Finite Group Databasebeta

← #14826439

Subgroups — #14826439

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#13073027C211yesmaximal, characteristic, complemented
2#13070029C211yesmaximal, characteristic, complemented
3#13069990C211yesmaximal, characteristic, complemented
4#13069802C211yesmaximal, characteristic
5#13069795C211yesmaximal, characteristic
6#13069384C211yesmaximal, characteristic, complemented
7#13069341C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic, complemented
9#13069194C211yesmaximal, characteristic, complemented
10#13069184C211yesmaximal, characteristic, complemented
11#13068877C211yesmaximal, characteristic, complemented
12#13068809C211yesmaximal, characteristic, complemented
13#13068706C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2361C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C11×#390C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#388—21no—
23C11×#386—21no—
24C11×#385—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31#10622825C2211yescharacteristic
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622565—21no—
40#10622557—21no—
41#10622549C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622271—21no—
48#10622264—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×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C11×#121—22no—
65C11×#121—22no—
66C4×D4×C11—22no—
67C4×D4×C11—41no—
68C4×D4×C11—44no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C11×#95—21no—
99C11×#95—21no—
100C11×#95D411yescharacteristic
101C11×#95D411yescharacteristic
102#66896—22no—
103#66896—22no—
104#66896—22no—
105#66896—41no—
106C11⋊#95—21no—
107C11⋊#95—21no—
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#27031—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—42no—
131C2×D4×C11—42no—
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—42no—
145C22×C4×C11—42no—
146C22×C4×C11—81no—
147C22×C4×C11—81no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4#4112yes—
165C11×C4⋊C4#4112yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—81no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—42no—
177C22⋊Dic11—42no—
178C22⋊Dic11—81no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187Dic11⋊C4—81no—
188Dic11⋊C4—81no—
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#2495—111no—
203#2361D1111yescharacteristic
204#2073—111no—
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—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—22no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11#13512yes—
231C23×C11C22×D411yescharacteristic
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—48no—
235D4×C11—41no—
236D4×C11—41no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
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—21no—
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—84no—
265C2×C4×C11—84no—
266C2×C4×C11AGL(1,ℤ/8)12yes—
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C112−1+411yescharacteristic
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—
284C2×Dic11—41no—
285C11⋊C8—22no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C11⋊C8—41no—
289C2×#121C2×D1111yescharacteristic
290C2×C4×D4—21no—
291C2×C4×D4C2×D1111yescharacteristic
292C22×C4⋊C4C2×D1111yescharacteristic
293C2×#107—111no—
294C2×#106—111no—
295C2×#106—111no—
296C2×#106—111no—
297C2×C4⋊C8—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#102—111no—
301C2×#102—111no—
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#389C2×D1111yescharacteristic
311#388—21no—
312#388—221no—
313#386—21no—
314#385—21no—
315#383—221no—
316#382—111no—
317#380—111no—
318#380—111no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4C2×D1111yescharacteristic
321C4×C22⋊C4C2×D1111yescharacteristic
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#336—111no—
331#336—111no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11#52511yescharacteristic
347C22×C11#54611yescharacteristic
348C22×C11#54711yescharacteristic
349C22×C11C2×#13511yescharacteristic
350C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C11#57711yescharacteristic
352C22×C11#57711yescharacteristic
353C4×C11—22no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—42no—
360C4×C11—81no—
361C4×C11#52911yescharacteristic
362C4×C11#53911yescharacteristic
363C4×C11#55311yescharacteristic
364C4×C11#55611yescharacteristic
365Dic11—81no—
366Dic11—81no—
367Dic11—81no—
368Dic11—81no—
369C22×D4—21no—
370C22×D4C22×D1111yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4C22×D1111yescharacteristic
374C22×C8—111no—
375C22×C8—111no—
376C22×C8—111no—
377C22×C8—111no—
378#121—22no—
379#121—22no—
380C4×D4—22no—
381C4×D4—41no—
382C4×D4—44no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—41no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
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—221no—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408#107—222no—
409#106—222no—
410#106—222no—
411#106—441no—
412C4⋊C8—222no—
413#102—222no—
414#102—222no—
415#102—222no—
416#102—441no—
417C22⋊C8—222no—
418C22⋊C8—441no—
419C4×C8—441no—
420#95—21no—
421#95—21no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95C22⋊D1111yescharacteristic
430#95C22⋊D1111yescharacteristic
431C2×C11—42no—
432C2×C11—82no—
433C2×C11#246611yescharacteristic
434C2×C11#310511yescharacteristic
435C2×C11#312511yescharacteristic
436C2×C11#330111yescharacteristic
437C2×C11#331011yescharacteristic
438C2×C11#333711yescharacteristic
439C2×C11#335411yescharacteristic
440C24—21no—
441C24C2×C22⋊D1111yescharacteristic
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4#433912yes—
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—21no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—81no—
465C22×C4—81no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476C2×C8—112no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
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—42no—
493C4⋊C4—42no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—881no—
503C4⋊C4—881no—
504C4⋊C4#433912yes—
505C4⋊C4#434112yes—
506C22⋊C4—24no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—81no—
512C22⋊C4—442no—
513C22⋊C4—881no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—42no—
519C42—442no—
520C11#2703111yescharacteristic, complemented, Sylow
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—22no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23#6700312yes—
535C23C22×C22⋊D1111yescharacteristic
536D4—22no—
537D4—22no—
538D4—48no—
539D4—41no—
540D4—41no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
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—41no—
567C2×C4—41no—
568C2×C4—84no—
569C2×C4—84no—
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—441no—
582C2×C4#6698512yes—
583C2×C4C2×#433911yescharacteristic
584C2×C4C2×#433911yescharacteristic
585C2×C4C2×#434111yescharacteristic
586C2×C4#6703711yescharacteristic
587C2×C4#41×D1111yescharacteristic
588C2×C4#6704311yescharacteristic
589C8—222no—
590C8—441no—
591C8—441no—
592C8—441no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#1062332211yescharacteristic
608C22C2×#6698511yescharacteristic
609C22#1062333711yescharacteristic
610C22C2×#6700311yescharacteristic
611C22#1062335511yescharacteristic
612C22#1062336711yescharacteristic
613C22#1062336811yescharacteristic
614C4—22no—
615C4—41no—
616C4—42no—
617C4—41no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—881no—
623C4—881no—
624C4—881no—
625C4—881no—
626C4#1062306911yescharacteristic
627C4#1062307311yescharacteristic
628C4#1062308911yescharacteristic
629C4#1062309511yescharacteristic
630C2—42no—
631C2—82no—
632C2#1307264611yescharacteristic
633C2#1307866311yescharacteristic
634C2#1307889311yescharacteristic
635C2#1308051811yescharacteristic
636C2#1308063711yescharacteristic
637C2#1308098911yescharacteristic
638C2#1308121111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2361C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2361D11
hypocenterC11#27031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
1. #13073027C2semidirect
2. #13070029C2semidirect
3. #13069990C2semidirect
6. #13069384C2semidirect
7. #13069341C2semidirect
8. #13069224C2semidirect
9. #13069194C2semidirect
10. #13069184C2semidirect
11. #13068877C2semidirect
12. #13068809C2semidirect
13. #13068706C2semidirect
14. C4×#66896C2semidirect
520. C11#27031semidirect

Maximal subgroups

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

subgroupindex
#130730272
#130700292
#130699902
#130698022
#130697952
#130693842
#130693412
#130692242
#130691942
#130691842
#130688772
#130688092
#130687062
C4×#668962
C11×#23612
#2703111