Finite Group Databasebeta

← #14826971

Subgroups — #14826971

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073204C211yesmaximal, characteristic
2#13071673C211yesmaximal, characteristic, complemented
3#13070159C211yesmaximal, characteristic, complemented
4#13069860C211yesmaximal, characteristic, complemented
5#13069697C211yesmaximal, characteristic
6#13069471C211yesmaximal, characteristic
7#13069248C211yesmaximal, characteristic, complemented
8#13069246C211yesmaximal, characteristic
9#13069192C211yesmaximal, characteristic, complemented
10#13069170C211yesmaximal, characteristic, complemented
11#13068974C211yesmaximal, characteristic
12#13068973C211yesmaximal, characteristic
13#13068622C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#2055C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×#66997C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×#66932—21no—
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622834C2211yescharacteristic
30#10622834C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42#10622566—21no—
43#10622564—21no—
44#10622561—21no—
45#10622548C2211yescharacteristic
46C4×Dic11⋊C4C2211yescharacteristic
47#10622268—21no—
48#10622265—21no—
49#10622262—21no—
50#10622260—21no—
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C2×C11×SD16—22no—
63C2×C11×SD16—41no—
64C2×C11×SD16—41no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76Q8×Dic11—22no—
77Q8×Dic11—41no—
78#66997—22no—
79#66997—22no—
80C2×#4324—22no—
81C2×#4324—22no—
82C2×#4324—41no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4D411yescharacteristic
94C2×Dic11⋊C4D411yescharacteristic
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66932—44no—
104C4×Dic22—22no—
105C4×Dic22—41no—
106C11×C4⋊C8—41no—
107C11×#103—22no—
108C11×#102—41no—
109C11×#95—21no—
110C11×#95—21no—
111#66899—22no—
112#66899—41no—
113#66896—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66880—41no—
122#66880—41no—
123C8×Dic11—41no—
124#66874—22no—
125#66872—22no—
126#66872—41no—
127#27066—111nomaximal, Sylow
128C24×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11#4112yes—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C22×C4×C11—21no—
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×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22#4112yes—
161C11×SD16—44no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C22⋊C4—42no—
173C11×C22⋊C4—42no—
174C42×C11—21no—
175C42×C11—21no—
176C22⋊Dic11—42no—
177C22⋊Dic11—42no—
178C22⋊Dic11—81no—
179C22⋊Dic11—81no—
180#4324—44no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—42no—
187C4⋊Dic11—42no—
188C4⋊Dic11—81no—
189C4⋊Dic11#4112yes—
190Dic11⋊C4—24no—
191Dic11⋊C4—24no—
192Dic11⋊C4—41no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4SD1614yescomplemented
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8#4112yes—
210#2512—111no—
211#2365—111no—
212#2096—111no—
213#2055D1111yescharacteristic
214#2043—111no—
215#2013—111no—
216#1968—111no—
217#1927—111no—
218#1926—111no—
219#1919—111no—
220#1916—111no—
221#1880—111no—
222#1880—111no—
223#1803—111no—
224C4×#103—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11C22×D411yescharacteristic
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—41no—
236Q8×C11—41no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
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—41no—
255C2×C4×C11C2×SD1612yes—
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
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—41no—
283C2×Dic11—41no—
284C2×Dic11C2×SD1612yes—
285C2×Dic11C2×SD1612yes—
286Dic22—22no—
287Dic22—22no—
288Dic22—41no—
289Dic22—41no—
290C8×C11—41no—
291C8×C11—41no—
292C11⋊C8—22no—
293C11⋊C8—41no—
294C22×SD16—111no—
295C22×SD16C2×D1111yescharacteristic
296C2×C4⋊Q8—111no—
297C2×#126—221no—
298C2×C4×Q8—111no—
299C2×C4×Q8—111no—
300C2×#106—111no—
301C2×#106—111no—
302C2×C4⋊C8C2×D1111yescharacteristic
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103C2×D1111yescharacteristic
309C2×#102—111no—
310C2×#102C2×D1111yescharacteristic
311C2×C4×C8—111no—
312#397—221no—
313#396—221no—
314#391—111no—
315#391C2×D1111yescharacteristic
316#390—111no—
317#390—111no—
318#390C2×D1111yescharacteristic
319#389—111no—
320#389—221no—
321#388—221no—
322#387—221no—
323#387—221no—
324#384—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—221no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340C2×D1111yescharacteristic
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11#52511yescharacteristic
345C22×C11#54611yescharacteristic
346C22×C11#55011yescharacteristic
347C22×C11C22×SD1611yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57711yescharacteristic
350C22×C11#57811yescharacteristic
351C4×C11—22no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11#52911yescharacteristic
357C4×C11#53811yescharacteristic
358C4×C11#55111yescharacteristic
359C4×C11#55311yescharacteristic
360Dic11—22no—
361Dic11—22no—
362Dic11—41no—
363Dic11—42no—
364Dic11—41no—
365Dic11—42no—
366Dic11—81no—
367Dic11—81no—
368C22×Q8—111no—
369C22×Q8C22×D1111yescharacteristic
370C22×D4C22×D1111yescharacteristic
371C2×SD16—22no—
372C2×SD16—41no—
373C2×SD16—41no—
374C2×SD16—222no—
375C2×SD16—222no—
376C2×SD16—441no—
377C22×C8—111no—
378C22×C8—111no—
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381C4⋊Q8—222no—
382C4⋊Q8—222no—
383#126—444no—
384C4×Q8—222no—
385C4×Q8—222no—
386C4×Q8—441no—
387C4×Q8—441no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
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×C42—221no—
413C2×C42—221no—
414C2×C42C22×D1111yescharacteristic
415#106—222no—
416#106—441no—
417C4⋊C8—41no—
418#103—22no—
419#103—222no—
420#103—222no—
421#103—441no—
422#103—441no—
423#103—441no—
424#102—41no—
425#102—222no—
426C4×C8—441no—
427#95—21no—
428#95—21no—
429#95—111no—
430#95—111no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436C2×C11—161no—
437C2×C11#246711yescharacteristic
438C2×C11#310311yescharacteristic
439C2×C11#312111yescharacteristic
440C2×C11#329811yescharacteristic
441C2×C11#330711yescharacteristic
442C2×C11#339211yescharacteristic
443C2×C11#340211yescharacteristic
444C24—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—112no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8#434112yes—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C22×C4—21no—
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×C4D4×D1111yescharacteristic
475C22×C4D4×D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477SD16—44no—
478SD16—444no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—112no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—114no—
496C4⋊C4—112no—
497C4⋊C4—224no—
498C4⋊C4—224no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—441no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—442no—
509C4⋊C4—881no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—442no—
513C22⋊C4—442no—
514C22⋊C4—881no—
515C22⋊C4—881no—
516C42—21no—
517C42—21no—
518C42—221no—
519C42—221no—
520C42—221no—
521C42—221no—
522C42—442no—
523C42—442no—
524C42—442no—
525C42—442no—
526C11#2706611yescharacteristic, complemented, Sylow
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C2×D4×D1111yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—41no—
538Q8—41no—
539Q8—222no—
540Q8—222no—
541Q8—441no—
542Q8—441no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—112no—
562C2×C4—112no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—222no—
573C2×C4—221no—
574C2×C4—222no—
575C2×C4—441no—
576C2×C4—441no—
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×C4SD16×D1112yes—
586C2×C4C2×#434111yescharacteristic
587C2×C4#6703711yescharacteristic
588C2×C4#6703711yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C2×C4#41×D1111yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C8—41no—
593C8—41no—
594C8—222no—
595C8—441no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22#1062313011yescharacteristic
604C22#1062313711yescharacteristic
605C22#1062314111yescharacteristic
606C22C2×SD16×D1111yescharacteristic
607C22#1062330211yescharacteristic
608C22#1062330411yescharacteristic
609C22#1062330911yescharacteristic
610C4—22no—
611C4—41no—
612C4—42no—
613C4—81no—
614C4—81no—
615C4—222no—
616C4—222no—
617C4—441no—
618C4—442no—
619C4—442no—
620C4—441no—
621C4—881no—
622C4—881no—
623C4#1062312411yescharacteristic
624C4#1062318011yescharacteristic
625C4#1062319211yescharacteristic
626C4#1062321011yescharacteristic
627C2—161no—
628C2#1307266811yescharacteristic
629C2#1307864611yescharacteristic
630C2#1307884411yescharacteristic
631C2#1308047611yescharacteristic
632C2#1308058711yescharacteristic
633C2#1308159211yescharacteristic
634C2#1308169411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2055C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2055D11
hypocenterC11#27066
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
2. #13071673C2semidirect
3. #13070159C2semidirect
4. #13069860C2semidirect
7. #13069248C2semidirect
9. #13069192C2semidirect
10. #13069170C2semidirect
13. #13068622C2semidirect
14. #103×Dic11C2semidirect
195. Dic11⋊C4SD16semidirect
526. C11#27066semidirect

Maximal subgroups

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

subgroupindex
#130732042
#130716732
#130701592
#130698602
#130696972
#130694712
#130692482
#130692462
#130691922
#130691702
#130689742
#130689732
#130686222
#103×Dic112
C11×#20552
#2706611