Finite Group Databasebeta

← #14827021

Subgroups — #14827021

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073214C211yesmaximal, characteristic
2#13071673C211yesmaximal, characteristic, complemented
3#13070165C211yesmaximal, characteristic, complemented
4#13069932C211yesmaximal, characteristic
5#13069861C211yesmaximal, characteristic, complemented
6#13069697C211yesmaximal, characteristic
7#13069254C211yesmaximal, characteristic, complemented
8#13069239C211yesmaximal, characteristic
9#13069203C211yesmaximal, characteristic, complemented
10#13069173C211yesmaximal, characteristic, complemented
11#13068974C211yesmaximal, characteristic
12#13068973C211yesmaximal, characteristic
13#13068629C211yesmaximal, characteristic, complemented
14C4×#66880C211yesmaximal, characteristic, complemented
15C11×#1968C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×#66997C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622834C2211yescharacteristic
30#10622834C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622590C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622587C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622566—21no—
42#10622565—21no—
43#10622564—21no—
44#10622558—21no—
45C4×C4⋊Dic11C2211yescharacteristic
46C4×Dic11⋊C4C2211yescharacteristic
47#10622268—21no—
48#10622265—21no—
49#10622262—21no—
50#10622260—21no—
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C2×C11×SD16—22no—
63C2×C11×SD16—22no—
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—41no—
82C2×#4324—41no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4D411yescharacteristic
92C2×Dic11⋊C4D411yescharacteristic
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C4×Dic22—22no—
102C4×Dic22—41no—
103C11×#106—22no—
104C11×#103—41no—
105C11×#102—41no—
106C4×C8×C11—41no—
107C11×#95—21no—
108C11×#95—21no—
109#66899—22no—
110#66899—41no—
111#66896—22no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66880—22no—
122#66880—22no—
123Dic11⋊C8—41no—
124#66874—41no—
125#66871—41no—
126#27069—111nomaximal, Sylow
127C24×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11#4112yes—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22#4112yes—
160C11×SD16—44no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11#4112yes—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C22⋊C4—42no—
172C11×C22⋊C4—81no—
173C42×C11—21no—
174C42×C11—21no—
175C22⋊Dic11—42no—
176C22⋊Dic11—81no—
177C22⋊Dic11—81no—
178C22⋊Dic11—81no—
179#4324—44no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—42no—
186C4⋊Dic11—81no—
187C4⋊Dic11#4112yes—
188Dic11⋊C4—24no—
189Dic11⋊C4—24no—
190Dic11⋊C4—22no—
191Dic11⋊C4—22no—
192Dic11⋊C4—42no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207#2513—111no—
208#2365—111no—
209#2097—111no—
210#2055—111no—
211#2043—111no—
212#2013—111no—
213#1968D1111yescharacteristic
214#1928—111no—
215#1925—111no—
216#1920—111no—
217#1916—111no—
218#1880—111no—
219#1880—111no—
220#1805—111no—
221C4×#103—111no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11C22×D411yescharacteristic
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—41no—
233Q8×C11—41no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—41no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11#13712yes—
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—22no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—41no—
273C2×Dic11—41no—
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#13512yes—
283Dic22—22no—
284Dic22—22no—
285Dic22—41no—
286Dic22—41no—
287C8×C11—22no—
288C8×C11—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C22×SD16—111no—
292C22×SD16C2×D1111yescharacteristic
293C2×C4⋊Q8—111no—
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×#107—111no—
297C2×#106C2×D1111yescharacteristic
298C2×C4⋊C8—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103C2×D1111yescharacteristic
305C2×#102—111no—
306C2×#102C2×D1111yescharacteristic
307C2×C4×C8C2×D1111yescharacteristic
308#397—221no—
309#397—221no—
310#391—111no—
311#391C2×D1111yescharacteristic
312#390—111no—
313#390—111no—
314#390C2×D1111yescharacteristic
315#389—111no—
316#389—221no—
317#388—221no—
318#388—221no—
319#387—221no—
320#387—221no—
321#382—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—221no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#336—111no—
331#336—111no—
332#336—111no—
333#336—111no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11#52511yescharacteristic
342C22×C11#54611yescharacteristic
343C22×C11#55011yescharacteristic
344C22×C11C2×#13511yescharacteristic
345C22×C11C2×#13711yescharacteristic
346C22×C11#57711yescharacteristic
347C22×C11#57711yescharacteristic
348C4×C11—22no—
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11#52911yescharacteristic
354C4×C11#53811yescharacteristic
355C4×C11#55111yescharacteristic
356C4×C11#55311yescharacteristic
357Dic11—22no—
358Dic11—41no—
359Dic11—42no—
360Dic11—41no—
361Dic11—42no—
362Dic11—41no—
363Dic11—81no—
364Dic11—81no—
365C22×Q8—111no—
366C22×Q8C22×D1111yescharacteristic
367C22×D4C22×D1111yescharacteristic
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16—41no—
371C2×SD16—222no—
372C2×SD16—441no—
373C2×SD16—441no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378C4⋊Q8—222no—
379C4⋊Q8—222no—
380C4×Q8—222no—
381C4×Q8—222no—
382C4×Q8—441no—
383C4×Q8—441no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42C22×D1111yescharacteristic
409#107—441no—
410#106—22no—
411C4⋊C8—441no—
412#103—41no—
413#103—222no—
414#103—222no—
415#103—222no—
416#103—441no—
417#103—441no—
418#102—41no—
419#102—222no—
420C4×C8—41no—
421#95—21no—
422#95—21no—
423#95—111no—
424#95—111no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432C2×C11—161no—
433C2×C11#246711yescharacteristic
434C2×C11#310811yescharacteristic
435C2×C11#312611yescharacteristic
436C2×C11#330311yescharacteristic
437C2×C11#332011yescharacteristic
438C2×C11#339411yescharacteristic
439C2×C11#340011yescharacteristic
440C24—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—112no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8#433912yes—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4D4×D1111yescharacteristic
471C22×C4D4×D1111yescharacteristic
472C22×C4C23×D1111yescharacteristic
473SD16—44no—
474SD16—444no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8#434112yes—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—112no—
492C4⋊C4—222no—
493C4⋊C4—224no—
494C4⋊C4—224no—
495C4⋊C4—222no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—881no—
504C22⋊C4—42no—
505C22⋊C4—81no—
506C22⋊C4—442no—
507C22⋊C4—881no—
508C22⋊C4—881no—
509C22⋊C4—881no—
510C42—21no—
511C42—21no—
512C42—221no—
513C42—221no—
514C42—221no—
515C42—221no—
516C42—442no—
517C42—442no—
518C42—442no—
519C42—881no—
520C11#2706911yescharacteristic, complemented, Sylow
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C2×D4×D1111yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533Q8—222no—
534Q8—222no—
535Q8—441no—
536Q8—441no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—112no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—222no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—222no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4#6696812yes—
580C2×C4C2×#433911yescharacteristic
581C2×C4C2×#434111yescharacteristic
582C2×C4#6703711yescharacteristic
583C2×C4#6703711yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C8—22no—
587C8—41no—
588C8—441no—
589C8—441no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22#1062307811yescharacteristic
598C22#1062314111yescharacteristic
599C22#1062324911yescharacteristic
600C22C2×#6696811yescharacteristic
601C22#1062329311yescharacteristic
602C22D11×#13511yescharacteristic
603C22#1062330111yescharacteristic
604C4—22no—
605C4—42no—
606C4—41no—
607C4—81no—
608C4—81no—
609C4—222no—
610C4—442no—
611C4—441no—
612C4—441no—
613C4—441no—
614C4—442no—
615C4—881no—
616C4—881no—
617C4#1062302611yescharacteristic
618C4#1062307111yescharacteristic
619C4#1062314411yescharacteristic
620C4#1062321111yescharacteristic
621C2—161no—
622C2#1307267311yescharacteristic
623C2#1307869411yescharacteristic
624C2#1307890411yescharacteristic
625C2#1308053911yescharacteristic
626C2#1308079311yescharacteristic
627C2#1308160911yescharacteristic
628C2#1308167411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1968C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1968D11
hypocenterC11#27069
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
2. #13071673C2semidirect
3. #13070165C2semidirect
5. #13069861C2semidirect
7. #13069254C2semidirect
9. #13069203C2semidirect
10. #13069173C2semidirect
13. #13068629C2semidirect
14. C4×#66880C2semidirect
520. C11#27069semidirect

Maximal subgroups

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

subgroupindex
#130732142
#130716732
#130701652
#130699322
#130698612
#130696972
#130692542
#130692392
#130692032
#130691732
#130689742
#130689732
#130686292
C4×#668802
C11×#19682
#2706911