
23C2×C42×D11C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C11×#103C2212yes—
26C11×#391C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2212yes—
29C2×#66885C2212yes—
30#10622601C2211yescharacteristic
31C2×#66873C2212yes—
32#10622552C2211yescharacteristic
33#10622417—28no—
34#10622279—21no—
35#10622279—21no—
36#10622278—21no—
37#10622278—21no—
38C11×#340C2212yes—
39C11×#336C2211yescharacteristic
40#10622189C2212yes—
41#10622188C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622162C2211yescharacteristic
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C2×#4343—22no—
48C2×#4343—24no—
49C2×#4343—24no—
50C2×#4343Q814yescomplemented
51C22×D44—21no—
52C22×D44C2311yescharacteristic
53C22×C4×D11—21no—
54C22×C4×D11D411yescharacteristic
55C22×C4×D11D411yescharacteristic
56C22×C4×D11C2311yescharacteristic
57C22×Dic22—21no—
58C22×C8×C11C2312yes—
59C11×C4⋊Q8—24no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11C2311yescharacteristic
64#66999—28no—
65Q8×Dic11—28no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4—22no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2312yes—
83C2×C8×D11—24no—
84C2×C8×D11—24no—
85C2×C8×D11—24no—
86#66950—28no—
87#66945—24no—
88#66945—24no—
89#66945D418yes—
90#66943—24no—
91#66943—24no—
92#66940—28no—
93C42×D11—24no—
94#66922—24no—
95C11×#103—24no—
96C11×#95—21no—
97C11×#95—21no—
98#66899—24no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101#66885—24no—
102#66873—24no—
103#23451—111nomaximal, Sylow
104C23×D11—21no—
105C23×D11C2×D411yescharacteristic
106C2×Q8×C11—24no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—42no—
111C2×Q8×C11—42no—
112C2×Q8×C11C2×Q812yes—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C22×Dic11—22no—
120C22×Dic11—21no—
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123C22×Dic11C2×D411yescharacteristic
124#4343—216no—
125#4343—48no—
126C2×D44—24no—
127C2×D44—22no—
128C2×D44—21no—
129C2×D44—22no—
130C2×D44—42no—
131C2×D44—42no—
132C2×D44C2×Q812yes—
133C2×C4×D11—24no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×C4×D11C2×D414yes—
143C2×C4×D11C2×Q812yes—
144C2×C4×D11#4112yes—
145C2×C4×D11#4114yes—
146C2×Dic22—24no—
147C2×Dic22—42no—
148C2×Dic22—42no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4C2×D414yes—
156C42×C11—22no—
157(C2×D11)⋊C4—28no—
158(C2×D11)⋊C4—42no—
159(C2×D11)⋊C4—42no—
160(C2×D11)⋊C4—42no—
161(C2×D11)⋊C4—42no—
162(C2×D11)⋊C4—42no—
163C4⋊Dic11—24no—
164C4⋊Dic11—28no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11C2×D414yes—
168Dic11⋊C4—28no—
169C4×Dic11—22no—
170C4×Dic11—22no—
171C4×Dic11—28no—
172C4×Dic11—22no—
173C4×Dic11—42no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C8×D11—48no—
178C2×#533—111no—
179C2×#416—112no—
180#2297—111no—
181#2026—112no—
182#2025—112no—
183#2024—111no—
184#2024D1111yescharacteristic, complemented
185#2023—111no—
186#2023—111no—
187#1735—112no—
188C2×#336—111no—
189C23×C11C22×D411yescharacteristic
190C22×D11—21no—
191C22×D11—21no—
192C22×D11—21no—
193C22×D11—21no—
194C22×D11—22no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11#12012yes—
202C22×D11C22⋊Q812yes—
203C22×D11#12412yes—
204Q8×C11—24no—
205Q8×C11—48no—
206Q8×C11—42no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11#13512yes—
221C2×C4×C11#13512yes—
222C2×C4×C11C22×D412yes—
223C2×C4×C11C22×Q811yescharacteristic
224C2×C4×C11C2×#4112yes—
225C2×C4×C11C2×#4111yescharacteristic
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—24no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11#12012yes—
239C2×Dic11C22⋊Q812yes—
240C2×Dic11#12412yes—
241D44—24no—
242D44—48no—
243D44—42no—
244C4×D11—44no—
245C4×D11—44no—
246C4×D11—48no—
247C4×D11C22⋊Q818yes—
248C4×D11#12418yes—
249Dic22—48no—
250C8×C11—42no—
251C11⋊C8—42no—
252C22×#41—111no—
253C23×C8—112no—
254#533—228no—
255C2×C4⋊Q8—111no—
256C2×C4⋊Q8C2×D1111yescharacteristic
257C2×#125—112no—
258C2×C22⋊Q8—221no—
259C2×C22⋊Q8—221no—
260C2×C4×Q8—221no—
261C2×C4×Q8—221no—
262C2×#117—112no—
263C2×#117—111no—
264C22×C42—111no—
265#416—228no—
266C2×#103—112no—
267C2×#103C2×D1112yes—
268C2×#102—112no—
269C2×#102—112no—
270#391—111no—
271#391C2×D1111yescharacteristic
272#390—111no—
273#390—111no—
274#386—221no—
275#386—221no—
276C4×C22⋊C4—221no—
277C4×C22⋊C4—221no—
278#340—112no—
279#340—112no—
280#340—112no—
281#340C2×D1112yes—
282#336—112no—
283#336—111no—
284#336C2×D1111yescharacteristic
285C22×C11C2×#12011yescharacteristic
286C22×C11C2×C22⋊Q811yescharacteristic
287C22×C11C2×#12411yescharacteristic
288C22×C11C2×#13511yescharacteristic
289C22×C11C2×#13511yescharacteristic
290C22×C11#57511yescharacteristic
291C22×C11#57511yescharacteristic
292C2×D11—22no—
293C2×D11—22no—
294C2×D11—22no—
295C2×D11—22no—
296C2×D11—22no—
297C2×D11—22no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11#39314yes—
306C4×C11—22no—
307C4×C11—22no—
308C4×C11—42no—
309C4×C11—44no—
310C4×C11—81no—
311C4×C11C2×C22⋊Q812yes—
312C4×C11C2×#12412yes—
313Dic11—44no—
314Dic11—41no—
315Dic11—41no—
316Dic11—81no—
317Dic11#39314yes—
318C2×#41—114no—
319C2×#41—222no—
320C2×#41—224no—
321C2×#41—224no—
322C22×Q8—21no—
323C22×Q8—221no—
324C22×Q8C22×D1111yescharacteristic
325C22×D4—111no—
326C22×D4—221no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—221no—
331C22×C8—112no—
332C22×C8—224no—
333C22×C8—224no—
334C22×C8—224no—
335C22×C8C22×D1112yes—
336C4⋊Q8—24no—
337C4⋊Q8—224no—
338#125—224no—
339#125—224no—
340C22⋊Q8—228no—
341C22⋊Q8—228no—
342C4×Q8—228no—
343C4×Q8—228no—
344#117—118no—
345#117—224no—
346#117—224no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C4⋊C4C22×D1112yes—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—221no—
359C2×C22⋊C4—221no—
360C2×C22⋊C4—221no—
361C2×C42—111no—
362C2×C42—111no—
363C2×C42—111no—
364C2×C42—224no—
365C2×C42—222no—
366C2×C42—221no—
367C2×C42C22×D1111yescharacteristic
368#103—24no—
369#103—224no—
370#102—224no—
371#102—224no—
372#95—21no—
373#95—21no—
374#95—221no—
375#95—221no—
376C2×C11C2×#39311yescharacteristic
377C2×C11#300211yescharacteristic
378C2×C11#300211yescharacteristic
379C2×C11#307611yescharacteristic
380C2×C11#307611yescharacteristic
381C2×C11#313111yescharacteristic
382C2×C11#313511yescharacteristic
383D11—24no—
384D11—82no—
385C24—111no—
386C24—221no—
387#41—2216no—
388#41—448no—
389C2×Q8—24no—
390C2×Q8—21no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—42no—
394C2×Q8—42no—
395C2×Q8—224no—
396C2×Q8—442no—
397C2×Q8—442no—
398C2×Q8Q8×D1112yes—
399C2×D4—112no—
400C2×D4—224no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—221no—
404C2×D4—442no—
405C2×D4—442no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—111no—
410C22×C4—114no—
411C22×C4—112no—
412C22×C4—114no—
413C22×C4—112no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—224no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—221no—
423C22×C4—441no—
424C22×C4—441no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4D4×D1111yescharacteristic
428C22×C4D4×D1111yescharacteristic
429C22×C4C23×D1111yescharacteristic
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—448no—
437C4⋊C4—24no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—114no—
441C4⋊C4—228no—
442C4⋊C4—228no—
443C4⋊C4—224no—
444C4⋊C4—222no—
445C4⋊C4—222no—
446C4⋊C4D4×D1114yes—
447C22⋊C4—228no—
448C22⋊C4—442no—
449C22⋊C4—442no—
450C22⋊C4—442no—
451C22⋊C4—442no—
452C22⋊C4—442no—
453C42—22no—
454C42—222no—
455C42—222no—
456C42—228no—
457C42—222no—
458C42—442no—
459C11#2345111yescharacteristic, complemented, Sylow
460C23—112no—
461C23—112no—
462C23—112no—
463C23—221no—
464C23—221no—
465C23—221no—
466C23—221no—
467C23—222no—
468C23—441no—
469C23—441no—
470C23—441no—
471C23—441no—
472C23—441no—
473C23—441no—
474C23C2×D4×D1111yescharacteristic
475Q8—24no—
476Q8—48no—
477Q8—42no—
478Q8—448no—
479D4—224no—
480D4—448no—
481D4—442no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—112no—
498C2×C4—118no—
499C2×C4—118no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—224no—
507C2×C4—444no—
508C2×C4—444no—
509C2×C4—448no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4#6696912yes—
516C2×C4#6697212yes—
517C2×C4C2×D4×D1112yes—
518C2×C4C2×Q8×D1111yescharacteristic
519C2×C4#41×D1112yes—
520C2×C4#41×D1111yescharacteristic
521C8—42no—
522C8—442no—
523C22—114no—
524C22—222no—
525C22—222no—
526C22—222no—
527C22—222no—
528C22—222no—
529C22—222no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22—881no—
537C22D11×#12011yescharacteristic
538C22D11×C22⋊Q811yescharacteristic
539C22D11×#12411yescharacteristic
540C22C2×#6696911yescharacteristic
541C22C2×#6697211yescharacteristic
542C22#1062330411yescharacteristic
543C22#1062330811yescharacteristic
544C4—22no—
545C4—22no—
546C4—44no—
547C4—42no—
548C4—81no—
549C4—114no—
550C4—441no—
551C4—441no—
552C4—444no—
553C4—881no—
554C4D11×C22⋊Q812yes—
555C4D11×#12412yes—
556C2—224no—
557C2—882no—
558C2D11×#39311yescharacteristic
559C2#1307783511yescharacteristic
560C2#1307783911yescharacteristic
561C2#1307839911yescharacteristic
562C2#1307840711yescharacteristic
563C2#1307894011yescharacteristic
564C2#1307895811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2024C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
hypercenter#2024D11
hypocenterC11#23451
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
4. #13069765C2semidirect
5. #13069761C2semidirect
6. #13069757C2semidirect
7. #13069753C2semidirect
8. #13069749C2semidirect
9. #13068331C2semidirect
10. D11×#336C2semidirect
11. C11×#2024C2semidirect
50. C2×#4343Q8semidirect
184. #2024D11semidirect
459. C11#23451semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106224172
#130711052
#130697652
#130697612
#130697572
#130697532
#130697492
#130683312
D11×#3362
C11×#20242
#2345111