Finite Group Databasebeta

← #14757444

Subgroups — #14757444

Order 2816.

1638 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C2×#10622746C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic, complemented
4C2×#10622579C211yesmaximal, characteristic, complemented
5C2×M16×Dic11C211yesmaximal, characteristic, complemented
6C2×#10622590C211yesmaximal, characteristic, complemented
7#13069438C212yesmaximal, complemented
8#13069434C212yesmaximal, complemented
9#13069426C212yesmaximal, complemented
10#13069424C212yesmaximal, complemented
11C2×C11×#417C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16#10623363—24no—
17#10623363C418yescomplemented
18C2×#67000C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C2×#66993C2211yescharacteristic
21C2×#66992—22no—
22C2×#66989C2211yescharacteristic
23C2×C4×C22⋊D11—22no—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C11×#417—24no—
28C2×C11×#103C2212yes—
29C2×C11×#102C2212yes—
30#10622845—24no—
31C2×#66899C2212yes—
32C2×#66896C2212yes—
33C2×C11⋊#95—22no—
34#10622746—24no—
35M16×Dic11—24no—
36C2×#66885C2212yes—
37C2×#66880C2212yes—
38C2×#66879C2212yes—
39C2×C8×Dic11C2212yes—
40#10622590—22no—
41#10622590C2212yes—
42#10622590C2212yes—
43C2×#66874C2212yes—
44#10622579—24no—
45C2×#66873C2212yes—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41C2×C414yes—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—21no—
59C22×C22⋊D11—22no—
60C23×Dic11—21no—
61C23×Dic11D412yes—
62C2×#4339—22no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339—22no—
66C2×#4339—22no—
67C2×#4339C2×C414yes—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×Dic22C2311yescharacteristic
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16D414yescomplemented
74C22×C8×C11C2312yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2312yes—
79C2×C22⋊Dic11—22no—
80#67000—22no—
81#67000C2×C414yescomplemented
82#66997—22no—
83#66997C2×C414yescomplemented
84#66993—22no—
85#66993C2×C414yescomplemented
86#66992—216no—
87#66989—22no—
88#66989C2×C414yescomplemented
89C4×C22⋊D11—216no—
90C2×(C2×D11)⋊C4—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2312yes—
95C2×Dic11⋊C4—22no—
96C2×C4×Dic11C2×C414yes—
97C2×C4×Dic11D412yes—
98C2×C4×Dic11D414yes—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×#4318—22no—
102C2×#4318—22no—
103C2×#4318D414yescomplemented
104C22×C11⋊C8C2312yes—
105C11×#103—24no—
106C11×#102—24no—
107#66899—24no—
108#66896—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111#66885—24no—
112#66880—24no—
113#66879—24no—
114C8×Dic11—24no—
115#66874—24no—
116#66873—24no—
117#21201—111nomaximal, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C23×D11—21no—
121C11×#41—28no—
122C11×#41—28no—
123C11×#41—44no—
124C11×#41—44no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11C22×C412yes—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11C22×C412yes—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—44no—
146C22×C4×C11—42no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—28no—
156C2×C22⋊D11—24no—
157C2×C22⋊D11—44no—
158C2×C22⋊D11—44no—
159C2×C22⋊D11—42no—
160C2×C22⋊D11—42no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—42no—
164C22×Dic11—42no—
165C22×Dic11—44no—
166C22×Dic11—42no—
167C22×Dic11C22⋊C418yes—
168C22×Dic11C2×D412yes—
169C22×Dic11C2×D412yes—
170#4339—28no—
171#4339—28no—
172#4339—44no—
173#4339—44no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44C22×C412yes—
180C2×C4×D11—24no—
181C2×C4×D11—42no—
182C2×C4×D11—42no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22C22×C412yes—
189C11×M16—28no—
190C2×C8×C11—22no—
191C2×C8×C11—22no—
192C2×C8×C11C2×D414yes—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—42no—
196C22⋊Dic11—28no—
197(C2×D11)⋊C4—28no—
198C4⋊Dic11—22no—
199C4⋊Dic11—22no—
200C4⋊Dic11—42no—
201Dic11⋊C4—28no—
202C4×Dic11C22⋊C418yes—
203C4×Dic11C22×C412yes—
204C4×Dic11C22×C412yes—
205C4×Dic11C2×D412yes—
206C4×Dic11C2×D412yes—
207#4318—28no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8C2×D414yes—
211C2×#532—111no—
212C2×#417—111no—
213C2×#417—111no—
214C2×#417—111no—
215C2×#417D1111yescharacteristic, complemented
216C2×C4×M16—111no—
217C2×#382—111no—
218#1961—112no—
219#1960—112no—
220#1958—112no—
221#1958—112no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11C2×C22⋊C412yes—
230C23×C11#12412yes—
231C23×C11#12712yes—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—42no—
237C22×D11—42no—
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—41no—
241Q8×C11—41no—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—48no—
245D4×C11—41no—
246D4×C11—41no—
247C2×C4×C11—22no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—48no—
251C2×C4×C11—42no—
252C2×C4×C11—44no—
253C2×C4×C11—84no—
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C4×D414yes—
256C2×C4×C11C4×D414yes—
257C2×C4×C11#12114yes—
258C2×C4×C11#12114yes—
259C2×C4×C11#12412yes—
260C2×C4×C11#12712yes—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C22⋊D11—416no—
268C22⋊D11—48no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—48no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—42no—
278C2×Dic11—44no—
279C2×Dic11—84no—
280C2×Dic11C2×C22⋊C414yes—
281C2×Dic11C2×C22⋊C414yes—
282D44—22no—
283D44—22no—
284D44—41no—
285D44—41no—
286C4×D11—48no—
287Dic22—22no—
288Dic22—22no—
289Dic22—41no—
290Dic22—41no—
291C8×C11—24no—
292C11⋊C8—24no—
293C22×#41—111no—
294C22×#41C2×D1111yescharacteristic
295C22×M16—111no—
296C22×M16C2×D1111yescharacteristic
297#532—118no—
298#532—224no—
299C2×C4⋊Q8—111no—
300C2×#127—111no—
301C2×#124—111no—
302C2×#124—111no—
303C2×#121—222no—
304C2×C4×D4—222no—
305C22×C4⋊C4—111no—
306C22×C4⋊C4C2×D1111yescharacteristic
307C22×C42—111no—
308#417—24no—
309#417—224no—
310#417—224no—
311#417—224no—
312C2×#103—112no—
313C2×#103—112no—
314C2×#103—112no—
315C2×#103C2×D1112yes—
316C2×#102—112no—
317C2×#102—112no—
318C2×#102—112no—
319C2×#102C2×D1112yes—
320C4×M16—224no—
321C2×#97—112no—
322C2×C4×C8—112no—
323#382—112no—
324#382—112no—
325#382—222no—
326C2×#95—222no—
327C22×C11—24no—
328C22×C11—24no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—44no—
332C22×C11—42no—
333C22×C11—82no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11#39014yes—
337C22×C11C22×C22⋊C411yescharacteristic
338C22×C11C2×#12411yescharacteristic
339C22×C11C2×#12711yescharacteristic
340C22×C11#57512yes—
341C22×C11#57512yes—
342C2×D11—44no—
343C2×D11—42no—
344C2×D11—82no—
345C2×D11—81no—
346C2×D11—81no—
347C4×C11—42no—
348C4×C11—82no—
349C4×C11#39014yes—
350C4×C11C2×C4×D411yescharacteristic
351C4×C11C2×C4×D411yescharacteristic
352C4×C11C2×#12111yescharacteristic
353C4×C11C2×#12111yescharacteristic
354Dic11—24no—
355Dic11—24no—
356Dic11—42no—
357Dic11—82no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—114no—
364C2×#41—222no—
365C2×#41—222no—
366C2×#41—222no—
367C2×#41—222no—
368C2×#41—222no—
369C2×#41C4×D1114yes—
370C22×Q8—111no—
371C22×Q8C22×D1111yescharacteristic
372C22×D4—21no—
373C22×D4—111no—
374C22×D4—222no—
375C22×D4—221no—
376C22×D4C22×D1111yescharacteristic
377C23×C4—21no—
378C23×C4—21no—
379C23×C4—112no—
380C23×C4—221no—
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C2×M16—22no—
384C2×M16—22no—
385C2×M16—114no—
386C2×M16—222no—
387C2×M16—222no—
388C2×M16C22⋊D1114yescomplemented
389C22×C8—112no—
390C22×C8C22×D1112yes—
391C4⋊Q8—114no—
392C4⋊Q8—222no—
393#127—114no—
394#127—222no—
395#124—114no—
396#124—114no—
397#124—222no—
398#124—222no—
399#121—2216no—
400C4×D4—2216no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4C22×D1112yes—
410C2×C22⋊C4—222no—
411C2×C22⋊C4—222no—
412C2×C42—114no—
413C2×C42—112no—
414C2×C42—114no—
415C2×C42—111no—
416C2×C42—111no—
417#103—24no—
418#103—224no—
419#103—224no—
420#103—224no—
421#102—24no—
422#102—224no—
423#102—224no—
424#102—224no—
425#97—224no—
426C4×C8—224no—
427#95—224no—
428#95—224no—
429C2×C11—24no—
430C2×C11—82no—
431C2×C11C2×#39011yescharacteristic
432C2×C11#289612yes—
433C2×C11#314212yes—
434C2×C11#315311yescharacteristic
435C2×C11#315311yescharacteristic
436D11—82no—
437C24—21no—
438C24—221no—
439C24D4×D1111yescharacteristic
440#41—28no—
441#41—28no—
442#41—44no—
443#41—44no—
444#41—228no—
445#41—228no—
446#41—444no—
447#41—444no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—112no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8C2×C4×D1112yes—
460C2×D4—24no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—112no—
469C2×D4—228no—
470C2×D4—224no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—444no—
477C2×D4—444no—
478C2×D4—442no—
479C2×D4—442no—
480C2×D4C2×C4×D1112yes—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—44no—
487C22×C4—42no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—118no—
491C22×C4—221no—
492C22×C4—224no—
493C22×C4—222no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—444no—
499C22×C4—442no—
500C22×C4C2×C4×D1112yes—
501C22×C4#433912yes—
502C22×C4D4×D1111yescharacteristic
503C22×C4D4×D1112yes—
504C22×C4D4×D1112yes—
505C22×C4#434112yes—
506C22×C4C2×C22⋊D1112yes—
507C22×C4C23×D1111yescharacteristic
508M16—28no—
509M16—228no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—114no—
513C2×C8—222no—
514C2×C8—222no—
515C2×C8C2×C22⋊D1114yes—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—42no—
519C4⋊C4—228no—
520C4⋊C4—222no—
521C4⋊C4—222no—
522C4⋊C4—442no—
523C22⋊C4—228no—
524C22⋊C4—228no—
525C42—118no—
526C42—112no—
527C42—112no—
528C42—112no—
529C42—112no—
530C11#2120111yescharacteristic, complemented, Sylow
531C23—22no—
532C23—22no—
533C23—22no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23—222no—
539C23—441no—
540C23—442no—
541C23—442no—
542C23—441no—
543C23C22⋊C4×D1112yes—
544C23#6693812yes—
545C23#6699312yes—
546C23C2×D4×D1111yescharacteristic
547Q8—22no—
548Q8—22no—
549Q8—41no—
550Q8—41no—
551Q8—222no—
552Q8—222no—
553Q8—441no—
554Q8—441no—
555D4—22no—
556D4—22no—
557D4—48no—
558D4—41no—
559D4—41no—
560D4—222no—
561D4—222no—
562D4—4416no—
563D4—448no—
564D4—441no—
565D4—441no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—48no—
570C2×C4—44no—
571C2×C4—42no—
572C2×C4—84no—
573C2×C4—114no—
574C2×C4—114no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—448no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—448no—
584C2×C4—444no—
585C2×C4—442no—
586C2×C4—884no—
587C2×C4C22⋊C4×D1112yes—
588C2×C4(C22⋊D11)⋊C414yes—
589C2×C4#6693714yes—
590C2×C4#6693812yes—
591C2×C4C4×C22⋊D1114yes—
592C2×C4#6699214yes—
593C2×C4#6699312yes—
594C2×C4C22×C4×D1111yescharacteristic
595C2×C4C2×#433911yescharacteristic
596C2×C4C2×D4×D1111yescharacteristic
597C2×C4C2×D4×D1111yescharacteristic
598C2×C4C2×#434111yescharacteristic
599C2×C4C22×C22⋊D1111yescharacteristic
600C8—24no—
601C8—224no—
602C22—22no—
603C22—22no—
604C22—24no—
605C22—24no—
606C22—44no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—82no—
611C22—444no—
612C22—442no—
613C22—881no—
614C22—881no—
615C22—882no—
616C22#1062257014yes—
617C22C2×C22⋊C4×D1111yescharacteristic
618C22C2×#6693811yescharacteristic
619C22#1062330412yes—
620C22#1062330812yes—
621C22C2×#6699311yescharacteristic
622C4—42no—
623C4—82no—
624C4—224no—
625C4—224no—
626C4—442no—
627C4—882no—
628C4#1062257014yes—
629C4C2×(C22⋊D11)⋊C411yescharacteristic
630C4C2×#6693711yescharacteristic
631C4C2×C4×C22⋊D1111yescharacteristic
632C4C2×#6699211yescharacteristic
633C2—24no—
634C2—82no—
635C2—882no—
636C2C2×#1062257011yescharacteristic
637C2#1307713212yes—
638C2#1307901412yes—
639C2#1307907811yescharacteristic
640C2#1307908311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623363C2
cosocleC22×C4×C11C24
hypercenterC2×#417D11
hypocenterC11#21201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#10622746C2semidirect
3. C2×#10622845C2semidirect
4. C2×#10622579C2semidirect
5. C2×M16×Dic11C2semidirect
6. C2×#10622590C2semidirect
7. #13069438C2semidirect
8. #13069434C2semidirect
9. #13069426C2semidirect
10. #13069424C2semidirect
11. C2×C11×#417C2semidirect
17. #10623363C4semidirect
73. C2×C11×M16D4semidirect
81. #67000C2×C4semidirect
83. #66997C2×C4semidirect
85. #66993C2×C4semidirect
88. #66989C2×C4semidirect
103. C2×#4318D4semidirect
215. C2×#417D11semidirect
388. C2×M16C22⋊D11semidirect
530. C11#21201semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106227462
C2×#106228452
C2×#106225792
C2×M16×Dic112
C2×#106225902
#130694382
#130694342
#130694262
#130694242
C2×C11×#4172
#2120111