Finite Group Databasebeta

← #14807099

Subgroups — #14807099

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622680C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic, complemented
3#13073562C211yesmaximal, characteristic, complemented
4#13069612C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069574C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068938C212yesmaximal, complemented
9#13068933C212yesmaximal, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C2×C11×#553C211yesmaximal, characteristic, complemented
12C11×#553—24no—
13C11×#553—24no—
14C2×C11×#126—21no—
15C2×C11×#125C2211yescharacteristic
16C2×C11×#123—21no—
17C2×C11×#121—21no—
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C2×#66993—21no—
26C22×#4323C2212yes—
27C2×#66983C2212yes—
28C2×#66983C2212yes—
29C2×#66927C2211yescharacteristic
30C2×#66896C2212yes—
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622680—24no—
34#10622628—24no—
35#10622601—21no—
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38C2×#66873C2212yes—
39#10622573—21no—
40#10622573—21no—
41C4×C4⋊Dic11C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×D44—21no—
58C22×D44—21no—
59C22×D44C2312yes—
60C11×#126—28no—
61C11×#125—22no—
62C11×#125D414yescomplemented
63C11×#123—28no—
64C11×#121—28no—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121—22no—
68C11×#121—22no—
69C4×D4×C11—28no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11D414yescomplemented
74C11×#117—22no—
75C11×#117—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93#66993—44no—
94C2×#4323—24no—
95C2×#4323—42no—
96C2×#4323—42no—
97#66983—24no—
98#66983—24no—
99#66983—42no—
100#66983—42no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11C2312yes—
104C2×C4×Dic11—21no—
105C22×C11⋊C8C2312yes—
106C22×C11⋊C8C2312yes—
107#66927—22no—
108#66927—22no—
109#66896—24no—
110C11⋊#95—21no—
111C22⋊(C11⋊C8)—42no—
112C22⋊(C11⋊C8)—42no—
113#66873—24no—
114#66873—24no—
115#66873—24no—
116C4⋊(C11⋊C8)—22no—
117#66867—22no—
118#25581—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11C2×D411yescharacteristic
121C24×C11C2×D411yescharacteristic
122C23×D11—22no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—24no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—41no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11—82no—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—24no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—82no—
149C22×C4×C11—82no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—44no—
156C2×C22⋊D11—44no—
157C2×C22⋊D11—44no—
158C2×C22⋊D11—44no—
159C2×C22⋊D11—82no—
160C2×C22⋊D11—82no—
161C22×Dic11—22no—
162C2×D44—22no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—22no—
168C2×D44—42no—
169C2×D44—42no—
170C2×D44—42no—
171C2×D44—42no—
172C2×D44—82no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C2×D412yes—
181C11×C4⋊C4C2×D412yes—
182C11×C4⋊C4C2×D412yes—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C42×C11—24no—
190C42×C11C2×D412yes—
191C42×C11C2×D412yes—
192#4323—48no—
193(C2×D11)⋊C4—44no—
194(C2×D11)⋊C4—44no—
195C4⋊Dic11—22no—
196C4⋊Dic11#4114yes—
197C4×Dic11—42no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×#553D1111yescharacteristic, complemented
205C2×#490—111no—
206C2×#459—111no—
207#2541—111no—
208#1999—112no—
209#1999—112no—
210#1989—111no—
211#1955—111no—
212#1875—112no—
213#1874—112no—
214#1762—111no—
215C23×C11—21no—
216C23×C11—22no—
217C23×C11—21no—
218C23×C11—22no—
219C23×C11—21no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—22no—
225C23×C11—42no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—42no—
229C23×C11AGL(1,ℤ/8)12yes—
230C23×C11C22×D411yescharacteristic
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—42no—
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—44no—
241D4×C11—48no—
242D4×C11—42no—
243D4×C11—84no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—84no—
265C2×C4×C11—84no—
266C2×C4×C11#12012yes—
267C2×C4×C11#12012yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C2×#4112yes—
271C2×C4×C11H(5,𝔽2)12yes—
272C22⋊D11—88no—
273C22⋊D11—88no—
274C2×Dic11—24no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277D44—42no—
278D44—42no—
279D44—42no—
280D44—42no—
281D44—84no—
282D44—84no—
283C11⋊C8—42no—
284C11⋊C8—42no—
285C22×D8—112no—
286#553—24no—
287#553—24no—
288C2×#127—111no—
289C2×#127—221no—
290C2×#126—21no—
291C2×#125C2×D1111yescharacteristic
292C2×#123—21no—
293C2×#121—21no—
294C2×#121—112no—
295C2×#121—112no—
296C2×#121C2×D1111yescharacteristic
297C2×#121C2×D1111yescharacteristic
298C2×C4×D4—21no—
299C2×C4×D4C2×D1111yescharacteristic
300C2×C4×D4C2×D1111yescharacteristic
301C2×#117C2×D1111yescharacteristic
302C22×C4⋊C4C2×D1111yescharacteristic
303#490—224no—
304#459—224no—
305C2×C4⋊C8—111no—
306C2×#102—112no—
307C2×#102—112no—
308C2×#102—112no—
309C2×#102—112no—
310C2×C22⋊C8—112no—
311C2×C22⋊C8—112no—
312C2×#97—111no—
313#392—221no—
314#392—221no—
315#390—221no—
316C4×C4⋊C4—111no—
317#340—112no—
318#340—112no—
319#340—112no—
320C22×C11—22no—
321C22×C11—24no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—42no—
325C22×C11—41no—
326C22×C11—42no—
327C22×C11—41no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—41no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—82no—
334C22×C11—82no—
335C22×C11C2×#12011yescharacteristic
336C22×C11#54612yes—
337C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C11#57511yescharacteristic
339C22×C11#57612yes—
340C2×D11—82no—
341C2×D11—82no—
342C2×D11—82no—
343C2×D11—82no—
344C2×D11—82no—
345C2×D11—82no—
346C2×D11—82no—
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11—42no—
354C4×C11#53211yescharacteristic
355C4×C11#53511yescharacteristic
356C4×C11#55012yes—
357Dic11—44no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—112no—
361C22×D4—222no—
362C22×D4—222no—
363C22×D4—221no—
364C22×D4—221no—
365C22×D4C22⋊D1111yescharacteristic
366C22×D4C22×D1111yescharacteristic
367C23×C4—21no—
368C23×C4—21no—
369C23×C4C22×D1111yescharacteristic
370C23×C4C22×D1111yescharacteristic
371C2×D8—224no—
372C2×D8—442no—
373C2×D8—442no—
374C22×C8—112no—
375C22×C8—112no—
376#127—222no—
377#127—222no—
378#127—444no—
379#126—28no—
380#125—22no—
381#125C22⋊D1114yescomplemented
382#123—28no—
383#121—28no—
384#121—22no—
385#121—22no—
386#121—22no—
387#121—22no—
388#121—224no—
389#121—224no—
390#121—442no—
391#121—442no—
392C4×D4—28no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4C22⋊D1114yescomplemented
397#117—22no—
398#117—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4C22⋊D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4C22⋊D1111yescharacteristic
416C2×C22⋊C4C22⋊D1111yescharacteristic
417C2×C42—21no—
418C2×C42—221no—
419C2×C42C22×D1111yescharacteristic
420C4⋊C8—222no—
421#102—224no—
422#102—224no—
423#102—224no—
424#102—224no—
425C22⋊C8—442no—
426C22⋊C8—442no—
427#97—222no—
428#95—221no—
429C2×C11—42no—
430C2×C11—81no—
431C2×C11—82no—
432C2×C11#243111yescharacteristic
433C2×C11#300611yescharacteristic
434C2×C11#300811yescharacteristic
435C2×C11#330912yes—
436C2×C11#331812yes—
437D11—162no—
438C24—21no—
439C24—222no—
440C24C2×C22⋊D1111yescharacteristic
441C24C2×C22⋊D1111yescharacteristic
442C2×D4—24no—
443C2×D4—22no—
444C2×D4—24no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—82no—
453C2×D4—222no—
454C2×D4—222no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—222no—
459C2×D4—442no—
460C2×D4—442no—
461C2×D4—444no—
462C2×D4—444no—
463C2×D4—444no—
464C2×D4—444no—
465C2×D4—442no—
466C2×D4—442no—
467C2×D4—882no—
468C2×D4—882no—
469C2×D4—882no—
470C2×D4C2×C22⋊D1112yes—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—82no—
485C22×C4—82no—
486C22×C4—222no—
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492D8—448no—
493C2×C8—222no—
494C2×C8—222no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8—222no—
498C2×C8—222no—
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—24no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—114no—
507C4⋊C4—222no—
508C4⋊C4C2×C22⋊D1112yes—
509C4⋊C4C2×C22⋊D1112yes—
510C4⋊C4C2×C22⋊D1112yes—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—444no—
518C22⋊C4—444no—
519C42—24no—
520C42—442no—
521C42C2×C22⋊D1112yes—
522C42C2×C22⋊D1112yes—
523C11#2558111yescharacteristic, complemented, Sylow
524C23—21no—
525C23—22no—
526C23—22no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—22no—
531C23—22no—
532C23—21no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—42no—
537C23—42no—
538C23—442no—
539C23—442no—
540C23—442no—
541C23—442no—
542C23—442no—
543C23—442no—
544C23—442no—
545C23#6700212yes—
546C23C22×C22⋊D1111yescharacteristic
547D4—22no—
548D4—22no—
549D4—44no—
550D4—48no—
551D4—42no—
552D4—84no—
553D4—442no—
554D4—442no—
555D4—442no—
556D4—442no—
557D4—884no—
558D4—884no—
559D4—888no—
560D4—888no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—84no—
582C2×C4—84no—
583C2×C4—224no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4#6700612yes—
587C2×C4#6700612yes—
588C2×C4#41×D1112yes—
589C2×C4#6704212yes—
590C2×C4C22×C22⋊D1111yescharacteristic
591C2×C4C22×C22⋊D1111yescharacteristic
592C8—442no—
593C8—442no—
594C22—22no—
595C22—24no—
596C22—42no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—42no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—41no—
606C22—42no—
607C22—82no—
608C22—82no—
609C22—882no—
610C22—882no—
611C22—882no—
612C22—882no—
613C22—882no—
614C22—882no—
615C22—882no—
616C22C2×#6700211yescharacteristic
617C22#1062335311yescharacteristic
618C22#1062336012yes—
619C22#1062336612yes—
620C22C2×#6700611yescharacteristic
621C4—22no—
622C4—22no—
623C4—41no—
624C4—41no—
625C4—42no—
626C4—42no—
627C4—42no—
628C4—444no—
629C4#1062336111yescharacteristic
630C4#1062336311yescharacteristic
631C4#1062336512yes—
632C2—42no—
633C2—81no—
634C2—82no—
635C2—1762no—
636C2#1307223111yescharacteristic
637C2#1307786811yescharacteristic
638C2#1307788411yescharacteristic
639C2#1308061612yes—
640C2#1308075112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#553C2
socleC23×C11C22×D4
hypercenterC2×#553D11
hypocenterC11#25581
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#10622680C2semidirect
2. C2×#10622628C2semidirect
3. #13073562C2semidirect
4. #13069612C2semidirect
5. #13069612C2semidirect
6. #13069574C2semidirect
7. #13069415C2semidirect
8. #13068938C2semidirect
9. #13068933C2semidirect
10. #13068441C2semidirect
11. C2×C11×#553C2semidirect
62. C11×#125D4semidirect
73. C4×D4×C11D4semidirect
204. C2×#553D11semidirect
381. #125C22⋊D11semidirect
396. C4×D4C22⋊D11semidirect
523. C11#25581semidirect

Maximal subgroups

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

subgroupindex
C2×#106226802
C2×#106226282
#130735622
#130696122
#130695742
#130694152
#130689382
#130689332
#130684412
C2×C11×#5532
#2558111