Finite Group Databasebeta

← #14826477

Subgroups — #14826477

Order 2816.

784 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073017C211yesmaximal, characteristic, complemented
2#13071628C211yesmaximal, characteristic
3#13070032C211yesmaximal, characteristic, complemented
4#13070000C211yesmaximal, characteristic, complemented
5#13069804C211yesmaximal, characteristic
6#13069796C211yesmaximal, characteristic
7#13069383C211yesmaximal, characteristic, complemented
8#13069346C211yesmaximal, characteristic, complemented
9#13069220C211yesmaximal, characteristic, complemented
10#13069210C211yesmaximal, characteristic, complemented
11#13069195C211yesmaximal, characteristic, complemented
12#13068802C211yesmaximal, characteristic, complemented
13#13068705C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#1862C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C2211yescharacteristic
18C2×C4×C22⋊D11—21no—
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#389C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27#10622823—21no—
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32#10622603—21no—
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622594—21no—
37#10622590C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622569—21no—
42#10622558—21no—
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622287—21no—
48C11⋊#401—21no—
49C11×#340C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×C22⋊D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×D4×C11—22no—
67C4×D4×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66991—22no—
78#66991—22no—
79C4×C22⋊D11—44no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×(C2×D11)⋊C4D411yescharacteristic
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×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C4⋊C4×D11—22no—
97C4⋊C4×D11—41no—
98C11×#107—22no—
99C11×#102—22no—
100C11×#102—41no—
101C11×#95—21no—
102#66896—22no—
103#66896—22no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8—41no—
116#66881—22no—
117Dic11⋊C8—22no—
118#66871—22no—
119#66871—41no—
120C4×C11⋊C8—41no—
121#27033—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×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—81no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—24no—
140C2×C22⋊D11—42no—
141C2×C22⋊D11—42no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
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×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—81no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4#4112yes—
171C11×C22⋊C4—42no—
172C42×C11—21no—
173C42×C11—21no—
174C22⋊Dic11—24no—
175C22⋊Dic11—42no—
176C22⋊Dic11—81no—
177(C2×D11)⋊C4—22no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—42no—
180(C2×D11)⋊C4—81no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—81no—
189C4⋊Dic11#4112yes—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192C4×Dic11—21no—
193C4×Dic11—21no—
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#4112yes—
202#2494—111no—
203#2361—111no—
204#2073—111no—
205#2067—111no—
206#2034—111no—
207#2033—111no—
208#1949—111no—
209#1942—111no—
210#1923—111no—
211#1921—111no—
212#1919—111no—
213#1862D1111yescharacteristic, complemented
214#1852—111no—
215#1824—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#13512yes—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—41no—
235D4×C11—41no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
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—84no—
251C2×C4×C11AGL(1,ℤ/8)12yes—
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C22⋊D11—48no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
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—41no—
279C2×Dic11—41no—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—41no—
283C4×D11—41no—
284C4×D11—84no—
285C8×C11—41no—
286C8×C11—41no—
287C11⋊C8—22no—
288C11⋊C8—41no—
289C2×#121—111no—
290C2×C4×D4—221no—
291C2×C4×D4C2×D1111yescharacteristic
292C22×C4⋊C4—111no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#107C2×D1111yescharacteristic
296C2×#106—111no—
297C2×C4⋊C8—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#102C2×D1111yescharacteristic
301C2×#102C2×D1111yescharacteristic
302C2×C22⋊C8—111no—
303C2×C22⋊C8—111no—
304C2×C4×C8—111no—
305#401—221no—
306#397—221no—
307#390—111no—
308#389—111no—
309#389—111no—
310#389C2×D1111yescharacteristic
311#388—221no—
312#388—221no—
313#387—221no—
314#386—221no—
315#385—221no—
316#382—111no—
317#380—111no—
318#380—111no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4—111no—
321C4×C22⋊C4—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340C2×D1111yescharacteristic
330#336—111no—
331#336C2×D1111yescharacteristic
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11#52511yescharacteristic
340C22×C11#54611yescharacteristic
341C22×C11#54711yescharacteristic
342C22×C11C2×#13511yescharacteristic
343C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C11#57611yescharacteristic
345C22×C11#57811yescharacteristic
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C4×C11—22no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11#52911yescharacteristic
359C4×C11#53911yescharacteristic
360C4×C11#55311yescharacteristic
361C4×C11#55611yescharacteristic
362Dic11—41no—
363Dic11—41no—
364Dic11—42no—
365Dic11—41no—
366Dic11—81no—
367Dic11—81no—
368Dic11—81no—
369C22×D4—221no—
370C22×D4C22×D1111yescharacteristic
371C23×C4—21no—
372C23×C4—111no—
373C23×C4—221no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#121—222no—
379#121—222no—
380C4×D4—22no—
381C4×D4—41no—
382C4×D4—444no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—441no—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
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×C42C22×D1111yescharacteristic
408#107—22no—
409#107—222no—
410#107—441no—
411#106—222no—
412C4⋊C8—222no—
413#102—22no—
414#102—41no—
415#102—222no—
416#102—222no—
417C22⋊C8—222no—
418C22⋊C8—441no—
419C4×C8—441no—
420#95—21no—
421#95—111no—
422#95—111no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431C2×C11—82no—
432C2×C11#246611yescharacteristic
433C2×C11#310511yescharacteristic
434C2×C11#312411yescharacteristic
435C2×C11#330011yescharacteristic
436C2×C11#331811yescharacteristic
437C2×C11#333911yescharacteristic
438C2×C11#335311yescharacteristic
439D11—42no—
440C24—21no—
441C24—111no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—224no—
448C2×D4—442no—
449C2×D4—442no—
450C2×D4#433912yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—81no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4—881no—
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—112no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—112no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—881no—
505C4⋊C4#434112yes—
506C22⋊C4—42no—
507C22⋊C4—222no—
508C22⋊C4—224no—
509C22⋊C4—222no—
510C22⋊C4—442no—
511C22⋊C4—442no—
512C22⋊C4—881no—
513C22⋊C4—881no—
514C42—21no—
515C42—21no—
516C42—221no—
517C42—221no—
518C42—442no—
519C42—881no—
520C11#2703311yescharacteristic, complemented, Sylow
521C23—22no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—112no—
529C23—221no—
530C23—221no—
531C23—221no—
532C23—221no—
533C23—221no—
534C23—221no—
535C23C2×D4×D1111yescharacteristic
536D4—22no—
537D4—22no—
538D4—41no—
539D4—41no—
540D4—448no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—84no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—222no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
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—441no—
580C2×C4—441no—
581C2×C4—884no—
582C2×C4#6696412yes—
583C2×C4C2×#433911yescharacteristic
584C2×C4C2×#434111yescharacteristic
585C2×C4#6703711yescharacteristic
586C2×C4#6704011yescharacteristic
587C2×C4#41×D1111yescharacteristic
588C2×C4#41×D1111yescharacteristic
589C8—41no—
590C8—41no—
591C8—222no—
592C8—441no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—222no—
601C22—222no—
602C22—222no—
603C22—441no—
604C22—441no—
605C22—441no—
606C22—441no—
607C22#1062307811yescharacteristic
608C22#1062312211yescharacteristic
609C22#1062316211yescharacteristic
610C22C2×#6696411yescharacteristic
611C22D11×#13511yescharacteristic
612C22#1062330511yescharacteristic
613C22#1062331011yescharacteristic
614C4—22no—
615C4—41no—
616C4—42no—
617C4—81no—
618C4—81no—
619C4—441no—
620C4—441no—
621C4—442no—
622C4—441no—
623C4—881no—
624C4—881no—
625C4—881no—
626C4#1062304611yescharacteristic
627C4#1062306911yescharacteristic
628C4#1062317211yescharacteristic
629C4#1062319211yescharacteristic
630C2—82no—
631C2—442no—
632C2#1307265411yescharacteristic
633C2#1307866111yescharacteristic
634C2#1307888211yescharacteristic
635C2#1308049611yescharacteristic
636C2#1308076111yescharacteristic
637C2#1308101511yescharacteristic
638C2#1308119711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#1862D11
hypocenterC11#27033
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
1. #13073017C2semidirect
3. #13070032C2semidirect
4. #13070000C2semidirect
7. #13069383C2semidirect
8. #13069346C2semidirect
9. #13069220C2semidirect
10. #13069210C2semidirect
11. #13069195C2semidirect
12. #13068802C2semidirect
13. #13068705C2semidirect
14. C4×#66896C2semidirect
15. C11×#1862C2semidirect
213. #1862D11semidirect
520. C11#27033semidirect

Maximal subgroups

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

subgroupindex
#130730172
#130716282
#130700322
#130700002
#130698042
#130697962
#130693832
#130693462
#130692202
#130692102
#130691952
#130688022
#130687052
C4×#668962
C11×#18622
#2703311