Finite Group Databasebeta

← #14790452

Subgroups — #14790452

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074423C212yesmaximal, complemented
2#13071270C211yesmaximal, characteristic
3#13069968C212yesmaximal, complemented
4#13069779C212yesmaximal, complemented
5#13069602C212yesmaximal, complemented
6#13069024C212yesmaximal
7#13068897C212yesmaximal, complemented
8#13068604C211yesmaximal, characteristic, complemented
9C11×#3501C211yesmaximal, characteristic, complemented
10C11×#554—22no—
11C11×#554—24no—
12D4×Q8×C11—22no—
13C11×#544—21no—
14C11×#543—21no—
15C11×#543C2212yes—
16C11×#533—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C11×#518C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66990C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23#10622844—22no—
24#10622833C2211yescharacteristic
25C2×#66898C2212yes—
26#10622826—21no—
27#10622825C2212yes—
28C4×C22⋊Dic11C2211yescharacteristic
29#10622607—24no—
30#10622605—22no—
31#10622603—21no—
32#10622570—21no—
33#10622568C2211yescharacteristic
34#10622568C2214yes—
35#10622559C2214yes—
36#10622559C2211yescharacteristic
37#10622553—21no—
38#10622164C2214yes—
39#10622164C2214yes—
40#10622164C2212yes—
41C24×D11C2311yescharacteristic
42C22×Q8×C11—21no—
43C22×Q8×C11D412yescomplemented
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—21no—
48C23×Dic11C2311yescharacteristic
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—24no—
52C11×#125—22no—
53C11×#125—24no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—24no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—24no—
71C4×D4×C11—24no—
72C11×#117—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D412yescomplemented
77C2×C11×C4⋊C4D414yescomplemented
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4C2314yes—
82C2×C42×C11D411yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11C2314yes—
85C2×C22⋊Dic11C2311yescharacteristic
86C2×C22⋊Dic11C2311yescharacteristic
87#66990—22no—
88#66990Q814yescomplemented
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×C4⋊Dic11—22no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—24no—
101C2×C4×Dic11—21no—
102#66898—24no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—24no—
107C11⋊#95—22no—
108#24352—111nomaximal, Sylow
109C24×C11C2×D411yescharacteristic
110C24×C11C2411yescharacteristic
111C23×D11—22no—
112C23×D11—21no—
113C23×D11—21no—
114C23×D11—22no—
115C23×D11—81no—
116C23×D11—81no—
117C23×D11C2×Q812yescomplemented
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—82no—
123C2×Q8×C11—82no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11C2×Q812yes—
127C2×D4×C11#4112yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—81no—
133C22×C4×C11—81no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D414yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C2×C22⋊D11—24no—
144C2×C22⋊D11—81no—
145C2×C22⋊D11—81no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—24no—
150C22×Dic11—21no—
151C22×Dic11—81no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C42×C11—24no—
169C42×C11—21no—
170C42×C11—21no—
171C22⋊Dic11—21no—
172C22⋊Dic11—24no—
173C22⋊Dic11—22no—
174C22⋊Dic11—24no—
175C22⋊Dic11—81no—
176C22⋊Dic11C2×Q812yescomplemented
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—84no—
182(C2×D11)⋊C4—81no—
183(C2×D11)⋊C4—81no—
184(C2×D11)⋊C4—84no—
185C4⋊Dic11—82no—
186Dic11⋊C4—81no—
187Dic11⋊C4—84no—
188C4×Dic11—81no—
189#3501D1111yescharacteristic, complemented
190#2626—112no—
191#2321—111no—
192#2062—112no—
193#2029—112no—
194#1996—112no—
195#1889—112no—
196#1867—112no—
197#1799—111no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11C22⋊Q812yes—
205C23×C11C22×D411yescharacteristic
206C23×C11C22×D412yes—
207C23×C11C22×Q811yescharacteristic
208C23×C11C2×#4111yescharacteristic
209C23×C112−1+412yes—
210C22×D11—22no—
211C22×D11—24no—
212C22×D11—44no—
213C22×D11—41no—
214C22×D11—44no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—42no—
221C22×D11—82no—
222C22×D11—84no—
223C22×D11—82no—
224Q8×C11—44no—
225Q8×C11—82no—
226Q8×C11—82no—
227Q8×C11—82no—
228D4×C11—24no—
229D4×C11—24no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—44no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—44no—
245C2×C4×C11—81no—
246C2×C4×C11—82no—
247C2×C4×C11—82no—
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11#12011yescharacteristic
250C2×C4×C11#12012yes—
251C2×C4×C11C22⋊Q812yes—
252C22⋊D11—84no—
253C2×Dic11—22no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—44no—
258C2×Dic11—44no—
259C2×Dic11—41no—
260C2×Dic11—44no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—44no—
266#554—24no—
267#554—22no—
268D4×Q8—22no—
269#544—21no—
270#543—21no—
271#543C2×D1112yes—
272#533—21no—
273C2×C22⋊Q8—21no—
274C2×C22⋊Q8C2×D1112yes—
275C2×#120—111no—
276#518C2×D1112yes—
277C2×C4×D4C2×D1111yescharacteristic
278C22×C22⋊C4—111no—
279C2×#99—112no—
280#399—222no—
281#396—224no—
282#393—222no—
283#390—221no—
284#388—221no—
285#388—221no—
286#386—111no—
287#386—221no—
288#385—111no—
289#385—114no—
290#380—112no—
291#379—111no—
292#379—114no—
293C4×C22⋊C4—111no—
294#342—112no—
295#342—114no—
296#342—114no—
297C22×C11—22no—
298C22×C11—21no—
299C22×C11—22no—
300C22×C11—21no—
301C22×C11—22no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11—81no—
309C22×C11C2×#12011yescharacteristic
310C22×C11C2×C22⋊Q811yescharacteristic
311C22×C11#53611yescharacteristic
312C22×C11#54812yes—
313C22×C11D4×Q812yes—
314C2×D11—42no—
315C2×D11—48no—
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—84no—
319C2×D11—81no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C4×C11—22no—
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—22no—
327C4×C11—41no—
328C4×C11—44no—
329C4×C11—44no—
330C4×C11—41no—
331Dic11—42no—
332Dic11—84no—
333Dic11—81no—
334Dic11—81no—
335C25—111no—
336C22×Q8—21no—
337C22×Q8C22⋊D1112yescomplemented
338C22×D4—221no—
339C22×D4C22×D1111yescharacteristic
340C23×C4—111no—
341C23×C4C22⋊D1111yescharacteristic
342C23×C4C22×D1111yescharacteristic
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—24no—
346#125—22no—
347#125—24no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—24no—
351C22⋊Q8—24no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—24no—
359C22⋊Q8—24no—
360#120—114no—
361#120—222no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—24no—
367C4×D4—24no—
368#117—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4C22⋊D1111yescharacteristic
375C2×C4⋊C4C22⋊D1114yescomplemented
376C2×C4⋊C4C22⋊D1112yescomplemented
377C2×C22⋊C4—22no—
378C2×C22⋊C4—111no—
379C2×C22⋊C4—111no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—222no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4C22⋊D1111yescharacteristic
392C2×C22⋊C4C22×D1111yescharacteristic
393C2×C22⋊C4C22×D1114yes—
394C2×C42—221no—
395C2×C42C22⋊D1111yescharacteristic
396#99—224no—
397#95—221no—
398#95—222no—
399#95—221no—
400#95—224no—
401#95—221no—
402C2×C11—21no—
403C2×C11—22no—
404C2×C11—21no—
405C2×C11—22no—
406C2×C11—42no—
407C2×C11#240911yescharacteristic
408C2×C11#302611yescharacteristic
409C2×C11#302711yescharacteristic
410D11—82no—
411C24—112no—
412C24—222no—
413C24—221no—
414C24—221no—
415C24—222no—
416C24—881no—
417C24—881no—
418C24C2×C22⋊D1111yescharacteristic
419C24C23×D1111yescharacteristic
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—82no—
425C2×Q8—82no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—224no—
429C2×D4—881no—
430C2×D4—881no—
431C2×D4Q8×D1112yes—
432C2×D4#434312yes—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—81no—
438C22×C4—81no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—224no—
442C22×C4—221no—
443C22×C4—222no—
444C22×C4—881no—
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1114yes—
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1114yes—
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1112yes—
454C4⋊C4—22no—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—24no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—24no—
465C4⋊C4—881no—
466C4⋊C4—884no—
467C4⋊C4—882no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—22no—
471C22⋊C4—24no—
472C22⋊C4—22no—
473C22⋊C4—112no—
474C22⋊C4—221no—
475C22⋊C4—224no—
476C22⋊C4—224no—
477C22⋊C4—222no—
478C22⋊C4—224no—
479C22⋊C4—441no—
480C22⋊C4—441no—
481C22⋊C4—442no—
482C22⋊C4—881no—
483C22⋊C4—884no—
484C22⋊C4—881no—
485C22⋊C4—884no—
486C22⋊C4—881no—
487C42—24no—
488C42—21no—
489C42—21no—
490C42—881no—
491C11#2435211yescharacteristic, complemented, Sylow
492C23—21no—
493C23—21no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—222no—
499C23—224no—
500C23—444no—
501C23—441no—
502C23—444no—
503C23—441no—
504C23—441no—
505C23—441no—
506C23—441no—
507C23—442no—
508C23—441no—
509C23—882no—
510C23—882no—
511C23—884no—
512C23#6699912yes—
513C23C2×Q8×D1111yescharacteristic
514C23C2×#434311yescharacteristic
515C23#6704012yes—
516C23C22×C22⋊D1111yescharacteristic
517C23C22×C22⋊D1112yes—
518Q8—44no—
519Q8—82no—
520Q8—82no—
521Q8—82no—
522D4—24no—
523D4—24no—
524D4—884no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—44no—
540C2×C4—81no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—222no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—444no—
549C2×C4—444no—
550C2×C4—441no—
551C2×C4—444no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—444no—
555C2×C4—441no—
556C2×C4#6699912yes—
557C2×C4#6700611yescharacteristic
558C2×C4#6700611yescharacteristic
559C2×C4#6700612yes—
560C22—22no—
561C22—21no—
562C22—22no—
563C22—21no—
564C22—22no—
565C22—41no—
566C22—41no—
567C22—42no—
568C22—42no—
569C22—41no—
570C22—41no—
571C22—81no—
572C22—442no—
573C22—442no—
574C22—448no—
575C22—442no—
576C22—884no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22C2×#6699911yescharacteristic
582C22Q8×C22⋊D1112yes—
583C22#1062334711yescharacteristic
584C22#1062334812yes—
585C22C2×#6700611yescharacteristic
586C4—22no—
587C4—21no—
588C4—21no—
589C4—22no—
590C4—44no—
591C4—41no—
592C4—41no—
593C4—44no—
594C4—442no—
595C4—884no—
596C4—881no—
597C4—881no—
598C2—21no—
599C2—22no—
600C2—21no—
601C2—22no—
602C2—42no—
603C2—882no—
604C2#1307197511yescharacteristic
605C2#1307801311yescharacteristic
606C2#1307801811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radicalC2×#66990C22
hypercenter#3501D11
hypocenterC11#24352
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13074423C2semidirect
3. #13069968C2semidirect
4. #13069779C2semidirect
5. #13069602C2semidirect
7. #13068897C2semidirect
8. #13068604C2semidirect
9. C11×#3501C2semidirect
43. C22×Q8×C11D4semidirect
76. C2×C11×C4⋊C4D4semidirect
77. C2×C11×C4⋊C4D4semidirect
88. #66990Q8semidirect
117. C23×D11C2×Q8semidirect
176. C22⋊Dic11C2×Q8semidirect
189. #3501D11semidirect
337. C22×Q8C22⋊D11semidirect
375. C2×C4⋊C4C22⋊D11semidirect
376. C2×C4⋊C4C22⋊D11semidirect
491. C11#24352semidirect

Maximal subgroups

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

subgroupindex
#130744232
#130712702
#130699682
#130697792
#130696022
#130690242
#130688972
#130686042
C11×#35012
#2435211