Finite Group Databasebeta

← #14821859

Subgroups — #14821859

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072981C211yesmaximal, characteristic
2#13071625C211yesmaximal, characteristic, complemented
3#13069929C211yesmaximal, characteristic, complemented
4#13069809C211yesmaximal, characteristic, complemented
5#13069755C211yesmaximal, characteristic, complemented
6#13069566C211yesmaximal, characteristic, complemented
7#13069301C211yesmaximal, characteristic, complemented
8#13069246C211yesmaximal, characteristic, complemented
9#13069219C211yesmaximal, characteristic, complemented
10#13069204C211yesmaximal, characteristic, complemented
11#13068973C211yesmaximal, characteristic, complemented
12#13068934C211yesmaximal, characteristic
13#13068707C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#2000C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×#66989—21no—
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66941C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622835—21no—
30#10622834C2211yescharacteristic
31#10622834C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622825C2211yescharacteristic
35C4×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622598—21no—
40#10622598C2211yescharacteristic
41#10622594—21no—
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45#10622563—21no—
46#10622560—21no—
47#10622558—21no—
48C22⋊C4×Dic11—21no—
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×Dic22—21no—
65C2×C11×SD16—22no—
66C2×C11×SD16—41no—
67C2×C11×SD16—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×#121—22no—
73C11×#121—41no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11D411yescharacteristic
85C2×C22⋊Dic11D411yescharacteristic
86Q8×Dic11—22no—
87Q8×Dic11—41no—
88#66989—44no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—41no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66941—22no—
107#66941—41no—
108C11×#103—22no—
109C11×#102—22no—
110C11×C22⋊C8—41no—
111#66899—22no—
112#66899—41no—
113#66896—22no—
114#66896—41no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123C22⋊(C11⋊C8)—41no—
124Dic11⋊C8—41no—
125C8×Dic11—41no—
126#66872—22no—
127#26724—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11#4112yes—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—42no—
143C2×D4×C11—42no—
144C2×D4×C11—81no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—81no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C2×Dic22—42no—
168C2×Dic22—42no—
169C2×Dic22—81no—
170C11×SD16—44no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4#4112yes—
181C11×C4⋊C4#4112yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—42no—
184C22⋊Dic11—41no—
185C22⋊Dic11—42no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188C22⋊Dic11—42no—
189C22⋊Dic11—81no—
190C22⋊Dic11SD1614yescomplemented
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200C4⋊Dic11—81no—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—42no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
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#2491—111no—
217#2360—111no—
218#2055—111no—
219#2035—111no—
220#2024—111no—
221#2000D1111yescharacteristic
222#1988—111no—
223#1934—111no—
224#1926—111no—
225#1923—111no—
226#1920—111no—
227#1880—111no—
228#1874—111no—
229#1824—111no—
230C4×#103—111no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11C2×SD1612yes—
245C23×C11C22×D411yescharacteristic
246Q8×C11—22no—
247Q8×C11—22no—
248Q8×C11—41no—
249Q8×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11—84no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
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—41no—
270C2×C4×C11—41no—
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—22no—
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×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—84no—
300C2×Dic11C2×SD1612yes—
301C2×Dic11C2×SD1612yes—
302Dic22—84no—
303C8×C11—41no—
304C8×C11—41no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C22×SD16C2×D1111yescharacteristic
308C2×C4⋊Q8—111no—
309C2×#124—221no—
310C2×C22⋊Q8C2×D1111yescharacteristic
311C2×#121C2×D1111yescharacteristic
312C2×C4×Q8—111no—
313C22×C4⋊C4—111no—
314C2×#106—111no—
315C2×C4⋊C8—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103C2×D1111yescharacteristic
319C2×#102—111no—
320C2×#102—111no—
321C2×#102C2×D1111yescharacteristic
322C2×C22⋊C8—111no—
323C2×C22⋊C8C2×D1111yescharacteristic
324C2×C4×C8—111no—
325#394—221no—
326#393—221no—
327#391—111no—
328#390—111no—
329#390—111no—
330#389—111no—
331#389—221no—
332#388—221no—
333#387—221no—
334#385—221no—
335#380—111no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4—111no—
338C4×C22⋊C4—111no—
339C4×C22⋊C4—221no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340C2×D1111yescharacteristic
348#336—111no—
349#336—111no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11#52511yescharacteristic
365C22×C11#54611yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11C22×SD1611yescharacteristic
368C22×C11#57511yescharacteristic
369C22×C11#57611yescharacteristic
370C22×C11#57811yescharacteristic
371C4×C11—42no—
372C4×C11—41no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11#52911yescharacteristic
376C4×C11#53811yescharacteristic
377C4×C11#55511yescharacteristic
378C4×C11#55911yescharacteristic
379Dic11—22no—
380Dic11—22no—
381Dic11—41no—
382Dic11—42no—
383Dic11—41no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387C22×Q8—221no—
388C22×Q8C22×D1111yescharacteristic
389C22×D4—21no—
390C22×D4C22×D1111yescharacteristic
391C23×C4—221no—
392C23×C4C22×D1111yescharacteristic
393C2×SD16—22no—
394C2×SD16—41no—
395C2×SD16—41no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C4⋊Q8—222no—
401C4⋊Q8—441no—
402#124—444no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405#121—22no—
406#121—41no—
407C4×Q8—222no—
408C4×Q8—441no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—111no—
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×C22⋊C4—21no—
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—
435C2×C42—221no—
436#106—222no—
437C4⋊C8—441no—
438#103—22no—
439#103—222no—
440#103—441no—
441#102—22no—
442#102—222no—
443#102—441no—
444C22⋊C8—41no—
445C22⋊C8—441no—
446C4×C8—441no—
447#95—111no—
448#95—111no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455C2×C11—42no—
456C2×C11—161no—
457C2×C11#245911yescharacteristic
458C2×C11#310311yescharacteristic
459C2×C11#312411yescharacteristic
460C2×C11#329511yescharacteristic
461C2×C11#329811yescharacteristic
462C2×C11#331911yescharacteristic
463C2×C11#332711yescharacteristic
464C24—21no—
465C24D4×D1111yescharacteristic
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—442no—
472C2×Q8—442no—
473C2×Q8—881no—
474C2×Q8#434112yes—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—81no—
484C22×C4—21no—
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—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—881no—
504C22×C4D4×D1111yescharacteristic
505C22×C4C23×D1111yescharacteristic
506SD16—44no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C4⋊C4—24no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—112no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—881no—
534C4⋊C4#434112yes—
535C4⋊C4#434112yes—
536C22⋊C4—24no—
537C22⋊C4—42no—
538C22⋊C4—114no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—441no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—881no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—221no—
549C42—442no—
550C42—442no—
551C42—881no—
552C11#2672411yescharacteristic, complemented, Sylow
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23SD16×D1112yes—
567C23C2×D4×D1111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—884no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—84no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
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—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—222no—
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—884no—
619C2×C4C2×#434111yescharacteristic
620C2×C4C2×#434111yescharacteristic
621C2×C4C2×#434111yescharacteristic
622C2×C4#6703711yescharacteristic
623C2×C4#6703711yescharacteristic
624C2×C4#41×D1111yescharacteristic
625C8—41no—
626C8—41no—
627C8—441no—
628C8—441no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22#1062311711yescharacteristic
644C22#1062312211yescharacteristic
645C22#1062314111yescharacteristic
646C22C2×SD16×D1111yescharacteristic
647C22#1062330211yescharacteristic
648C22#1062330511yescharacteristic
649C22#1062330811yescharacteristic
650C4—42no—
651C4—42no—
652C4—41no—
653C4—42no—
654C4—222no—
655C4—222no—
656C4—441no—
657C4—441no—
658C4—442no—
659C4—881no—
660C4—881no—
661C4—881no—
662C4#1062312411yescharacteristic
663C4#1062313111yescharacteristic
664C4#1062314711yescharacteristic
665C4#1062324411yescharacteristic
666C2—42no—
667C2—161no—
668C2#1307254811yescharacteristic
669C2#1307864211yescharacteristic
670C2#1307887111yescharacteristic
671C2#1308043311yescharacteristic
672C2#1308047611yescharacteristic
673C2#1308076711yescharacteristic
674C2#1308087711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2000C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2000D11
hypocenterC11#26724
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
2. #13071625C2semidirect
3. #13069929C2semidirect
4. #13069809C2semidirect
5. #13069755C2semidirect
6. #13069566C2semidirect
7. #13069301C2semidirect
8. #13069246C2semidirect
9. #13069219C2semidirect
10. #13069204C2semidirect
11. #13068973C2semidirect
13. #13068707C2semidirect
14. #103×Dic11C2semidirect
190. C22⋊Dic11SD16semidirect
552. C11#26724semidirect

Maximal subgroups

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

subgroupindex
#130729812
#130716252
#130699292
#130698092
#130697552
#130695662
#130693012
#130692462
#130692192
#130692042
#130689732
#130689342
#130687072
#103×Dic112
C11×#20002
#2672411