Finite Group Databasebeta

← #14765485

Subgroups — #14765485

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622479C211yesmaximal, characteristic
2#13071124C211yesmaximal, characteristic
3#13071097C211yesmaximal, characteristic, complemented
4#13069351C211yesmaximal, characteristic, complemented
5#13069313C211yesmaximal, characteristic, complemented
6#13069312C211yesmaximal, characteristic, complemented
7#13069203C211yesmaximal, characteristic, complemented
8#13069185C211yesmaximal, characteristic, complemented
9#13068937C211yesmaximal, characteristic
10#13068878C211yesmaximal, characteristic, complemented
11#13068860C211yesmaximal, characteristic, complemented
12#13068812C211yesmaximal, characteristic, complemented
13#13068709C211yesmaximal, characteristic, complemented
14#13068379C211yesmaximal, characteristic, complemented
15C11×#1944C211yesmaximal, characteristic, complemented
16C2×#66948C2211yescharacteristic
17C2×#66946—21no—
18C2×#66946C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C42×D11C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31#10622603—21no—
32#10622602—21no—
33#10622600C2211yescharacteristic
34#10622598C2211yescharacteristic
35C4⋊C4×Dic11—21no—
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622479C418yescomplemented
46#10622281—21no—
47#10622279—21no—
48#10622278—21no—
49#10622262—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D44—21no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11D411yescharacteristic
64C22×C4×D11D411yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96#66948—22no—
97#66948C2×C414yes—
98#66946—41no—
99#66946—41no—
100#66946—44no—
101#66945—22no—
102#66945—41no—
103#66945—41no—
104#66945C2×C414yescomplemented
105C42×D11—41no—
106C42×D11—41no—
107C11×#107—41no—
108C11×#106C2×C414yescomplemented
109C11×#97—41no—
110C11×#95—21no—
111C11×#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66885—41no—
118#66885C2×C414yescomplemented
119(C2×D11)⋊C8—22no—
120(C2×D11)⋊C8C2×C414yescomplemented
121#66873—41no—
122#66873C2×C414yescomplemented
123#66872—41no—
124#66871C2×C414yescomplemented
125#66867—41no—
126#22086—111nomaximal, Sylow
127C23×D11—21no—
128C23×D11C2×D411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×D44—24no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—42no—
149C2×D44—42no—
150C2×D44C22×C412yes—
151C2×C4×D11—22no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—41no—
157C2×C4×D11—41no—
158C2×C4×D11—41no—
159C2×C4×D11—41no—
160C2×C4×D11—41no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11C22×C412yes—
165C2×C4×D11#4112yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C412yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4C22×C412yes—
181C11×C4⋊C4C22×C412yes—
182C42×C11—21no—
183C42×C11—21no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11C22×C412yes—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200C4×Dic11—24no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—41no—
204C4×Dic11—41no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C22×C412yes—
213C2×#482—111no—
214C4×#121—111no—
215#2296—111no—
216#1944D1111yescharacteristic, complemented
217#1943—111no—
218#1936—111no—
219#1936—111no—
220#1920—111no—
221#1918—111no—
222#1875—111no—
223#1864—111no—
224#1862—111no—
225#1854—111no—
226#1825—111no—
227#1749—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—22no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11C4×D412yes—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11C4×D412yes—
284C2×Dic11AGL(1,ℤ/8)12yes—
285D44—22no—
286D44—22no—
287D44—48no—
288D44—41no—
289D44—41no—
290C4×D11—22no—
291C4×D11—22no—
292C4×D11—22no—
293C4×D11—22no—
294C4×D11—44no—
295C4×D11—44no—
296C4×D11—84no—
297C8×C11—22no—
298C8×C11—41no—
299C11⋊C8—22no—
300C11⋊C8—41no—
301C2×#121—111no—
302C2×C4×D4—111no—
303C2×C4×D4—221no—
304C2×#117—111no—
305C2×#117—111no—
306C22×C42—111no—
307#482—118no—
308C2×#107—111no—
309C2×#107C2×D1111yescharacteristic
310C2×#106—111no—
311C2×#106C2×D1111yescharacteristic
312C2×#102—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8—111no—
318C2×#97—111no—
319C2×#97C2×D1111yescharacteristic
320#390—111no—
321#389—111no—
322#389—111no—
323#389—111no—
324#389C2×D1111yescharacteristic
325#389C2×D1111yescharacteristic
326#388—221no—
327#386—221no—
328#385—221no—
329#385—221no—
330#380—111no—
331C4×C4⋊C4—111no—
332C4×C4⋊C4—221no—
333C4×C4⋊C4—221no—
334C4×C22⋊C4—221no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340C2×D1111yescharacteristic
342#340C2×D1111yescharacteristic
343#336—111no—
344#336—111no—
345C22×C11C2×C4×D411yescharacteristic
346C22×C11#53411yescharacteristic
347C22×C11#53611yescharacteristic
348C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57511yescharacteristic
351C22×C11#57511yescharacteristic
352C2×D11—22no—
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—42no—
369C4×C11—42no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11#52011yescharacteristic
373C4×C11#52011yescharacteristic
374C4×C11#53911yescharacteristic
375C4×C11#53911yescharacteristic
376Dic11—22no—
377Dic11—22no—
378Dic11—41no—
379Dic11—42no—
380Dic11—81no—
381Dic11—81no—
382C22×D4—111no—
383C22×D4—221no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—221no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392#121—114no—
393#121—222no—
394C4×D4—441no—
395C4×D4—441no—
396C4×D4—444no—
397#117—114no—
398#117—222no—
399#117—441no—
400#117—441no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42—221no—
426C2×C42—441no—
427C2×C42—441no—
428C2×C42C22×D1111yescharacteristic
429#107—41no—
430#107—114no—
431#106—441no—
432#106C4×D1114yescomplemented
433#102—114no—
434#102—114no—
435#102—441no—
436#102—441no—
437C22⋊C8—114no—
438C22⋊C8—222no—
439#97—41no—
440#97—441no—
441#95—21no—
442#95—21no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448C2×C11#232211yescharacteristic
449C2×C11#294311yescharacteristic
450C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
451C2×C11#319411yescharacteristic
452C2×C11#319711yescharacteristic
453C2×C11#323511yescharacteristic
454C2×C11#324011yescharacteristic
455D11—42no—
456D11—82no—
457C24—111no—
458C24—221no—
459C2×D4—112no—
460C2×D4—224no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—442no—
467C2×D4—442no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—111no—
477C22×C4—222no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—441no—
486C22×C4—441no—
487C22×C4—441no—
488C22×C4—441no—
489C22×C4—441no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4D4×D1111yescharacteristic
494C22×C4D4×D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—112no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8C2×C4×D1112yes—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—42no—
516C4⋊C4—112no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4C2×C4×D1112yes—
526C4⋊C4C2×C4×D1112yes—
527C22⋊C4—224no—
528C22⋊C4—224no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C42—21no—
535C42—21no—
536C42—224no—
537C42—221no—
538C42—221no—
539C42—441no—
540C42—441no—
541C42—442no—
542C42—442no—
543C11#2208611yescharacteristic, complemented, Sylow
544C23—112no—
545C23—221no—
546C23—221no—
547C23—221no—
548C23—221no—
549C23—221no—
550C23—221no—
551C23—222no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23C2×D4×D1111yescharacteristic
559D4—222no—
560D4—222no—
561D4—448no—
562D4—441no—
563D4—441no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—112no—
583C2×C4—112no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—222no—
595C2×C4—221no—
596C2×C4—444no—
597C2×C4—444no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—884no—
607C2×C4C22×C4×D1111yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#6704011yescharacteristic
610C2×C4#6704011yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C2×C4#6704211yescharacteristic
613C8—22no—
614C8—41no—
615C8—222no—
616C8—441no—
617C22—222no—
618C22—222no—
619C22—222no—
620C22—441no—
621C22—441no—
622C22—441no—
623C22—441no—
624C22—442no—
625C22—442no—
626C22—442no—
627C22—881no—
628C22—881no—
629C22—881no—
630C22—881no—
631C22C4×D4×D1111yescharacteristic
632C22#1062313611yescharacteristic
633C22#1062325511yescharacteristic
634C22D11×AGL(1,ℤ/8)11yescharacteristic
635C22#1062330411yescharacteristic
636C22#1062330811yescharacteristic
637C22#1062330811yescharacteristic
638C4—41no—
639C4—42no—
640C4—41no—
641C4—42no—
642C4—81no—
643C4—81no—
644C4—222no—
645C4—222no—
646C4—441no—
647C4—442no—
648C4—881no—
649C4—881no—
650C4#1062303511yescharacteristic
651C4#1062310511yescharacteristic
652C4#1062316911yescharacteristic
653C4#1062322311yescharacteristic
654C2—442no—
655C2—882no—
656C2#1307128011yescharacteristic
657C2#1307741111yescharacteristic
658C2#1307742111yescharacteristic
659C2#1307942511yescharacteristic
660C2#1307945911yescharacteristic
661C2#1307981511yescharacteristic
662C2#1307985711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1944C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
cosocleC22×C4×C11C24
hypercenter#1944D11
hypocenterC11#22086
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
3. #13071097C2semidirect
4. #13069351C2semidirect
5. #13069313C2semidirect
6. #13069312C2semidirect
7. #13069203C2semidirect
8. #13069185C2semidirect
10. #13068878C2semidirect
11. #13068860C2semidirect
12. #13068812C2semidirect
13. #13068709C2semidirect
14. #13068379C2semidirect
15. C11×#1944C2semidirect
45. #10622479C4semidirect
104. #66945C2×C4semidirect
108. C11×#106C2×C4semidirect
118. #66885C2×C4semidirect
120. (C2×D11)⋊C8C2×C4semidirect
122. #66873C2×C4semidirect
124. #66871C2×C4semidirect
216. #1944D11semidirect
432. #106C4×D11semidirect
543. C11#22086semidirect

Maximal subgroups

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

subgroupindex
C2×#106224792
#130711242
#130710972
#130693512
#130693132
#130693122
#130692032
#130691852
#130689372
#130688782
#130688602
#130688122
#130687092
#130683792
C11×#19442
#2208611