Finite Group Databasebeta

← #25104453

Subgroups — #25104453

Order 11008.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144379C211yesmaximal, characteristic
2#19143533C211yesmaximal, characteristic, complemented
3#19143021C211yesmaximal, characteristic
4#19135537C211yesmaximal, characteristic, complemented
5#19135369C211yesmaximal, characteristic, complemented
6#19135197C211yesmaximal, characteristic, complemented
7#19135193C211yesmaximal, characteristic, complemented
8#19134872C211yesmaximal, characteristic
9#19134868C211yesmaximal, characteristic
10#19134613C211yesmaximal, characteristic
11#19134479C211yesmaximal, characteristic, complemented
12#19134475C211yesmaximal, characteristic, complemented
13#19134471C211yesmaximal, characteristic, complemented
14#19134430C211yesmaximal, characteristic
15C43×#1765C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583452C2211yescharacteristic
18#41×Dic43C2211yescharacteristic
19#14583208C411yescharacteristic, complemented
20#14583204C411yescharacteristic, complemented
21#14583201C411yescharacteristic, complemented
22#14583197C411yescharacteristic, complemented
23#14583192C411yescharacteristic, complemented
24#14583187C411yescharacteristic, complemented
25#14583182C411yescharacteristic, complemented
26#14583177C411yescharacteristic, complemented
27#14583029—21no—
28#14583029—21no—
29#14583027—21no—
30#14583027—21no—
31C2×#13063261C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33#14582937C2211yescharacteristic
34#14582935C2211yescharacteristic
35#14582927C2211yescharacteristic
36#14582926C2211yescharacteristic
37#14582922C2211yescharacteristic
38C2×Dic43⋊C8C2211yescharacteristic
39C2×#13063252C2211yescharacteristic
40#14582895C2211yescharacteristic
41#14582857—21no—
42#14582857C2211yescharacteristic
43#14582854—21no—
44#14582854C2211yescharacteristic
45#14582854C2211yescharacteristic
46M16×Dic43—21no—
47M16×Dic43C2211yescharacteristic
48C2×#13063235—21no—
49C2×#13063235C2211yescharacteristic
50C2×C8×Dic43C2211yescharacteristic
51C4×Dic43⋊C4C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582658C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582653C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic
61C2×#104×C43C2211yescharacteristic
62C43×#416C2211yescharacteristic
63C43×#405C2211yescharacteristic
64C2×#97×C43C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#339C2211yescharacteristic
67#13063332—22no—
68#13063332—22no—
69C2×#10621877—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C22×C43⋊C8—21no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063324C2×C411yescharacteristic
76#13063324C2×C411yescharacteristic
77#13063316C2×C411yescharacteristic
78#13063316C2×C411yescharacteristic
79#13063302—21no—
80#13063302—21no—
81Q8×Dic43C2×C411yescharacteristic
82Q8×Dic43C2×C411yescharacteristic
83C4×Dic86—21no—
84C4×Dic86—21no—
85D4×Dic43—21no—
86D4×Dic43—21no—
87D4×Dic43C2×C411yescharacteristic
88D4×Dic43C2×C411yescharacteristic
89#13063284—21no—
90#13063284C2311yescharacteristic
91#13063284C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063261—22no—
97#13063260—22no—
98#13063259C2×C411yescharacteristic
99#13063259C2×C411yescharacteristic
100#13063258C2×C411yescharacteristic
101#13063258C2×C411yescharacteristic
102#13063257C2×C411yescharacteristic
103#13063257C2×C411yescharacteristic
104#13063256C2×C411yescharacteristic
105#13063256C2×C411yescharacteristic
106C4⋊(C43⋊C8)—21no—
107C4⋊(C43⋊C8)—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8C2×C411yescharacteristic
113Dic43⋊C8C2×C411yescharacteristic
114Dic43⋊C8C2×C411yescharacteristic
115Dic43⋊C8C2×C411yescharacteristic
116#13063252—22no—
117#13063249C2×C411yescharacteristic
118#13063249C2×C411yescharacteristic
119#13063246C2×C411yescharacteristic
120#13063246C2×C411yescharacteristic
121#13063235—21no—
122#13063235—21no—
123#13063235—21no—
124#13063235—21no—
125#13063235D411yescharacteristic
126#13063235D411yescharacteristic
127#13063235D411yescharacteristic
128#13063235D411yescharacteristic
129C8×Dic43—21no—
130C8×Dic43—21no—
131C8×Dic43—22no—
132C8×Dic43—21no—
133C8×Dic43—21no—
134C43⋊#95—21no—
135C2×#41×C43C2311yescharacteristic
136#131×C43—22no—
137#131×C43Q814yescomplemented
138C2×M16×C43—21no—
139C2×M16×C43C2311yescharacteristic
140C2×M16×C43C2311yescharacteristic
141C22×C8×C43—21no—
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144#117×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#104×C43—22no—
147#103×C43C2×C411yescharacteristic
148#103×C43C2×C411yescharacteristic
149#102×C43C2×C411yescharacteristic
150#102×C43C2×C411yescharacteristic
151#97×C43—21no—
152#97×C43—22no—
153C4×C8×C43—21no—
154#41×C43—21no—
155#41×C43—21no—
156#41×C43C2×Q812yes—
157#41×C43#4112yes—
158C2×Q8×C43C22×C411yescharacteristic
159C2×D4×C43—21no—
160C2×D4×C43C22×C411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C2411yescharacteristic
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43#4111yescharacteristic
168C22×Dic43#4111yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171M16×C43—21no—
172M16×C43—24no—
173M16×C43—21no—
174M16×C43—21no—
175M16×C43C2×Q812yes—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—24no—
180C2×C8×C43—21no—
181C2×C8×C43C22×C411yescharacteristic
182C2×C8×C43C22×C411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×Q812yes—
186C2×C8×C43#4112yes—
187C4⋊C4×C43C22×C411yescharacteristic
188C4⋊C4×C43C22×C411yescharacteristic
189C22⋊C4×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C22⋊Dic43—21no—
194C22⋊Dic43—21no—
195C22⋊Dic43—21no—
196C22⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43C22×C411yescharacteristic
202C4⋊Dic43C22×C411yescharacteristic
203C4⋊Dic43C22×C411yescharacteristic
204C4⋊Dic43C22×C411yescharacteristic
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208Dic43⋊C4—21no—
209Dic43⋊C4—42no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43C22×C411yescharacteristic
217C4×Dic43C22×C411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220#10621877—24no—
221#10621877—21no—
222#10621877—21no—
223#10621877—21no—
224#10621877#4112yes—
225C2×C43⋊C8—24no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8C22×C411yescharacteristic
233C2×C43⋊C8C22×C411yescharacteristic
234C2×C43⋊C8C2×D411yescharacteristic
235C2×C43⋊C8C2×D411yescharacteristic
236C23×C43—21no—
237C23×C43C2×#4111yescharacteristic
238Q8×C43—21no—
239Q8×C43C4×Q812yes—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—21no—
243D4×C43C4×Q812yes—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×Q811yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—81no—
268C2×Dic43—81no—
269C2×Dic43C4×D411yescharacteristic
270C2×Dic43C4×D411yescharacteristic
271C2×Dic43C4×D411yescharacteristic
272C2×Dic43C4×D411yescharacteristic
273Dic86—81no—
274Dic86—81no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—22no—
278C8×C43—41no—
279C8×C43C22⋊Q812yes—
280C8×C43C22⋊Q812yes—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—21no—
284C43⋊C8—22no—
285C43⋊C8—21no—
286C43⋊C8—41no—
287#21629—431nomaximal, Sylow
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—22no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43C2×C4×D411yescharacteristic
294C22×C43#52911yescharacteristic
295C22×C43#53311yescharacteristic
296C4×C43—22no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—81no—
300C4×C43C2×C4×Q811yescharacteristic
301C4×C43C4×#4111yescharacteristic
302C4×C43C2×C22⋊Q811yescharacteristic
303C4×C43#52511yescharacteristic
304Dic43—21no—
305Dic43—21no—
306Dic43—21no—
307Dic43—21no—
308Dic43—42no—
309Dic43—41no—
310Dic43—41no—
311Dic43—41no—
312Dic43—41no—
313#3076—431no—
314#2961—431no—
315#2875—431no—
316#1986—431no—
317#1950—431no—
318#1922—431no—
319#1922—431no—
320#1866—431no—
321#1866—431no—
322#1806—431no—
323#1773—431no—
324#1772—431no—
325#1771—431no—
326#1765D4311yescharacteristic
327#1764—431no—
328C2×C43—21no—
329C2×C43—21no—
330C2×C43—42no—
331C2×C43C4×C22⋊Q811yescharacteristic
332C2×C43#295611yescharacteristic
333C2×C43#295711yescharacteristic
334C2×#131—431no—
335C2×#131C2×D4311yescharacteristic
336#533—431no—
337C4×#41—431no—
338#479—431no—
339#479—431no—
340#478—431no—
341#478—431no—
342#477—431no—
343#476—431no—
344#475—431no—
345#474—431no—
346#446—861no—
347#446—861no—
348#446—861no—
349#446—861no—
350C2×#108—431no—
351C2×#108—431no—
352#427—431no—
353#427—431no—
354#424—431no—
355#424—431no—
356#423—431no—
357C2×C4⋊C8—431no—
358C2×#104—431no—
359C2×#104C2×D4311yescharacteristic
360#416—431no—
361#416C2×D4311yescharacteristic
362#405—431no—
363#405—431no—
364#405—431no—
365#405—861no—
366#405—861no—
367#405C2×D4311yescharacteristic
368C4×M16—431no—
369C4×M16—861no—
370C2×#97—431no—
371C2×#97—861no—
372C2×#97C2×D4311yescharacteristic
373C2×C4×C8—431no—
374C4×C4⋊C4—431no—
375#341—431no—
376#341C2×D4311yescharacteristic
377#339—431no—
378#339—431no—
379#339—431no—
380#339—431no—
381#339—431no—
382#339C2×D4311yescharacteristic
383#336—431no—
384#336—431no—
385C43#2162911yescharacteristic, complemented, Sylow
386C2×#41C22×D4311yescharacteristic
387#131—22no—
388#131—862no—
389#131—862no—
390#131Dic8614yescomplemented
391C2×M16—21no—
392C2×M16—431no—
393C2×M16—431no—
394C2×M16—861no—
395C2×M16C22×D4311yescharacteristic
396C2×M16C22×D4311yescharacteristic
397C22×C8—21no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8—861no—
401C22×C8C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403C4⋊Q8—431no—
404C4⋊Q8—431no—
405#125—431no—
406#125—431no—
407C22⋊Q8—861no—
408C22⋊Q8—861no—
409C4×Q8—431no—
410C4×Q8—431no—
411C4×Q8—861no—
412C4×Q8—861no—
413C4×D4—431no—
414C4×D4—431no—
415C4×D4—861no—
416C4×D4—861no—
417#117—431no—
418#117—431no—
419#117—861no—
420#117C22×D4311yescharacteristic
421C2×C4⋊C4—861no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—861no—
425C2×C42C22×D4311yescharacteristic
426#108—862no—
427#108—862no—
428#107—431no—
429#107—431no—
430#107—431no—
431#107—431no—
432#106—431no—
433#106—431no—
434#106—431no—
435#106—431no—
436C4⋊C8—431no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—861no—
441C4⋊C8—861no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445C4⋊C8—861no—
446#104—22no—
447#104—862no—
448#103—431no—
449#103—431no—
450#103C4×D4311yescharacteristic
451#103C4×D4311yescharacteristic
452#102—431no—
453#102—431no—
454#102C4×D4311yescharacteristic
455#102C4×D4311yescharacteristic
456#97—21no—
457#97—22no—
458#97—431no—
459#97—431no—
460#97—431no—
461#97—431no—
462#97—861no—
463#97—861no—
464#97—861no—
465#97—861no—
466C4×C8—21no—
467C4×C8—861no—
468C4×C8—861no—
469C4×C8—861no—
470C4×C8—861no—
471C4×C8—862no—
472#95—861no—
473#41—21no—
474#41—21no—
475#41C2×Dic8612yes—
476#41#1062189812yes—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8C2×C4×D4311yescharacteristic
480C2×D4—21no—
481C2×D4C2×C4×D4311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4C23×D4311yescharacteristic
490M16—21no—
491M16—24no—
492M16—21no—
493M16—21no—
494M16—432no—
495M16—864no—
496M16—861no—
497M16—861no—
498M16—861no—
499M16C2×Dic8612yes—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—24no—
504C2×C8—21no—
505C2×C8—431no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—864no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8C2×Dic8612yes—
517C2×C8C2×C4×D4311yescharacteristic
518C2×C8C2×C4×D4311yescharacteristic
519C2×C8D4×D4311yescharacteristic
520C2×C8D4×D4311yescharacteristic
521C2×C8#1062190012yes—
522C4⋊C4—431no—
523C4⋊C4—431no—
524C4⋊C4—431no—
525C4⋊C4—431no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—1722no—
535C4⋊C4C2×C4×D4311yescharacteristic
536C4⋊C4C2×C4×D4311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—861no—
550C42—861no—
551C42—861no—
552C42—861no—
553C42—861no—
554C42—861no—
555C23—21no—
556C23#41×D4311yescharacteristic
557Q8—21no—
558Q8—3441no—
559Q8—3441no—
560Q8C4×Dic8612yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4C4×Dic8612yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—862no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—3441no—
583C2×C4—3441no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4C22×C4×D4311yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C22×Dic8611yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4C2×#1062190011yescharacteristic
593C2×C4C2×#1062189811yescharacteristic
594C8—21no—
595C8—21no—
596C8—22no—
597C8—41no—
598C8—861no—
599C8—861no—
600C8—861no—
601C8—861no—
602C8—862no—
603C8—1721no—
604C8#1306330212yes—
605C8#1306330212yes—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22C4×D4×D4311yescharacteristic
612C22#1458342911yescharacteristic
613C22#1458345211yescharacteristic
614C4—22no—
615C4—41no—
616C4—41no—
617C4—81no—
618C4—861no—
619C4—861no—
620C4—861no—
621C4—861no—
622C4—1722no—
623C4—1721no—
624C4—1721no—
625C4—1721no—
626C4—1721no—
627C4C2×C4×Dic8611yescharacteristic
628C4C4×#1062190011yescharacteristic
629C4C2×#1306330211yescharacteristic
630C4#1458340811yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2C4×#1306330211yescharacteristic
635C2#1914350311yescharacteristic
636C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1765C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×C43C23
cosocleC22×C4×C43C24
hypercenter#1765D43
hypocenterC43#21629
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
2. #19143533C2semidirect
4. #19135537C2semidirect
5. #19135369C2semidirect
6. #19135197C2semidirect
7. #19135193C2semidirect
11. #19134479C2semidirect
12. #19134475C2semidirect
13. #19134471C2semidirect
19. #14583208C4semidirect
20. #14583204C4semidirect
21. #14583201C4semidirect
22. #14583197C4semidirect
23. #14583192C4semidirect
24. #14583187C4semidirect
25. #14583182C4semidirect
26. #14583177C4semidirect
137. #131×C43Q8semidirect
385. C43#21629semidirect
390. #131Dic86semidirect

Maximal subgroups

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

subgroupindex
#191443792
#191435332
#191430212
#191355372
#191353692
#191351972
#191351932
#191348722
#191348682
#191346132
#191344792
#191344752
#191344712
#191344302
C43×#17652
#2162943