Finite Group Databasebeta

← #14782681

Subgroups — #14782681

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622494C211yesmaximal, characteristic, complemented
2#13077132C211yesmaximal, characteristic
3D11×#417C211yesmaximal, characteristic
4#13077058C211yesmaximal, characteristic
5#13070065C211yesmaximal, characteristic, complemented
6#13070064C211yesmaximal, characteristic, complemented
7#13070063C211yesmaximal, characteristic, complemented
8#13070061C211yesmaximal, characteristic, complemented
9#13070060C211yesmaximal, characteristic, complemented
10#13070059C211yesmaximal, characteristic, complemented
11#13070057C211yesmaximal, characteristic, complemented
12#13068353C211yesmaximal, characteristic, complemented
13D11×#343C211yesmaximal, characteristic, complemented
14#13068341C211yesmaximal, characteristic, complemented
15C11×#2078C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×M16×D11C2211yescharacteristic
18C2×M16×D11C2211yescharacteristic
19C2×M16×D11C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic, complemented
24C11×#417C2211yescharacteristic
25C11×#417C2211yescharacteristic
26C11×#408C2211yescharacteristic
27#10622847C2211yescharacteristic
28#10622845C2211yescharacteristic
29#10622845C2211yescharacteristic
30#10622746C2211yescharacteristic
31#10622746C2211yescharacteristic
32#10622742C2211yescharacteristic
33#10622723C2211yescharacteristic
34C2×#66881C2211yescharacteristic, complemented
35#10622579C2211yescharacteristic
36#10622579C2211yescharacteristic
37C2×#66872C2211yescharacteristic, complemented
38C2×#66871C2211yescharacteristic, complemented
39#10622494—22no—
40#10622494—22no—
41#10622417—21no—
42#10622416—21no—
43#10622415—21no—
44D11×#103—21no—
45#10622385—21no—
46#10622384—21no—
47#10622383—21no—
48D11×#102—21no—
49#10622340—22no—
50#10622339—22no—
51C11×#343C2211yescharacteristic, complemented
52C11×#343C2211yescharacteristic, complemented
53C11×#341C2211yescharacteristic, complemented
54#10622196C2211yescharacteristic, complemented
55#10622196C2211yescharacteristic, complemented
56#10622192C2211yescharacteristic, complemented
57#10622192C2211yescharacteristic, complemented
58#10622192C2211yescharacteristic, complemented
59#10622192C2211yescharacteristic, complemented
60#10622190C2211yescharacteristic, complemented
61#10622168C2211yescharacteristic, complemented
62#10622168C2211yescharacteristic, complemented
63C2×C11×#41C2311yescharacteristic
64#41×D11—22no—
65#41×D11—22no—
66#41×D11—22no—
67#41×D11—22no—
68C2×#4343D411yescharacteristic
69C2×Q8×D11D411yescharacteristic
70C2×#4341—21no—
71C2×#4341D411yescharacteristic
72C2×D4×D11—21no—
73C2×D4×D11D411yescharacteristic
74C2×#4339—21no—
75C2×#4339C2311yescharacteristic
76C22×C4×D11—21no—
77C22×C4×D11—21no—
78C22×C4×D11C2311yescharacteristic
79C2×C11×M16C2311yescharacteristic
80C2×C11×M16C2311yescharacteristic
81C2×C11×M16C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×#4318C2311yescharacteristic
91C2×#4318C2311yescharacteristic
92C2×#4318C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94M16×D11—22no—
95M16×D11—22no—
96M16×D11—22no—
97M16×D11—22no—
98M16×D11—22no—
99M16×D11—22no—
100C2×#4313—22no—
101C2×#4313—22no—
102C2×#4313—21no—
103C2×#4313—21no—
104C2×#4313—21no—
105C2×#4313D412yes—
106C2×#4313D412yes—
107C2×C8×D11—21no—
108C2×C8×D11—21no—
109C2×C8×D11—21no—
110#66945—21no—
111#66945—21no—
112#66945—21no—
113#66945—21no—
114C4⋊C4×D11—21no—
115C4⋊C4×D11—21no—
116C4⋊C4×D11—21no—
117C4⋊C4×D11—21no—
118C11×#107—22no—
119C11×#103—21no—
120C11×#103—21no—
121C11×#102—21no—
122C11×#102—21no—
123C11×C22⋊C8—22no—
124#66899—21no—
125#66899—21no—
126#66896—21no—
127#66896—21no—
128C22⋊(C11⋊C8)—22no—
129#66885—21no—
130#66885—21no—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133#66881—22no—
134#66880—21no—
135#66880—21no—
136#66874—21no—
137#66874—21no—
138#66873—21no—
139#66873—21no—
140#66872—22no—
141#66871—22no—
142#23647—111nomaximal, Sylow
143C23×D11—21no—
144C23×D11#4111yescharacteristic
145C11×#41—21no—
146C11×#41—21no—
147C11×#41—21no—
148C11×#41—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—21no—
157C2×C22⋊D11—21no—
158C2×C22⋊D11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11#4111yescharacteristic
163#4343—22no—
164#4343—22no—
165Q8×D11—22no—
166Q8×D11—22no—
167#4341—22no—
168#4341—22no—
169#4341—42no—
170#4341—42no—
171D4×D11—22no—
172D4×D11—22no—
173D4×D11—42no—
174D4×D11—42no—
175#4339—21no—
176#4339—21no—
177#4339—21no—
178#4339—21no—
179#4339—42no—
180#4339—42no—
181C2×D44—21no—
182C2×D44C2×D411yescharacteristic
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—42no—
187C2×C4×D11—42no—
188C2×C4×D11—41no—
189C2×C4×D11—41no—
190C2×C4×D11—82no—
191C2×C4×D11C2×D411yescharacteristic
192C2×C4×D11C2×D411yescharacteristic
193C2×C4×D11C2×D411yescharacteristic
194C2×C4×D11C2×D411yescharacteristic
195C2×C4×D11#4112yes—
196C2×C4×D11#4112yes—
197C2×C4×D11#4112yes—
198C2×C4×D11#4112yes—
199C2×Dic22—21no—
200C2×Dic22C2×D411yescharacteristic
201C11×M16—21no—
202C11×M16—21no—
203C11×M16—21no—
204C11×M16—21no—
205C11×M16—21no—
206C11×M16—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11C2×D412yes—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217(C2×D11)⋊C4—41no—
218(C2×D11)⋊C4—41no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223Dic11⋊C4—41no—
224Dic11⋊C4—41no—
225C4×Dic11—41no—
226C4×Dic11—41no—
227#4318—21no—
228#4318—21no—
229#4318—21no—
230#4318—21no—
231#4318—21no—
232#4318—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8C2×D412yes—
239#4313—24no—
240#4313—24no—
241#4313—42no—
242#4313—42no—
243#4313—42no—
244C8×D11—42no—
245C8×D11—42no—
246C8×D11—42no—
247C2×#428—111no—
248#2896—111no—
249C2×#417—111no—
250#2879—111no—
251#2079—111no—
252#2079—111no—
253#2079—111no—
254#2079—111no—
255#2078—111no—
256#2078—111no—
257#2078—111no—
258#2078D1111yescharacteristic, complemented
259#1742—111no—
260C2×#343—111no—
261#1738—111no—
262C23×C11—21no—
263C23×C11C2×#4111yescharacteristic
264C22×D11—21no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—42no—
268C22×D11—81no—
269C22×D11—81no—
270C22×D11#12111yescharacteristic
271C22×D11#12111yescharacteristic
272C22×D11#12612yes—
273C22×D11#12612yes—
274Q8×C11—21no—
275Q8×C11—21no—
276D4×C11—21no—
277D4×C11—21no—
278D4×C11—41no—
279D4×C11—41no—
280C2×C4×C11—21no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—81no—
286C2×C4×C11—81no—
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C22⋊D11—41no—
294C22⋊D11—41no—
295C22⋊D11—42no—
296C22⋊D11—42no—
297C2×Dic11—21no—
298C2×Dic11—42no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—81no—
302C2×Dic11—81no—
303C2×Dic11#12111yescharacteristic
304C2×Dic11#12111yescharacteristic
305C2×Dic11#12612yes—
306C2×Dic11#12612yes—
307D44—21no—
308D44—21no—
309D44—42no—
310C4×D11—42no—
311C4×D11—41no—
312C4×D11—41no—
313C4×D11—42no—
314C4×D11—82no—
315C4×D11—82no—
316C4×D11#12312yes—
317C4×D11#12312yes—
318C4×D11#12312yes—
319C4×D11#12312yes—
320C4×D11#12312yes—
321C4×D11#12312yes—
322C4×D11#12412yes—
323C4×D11#12412yes—
324Dic22—21no—
325Dic22—21no—
326Dic22—42no—
327C8×C11—22no—
328C8×C11—41no—
329C8×C11—41no—
330C8×C11—41no—
331C11⋊C8—22no—
332C11⋊C8—41no—
333C11⋊C8—41no—
334C11⋊C8—41no—
335C22×#41—111no—
336C22×M16—111no—
337C22×M16—111no—
338C22×M16—111no—
339C22×M16—111no—
340C2×#117—111no—
341C22×C4⋊C4—111no—
342#428—222no—
343#428—222no—
344C2×#107—111no—
345C2×#107C2×D1111yescharacteristic, complemented
346C2×#106—111no—
347C2×#106—111no—
348#419—221no—
349#418—221no—
350#417—111no—
351#417—111no—
352#417—111no—
353#417—111no—
354#417—111no—
355#417—111no—
356#417—221no—
357#417—221no—
358#417C2×D1111yescharacteristic
359#417C2×D1111yescharacteristic
360#416—221no—
361#416—221no—
362C2×#103—221no—
363C2×#102—221no—
364#408—111no—
365#408—111no—
366#408—111no—
367#408—222no—
368#408C2×D1111yescharacteristic
369#407—222no—
370#343—111no—
371#343—111no—
372#343—111no—
373#343—111no—
374#343—111no—
375#343—111no—
376#343C2×D1111yescharacteristic, complemented
377#343C2×D1111yescharacteristic, complemented
378#341—111no—
379#341—111no—
380#341—111no—
381#341C2×D1111yescharacteristic, complemented
382C22×C11—21no—
383C22×C11—21no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11C2×#12111yescharacteristic
388C22×C11C2×#12611yescharacteristic
389C22×C11C2×#12611yescharacteristic
390C2×D11—21no—
391C2×D11—21no—
392C2×D11—21no—
393C2×D11—21no—
394C2×D11—42no—
395C2×D11—42no—
396C2×D11—41no—
397C2×D11—41no—
398C2×D11—41no—
399C2×D11—84no—
400C2×D11#39712yes—
401C2×D11#39712yes—
402C4×C11—41no—
403C4×C11—81no—
404C4×C11—81no—
405C4×C11C2×#12311yescharacteristic
406C4×C11C2×#12311yescharacteristic
407C4×C11C2×#12311yescharacteristic
408C4×C11C2×#12411yescharacteristic
409Dic11—41no—
410Dic11—81no—
411Dic11—81no—
412Dic11#39712yes—
413Dic11#39712yes—
414C2×#41—111no—
415C2×#41—111no—
416C2×#41—111no—
417C2×#41—221no—
418C2×#41—221no—
419C2×#41—222no—
420C2×#41—222no—
421C2×#41—222no—
422C2×#41—222no—
423C2×#41C22×D1111yescharacteristic
424C22×Q8—111no—
425C22×D4—111no—
426C22×D4—221no—
427C23×C4—111no—
428C23×C4—221no—
429C23×C4—221no—
430C2×M16—112no—
431C2×M16—112no—
432C2×M16—111no—
433C2×M16—111no—
434C2×M16—111no—
435C2×M16—222no—
436C2×M16—222no—
437C2×M16—221no—
438C2×M16—221no—
439C2×M16—221no—
440C2×M16—222no—
441C2×M16—222no—
442C2×M16—222no—
443C2×M16—222no—
444C2×M16—222no—
445C2×M16—222no—
446C2×M16C22×D1111yescharacteristic
447C2×M16C22×D1111yescharacteristic
448C2×M16C22×D1111yescharacteristic
449C22×C8—111no—
450C22×C8—221no—
451C22×C8—221no—
452C22×C8—221no—
453C22×C8C22×D1111yescharacteristic
454#117—221no—
455#117—221no—
456#117—221no—
457#117—221no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—221no—
461C2×C4⋊C4—221no—
462C2×C4⋊C4—221no—
463C2×C4⋊C4—221no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4C22×D1111yescharacteristic
466C2×C4⋊C4C22×D1111yescharacteristic
467C2×C22⋊C4—221no—
468C2×C42—221no—
469#107—22no—
470#107—222no—
471#106—222no—
472#106—222no—
473#103—21no—
474#103—21no—
475#103—221no—
476#103—221no—
477#103—221no—
478#103—221no—
479#103—221no—
480#103—221no—
481#102—21no—
482#102—21no—
483#102—221no—
484#102—221no—
485#102—221no—
486#102—221no—
487#102—221no—
488#102—221no—
489C22⋊C8—22no—
490C22⋊C8—222no—
491C22⋊C8—222no—
492C22⋊C8—222no—
493C2×C11—21no—
494C2×C11—21no—
495C2×C11—81no—
496C2×C11C2×#39711yescharacteristic
497C2×C11#306811yescharacteristic
498C2×C11#306911yescharacteristic
499D11—22no—
500D11—22no—
501D11—81no—
502C24—111no—
503C24—221no—
504#41—21no—
505#41—21no—
506#41—21no—
507#41—21no—
508#41—222no—
509#41—222no—
510#41—222no—
511#41—222no—
512#41—221no—
513#41—221no—
514#41—221no—
515#41—221no—
516#41—442no—
517#41—442no—
518#41—442no—
519#41—442no—
520C2×Q8—111no—
521C2×Q8—221no—
522C2×Q8—222no—
523C2×Q8—222no—
524C2×Q8D4×D1111yescharacteristic
525C2×D4—21no—
526C2×D4—111no—
527C2×D4—221no—
528C2×D4—222no—
529C2×D4—222no—
530C2×D4—221no—
531C2×D4—221no—
532C2×D4—221no—
533C2×D4—442no—
534C2×D4—442no—
535C2×D4D4×D1111yescharacteristic
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—111no—
540C22×C4—111no—
541C22×C4—111no—
542C22×C4—111no—
543C22×C4—111no—
544C22×C4—112no—
545C22×C4—112no—
546C22×C4—112no—
547C22×C4—112no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—442no—
555C22×C4—442no—
556C22×C4—441no—
557C22×C4—441no—
558C22×C4—882no—
559C22×C4C23×D1111yescharacteristic
560M16—21no—
561M16—21no—
562M16—21no—
563M16—21no—
564M16—21no—
565M16—21no—
566M16—224no—
567M16—224no—
568M16—221no—
569M16—221no—
570M16—221no—
571M16—221no—
572M16—221no—
573M16—221no—
574M16—442no—
575M16—442no—
576M16—442no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—112no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—442no—
589C2×C8—442no—
590C2×C8—442no—
591C2×C8D4×D1112yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—441no—
601C4⋊C4—441no—
602C22⋊C4—441no—
603C22⋊C4—441no—
604C42—441no—
605C42—441no—
606C11#2364711yescharacteristic, complemented, Sylow
607C23—21no—
608C23—111no—
609C23—111no—
610C23—112no—
611C23—112no—
612C23—221no—
613C23—441no—
614C23—441no—
615C23—442no—
616C23—881no—
617C23—881no—
618C23#41×D1111yescharacteristic
619Q8—21no—
620Q8—21no—
621Q8—221no—
622Q8—221no—
623Q8—442no—
624D4—21no—
625D4—21no—
626D4—41no—
627D4—41no—
628D4—221no—
629D4—221no—
630D4—442no—
631D4—442no—
632D4—442no—
633D4—441no—
634D4—441no—
635C2×C4—21no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—112no—
643C2×C4—112no—
644C2×C4—111no—
645C2×C4—111no—
646C2×C4—112no—
647C2×C4—112no—
648C2×C4—112no—
649C2×C4—112no—
650C2×C4—112no—
651C2×C4—112no—
652C2×C4—112no—
653C2×C4—112no—
654C2×C4—221no—
655C2×C4—442no—
656C2×C4—442no—
657C2×C4—442no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4—882no—
663C2×C4—882no—
664C2×C4—881no—
665C2×C4—881no—
666C2×C4C2×D4×D1111yescharacteristic
667C2×C4C2×D4×D1111yescharacteristic
668C2×C4#41×D1111yescharacteristic
669C2×C4#41×D1111yescharacteristic
670C2×C4#41×D1111yescharacteristic
671C2×C4#41×D1111yescharacteristic
672C8—22no—
673C8—41no—
674C8—41no—
675C8—41no—
676C8—222no—
677C8—441no—
678C8—441no—
679C8—441no—
680C22—21no—
681C22—21no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—112no—
686C22—112no—
687C22—221no—
688C22—221no—
689C22—221no—
690C22—221no—
691C22—442no—
692C22—442no—
693C22—441no—
694C22—441no—
695C22—441no—
696C22—884no—
697C22D11×#12111yescharacteristic
698C22D11×#12611yescharacteristic
699C22D11×#12611yescharacteristic
700C4—41no—
701C4—81no—
702C4—81no—
703C4—112no—
704C4—112no—
705C4—441no—
706C4—881no—
707C4—881no—
708C4D11×#12311yescharacteristic
709C4D11×#12311yescharacteristic
710C4D11×#12311yescharacteristic
711C4D11×#12411yescharacteristic
712C2—21no—
713C2—21no—
714C2—81no—
715C2—222no—
716C2—222no—
717C2—881no—
718C2D11×#39711yescharacteristic
719C2#1307834211yescharacteristic
720C2#1307835111yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2078C2
socleC22×C11C2×#121
prime radicalC2×#41×D11C22
hypercenter#2078D11
hypocenterC11#23647
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2078

Complements

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

NH ≅ G/Ntype
1. C2×#10622494C2semidirect
5. #13070065C2semidirect
6. #13070064C2semidirect
7. #13070063C2semidirect
8. #13070061C2semidirect
9. #13070060C2semidirect
10. #13070059C2semidirect
11. #13070057C2semidirect
12. #13068353C2semidirect
13. D11×#343C2semidirect
14. #13068341C2semidirect
15. C11×#2078C2semidirect
23. C2×C11×#107C22semidirect
34. C2×#66881C22semidirect
37. C2×#66872C22semidirect
38. C2×#66871C22semidirect
51. C11×#343C22semidirect
52. C11×#343C22semidirect
53. C11×#341C22semidirect
54. #10622196C22semidirect
55. #10622196C22semidirect
56. #10622192C22semidirect
57. #10622192C22semidirect
58. #10622192C22semidirect
59. #10622192C22semidirect
60. #10622190C22semidirect
61. #10622168C22semidirect
62. #10622168C22semidirect
258. #2078D11semidirect
345. C2×#107C2×D11semidirect
376. #343C2×D11semidirect
377. #343C2×D11semidirect
381. #341C2×D11semidirect
606. C11#23647semidirect

Maximal subgroups

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

subgroupindex
C2×#106224942
#130771322
D11×#4172
#130770582
#130700652
#130700642
#130700632
#130700612
#130700602
#130700592
#130700572
#130683532
D11×#3432
#130683412
C11×#20782
#2364711