Finite Group Databasebeta

← #14821968

Subgroups — #14821968

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072992C211yesmaximal, characteristic, complemented
2#13071654C211yesmaximal, characteristic
3#13069930C211yesmaximal, characteristic, complemented
4#13069799C211yesmaximal, characteristic
5#13069751C211yesmaximal, characteristic, complemented
6#13069617C211yesmaximal, characteristic
7#13069566C211yesmaximal, characteristic, complemented
8#13069289C211yesmaximal, characteristic, complemented
9#13069259C211yesmaximal, characteristic, complemented
10#13069225C211yesmaximal, characteristic, complemented
11#13069207C211yesmaximal, characteristic, complemented
12#13068947C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1873C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622843C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622825C2211yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622601C2211yescharacteristic
37#10622595—21no—
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587—21no—
41#10622586C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43#10622570—21no—
44#10622569—21no—
45#10622560—21no—
46#10622558—21no—
47#10622553—21no—
48C4×(C2×D11)⋊C4—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×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×Dic22—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—41no—
69C11×#117—22no—
70C11×#117—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—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—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66946—22no—
102#66946—41no—
103#66941—22no—
104#66941—41no—
105C11×#103—22no—
106C11×#103—41no—
107C11×C22⋊C8—41no—
108#66899—22no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119C22⋊(C11⋊C8)—41no—
120#66885—22no—
121#66885—41no—
122#66882—22no—
123Dic11⋊C8—41no—
124C8×Dic11—41no—
125#66873—22no—
126#26731—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C22×C4×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×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—24no—
148C2×C22⋊D11—81no—
149C2×C22⋊D11—81no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44#4112yes—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×Dic22—42no—
167C2×Dic22—42no—
168C2×Dic22—81no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4#4112yes—
181C11×C4⋊C4#4112yes—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C42×C11—42no—
185C22⋊Dic11—22no—
186C22⋊Dic11—22no—
187C22⋊Dic11—81no—
188#4325—44no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11#4112yes—
199Dic11⋊C4—42no—
200Dic11⋊C4—81no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—81no—
206C4×Dic11—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213#2492—111no—
214#2363—111no—
215#2055—111no—
216#2033—111no—
217#2023—111no—
218#2000—111no—
219#1988—111no—
220#1933—111no—
221#1928—111no—
222#1923—111no—
223#1921—111no—
224#1877—111no—
225#1873D1111yescharacteristic, complemented
226#1825—111no—
227C4×#102—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
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×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—84no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
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#13512yes—
293C2×Dic11#13712yes—
294D44—22no—
295D44—22no—
296D44—41no—
297D44—41no—
298C4×D11—84no—
299Dic22—84no—
300C8×C11—41no—
301C8×C11—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×SD16—111no—
305C2×C4⋊Q8—111no—
306C2×C22⋊Q8C2×D1111yescharacteristic
307C2×#121—111no—
308C2×C4×D4—111no—
309C2×#117C2×D1111yescharacteristic
310C2×#107—111no—
311C2×C4⋊C8—111no—
312C2×#103—111no—
313C2×#103C2×D1111yescharacteristic
314C2×#103C2×D1111yescharacteristic
315C2×#102—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×C22⋊C8—111no—
319C2×C22⋊C8C2×D1111yescharacteristic
320C2×C4×C8—111no—
321#400—221no—
322#393—221no—
323#391—111no—
324#391—111no—
325#391—221no—
326#390—111no—
327#390—221no—
328#389—111no—
329#388—221no—
330#388—221no—
331#386—221no—
332#380—111no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4—111no—
335C4×C22⋊C4—111no—
336C4×C22⋊C4—221no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345#336—111no—
346#336—111no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11#52511yescharacteristic
355C22×C11#54611yescharacteristic
356C22×C11#54611yescharacteristic
357C22×C11C2×#13511yescharacteristic
358C22×C11C2×#13711yescharacteristic
359C22×C11#57611yescharacteristic
360C22×C11#57711yescharacteristic
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—42no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C4×C11—41no—
369C4×C11—42no—
370C4×C11—42no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11#52911yescharacteristic
374C4×C11#53811yescharacteristic
375C4×C11#55511yescharacteristic
376C4×C11#55911yescharacteristic
377Dic11—22no—
378Dic11—22no—
379Dic11—41no—
380Dic11—42no—
381Dic11—41no—
382Dic11—81no—
383Dic11—81no—
384C22×Q8—221no—
385C22×Q8C22×D1111yescharacteristic
386C22×D4—111no—
387C22×D4—221no—
388C23×C4—221no—
389C23×C4C22×D1111yescharacteristic
390C2×SD16—222no—
391C2×SD16—441no—
392C2×SD16—441no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C4⋊Q8—222no—
398C4⋊Q8—441no—
399C22⋊Q8—22no—
400C22⋊Q8—41no—
401#121—222no—
402#121—222no—
403C4×D4—222no—
404C4×D4—441no—
405#117—22no—
406#117—41no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—111no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C42—21no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—221no—
429C2×C42—221no—
430#107—222no—
431C4⋊C8—441no—
432#103—22no—
433#103—41no—
434#103—222no—
435#102—222no—
436#102—222no—
437#102—441no—
438C22⋊C8—41no—
439C22⋊C8—441no—
440C4×C8—441no—
441#95—111no—
442#95—111no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11—81no—
452C2×C11#245911yescharacteristic
453C2×C11#310711yescharacteristic
454C2×C11#311811yescharacteristic
455C2×C11#329711yescharacteristic
456C2×C11#330411yescharacteristic
457C2×C11#331411yescharacteristic
458C2×C11#332911yescharacteristic
459D11—82no—
460C24—221no—
461C24D4×D1111yescharacteristic
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—442no—
469C2×Q8—442no—
470C2×Q8—881no—
471C2×D4—112no—
472C2×D4—224no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—881no—
479C2×D4—881no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—881no—
500C22×C4D4×D1111yescharacteristic
501C22×C4C23×D1111yescharacteristic
502SD16—444no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—112no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—442no—
527C4⋊C4—881no—
528C4⋊C4#433912yes—
529C4⋊C4#434112yes—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—224no—
533C22⋊C4—222no—
534C22⋊C4—222no—
535C22⋊C4—442no—
536C22⋊C4—442no—
537C22⋊C4—881no—
538C22⋊C4—881no—
539C42—42no—
540C42—221no—
541C42—221no—
542C42—221no—
543C42—221no—
544C42—881no—
545C42—881no—
546C11#2673111yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—222no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23C2×D4×D1111yescharacteristic
562Q8—41no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566Q8—884no—
567D4—222no—
568D4—222no—
569D4—441no—
570D4—441no—
571D4—884no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—222no—
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—884no—
613C2×C4C2×#433911yescharacteristic
614C2×C4C2×#434111yescharacteristic
615C2×C4#6703711yescharacteristic
616C2×C4#6703711yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C2×C4#41×D1111yescharacteristic
619C8—41no—
620C8—41no—
621C8—441no—
622C8—441no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—442no—
631C22—442no—
632C22—442no—
633C22—881no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22#1062302111yescharacteristic
638C22#1062312211yescharacteristic
639C22#1062318711yescharacteristic
640C22D11×#13511yescharacteristic
641C22#1062330011yescharacteristic
642C22D11×#13711yescharacteristic
643C22#1062330911yescharacteristic
644C4—42no—
645C4—42no—
646C4—41no—
647C4—81no—
648C4—81no—
649C4—222no—
650C4—222no—
651C4—442no—
652C4—441no—
653C4—441no—
654C4—881no—
655C4—881no—
656C4#1062308811yescharacteristic
657C4#1062309011yescharacteristic
658C4#1062314411yescharacteristic
659C4#1062314711yescharacteristic
660C2—81no—
661C2—882no—
662C2#1307255211yescharacteristic
663C2#1307868211yescharacteristic
664C2#1307880311yescharacteristic
665C2#1308046711yescharacteristic
666C2#1308054811yescharacteristic
667C2#1308069011yescharacteristic
668C2#1308090611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1873D11
hypocenterC11#26731
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
1. #13072992C2semidirect
3. #13069930C2semidirect
5. #13069751C2semidirect
7. #13069566C2semidirect
8. #13069289C2semidirect
9. #13069259C2semidirect
10. #13069225C2semidirect
11. #13069207C2semidirect
12. #13068947C2semidirect
13. #13068711C2semidirect
14. #13068430C2semidirect
15. C11×#1873C2semidirect
225. #1873D11semidirect
546. C11#26731semidirect

Maximal subgroups

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

subgroupindex
#130729922
#130716542
#130699302
#130697992
#130697512
#130696172
#130695662
#130692892
#130692592
#130692252
#130692072
#130689472
#130687112
#130684302
C11×#18732
#2673111