Finite Group Databasebeta

← #14826568

Subgroups — #14826568

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073036C211yesmaximal, characteristic, complemented
2#13071659C211yesmaximal, characteristic
3#13070019C211yesmaximal, characteristic, complemented
4#13069804C211yesmaximal, characteristic
5#13069804C211yesmaximal, characteristic
6#13069380C211yesmaximal, characteristic, complemented
7#13069342C211yesmaximal, characteristic, complemented
8#13069221C211yesmaximal, characteristic, complemented
9#13069205C211yesmaximal, characteristic, complemented
10#13069200C211yesmaximal, characteristic, complemented
11#13068861C211yesmaximal, characteristic, complemented
12#13068814C211yesmaximal, characteristic, complemented
13#13068709C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#2065C211yesmaximal, characteristic, complemented
16C2×#66991C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×#66951—21no—
19C2×#66945C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622599—21no—
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622571—21no—
41#10622570—21no—
42#10622558—21no—
43C22⋊C4×Dic11—21no—
44C4×(C2×D11)⋊C4C2211yescharacteristic
45#10622548C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47#10622287—21no—
48#10622267—21no—
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74#66991—22no—
75#66991—22no—
76D4×Dic11—22no—
77D4×Dic11—41no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4D411yescharacteristic
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66951—44no—
98#66945—22no—
99#66945—41no—
100C11×#106—41no—
101C11×C4⋊C8—22no—
102C11×#102—22no—
103C11×#102—41no—
104C11×#95—21no—
105#66896—22no—
106#66896—22no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—41no—
117#66881—22no—
118#66881—22no—
119C8×Dic11—41no—
120#66871—22no—
121#27039—111nomaximal, Sylow
122C24×C11—21no—
123C23×D11C2×D411yescharacteristic
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11#4112yes—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—24no—
137C2×C22⋊D11—81no—
138C2×C22⋊D11—81no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11—81no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11#4112yes—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—42no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—81no—
170C42×C11—21no—
171C42×C11—21no—
172C22⋊Dic11—24no—
173C22⋊Dic11—42no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—22no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—42no—
186C4⋊Dic11—42no—
187C4⋊Dic11#4112yes—
188C4⋊Dic11#4112yes—
189Dic11⋊C4—42no—
190Dic11⋊C4—81no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C4×Dic11—81no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202#2496—111no—
203#2363—111no—
204#2071—111no—
205#2065D1111yescharacteristic, complemented
206#2034—111no—
207#2034—111no—
208#1948—111no—
209#1941—111no—
210#1923—111no—
211#1921—111no—
212#1920—111no—
213#1862—111no—
214#1854—111no—
215#1825—111no—
216C4×#102—111no—
217C23×C11—22no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11C22×D411yescharacteristic
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—41no—
235D4×C11—41no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11#13512yes—
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C22⋊D11—84no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—22no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—22no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—84no—
279C2×Dic11AGL(1,ℤ/8)12yes—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—41no—
283C4×D11—41no—
284C8×C11—22no—
285C8×C11—41no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C2×#126—221no—
289C2×#121—111no—
290C2×C4×D4—111no—
291C2×#117—111no—
292C2×#107—111no—
293C2×#106—111no—
294C2×#106—111no—
295C2×#106C2×D1111yescharacteristic
296C2×C4⋊C8C2×D1111yescharacteristic
297C2×#102—111no—
298C2×#102—111no—
299C2×#102C2×D1111yescharacteristic
300C2×#102C2×D1111yescharacteristic
301C2×C22⋊C8—111no—
302C2×C22⋊C8—111no—
303C2×C4×C8—111no—
304#400—221no—
305#397—221no—
306#390—221no—
307#390C2×D1111yescharacteristic
308#389—111no—
309#389—111no—
310#389C2×D1111yescharacteristic
311#388—221no—
312#387—221no—
313#386—221no—
314#384—111no—
315#380—111no—
316#380—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4—111no—
319C4×C22⋊C4—111no—
320C4×C22⋊C4—221no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340C2×D1111yescharacteristic
329#336—111no—
330#336—111no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11#52511yescharacteristic
339C22×C11#54611yescharacteristic
340C22×C11#54711yescharacteristic
341C22×C11C2×#13511yescharacteristic
342C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C11#57711yescharacteristic
344C22×C11#57711yescharacteristic
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11#52911yescharacteristic
358C4×C11#53911yescharacteristic
359C4×C11#55311yescharacteristic
360C4×C11#55611yescharacteristic
361Dic11—22no—
362Dic11—42no—
363Dic11—41no—
364Dic11—41no—
365Dic11—42no—
366Dic11—81no—
367Dic11—81no—
368C22×D4—221no—
369C22×D4C22×D1111yescharacteristic
370C23×C4—111no—
371C23×C4—221no—
372C22×C8—111no—
373C22×C8—111no—
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376#126—444no—
377#121—222no—
378#121—222no—
379C4×D4—222no—
380C4×D4—441no—
381#117—222no—
382#117—441no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—111no—
398C2×C22⋊C4—111no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C42—111no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42C22×D1111yescharacteristic
409#107—222no—
410#106—41no—
411#106—222no—
412#106—222no—
413C4⋊C8—22no—
414#102—22no—
415#102—41no—
416#102—222no—
417#102—222no—
418C22⋊C8—222no—
419C22⋊C8—441no—
420C4×C8—441no—
421#95—21no—
422#95—111no—
423#95—111no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430C2×C11—82no—
431C2×C11#246611yescharacteristic
432C2×C11#310611yescharacteristic
433C2×C11#312311yescharacteristic
434C2×C11#330411yescharacteristic
435C2×C11#330611yescharacteristic
436C2×C11#333711yescharacteristic
437C2×C11#335411yescharacteristic
438D11—81no—
439C24—21no—
440C24—111no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—224no—
447C2×D4—881no—
448C2×D4—881no—
449C2×D4#434312yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—442no—
467C22×C4—442no—
468C22×C4—881no—
469C22×C4D4×D1111yescharacteristic
470C22×C4D4×D1111yescharacteristic
471C22×C4C23×D1111yescharacteristic
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8#434112yes—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—42no—
491C4⋊C4—112no—
492C4⋊C4—112no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—881no—
503C22⋊C4—42no—
504C22⋊C4—81no—
505C22⋊C4—222no—
506C22⋊C4—224no—
507C22⋊C4—222no—
508C22⋊C4—442no—
509C22⋊C4—442no—
510C22⋊C4—442no—
511C22⋊C4—442no—
512C42—21no—
513C42—21no—
514C42—221no—
515C42—221no—
516C42—442no—
517C42—442no—
518C42—881no—
519C11#2703911yescharacteristic, complemented, Sylow
520C23—22no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—221no—
528C23—221no—
529C23—221no—
530C23—221no—
531C23—221no—
532C23—221no—
533C23—221no—
534C23C2×D4×D1111yescharacteristic
535D4—22no—
536D4—22no—
537D4—41no—
538D4—41no—
539D4—884no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—112no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—222no—
563C2×C4—221no—
564C2×C4—222no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—884no—
580C2×C4#6696912yes—
581C2×C4C2×#434111yescharacteristic
582C2×C4#6703711yescharacteristic
583C2×C4C2×#434311yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#6704311yescharacteristic
587C8—22no—
588C8—41no—
589C8—441no—
590C8—441no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—441no—
599C22—441no—
600C22—441no—
601C22—441no—
602C22—441no—
603C22—441no—
604C22—441no—
605C22#1062314211yescharacteristic
606C22#1062314311yescharacteristic
607C22#1062315811yescharacteristic
608C22C2×#6696911yescharacteristic
609C22#1062330111yescharacteristic
610C22D11×AGL(1,ℤ/8)11yescharacteristic
611C22#1062330611yescharacteristic
612C4—22no—
613C4—41no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4—222no—
618C4—442no—
619C4—441no—
620C4—442no—
621C4—441no—
622C4—881no—
623C4—881no—
624C4#1062313211yescharacteristic
625C4#1062315511yescharacteristic
626C4#1062317611yescharacteristic
627C4#1062323311yescharacteristic
628C2—82no—
629C2—881no—
630C2#1307265511yescharacteristic
631C2#1307867811yescharacteristic
632C2#1307887011yescharacteristic
633C2#1308055811yescharacteristic
634C2#1308058411yescharacteristic
635C2#1308100111yescharacteristic
636C2#1308120611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2065C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#2065D11
hypocenterC11#27039
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. #13073036C2semidirect
3. #13070019C2semidirect
6. #13069380C2semidirect
7. #13069342C2semidirect
8. #13069221C2semidirect
9. #13069205C2semidirect
10. #13069200C2semidirect
11. #13068861C2semidirect
12. #13068814C2semidirect
13. #13068709C2semidirect
14. #102×Dic11C2semidirect
15. C11×#2065C2semidirect
205. #2065D11semidirect
519. C11#27039semidirect

Maximal subgroups

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

subgroupindex
#130730362
#130716592
#130700192
#130698042
#130693802
#130693422
#130692212
#130692052
#130692002
#130688612
#130688142
#130687092
#102×Dic112
C11×#20652
#2703911