Finite Group Databasebeta

← #14827008

Subgroups — #14827008

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#13073216C211yesmaximal, characteristic
2#13071676C211yesmaximal, characteristic, complemented
3#13070162C211yesmaximal, characteristic, complemented
4#13069930C211yesmaximal, characteristic
5#13069699C211yesmaximal, characteristic
6#13069467C211yesmaximal, characteristic
7#13069259C211yesmaximal, characteristic, complemented
8#13069237C211yesmaximal, characteristic
9#13069198C211yesmaximal, characteristic, complemented
10#13069174C211yesmaximal, characteristic, complemented
11#13068969C211yesmaximal, characteristic
12#13068969C211yesmaximal, characteristic
13#13068629C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#2043C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#389C2211yescharacteristic
26#10622843C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622606—21no—
36#10622603—21no—
37#10622601C2211yescharacteristic
38#10622601C2211yescharacteristic
39#10622598—21no—
40#10622594—21no—
41#10622594—21no—
42#10622590C2211yescharacteristic
43C4⋊C4×Dic11—21no—
44C4⋊C4×Dic11C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46#10622552C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49#10622287—21no—
50#10622283—21no—
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72Q8×Dic11—22no—
73Q8×Dic11—22no—
74Q8×Dic11—41no—
75Q8×Dic11—41no—
76C2×#4325—22no—
77C2×#4325—22no—
78C2×#4325—22no—
79C2×#4325—41no—
80C2×#4325—41no—
81C2×#4325—41no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
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
103C11×#103—22no—
104C11×#103—22no—
105C11×#103—41no—
106C11×#103—41no—
107C11×#95—21no—
108#66899—22no—
109#66899—41no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120#66885—22no—
121#66885—41no—
122#66882—41no—
123Dic11⋊C8—41no—
124C8×Dic11—41no—
125#66872—22no—
126#27069—111nomaximal, Sylow
127C23×D11—21no—
128C2×Q8×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—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11#4112yes—
139C2×Q8×C11#4112yes—
140C22×C4×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×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—81no—
173C42×C11—21no—
174C42×C11—21no—
175#4325—44no—
176#4325—44no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—81no—
180(C2×D11)⋊C4—81no—
181(C2×D11)⋊C4—81no—
182(C2×D11)⋊C4—81no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—42no—
191C4⋊Dic11—42no—
192C4⋊Dic11#4112yes—
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#4112yes—
207#2513—111no—
208#2365—111no—
209#2097—111no—
210#2055—111no—
211#2043D1111yescharacteristic, complemented
212#2013—111no—
213#1968—111no—
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×C11C22×D411yescharacteristic
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
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—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11#13512yes—
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—21no—
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#13712yes—
283D44—41no—
284D44—41no—
285D44—41no—
286D44—41no—
287C8×C11—41no—
288C8×C11—41no—
289C11⋊C8—22no—
290C11⋊C8—41no—
291C22×SD16—111no—
292C22×SD16—111no—
293C2×C4⋊Q8C2×D1111yescharacteristic
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×#107—111no—
297C2×#106—111no—
298C2×C4⋊C8—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103C2×D1111yescharacteristic
302C2×#103C2×D1111yescharacteristic
303C2×#103C2×D1111yescharacteristic
304C2×#103C2×D1111yescharacteristic
305C2×#102—111no—
306C2×#102—111no—
307C2×C4×C8—111no—
308#397—221no—
309#397—221no—
310#391—111no—
311#391—111no—
312#390—111no—
313#390—111no—
314#390—111no—
315#389—221no—
316#389C2×D1111yescharacteristic
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#336C2×D1111yescharacteristic
334C22×C11#52511yescharacteristic
335C22×C11#54611yescharacteristic
336C22×C11#55011yescharacteristic
337C22×C11C2×#13511yescharacteristic
338C22×C11C2×#13711yescharacteristic
339C22×C11#57711yescharacteristic
340C22×C11#57711yescharacteristic
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C4×C11—22no—
349C4×C11—41no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11#52911yescharacteristic
355C4×C11#53811yescharacteristic
356C4×C11#55111yescharacteristic
357C4×C11#55311yescharacteristic
358Dic11—22no—
359Dic11—41no—
360Dic11—41no—
361Dic11—42no—
362Dic11—41no—
363Dic11—81no—
364Dic11—81no—
365C22×Q8C22×D1111yescharacteristic
366C22×Q8C22×D1111yescharacteristic
367C22×D4—111no—
368C2×SD16—222no—
369C2×SD16—222no—
370C2×SD16—222no—
371C2×SD16—441no—
372C2×SD16—441no—
373C2×SD16—441no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4×Q8—222no—
381C4×Q8—222no—
382C4×Q8—441no—
383C4×Q8—441no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
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—222no—
411C4⋊C8—441no—
412#103—22no—
413#103—22no—
414#103—41no—
415#103—41no—
416#103—222no—
417#103—441no—
418#102—222no—
419#102—441no—
420C4×C8—441no—
421#95—21no—
422#95—111no—
423#95—111no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432C2×C11#246711yescharacteristic
433C2×C11#310811yescharacteristic
434C2×C11#312611yescharacteristic
435C2×C11#330311yescharacteristic
436C2×C11#332011yescharacteristic
437C2×C11#339411yescharacteristic
438C2×C11#340011yescharacteristic
439D11—161no—
440C24—221no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8#434112yes—
452C2×Q8#434112yes—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4D4×D1111yescharacteristic
471C22×C4D4×D1111yescharacteristic
472C22×C4C23×D1111yescharacteristic
473SD16—444no—
474SD16—444no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—112no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C4⋊C4—24no—
488C4⋊C4—24no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—81no—
494C4⋊C4—112no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C22⋊C4—442no—
505C22⋊C4—442no—
506C22⋊C4—881no—
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—441no—
522C23—441no—
523C23—441no—
524C23—441no—
525C23—441no—
526C23—441no—
527C23—441no—
528C23C2×D4×D1111yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537D4—441no—
538D4—441no—
539D4—441no—
540D4—441no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—112no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—222no—
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#6697212yes—
580C2×C4C2×#434111yescharacteristic
581C2×C4C2×#434111yescharacteristic
582C2×C4#6703711yescharacteristic
583C2×C4#41×D1111yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#6704211yescharacteristic
586C8—41no—
587C8—41no—
588C8—222no—
589C8—441no—
590C22—881no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22—881no—
595C22—881no—
596C22—881no—
597C22#1062311711yescharacteristic
598C22#1062313011yescharacteristic
599C22#1062320711yescharacteristic
600C22#1062329311yescharacteristic
601C22C2×#6697211yescharacteristic
602C22D11×#13711yescharacteristic
603C22#1062330911yescharacteristic
604C4—22no—
605C4—42no—
606C4—42no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4—222no—
611C4—441no—
612C4—441no—
613C4—441no—
614C4—442no—
615C4—881no—
616C4—881no—
617C4#1062313211yescharacteristic
618C4#1062314811yescharacteristic
619C4#1062318011yescharacteristic
620C4#1062318911yescharacteristic
621C2—1761no—
622C2#1307266011yescharacteristic
623C2#1307869711yescharacteristic
624C2#1307890111yescharacteristic
625C2#1308054311yescharacteristic
626C2#1308078611yescharacteristic
627C2#1308161111yescharacteristic
628C2#1308166411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2043C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2043D11
hypocenterC11#27069
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
2. #13071676C2semidirect
3. #13070162C2semidirect
7. #13069259C2semidirect
9. #13069198C2semidirect
10. #13069174C2semidirect
13. #13068629C2semidirect
14. #103×Dic11C2semidirect
15. C11×#2043C2semidirect
211. #2043D11semidirect
520. C11#27069semidirect

Maximal subgroups

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

subgroupindex
#130732162
#130716762
#130701622
#130699302
#130696992
#130694672
#130692592
#130692372
#130691982
#130691742
#130689692
#130686292
#103×Dic112
C11×#20432
#2706911