Finite Group Databasebeta

← #15617453

Subgroups — #15617453

Order 2816.

2694 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623281C211yesmaximal, characteristic
2#13081816C211yesmaximal, characteristic
3D11×#520C211yesmaximal, characteristic
4#13077216C211yesmaximal, characteristic, complemented
5#13077215C213yesmaximal, complemented
6#13077214C211yesmaximal, characteristic, complemented
7#13077213C213yesmaximal, complemented
8#13077210C213yesmaximal, complemented
9#13077209C211yesmaximal, characteristic, complemented
10#13077207C213yesmaximal, complemented
11#13077204C213yesmaximal, complemented
12#13077203C213yesmaximal, complemented
13C2×#10622474C213yesmaximal, complemented
14D11×#428C213yesmaximal, complemented
15C11×#2912C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C11×#520C2211yescharacteristic
19C11×#520C2211yescharacteristic
20#10623358C2211yescharacteristic
21#10623358C2211yescharacteristic
22C2×#67001C2211yescharacteristic
23#10623281C4116yescomplemented
24C2×#66960C2213yes—
25C2×M16×D11C2213yes—
26C2×#66954C2213yes—
27C22×#4313C2213yes—
28#10623105—21no—
29C4×#4343—21no—
30#10623103—21no—
31C4×Q8×D11—21no—
32#10623077—23no—
33#10623076—23no—
34C4×D4×D11—23no—
35C4×#4341—23no—
36#10623054C2213yes—
37#10623054C2213yes—
38D11×#117C2213yes—
39D11×#117C2213yes—
40#10623035C2213yes—
41#10623035C2213yes—
42C2×#66945C2213yes—
43C2×C4⋊C4×D11C2213yes—
44C11×#428C2213yescomplemented
45C11×#428C2213yescomplemented
46C11×#427C2213yescomplemented
47C2×C11×#106C2213yescomplemented
48#10622734C2213yescomplemented
49#10622734C2213yescomplemented
50#10622719C2213yescomplemented
51C2×#66882C2213yescomplemented
52#10622611C2213yescomplemented
53#10622611C2213yescomplemented
54#10622608C2213yescomplemented
55#10622608C2213yescomplemented
56#10622577C2213yescomplemented
57#10622577C2213yescomplemented
58C2×#66872C2213yescomplemented
59C2×#66871C2213yescomplemented
60#10622494C2213yes—
61#10622494C2213yes—
62#10622494C2213yescomplemented
63#10622494C2213yescomplemented
64#10622493C2216yescomplemented
65D11×#107C2216yescomplemented
66#10622474C2216yes—
67#10622474C2213yes—
68#10622474C2211yescharacteristic
69#10622474C2216yescomplemented
70#10622474C2216yescomplemented
71#10622474C2213yescomplemented
72#10622474C2213yescomplemented
73#10622473C2216yescomplemented
74D11×#106C2216yescomplemented
75C2×C11×#41C2311yescharacteristic
76#41×D11C2×C418yes—
77#41×D11Q818yes—
78C2×#4343D411yescharacteristic
79C2×Q8×D11D411yescharacteristic
80C2×#4341D413yes—
81C2×D4×D11D413yes—
82C2×#4339C2313yes—
83C22×C4×D11—23no—
84C22×C4×D11C2313yes—
85C11×#131C2×C418yescomplemented
86C2×C11×M16C2313yes—
87C22×C8×C11C2313yes—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×D4×C11—23no—
91C4×D4×C11—23no—
92C11×#117C2313yes—
93C11×#117C2313yes—
94C2×C11×C4⋊C4C2313yes—
95C2×C11×C4⋊C4C2313yes—
96#67001C2×C418yescomplemented
97Q8×Dic11—21no—
98Q8×Dic11—21no—
99D4×Dic11—23no—
100D4×Dic11—23no—
101C4×C22⋊D11—26no—
102C4×C22⋊D11—26no—
103C2×(C2×D11)⋊C4—23no—
104#66979C2313yes—
105#66979C2313yes—
106C2×C4⋊Dic11C2313yes—
107C2×C4⋊Dic11C2313yes—
108C2×Dic11⋊C4—23no—
109C2×C4×Dic11—23no—
110C2×#4318C2313yes—
111C22×C11⋊C8C2313yes—
112#66960C2×C4124yescomplemented
113M16×D11C2×C4124yescomplemented
114#66954C2×C4124yescomplemented
115C2×#4313C2×C4124yescomplemented
116C2×#4313C2311yescharacteristic
117C2×#4313C2313yes—
118C2×#4313C2313yes—
119C2×#4313C2313yes—
120C2×C8×D11C2316yes—
121#66946—23no—
122#66946—23no—
123#66945—23no—
124#66945—23no—
125#66945C2313yes—
126#66945C2316yes—
127#66945C2313yes—
128#66945C2311yescharacteristic
129#66945C2313yes—
130C4⋊C4×D11—23no—
131C4⋊C4×D11—23no—
132C4⋊C4×D11C2313yes—
133C4⋊C4×D11C2316yes—
134C4⋊C4×D11C2313yes—
135C4⋊C4×D11C2311yescharacteristic
136C4⋊C4×D11C2313yes—
137#66940—23no—
138#66940—23no—
139(C22⋊D11)⋊C4—26no—
140(C22⋊D11)⋊C4—26no—
141C22⋊C4×D11—23no—
142C22⋊C4×D11—23no—
143#66930—23no—
144#66930—23no—
145C4×D44—23no—
146C4×D44—23no—
147#66925—23no—
148#66925—23no—
149C42×D11—23no—
150C42×D11—23no—
151C4×Dic22—23no—
152C4×Dic22—23no—
153C11×#107C2313yes—
154C11×#107C2313yes—
155C11×#106C2316yes—
156C11×#106C2313yes—
157C11×#106C2311yescharacteristic
158#66882C2313yes—
159#66882C2311yescharacteristic
160#66882C2316yes—
161#66881C2313yes—
162#66881C2313yes—
163#66872C2313yes—
164#66872C2316yes—
165#66872C2313yes—
166#66872C2311yescharacteristic
167#66872C2313yes—
168#66871C2313yes—
169#66871C2316yes—
170#66871C2313yes—
171#66871C2311yescharacteristic
172#66871C2313yes—
173#60109—111nomaximal, Sylow
174C23×D11C2×D413yes—
175C11×#41C22×C414yes—
176C11×#41C2×Q814yes—
177C2×Q8×C11C2×D411yescharacteristic
178C2×D4×C11C2×D413yes—
179C22×C4×C11—23no—
180C22×C4×C11—23no—
181C22×C4×C11C2413yes—
182C2×C22⋊D11C2×D416yes—
183C22×Dic11—23no—
184C22×Dic11—23no—
185C22×Dic11C2×D413yes—
186#4343C4⋊C418yes—
187Q8×D11C4⋊C418yes—
188#4341C4⋊C4124yes—
189D4×D11C4⋊C4124yes—
190#4339C22×C4112yes—
191#4339C2×Q8112yes—
192C2×D44C2×D413yes—
193C2×C4×D11—21no—
194C2×C4×D11—23no—
195C2×C4×D11—23no—
196C2×C4×D11—23no—
197C2×C4×D11—26no—
198C2×C4×D11—86no—
199C2×C4×D11C22×C4112yes—
200C2×C4×D11C2×D413yes—
201C2×C4×D11C2×D413yes—
202C2×C4×D11C2×Q8112yes—
203C2×C4×D11C2413yes—
204C2×C4×D11C2411yescharacteristic
205C2×Dic22C2×D413yes—
206C11×M16C22×C4112yescomplemented
207C2×C8×C11C22×C4112yescomplemented
208C2×C8×C11C2413yes—
209C2×C8×C11C2411yescharacteristic
210C11×C4⋊C4—23no—
211C11×C4⋊C4—23no—
212C11×C4⋊C4C2413yes—
213C11×C4⋊C4C2411yescharacteristic
214C11×C4⋊C4C2413yes—
215C11×C4⋊C4C2411yescharacteristic
216C11×C22⋊C4—23no—
217C11×C22⋊C4—23no—
218C42×C11—23no—
219C42×C11—23no—
220C22⋊Dic11—23no—
221C22⋊Dic11—23no—
222(C2×D11)⋊C4—21no—
223(C2×D11)⋊C4—23no—
224(C2×D11)⋊C4—23no—
225(C2×D11)⋊C4—23no—
226(C2×D11)⋊C4—26no—
227C4⋊Dic11—23no—
228C4⋊Dic11—23no—
229C4⋊Dic11C2411yescharacteristic
230C4⋊Dic11C2413yes—
231C4⋊Dic11C2411yescharacteristic
232C4⋊Dic11C2413yes—
233Dic11⋊C4—23no—
234Dic11⋊C4—26no—
235Dic11⋊C4—21no—
236Dic11⋊C4—23no—
237Dic11⋊C4—23no—
238C4×Dic11—23no—
239C4×Dic11—26no—
240C4×Dic11—21no—
241C4×Dic11—23no—
242C4×Dic11—23no—
243C4×Dic11—23no—
244C4×Dic11—23no—
245#4318C22×C4112yescomplemented
246C2×C11⋊C8C22×C4112yescomplemented
247C2×C11⋊C8C2413yes—
248C2×C11⋊C8C2411yescharacteristic
249#4313C22×C414yes—
250#4313C22×C4112yes—
251#4313C22×C4112yescomplemented
252#4313C22×C4112yescomplemented
253C8×D11C22×C4124yescomplemented
254C2×#568—111no—
255#3428—111no—
256C2×#520—111no—
257#2913—113no—
258#2913—113no—
259#2913—111no—
260#2913—111no—
261#2912—113no—
262#2912—113no—
263#2912—111no—
264#2912D1111yescharacteristic, complemented
265#2911—113no—
266#2911—113no—
267C2×#428—113no—
268C2×#428—113no—
269C23×C11C22×D413yes—
270C22×D11—43no—
271C22×D11—43no—
272C22×D11C2×C4⋊C4112yes—
273C22×D11C22×D411yescharacteristic
274C22×D11C22×D413yes—
275Q8×C11C2×C4⋊C414yes—
276D4×C11C2×C4⋊C4112yes—
277C2×C4×C11—21no—
278C2×C4×C11—23no—
279C2×C4×C11—21no—
280C2×C4×C11—23no—
281C2×C4×C11—83no—
282C2×C4×C11—83no—
283C2×C4×C11C23×C416yes—
284C2×C4×C11C22×D413yes—
285C2×C4×C11C22×Q816yes—
286C2×C4×C11C2511yescharacteristic
287C22⋊D11C2×C4⋊C4124yes—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—23no—
291C2×Dic11—23no—
292C2×Dic11—83no—
293C2×Dic11—83no—
294C2×Dic11C2×C4⋊C4112yes—
295C2×Dic11C22×D413yes—
296C2×Dic11C22×D411yescharacteristic
297D44C2×C4⋊C4112yes—
298C4×D11—42no—
299C4×D11—46no—
300C4×D11—83no—
301C4×D11—83no—
302C4×D11—86no—
303C4×D11C2×C4⋊C4112yes—
304C4×D11C2×C4⋊C4112yes—
305C4×D11C23×C416yes—
306C4×D11C23×C412yes—
307C4×D11C22×Q812yes—
308C4×D11C22×Q816yes—
309Dic22C2×C4⋊C4112yes—
310C8×C11C23×C416yes—
311C8×C11C23×C412yes—
312C11⋊C8C23×C416yes—
313C11⋊C8C23×C412yes—
314C22×#41—111no—
315#568—1116no—
316C2×#131—111no—
317C2×#131—113no—
318C2×#131—113no—
319C2×#131C2×D1111yescharacteristic
320C22×M16—113no—
321C22×M16—113no—
322#520—111no—
323#520—111no—
324#520—113no—
325#520—113no—
326#520—113no—
327#520—113no—
328#520—223no—
329#520—221no—
330#520C2×D1111yescharacteristic
331#520C2×D1111yescharacteristic
332#519—221no—
333#518—223no—
334C4×#41—223no—
335C4×#41—221no—
336C2×C4×Q8—221no—
337C2×C4×D4—223no—
338C2×#117—113no—
339C2×#117—113no—
340C2×#117—113no—
341C22×C4⋊C4—113no—
342#428—113no—
343#428—113no—
344#428—113no—
345#428—113no—
346#428—113no—
347#428—113no—
348#428—113no—
349#428—113no—
350#428—113no—
351#428—113no—
352#428—116no—
353#428—113no—
354#428—111no—
355#428—116no—
356#428—116no—
357#428—113no—
358#428—113no—
359#428C2×D1113yescomplemented
360#428C2×D1113yescomplemented
361#427—113no—
362#427—113no—
363#427—113no—
364#427—116no—
365#427—116no—
366#427C2×D1113yescomplemented
367C2×#107—113no—
368C2×#107—113no—
369C2×#107—116no—
370C2×#106—113no—
371C2×#106—116no—
372C2×#106C2×D1113yescomplemented
373C22×C11—23no—
374C22×C11—23no—
375C22×C11C22×C4⋊C416yes—
376C22×C11C23×D411yescharacteristic
377C2×D11—21no—
378C2×D11—23no—
379C2×D11—21no—
380C2×D11—23no—
381C2×D11—412no—
382C2×D11C22×C4⋊C412yes—
383C2×D11C22×C4⋊C416yes—
384C4×C11—43no—
385C4×C11—41no—
386C4×C11—43no—
387C4×C11—41no—
388C4×C11C22×C4⋊C416yes—
389C4×C11C24×C411yescharacteristic
390C4×C11C23×Q811yescharacteristic
391Dic11—43no—
392Dic11—43no—
393Dic11—41no—
394Dic11—41no—
395Dic11C22×C4⋊C416yes—
396Dic11C22×C4⋊C412yes—
397C2×#41—118no—
398C2×#41—118no—
399C2×#41—111no—
400C2×#41—113no—
401C2×#41—113no—
402C2×#41C22×D1111yescharacteristic
403C22×Q8—111no—
404C22×D4—113no—
405C23×C4—113no—
406C23×C4—223no—
407#131—118no—
408#131—1124no—
409#131—1124no—
410#131C4×D1118yescomplemented
411C2×M16—113no—
412C2×M16—1124no—
413C2×M16—1124no—
414C2×M16—113no—
415C2×M16—111no—
416C2×M16—113no—
417C2×M16—113no—
418C2×M16C22×D1113yes—
419C22×C8—113no—
420C22×C8—116no—
421C22×C8C22×D1113yes—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—223no—
425C4×Q8—223no—
426C4×Q8—223no—
427C4×Q8—223no—
428C4×Q8—221no—
429C4×Q8—221no—
430C4×D4—23no—
431C4×D4—23no—
432C4×D4—223no—
433C4×D4—223no—
434C4×D4—226no—
435C4×D4—226no—
436C4×D4—223no—
437C4×D4—223no—
438C4×D4—226no—
439C4×D4—226no—
440C4×D4—223no—
441C4×D4—223no—
442#117—113no—
443#117—113no—
444#117—111no—
445#117—113no—
446#117—113no—
447#117—113no—
448#117—116no—
449#117—223no—
450#117—223no—
451#117—223no—
452#117—223no—
453#117—223no—
454#117—223no—
455#117C22×D1113yes—
456#117C22×D1113yes—
457C2×C4⋊C4—113no—
458C2×C4⋊C4—113no—
459C2×C4⋊C4—113no—
460C2×C4⋊C4—116no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—113no—
463C2×C4⋊C4—113no—
464C2×C4⋊C4—223no—
465C2×C4⋊C4—223no—
466C2×C4⋊C4—223no—
467C2×C4⋊C4C22×D1113yes—
468C2×C4⋊C4C22×D1113yes—
469C2×C22⋊C4—223no—
470C2×C22⋊C4—223no—
471C2×C22⋊C4—223no—
472C2×C42—223no—
473C2×C42—223no—
474C2×C42—223no—
475#107—116no—
476#107—113no—
477#107—111no—
478#107—113no—
479#107—116no—
480#107—113no—
481#107—111no—
482#107—113no—
483#107C22×D1113yes—
484#107C22×D1113yes—
485#106—113no—
486#106—113no—
487#106—113no—
488#106—116no—
489#106—113no—
490#106—111no—
491#106—113no—
492#106C22×D1116yes—
493#106C22×D1113yes—
494#106C22×D1111yescharacteristic
495C2×C11—26no—
496C2×C11C23×C4⋊C411yescharacteristic
497C2×C11#358511yescharacteristic
498C2×C11#358611yescharacteristic
499D11—22no—
500D11—26no—
501C24—113no—
502#41—118no—
503#41—1124no—
504#41—1112no—
505#41—1112no—
506#41C2×C4×D1114yes—
507#41Q8×D1114yes—
508C2×Q8—118no—
509C2×Q8—113no—
510C2×Q8D4×D1111yescharacteristic
511C2×D4—116no—
512C2×D4—1124no—
513C2×D4—113no—
514C2×D4D4×D1113yes—
515C22×C4—23no—
516C22×C4—23no—
517C22×C4—113no—
518C22×C4—1112no—
519C22×C4—113no—
520C22×C4—113no—
521C22×C4—1112no—
522C22×C4—113no—
523C22×C4—111no—
524C22×C4—221no—
525C22×C4—223no—
526C22×C4—223no—
527C22×C4—223no—
528C22×C4—226no—
529C22×C4—223no—
530C22×C4—223no—
531C22×C4—886no—
532C22×C4C23×D1113yes—
533M16—1112no—
534M16—1112no—
535M16—114no—
536M16—1112no—
537M16—1112no—
538M16C2×C4×D11112yescomplemented
539C2×C8—1112no—
540C2×C8—111no—
541C2×C8—113no—
542C2×C8—1124no—
543C2×C8C2×C4×D11112yescomplemented
544C2×C8C23×D1113yes—
545C2×C8C23×D1111yescharacteristic
546C4⋊C4—23no—
547C4⋊C4—23no—
548C4⋊C4—111no—
549C4⋊C4—113no—
550C4⋊C4—111no—
551C4⋊C4—113no—
552C4⋊C4—223no—
553C4⋊C4—226no—
554C4⋊C4—221no—
555C4⋊C4—223no—
556C4⋊C4—223no—
557C4⋊C4—223no—
558C4⋊C4—223no—
559C4⋊C4C23×D1113yes—
560C4⋊C4C23×D1111yescharacteristic
561C4⋊C4C23×D1113yes—
562C4⋊C4C23×D1111yescharacteristic
563C22⋊C4—23no—
564C22⋊C4—23no—
565C22⋊C4—221no—
566C22⋊C4—223no—
567C22⋊C4—223no—
568C22⋊C4—226no—
569C22⋊C4—223no—
570C22⋊C4—223no—
571C22⋊C4—223no—
572C42—23no—
573C42—23no—
574C42—221no—
575C42—223no—
576C42—223no—
577C42—226no—
578C42—223no—
579C42—223no—
580C42—223no—
581C11#6010911yescharacteristic, complemented, Sylow
582C23—111no—
583C23—113no—
584C23—1112no—
585C23—443no—
586C23—443no—
587C23C2×D4×D1113yes—
588Q8—1112no—
589Q8C4⋊C4×D1114yes—
590D4—1124no—
591D4—1112no—
592D4C4⋊C4×D11112yes—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—23no—
596C2×C4—23no—
597C2×C4—83no—
598C2×C4—83no—
599C2×C4—1112no—
600C2×C4—111no—
601C2×C4—113no—
602C2×C4—1112no—
603C2×C4—1112no—
604C2×C4—116no—
605C2×C4—112no—
606C2×C4—112no—
607C2×C4—116no—
608C2×C4—221no—
609C2×C4—223no—
610C2×C4—221no—
611C2×C4—223no—
612C2×C4—446no—
613C2×C4—442no—
614C2×C4—886no—
615C2×C4—883no—
616C2×C4—883no—
617C2×C4—883no—
618C2×C4—883no—
619C2×C4C22×C4×D1116yes—
620C2×C4C2×D4×D1113yes—
621C2×C4C2×Q8×D1116yes—
622C2×C4C24×D1111yescharacteristic
623C8—112no—
624C8—116no—
625C8C22×C4×D1116yes—
626C8C22×C4×D1112yes—
627C22—23no—
628C22—23no—
629C22—112no—
630C22—116no—
631C22—221no—
632C22—223no—
633C22—221no—
634C22—223no—
635C22—4412no—
636C22C2×C4⋊C4×D1116yes—
637C22C22×D4×D1111yescharacteristic
638C4—43no—
639C4—41no—
640C4—43no—
641C4—41no—
642C4—112no—
643C4—116no—
644C4—443no—
645C4—443no—
646C4—441no—
647C4—441no—
648C4C2×C4⋊C4×D1116yes—
649C4C23×C4×D1111yescharacteristic
650C4C22×Q8×D1111yescharacteristic
651C2—26no—
652C2—222no—
653C2—226no—
654C2C22×C4⋊C4×D1111yescharacteristic
655C2#1308339411yescharacteristic
656C2#1308339811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#2912C2
socleC22×C11C23×D4
prime radicalC2×#41×D11C22
cosocleC2×C4×C11C25
hypercenter#2912D11
hypocenterC11#60109
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2912

Complements

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

NH ≅ G/Ntype
4. #13077216C2semidirect
5. #13077215C2semidirect
6. #13077214C2semidirect
7. #13077213C2semidirect
8. #13077210C2semidirect
9. #13077209C2semidirect
10. #13077207C2semidirect
11. #13077204C2semidirect
12. #13077203C2semidirect
13. C2×#10622474C2semidirect
14. D11×#428C2semidirect
15. C11×#2912C2semidirect
23. #10623281C4semidirect
44. C11×#428C22semidirect
45. C11×#428C22semidirect
46. C11×#427C22semidirect
47. C2×C11×#106C22semidirect
48. #10622734C22semidirect
49. #10622734C22semidirect
50. #10622719C22semidirect
51. C2×#66882C22semidirect
52. #10622611C22semidirect
53. #10622611C22semidirect
54. #10622608C22semidirect
55. #10622608C22semidirect
56. #10622577C22semidirect
57. #10622577C22semidirect
58. C2×#66872C22semidirect
59. C2×#66871C22semidirect
62. #10622494C22semidirect
63. #10622494C22semidirect
64. #10622493C22semidirect
65. D11×#107C22semidirect
69. #10622474C22semidirect
70. #10622474C22semidirect
71. #10622474C22semidirect
72. #10622474C22semidirect
73. #10622473C22semidirect
74. D11×#106C22semidirect
85. C11×#131C2×C4semidirect
96. #67001C2×C4semidirect
112. #66960C2×C4semidirect
113. M16×D11C2×C4semidirect
114. #66954C2×C4semidirect
115. C2×#4313C2×C4semidirect
206. C11×M16C22×C4semidirect
207. C2×C8×C11C22×C4semidirect
245. #4318C22×C4semidirect
246. C2×C11⋊C8C22×C4semidirect
251. #4313C22×C4semidirect
252. #4313C22×C4semidirect
253. C8×D11C22×C4semidirect
264. #2912D11semidirect
359. #428C2×D11semidirect
360. #428C2×D11semidirect
366. #427C2×D11semidirect
372. C2×#106C2×D11semidirect
410. #131C4×D11semidirect
538. M16C2×C4×D11semidirect
543. C2×C8C2×C4×D11semidirect
581. C11#60109semidirect

Maximal subgroups

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

subgroupindex
C2×#106232812
#130818162
D11×#5202
#130772162
#130772152
#130772142
#130772132
#130772102
#130772092
#130772072
#130772042
#130772032
C2×#106224742
D11×#4282
C11×#29122
#6010911