Finite Group Databasebeta

← #25164748

Subgroups — #25164748

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138930C211yesmaximal, characteristic, complemented
2#19137629C211yesmaximal, characteristic
3#19135911C211yesmaximal, characteristic, complemented
4#19135782C211yesmaximal, characteristic
5#19135739C211yesmaximal, characteristic, complemented
6#19135599C211yesmaximal, characteristic
7#19135551C211yesmaximal, characteristic, complemented
8#19135271C211yesmaximal, characteristic, complemented
9#19135227C211yesmaximal, characteristic, complemented
10#19135201C211yesmaximal, characteristic, complemented
11#19135180C211yesmaximal, characteristic, complemented
12#19134929C211yesmaximal, characteristic, complemented
13#19134906C211yesmaximal, characteristic, complemented
14#19134688C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29#14582839—21no—
30#14582826—21no—
31#14582805C2211yescharacteristic
32#14582804C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582799—21no—
35#14582797C2211yescharacteristic
36#14582790—21no—
37#14582787—21no—
38#14582778—21no—
39#14582765—21no—
40#14582756C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×(C2×D43)⋊C4C2211yescharacteristic
43C4×C22⋊Dic43—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43C2311yescharacteristic
62C2×#10621883—22no—
63C2×#10621883—41no—
64C2×#10621883—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063316—22no—
68#13063316—41no—
69#13063305—22no—
70#13063305—41no—
71#13063296—22no—
72#13063296—22no—
73#13063283—22no—
74#13063283—41no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4D411yescharacteristic
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93#13063256—22no—
94Dic43⋊C8—41no—
95#13063250—22no—
96#13063250—41no—
97#13063248—22no—
98#13063246—41no—
99(C2×D43)⋊C8—41no—
100(C2×D43)⋊C8—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C4×D4×C43—22no—
115C4×D4×C43—41no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#102×C43—22no—
123#102×C43—22no—
124C4×C8×C43—41no—
125#95×C43—21no—
126C24×C43—21no—
127C23×D43C2×D411yescharacteristic
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43#4112yes—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43—81no—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C2×C22⋊D43—24no—
144C2×C22⋊D43—81no—
145C2×C22⋊D43—81no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43#4112yes—
176C4⋊C4×C43#4112yes—
177C22⋊C4×C43—42no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—42no—
181C22⋊Dic43—24no—
182C22⋊Dic43—42no—
183C22⋊Dic43—81no—
184#10621883—44no—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—42no—
196C4⋊Dic43—42no—
197C4⋊Dic43#4112yes—
198Dic43⋊C4—42no—
199Dic43⋊C4—81no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—42no—
203C4×Dic43—81no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C23×C43—22no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43C22×D411yescharacteristic
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225D4×C43—22no—
226D4×C43—22no—
227D4×C43—41no—
228D4×C43—41no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—84no—
244C2×C4×C43#13512yes—
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C22⋊D43—84no—
252C2×Dic43—22no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—41no—
277Dic86—41no—
278Dic86—41no—
279Dic86—41no—
280Dic86—41no—
281C8×C43—41no—
282C8×C43—41no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285#26728—431nomaximal, Sylow
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43#52511yescharacteristic
294C22×C43#54611yescharacteristic
295C22×C43#54611yescharacteristic
296C22×C43C2×#13511yescharacteristic
297C22×C43#57511yescharacteristic
298C22×C43#57711yescharacteristic
299C22×C43#57711yescharacteristic
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—41no—
306C2×D43—41no—
307C4×C43—22no—
308C4×C43—42no—
309C4×C43—42no—
310C4×C43—41no—
311C4×C43—81no—
312C4×C43#52911yescharacteristic
313C4×C43#53811yescharacteristic
314C4×C43#55511yescharacteristic
315C4×C43#55911yescharacteristic
316Dic43—42no—
317Dic43—41no—
318Dic43—41no—
319Dic43—41no—
320Dic43—81no—
321Dic43—81no—
322Dic43—81no—
323#2489—431no—
324#2363—431no—
325#2055—431no—
326#2034—431no—
327#2025—431no—
328#2000—431no—
329#1989—431no—
330#1933—431no—
331#1927—431no—
332#1923—431no—
333#1920—431no—
334#1877—431no—
335#1873—431no—
336#1825—431no—
337C4×#102D4311yescharacteristic, complemented
338C2×C43—82no—
339C2×C43#245911yescharacteristic
340C2×C43#310211yescharacteristic
341C2×C43#312311yescharacteristic
342C2×C43#329611yescharacteristic
343C2×C43#330311yescharacteristic
344C2×C43#331711yescharacteristic
345C2×C43#332611yescharacteristic
346D43—81no—
347C22×SD16—431no—
348C2×#125—431no—
349C2×C22⋊Q8—431no—
350C2×#121—431no—
351C2×C4×D4C2×D4311yescharacteristic
352C2×#117—431no—
353C2×#106—431no—
354C2×C4⋊C8—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#102—431no—
359C2×#102C2×D4311yescharacteristic
360C2×#102C2×D4311yescharacteristic
361C2×C22⋊C8—431no—
362C2×C22⋊C8—431no—
363C2×C4×C8C2×D4311yescharacteristic
364#400—861no—
365#397—861no—
366#391—431no—
367#391—431no—
368#390—431no—
369#390—861no—
370#389—431no—
371#388—861no—
372#388—861no—
373#386—861no—
374#382—861no—
375#380—431no—
376C4×C4⋊C4—431no—
377C4×C4⋊C4C2×D4311yescharacteristic
378C4×C22⋊C4—431no—
379C4×C22⋊C4—861no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#340C2×D4311yescharacteristic
388#336—431no—
389#336—431no—
390C43#2672811yescharacteristic, complemented, Sylow
391C22×Q8—431no—
392C22×D4—861no—
393C22×D4C22×D4311yescharacteristic
394C23×C4—21no—
395C23×C4—431no—
396C2×SD16—862no—
397C2×SD16—1721no—
398C2×SD16—1721no—
399C22×C8—431no—
400C22×C8—431no—
401C22×C8C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403#125—862no—
404#125—1721no—
405C22⋊Q8—862no—
406C22⋊Q8—1721no—
407#121—862no—
408#121—862no—
409C4×D4—22no—
410C4×D4—41no—
411#117—862no—
412#117—1721no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—431no—
425C2×C22⋊C4—431no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—21no—
433C2×C42—431no—
434C2×C42—861no—
435C2×C42—861no—
436C2×C42C22×D4311yescharacteristic
437#106—862no—
438C4⋊C8—1721no—
439#103—862no—
440#103—862no—
441#103—1721no—
442#102—22no—
443#102—22no—
444#102—1721no—
445C22⋊C8—1721no—
446C22⋊C8—1721no—
447C4×C8—41no—
448#95—21no—
449#95—431no—
450#95—431no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458C24—21no—
459C24—431no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—864no—
472C2×D4—3441no—
473C2×D4—3441no—
474C2×D4#1062189812yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—81no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4D4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497SD16—1724no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—432no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—3441no—
521C4⋊C4—1722no—
522C4⋊C4—1722no—
523C4⋊C4—1722no—
524C4⋊C4#1062189812yes—
525C4⋊C4#1062189812yes—
526C22⋊C4—42no—
527C22⋊C4—864no—
528C22⋊C4—862no—
529C22⋊C4—3441no—
530C22⋊C4—1721no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C42—21no—
536C42—21no—
537C42—42no—
538C42—861no—
539C42—861no—
540C42—3441no—
541C42—1722no—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—861no—
550C23—861no—
551C23—861no—
552C23—861no—
553C23—861no—
554C23—861no—
555C23—861no—
556C23C2×D4×D4311yescharacteristic
557Q8—1721no—
558Q8—1721no—
559Q8—1721no—
560Q8—1721no—
561D4—22no—
562D4—22no—
563D4—41no—
564D4—41no—
565D4—3444no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4—861no—
582C2×C4—862no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4#1306334412yes—
607C2×C4#41×D4311yescharacteristic
608C2×C4C2×#1062189811yescharacteristic
609C2×C4C2×#1062189811yescharacteristic
610C2×C4C2×#1062189811yescharacteristic
611C2×C4#1306337011yescharacteristic
612C2×C4#1306337111yescharacteristic
613C8—41no—
614C8—41no—
615C8—1721no—
616C8—1721no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—1721no—
625C22—1721no—
626C22—1721no—
627C22—1721no—
628C22—1721no—
629C22—1721no—
630C22—1721no—
631C22#1458340811yescharacteristic
632C22#1458353911yescharacteristic
633C22#1458354511yescharacteristic
634C22C2×#1306334411yescharacteristic
635C22#1458369611yescharacteristic
636C22#1458370511yescharacteristic
637C22#1458370611yescharacteristic
638C4—22no—
639C4—42no—
640C4—42no—
641C4—41no—
642C4—81no—
643C4—3441no—
644C4—3441no—
645C4—3441no—
646C4—1721no—
647C4—1721no—
648C4—1722no—
649C4—1721no—
650C4#1458343311yescharacteristic
651C4#1458348211yescharacteristic
652C4#1458361211yescharacteristic
653C4#1458363211yescharacteristic
654C2—82no—
655C2—3441no—
656C2#1913853211yescharacteristic
657C2#1914460911yescharacteristic
658C2#1914484411yescharacteristic
659C2#1914642611yescharacteristic
660C2#1914652511yescharacteristic
661C2#1914671711yescharacteristic
662C2#1914685311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC4×#102D43
hypocenterC43#26728
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #19138930C2semidirect
3. #19135911C2semidirect
5. #19135739C2semidirect
7. #19135551C2semidirect
8. #19135271C2semidirect
9. #19135227C2semidirect
10. #19135201C2semidirect
11. #19135180C2semidirect
12. #19134929C2semidirect
13. #19134906C2semidirect
14. #19134688C2semidirect
15. C4×#102×C43C2semidirect
337. C4×#102D43semidirect
390. C43#26728semidirect

Maximal subgroups

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

subgroupindex
#191389302
#191376292
#191359112
#191357822
#191357392
#191355992
#191355512
#191352712
#191352272
#191352012
#191351802
#191349292
#191349062
#191346882
C4×#102×C432
#2672843