Finite Group Databasebeta

← #14821834

Subgroups — #14821834

Order 2816.

848 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
1#13072984C211yesmaximal, characteristic, complemented
2#13071628C211yesmaximal, characteristic
3#13069932C211yesmaximal, characteristic, complemented
4#13069803C211yesmaximal, characteristic
5#13069750C211yesmaximal, characteristic, complemented
6#13069620C211yesmaximal, characteristic
7#13069562C211yesmaximal, characteristic, complemented
8#13069292C211yesmaximal, characteristic, complemented
9#13069248C211yesmaximal, characteristic, complemented
10#13069222C211yesmaximal, characteristic, complemented
11#13069194C211yesmaximal, characteristic, complemented
12#13068950C211yesmaximal, characteristic, complemented
13#13068922C211yesmaximal, characteristic, complemented
14#13068701C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C2211yescharacteristic
18C22×#4324C2211yescharacteristic
19C2×C4×C22⋊D11—21no—
20C2×#66950C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×#66941C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27#10622834C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622823—21no—
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622600C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40#10622569—21no—
41#10622558—21no—
42#10622553—21no—
43C4×(C2×D11)⋊C4C2211yescharacteristic
44#10622542—21no—
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622286—21no—
48#10622272—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×C22⋊D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×Dic22—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66991—22no—
80#66991—22no—
81C2×#4324—22no—
82C2×#4324—41no—
83C2×#4324—41no—
84C4×C22⋊D11—44no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66950—22no—
101#66950—41no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—41no—
104#66941—22no—
105#66941—41no—
106C11×#102—22no—
107C11×#102—22no—
108C4×C8×C11—41no—
109C11×#95—21no—
110#66896—41no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120(C2×D11)⋊C8—41no—
121(C2×D11)⋊C8—41no—
122#66880—22no—
123#66880—41no—
124Dic11⋊C8—41no—
125#66874—22no—
126#66872—22no—
127#26722—111nomaximal, Sylow
128C24×C11—21no—
129C23×D11C2×D411yescharacteristic
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11#4112yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—81no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—24no—
146C2×C22⋊D11—42no—
147C2×C22⋊D11—42no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—81no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—42no—
171C2×Dic22—42no—
172C2×Dic22—81no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4#4112yes—
184C11×C4⋊C4#4112yes—
185C11×C22⋊C4—42no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—81no—
189C22⋊Dic11—24no—
190C22⋊Dic11—42no—
191C22⋊Dic11—81no—
192#4324—44no—
193(C2×D11)⋊C4—41no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196(C2×D11)⋊C4SD1614yescomplemented
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—42no—
203C4⋊Dic11#4112yes—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—42no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216#2492—111no—
217#2361—111no—
218#2055—111no—
219#2034—111no—
220#2023—111no—
221#2000—111no—
222#1987—111no—
223#1933—111no—
224#1927—111no—
225#1923—111no—
226#1919—111no—
227#1877—111no—
228#1872—111no—
229#1823—111no—
230C4×#102D1111yescharacteristic, complemented
231C23×C11—22no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C22×D411yescharacteristic
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11C2×SD1612yes—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—41no—
249D4×C11—41no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
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—84no—
265C2×C4×C11C2×SD1612yes—
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C22⋊D11—48no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11C2×SD1612yes—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—84no—
299Dic22—41no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303Dic22—84no—
304C8×C11—41no—
305C8×C11—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C22×SD16—111no—
309C2×C4⋊Q8—111no—
310C2×C22⋊Q8—111no—
311C2×#121—111no—
312C2×C4×D4—221no—
313C2×C4×D4C2×D1111yescharacteristic
314C22×C4⋊C4—111no—
315C2×#106—111no—
316C2×C4⋊C8—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#102—111no—
321C2×#102C2×D1111yescharacteristic
322C2×#102C2×D1111yescharacteristic
323C2×C22⋊C8—111no—
324C2×C22⋊C8—111no—
325C2×C4×C8C2×D1111yescharacteristic
326#400—221no—
327#393—221no—
328#391—111no—
329#391—111no—
330#391—221no—
331#390—111no—
332#389—111no—
333#388—221no—
334#388—221no—
335#386—221no—
336#385—221no—
337#380—111no—
338C4×C4⋊C4—111no—
339C4×C4⋊C4C2×D1111yescharacteristic
340C4×C22⋊C4—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340C2×D1111yescharacteristic
348#340C2×D1111yescharacteristic
349#336—111no—
350#336—111no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11#52511yescharacteristic
359C22×C11#54611yescharacteristic
360C22×C11#54611yescharacteristic
361C22×C11C22×SD1611yescharacteristic
362C22×C11#57511yescharacteristic
363C22×C11#57611yescharacteristic
364C22×C11#57811yescharacteristic
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C4×C11—22no—
373C4×C11—42no—
374C4×C11—41no—
375C4×C11—42no—
376C4×C11—81no—
377C4×C11#52911yescharacteristic
378C4×C11#53811yescharacteristic
379C4×C11#55511yescharacteristic
380C4×C11#55911yescharacteristic
381Dic11—22no—
382Dic11—42no—
383Dic11—41no—
384Dic11—41no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—111no—
389C22×Q8—221no—
390C22×D4—221no—
391C22×D4C22×D1111yescharacteristic
392C23×C4—21no—
393C23×C4—111no—
394C23×C4—221no—
395C2×SD16—222no—
396C2×SD16—441no—
397C2×SD16—441no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C4⋊Q8—222no—
403C4⋊Q8—441no—
404C22⋊Q8—222no—
405C22⋊Q8—441no—
406#121—222no—
407#121—222no—
408C4×D4—22no—
409C4×D4—41no—
410C4×D4—444no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—441no—
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—111no—
425C2×C22⋊C4—111no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C42—21no—
432C2×C42—111no—
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435#106—222no—
436C4⋊C8—441no—
437#103—222no—
438#103—222no—
439#103—441no—
440#102—22no—
441#102—22no—
442#102—441no—
443C22⋊C8—441no—
444C22⋊C8—441no—
445C4×C8—41no—
446#95—21no—
447#95—111no—
448#95—111no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11—82no—
457C2×C11#245911yescharacteristic
458C2×C11#310111yescharacteristic
459C2×C11#312411yescharacteristic
460C2×C11#329511yescharacteristic
461C2×C11#329811yescharacteristic
462C2×C11#331311yescharacteristic
463C2×C11#332211yescharacteristic
464D11—42no—
465C24—21no—
466C24—111no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—442no—
474C2×Q8—442no—
475C2×Q8—881no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—224no—
482C2×D4—442no—
483C2×D4—442no—
484C2×D4#433912yes—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—81no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4—881no—
507C22×C4D4×D1111yescharacteristic
508C22×C4D4×D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510SD16—444no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—112no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4#433912yes—
538C4⋊C4#433912yes—
539C22⋊C4—42no—
540C22⋊C4—114no—
541C22⋊C4—224no—
542C22⋊C4—441no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—881no—
546C22⋊C4—881no—
547C42—21no—
548C42—21no—
549C42—81no—
550C42—221no—
551C42—221no—
552C42—442no—
553C11#2672211yescharacteristic, complemented, Sylow
554C23—22no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—112no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23C2×D4×D1111yescharacteristic
569Q8—441no—
570Q8—441no—
571Q8—441no—
572Q8—441no—
573Q8—884no—
574D4—22no—
575D4—22no—
576D4—41no—
577D4—41no—
578D4—448no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—84no—
594C2×C4—112no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—222no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
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×C4SD16×D1112yes—
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×#433911yescharacteristic
623C2×C4C2×#433911yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#6704211yescharacteristic
627C8—41no—
628C8—41no—
629C8—441no—
630C8—441no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—222no—
639C22—222no—
640C22—222no—
641C22—441no—
642C22—441no—
643C22—441no—
644C22—441no—
645C22#1062302111yescharacteristic
646C22#1062307811yescharacteristic
647C22#1062308111yescharacteristic
648C22#1062328811yescharacteristic
649C22C2×SD16×D1111yescharacteristic
650C22#1062329911yescharacteristic
651C22#1062330211yescharacteristic
652C4—22no—
653C4—41no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—222no—
658C4—442no—
659C4—441no—
660C4—441no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062301011yescharacteristic
665C4#1062306311yescharacteristic
666C4#1062309011yescharacteristic
667C4#1062309111yescharacteristic
668C2—82no—
669C2—442no—
670C2#1307255311yescharacteristic
671C2#1307862211yescharacteristic
672C2#1307887411yescharacteristic
673C2#1308043611yescharacteristic
674C2#1308048311yescharacteristic
675C2#1308067811yescharacteristic
676C2#1308082211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenterC4×#102D11
hypocenterC11#26722
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #13072984C2semidirect
3. #13069932C2semidirect
5. #13069750C2semidirect
7. #13069562C2semidirect
8. #13069292C2semidirect
9. #13069248C2semidirect
10. #13069222C2semidirect
11. #13069194C2semidirect
12. #13068950C2semidirect
13. #13068922C2semidirect
14. #13068701C2semidirect
15. C4×C11×#102C2semidirect
196. (C2×D11)⋊C4SD16semidirect
230. C4×#102D11semidirect
553. C11#26722semidirect

Maximal subgroups

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

subgroupindex
#130729842
#130716282
#130699322
#130698032
#130697502
#130696202
#130695622
#130692922
#130692482
#130692222
#130691942
#130689502
#130689222
#130687012
C4×C11×#1022
#2672211