Finite Group Databasebeta

← #14826446

Subgroups — #14826446

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#13073030C211yesmaximal, characteristic, complemented
2#13071637C211yesmaximal, characteristic
3#13069990C211yesmaximal, characteristic, complemented
4#13069803C211yesmaximal, characteristic
5#13069796C211yesmaximal, characteristic
6#13069382C211yesmaximal, characteristic, complemented
7#13069343C211yesmaximal, characteristic, complemented
8#13069223C211yesmaximal, characteristic, complemented
9#13069195C211yesmaximal, characteristic, complemented
10#13069185C211yesmaximal, characteristic, complemented
11#13068879C211yesmaximal, characteristic, complemented
12#13068810C211yesmaximal, characteristic, complemented
13#13068705C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#2073C211yesmaximal, characteristic, complemented
16C2×#66991C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×(C22⋊D11)⋊C4—21no—
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#382C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622600C2211yescharacteristic
31#10622600C2211yescharacteristic
32#10622598C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34#10622586C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38#10622569—21no—
39#10622559—21no—
40#10622557—21no—
41C4×(C2×D11)⋊C4C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622287—21no—
46#10622282—21no—
47#10622273—21no—
48#10622264—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
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)⋊C4D411yescharacteristic
81C2×(C2×D11)⋊C4D411yescharacteristic
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C4⋊C4×D11—22no—
96C4⋊C4×D11—41no—
97(C22⋊D11)⋊C4—44no—
98C11×#102—22no—
99C11×#102—22no—
100C11×#95—21no—
101C11×#95—21no—
102#66896—22no—
103#66896—41no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113(C2×D11)⋊C8—22no—
114(C2×D11)⋊C8—41no—
115#66881—22no—
116C8×Dic11—41no—
117#66872—22no—
118#66872—41no—
119#66871—22no—
120C4⋊(C11⋊C8)—22no—
121#27031—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—42no—
138C2×C22⋊D11—42no—
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×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—21no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—81no—
172C42×C11—21no—
173C42×C11—21no—
174C22⋊Dic11—24no—
175C22⋊Dic11—42no—
176(C2×D11)⋊C4—22no—
177(C2×D11)⋊C4—22no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—81no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—81no—
187C4⋊Dic11#4112yes—
188C4⋊Dic11#4112yes—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—81no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—42no—
195C4×Dic11—42no—
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#2495—111no—
203#2361—111no—
204#2073D1111yescharacteristic, complemented
205#2065—111no—
206#2034—111no—
207#2033—111no—
208#1949—111no—
209#1941—111no—
210#1923—111no—
211#1919—111no—
212#1918—111no—
213#1864—111no—
214#1853—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—21no—
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—41no—
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—48no—
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—
284C4×D11—84no—
285C8×C11—41no—
286C8×C11—41no—
287C11⋊C8—22no—
288C11⋊C8—41no—
289C2×#121—111no—
290C2×C4×D4—111no—
291C2×C4×D4—221no—
292C22×C4⋊C4—111no—
293C2×#107—111no—
294C2×#106—111no—
295C2×#106—111no—
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#400—221no—
306#397—221no—
307#390C2×D1111yescharacteristic
308#389—111no—
309#389—111no—
310#389—111no—
311#388—221no—
312#388—221no—
313#386—221no—
314#385—221no—
315#383—221no—
316#382C2×D1111yescharacteristic
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#340C2×D1111yescharacteristic
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#57711yescharacteristic
345C22×C11#57711yescharacteristic
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11#52911yescharacteristic
359C4×C11#53911yescharacteristic
360C4×C11#55311yescharacteristic
361C4×C11#55611yescharacteristic
362Dic11—22no—
363Dic11—42no—
364Dic11—41no—
365Dic11—41no—
366Dic11—42no—
367Dic11—81no—
368Dic11—81no—
369C22×D4—221no—
370C22×D4C22×D1111yescharacteristic
371C23×C4—111no—
372C23×C4—221no—
373C23×C4—221no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#121—222no—
379#121—222no—
380C4×D4—222no—
381C4×D4—441no—
382C4×D4—444no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—221no—
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—21no—
398C2×C22⋊C4—111no—
399C2×C22⋊C4—111no—
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—222no—
409#106—222no—
410#106—222no—
411#106—441no—
412C4⋊C8—222no—
413#102—22no—
414#102—22no—
415#102—222no—
416#102—441no—
417C22⋊C8—222no—
418C22⋊C8—441no—
419C4×C8—441no—
420#95—21no—
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—
430#95—221no—
431C2×C11—82no—
432C2×C11#246611yescharacteristic
433C2×C11#310511yescharacteristic
434C2×C11#312511yescharacteristic
435C2×C11#330111yescharacteristic
436C2×C11#331011yescharacteristic
437C2×C11#333711yescharacteristic
438C2×C11#335411yescharacteristic
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#434112yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
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—221no—
467C22×C4—442no—
468C22×C4—442no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4—881no—
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—21no—
494C4⋊C4—112no—
495C4⋊C4—112no—
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—881no—
506C22⋊C4—42no—
507C22⋊C4—81no—
508C22⋊C4—222no—
509C22⋊C4—222no—
510C22⋊C4—224no—
511C22⋊C4—442no—
512C22⋊C4—442no—
513C22⋊C4—881no—
514C42—21no—
515C42—21no—
516C42—221no—
517C42—221no—
518C42—442no—
519C42—442no—
520C11#2703111yescharacteristic, 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—21no—
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—41no—
556C2×C4—112no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—222no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—222no—
566C2×C4—221no—
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—884no—
583C2×C4C2×#434111yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#41×D1111yescharacteristic
587C2×C4#6704211yescharacteristic
588C2×C4#6704311yescharacteristic
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#1062313711yescharacteristic
608C22#1062318611yescharacteristic
609C22#1062320711yescharacteristic
610C22D11×#13511yescharacteristic
611C22#1062330111yescharacteristic
612C22D11×AGL(1,ℤ/8)11yescharacteristic
613C22#1062330611yescharacteristic
614C4—41no—
615C4—41no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—222no—
620C4—441no—
621C4—442no—
622C4—442no—
623C4—441no—
624C4—881no—
625C4—881no—
626C4#1062318011yescharacteristic
627C4#1062319611yescharacteristic
628C4#1062323311yescharacteristic
629C4#1062324011yescharacteristic
630C2—82no—
631C2—442no—
632C2#1307265311yescharacteristic
633C2#1307866211yescharacteristic
634C2#1307889011yescharacteristic
635C2#1308051711yescharacteristic
636C2#1308063611yescharacteristic
637C2#1308098811yescharacteristic
638C2#1308120911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2073C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#2073D11
hypocenterC11#27031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2073

Complements

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

NH ≅ G/Ntype
1. #13073030C2semidirect
3. #13069990C2semidirect
6. #13069382C2semidirect
7. #13069343C2semidirect
8. #13069223C2semidirect
9. #13069195C2semidirect
10. #13069185C2semidirect
11. #13068879C2semidirect
12. #13068810C2semidirect
13. #13068705C2semidirect
14. #102×Dic11C2semidirect
15. C11×#2073C2semidirect
204. #2073D11semidirect
520. C11#27031semidirect

Maximal subgroups

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

subgroupindex
#130730302
#130716372
#130699902
#130698032
#130697962
#130693822
#130693432
#130692232
#130691952
#130691852
#130688792
#130688102
#130687052
#102×Dic112
C11×#20732
#2703111