Finite Group Databasebeta

← #14821833

Subgroups — #14821833

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#13072992C211yesmaximal, characteristic, complemented
2#13071632C211yesmaximal, characteristic
3#13069930C211yesmaximal, characteristic, complemented
4#13069806C211yesmaximal, characteristic
5#13069751C211yesmaximal, characteristic, complemented
6#13069617C211yesmaximal, characteristic
7#13069562C211yesmaximal, characteristic, complemented
8#13069289C211yesmaximal, characteristic, complemented
9#13069252C211yesmaximal, characteristic, complemented
10#13069225C211yesmaximal, characteristic, complemented
11#13069193C211yesmaximal, characteristic, complemented
12#13068947C211yesmaximal, characteristic, complemented
13#13068702C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1872C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21C2×#66946C2211yescharacteristic
22C2×#66941C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622843C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622826—21no—
30#10622825C2211yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622603—21no—
39#10622602—21no—
40#10622601C2211yescharacteristic
41#10622595—21no—
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44#10622587—21no—
45#10622586C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47#10622560—21no—
48#10622558—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—41no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11D411yescharacteristic
80C2×C22⋊Dic11D411yescharacteristic
81C2×#4325—22no—
82C2×#4325—41no—
83C2×#4325—41no—
84#66983—22no—
85#66983—22no—
86C4×C22⋊D11—44no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66946—22no—
103#66946—41no—
104#66941—22no—
105#66941—41no—
106C11×#103—22no—
107C11×#103—41no—
108C11×C22⋊C8—41no—
109#66899—22no—
110C11⋊#95—21no—
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
120C22⋊(C11⋊C8)—41no—
121#66885—22no—
122#66885—41no—
123#66881—22no—
124Dic11⋊C8—41no—
125C8×Dic11—41no—
126#66873—22no—
127#26722—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—42no—
153C2×C22⋊D11—42no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44#4112yes—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
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—42no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4#4112yes—
186C11×C4⋊C4#4112yes—
187C11×C22⋊C4—42no—
188C22⋊Dic11—41no—
189C22⋊Dic11—81no—
190C22⋊Dic11SD1614yescomplemented
191#4325—44no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C4×Dic11—81no—
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#1872D1111yescharacteristic, complemented
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—
246Q8×C11—41no—
247Q8×C11—41no—
248Q8×C11—41no—
249Q8×C11—41no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
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×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—84no—
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C22⋊D11—48no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—22no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11C2×SD1612yes—
297C2×Dic11C2×SD1612yes—
298D44—22no—
299D44—22no—
300D44—41no—
301D44—41no—
302C4×D11—84no—
303Dic22—84no—
304C8×C11—41no—
305C8×C11—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C22×SD16—111no—
309C2×C4⋊Q8—111no—
310C2×C22⋊Q8C2×D1111yescharacteristic
311C2×#121—111no—
312C2×C4×D4—111no—
313C2×C4×D4—221no—
314C22×C4⋊C4C2×D1111yescharacteristic
315C2×#106—111no—
316C2×C4⋊C8—111no—
317C2×#103—111no—
318C2×#103C2×D1111yescharacteristic
319C2×#103C2×D1111yescharacteristic
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×C22⋊C8—111no—
324C2×C22⋊C8C2×D1111yescharacteristic
325C2×C4×C8—111no—
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⋊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—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—41no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11#52911yescharacteristic
378C4×C11#53811yescharacteristic
379C4×C11#55511yescharacteristic
380C4×C11#55911yescharacteristic
381Dic11—22no—
382Dic11—22no—
383Dic11—42no—
384Dic11—41no—
385Dic11—41no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—221no—
389C22×Q8C22×D1111yescharacteristic
390C22×D4—111no—
391C22×D4—221no—
392C23×C4—21no—
393C23×C4—221no—
394C23×C4C22×D1111yescharacteristic
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—22no—
405C22⋊Q8—41no—
406#121—222no—
407#121—222no—
408C4×D4—222no—
409C4×D4—441no—
410C4×D4—444no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
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—111no—
432C2×C42—111no—
433C2×C42—221no—
434C2×C42—221no—
435#106—222no—
436C4⋊C8—441no—
437#103—22no—
438#103—41no—
439#103—222no—
440#102—222no—
441#102—222no—
442#102—441no—
443C22⋊C8—41no—
444C22⋊C8—441no—
445C4×C8—441no—
446#95—111no—
447#95—111no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
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—
466C24D4×D1111yescharacteristic
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
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—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—81no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—881no—
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—42no—
528C4⋊C4—42no—
529C4⋊C4—112no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4#433912yes—
538C4⋊C4#434112yes—
539C22⋊C4—42no—
540C22⋊C4—114no—
541C22⋊C4—224no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—441no—
545C22⋊C4—881no—
546C22⋊C4—881no—
547C42—221no—
548C42—221no—
549C42—221no—
550C42—221no—
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—
567C23SD16×D1112yes—
568C23C2×D4×D1111yescharacteristic
569Q8—41no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—884no—
574D4—222no—
575D4—222no—
576D4—448no—
577D4—441no—
578D4—441no—
579C2×C4—22no—
580C2×C4—21no—
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—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—84no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—222no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—884no—
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×#434111yescharacteristic
623C2×C4#6703711yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C8—41no—
628C8—41no—
629C8—441no—
630C8—441no—
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#1062302111yescharacteristic
646C22#1062312211yescharacteristic
647C22#1062318711yescharacteristic
648C22C2×SD16×D1111yescharacteristic
649C22#1062329711yescharacteristic
650C22#1062330511yescharacteristic
651C22#1062330811yescharacteristic
652C4—42no—
653C4—41no—
654C4—42no—
655C4—81no—
656C4—81no—
657C4—222no—
658C4—222no—
659C4—442no—
660C4—441no—
661C4—441no—
662C4—881no—
663C4—881no—
664C4#1062308811yescharacteristic
665C4#1062309011yescharacteristic
666C4#1062314411yescharacteristic
667C4#1062314711yescharacteristic
668C2—42no—
669C2—882no—
670C2#1307255211yescharacteristic
671C2#1307862111yescharacteristic
672C2#1307888111yescharacteristic
673C2#1308043311yescharacteristic
674C2#1308047711yescharacteristic
675C2#1308067511yescharacteristic
676C2#1308081811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1872D11
hypocenterC11#26722
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
1. #13072992C2semidirect
3. #13069930C2semidirect
5. #13069751C2semidirect
7. #13069562C2semidirect
8. #13069289C2semidirect
9. #13069252C2semidirect
10. #13069225C2semidirect
11. #13069193C2semidirect
12. #13068947C2semidirect
13. #13068702C2semidirect
14. #13068430C2semidirect
15. C11×#1872C2semidirect
190. C22⋊Dic11SD16semidirect
228. #1872D11semidirect
553. C11#26722semidirect

Maximal subgroups

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

subgroupindex
#130729922
#130716322
#130699302
#130698062
#130697512
#130696172
#130695622
#130692892
#130692522
#130692252
#130691932
#130689472
#130687022
#130684302
C11×#18722
#2672211