Finite Group Databasebeta

← #14826600

Subgroups — #14826600

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073052C211yesmaximal, characteristic, complemented
2#13071656C211yesmaximal, characteristic
3#13070020C211yesmaximal, characteristic, complemented
4#13070003C211yesmaximal, characteristic, complemented
5#13069800C211yesmaximal, characteristic
6#13069800C211yesmaximal, characteristic
7#13069350C211yesmaximal, characteristic, complemented
8#13069221C211yesmaximal, characteristic, complemented
9#13069210C211yesmaximal, characteristic, complemented
10#13069194C211yesmaximal, characteristic, complemented
11#13068878C211yesmaximal, characteristic, complemented
12#13068818C211yesmaximal, characteristic, complemented
13#13068710C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1947C211yesmaximal, characteristic, complemented
16C2×#66948C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C11×#384C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622607—21no—
31#10622603—21no—
32#10622600C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622599—21no—
35#10622598C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622591—21no—
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42#10622552—21no—
43#10622552C2211yescharacteristic
44C4×(C2×D11)⋊C4—21no—
45C4×(C2×D11)⋊C4C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622283—21no—
48#10622278—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44—21no—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4D411yescharacteristic
81C2×(C2×D11)⋊C4D411yescharacteristic
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66948—22no—
94#66948—22no—
95#66946—22no—
96#66946—41no—
97#66945—22no—
98#66945—41no—
99C11×#107—22no—
100C11×#107—22no—
101C11×C4⋊C8—22no—
102C11×#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95D411yescharacteristic
110C11⋊#95D411yescharacteristic
111#66885—22no—
112#66885—41no—
113(C2×D11)⋊C8—22no—
114(C2×D11)⋊C8—41no—
115#66882—41no—
116C8×Dic11—41no—
117#66873—22no—
118#66873—22no—
119#66872—22no—
120#27041—111nomaximal, Sylow
121C23×D11—21no—
122C23×D11C2×D411yescharacteristic
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×D44—24no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—81no—
143C2×D44—81no—
144C2×D44#4112yes—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11—81no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11#4112yes—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4—81no—
168C11×C4⋊C4#4112yes—
169C11×C4⋊C4#4112yes—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—81no—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—22no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—81no—
180(C2×D11)⋊C4—81no—
181(C2×D11)⋊C4—81no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—81no—
189C4⋊Dic11—81no—
190Dic11⋊C4—42no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—42no—
194C4×Dic11—81no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201#2497—111no—
202#2363—111no—
203#2071—111no—
204#2067—111no—
205#2033—111no—
206#2033—111no—
207#1947D1111yescharacteristic, complemented
208#1942—111no—
209#1923—111no—
210#1921—111no—
211#1919—111no—
212#1864—111no—
213#1854—111no—
214#1825—111no—
215C4×#102—111no—
216C23×C11C22×D411yescharacteristic
217C22×D11—22no—
218C22×D11—21no—
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
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#13512yes—
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11#13712yes—
273D44—22no—
274D44—22no—
275D44—41no—
276D44—41no—
277D44—84no—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—84no—
283C8×C11—22no—
284C8×C11—41no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C2×#121—111no—
288C2×C4×D4—111no—
289C2×#117—111no—
290C2×#107—111no—
291C2×#107C2×D1111yescharacteristic
292C2×#107C2×D1111yescharacteristic
293C2×#106—111no—
294C2×C4⋊C8C2×D1111yescharacteristic
295C2×#102—111no—
296C2×#102—111no—
297C2×#102—111no—
298C2×#102—111no—
299C2×C22⋊C8—111no—
300C2×C22⋊C8—111no—
301C2×C4×C8—111no—
302#400—221no—
303#396—221no—
304#390—111no—
305#390—221no—
306#389—111no—
307#389—111no—
308#389—111no—
309#388—221no—
310#388—221no—
311#387—221no—
312#386—221no—
313#384C2×D1111yescharacteristic
314#380—111no—
315#380—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4C2×D1111yescharacteristic
318C4×C22⋊C4—111no—
319C4×C22⋊C4—221no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340C2×D1111yescharacteristic
327#340C2×D1111yescharacteristic
328#336—111no—
329#336—111no—
330C22×C11#52511yescharacteristic
331C22×C11#54611yescharacteristic
332C22×C11#54711yescharacteristic
333C22×C11C2×#13511yescharacteristic
334C22×C11C2×#13711yescharacteristic
335C22×C11#57611yescharacteristic
336C22×C11#57611yescharacteristic
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—42no—
341C2×D11—41no—
342C2×D11—42no—
343C2×D11—41no—
344C2×D11—42no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C4×C11—22no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11#52911yescharacteristic
358C4×C11#53911yescharacteristic
359C4×C11#55311yescharacteristic
360C4×C11#55611yescharacteristic
361Dic11—22no—
362Dic11—41no—
363Dic11—41no—
364Dic11—81no—
365Dic11—81no—
366Dic11—81no—
367C22×D4—111no—
368C22×D4—221no—
369C23×C4—111no—
370C23×C4—221no—
371C22×C8—111no—
372C22×C8—111no—
373C22×C8C22×D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375#121—222no—
376#121—222no—
377C4×D4—222no—
378C4×D4—441no—
379#117—222no—
380#117—441no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C22⋊C4—111no—
394C2×C22⋊C4—111no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C42—21no—
403C2×C42—111no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407#107—22no—
408#107—22no—
409#107—441no—
410#106—222no—
411C4⋊C8—22no—
412#102—222no—
413#102—222no—
414#102—222no—
415#102—441no—
416C22⋊C8—222no—
417C22⋊C8—441no—
418C4×C8—441no—
419#95—21no—
420#95—111no—
421#95—111no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428C2×C11#246611yescharacteristic
429C2×C11#310711yescharacteristic
430C2×C11#312211yescharacteristic
431C2×C11#330511yescharacteristic
432C2×C11#331411yescharacteristic
433C2×C11#333911yescharacteristic
434C2×C11#335711yescharacteristic
435D11—81no—
436D11—82no—
437C24—111no—
438C24—221no—
439C2×D4—112no—
440C2×D4—224no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—881no—
447C2×D4—881no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4—881no—
467C22×C4D4×D1111yescharacteristic
468C22×C4D4×D1111yescharacteristic
469C22×C4C23×D1111yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8#433912yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—81no—
489C4⋊C4—81no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—442no—
497C4⋊C4—881no—
498C4⋊C4—881no—
499C4⋊C4#434112yes—
500C4⋊C4#434312yes—
501C22⋊C4—222no—
502C22⋊C4—224no—
503C22⋊C4—222no—
504C22⋊C4—442no—
505C22⋊C4—442no—
506C22⋊C4—442no—
507C22⋊C4—881no—
508C22⋊C4—881no—
509C22⋊C4—881no—
510C42—21no—
511C42—21no—
512C42—81no—
513C42—221no—
514C42—221no—
515C42—442no—
516C42—881no—
517C11#2704111yescharacteristic, complemented, Sylow
518C23—221no—
519C23—221no—
520C23—221no—
521C23—221no—
522C23—221no—
523C23—222no—
524C23—221no—
525C23—221no—
526C23—441no—
527C23—441no—
528C23—441no—
529C23—441no—
530C23—441no—
531C23—441no—
532C23C2×D4×D1111yescharacteristic
533D4—222no—
534D4—222no—
535D4—441no—
536D4—441no—
537D4—884no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—22no—
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—112no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—441no—
565C2×C4—441no—
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—884no—
578C2×C4#6697212yes—
579C2×C4C2×#433911yescharacteristic
580C2×C4C2×#434111yescharacteristic
581C2×C4C2×#434311yescharacteristic
582C2×C4#6704011yescharacteristic
583C2×C4#41×D1111yescharacteristic
584C2×C4#6704211yescharacteristic
585C8—22no—
586C8—41no—
587C8—441no—
588C8—441no—
589C22—441no—
590C22—442no—
591C22—441no—
592C22—442no—
593C22—441no—
594C22—441no—
595C22—441no—
596C22—442no—
597C22—441no—
598C22—441no—
599C22—881no—
600C22—881no—
601C22—881no—
602C22—881no—
603C22#1062303811yescharacteristic
604C22#1062313711yescharacteristic
605C22#1062316111yescharacteristic
606C22#1062328811yescharacteristic
607C22C2×#6697211yescharacteristic
608C22#1062330511yescharacteristic
609C22D11×#13711yescharacteristic
610C4—22no—
611C4—42no—
612C4—42no—
613C4—41no—
614C4—81no—
615C4—81no—
616C4—222no—
617C4—441no—
618C4—441no—
619C4—881no—
620C4—881no—
621C4—881no—
622C4#1062309611yescharacteristic
623C4#1062311111yescharacteristic
624C4#1062322311yescharacteristic
625C4#1062326311yescharacteristic
626C2—881no—
627C2—882no—
628C2#1307265711yescharacteristic
629C2#1307868611yescharacteristic
630C2#1307885711yescharacteristic
631C2#1308056311yescharacteristic
632C2#1308069411yescharacteristic
633C2#1308101411yescharacteristic
634C2#1308123811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1947D11
hypocenterC11#27041
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
1. #13073052C2semidirect
3. #13070020C2semidirect
4. #13070003C2semidirect
7. #13069350C2semidirect
8. #13069221C2semidirect
9. #13069210C2semidirect
10. #13069194C2semidirect
11. #13068878C2semidirect
12. #13068818C2semidirect
13. #13068710C2semidirect
14. #13068430C2semidirect
15. C11×#1947C2semidirect
207. #1947D11semidirect
517. C11#27041semidirect

Maximal subgroups

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

subgroupindex
#130730522
#130716562
#130700202
#130700032
#130698002
#130693502
#130692212
#130692102
#130691942
#130688782
#130688182
#130687102
#130684302
C11×#19472
#2704111