Finite Group Databasebeta

← #14788847

Subgroups — #14788847

Order 2816.

1482 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622703C211yesmaximal, characteristic, complemented
2C2×#10622688C211yesmaximal, characteristic, complemented
3C2×#10622852C212yesmaximal, complemented
4C4×#66977C211yesmaximal, characteristic, complemented
5#13069852C212yesmaximal, complemented
6#13069710C212yesmaximal, complemented
7#13069544C211yesmaximal, characteristic, complemented
8#13069540C211yesmaximal, characteristic, complemented
9#13068596C211yesmaximal, characteristic, complemented
10#13068556C212yesmaximal, complemented
11C2×C11×#532C211yesmaximal, characteristic
12C22×C11×#41C2212yes—
13C11×#532—24no—
14C11×#532—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#127C2211yescharacteristic
17C2×C11×#124C2212yes—
18C2×C11×#121—21no—
19C2×C11×#121—21no—
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11—21no—
22C22×C42×C11C2211yescharacteristic
23C22×#4326C2212yes—
24C22×#4324C2212yes—
25C2×#66977C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27#10622852—28no—
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31C2×#66896C2212yes—
32C2×#66896C2212yes—
33C2×#66896C2212yes—
34#10622825C2211yescharacteristic
35#10622823—21no—
36C4×C22⋊Dic11—21no—
37C2×C22⋊(C11⋊C8)C2212yes—
38#10622703—24no—
39#10622688—24no—
40C4×C4⋊Dic11C2211yescharacteristic
41#10622546—21no—
42C4×Dic11⋊C4—21no—
43#10622542C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622162C2212yes—
48C2×C11×#41—24no—
49C2×C11×#41—24no—
50C2×C11×#41—24no—
51C2×C11×#41—24no—
52C2×C11×#41—42no—
53C2×C11×#41—42no—
54C22×Q8×C11C2312yes—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11C2312yes—
59C23×C4×C11—22no—
60C23×C4×C11D411yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8D414yes—
66C11×#127—22no—
67C11×#127D414yes—
68C11×#124—24no—
69C11×#124—24no—
70C11×#121—28no—
71C11×#121—28no—
72C4×D4×C11—28no—
73C4×D4×C11—28no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C42×C11—22no—
79C2×C42×C11—22no—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×#4326—24no—
87C2×#4326—24no—
88C2×#4326—42no—
89C2×#4324—24no—
90C2×#4324—24no—
91C2×#4324—42no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—22no—
96#66977D414yescomplemented
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C22×C11⋊C8C2312yes—
103C22×C11⋊C8C2312yes—
104C4×Dic22—22no—
105C4×Dic22—22no—
106#66899—24no—
107#66899—24no—
108#66899—42no—
109#66896—24no—
110#66896—24no—
111#66896—42no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—24no—
118C4⋊(C11⋊C8)—22no—
119C4⋊(C11⋊C8)—22no—
120#24213—111nomaximal, Sylow
121C24×C11—22no—
122C24×C11C2×D411yescharacteristic
123C11×#41—48no—
124C11×#41—48no—
125C11×#41—48no—
126C11×#41—48no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11C2×D414yes—
133C2×D4×C11—28no—
134C2×D4×C11—24no—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11—44no—
144C2×D4×C11—44no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11C2×D414yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—28no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—41no—
159C22×C4×C11—41no—
160C22×C4×C11—44no—
161C22×C4×C11—44no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11#4112yes—
169C22×C4×C11C2411yescharacteristic
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22C2×D412yes—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C22⋊C4—28no—
183C11×C22⋊C4—28no—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11C2×D412yes—
189C42×C11C2×D412yes—
190C22⋊Dic11—24no—
191C22⋊Dic11—42no—
192#4326—48no—
193#4324—48no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11C2×D412yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211C2×#532D1111yescharacteristic
212C2×#462—111no—
213C2×#460—111no—
214C2×#452—112no—
215C4×C22⋊Q8—111no—
216#2042—112no—
217#2015—112no—
218#1982—111no—
219#1981—111no—
220#1797—111no—
221#1788—112no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—24no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11#12112yes—
236C23×C11C22×D411yescharacteristic
237Q8×C11—24no—
238Q8×C11—24no—
239Q8×C11—42no—
240Q8×C11—42no—
241D4×C11—24no—
242D4×C11—24no—
243D4×C11—48no—
244D4×C11—416no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—48no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—24no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—44no—
264C2×C4×C11—416no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—44no—
268C2×C4×C11#12012yes—
269C2×C4×C11#12012yes—
270C2×C4×C11#12112yes—
271C2×C4×C11#13512yes—
272C2×C4×C11#13712yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291Dic22—22no—
292Dic22—22no—
293Dic22—41no—
294Dic22—41no—
295C11⋊C8—42no—
296C11⋊C8—42no—
297C22×#41C2×D1112yes—
298C22×Q16—112no—
299C22×SD16—112no—
300#532—24no—
301#532—24no—
302C2×C4⋊Q8C2×D1111yescharacteristic
303C2×#127C2×D1111yescharacteristic
304C2×#124C2×D1112yes—
305C2×C22⋊Q8—111no—
306C2×#121—21no—
307C2×#121—21no—
308C2×C4×Q8—111no—
309C2×C4×D4—21no—
310C2×C4×D4—21no—
311C22×C42C2×D1111yescharacteristic
312#462—224no—
313#460—224no—
314#452—228no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8—111no—
317C2×#103—112no—
318C2×#103—112no—
319C2×#103—112no—
320C2×#102—112no—
321C2×#102—112no—
322C2×#102—112no—
323C2×C22⋊C8—112no—
324#391—111no—
325#389—111no—
326#387—221no—
327#385—221no—
328#380—111no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—221no—
331C4×C22⋊C4—221no—
332#336—112no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—44no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—82no—
344C22×C11—82no—
345C22×C11—82no—
346C22×C11—82no—
347C22×C11C2×#12011yescharacteristic
348C22×C11C2×#12111yescharacteristic
349C22×C11#53511yescharacteristic
350C22×C11C2×#13511yescharacteristic
351C22×C11C2×#13711yescharacteristic
352C22×C11#57511yescharacteristic
353C22×C11#57511yescharacteristic
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—44no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11#45214yescomplemented
360C4×C11D4211yescharacteristic
361C4×C11D4211yescharacteristic
362C4×C11#54611yescharacteristic
363C4×C11#54611yescharacteristic
364Dic11—42no—
365Dic11—42no—
366Dic11—81no—
367Dic11—81no—
368C2×#41—24no—
369C2×#41—24no—
370C2×#41—24no—
371C2×#41—24no—
372C2×#41—42no—
373C2×#41—42no—
374C22×Q8—111no—
375C22×Q8C22×D1112yes—
376C22×D4—22no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4C22×D1112yes—
380C23×C4—22no—
381C23×C4C22⋊D1111yescharacteristic
382C23×C4C22⋊D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C2×Q16—224no—
385C2×Q16—224no—
386C2×Q16—442no—
387C2×SD16—224no—
388C2×SD16—224no—
389C2×SD16—442no—
390C22×C8—112no—
391C22×C8—112no—
392C4⋊Q8—22no—
393C4⋊Q8C22⋊D1114yes—
394#127—22no—
395#127C22⋊D1114yes—
396#124—24no—
397#124—24no—
398C22⋊Q8—114no—
399C22⋊Q8—222no—
400#121—28no—
401#121—28no—
402C4×Q8—222no—
403C4×Q8—222no—
404C4×D4—28no—
405C4×D4—28no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42C22⋊D1111yescharacteristic
423C2×C42C22⋊D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426C4⋊C8—222no—
427C4⋊C8—222no—
428#103—224no—
429#103—224no—
430#103—442no—
431#102—224no—
432#102—224no—
433#102—442no—
434C22⋊C8—224no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440C2×C11—42no—
441C2×C11—84no—
442C2×C11#240811yescharacteristic
443C2×C11C2×#45211yescharacteristic
444C2×C11#300511yescharacteristic
445C2×C11#303511yescharacteristic
446C2×C11#303711yescharacteristic
447C2×C11#321211yescharacteristic
448C2×C11#321611yescharacteristic
449C24—22no—
450C24C2×C22⋊D1111yescharacteristic
451#41—48no—
452#41—48no—
453#41—48no—
454#41—48no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—112no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8C2×C22⋊D1114yes—
467C2×D4—28no—
468C2×D4—24no—
469C2×D4—24no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4C2×C22⋊D1114yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—28no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4D4×D1112yes—
501C22×C4#434112yes—
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C23×D1111yescharacteristic
508Q16—448no—
509SD16—448no—
510C2×C8—222no—
511C2×C8—222no—
512C2×C8—222no—
513C2×C8—222no—
514C2×C8—222no—
515C2×C8—222no—
516C4⋊C4—24no—
517C4⋊C4—24no—
518C4⋊C4—112no—
519C4⋊C4—224no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C22⋊C4—28no—
528C22⋊C4—28no—
529C22⋊C4—224no—
530C22⋊C4—442no—
531C42—22no—
532C42—22no—
533C42—21no—
534C42—21no—
535C42—442no—
536C42—442no—
537C42C2×C22⋊D1112yes—
538C42C2×C22⋊D1112yes—
539C11#2421311yescharacteristic, complemented, Sylow
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—24no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23#6699112yes—
554C23C22×C22⋊D1111yescharacteristic
555Q8—24no—
556Q8—24no—
557Q8—42no—
558Q8—42no—
559Q8—222no—
560Q8—222no—
561Q8—441no—
562Q8—441no—
563D4—24no—
564D4—24no—
565D4—48no—
566D4—416no—
567D4—42no—
568D4—42no—
569D4—48no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—24no—
585C2×C4—44no—
586C2×C4—416no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—44no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4#6699112yes—
603C2×C4#6700312yes—
604C2×C4#6700412yes—
605C2×C4#6700612yes—
606C2×C4#6700612yes—
607C2×C4C2×D4×D1111yescharacteristic
608C2×C4C2×#434111yescharacteristic
609C2×C4#6703711yescharacteristic
610C2×C4#6703711yescharacteristic
611C2×C4C22×C22⋊D1111yescharacteristic
612C2×C4C22×C22⋊D1111yescharacteristic
613C8—442no—
614C8—442no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—44no—
623C22—44no—
624C22—44no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22C2×#6699111yescharacteristic
630C22#1062333611yescharacteristic
631C22C2×#6700311yescharacteristic
632C22#1062335311yescharacteristic
633C22#1062335311yescharacteristic
634C22C2×#6700411yescharacteristic
635C22C2×#6700611yescharacteristic
636C4—22no—
637C4—22no—
638C4—41no—
639C4—44no—
640C4—41no—
641C4—442no—
642C4—442no—
643C4—881no—
644C4—881no—
645C4#1062285214yescomplemented
646C4D4×C22⋊D1111yescharacteristic
647C4D4×C22⋊D1111yescharacteristic
648C4#1062333711yescharacteristic
649C4#1062333711yescharacteristic
650C2—42no—
651C2—84no—
652C2#1307196611yescharacteristic
653C2C2×#1062285211yescharacteristic
654C2#1307785811yescharacteristic
655C2#1307806511yescharacteristic
656C2#1307808411yescharacteristic
657C2#1307959211yescharacteristic
658C2#1307962711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#532C2
socleC23×C11C22×D4
hypercenterC2×#532D11
hypocenterC11#24213
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10622703C2semidirect
2. C2×#10622688C2semidirect
3. C2×#10622852C2semidirect
4. C4×#66977C2semidirect
5. #13069852C2semidirect
6. #13069710C2semidirect
7. #13069544C2semidirect
8. #13069540C2semidirect
9. #13068596C2semidirect
10. #13068556C2semidirect
96. #66977D4semidirect
359. C4×C11#452semidirect
539. C11#24213semidirect
645. C4#10622852semidirect

Maximal subgroups

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

subgroupindex
C2×#106227032
C2×#106226882
C2×#106228522
C4×#669772
#130698522
#130697102
#130695442
#130695402
#130685962
#130685562
C2×C11×#5322
#2421311