Finite Group Databasebeta

← #14822306

Subgroups — #14822306

Order 2816.

804 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073156C211yesmaximal, characteristic, complemented
2#13071678C211yesmaximal, characteristic
3#13070031C211yesmaximal, characteristic, complemented
4#13070001C211yesmaximal, characteristic, complemented
5#13069849C211yesmaximal, characteristic
6#13069849C211yesmaximal, characteristic
7#13069296C211yesmaximal, characteristic, complemented
8#13069239C211yesmaximal, characteristic, complemented
9#13069211C211yesmaximal, characteristic, complemented
10#13069196C211yesmaximal, characteristic, complemented
11#13069176C211yesmaximal, characteristic, complemented
12#13068874C211yesmaximal, characteristic, complemented
13#13068626C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66993C2211yescharacteristic
18C2×C4×C22⋊D11—21no—
19C2×#66946C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#389C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27#10622826—21no—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622597—21no—
34#10622590—21no—
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622570—21no—
42#10622569—21no—
43#10622552C2211yescharacteristic
44#10622549C2211yescharacteristic
45C4×Dic11⋊C4C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622273—21no—
48#10622267—21no—
49C11×#340C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66993—22no—
78#66993—22no—
79C4×C22⋊D11—44no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4D411yescharacteristic
90C2×Dic11⋊C4D411yescharacteristic
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66946—22no—
98#66946—41no—
99C11×#106—22no—
100C11×#102—22no—
101C11×#102—41no—
102C11×#95—21no—
103#66896—22no—
104#66896—22no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114#66885—22no—
115#66885—22no—
116C8×Dic11—41no—
117#66873—22no—
118#66873—41no—
119#66871—22no—
120C4⋊(C11⋊C8)—41no—
121#26753—111nomaximal, Sylow
122C24×C11—21no—
123C23×D11—21no—
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×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—81no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—24no—
140C2×C22⋊D11—24no—
141C2×C22⋊D11—42no—
142C2×C22⋊D11—42no—
143C2×C22⋊D11—81no—
144C2×C22⋊D11—81no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44#4112yes—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4#4112yes—
173C11×C4⋊C4#4112yes—
174C11×C22⋊C4—42no—
175C42×C11—21no—
176C42×C11—21no—
177C22⋊Dic11—42no—
178C22⋊Dic11—81no—
179(C2×D11)⋊C4—42no—
180(C2×D11)⋊C4—42no—
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—42no—
189C4⋊Dic11—81no—
190Dic11⋊C4—22no—
191Dic11⋊C4—22no—
192Dic11⋊C4—81no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205#2508—111no—
206#2366—111no—
207#2073—111no—
208#2067—111no—
209#2041—111no—
210#2041—111no—
211#1934—111no—
212#1925—111no—
213#1921—111no—
214#1919—111no—
215#1916—111no—
216#1864—111no—
217#1864D1111yescharacteristic, complemented
218#1804—111no—
219C4×#102—111no—
220C23×C11—22no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11C22×D411yescharacteristic
228C22×D11—22no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235D4×C11—22no—
236D4×C11—22no—
237D4×C11—41no—
238D4×C11—41no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
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—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—84no—
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C22⋊D11—48no—
262C22⋊D11—84no—
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—21no—
272C2×Dic11—21no—
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#13512yes—
283C2×Dic11AGL(1,ℤ/8)12yes—
284D44—22no—
285D44—22no—
286D44—41no—
287D44—41no—
288C4×D11—84no—
289C8×C11—41no—
290C8×C11—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C2×#127—111no—
294C2×C4×D4—111no—
295C2×C4×D4—221no—
296C2×C4×D4C2×D1111yescharacteristic
297C2×#107—111no—
298C2×#106C2×D1111yescharacteristic
299C2×C4⋊C8—111no—
300C2×#102—111no—
301C2×#102—111no—
302C2×#102—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102C2×D1111yescharacteristic
307C2×#102C2×D1111yescharacteristic
308C2×C4×C8—111no—
309#400—221no—
310#398—221no—
311#390—111no—
312#390—111no—
313#390—221no—
314#389—111no—
315#389—111no—
316#389—111no—
317#389C2×D1111yescharacteristic
318#387—221no—
319#386—221no—
320#386—221no—
321#382—111no—
322#382—221no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340C2×D1111yescharacteristic
332#336—111no—
333#336—111no—
334#336—111no—
335#336C2×D1111yescharacteristic
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11#52511yescharacteristic
344C22×C11#54611yescharacteristic
345C22×C11#54811yescharacteristic
346C22×C11C2×#13511yescharacteristic
347C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C11#57611yescharacteristic
349C22×C11#57711yescharacteristic
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—81no—
362C4×C11#52911yescharacteristic
363C4×C11#53911yescharacteristic
364C4×C11#55211yescharacteristic
365C4×C11#55311yescharacteristic
366Dic11—22no—
367Dic11—22no—
368Dic11—41no—
369Dic11—41no—
370Dic11—81no—
371Dic11—81no—
372Dic11—81no—
373C22×D4—111no—
374C22×D4—221no—
375C22×D4—221no—
376C22×D4C22×D1111yescharacteristic
377C23×C4—21no—
378C23×C4—221no—
379C22×C8—111no—
380C22×C8—111no—
381C22×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
383#127—222no—
384#127—222no—
385C4×D4—22no—
386C4×D4—41no—
387C4×D4—222no—
388C4×D4—441no—
389C4×D4—444no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42C22×D1111yescharacteristic
413#107—222no—
414#106—22no—
415C4⋊C8—441no—
416#102—22no—
417#102—41no—
418#102—222no—
419#102—222no—
420#102—222no—
421#102—222no—
422#102—222no—
423#102—441no—
424C4×C8—441no—
425#95—21no—
426#95—111no—
427#95—111no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435C2×C11—82no—
436C2×C11#246011yescharacteristic
437C2×C11#310511yescharacteristic
438C2×C11#311811yescharacteristic
439C2×C11#330511yescharacteristic
440C2×C11#331011yescharacteristic
441C2×C11#336511yescharacteristic
442C2×C11#336611yescharacteristic
443D11—82no—
444C24—21no—
445C24—221no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—112no—
452C2×D4—224no—
453C2×D4—224no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—442no—
460C2×D4—442no—
461C2×D4—881no—
462C2×D4—881no—
463C2×D4#434312yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—81no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4—881no—
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—81no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—442no—
509C4⋊C4—881no—
510C4⋊C4—881no—
511C4⋊C4#433912yes—
512C4⋊C4#434112yes—
513C22⋊C4—42no—
514C22⋊C4—442no—
515C22⋊C4—442no—
516C22⋊C4—442no—
517C22⋊C4—881no—
518C22⋊C4—881no—
519C42—21no—
520C42—21no—
521C42—221no—
522C42—221no—
523C42—221no—
524C42—221no—
525C42—442no—
526C42—442no—
527C11#2675311yescharacteristic, complemented, Sylow
528C23—22no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—222no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23C2×D4×D1111yescharacteristic
543D4—22no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—222no—
548D4—222no—
549D4—448no—
550D4—441no—
551D4—441no—
552D4—884no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
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—112no—
570C2×C4—112no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—884no—
591C2×C4C2×#433911yescharacteristic
592C2×C4C2×#434111yescharacteristic
593C2×C4#6703711yescharacteristic
594C2×C4C2×#434311yescharacteristic
595C2×C4#41×D1111yescharacteristic
596C2×C4#6704311yescharacteristic
597C8—41no—
598C8—41no—
599C8—441no—
600C8—441no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—442no—
609C22—442no—
610C22—442no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22#1062308311yescharacteristic
616C22#1062312211yescharacteristic
617C22#1062315811yescharacteristic
618C22#1062329311yescharacteristic
619C22D11×#13511yescharacteristic
620C22D11×AGL(1,ℤ/8)11yescharacteristic
621C22#1062330511yescharacteristic
622C4—41no—
623C4—42no—
624C4—42no—
625C4—41no—
626C4—81no—
627C4—222no—
628C4—222no—
629C4—441no—
630C4—441no—
631C4—881no—
632C4—881no—
633C4—881no—
634C4#1062304511yescharacteristic
635C4#1062308811yescharacteristic
636C4#1062317311yescharacteristic
637C4#1062319111yescharacteristic
638C2—82no—
639C2—882no—
640C2#1307257511yescharacteristic
641C2#1307866811yescharacteristic
642C2#1307880511yescharacteristic
643C2#1308055911yescharacteristic
644C2#1308063011yescharacteristic
645C2#1308131311yescharacteristic
646C2#1308132411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC2×#66993C22
hypercenter#1864D11
hypocenterC11#26753
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
1. #13073156C2semidirect
3. #13070031C2semidirect
4. #13070001C2semidirect
7. #13069296C2semidirect
8. #13069239C2semidirect
9. #13069211C2semidirect
10. #13069196C2semidirect
11. #13069176C2semidirect
12. #13068874C2semidirect
13. #13068626C2semidirect
14. #13068430C2semidirect
15. C11×#1864C2semidirect
217. #1864D11semidirect
527. C11#26753semidirect

Maximal subgroups

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

subgroupindex
#130731562
#130716782
#130700312
#130700012
#130698492
#130692962
#130692392
#130692112
#130691962
#130691762
#130688742
#130686262
#130684302
C11×#18642
#2675311