Finite Group Databasebeta

← #14756528

Subgroups — #14756528

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077177C211yesmaximal, characteristic, complemented
2C2×D11×#104C211yesmaximal, characteristic
3#13077131C211yesmaximal, characteristic
4#13077058C211yesmaximal, characteristic
5C2×C4×#4313C211yesmaximal, characteristic, complemented
6#13069330C211yesmaximal, characteristic, complemented
7#13069329C211yesmaximal, characteristic, complemented
8#13069326C211yesmaximal, characteristic, complemented
9#13069325C211yesmaximal, characteristic, complemented
10#13069321C211yesmaximal, characteristic, complemented
11#13069320C211yesmaximal, characteristic, complemented
12#13069317C211yesmaximal, characteristic, complemented
13#13068341C211yesmaximal, characteristic, complemented
14D11×#339C211yesmaximal, characteristic, complemented
15C11×#1937C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×M16×D11C2211yescharacteristic
18C2×M16×D11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21D11×#117C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C11×#424C2211yescharacteristic, complemented
24C2×C11×#104C2211yescharacteristic
25C11×#416C2211yescharacteristic
26C11×#408C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic, complemented
28C2×#66901C2211yescharacteristic
29#10622847C2211yescharacteristic
30#10622846C2211yescharacteristic
31C2×#66889C2211yescharacteristic
32#10622742C2211yescharacteristic
33#10622732C2211yescharacteristic, complemented
34#10622726C2211yescharacteristic
35#10622723C2211yescharacteristic
36#10622715C2211yescharacteristic, complemented
37C2×#66879C2211yescharacteristic, complemented
38C2×#66879C2211yescharacteristic, complemented
39#10622615C2211yescharacteristic
40#10622612C2211yescharacteristic, complemented
41C2×#66869C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic, complemented
43#10622452—22no—
44#10622450—22no—
45D11×#104—24no—
46#10622416C412yescomplemented
47#10622415C412yescomplemented
48#10622384C412yescomplemented
49#10622383C412yescomplemented
50#10622340—22no—
51#10622339—22no—
52C4×#4313—24no—
53C11×#341C2211yescharacteristic, complemented
54C11×#339C2211yescharacteristic, complemented
55#10622196C2211yescharacteristic, complemented
56#10622196C2211yescharacteristic, complemented
57#10622193C2211yescharacteristic, complemented
58#10622190C2211yescharacteristic, complemented
59#10622170C2211yescharacteristic, complemented
60#10622161C2211yescharacteristic, complemented
61C2×C11×#41C2311yescharacteristic
62#41×D11—22no—
63#41×D11—22no—
64#41×D11—22no—
65#41×D11—22no—
66C2×#4343C2×C411yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×#4341—21no—
69C2×#4341C2×C411yescharacteristic
70C2×D4×D11—21no—
71C2×D4×D11C2×C411yescharacteristic
72C2×#4339—21no—
73C2×#4339C2311yescharacteristic
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C22×C4×D11C2311yescharacteristic
77C2×C11×M16C2311yescharacteristic
78C2×C11×M16C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×#117C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83#66979C2311yescharacteristic
84C2×C4×Dic11—21no—
85C2×C4×Dic11C2311yescharacteristic
86C2×#4318C2311yescharacteristic
87C2×#4318C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90M16×D11—22no—
91M16×D11—22no—
92M16×D11—22no—
93M16×D11—22no—
94C2×#4313—22no—
95C2×#4313—22no—
96C2×#4313—22no—
97C2×#4313—22no—
98C2×#4313—21no—
99C2×#4313—21no—
100C2×#4313C2×C412yes—
101C2×#4313C2×C412yes—
102C2×#4313D412yes—
103C2×#4313D412yes—
104C2×C8×D11—21no—
105C2×C8×D11—21no—
106#66945C2×C412yes—
107C4⋊C4×D11C2×C412yes—
108C22⋊C4×D11—21no—
109#66930—21no—
110#66925—21no—
111C42×D11—21no—
112C42×D11—22no—
113C42×D11D414yes—
114C11×C4⋊C8—22no—
115C11×#104—22no—
116C11×#103C2×C412yescomplemented
117C11×#102C2×C412yescomplemented
118C11×C22⋊C8—22no—
119C4×C8×C11—22no—
120#66901—22no—
121#66899C2×C412yescomplemented
122#66896C2×C412yescomplemented
123C22⋊(C11⋊C8)—22no—
124#66889—22no—
125#66885C2×C412yescomplemented
126(C2×D11)⋊C8—22no—
127(C2×D11)⋊C8—22no—
128#66880C2×C412yescomplemented
129#66879—22no—
130#66879—22no—
131Dic11⋊C8—22no—
132Dic11⋊C8—22no—
133#66874C2×C412yescomplemented
134#66873C2×C412yescomplemented
135#66869—22no—
136C4⋊(C11⋊C8)—22no—
137C4×C11⋊C8—22no—
138#21099—111nomaximal, Sylow
139C23×D11—21no—
140C23×D11#4111yescharacteristic
141C11×#41—21no—
142C11×#41—21no—
143C11×#41—21no—
144C11×#41—21no—
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11#4111yescharacteristic
157#4343—22no—
158#4343—22no—
159Q8×D11—22no—
160Q8×D11—22no—
161#4341—22no—
162#4341—22no—
163#4341—42no—
164#4341—42no—
165D4×D11—22no—
166D4×D11—22no—
167D4×D11—42no—
168D4×D11—42no—
169#4339—21no—
170#4339—21no—
171#4339—21no—
172#4339—21no—
173#4339—42no—
174#4339—42no—
175C2×D44—21no—
176C2×D44C22×C411yescharacteristic
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—22no—
180C2×C4×D11—24no—
181C2×C4×D11—21no—
182C2×C4×D11—44no—
183C2×C4×D11—42no—
184C2×C4×D11—42no—
185C2×C4×D11C22×C411yescharacteristic
186C2×C4×D11C22×C411yescharacteristic
187C2×C4×D11C2×D411yescharacteristic
188C2×C4×D11C2×D411yescharacteristic
189C2×C4×D11C2×D412yes—
190C2×C4×D11#4112yes—
191C2×C4×D11#4112yes—
192C2×C4×D11#4112yes—
193C2×Dic22—21no—
194C2×Dic22C22×C411yescharacteristic
195C11×M16—21no—
196C11×M16—21no—
197C11×M16—21no—
198C11×M16—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11C22×C412yes—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4C22×C412yes—
208C11×C22⋊C4—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11C2×D412yes—
212C22⋊Dic11—21no—
213(C2×D11)⋊C4—22no—
214C4⋊Dic11C22×C412yes—
215Dic11⋊C4—22no—
216C4×Dic11—22no—
217C4×Dic11—24no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11C2×D412yes—
221#4318—21no—
222#4318—21no—
223#4318—21no—
224#4318—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8C22×C412yes—
232C2×C11⋊C8C2×D412yes—
233#4313—24no—
234#4313—24no—
235#4313—24no—
236#4313—24no—
237#4313—42no—
238#4313—42no—
239C8×D11—42no—
240C8×D11—42no—
241#2905—111no—
242C22×#104—111no—
243#2896—111no—
244#2879—111no—
245C2×C4×M16—111no—
246#1938—111no—
247#1938—111no—
248#1938—111no—
249#1938—111no—
250#1937—111no—
251#1937—111no—
252#1937—111no—
253#1937D1111yescharacteristic, complemented
254#1738—111no—
255C2×#339—111no—
256C23×C11—21no—
257C23×C11C2×#4111yescharacteristic
258C22×D11—21no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11—82no—
262C22×D11C4×D411yescharacteristic
263C22×D11C4×D411yescharacteristic
264C22×D11#12312yes—
265C22×D11#12612yes—
266Q8×C11—21no—
267Q8×C11—21no—
268D4×C11—21no—
269D4×C11—21no—
270D4×C11—41no—
271D4×C11—41no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11C23×C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C22⋊D11—41no—
285C22⋊D11—41no—
286C22⋊D11—42no—
287C22⋊D11—42no—
288C2×Dic11—22no—
289C2×Dic11—21no—
290C2×Dic11—22no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11C4×D411yescharacteristic
294C2×Dic11C4×D411yescharacteristic
295C2×Dic11#12312yes—
296C2×Dic11#12612yes—
297D44—21no—
298D44—21no—
299D44—42no—
300C4×D11—48no—
301C4×D11—42no—
302C4×D11—41no—
303C4×D11—41no—
304C4×D11—42no—
305C4×D11—82no—
306C4×D11#11712yes—
307C4×D11#11712yes—
308C4×D11C4×D412yes—
309C4×D11C4×D412yes—
310C4×D11#12112yes—
311C4×D11#12112yes—
312C4×D11#12412yes—
313C4×D11#12412yes—
314Dic22—21no—
315Dic22—21no—
316Dic22—42no—
317C8×C11—22no—
318C8×C11—22no—
319C8×C11—41no—
320C8×C11—41no—
321C11⋊C8—22no—
322C11⋊C8—22no—
323C11⋊C8—41no—
324C11⋊C8—41no—
325C22×#41—111no—
326C22×M16—111no—
327C22×M16—111no—
328C22×M16—111no—
329C22×M16—111no—
330C2×#117—111no—
331C22×C42—111no—
332#424—111no—
333#424—111no—
334#424—111no—
335#424—222no—
336#424C2×D1111yescharacteristic, complemented
337#423—222no—
338C2×#104—111no—
339C2×#104—111no—
340C2×#104—111no—
341C2×#104—224no—
342C2×#104C2×D1111yescharacteristic
343#419—112no—
344#418—112no—
345#417—112no—
346#417—112no—
347#416—111no—
348#416—111no—
349#416—111no—
350#416C2×D1111yescharacteristic
351#408—111no—
352#408—111no—
353#408—111no—
354#408—222no—
355#408C2×D1111yescharacteristic
356#407—222no—
357C4×M16—224no—
358C2×#97—111no—
359C2×#97—111no—
360C2×C4×C8—111no—
361C2×C4×C8C2×D1111yescharacteristic, complemented
362#341—111no—
363#341—111no—
364#341—111no—
365#341C2×D1111yescharacteristic, complemented
366#339—111no—
367#339—111no—
368#339—111no—
369#339C2×D1111yescharacteristic, complemented
370C22×C11—22no—
371C22×C11—42no—
372C22×C11—41no—
373C22×C11C2×C4×D411yescharacteristic
374C22×C11C2×#12311yescharacteristic
375C22×C11C2×#12611yescharacteristic
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—42no—
379C2×D11—42no—
380C2×D11—42no—
381C2×D11—41no—
382C2×D11—84no—
383C2×D11#38812yes—
384C2×D11#38812yes—
385C4×C11—24no—
386C4×C11—42no—
387C4×C11—41no—
388C4×C11C2×#11711yescharacteristic
389C4×C11C2×C4×D411yescharacteristic
390C4×C11C2×#12111yescharacteristic
391C4×C11C2×#12411yescharacteristic
392Dic11—42no—
393Dic11—42no—
394Dic11—41no—
395Dic11#38812yes—
396Dic11#38812yes—
397C2×#41—111no—
398C2×#41—111no—
399C2×#41—111no—
400C2×#41—221no—
401C2×#41—221no—
402C2×#41—222no—
403C2×#41—222no—
404C2×#41—222no—
405C2×#41—222no—
406C2×#41C22×D1111yescharacteristic
407C22×Q8—111no—
408C22×D4—111no—
409C22×D4—221no—
410C23×C4—111no—
411C23×C4—221no—
412C23×C4—221no—
413C2×M16—112no—
414C2×M16—112no—
415C2×M16—112no—
416C2×M16—112no—
417C2×M16—111no—
418C2×M16—111no—
419C2×M16—222no—
420C2×M16—222no—
421C2×M16—222no—
422C2×M16—222no—
423C2×M16—221no—
424C2×M16—221no—
425C2×M16—222no—
426C2×M16—222no—
427C2×M16—222no—
428C2×M16—222no—
429C2×M16C22×D1111yescharacteristic
430C2×M16C22×D1111yescharacteristic
431C22×C8—111no—
432C22×C8—111no—
433C22×C8—221no—
434C22×C8—221no—
435C22×C8C22×D1111yescharacteristic
436C22×C8C22×D1111yescharacteristic
437#117—111no—
438#117—112no—
439#117—221no—
440#117—221no—
441#117C22×D1111yescharacteristic
442C2×C4⋊C4—112no—
443C2×C22⋊C4—221no—
444C2×C42—111no—
445C2×C42—114no—
446C2×C42—221no—
447C2×C42—222no—
448C2×C42—221no—
449C2×C42C22×D1111yescharacteristic
450C4⋊C8—22no—
451C4⋊C8—222no—
452C4⋊C8—222no—
453C4⋊C8—222no—
454#104—22no—
455#104—222no—
456#104—222no—
457#104—222no—
458#103—112no—
459#103—112no—
460#103—112no—
461#103C4×D1112yescomplemented
462#102—112no—
463#102—112no—
464#102—112no—
465#102C4×D1112yescomplemented
466C22⋊C8—22no—
467C22⋊C8—222no—
468C22⋊C8—222no—
469C22⋊C8—222no—
470#97—222no—
471#97—222no—
472C4×C8—22no—
473C4×C8—222no—
474C2×C11—21no—
475C2×C11—21no—
476C2×C11—81no—
477C2×C11C2×#38811yescharacteristic
478C2×C11#295612yes—
479D11—22no—
480D11—22no—
481D11—81no—
482C24—111no—
483C24—221no—
484#41—21no—
485#41—21no—
486#41—21no—
487#41—21no—
488#41—222no—
489#41—222no—
490#41—222no—
491#41—222no—
492#41—221no—
493#41—221no—
494#41—221no—
495#41—221no—
496#41—442no—
497#41—442no—
498#41—442no—
499#41—442no—
500C2×Q8—111no—
501C2×Q8—221no—
502C2×Q8—222no—
503C2×Q8—222no—
504C2×Q8C2×C4×D1111yescharacteristic
505C2×D4—21no—
506C2×D4—111no—
507C2×D4—221no—
508C2×D4—222no—
509C2×D4—222no—
510C2×D4—221no—
511C2×D4—221no—
512C2×D4—221no—
513C2×D4—442no—
514C2×D4—442no—
515C2×D4C2×C4×D1111yescharacteristic
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—111no—
519C22×C4—111no—
520C22×C4—111no—
521C22×C4—112no—
522C22×C4—111no—
523C22×C4—111no—
524C22×C4—112no—
525C22×C4—112no—
526C22×C4—112no—
527C22×C4—221no—
528C22×C4—224no—
529C22×C4—221no—
530C22×C4—222no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—221no—
534C22×C4—444no—
535C22×C4—442no—
536C22×C4—442no—
537C22×C4C23×D1111yescharacteristic
538M16—21no—
539M16—21no—
540M16—21no—
541M16—21no—
542M16—224no—
543M16—224no—
544M16—224no—
545M16—224no—
546M16—221no—
547M16—221no—
548M16—221no—
549M16—221no—
550M16—442no—
551M16—442no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—112no—
559C2×C8—112no—
560C2×C8—221no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—221no—
565C2×C8—221no—
566C2×C8—442no—
567C2×C8—442no—
568C2×C8C2×C4×D1112yes—
569C2×C8D4×D1112yes—
570C4⋊C4—112no—
571C4⋊C4—222no—
572C4⋊C4C2×C4×D1112yes—
573C22⋊C4—21no—
574C22⋊C4—222no—
575C22⋊C4—221no—
576C42—21no—
577C42—21no—
578C42—112no—
579C42—224no—
580C42—222no—
581C42—221no—
582C42—221no—
583C42D4×D1112yes—
584C11#2109911yescharacteristic, complemented, Sylow
585C23—21no—
586C23—111no—
587C23—111no—
588C23—112no—
589C23—112no—
590C23—221no—
591C23—442no—
592C23—442no—
593C23—882no—
594C23#41×D1111yescharacteristic
595Q8—21no—
596Q8—21no—
597Q8—221no—
598Q8—221no—
599Q8—442no—
600D4—21no—
601D4—21no—
602D4—41no—
603D4—41no—
604D4—221no—
605D4—221no—
606D4—442no—
607D4—442no—
608D4—442no—
609D4—441no—
610D4—441no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—112no—
618C2×C4—111no—
619C2×C4—111no—
620C2×C4—112no—
621C2×C4—112no—
622C2×C4—112no—
623C2×C4—112no—
624C2×C4—112no—
625C2×C4—112no—
626C2×C4—112no—
627C2×C4—112no—
628C2×C4—112no—
629C2×C4—222no—
630C2×C4—221no—
631C2×C4—222no—
632C2×C4—448no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—882no—
640C2×C4C22×C4×D1111yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4C2×D4×D1111yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C2×C4#41×D1111yescharacteristic
645C2×C4#41×D1111yescharacteristic
646C8—22no—
647C8—22no—
648C8—41no—
649C8—41no—
650C8—222no—
651C8—222no—
652C8—441no—
653C8—441no—
654C22—22no—
655C22—42no—
656C22—41no—
657C22—112no—
658C22—112no—
659C22—222no—
660C22—222no—
661C22—442no—
662C22—442no—
663C22—442no—
664C22—441no—
665C22—884no—
666C22C4×D4×D1111yescharacteristic
667C22D11×#12311yescharacteristic
668C22D11×#12611yescharacteristic
669C4—24no—
670C4—42no—
671C4—41no—
672C4—112no—
673C4—112no—
674C4—442no—
675C4—442no—
676C4—441no—
677C4D11×#11711yescharacteristic
678C4C4×D4×D1111yescharacteristic
679C4D11×#12111yescharacteristic
680C4D11×#12411yescharacteristic
681C2—21no—
682C2—21no—
683C2—81no—
684C2—222no—
685C2—222no—
686C2—881no—
687C2D11×#38811yescharacteristic
688C2#1307752112yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1937C2
socleC22×C11C2×C4×D4
prime radicalC2×#41×D11C22
cosocleC22×C4×C11C24
hypercenter#1937D11
hypocenterC11#21099
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1937

Complements

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

NH ≅ G/Ntype
1. #13077177C2semidirect
5. C2×C4×#4313C2semidirect
6. #13069330C2semidirect
7. #13069329C2semidirect
8. #13069326C2semidirect
9. #13069325C2semidirect
10. #13069321C2semidirect
11. #13069320C2semidirect
12. #13069317C2semidirect
13. #13068341C2semidirect
14. D11×#339C2semidirect
15. C11×#1937C2semidirect
23. C11×#424C22semidirect
27. C2×C4×C8×C11C22semidirect
33. #10622732C22semidirect
36. #10622715C22semidirect
37. C2×#66879C22semidirect
38. C2×#66879C22semidirect
40. #10622612C22semidirect
42. C2×C4×C11⋊C8C22semidirect
46. #10622416C4semidirect
47. #10622415C4semidirect
48. #10622384C4semidirect
49. #10622383C4semidirect
53. C11×#341C22semidirect
54. C11×#339C22semidirect
55. #10622196C22semidirect
56. #10622196C22semidirect
57. #10622193C22semidirect
58. #10622190C22semidirect
59. #10622170C22semidirect
60. #10622161C22semidirect
116. C11×#103C2×C4semidirect
117. C11×#102C2×C4semidirect
121. #66899C2×C4semidirect
122. #66896C2×C4semidirect
125. #66885C2×C4semidirect
128. #66880C2×C4semidirect
133. #66874C2×C4semidirect
134. #66873C2×C4semidirect
253. #1937D11semidirect
336. #424C2×D11semidirect
361. C2×C4×C8C2×D11semidirect
365. #341C2×D11semidirect
369. #339C2×D11semidirect
461. #103C4×D11semidirect
465. #102C4×D11semidirect
584. C11#21099semidirect

Maximal subgroups

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

subgroupindex
#130771772
C2×D11×#1042
#130771312
#130770582
C2×C4×#43132
#130693302
#130693292
#130693262
#130693252
#130693212
#130693202
#130693172
#130683412
D11×#3392
C11×#19372
#2109911