Finite Group Databasebeta

← #25103546

Subgroups — #25103546

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144314C211yesmaximal, characteristic
2#19143497C211yesmaximal, characteristic, complemented
3#19143494C211yesmaximal, characteristic, complemented
4C2×#14583018C211yesmaximal, characteristic, complemented
5#19143024C211yesmaximal, characteristic, complemented
6#19135492C211yesmaximal, characteristic, complemented
7#19135382C211yesmaximal, characteristic, complemented
8#19135264C211yesmaximal, characteristic, complemented
9#19135099C211yesmaximal, characteristic, complemented
10#19135095C211yesmaximal, characteristic, complemented
11#19134648C211yesmaximal, characteristic, complemented
12#19134478C211yesmaximal, characteristic, complemented
13#19134398C211yesmaximal, characteristic, complemented
14#19134394C211yesmaximal, characteristic, complemented
15C43×#1932C211yesmaximal, characteristic, complemented
16#14583699C2211yescharacteristic
17#14583697C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063333C2211yescharacteristic
21C2×#13063333C2211yescharacteristic
22C2×#13063332C2211yescharacteristic
23C4×#10621898C2211yescharacteristic
24#14583173C412yescomplemented
25#14583168C412yescomplemented
26#14583165C412yescomplemented
27#14583161C412yescomplemented
28#14583020—22no—
29#14583018—22no—
30#14583018—21no—
31#14583018—21no—
32#14583018—21no—
33#14583018—21no—
34#14583015—22no—
35#14583013—22no—
36#14582947C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38C2×#13063260C2211yescharacteristic
39#14582935C2211yescharacteristic
40#14582917C2211yescharacteristic
41#14582915C2211yescharacteristic
42#14582915C2211yescharacteristic
43C2×#13063253C2211yescharacteristic
44#14582881C2211yescharacteristic
45#14582873C2211yescharacteristic
46#14582872C2211yescharacteristic
47#14582857C2211yescharacteristic
48#14582857C2211yescharacteristic
49#14582857C2211yescharacteristic
50#14582855C2211yescharacteristic
51#14582853—21no—
52#14582853—21no—
53#14582851—21no—
54C2×#13063236C2211yescharacteristic
55#97×D43—21no—
56#14582671C2211yescharacteristic
57#14582671C2211yescharacteristic
58#14582670C2211yescharacteristic
59#14582659C2211yescharacteristic
60C43×#430C2211yescharacteristic
61C43×#421C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C43×#413C2211yescharacteristic
64C4×M16×C43C2211yescharacteristic
65C43×#344C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C2×#10621898C2311yescharacteristic
69#13063358—21no—
70#13063358C2×C412yes—
71#13063356C2×C412yes—
72#13063355—21no—
73#13063353—21no—
74#13063353C2×C412yes—
75#13063351C2×C412yes—
76#13063350—21no—
77#13063347—22no—
78#13063345—22no—
79#13063345—21no—
80#13063345—21no—
81#13063345—21no—
82#13063345—21no—
83C2×#10621885C2×C411yescharacteristic, complemented
84C2×#10621883C2×C411yescharacteristic, complemented
85C2×#10621884C2×C411yescharacteristic, complemented
86C2×#10621882C2×C411yescharacteristic, complemented
87#13063333—21no—
88#13063333—21no—
89#13063333—21no—
90#13063333—21no—
91#13063333—21no—
92#13063333—21no—
93#13063333—21no—
94#13063333—21no—
95#13063333C2×C412yes—
96#13063333C2×C412yes—
97#13063333D412yes—
98#13063333D412yes—
99#13063332—21no—
100#13063332—21no—
101#13063332—21no—
102#13063332—21no—
103C2×#10621877—21no—
104C2×#10621877C2311yescharacteristic
105C2×#10621877C2311yescharacteristic
106C2×#10621872—21no—
107C2×#10621872—21no—
108C2×#10621872—21no—
109C22×C43⋊C8—21no—
110C22×C43⋊C8C2311yescharacteristic
111C22×C43⋊C8C2311yescharacteristic
112C2×C8×D43—21no—
113C2×C8×D43—21no—
114C2×C8×D43—21no—
115C4×Dic86—21no—
116C4×D172—21no—
117C4×C22⋊D43—22no—
118#13063284C2311yescharacteristic
119#13063284C2311yescharacteristic
120#13063282—21no—
121C42×D43—21no—
122#13063260—22no—
123#13063260—21no—
124#13063260—21no—
125#13063260C2×C412yescomplemented
126#13063260C2×C412yescomplemented
127#13063258—21no—
128#13063256—21no—
129#13063253—22no—
130#13063253—21no—
131#13063253—21no—
132#13063251—22no—
133#13063251—22no—
134#13063243C2×C412yescomplemented
135#13063241C2×C412yescomplemented
136#13063240—22no—
137#13063239—22no—
138#13063236—21no—
139#13063236D411yescharacteristic
140#13063236D411yescharacteristic
141#13063236D411yescharacteristic
142#13063236D411yescharacteristic
143#13063235—21no—
144#13063235—21no—
145#13063235—21no—
146C4×C43⋊C8—21no—
147C8×Dic43—21no—
148C8×Dic43—21no—
149C8×Dic43—21no—
150C2×#41×C43C2311yescharacteristic
151C2×M16×C43C2311yescharacteristic
152C2×M16×C43C2311yescharacteristic
153C2×M16×C43C2311yescharacteristic
154C2×M16×C43C2311yescharacteristic
155#117×C43C2311yescharacteristic
156C2×C42×C43C2311yescharacteristic
157#108×C43—22no—
158#104×C43—22no—
159#104×C43—21no—
160#104×C43—21no—
161#101×C43C2×C412yescomplemented
162#100×C43C2×C412yescomplemented
163#97×C43—21no—
164C4×C8×C43—21no—
165#41×C43—21no—
166#41×C43—21no—
167#41×C43—21no—
168#41×C43—21no—
169C2×Q8×C43C22×C411yescharacteristic
170C2×D4×C43—21no—
171C2×D4×C43C22×C411yescharacteristic
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43C2411yescharacteristic
175C2×C22⋊D43—21no—
176C2×C22⋊D43—21no—
177#10621898—21no—
178#10621898—21no—
179#10621898—21no—
180#10621898—21no—
181#10621898—21no—
182#10621898—21no—
183#10621898C22×C412yes—
184#10621898C2×D412yes—
185C2×D172C22×C411yescharacteristic
186C2×D172#4111yescharacteristic
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—22no—
190C2×Dic86C22×C411yescharacteristic
191C2×Dic86#4111yescharacteristic
192M16×C43—21no—
193M16×C43—21no—
194M16×C43—21no—
195M16×C43—21no—
196M16×C43—21no—
197M16×C43C22×C412yes—
198M16×C43C22×C412yes—
199M16×C43C2×D412yes—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C4⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C42×C43—21no—
207C42×C43—21no—
208C42×C43C2×D411yescharacteristic
209C42×C43C2×D411yescharacteristic
210C22⋊Dic43—21no—
211C22⋊Dic43#4112yes—
212#10621885—22no—
213#10621885—21no—
214#10621885—21no—
215#10621884—22no—
216#10621884—21no—
217#10621884—21no—
218#10621883—22no—
219#10621883—21no—
220#10621883—21no—
221#10621882—22no—
222#10621882—21no—
223#10621882—21no—
224(C2×D43)⋊C4—22no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227Dic43⋊C4—22no—
228C4×Dic43—22no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877—21no—
234#10621877—41no—
235#10621877—41no—
236#10621877C22×C412yes—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—41no—
240C2×C43⋊C8—41no—
241C2×C43⋊C8C22×C411yescharacteristic
242C2×C43⋊C8C22×C411yescharacteristic
243C2×C43⋊C8C2×D411yescharacteristic
244C2×C43⋊C8C2×D411yescharacteristic
245C2×C43⋊C8C2×D411yescharacteristic
246C2×C43⋊C8C2×D411yescharacteristic
247C2×C43⋊C8C2×D411yescharacteristic
248C2×C43⋊C8C2×D411yescharacteristic
249C2×C43⋊C8#4111yescharacteristic
250C2×C43⋊C8#4111yescharacteristic
251C2×C43⋊C8#4111yescharacteristic
252C2×C43⋊C8#4111yescharacteristic
253Dic172—22no—
254D344—22no—
255#10621873—22no—
256#10621873—22no—
257#10621872—22no—
258#10621872—22no—
259#10621872—22no—
260#10621872—22no—
261#10621872—41no—
262#10621872—41no—
263C8×D43—22no—
264C8×D43—22no—
265C8×D43—22no—
266C8×D43—22no—
267C8×D43—41no—
268C8×D43—41no—
269C23×C43—21no—
270C23×C43C2×#4111yescharacteristic
271C22×D43—21no—
272C22×D43—21no—
273Q8×C43—21no—
274Q8×C43—21no—
275D4×C43—21no—
276D4×C43—21no—
277D4×C43—41no—
278D4×C43—41no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—81no—
286C2×C4×C43C23×C411yescharacteristic
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C22⋊D43—22no—
293C22⋊D43—22no—
294C22⋊D43—41no—
295C22⋊D43—41no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—22no—
299C2×Dic43—41no—
300D172—21no—
301D172—21no—
302D172—21no—
303D172C4×D412yes—
304C4×D43—22no—
305C4×D43—22no—
306C4×D43—41no—
307C4×D43—41no—
308C4×D43—82no—
309Dic86—21no—
310Dic86—21no—
311Dic86—21no—
312Dic86C4×D412yes—
313C8×C43—22no—
314C8×C43—22no—
315C8×C43—22no—
316C8×C43—41no—
317C43⋊C8—22no—
318C43⋊C8—41no—
319C43⋊C8C4×D411yescharacteristic
320C43⋊C8C4×D411yescharacteristic
321C43⋊C8C4×D411yescharacteristic
322C43⋊C8C4×D411yescharacteristic
323C43⋊C8#12111yescharacteristic
324C43⋊C8#12111yescharacteristic
325C43⋊C8#12111yescharacteristic
326C43⋊C8#12111yescharacteristic
327#21559—431nomaximal, Sylow
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—81no—
331C22×C43C4×#4111yescharacteristic
332C22×C43#52511yescharacteristic
333C22×C43#53211yescharacteristic
334C2×D43—22no—
335C2×D43—42no—
336C2×D43—41no—
337C2×D43—81no—
338C4×C43—41no—
339C4×C43—41no—
340C4×C43—41no—
341C4×C43—81no—
342C4×C43C2×C4×D411yescharacteristic
343C4×C43C2×C4×D411yescharacteristic
344C4×C43C2×#12111yescharacteristic
345C4×C43#52911yescharacteristic
346Dic43—22no—
347Dic43—42no—
348Dic43—41no—
349Dic43—81no—
350#3067—431no—
351#2955—431no—
352#2955—431no—
353C2×#444—431no—
354#2875—431no—
355#1976—431no—
356#1953—431no—
357#1932—431no—
358#1932D4311yescharacteristic, complemented
359#1906—431no—
360#1906—431no—
361#1814—431no—
362#1773—431no—
363#1757—431no—
364#1757—431no—
365C2×C43—21no—
366C2×C43—21no—
367C2×C43—21no—
368C2×C43—81no—
369C2×C43C4×#12111yescharacteristic
370D43—42no—
371D43—81no—
372#575—431no—
373#575—431no—
374C2×#135—431no—
375C2×#131—431no—
376C2×#131—431no—
377C2×#131—431no—
378C2×#131—431no—
379C4×#41—431no—
380#473—432no—
381#472—432no—
382#471—432no—
383#471—432no—
384#444—861no—
385#444—861no—
386#444—861no—
387#444—861no—
388#444—862no—
389#444—862no—
390#443—862no—
391#443—862no—
392#430—431no—
393#430C2×D4311yescharacteristic
394C2×#108—431no—
395C2×#108—431no—
396#427—431no—
397#421—431no—
398#421—431no—
399#421—431no—
400#421C2×D4311yescharacteristic
401C2×#104—431no—
402C2×#104C2×D4311yescharacteristic
403#413—431no—
404#413C2×D4311yescharacteristic
405#410—431no—
406#410—431no—
407#405—431no—
408#405—431no—
409#405—431no—
410#405—431no—
411#405—861no—
412#405—861no—
413C4×M16—861no—
414C4×M16C2×D4311yescharacteristic
415C2×#97—431no—
416C2×#97—861no—
417#344—431no—
418#344—431no—
419#344—431no—
420#344C2×D4311yescharacteristic
421#339—431no—
422#339C2×D4311yescharacteristic
423C43#2155911yescharacteristic, complemented, Sylow
424C2×#41—431no—
425C2×#41—431no—
426C2×#41C22×D4311yescharacteristic
427#137—432no—
428#137—432no—
429#137—861no—
430#137—861no—
431AGL(1,ℤ/8)—432no—
432AGL(1,ℤ/8)—432no—
433AGL(1,ℤ/8)—861no—
434AGL(1,ℤ/8)—861no—
435#135—862no—
436#135—861no—
437#135—861no—
438#135—861no—
439#135—861no—
440#135—862no—
441C2×Q16—431no—
442C2×SD16—431no—
443C2×SD16—431no—
444C2×D8—431no—
445#131—432no—
446#131—432no—
447#131—432no—
448#131—432no—
449#131—861no—
450#131—861no—
451#131—861no—
452#131—861no—
453#131—861no—
454#131—861no—
455#131—861no—
456#131—861no—
457#131—861no—
458#131—861no—
459#131—861no—
460#131—861no—
461C2×M16—431no—
462C2×M16—431no—
463C2×M16—861no—
464C2×M16—861no—
465C2×M16—861no—
466C2×M16—861no—
467C2×M16C22×D4311yescharacteristic
468C2×M16C22×D4311yescharacteristic
469C2×M16C22×D4311yescharacteristic
470C2×M16C22×D4311yescharacteristic
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—861no—
474C22×C8—861no—
475C22×C8—861no—
476C22×C8—861no—
477C4×Q8—861no—
478C4×D4—861no—
479C4×D4—862no—
480#117—431no—
481#117—431no—
482#117—861no—
483#117C22×D4311yescharacteristic
484C2×C42—861no—
485C2×C42C22×D4311yescharacteristic
486#108—22no—
487#108—432no—
488#108—432no—
489#108—861no—
490#108—861no—
491#108—862no—
492#107—861no—
493#106—861no—
494#104—22no—
495#104—21no—
496#104—21no—
497#104—862no—
498#104—862no—
499#104—862no—
500#104—861no—
501#104—861no—
502#101—432no—
503#101C4×D4312yescomplemented
504#100—432no—
505#100C4×D4312yescomplemented
506#99—862no—
507#99—862no—
508#97—21no—
509#97—431no—
510#97—431no—
511#97—431no—
512#97—431no—
513#97—861no—
514#97—861no—
515#97—861no—
516#97—861no—
517C4×C8—21no—
518C4×C8—861no—
519C4×C8—861no—
520C4×C8—861no—
521C4×C8—861no—
522#41—21no—
523#41—21no—
524#41—21no—
525#41—21no—
526#41—432no—
527#41—432no—
528#41—861no—
529#41—861no—
530#41—861no—
531#41—861no—
532#41—861no—
533#41—861no—
534C2×Q8—431no—
535C2×Q8—431no—
536C2×Q8C2×C4×D4311yescharacteristic
537C2×D4—21no—
538C2×D4—431no—
539C2×D4—431no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4C2×C4×D4311yescharacteristic
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—862no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4C23×D4311yescharacteristic
549Q16—862no—
550Q16—861no—
551Q16—861no—
552Q16—862no—
553SD16—862no—
554SD16—862no—
555SD16—861no—
556SD16—861no—
557SD16—861no—
558SD16—861no—
559SD16—862no—
560SD16—862no—
561D8—862no—
562D8—861no—
563D8—861no—
564D8—862no—
565M16—21no—
566M16—21no—
567M16—21no—
568M16—21no—
569M16—21no—
570M16—432no—
571M16—862no—
572M16—862no—
573M16—862no—
574M16—862no—
575M16—861no—
576M16—861no—
577M16—861no—
578M16—1721no—
579M16—1721no—
580M16—1721no—
581M16—1721no—
582M16C2×C4×D4312yes—
583M16C2×C4×D4312yes—
584M16D4×D4312yes—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—431no—
590C2×C8—431no—
591C2×C8—431no—
592C2×C8—431no—
593C2×C8—431no—
594C2×C8—431no—
595C2×C8—431no—
596C2×C8—431no—
597C2×C8—431no—
598C2×C8—431no—
599C2×C8—431no—
600C2×C8—431no—
601C2×C8—862no—
602C2×C8—862no—
603C2×C8—862no—
604C2×C8—862no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—1721no—
608C2×C8—1721no—
609C2×C8—1721no—
610C2×C8—1721no—
611C4⋊C4—21no—
612C4⋊C4—862no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C22⋊C4—21no—
616C22⋊C4—432no—
617C22⋊C4—862no—
618C22⋊C4—861no—
619C42—21no—
620C42—21no—
621C42—862no—
622C42—861no—
623C42—861no—
624C42D4×D4311yescharacteristic
625C42D4×D4311yescharacteristic
626C23—21no—
627C23—861no—
628C23—861no—
629C23#41×D4311yescharacteristic
630Q8—21no—
631Q8—21no—
632Q8—432no—
633Q8—861no—
634Q8—861no—
635Q8—861no—
636D4—21no—
637D4—21no—
638D4—41no—
639D4—41no—
640D4—432no—
641D4—862no—
642D4—862no—
643D4—861no—
644D4—861no—
645D4—861no—
646D4—1721no—
647D4—1721no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—81no—
655C2×C4—861no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—861no—
659C2×C4—862no—
660C2×C4—3442no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4C22×C4×D4311yescharacteristic
665C2×C4C2×D4×D4311yescharacteristic
666C2×C4C2×D4×D4311yescharacteristic
667C2×C4#41×D4311yescharacteristic
668C2×C4#41×D4311yescharacteristic
669C2×C4#41×D4311yescharacteristic
670C8—22no—
671C8—22no—
672C8—22no—
673C8—41no—
674C8—431no—
675C8—431no—
676C8—431no—
677C8—431no—
678C8—431no—
679C8—431no—
680C8—431no—
681C8—431no—
682C8—862no—
683C8—1721no—
684C22—41no—
685C22—41no—
686C22—81no—
687C22—862no—
688C22—3441no—
689C22—1722no—
690C22—1721no—
691C22#1458336711yescharacteristic
692C22#1458340711yescharacteristic
693C22#1458344811yescharacteristic
694C4—41no—
695C4—41no—
696C4—41no—
697C4—81no—
698C4—862no—
699C4—3441no—
700C4—1722no—
701C4—1721no—
702C4C4×D4×D4311yescharacteristic
703C4C4×D4×D4311yescharacteristic
704C4#121×D4311yescharacteristic
705C4#1458343211yescharacteristic
706C2—21no—
707C2—21no—
708C2—21no—
709C2—81no—
710C2—3441no—
711C2—1722no—
712C2#1913710711yescharacteristic
subgroupG/H
centerC4#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1932C2
socleC2×C43C4×#121
prime radical#19144314C2
cosocleC22×C4×C43C24
hypercenter#1932D43
hypocenterC43#21559
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1932

Complements

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

NH ≅ G/Ntype
2. #19143497C2semidirect
3. #19143494C2semidirect
4. C2×#14583018C2semidirect
5. #19143024C2semidirect
6. #19135492C2semidirect
7. #19135382C2semidirect
8. #19135264C2semidirect
9. #19135099C2semidirect
10. #19135095C2semidirect
11. #19134648C2semidirect
12. #19134478C2semidirect
13. #19134398C2semidirect
14. #19134394C2semidirect
15. C43×#1932C2semidirect
24. #14583173C4semidirect
25. #14583168C4semidirect
26. #14583165C4semidirect
27. #14583161C4semidirect
83. C2×#10621885C2×C4semidirect
84. C2×#10621883C2×C4semidirect
85. C2×#10621884C2×C4semidirect
86. C2×#10621882C2×C4semidirect
125. #13063260C2×C4semidirect
126. #13063260C2×C4semidirect
134. #13063243C2×C4semidirect
135. #13063241C2×C4semidirect
161. #101×C43C2×C4semidirect
162. #100×C43C2×C4semidirect
358. #1932D43semidirect
423. C43#21559semidirect
503. #101C4×D43semidirect
505. #100C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191443142
#191434972
#191434942
C2×#145830182
#191430242
#191354922
#191353822
#191352642
#191350992
#191350952
#191346482
#191344782
#191343982
#191343942
C43×#19322
#2155943