Finite Group Databasebeta

← #14826559

Subgroups — #14826559

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#13073038C211yesmaximal, characteristic, complemented
2#13070019C211yesmaximal, characteristic, complemented
3#13069990C211yesmaximal, characteristic, complemented
4#13069802C211yesmaximal, characteristic
5#13069802C211yesmaximal, characteristic
6#13069379C211yesmaximal, characteristic, complemented
7#13069341C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic, complemented
9#13069208C211yesmaximal, characteristic, complemented
10#13069198C211yesmaximal, characteristic, complemented
11#13068863C211yesmaximal, characteristic, complemented
12#13068815C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2363C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66932—21no—
20C11×#390—21no—
21C11×#390C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#388—21no—
24C11×#386—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C22⋊C4—21no—
27C4×C11×C22⋊C4C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622825C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622566—21no—
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622272—21no—
48#10622266—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C11×#121—22no—
64C11×#121—22no—
65C4×D4×C11—22no—
66C4×D4×C11—41no—
67C11×#117—22no—
68C11×#117—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66932—44no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104#66896—22no—
105#66896—22no—
106#66896—22no—
107#66896—41no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C22⋊(C11⋊C8)—22no—
114C22⋊(C11⋊C8)—41no—
115#66872—22no—
116#66872—22no—
117#66872—41no—
118#66871—22no—
119C4⋊(C11⋊C8)—22no—
120C4×C11⋊C8—41no—
121#27039—111nomaximal, Sylow
122C24×C11—21no—
123C24×C11C2×D411yescharacteristic
124C2×D4×C11—24no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—81no—
131C2×D4×C11—81no—
132C2×D4×C11#4112yes—
133C22×C4×C11—21no—
134C22×C4×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—42no—
143C22×C4×C11—42no—
144C22×C4×C11—81no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—81no—
160C11×C4⋊C4#4112yes—
161C11×C4⋊C4#4112yes—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—42no—
168C11×C22⋊C4—81no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—42no—
174C42×C11—81no—
175C22⋊Dic11—42no—
176C22⋊Dic11—42no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—42no—
186C4⋊Dic11—42no—
187Dic11⋊C4—42no—
188Dic11⋊C4—42no—
189C4×Dic11—42no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
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#2496—111no—
203#2363D1111yescharacteristic
204#2071—111no—
205#2065—111no—
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—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11C22×D411yescharacteristic
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—84no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
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—84no—
264C2×C4×C11#13512yes—
265C2×C4×C11AGL(1,ℤ/8)12yes—
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C112−1+411yescharacteristic
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C11⋊C8—22no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C2×#126—221no—
289C2×#121C2×D1111yescharacteristic
290C2×C4×D4C2×D1111yescharacteristic
291C2×#117C2×D1111yescharacteristic
292C2×#107—111no—
293C2×#106—111no—
294C2×#106—111no—
295C2×#106—111no—
296C2×C4⋊C8—111no—
297C2×#102—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#102—111no—
301C2×C22⋊C8—111no—
302C2×C22⋊C8—111no—
303C2×C4×C8—111no—
304#400—221no—
305#397—221no—
306#390—21no—
307#390C2×D1111yescharacteristic
308#389—111no—
309#389—111no—
310#389C2×D1111yescharacteristic
311#388—21no—
312#387—221no—
313#386—21no—
314#384—111no—
315#380—111no—
316#380—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4C2×D1111yescharacteristic
319C4×C22⋊C4—21no—
320C4×C22⋊C4C2×D1111yescharacteristic
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#336—111no—
330#336—111no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—42no—
335C22×C11—41no—
336C22×C11—42no—
337C22×C11—41no—
338C22×C11—42no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11#52511yescharacteristic
346C22×C11#54611yescharacteristic
347C22×C11#54711yescharacteristic
348C22×C11C2×#13511yescharacteristic
349C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C11#57711yescharacteristic
351C22×C11#57711yescharacteristic
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—81no—
360C4×C11#52911yescharacteristic
361C4×C11#53911yescharacteristic
362C4×C11#55311yescharacteristic
363C4×C11#55611yescharacteristic
364Dic11—81no—
365Dic11—81no—
366Dic11—81no—
367Dic11—81no—
368C22×D4—21no—
369C22×D4C22×D1111yescharacteristic
370C23×C4—21no—
371C23×C4C22×D1111yescharacteristic
372C22×C8—111no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8—111no—
376#126—444no—
377#121—22no—
378#121—22no—
379C4×D4—22no—
380C4×D4—41no—
381#117—22no—
382#117—41no—
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—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4C22⋊D1111yescharacteristic
403C2×C22⋊C4C22⋊D1111yescharacteristic
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—221no—
407C2×C42C22×D1111yescharacteristic
408C2×C42C22×D1111yescharacteristic
409#107—222no—
410#106—222no—
411#106—222no—
412#106—441no—
413C4⋊C8—222no—
414#102—222no—
415#102—222no—
416#102—222no—
417#102—441no—
418C22⋊C8—222no—
419C22⋊C8—441no—
420C4×C8—441no—
421#95—21no—
422#95—21no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95C22⋊D1111yescharacteristic
429#95C22⋊D1111yescharacteristic
430C2×C11—81no—
431C2×C11—82no—
432C2×C11#246611yescharacteristic
433C2×C11#310611yescharacteristic
434C2×C11#312311yescharacteristic
435C2×C11#330411yescharacteristic
436C2×C11#330611yescharacteristic
437C2×C11#333711yescharacteristic
438C2×C11#335411yescharacteristic
439C24—21no—
440C24C2×C22⋊D1111yescharacteristic
441C2×D4—24no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4#433912yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—81no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C23×D1111yescharacteristic
472C2×C8—112no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—81no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4#433912yes—
502C4⋊C4#434112yes—
503C22⋊C4—24no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—81no—
510C22⋊C4—442no—
511C22⋊C4—442no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—42no—
517C42—81no—
518C42—442no—
519C11#2703911yescharacteristic, complemented, Sylow
520C23—22no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C22×C22⋊D1111yescharacteristic
535D4—22no—
536D4—22no—
537D4—41no—
538D4—41no—
539D4—84no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—84no—
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#6700212yes—
580C2×C4#6700312yes—
581C2×C4C2×#433911yescharacteristic
582C2×C4C2×#433911yescharacteristic
583C2×C4C2×#434111yescharacteristic
584C2×C4#6703711yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#6704311yescharacteristic
587C8—222no—
588C8—441no—
589C8—441no—
590C8—441no—
591C22—41no—
592C22—41no—
593C22—42no—
594C22—41no—
595C22—42no—
596C22—41no—
597C22—41no—
598C22—42no—
599C22—41no—
600C22—41no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22#1062332211yescharacteristic
606C22#1062333711yescharacteristic
607C22C2×#6700211yescharacteristic
608C22C2×#6700311yescharacteristic
609C22#1062335511yescharacteristic
610C22#1062336711yescharacteristic
611C22#1062336711yescharacteristic
612C4—22no—
613C4—22no—
614C4—42no—
615C4—41no—
616C4—42no—
617C4—41no—
618C4—41no—
619C4—81no—
620C4—881no—
621C4—881no—
622C4—881no—
623C4—881no—
624C4#1062306911yescharacteristic
625C4#1062307311yescharacteristic
626C4#1062308911yescharacteristic
627C4#1062309511yescharacteristic
628C2—81no—
629C2—82no—
630C2#1307264611yescharacteristic
631C2#1307867611yescharacteristic
632C2#1307886811yescharacteristic
633C2#1308055511yescharacteristic
634C2#1308057711yescharacteristic
635C2#1308098911yescharacteristic
636C2#1308120511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2363C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2363D11
hypocenterC11#27039
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. #13073038C2semidirect
2. #13070019C2semidirect
3. #13069990C2semidirect
6. #13069379C2semidirect
7. #13069341C2semidirect
8. #13069224C2semidirect
9. #13069208C2semidirect
10. #13069198C2semidirect
11. #13068863C2semidirect
12. #13068815C2semidirect
13. #13068711C2semidirect
14. C4×#66896C2semidirect
519. C11#27039semidirect

Maximal subgroups

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

subgroupindex
#130730382
#130700192
#130699902
#130698022
#130693792
#130693412
#130692242
#130692082
#130691982
#130688632
#130688152
#130687112
C4×#668962
C11×#23632
#2703911