Finite Group Databasebeta

← #14762839

Subgroups — #14762839

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic, complemented
3#13070995C211yesmaximal, characteristic, complemented
4#13069053C212yesmaximal, complemented
5#13069046C212yesmaximal, complemented
6#13068938C211yesmaximal, characteristic, complemented
7#13068936C211yesmaximal, characteristic, complemented
8#13068929C211yesmaximal, characteristic, complemented
9#13068710C212yesmaximal, complemented
10#13068555C212yesmaximal, complemented
11C11×#1873C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×#66999C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4313C2212yes—
20#10623158—24no—
21#10623158C418yescomplemented
22C2×#66948C2211yescharacteristic
23C2×#66947—21no—
24C2×#66946—21no—
25C2×#66945C2211yescharacteristic
26C2×#66935—21no—
27C2×(C22⋊D11)⋊C4—21no—
28C2×C11×#103C2212yescomplemented
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×#66899C2212yescomplemented
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66885C2212yescomplemented
33C2×(C2×D11)⋊C8C2212yes—
34#10622600C2212yes—
35#10622600C2212yes—
36C2×#66873C2212yescomplemented
37#10622568—21no—
38#10622556—21no—
39C4×(C2×D11)⋊C4—21no—
40C4×(C2×D11)⋊C4—21no—
41#10622339—24no—
42C11×#340C2212yescomplemented
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46C24×D11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C23×Dic11D411yescharacteristic
51C2×#4343—22no—
52C2×#4343—42no—
53C2×#4343—42no—
54C2×#4343C2×C414yes—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44C2311yescharacteristic
58C22×C4×D11—21no—
59C22×C4×D11—42no—
60C22×C4×D11—42no—
61C22×C4×D11C2×C414yes—
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11D414yes—
65C22×C4×D11C2311yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2312yes—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8C2×C414yes—
70C11×#117—42no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C22⋊Dic11—21no—
78#66999—22no—
79#66999C2×C414yes—
80#66983—22no—
81#66983C2×C414yes—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88#66979—42no—
89C2×C4⋊Dic11C2312yes—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C22×C11⋊C8C2312yes—
95C2×#4313—24no—
96C2×#4313—42no—
97C2×#4313—42no—
98#66948—22no—
99#66948C2×C414yes—
100#66947—28no—
101#66946—28no—
102#66945—22no—
103#66945C2×C414yes—
104#66935—28no—
105(C22⋊D11)⋊C4—28no—
106C11×#103—42no—
107C11×C22⋊C8—22no—
108#66899—42no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C22⋊(C11⋊C8)—22no—
112#66885—42no—
113(C2×D11)⋊C8—24no—
114#66873—42no—
115#21766—111nomaximal, Sylow
116C24×C11C2×D411yescharacteristic
117C23×D11—21no—
118C23×D11—41no—
119C23×D11—41no—
120C23×D11—42no—
121C23×D11—42no—
122C23×D11C22⋊C414yes—
123C23×D11C2×D411yescharacteristic
124C23×D11C2×D411yescharacteristic
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11C22×C412yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2411yescharacteristic
138C2×C22⋊D11—24no—
139C2×C22⋊D11—44no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—41no—
143C22×Dic11—41no—
144C22×Dic11C22⋊C414yes—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147#4343—48no—
148#4343—48no—
149C2×D44—24no—
150C2×D44—24no—
151C2×D44—21no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—44no—
155C2×D44—42no—
156C2×D44—42no—
157C2×D44C22×C412yes—
158C2×C4×D11—24no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—41no—
164C2×C4×D11—41no—
165C2×C4×D11—41no—
166C2×C4×D11—41no—
167C2×C4×D11—48no—
168C2×C4×D11—48no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11C22⋊C414yes—
172C2×C4×D11C22⋊C414yes—
173C2×C4×D11C22×C412yes—
174C2×C4×D11C22×C412yes—
175C2×C4×D11C2×D412yes—
176C2×C4×D11C2×D412yes—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4C22×C412yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—42no—
187C42×C11—42no—
188C22⋊Dic11—42no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—44no—
194(C2×D11)⋊C4—44no—
195C4⋊Dic11—21no—
196C4⋊Dic11—22no—
197C4⋊Dic11—22no—
198C4⋊Dic11C22×C412yes—
199Dic11⋊C4—24no—
200C4×Dic11—24no—
201C4×Dic11—42no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205#4313—48no—
206C2×#525—111no—
207C2×#407—111no—
208#2280—111no—
209#1895—112no—
210#1894—112no—
211#1875—111no—
212#1875—111no—
213#1873—111no—
214#1873D1111yescharacteristic, complemented
215#1825—112no—
216#1788—112no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11C2×C22⋊C412yes—
222C23×C11C22×D411yescharacteristic
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—44no—
235C22×D11—48no—
236C22×D11—48no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11C2×C22⋊C412yes—
242C22×D11C2×C22⋊C412yes—
243Q8×C11—24no—
244Q8×C11—42no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11C2×C22⋊C412yes—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11H(5,𝔽2)12yes—
261C2×C4×C11H(5,𝔽2)12yes—
262C22⋊D11—48no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—44no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11C2×C22⋊C412yes—
274C2×Dic11C2×C22⋊C412yes—
275D44—24no—
276D44—48no—
277D44—48no—
278D44—42no—
279C4×D11—24no—
280C4×D11—24no—
281C4×D11—24no—
282C4×D11—24no—
283C4×D11—44no—
284C4×D11—44no—
285C4×D11—48no—
286C8×C11—42no—
287C11⋊C8—42no—
288C22×#41—111no—
289C24×C4—111no—
290C22×M16—112no—
291#525—118no—
292#525—224no—
293C2×#123—221no—
294C2×C22⋊Q8—111no—
295C2×C22⋊Q8C2×D1111yescharacteristic
296C2×#121—111no—
297C2×#121—111no—
298C2×#120—221no—
299C2×C4×D4—221no—
300C2×C4×D4—221no—
301C2×#117—111no—
302C2×#117—111no—
303C2×#117C2×D1111yescharacteristic
304C2×#103—112no—
305C2×#103C2×D1112yescomplemented
306C2×#102—112no—
307C2×#102—112no—
308#407—224no—
309C2×C22⋊C8—111no—
310C2×C22⋊C8—112no—
311C2×C22⋊C8C2×D1111yescharacteristic
312#381—221no—
313#380—112no—
314#380—112no—
315#379—221no—
316C4×C22⋊C4—221no—
317C4×C22⋊C4—221no—
318#340—112no—
319#340—112no—
320#340—112no—
321#340C2×D1112yescomplemented
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11C22×C22⋊C411yescharacteristic
328C22×C11#53411yescharacteristic
329C22×C11#53411yescharacteristic
330C22×C11#57512yes—
331C22×C11#57512yes—
332C2×D11—22no—
333C2×D11—22no—
334C2×D11—22no—
335C2×D11—22no—
336C2×D11—22no—
337C2×D11—22no—
338C2×D11—416no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—42no—
343C2×D11—42no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—82no—
347C2×D11—82no—
348C4×C11—22no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—82no—
352C4×C11#51812yes—
353C4×C11#53412yes—
354Dic11—22no—
355Dic11—22no—
356Dic11—42no—
357Dic11—82no—
358C25—111no—
359C2×#41—114no—
360C2×#41—222no—
361C2×#41—442no—
362C2×#41—442no—
363C22×Q8C22×D1111yescharacteristic
364C22×D4—111no—
365C22×D4—221no—
366C22×D4—221no—
367C22×D4—221no—
368C23×C4—111no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—114no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—114no—
375C23×C4—221no—
376C23×C4—442no—
377C23×C4—442no—
378C23×C4C22×D1111yescharacteristic
379C2×M16—224no—
380C2×M16—442no—
381C2×M16—442no—
382C22×C8—112no—
383C22×C8C22×D1112yes—
384#123—228no—
385C22⋊Q8—22no—
386C22⋊Q8—114no—
387C22⋊Q8—222no—
388C22⋊Q8C4×D1114yes—
389#121—114no—
390#121—114no—
391#121—222no—
392#121—222no—
393#120—228no—
394C4×D4—228no—
395C4×D4—228no—
396#117—42no—
397#117—114no—
398#117—222no—
399#117—442no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22×D1112yes—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—221no—
415C2×C42—21no—
416C2×C42—221no—
417C2×C42—221no—
418#103—42no—
419#103—442no—
420#102—442no—
421#102—442no—
422C22⋊C8—22no—
423C22⋊C8—224no—
424C22⋊C8—222no—
425#95—222no—
426#95—222no—
427C2×C11—42no—
428C2×C11#230811yescharacteristic
429C2×C11#289611yescharacteristic
430C2×C11#289611yescharacteristic
431C2×C11#319712yes—
432C2×C11#319712yes—
433D11—42no—
434D11—42no—
435D11—82no—
436C24—111no—
437C24—111no—
438C24—114no—
439C24—221no—
440C24—441no—
441C24—441no—
442C24—442no—
443C24—442no—
444C24D4×D1111yescharacteristic
445#41—448no—
446#41—448no—
447C2×Q8—21no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8C2×C4×D1112yes—
451C2×D4—112no—
452C2×D4—224no—
453C2×D4—224no—
454C2×D4—224no—
455C2×D4—221no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—442no—
459C2×D4—442no—
460C2×D4—444no—
461C2×D4—444no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—114no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—112no—
474C22×C4—114no—
475C22×C4—114no—
476C22×C4—224no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—221no—
482C22×C4—222no—
483C22×C4—448no—
484C22×C4—448no—
485C22×C4—441no—
486C22×C4—441no—
487C22×C4—441no—
488C22×C4—441no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—441no—
492C22×C4—441no—
493C22×C4C2×C4×D1112yes—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1112yes—
496C22×C4C23×D1111yescharacteristic
497M16—448no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—222no—
502C2×C8—222no—
503C2×C8—222no—
504C4⋊C4—24no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—112no—
509C4⋊C4—224no—
510C4⋊C4—221no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4C2×C4×D1112yes—
514C22⋊C4—24no—
515C22⋊C4—42no—
516C22⋊C4—224no—
517C22⋊C4—224no—
518C22⋊C4—224no—
519C22⋊C4—224no—
520C22⋊C4—444no—
521C22⋊C4—444no—
522C22⋊C4—442no—
523C42—42no—
524C42—224no—
525C42—442no—
526C11#2176611yescharacteristic, complemented, Sylow
527C23—22no—
528C23—22no—
529C23—21no—
530C23—21no—
531C23—112no—
532C23—112no—
533C23—222no—
534C23—222no—
535C23—222no—
536C23—222no—
537C23—221no—
538C23—221no—
539C23—221no—
540C23—221no—
541C23—222no—
542C23—444no—
543C23—444no—
544C23—444no—
545C23—448no—
546C23—448no—
547C23—442no—
548C23—442no—
549C23—441no—
550C23—441no—
551C23C22⋊C4×D1112yes—
552C23C2×D4×D1111yescharacteristic
553Q8—24no—
554Q8—42no—
555D4—224no—
556D4—448no—
557D4—448no—
558D4—448no—
559D4—442no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—112no—
573C2×C4—112no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—222no—
583C2×C4—444no—
584C2×C4—444no—
585C2×C4—448no—
586C2×C4—444no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4C22⋊C4×D1112yes—
592C2×C4C22×C4×D1111yescharacteristic
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4#6703712yes—
595C2×C4#6704212yes—
596C8—42no—
597C8—442no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—42no—
602C22—42no—
603C22—222no—
604C22—222no—
605C22—222no—
606C22—222no—
607C22—222no—
608C22—222no—
609C22—4416no—
610C22—442no—
611C22—442no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22—442no—
616C22—442no—
617C22—882no—
618C22—882no—
619C22C2×C22⋊C4×D1111yescharacteristic
620C22#1062312011yescharacteristic
621C22#1062318411yescharacteristic
622C22#1062329912yes—
623C22#1062330812yes—
624C4—22no—
625C4—42no—
626C4—42no—
627C4—82no—
628C4—222no—
629C4—222no—
630C4—442no—
631C4—882no—
632C4#1062307612yes—
633C4#1062313612yes—
634C2—42no—
635C2—442no—
636C2—442no—
637C2—882no—
638C2#1307119011yescharacteristic
639C2#1307713111yescharacteristic
640C2#1307713411yescharacteristic
641C2#1307945712yes—
642C2#1307946012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC2×#10623158C2
cosocleC22×C4×C11C24
hypercenter#1873D11
hypocenterC11#21766
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. C2×#10622339C2semidirect
3. #13070995C2semidirect
4. #13069053C2semidirect
5. #13069046C2semidirect
6. #13068938C2semidirect
7. #13068936C2semidirect
8. #13068929C2semidirect
9. #13068710C2semidirect
10. #13068555C2semidirect
11. C11×#1873C2semidirect
21. #10623158C4semidirect
28. C2×C11×#103C22semidirect
30. C2×#66899C22semidirect
32. C2×#66885C22semidirect
36. C2×#66873C22semidirect
42. C11×#340C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
214. #1873D11semidirect
305. C2×#103C2×D11semidirect
321. #340C2×D11semidirect
526. C11#21766semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×#106223392
#130709952
#130690532
#130690462
#130689382
#130689362
#130689292
#130687102
#130685552
C11×#18732
#2176611