Finite Group Databasebeta

← #25200309

Subgroups — #25200309

Order 11008.

742 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140385C211yesmaximal, characteristic
2#19137273C211yesmaximal, characteristic, complemented
3#19136031C211yesmaximal, characteristic, complemented
4#19135792C211yesmaximal, characteristic, complemented
5#19135598C211yesmaximal, characteristic
6#19135450C211yesmaximal, characteristic, complemented
7#19135321C211yesmaximal, characteristic, complemented
8#19135289C211yesmaximal, characteristic, complemented
9#19135283C211yesmaximal, characteristic, complemented
10#19135224C211yesmaximal, characteristic, complemented
11#19135178C211yesmaximal, characteristic, complemented
12#19134947C211yesmaximal, characteristic, complemented
13#19134860C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#2034C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582835—21no—
30#14582824—21no—
31#14582813—21no—
32#14582813—21no—
33#14582804C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582796—21no—
37#14582795C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582793—21no—
41#14582787—21no—
42#14582786—21no—
43#14582759C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C2×#10621883—22no—
61C2×#10621883—22no—
62C2×#10621883—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063304—22no—
66#13063304—22no—
67#13063290—41no—
68#13063290—41no—
69#13063284—41no—
70#13063284—41no—
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43D411yescharacteristic
88C2×C22⋊Dic43D411yescharacteristic
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063257—22no—
94#13063256—22no—
95#13063250—22no—
96#13063250—22no—
97#13063248—41no—
98#13063246—22no—
99C22⋊(C43⋊C8)—22no—
100#13063235—41no—
101C8×Dic43—41no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×D4×C43—21no—
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114#121×C43—41no—
115#121×C43—41no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121#106×C43—41no—
122#102×C43—22no—
123#102×C43—41no—
124C22⋊C8×C43—22no—
125#95×C43—21no—
126C24×C43—21no—
127C24×C43C2×D411yescharacteristic
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—42no—
135C2×D4×C43—81no—
136C2×D4×C43—81no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86#4112yes—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43#4112yes—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C22⋊C4×C43—42no—
175C22⋊C4×C43—81no—
176C22⋊Dic43—24no—
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179C22⋊Dic43—81no—
180C22⋊Dic43—81no—
181C22⋊Dic43—81no—
182C22⋊Dic43—81no—
183C22⋊Dic43—81no—
184#10621883—44no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43—41no—
192C4⋊Dic43#4112yes—
193Dic43⋊C4—24no—
194Dic43⋊C4—42no—
195Dic43⋊C4—81no—
196Dic43⋊C4—81no—
197Dic43⋊C4—81no—
198C4×Dic43—21no—
199C4×Dic43—21no—
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#4112yes—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43C22×D411yescharacteristic
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—84no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
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—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C2×Dic43—22no—
253C2×Dic43—22no—
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—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276Dic86—22no—
277Dic86—22no—
278Dic86—41no—
279Dic86—41no—
280C8×C43—22no—
281C8×C43—41no—
282C43⋊C8—22no—
283C43⋊C8—41no—
284#29474—431nomaximal, Sylow
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43#52511yescharacteristic
300C22×C43#53211yescharacteristic
301C22×C43#53411yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57711yescharacteristic
304C22×C43#57711yescharacteristic
305C22×C43#57711yescharacteristic
306C4×C43—41no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43#55111yescharacteristic
311C4×C43#55311yescharacteristic
312C4×C43#55311yescharacteristic
313C4×C43#55911yescharacteristic
314Dic43—42no—
315Dic43—42no—
316Dic43—41no—
317Dic43—41no—
318Dic43—41no—
319Dic43—41no—
320Dic43—81no—
321Dic43—81no—
322#2624—431no—
323#2323—431no—
324#2077—431no—
325#2035—431no—
326#2034D4311yescharacteristic
327#2000—431no—
328#1968—431no—
329#1941—431no—
330#1936—431no—
331#1935—431no—
332#1926—431no—
333#1920—431no—
334#1880—431no—
335#1865—431no—
336#1750—431no—
337C2×C43—81no—
338C2×C43—161no—
339C2×C43#260211yescharacteristic
340C2×C43#312511yescharacteristic
341C2×C43#312611yescharacteristic
342C2×C43#317311yescharacteristic
343C2×C43#317411yescharacteristic
344C2×C43#320011yescharacteristic
345C2×C43#320411yescharacteristic
346C22×SD16—431no—
347C2×C22⋊Q8—431no—
348C2×#121C2×D4311yescharacteristic
349C2×C4×Q8—431no—
350C2×#117—431no—
351C2×#106—431no—
352C2×#106—431no—
353C2×#106C2×D4311yescharacteristic
354C2×#103—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#102—431no—
358C2×#102C2×D4311yescharacteristic
359C2×#102C2×D4311yescharacteristic
360C2×C22⋊C8—431no—
361C2×C22⋊C8C2×D4311yescharacteristic
362C2×#97—431no—
363C2×C4×C8—431no—
364#399—861no—
365#397—861no—
366#394—861no—
367#394—861no—
368#391—431no—
369#390—431no—
370#390—431no—
371#389—431no—
372#389—431no—
373#389—431no—
374#389—861no—
375#388—861no—
376#388—861no—
377#387—861no—
378#380—431no—
379#380C2×D4311yescharacteristic
380C4×C4⋊C4—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#336—431no—
388#336—431no—
389C43#2947411yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×D4—21no—
392C22×D4C22×D4311yescharacteristic
393C23×C4C22×D4311yescharacteristic
394C2×SD16—862no—
395C2×SD16—862no—
396C2×SD16—1721no—
397C22×C8—431no—
398C22×C8—431no—
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401C22⋊Q8—862no—
402C22⋊Q8—862no—
403#121—41no—
404#121—41no—
405C4×Q8—1721no—
406C4×Q8—1721no—
407#117—1721no—
408#117—1721no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
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—431no—
433C2×C42—431no—
434C2×C42—861no—
435C2×C42—861no—
436#106—41no—
437#106—862no—
438#106—862no—
439#103—862no—
440#103—862no—
441#103—1721no—
442#102—22no—
443#102—41no—
444#102—862no—
445C22⋊C8—22no—
446C22⋊C8—862no—
447#97—1721no—
448C4×C8—1721no—
449#95—21no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457C24—21no—
458C24D4×D4311yescharacteristic
459C2×Q8—432no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—42no—
472C2×D4—81no—
473C2×D4—81no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4D4×D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493SD16—1724no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—432no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8#1062190012yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—432no—
513C4⋊C4—864no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—3441no—
520C4⋊C4—3441no—
521C4⋊C4—3441no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4—1722no—
525C22⋊C4—42no—
526C22⋊C4—81no—
527C22⋊C4—864no—
528C22⋊C4—3441no—
529C22⋊C4—3441no—
530C22⋊C4—3441no—
531C22⋊C4—3441no—
532C22⋊C4—3441no—
533C22⋊C4—1721no—
534C22⋊C4—1721no—
535C42—861no—
536C42—861no—
537C42—861no—
538C42—861no—
539C42—3441no—
540C42—1722no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C2×D4×D4311yescharacteristic
556Q8—862no—
557Q8—862no—
558Q8—1721no—
559Q8—1721no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—84no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—862no—
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—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
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#41×D4311yescharacteristic
606C2×C4#41×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4C2×#1062190011yescharacteristic
609C2×C4#1306337011yescharacteristic
610C2×C4#1306337011yescharacteristic
611C8—22no—
612C8—41no—
613C8—862no—
614C8—1721no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22#1458340711yescharacteristic
630C22#1458344411yescharacteristic
631C22#1458345911yescharacteristic
632C22#1458370511yescharacteristic
633C22#1458370611yescharacteristic
634C22#1458370911yescharacteristic
635C22#1458370911yescharacteristic
636C4—41no—
637C4—81no—
638C4—81no—
639C4—81no—
640C4—3441no—
641C4—3441no—
642C4—1721no—
643C4—1721no—
644C4—1722no—
645C4—1722no—
646C4—1721no—
647C4—1721no—
648C4#1458357911yescharacteristic
649C4#1458359211yescharacteristic
650C4#1458359611yescharacteristic
651C4#1458363311yescharacteristic
652C2—81no—
653C2—161no—
654C2#1914021011yescharacteristic
655C2#1914487511yescharacteristic
656C2#1914488211yescharacteristic
657C2#1914520711yescharacteristic
658C2#1914521611yescharacteristic
659C2#1914546411yescharacteristic
660C2#1914550411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2034C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2034D43
hypocenterC43#29474
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
2. #19137273C2semidirect
3. #19136031C2semidirect
4. #19135792C2semidirect
6. #19135450C2semidirect
7. #19135321C2semidirect
8. #19135289C2semidirect
9. #19135283C2semidirect
10. #19135224C2semidirect
11. #19135178C2semidirect
12. #19134947C2semidirect
13. #19134860C2semidirect
14. #19134363C2semidirect
389. C43#29474semidirect

Maximal subgroups

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

subgroupindex
#191403852
#191372732
#191360312
#191357922
#191355982
#191354502
#191353212
#191352892
#191352832
#191352242
#191351782
#191349472
#191348602
#191343632
C43×#20342
#2947443