Finite Group Databasebeta

← #14757437

Subgroups — #14757437

Order 2816.

1726 conjugacy classes of subgroups.

The subgroup lattice has 648 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×#10622589C211yesmaximal, characteristic, complemented
7#13069431C212yesmaximal, complemented
8#13069429C212yesmaximal, complemented
9#13069420C212yesmaximal, complemented
10#13069416C212yesmaximal, 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×Dic11⋊C4—22no—
26C22×C4×Dic11C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C11×#417—24no—
29C2×C11×#103C2212yes—
30C2×C11×#102C2212yes—
31#10622845—24no—
32C2×#66899C2212yes—
33C2×#66896C2212yes—
34#10622746—24no—
35M16×Dic11—24no—
36C2×#66885C2212yes—
37C2×#66880C2212yes—
38C2×#66879C2212yes—
39C2×C8×Dic11C2212yes—
40#10622589—22no—
41#10622589C2212yes—
42#10622589C2212yes—
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×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—48no—
99C2×C4×Dic11C2×C414yes—
100C2×C4×Dic11D412yes—
101C2×C4×Dic11D414yes—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×#4318—22no—
105C2×#4318—22no—
106C2×#4318D414yescomplemented
107C22×C11⋊C8C2312yes—
108C11×#103—24no—
109C11×#102—24no—
110#66899—24no—
111#66896—24no—
112#66885—24no—
113#66880—24no—
114#66879—24no—
115C8×Dic11—24no—
116#66874—24no—
117#66873—24no—
118#21200—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11C2×D411yescharacteristic
121C23×D11—21no—
122C11×#41—28no—
123C11×#41—28no—
124C11×#41—44no—
125C11×#41—44no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11C22×C412yes—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11C22×C412yes—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—44no—
147C22×C4×C11—42no—
148C22×C4×C11C22×C412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—28no—
157C2×C22⋊D11—24no—
158C2×C22⋊D11—44no—
159C2×C22⋊D11—44no—
160C2×C22⋊D11—42no—
161C2×C22⋊D11—42no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166C22×Dic11—44no—
167C22×Dic11—42no—
168C22×Dic11C22⋊C418yes—
169C22×Dic11C2×D412yes—
170C22×Dic11C2×D412yes—
171#4339—28no—
172#4339—28no—
173#4339—44no—
174#4339—44no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44C22×C412yes—
181C2×C4×D11—24no—
182C2×C4×D11—42no—
183C2×C4×D11—42no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22—21no—
189C2×Dic22C22×C412yes—
190C11×M16—28no—
191C2×C8×C11—22no—
192C2×C8×C11—22no—
193C2×C8×C11C2×D414yes—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—42no—
197C22⋊Dic11—28no—
198(C2×D11)⋊C4—28no—
199C4⋊Dic11—22no—
200C4⋊Dic11—22no—
201C4⋊Dic11—42no—
202Dic11⋊C4—28no—
203Dic11⋊C4—48no—
204Dic11⋊C4—48no—
205C4×Dic11C22⋊C418yes—
206C4×Dic11C22×C412yes—
207C4×Dic11C22×C412yes—
208C4×Dic11C2×D412yes—
209C4×Dic11C2×D412yes—
210#4318—28no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8C2×D414yes—
214C2×#532—111no—
215C2×#417—111no—
216C2×#417—111no—
217C2×#417—111no—
218C2×#417D1111yescharacteristic, complemented
219C2×C4×M16—111no—
220C2×#384—111no—
221#1959—112no—
222#1959—112no—
223#1957—112no—
224#1956—112no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11C2×C22⋊C412yes—
233C23×C11#12412yes—
234C23×C11#12712yes—
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—42no—
240C22×D11—42no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—48no—
248D4×C11—41no—
249D4×C11—41no—
250C2×C4×C11—22no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—48no—
254C2×C4×C11—42no—
255C2×C4×C11—44no—
256C2×C4×C11—84no—
257C2×C4×C11C2×C22⋊C412yes—
258C2×C4×C11C4×D414yes—
259C2×C4×C11C4×D414yes—
260C2×C4×C11#12114yes—
261C2×C4×C11#12114yes—
262C2×C4×C11#12412yes—
263C2×C4×C11#12712yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C22⋊D11—48no—
271C22⋊D11—416no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—216no—
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—42no—
279C2×Dic11—44no—
280C2×Dic11—84no—
281C2×Dic11C2×C22⋊C414yes—
282C2×Dic11C2×C22⋊C414yes—
283C2×Dic11AGL(1,ℤ/8)14yes—
284C2×Dic11#13714yes—
285D44—22no—
286D44—22no—
287D44—41no—
288D44—41no—
289C4×D11—48no—
290Dic22—22no—
291Dic22—22no—
292Dic22—41no—
293Dic22—41no—
294C8×C11—24no—
295C11⋊C8—24no—
296C22×#41—111no—
297C22×#41C2×D1111yescharacteristic
298C22×M16—111no—
299C22×M16C2×D1111yescharacteristic
300#532—118no—
301#532—224no—
302C2×C4⋊Q8—111no—
303C2×#127—111no—
304C2×#124—111no—
305C2×#124—111no—
306C2×#121—222no—
307C2×C4×D4—222no—
308C22×C4⋊C4—111no—
309C22×C4⋊C4—222no—
310C22×C4⋊C4C2×D1111yescharacteristic
311C22×C42—111no—
312#417—24no—
313#417—224no—
314#417—224no—
315#417—224no—
316C2×#103—112no—
317C2×#103—112no—
318C2×#103—112no—
319C2×#103C2×D1112yes—
320C2×#102—112no—
321C2×#102—112no—
322C2×#102—112no—
323C2×#102C2×D1112yes—
324C4×M16—224no—
325C2×#97—112no—
326C2×C4×C8—112no—
327#384—112no—
328#384—112no—
329#384—222no—
330C22×C11—24no—
331C22×C11—24no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—44no—
335C22×C11—42no—
336C22×C11—82no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11#39014yes—
340C22×C11C22×C22⋊C411yescharacteristic
341C22×C11C2×#12411yescharacteristic
342C22×C11C2×#12711yescharacteristic
343C22×C11C2×AGL(1,ℤ/8)12yes—
344C22×C11C2×#13712yes—
345C2×D11—44no—
346C2×D11—42no—
347C2×D11—82no—
348C2×D11—81no—
349C2×D11—81no—
350C4×C11—42no—
351C4×C11—82no—
352C4×C11#39014yes—
353C4×C11C2×C4×D411yescharacteristic
354C4×C11C2×C4×D411yescharacteristic
355C4×C11C2×#12111yescharacteristic
356C4×C11C2×#12111yescharacteristic
357Dic11—24no—
358Dic11—42no—
359Dic11—82no—
360Dic11#41718yescomplemented
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—114no—
367C2×#41—222no—
368C2×#41—222no—
369C2×#41—222no—
370C2×#41—222no—
371C2×#41—222no—
372C2×#41C4×D1114yes—
373C22×Q8—111no—
374C22×Q8C22×D1111yescharacteristic
375C22×D4—21no—
376C22×D4—111no—
377C22×D4—222no—
378C22×D4—221no—
379C22×D4C22×D1111yescharacteristic
380C23×C4—21no—
381C23×C4—21no—
382C23×C4—112no—
383C23×C4—221no—
384C23×C4—221no—
385C23×C4C22×D1111yescharacteristic
386C2×M16—22no—
387C2×M16—22no—
388C2×M16—114no—
389C2×M16—222no—
390C2×M16—222no—
391C2×M16C22⋊D1114yescomplemented
392C22×C8—112no—
393C22×C8C22×D1112yes—
394C4⋊Q8—114no—
395C4⋊Q8—222no—
396#127—114no—
397#127—222no—
398#124—114no—
399#124—114no—
400#124—222no—
401#124—222no—
402#121—2216no—
403C4×D4—2216no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—224no—
412C2×C4⋊C4—224no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—448no—
415C2×C4⋊C4C22×D1112yes—
416C2×C22⋊C4—222no—
417C2×C22⋊C4—222no—
418C2×C42—114no—
419C2×C42—112no—
420C2×C42—114no—
421C2×C42—111no—
422C2×C42—111no—
423#103—24no—
424#103—224no—
425#103—224no—
426#103—224no—
427#102—24no—
428#102—224no—
429#102—224no—
430#102—224no—
431#97—224no—
432C4×C8—224no—
433C2×C11—24no—
434C2×C11—82no—
435C2×C11C2×#39011yescharacteristic
436C2×C11C2×#41712yes—
437C2×C11#314112yes—
438C2×C11#315111yescharacteristic
439C2×C11#315211yescharacteristic
440D11—82no—
441C24—21no—
442C24—221no—
443C24D4×D1111yescharacteristic
444#41—28no—
445#41—28no—
446#41—44no—
447#41—44no—
448#41—228no—
449#41—228no—
450#41—444no—
451#41—444no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—112no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8C2×C4×D1112yes—
464C2×D4—24no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—112no—
473C2×D4—228no—
474C2×D4—224no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—444no—
481C2×D4—444no—
482C2×D4—442no—
483C2×D4—442no—
484C2×D4C2×C4×D1112yes—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—44no—
491C22×C4—42no—
492C22×C4—112no—
493C22×C4—118no—
494C22×C4—112no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—221no—
498C22×C4—224no—
499C22×C4—222no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—444no—
503C22×C4—442no—
504C22×C4C2×C4×D1112yes—
505C22×C4#433912yes—
506C22×C4D4×D1111yescharacteristic
507C22×C4D4×D1112yes—
508C22×C4D4×D1112yes—
509C22×C4#434112yes—
510C22×C4C2×C22⋊D1112yes—
511C22×C4C23×D1111yescharacteristic
512M16—28no—
513M16—228no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—114no—
517C2×C8—222no—
518C2×C8—222no—
519C2×C8C2×C22⋊D1114yes—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—42no—
523C4⋊C4—228no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C4⋊C4—448no—
527C4⋊C4—448no—
528C4⋊C4—442no—
529C22⋊C4—228no—
530C22⋊C4—228no—
531C42—118no—
532C42—112no—
533C42—112no—
534C42—112no—
535C42—112no—
536C11#2120011yescharacteristic, complemented, Sylow
537C23—22no—
538C23—22no—
539C23—22no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—222no—
545C23—441no—
546C23—442no—
547C23—442no—
548C23—441no—
549C23C22⋊C4×D1112yes—
550C23#6693812yes—
551C23#6699312yes—
552C23C2×D4×D1111yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—41no—
556Q8—41no—
557Q8—222no—
558Q8—222no—
559Q8—441no—
560Q8—441no—
561D4—22no—
562D4—22no—
563D4—48no—
564D4—41no—
565D4—41no—
566D4—222no—
567D4—222no—
568D4—4416no—
569D4—448no—
570D4—441no—
571D4—441no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—48no—
576C2×C4—44no—
577C2×C4—42no—
578C2×C4—84no—
579C2×C4—114no—
580C2×C4—114no—
581C2×C4—114no—
582C2×C4—114no—
583C2×C4—2216no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—448no—
590C2×C4—444no—
591C2×C4—442no—
592C2×C4—884no—
593C2×C4C22⋊C4×D1112yes—
594C2×C4(C22⋊D11)⋊C414yes—
595C2×C4#6693714yes—
596C2×C4#6693812yes—
597C2×C4C4×C22⋊D1114yes—
598C2×C4#6699214yes—
599C2×C4#6699312yes—
600C2×C4C22×C4×D1111yescharacteristic
601C2×C4C2×#433911yescharacteristic
602C2×C4C2×D4×D1111yescharacteristic
603C2×C4C2×D4×D1111yescharacteristic
604C2×C4C2×#434111yescharacteristic
605C2×C4C22×C22⋊D1111yescharacteristic
606C8—24no—
607C8—224no—
608C22—22no—
609C22—22no—
610C22—24no—
611C22—24no—
612C22—44no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—82no—
617C22—444no—
618C22—442no—
619C22—881no—
620C22—881no—
621C22—882no—
622C22#1062257014yes—
623C22C2×C22⋊C4×D1111yescharacteristic
624C22C2×#6693811yescharacteristic
625C22D11×AGL(1,ℤ/8)12yes—
626C22D11×#13712yes—
627C22C2×#6699311yescharacteristic
628C4—42no—
629C4—82no—
630C4—118no—
631C4—224no—
632C4—442no—
633C4—882no—
634C4#1062257014yes—
635C4C2×(C22⋊D11)⋊C411yescharacteristic
636C4C2×#6693711yescharacteristic
637C4C2×C4×C22⋊D1111yescharacteristic
638C4C2×#6699211yescharacteristic
639C2—24no—
640C2—82no—
641C2—882no—
642C2C2×#1062257011yescharacteristic
643C2D11×#41712yes—
644C2#1307900712yes—
645C2#1307906411yescharacteristic
646C2#1307907111yescharacteristic
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#21200
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×#10622589C2semidirect
7. #13069431C2semidirect
8. #13069429C2semidirect
9. #13069420C2semidirect
10. #13069416C2semidirect
11. C2×C11×#417C2semidirect
17. #10623363C4semidirect
73. C2×C11×M16D4semidirect
81. #67000C2×C4semidirect
83. #66997C2×C4semidirect
85. #66993C2×C4semidirect
88. #66989C2×C4semidirect
106. C2×#4318D4semidirect
218. C2×#417D11semidirect
360. Dic11#417semidirect
391. C2×M16C22⋊D11semidirect
536. C11#21200semidirect

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×#106225892
#130694312
#130694292
#130694202
#130694162
C2×C11×#4172
#2120011