Finite Group Databasebeta

← #14765426

Subgroups — #14765426

Order 2816.

968 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622495C211yesmaximal, characteristic
2#13071124C211yesmaximal, characteristic
3D11×#389C211yesmaximal, characteristic, complemented
4#13069351C211yesmaximal, characteristic, complemented
5#13069313C211yesmaximal, characteristic, complemented
6#13069312C211yesmaximal, characteristic, complemented
7#13069210C211yesmaximal, characteristic, complemented
8#13069206C211yesmaximal, characteristic, complemented
9#13068932C211yesmaximal, characteristic
10#13068878C211yesmaximal, characteristic, complemented
11#13068874C211yesmaximal, characteristic, complemented
12#13068807C211yesmaximal, characteristic, complemented
13#13068701C211yesmaximal, characteristic, complemented
14#13068379C211yesmaximal, characteristic, complemented
15C11×#1943C211yesmaximal, characteristic, complemented
16C2×#66948C2211yescharacteristic
17C2×#66946—21no—
18C2×#66946C2211yescharacteristic
19C2×C4⋊C4×D11—21no—
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32#10622603—21no—
33#10622600C2211yescharacteristic
34#10622598C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622585—21no—
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622495C418yescomplemented
46#10622279—21no—
47#10622278—21no—
48D11×#95—21no—
49#10622260—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×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11D411yescharacteristic
66C22×C4×D11D411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
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×Dic11⋊C4—21no—
89C2×Dic11⋊C4—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—
101C4⋊C4×D11—22no—
102C4⋊C4×D11—41no—
103C4⋊C4×D11—41no—
104C4⋊C4×D11—44no—
105C4⋊C4×D11C2×C414yescomplemented
106C42×D11—41no—
107C42×D11—41no—
108C11×#107C2×C414yescomplemented
109C11×#106—41no—
110C11×#97—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66885—41no—
119#66885C2×C414yescomplemented
120(C2×D11)⋊C8—22no—
121(C2×D11)⋊C8C2×C414yescomplemented
122#66873—41no—
123#66873C2×C414yescomplemented
124#66872—41no—
125#66871C2×C414yescomplemented
126#66867—41no—
127#22081—111nomaximal, Sylow
128C23×D11—21no—
129C23×D11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C2×D44—24no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—42no—
150C2×D44—42no—
151C2×D44C22×C412yes—
152C2×C4×D11—22no—
153C2×C4×D11—24no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—41no—
161C2×C4×D11—41no—
162C2×C4×D11—41no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11C22×C412yes—
172C2×C4×D11#4112yes—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C22×C412yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4C22×C412yes—
188C11×C4⋊C4C22×C412yes—
189C42×C11—21no—
190C42×C11—21no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11C22×C412yes—
203Dic11⋊C4—24no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—41no—
210C4×Dic11—41no—
211C4×Dic11—42no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8C22×C412yes—
218C2×#480—111no—
219C4×#121—111no—
220C2×#389—111no—
221#1943—111no—
222#1943D1111yescharacteristic, complemented
223#1936—111no—
224#1936—111no—
225#1921—111no—
226#1921—111no—
227#1874—111no—
228#1864—111no—
229#1864—111no—
230#1853—111no—
231#1823—111no—
232#1749—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—22no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11C4×D412yes—
246C22×D11AGL(1,ℤ/8)12yes—
247C22×D11AGL(1,ℤ/8)12yes—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C2×C4×C112−1+411yescharacteristic
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11C4×D412yes—
289C2×Dic11#13712yes—
290D44—22no—
291D44—22no—
292D44—48no—
293D44—41no—
294D44—41no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—44no—
300C4×D11—44no—
301C4×D11—48no—
302C4×D11—84no—
303C4×D11—84no—
304C8×C11—22no—
305C8×C11—41no—
306C11⋊C8—22no—
307C11⋊C8—41no—
308C2×#121—111no—
309C2×C4×D4—111no—
310C2×C4×D4—221no—
311C22×C4⋊C4—111no—
312C22×C4⋊C4—111no—
313C22×C4⋊C4—221no—
314C22×C42—111no—
315#480—118no—
316C2×#107—111no—
317C2×#107C2×D1111yescharacteristic
318C2×#106—111no—
319C2×#106C2×D1111yescharacteristic
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×C22⋊C8—111no—
325C2×C22⋊C8—111no—
326C2×#97—111no—
327C2×#97C2×D1111yescharacteristic
328#390—111no—
329#389—111no—
330#389—111no—
331#389—111no—
332#389—221no—
333#389—221no—
334#389C2×D1111yescharacteristic
335#389C2×D1111yescharacteristic
336#388—221no—
337#386—221no—
338#380—111no—
339C4×C4⋊C4—111no—
340C4×C22⋊C4—221no—
341C2×#95—221no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340C2×D1111yescharacteristic
349#340C2×D1111yescharacteristic
350#336—111no—
351#336—111no—
352C22×C11C2×C4×D411yescharacteristic
353C22×C11#53411yescharacteristic
354C22×C11#53611yescharacteristic
355C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C11C2×#13711yescharacteristic
358C22×C11#57511yescharacteristic
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—22no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11#44214yes—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11#52011yescharacteristic
380C4×C11#52011yescharacteristic
381C4×C11#53911yescharacteristic
382C4×C11#53911yescharacteristic
383Dic11—22no—
384Dic11—22no—
385Dic11—41no—
386Dic11—42no—
387Dic11—81no—
388Dic11—81no—
389C22×D4—111no—
390C22×D4—221no—
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—221no—
395C23×C4—221no—
396C23×C4—221no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401#121—114no—
402#121—222no—
403C4×D4—441no—
404C4×D4—441no—
405C4×D4—444no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—222no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—441no—
419C2×C4⋊C4—441no—
420C2×C4⋊C4—444no—
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C42—111no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—221no—
434C2×C42—441no—
435C2×C42—441no—
436C2×C42C22×D1111yescharacteristic
437#107—114no—
438#107C4×D1114yescomplemented
439#106—41no—
440#106—441no—
441#102—114no—
442#102—114no—
443#102—441no—
444#102—441no—
445C22⋊C8—114no—
446C22⋊C8—222no—
447#97—41no—
448#97—441no—
449#95—21no—
450#95—21no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11#232211yescharacteristic
457C2×C11C2×#44211yescharacteristic
458C2×C11C4×#13711yescharacteristic
459C2×C11#319311yescharacteristic
460C2×C11#319411yescharacteristic
461C2×C11#323411yescharacteristic
462C2×C11#323811yescharacteristic
463D11—24no—
464D11—82no—
465C24—111no—
466C24—221no—
467C2×D4—112no—
468C2×D4—224no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—442no—
475C2×D4—442no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—111no—
485C22×C4—222no—
486C22×C4—224no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—441no—
497C22×C4—441no—
498C22×C4—441no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4D4×D1111yescharacteristic
508C22×C4D4×D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—112no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8C2×C4×D1112yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—112no—
531C4⋊C4—224no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4C2×C4×D1112yes—
542C4⋊C4C2×C4×D1112yes—
543C22⋊C4—224no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C42—21no—
549C42—21no—
550C42—221no—
551C42—221no—
552C42—441no—
553C42—441no—
554C42—442no—
555C11#2208111yescharacteristic, complemented, Sylow
556C23—112no—
557C23—112no—
558C23—112no—
559C23—221no—
560C23—221no—
561C23—221no—
562C23—221no—
563C23—222no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23C2×D4×D1111yescharacteristic
571D4—222no—
572D4—222no—
573D4—448no—
574D4—441no—
575D4—441no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—112no—
595C2×C4—112no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—222no—
607C2×C4—221no—
608C2×C4—444no—
609C2×C4—448no—
610C2×C4—444no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—884no—
620C2×C4—884no—
621C2×C4C22×C4×D1111yescharacteristic
622C2×C4#6703711yescharacteristic
623C2×C4#6704011yescharacteristic
624C2×C4#6704011yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#6704211yescharacteristic
627C8—22no—
628C8—41no—
629C8—222no—
630C8—441no—
631C22—114no—
632C22—222no—
633C22—222no—
634C22—222no—
635C22—222no—
636C22—222no—
637C22—222no—
638C22—442no—
639C22—442no—
640C22—442no—
641C22—881no—
642C22—881no—
643C22—881no—
644C22—881no—
645C22C4×D4×D1111yescharacteristic
646C22#1062313611yescharacteristic
647C22#1062325511yescharacteristic
648C22D11×AGL(1,ℤ/8)11yescharacteristic
649C22D11×AGL(1,ℤ/8)11yescharacteristic
650C22D11×#13711yescharacteristic
651C22#1062330811yescharacteristic
652C4—41no—
653C4—41no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—222no—
659C4—222no—
660C4—441no—
661C4—442no—
662C4—881no—
663C4—881no—
664C4#1062303511yescharacteristic
665C4#1062310511yescharacteristic
666C4#1062316911yescharacteristic
667C4#1062322311yescharacteristic
668C2—224no—
669C2—882no—
670C2#1307128011yescharacteristic
671C2D11×#44211yescharacteristic
672C2#1307743211yescharacteristic
673C2#1307941711yescharacteristic
674C2#1307943111yescharacteristic
675C2#1307980711yescharacteristic
676C2#1307983811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1943C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
cosocleC22×C4×C11C24
hypercenter#1943D11
hypocenterC11#22081
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
3. D11×#389C2semidirect
4. #13069351C2semidirect
5. #13069313C2semidirect
6. #13069312C2semidirect
7. #13069210C2semidirect
8. #13069206C2semidirect
10. #13068878C2semidirect
11. #13068874C2semidirect
12. #13068807C2semidirect
13. #13068701C2semidirect
14. #13068379C2semidirect
15. C11×#1943C2semidirect
45. #10622495C4semidirect
105. C4⋊C4×D11C2×C4semidirect
108. C11×#107C2×C4semidirect
119. #66885C2×C4semidirect
121. (C2×D11)⋊C8C2×C4semidirect
123. #66873C2×C4semidirect
125. #66871C2×C4semidirect
222. #1943D11semidirect
438. #107C4×D11semidirect
555. C11#22081semidirect

Maximal subgroups

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

subgroupindex
C2×#106224952
#130711242
D11×#3892
#130693512
#130693132
#130693122
#130692102
#130692062
#130689322
#130688782
#130688742
#130688072
#130687012
#130683792
C11×#19432
#2208111