Finite Group Databasebeta

← #14826444

Subgroups — #14826444

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#13073023C211yesmaximal, characteristic, complemented
2#13071632C211yesmaximal, characteristic
3#13070033C211yesmaximal, characteristic, complemented
4#13069991C211yesmaximal, characteristic, complemented
5#13069805C211yesmaximal, characteristic
6#13069799C211yesmaximal, characteristic
7#13069387C211yesmaximal, characteristic, complemented
8#13069343C211yesmaximal, characteristic, complemented
9#13069219C211yesmaximal, characteristic, complemented
10#13069192C211yesmaximal, characteristic, complemented
11#13069186C211yesmaximal, characteristic, complemented
12#13068878C211yesmaximal, characteristic, complemented
13#13068809C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1824C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×C4×C22⋊D11—21no—
19C2×#66946C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C11×#380C2211yescharacteristic
22#10622826—21no—
23#10622825C2211yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622603—21no—
32#10622602—21no—
33#10622601C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622590C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45#10622566—21no—
46#10622558—21no—
47#10622273—21no—
48#10622264—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11D411yescharacteristic
76C2×C22⋊Dic11D411yescharacteristic
77#66983—22no—
78#66983—22no—
79C4×C22⋊D11—44no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96#66946—22no—
97#66946—41no—
98C11×C22⋊C8—41no—
99C11×#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110C22⋊(C11⋊C8)—22no—
111#66885—22no—
112#66885—41no—
113#66882—22no—
114Dic11⋊C8—22no—
115C8×Dic11—41no—
116#66873—22no—
117#66873—22no—
118#66872—22no—
119#66872—22no—
120#66872—41no—
121#27031—111nomaximal, Sylow
122C24×C11C2×D411yescharacteristic
123C23×D11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—81no—
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×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44#4112yes—
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×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4#4112yes—
173C11×C22⋊C4—81no—
174C22⋊Dic11—22no—
175C22⋊Dic11—22no—
176C22⋊Dic11—42no—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—42no—
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—81no—
187C4⋊Dic11#4112yes—
188Dic11⋊C4—42no—
189Dic11⋊C4—81no—
190C4×Dic11—21no—
191C4×Dic11—21no—
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#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#1824D1111yescharacteristic, complemented
216C4×#102—111no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11#13512yes—
224C23×C11C22×D411yescharacteristic
225C22×D11—22no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
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—41no—
251C2×C4×C11—84no—
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—21no—
260C2×Dic11—21no—
261C2×Dic11—22no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
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×Dic11AGL(1,ℤ/8)12yes—
280D44—22no—
281D44—22no—
282D44—41no—
283D44—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⋊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⋊C8C2×D1111yescharacteristic
304C2×C4×C8—111no—
305#400—221no—
306#397—221no—
307#390—111no—
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#382—111no—
317#380—111no—
318#380C2×D1111yescharacteristic
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#340C2×D1111yescharacteristic
327#340C2×D1111yescharacteristic
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
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#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—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—81no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11#52911yescharacteristic
359C4×C11#53911yescharacteristic
360C4×C11#55311yescharacteristic
361C4×C11#55611yescharacteristic
362Dic11—22no—
363Dic11—41no—
364Dic11—41no—
365Dic11—42no—
366Dic11—41no—
367Dic11—81no—
368Dic11—81no—
369C22×D4—111no—
370C22×D4—221no—
371C23×C4—21no—
372C23×C4—221no—
373C23×C4C22×D1111yescharacteristic
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—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
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×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—111no—
406C2×C42—221no—
407C2×C42—221no—
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—41no—
418C22⋊C8—222no—
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—42no—
432C2×C11#246611yescharacteristic
433C2×C11#310511yescharacteristic
434C2×C11#312511yescharacteristic
435C2×C11#330111yescharacteristic
436C2×C11#331011yescharacteristic
437C2×C11#333711yescharacteristic
438C2×C11#335411yescharacteristic
439D11—82no—
440C24—221no—
441C24D4×D1111yescharacteristic
442C2×D4—112no—
443C2×D4—224no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—442no—
450C2×D4—442no—
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—21no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—81no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—442no—
472C22×C4—442no—
473C22×C4—881no—
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—21no—
495C4⋊C4—42no—
496C4⋊C4—112no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—442no—
503C4⋊C4—881no—
504C4⋊C4—881no—
505C4⋊C4#433912yes—
506C22⋊C4—81no—
507C22⋊C4—224no—
508C22⋊C4—222no—
509C22⋊C4—222no—
510C22⋊C4—442no—
511C22⋊C4—442no—
512C22⋊C4—442no—
513C22⋊C4—881no—
514C42—221no—
515C42—221no—
516C42—221no—
517C42—221no—
518C42—442no—
519C42—442no—
520C11#2703111yescharacteristic, complemented, Sylow
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—222no—
528C23—441no—
529C23—441no—
530C23—441no—
531C23—441no—
532C23—441no—
533C23—441no—
534C23#6697212yes—
535C23C2×D4×D1111yescharacteristic
536D4—222no—
537D4—222no—
538D4—448no—
539D4—441no—
540D4—441no—
541C2×C4—22no—
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—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—84no—
561C2×C4—112no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—222no—
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—884no—
583C2×C4C2×#433911yescharacteristic
584C2×C4#6703711yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#41×D1111yescharacteristic
587C2×C4#41×D1111yescharacteristic
588C2×C4#6704311yescharacteristic
589C8—41no—
590C8—41no—
591C8—222no—
592C8—441no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—442no—
601C22—442no—
602C22—442no—
603C22—881no—
604C22—881no—
605C22—881no—
606C22—881no—
607C22#1062302111yescharacteristic
608C22#1062318611yescharacteristic
609C22#1062318711yescharacteristic
610C22#1062329311yescharacteristic
611C22C2×#6697211yescharacteristic
612C22D11×AGL(1,ℤ/8)11yescharacteristic
613C22#1062330611yescharacteristic
614C4—41no—
615C4—42no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—222no—
620C4—441no—
621C4—442no—
622C4—441no—
623C4—441no—
624C4—881no—
625C4—881no—
626C4#1062305911yescharacteristic
627C4#1062306411yescharacteristic
628C4#1062319111yescharacteristic
629C4#1062319211yescharacteristic
630C2—42no—
631C2—882no—
632C2#1307265111yescharacteristic
633C2#1307866611yescharacteristic
634C2#1307889611yescharacteristic
635C2#1308051411yescharacteristic
636C2#1308063811yescharacteristic
637C2#1308099311yescharacteristic
638C2#1308120411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1824C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1824D11
hypocenterC11#27031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
1. #13073023C2semidirect
3. #13070033C2semidirect
4. #13069991C2semidirect
7. #13069387C2semidirect
8. #13069343C2semidirect
9. #13069219C2semidirect
10. #13069192C2semidirect
11. #13069186C2semidirect
12. #13068878C2semidirect
13. #13068809C2semidirect
14. #13068430C2semidirect
15. C11×#1824C2semidirect
215. #1824D11semidirect
520. C11#27031semidirect

Maximal subgroups

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

subgroupindex
#130730232
#130716322
#130700332
#130699912
#130698052
#130697992
#130693872
#130693432
#130692192
#130691922
#130691862
#130688782
#130688092
#130684302
C11×#18242
#2703111