Finite Group Databasebeta

← #14788074

Subgroups — #14788074

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic, complemented
2C2×#10622685C211yesmaximal, characteristic, complemented
3C4×#66983C211yesmaximal, characteristic, complemented
4#13069795C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069569C211yesmaximal, characteristic, complemented
7#13069544C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal, complemented
9#13068863C212yesmaximal, complemented
10#13068596C211yesmaximal, characteristic, complemented
11C2×C11×#532C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C11×#532—24no—
14C11×#532—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#127C2211yescharacteristic
17C2×C11×#124—21no—
18C2×C11×#121—21no—
19C2×C11×#121C2212yes—
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2212yes—
22C22×C42×C11C2211yescharacteristic
23C22×#4323C2212yes—
24C2×#66983C2211yescharacteristic
25C2×C4×C22⋊D11—21no—
26C2×C4×D44C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30#10622826—21no—
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622700—24no—
34#10622685—24no—
35C2×#66873C2212yes—
36C2×#66871C2212yes—
37#10622553—21no—
38#10622552C2211yescharacteristic
39C4×(C2×D11)⋊C4—21no—
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C2×C11×#41—28no—
48C2×C11×#41—44no—
49C2×C11×#41—44no—
50C22×Q8×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11C2312yes—
55C23×C4×C11—22no—
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D411yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—21no—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8D414yescomplemented
64C11×#127—22no—
65C11×#127D414yescomplemented
66C11×#124—28no—
67C11×#121—28no—
68C11×#121—24no—
69C11×#121—24no—
70C4×D4×C11—28no—
71C4×D4×C11—24no—
72C4×D4×C11—24no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C42×C11—22no—
78C2×C42×C11—22no—
79C2×C42×C11D411yescharacteristic
80C2×C42×C11D411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×#4323—24no—
85C2×#4323—24no—
86C2×#4323—42no—
87#66983—22no—
88#66983—22no—
89C4×C22⋊D11—44no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2312yes—
100C22×C11⋊C8C2312yes—
101C4×D44—22no—
102C4×D44—22no—
103#66896—24no—
104#66896—24no—
105#66896—42no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C22⋊(C11⋊C8)—42no—
110#66873—24no—
111#66871—24no—
112C4⋊(C11⋊C8)—22no—
113C4⋊(C11⋊C8)—22no—
114#24150—111nomaximal, Sylow
115C24×C11—22no—
116C24×C11C2×D411yescharacteristic
117C23×D11—21no—
118C11×#41—432no—
119C2×Q8×C11—24no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×D4×C11—28no—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11C2×D414yes—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—28no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—44no—
151C22×C4×C11—44no—
152C22×C4×C11D814yescomplemented
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—24no—
160C2×C22⋊D11—42no—
161C2×C22⋊D11—42no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44#4112yescomplemented
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4C2×D414yes—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—28no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11C2×D412yes—
184C42×C11C2×D412yes—
185C22⋊Dic11—42no—
186#4323—48no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11#4112yescomplemented
197Dic11⋊C4—42no—
198C4×Dic11—42no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×#532D1111yescharacteristic, complemented
206C2×#474—111no—
207C2×#459—111no—
208C4×#121—111no—
209#2033—112no—
210#1999—112no—
211#1988—111no—
212#1982—111no—
213#1879—112no—
214#1862—112no—
215#1797—111no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—24no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11C2×D812yes—
230C23×C11C22×D411yescharacteristic
231C22×D11—22no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238Q8×C11—48no—
239D4×C11—24no—
240D4×C11—24no—
241D4×C11—48no—
242D4×C11—416no—
243D4×C11—42no—
244D4×C11—42no—
245D4×C11—48no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—28no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—24no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—44no—
259C2×C4×C11—416no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11#12012yes—
267C2×C4×C11#12012yes—
268C2×C4×C11C2×D812yes—
269C2×C4×C11C2×D812yes—
270C2×C4×C11AGL(1,ℤ/8)12yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C22⋊D11—48no—
278C2×Dic11—22no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287D44—22no—
288D44—22no—
289D44—41no—
290D44—41no—
291C4×D11—84no—
292C11⋊C8—42no—
293C11⋊C8—42no—
294C22×#41—21no—
295C22×D8—112no—
296#532—24no—
297#532—24no—
298C2×C4⋊Q8C2×D1111yescharacteristic
299C2×#127C2×D1111yescharacteristic
300C2×#124—21no—
301C2×#121—21no—
302C2×#121—111no—
303C2×#121C2×D1112yes—
304C2×C4×D4—21no—
305C2×C4×D4—111no—
306C2×C4×D4—221no—
307C2×C4×D4C2×D1112yes—
308C22×C42C2×D1111yescharacteristic
309#474—224no—
310#459—224no—
311C2×#107—112no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8—111no—
314C2×#102—112no—
315C2×#102—112no—
316C2×#102—112no—
317C2×#102—112no—
318C2×C22⋊C8—112no—
319#390—111no—
320#389—111no—
321#388—221no—
322#386—221no—
323#380—111no—
324C4×C4⋊C4—111no—
325C4×C22⋊C4—221no—
326#340—112no—
327#340—112no—
328#336—112no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—44no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11—82no—
343C22×C11C2×#12011yescharacteristic
344C22×C11#52511yescharacteristic
345C22×C11#53711yescharacteristic
346C22×C11C22×D811yescharacteristic
347C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57511yescharacteristic
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—44no—
361C4×C11—41no—
362C4×C11#44714yes—
363C4×C11#54611yescharacteristic
364C4×C11#54711yescharacteristic
365C4×C11#54811yescharacteristic
366C4×C11#55011yescharacteristic
367Dic11—42no—
368Dic11—81no—
369Dic11—81no—
370C2×#41—28no—
371C2×#41—44no—
372C2×#41—44no—
373C22×Q8—21no—
374C22×D4—22no—
375C22×D4—21no—
376C22×D4—21no—
377C22×D4—111no—
378C22×D4—221no—
379C22×D4C22×D1112yes—
380C23×C4—22no—
381C23×C4—221no—
382C23×C4C22⋊D1111yescharacteristic
383C23×C4C22⋊D1111yescharacteristic
384C23×C4C22×D1111yescharacteristic
385C2×D8—224no—
386C2×D8—224no—
387C2×D8—442no—
388C22×C8—112no—
389C22×C8—112no—
390C4⋊Q8—22no—
391C4⋊Q8C22⋊D1114yescomplemented
392#127—22no—
393#127C22⋊D1114yescomplemented
394#124—28no—
395#121—28no—
396#121—24no—
397#121—24no—
398#121—222no—
399#121—222no—
400C4×D4—28no—
401C4×D4—24no—
402C4×D4—24no—
403C4×D4—222no—
404C4×D4—222no—
405C4×D4—444no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4C22×D1112yes—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—221no—
422C2×C42C22⋊D1111yescharacteristic
423C2×C42C22⋊D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426#107—224no—
427C4⋊C8—222no—
428C4⋊C8—222no—
429#102—224no—
430#102—224no—
431#102—224no—
432#102—442no—
433C22⋊C8—442no—
434#95—221no—
435#95—221no—
436#95—221no—
437C2×C11—42no—
438C2×C11—84no—
439C2×C11#240711yescharacteristic
440C2×C11C2×#44711yescharacteristic
441C2×C11#300511yescharacteristic
442C2×C11#310011yescharacteristic
443C2×C11#311511yescharacteristic
444C2×C11#324511yescharacteristic
445C2×C11#325111yescharacteristic
446D11—82no—
447C24—22no—
448C24—221no—
449C24C2×C22⋊D1111yescharacteristic
450#41—432no—
451C2×Q8—24no—
452C2×Q8—42no—
453C2×Q8—42no—
454C2×D4—28no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—112no—
469C2×D4—224no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—442no—
476C2×D4—442no—
477C2×D4C2×C22⋊D1114yes—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—28no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4#432314yescomplemented
500C22×C4C2×C22⋊D1111yescharacteristic
501C22×C4C2×C22⋊D1111yescharacteristic
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C23×D1111yescharacteristic
506D8—448no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—222no—
510C2×C8—222no—
511C2×C8—222no—
512C2×C8—222no—
513C4⋊C4—24no—
514C4⋊C4—22no—
515C4⋊C4—112no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—442no—
522C4⋊C4C2×C22⋊D1114yes—
523C22⋊C4—28no—
524C22⋊C4—28no—
525C22⋊C4—224no—
526C22⋊C4—442no—
527C22⋊C4—442no—
528C22⋊C4—442no—
529C22⋊C4—442no—
530C42—22no—
531C42—22no—
532C42—21no—
533C42—21no—
534C42—442no—
535C42C2×C22⋊D1112yes—
536C42C2×C22⋊D1112yes—
537C11#2415011yescharacteristic, complemented, Sylow
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—24no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—222no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23C2×#432312yes—
559C23C22×C22⋊D1111yescharacteristic
560Q8—48no—
561D4—24no—
562D4—24no—
563D4—48no—
564D4—416no—
565D4—48no—
566D4—42no—
567D4—42no—
568D4—222no—
569D4—222no—
570D4—448no—
571D4—441no—
572D4—441no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—28no—
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—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—222no—
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—884no—
603C2×C4C2×#432312yes—
604C2×C4C2×#432312yes—
605C2×C4#6698512yes—
606C2×C4#6700612yes—
607C2×C4#6700612yes—
608C2×C4#41×D1111yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704211yescharacteristic
611C2×C4#6704311yescharacteristic
612C2×C4C22×C22⋊D1111yescharacteristic
613C2×C4C22×C22⋊D1111yescharacteristic
614C8—442no—
615C8—442no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—44no—
624C22—44no—
625C22—44no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—442no—
631C22—442no—
632C22—442no—
633C22—881no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22C22×#432311yescharacteristic
638C22C2×#6698511yescharacteristic
639C22#1062335311yescharacteristic
640C22#1062335311yescharacteristic
641C22#1062335911yescharacteristic
642C22#1062336411yescharacteristic
643C22C2×#6700611yescharacteristic
644C4—22no—
645C4—22no—
646C4—44no—
647C4—41no—
648C4—41no—
649C4—442no—
650C4—881no—
651C4—881no—
652C4#1062283014yes—
653C4#1062335511yescharacteristic
654C4#1062336011yescharacteristic
655C4#1062336211yescharacteristic
656C4#1062336511yescharacteristic
657C2—42no—
658C2—84no—
659C2—882no—
660C2#1307195511yescharacteristic
661C2C2×#1062283011yescharacteristic
662C2#1307785811yescharacteristic
663C2#1307861211yescharacteristic
664C2#1307876111yescharacteristic
665C2#1307992311yescharacteristic
666C2#1307997211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#532C2
socleC23×C11C22×D4
hypercenterC2×#532D11
hypocenterC11#24150
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×#10622700C2semidirect
2. C2×#10622685C2semidirect
3. C4×#66983C2semidirect
4. #13069795C2semidirect
5. #13069612C2semidirect
6. #13069569C2semidirect
7. #13069544C2semidirect
8. #13068964C2semidirect
9. #13068863C2semidirect
10. #13068596C2semidirect
11. C2×C11×#532C2semidirect
63. C11×C4⋊Q8D4semidirect
65. C11×#127D4semidirect
152. C22×C4×C11D8semidirect
170. C2×D44#41semidirect
196. C4⋊Dic11#41semidirect
205. C2×#532D11semidirect
391. C4⋊Q8C22⋊D11semidirect
393. #127C22⋊D11semidirect
499. C22×C4#4323semidirect
537. C11#24150semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×#106226852
C4×#669832
#130697952
#130696122
#130695692
#130695442
#130689642
#130688632
#130685962
C2×C11×#5322
#2415011