Finite Group Databasebeta

← #14822294

Subgroups — #14822294

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#13073157C211yesmaximal, characteristic, complemented
2#13071681C211yesmaximal, characteristic
3#13070032C211yesmaximal, characteristic, complemented
4#13070000C211yesmaximal, characteristic, complemented
5#13069847C211yesmaximal, characteristic
6#13069301C211yesmaximal, characteristic, complemented
7#13069239C211yesmaximal, characteristic, complemented
8#13069205C211yesmaximal, characteristic, complemented
9#13069195C211yesmaximal, characteristic, complemented
10#13069174C211yesmaximal, characteristic, complemented
11#13068879C211yesmaximal, characteristic, complemented
12#13068879C211yesmaximal, characteristic, complemented
13#13068624C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#2041C211yesmaximal, characteristic
16C2×C11×#127C2211yescharacteristic
17C2×D4×Dic11—21no—
18C2×D4×Dic11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#389C2211yescharacteristic
25#10622834—21no—
26#10622834C2211yescharacteristic
27#10622834C2211yescharacteristic
28#10622833—21no—
29#10622833—21no—
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622599—21no—
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622590—21no—
41#10622590C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622274—21no—
48#10622268—21no—
49C11×#336C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#127—22no—
68C11×#127—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79D4×Dic11—22no—
80D4×Dic11—22no—
81D4×Dic11—41no—
82D4×Dic11—41no—
83D4×Dic11—44no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C11×#102—22no—
100C11×#102—22no—
101C11×#102—22no—
102C11×#102—22no—
103C11×#95—21no—
104#66896—22no—
105#66896—22no—
106#66896—41no—
107#66896—41no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117#66881—22no—
118Dic11⋊C8—41no—
119C8×Dic11—41no—
120#66871—22no—
121#26753—111nomaximal, Sylow
122C24×C11—21no—
123C24×C11—21no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—81no—
139C2×D4×C11—81no—
140C2×D4×C11#4112yes—
141C2×D4×C11#4112yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C22×Dic11—81no—
156C22×Dic11—81no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
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—81no—
171C11×C4⋊C4#4112yes—
172C42×C11—21no—
173C42×C11—21no—
174C22⋊Dic11—42no—
175C22⋊Dic11—42no—
176C22⋊Dic11—42no—
177C22⋊Dic11—42no—
178C22⋊Dic11—81no—
179C22⋊Dic11—81no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—81no—
190C4⋊Dic11—81no—
191C4⋊Dic11#4112yes—
192Dic11⋊C4—42no—
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#2041D1111yescharacteristic
211#1934—111no—
212#1925—111no—
213#1921—111no—
214#1919—111no—
215#1916—111no—
216#1864—111no—
217#1864—111no—
218#1804—111no—
219C4×#102—111no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11C22×D411yescharacteristic
235D4×C11—22no—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—48no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—84no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11#13512yes—
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—22no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
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—
285C2×Dic11—41no—
286C2×Dic11—84no—
287C2×Dic11—84no—
288C2×Dic11AGL(1,ℤ/8)12yes—
289C8×C11—41no—
290C8×C11—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C2×#127C2×D1111yescharacteristic
294C2×C4×D4—111no—
295C2×C4×D4—111no—
296C2×C4×D4—221no—
297C2×#107—111no—
298C2×#106—111no—
299C2×C4⋊C8—111no—
300C2×#102—111no—
301C2×#102—111no—
302C2×#102—111no—
303C2×#102—111no—
304C2×#102C2×D1111yescharacteristic
305C2×#102C2×D1111yescharacteristic
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#340—111no—
332#336—111no—
333#336—111no—
334#336—111no—
335#336C2×D1111yescharacteristic
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11#52511yescharacteristic
351C22×C11#54611yescharacteristic
352C22×C11#54811yescharacteristic
353C22×C11C2×#13511yescharacteristic
354C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C11#57611yescharacteristic
356C22×C11#57711yescharacteristic
357C4×C11—22no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—81no—
361C4×C11#52911yescharacteristic
362C4×C11#53911yescharacteristic
363C4×C11#55211yescharacteristic
364C4×C11#55311yescharacteristic
365Dic11—22no—
366Dic11—41no—
367Dic11—41no—
368Dic11—41no—
369Dic11—42no—
370Dic11—81no—
371Dic11—81no—
372Dic11—81no—
373C22×D4—21no—
374C22×D4—21no—
375C22×D4C22×D1111yescharacteristic
376C22×D4C22×D1111yescharacteristic
377C23×C4—221no—
378C23×C4—221no—
379C22×C8—111no—
380C22×C8—111no—
381C22×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
383#127—22no—
384#127—22no—
385C4×D4—222no—
386C4×D4—222no—
387C4×D4—441no—
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—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C22⋊C4—221no—
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—222no—
415C4⋊C8—441no—
416#102—22no—
417#102—22no—
418#102—22no—
419#102—22no—
420#102—222no—
421#102—222no—
422#102—441no—
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—82no—
437C2×C11#246011yescharacteristic
438C2×C11#310511yescharacteristic
439C2×C11#311811yescharacteristic
440C2×C11#330511yescharacteristic
441C2×C11#331011yescharacteristic
442C2×C11#336511yescharacteristic
443C2×C11#336611yescharacteristic
444C24—21no—
445C24—21no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—81no—
461C2×D4—81no—
462C2×D4#434112yes—
463C2×D4#434112yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—881no—
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—81no—
499C4⋊C4—112no—
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—221no—
509C4⋊C4—442no—
510C4⋊C4—881no—
511C4⋊C4—881no—
512C4⋊C4#434112yes—
513C22⋊C4—442no—
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—22no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23C2×D4×D1111yescharacteristic
543D4—22no—
544D4—22no—
545D4—22no—
546D4—22no—
547D4—48no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—84no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—112no—
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—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—222no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—884no—
589C2×C4—884no—
590C2×C4#6696912yes—
591C2×C4C2×#434111yescharacteristic
592C2×C4C2×#434111yescharacteristic
593C2×C4C2×#434111yescharacteristic
594C2×C4#41×D1111yescharacteristic
595C2×C4#6704211yescharacteristic
596C2×C4#6704311yescharacteristic
597C8—41no—
598C8—41no—
599C8—441no—
600C8—441no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22#1062311711yescharacteristic
616C22#1062312911yescharacteristic
617C22#1062320711yescharacteristic
618C22#1062328811yescharacteristic
619C22C2×#6696911yescharacteristic
620C22D11×AGL(1,ℤ/8)11yescharacteristic
621C22#1062330611yescharacteristic
622C4—22no—
623C4—41no—
624C4—42no—
625C4—81no—
626C4—222no—
627C4—441no—
628C4—442no—
629C4—441no—
630C4—441no—
631C4—881no—
632C4—881no—
633C4—881no—
634C4#1062313111yescharacteristic
635C4#1062314911yescharacteristic
636C4#1062318111yescharacteristic
637C4#1062319611yescharacteristic
638C2—82no—
639C2—82no—
640C2#1307256311yescharacteristic
641C2#1307866411yescharacteristic
642C2#1307879311yescharacteristic
643C2#1308056511yescharacteristic
644C2#1308063611yescharacteristic
645C2#1308131611yescharacteristic
646C2#1308131811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2041C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2041D11
hypocenterC11#26753
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2041

Complements

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

NH ≅ G/Ntype
1. #13073157C2semidirect
3. #13070032C2semidirect
4. #13070000C2semidirect
6. #13069301C2semidirect
7. #13069239C2semidirect
8. #13069205C2semidirect
9. #13069195C2semidirect
10. #13069174C2semidirect
11. #13068879C2semidirect
12. #13068879C2semidirect
13. #13068624C2semidirect
14. #102×Dic11C2semidirect
527. C11#26753semidirect

Maximal subgroups

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

subgroupindex
#130731572
#130716812
#130700322
#130700002
#130698472
#130693012
#130692392
#130692052
#130691952
#130691742
#130688792
#130686242
#102×Dic112
C11×#20412
#2675311