Finite Group Databasebeta

← #14821832

Subgroups — #14821832

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#13072990C211yesmaximal, characteristic, complemented
2#13071630C211yesmaximal, characteristic
3#13069934C211yesmaximal, characteristic, complemented
4#13069806C211yesmaximal, characteristic
5#13069753C211yesmaximal, characteristic, complemented
6#13069621C211yesmaximal, characteristic
7#13069563C211yesmaximal, characteristic, complemented
8#13069292C211yesmaximal, characteristic, complemented
9#13069251C211yesmaximal, characteristic, complemented
10#13069195C211yesmaximal, characteristic, complemented
11#13068949C211yesmaximal, characteristic, complemented
12#13068921C211yesmaximal, characteristic, complemented
13#13068703C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1923C211yesmaximal, characteristic, complemented
16C2×#66983C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C2×#66977C2211yescharacteristic
19C22×#4314C2211yescharacteristic
20C2×(C22⋊D11)⋊C4—21no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28#10622825C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36#10622571—21no—
37#10622564—21no—
38#10622560—21no—
39#10622552C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622542C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622283—21no—
46#10622281—21no—
47#10622273—21no—
48#10622259—21no—
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×Dic22—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76#66983—22no—
77#66983—22no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—41no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92#66977—22no—
93#66977—41no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×#4314—22no—
99C2×#4314—41no—
100C2×#4314—41no—
101(C22⋊D11)⋊C4—44no—
102C4×D44—22no—
103C4×D44—41no—
104#66922—22no—
105#66922—41no—
106C11×C4⋊C8—41no—
107C11×C22⋊C8—41no—
108C11×C22⋊C8—41no—
109C4×C8×C11—41no—
110C11×#95D411yescharacteristic
111C11×#95D411yescharacteristic
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66885—22no—
121#66885—22no—
122#66885—41no—
123#66881—22no—
124#66880—22no—
125#66880—22no—
126#66880—41no—
127#26722—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—24no—
143C2×C22⋊D11—42no—
144C2×C22⋊D11—42no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—81no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44#4112yes—
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—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4SD1614yescomplemented
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C22⋊Dic11—42no—
192C22⋊Dic11—81no—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—81no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207C4⋊Dic11—42no—
208C4⋊Dic11#4112yes—
209C4⋊Dic11#4112yes—
210C4⋊Dic11#4112yes—
211Dic11⋊C4—42no—
212Dic11⋊C4—42no—
213C4×Dic11—42no—
214C4×Dic11—81no—
215#4314—44no—
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#1923D1111yescharacteristic, complemented
226#1919—111no—
227#1877—111no—
228#1872—111no—
229#1823—111no—
230C4×#102—111no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11C2×SD1612yes—
238C23×C11C22×D411yescharacteristic
239C22×D11—22no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
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—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11C2×SD1612yes—
264C2×C4×C11C2×SD1612yes—
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C22⋊D11—48no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
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×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×Dic11—84no—
294D44—22no—
295D44—22no—
296D44—41no—
297D44—41no—
298C4×D11—84no—
299Dic22—41no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303Dic22—84no—
304C8×C11—41no—
305C8×C11—41no—
306C8×C11—41no—
307C8×C11—41no—
308C22×SD16—111no—
309C2×C4⋊Q8—111no—
310C2×C22⋊Q8—111no—
311C2×#121—111no—
312C2×C4×D4—111no—
313C2×C4×D4—221no—
314C22×C4⋊C4—111no—
315C2×#106—111no—
316C2×C4⋊C8C2×D1111yescharacteristic
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×C22⋊C8C2×D1111yescharacteristic
324C2×C22⋊C8C2×D1111yescharacteristic
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⋊C4—111no—
340C4×C22⋊C4C2×D1111yescharacteristic
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#336C2×D1111yescharacteristic
350#336C2×D1111yescharacteristic
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11#52511yescharacteristic
359C22×C11#54611yescharacteristic
360C22×C11#54611yescharacteristic
361C22×C11C22×SD1611yescharacteristic
362C22×C11#57511yescharacteristic
363C22×C11#57611yescharacteristic
364C22×C11#57811yescharacteristic
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11#52911yescharacteristic
378C4×C11#53811yescharacteristic
379C4×C11#55511yescharacteristic
380C4×C11#55911yescharacteristic
381Dic11—42no—
382Dic11—42no—
383Dic11—42no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—111no—
389C22×Q8—221no—
390C22×D4—111no—
391C22×D4—221no—
392C23×C4—221no—
393C23×C4—221no—
394C23×C4C22×D1111yescharacteristic
395C2×SD16—222no—
396C2×SD16—441no—
397C2×SD16—441no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
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—222no—
409C4×D4—441no—
410C4×D4—444no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—441no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4D4411yescharacteristic
430C2×C22⋊C4D4411yescharacteristic
431C2×C42—221no—
432C2×C42—221no—
433C2×C42C22×D1111yescharacteristic
434C2×C42C22×D1111yescharacteristic
435#106—222no—
436C4⋊C8—41no—
437#103—222no—
438#103—222no—
439#103—441no—
440#102—222no—
441#102—222no—
442#102—441no—
443C22⋊C8—41no—
444C22⋊C8—41no—
445C4×C8—41no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95D4411yescharacteristic
455#95D4411yescharacteristic
456C2×C11—42no—
457C2×C11#245911yescharacteristic
458C2×C11#310111yescharacteristic
459C2×C11#312411yescharacteristic
460C2×C11#329511yescharacteristic
461C2×C11#329811yescharacteristic
462C2×C11#331311yescharacteristic
463C2×C11#332211yescharacteristic
464D11—82no—
465C24—221no—
466C24C2×D4411yescharacteristic
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—112no—
477C2×D4—224no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—442no—
484C2×D4—442no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—881no—
503C22×C4—881no—
504C22×C4C2×D4411yescharacteristic
505C22×C4C2×D4411yescharacteristic
506C22×C4C2×D4411yescharacteristic
507C22×C4C2×D4411yescharacteristic
508C22×C4C2×D4411yescharacteristic
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—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C4⋊C4—112no—
524C4⋊C4—112no—
525C4⋊C4—112no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C22⋊C4—41no—
540C22⋊C4—224no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—881no—
545C22⋊C4—881no—
546C22⋊C4#431414yescomplemented
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—442no—
552C42—881no—
553C11#2672211yescharacteristic, complemented, Sylow
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—222no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23C2×#431412yes—
568C23C22×D4411yescharacteristic
569Q8—441no—
570Q8—441no—
571Q8—441no—
572Q8—441no—
573Q8—884no—
574D4—222no—
575D4—222no—
576D4—448no—
577D4—441no—
578D4—441no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
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—884no—
618C2×C4—884no—
619C2×C4C2×#431412yes—
620C2×C4C2×#431412yes—
621C2×C4#6703711yescharacteristic
622C2×C4#6703711yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C2×C4#41×D1111yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C8—41no—
628C8—41no—
629C8—41no—
630C8—41no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—442no—
639C22—442no—
640C22—442no—
641C22—881no—
642C22—881no—
643C22—881no—
644C22—881no—
645C22#1062305511yescharacteristic
646C22#1062308511yescharacteristic
647C22#1062308511yescharacteristic
648C22C22×#431411yescharacteristic
649C22#1062327911yescharacteristic
650C22#1062328311yescharacteristic
651C22#1062328411yescharacteristic
652C4—22no—
653C4—22no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—442no—
658C4—442no—
659C4—442no—
660C4—881no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062314411yescharacteristic
665C4#1062319511yescharacteristic
666C4#1062320111yescharacteristic
667C4#1062323711yescharacteristic
668C2—42no—
669C2—882no—
670C2#1307255111yescharacteristic
671C2#1307862511yescharacteristic
672C2#1307888011yescharacteristic
673C2#1308044111yescharacteristic
674C2#1308048211yescharacteristic
675C2#1308068411yescharacteristic
676C2#1308081911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1923C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1923D11
hypocenterC11#26722
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. #13072990C2semidirect
3. #13069934C2semidirect
5. #13069753C2semidirect
7. #13069563C2semidirect
8. #13069292C2semidirect
9. #13069251C2semidirect
10. #13069195C2semidirect
11. #13068949C2semidirect
12. #13068921C2semidirect
13. #13068703C2semidirect
14. C4×#66885C2semidirect
15. C11×#1923C2semidirect
186. C11×C22⋊C4SD16semidirect
225. #1923D11semidirect
546. C22⋊C4#4314semidirect
553. C11#26722semidirect

Maximal subgroups

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

subgroupindex
#130729902
#130716302
#130699342
#130698062
#130697532
#130696212
#130695632
#130692922
#130692512
#130691952
#130689492
#130689212
#130687032
C4×#668852
C11×#19232
#2672211