Finite Group Databasebeta

← #25103534

Subgroups — #25103534

Order 11008.

876 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#19143499C211yesmaximal, characteristic, complemented
3#19143496C211yesmaximal, characteristic, complemented
4C2×#14583014C211yesmaximal, characteristic, complemented
5#19143017C211yesmaximal, characteristic, complemented
6#19135490C211yesmaximal, characteristic, complemented
7#19135384C211yesmaximal, characteristic, complemented
8#19135266C211yesmaximal, characteristic, complemented
9#19135262C211yesmaximal, characteristic, complemented
10#19135097C211yesmaximal, characteristic, complemented
11#19135093C211yesmaximal, characteristic, complemented
12#19134648C211yesmaximal, characteristic, complemented
13#19134475C211yesmaximal, characteristic, complemented
14#19134396C211yesmaximal, characteristic, complemented
15C43×#1757C211yesmaximal, characteristic, complemented
16#14583699C2211yescharacteristic
17#14583697C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063331C2211yescharacteristic
21C2×#13063331C2211yescharacteristic
22#14583367C2211yescharacteristic
23#14583173C412yescomplemented
24#14583168C412yescomplemented
25#14583165C412yescomplemented
26#14583161C412yescomplemented
27#14583022—22no—
28#14583019—22no—
29#14583017—22no—
30#14583014—22no—
31#14583014—21no—
32#14583014—21no—
33#14583014—21no—
34#14583014—21no—
35#14582948C2211yescharacteristic
36#14582947C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38C2×#13063260C2211yescharacteristic
39#14582935C2211yescharacteristic
40#14582917C2211yescharacteristic
41#14582917C2211yescharacteristic
42#14582916C2211yescharacteristic
43#14582915C2211yescharacteristic
44C2×#13063252C2211yescharacteristic
45C2×#13063251C2211yescharacteristic
46#14582881C2211yescharacteristic
47#14582872C2211yescharacteristic
48#14582856—21no—
49#14582855C2211yescharacteristic
50#14582854C2211yescharacteristic
51#14582853—21no—
52#14582851—21no—
53M16×Dic43C2211yescharacteristic
54C2×C8×Dic43C2211yescharacteristic
55C4×C8×D43—21no—
56#14582671C2211yescharacteristic
57#14582669C2211yescharacteristic
58#14582660C2211yescharacteristic
59#14582658C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic
61C43×#413C2211yescharacteristic
62C43×#410C2211yescharacteristic
63C43×#405C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#344C2211yescharacteristic
66C43×#344C2211yescharacteristic
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#13063333C2×C412yes—
90#13063333C2×C412yes—
91#13063331—21no—
92#13063331—21no—
93#13063331—21no—
94#13063331—21no—
95#13063331—21no—
96#13063331—21no—
97#13063331D412yes—
98#13063331D412yes—
99C2×#10621877C2311yescharacteristic
100C2×#10621877C2311yescharacteristic
101C2×#10621877C2311yescharacteristic
102C2×#10621872—21no—
103C2×#10621872—21no—
104C2×#10621872—21no—
105C22×C43⋊C8C2311yescharacteristic
106C2×C8×D43—21no—
107C2×C8×D43—21no—
108C2×C8×D43—21no—
109#13063290—21no—
110#13063287—21no—
111(C22⋊D43)⋊C4—22no—
112#13063284C2311yescharacteristic
113#13063282—21no—
114C2×C4×Dic43C2311yescharacteristic
115C42×D43—21no—
116#13063261—22no—
117#13063260—22no—
118#13063260—21no—
119#13063260—21no—
120#13063260C2×C412yescomplemented
121#13063260C2×C412yescomplemented
122#13063258—21no—
123#13063256—21no—
124#13063253—22no—
125#13063253—22no—
126#13063252—21no—
127#13063252—21no—
128#13063252—22no—
129#13063251—22no—
130#13063251—21no—
131#13063251—21no—
132#13063243C2×C412yescomplemented
133#13063241C2×C412yescomplemented
134#13063239—22no—
135#13063236—21no—
136#13063235—21no—
137#13063235—21no—
138C4×C43⋊C8—21no—
139C8×Dic43—21no—
140C8×Dic43—21no—
141C8×Dic43D411yescharacteristic
142C8×Dic43D411yescharacteristic
143C8×Dic43D411yescharacteristic
144C8×Dic43D411yescharacteristic
145C2×#41×C43C2311yescharacteristic
146#131×C43—21no—
147#131×C43—21no—
148#131×C43—21no—
149#131×C43—21no—
150C2×M16×C43—21no—
151C2×M16×C43C2311yescharacteristic
152C2×M16×C43C2311yescharacteristic
153C2×M16×C43C2311yescharacteristic
154C22×C8×C43—21no—
155C22×C8×C43C2311yescharacteristic
156#117×C43C2311yescharacteristic
157#117×C43C2311yescharacteristic
158#101×C43C2×C412yescomplemented
159#100×C43C2×C412yescomplemented
160#99×C43—22no—
161#97×C43—21no—
162#97×C43—21no—
163C4×C8×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×C43C2411yescharacteristic
174C2×C22⋊D43—21no—
175C2×C22⋊D43—21no—
176C22×Dic43—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—22no—
189C2×C4×D43—21no—
190C2×Dic86C22×C411yescharacteristic
191C2×Dic86#4111yescharacteristic
192M16×C43—21no—
193M16×C43—21no—
194M16×C43—21no—
195M16×C43—21no—
196M16×C43—41no—
197M16×C43—41no—
198M16×C43C22×C412yes—
199M16×C43C22×C412yes—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—41no—
204C2×C8×C43—41no—
205C2×C8×C43C2×D411yescharacteristic
206C2×C8×C43C2×D411yescharacteristic
207C2×C8×C43C2×D411yescharacteristic
208C2×C8×C43C2×D411yescharacteristic
209C2×C8×C43#4111yescharacteristic
210C2×C8×C43#4111yescharacteristic
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C22⋊C4×C43—21no—
214C22⋊C4×C43#4112yes—
215C42×C43—21no—
216C42×C43—21no—
217C22⋊Dic43—21no—
218#10621885—22no—
219#10621885—21no—
220#10621885—21no—
221#10621884—22no—
222#10621884—21no—
223#10621884—21no—
224#10621883—22no—
225#10621883—21no—
226#10621883—21no—
227#10621882—22no—
228#10621882—21no—
229#10621882—21no—
230(C2×D43)⋊C4—22no—
231C4⋊Dic43—21no—
232Dic43⋊C4—22no—
233C4×Dic43—22no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43C2×D411yescharacteristic
237C4×Dic43C2×D411yescharacteristic
238#10621877—21no—
239#10621877—21no—
240#10621877—21no—
241#10621877—21no—
242#10621877C22×C412yes—
243#10621877C2×D412yes—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8C22×C411yescharacteristic
248C2×C43⋊C8C22×C411yescharacteristic
249C2×C43⋊C8C2×D411yescharacteristic
250C2×C43⋊C8C2×D411yescharacteristic
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—22no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43C23×C411yescharacteristic
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C22⋊D43—22no—
291C22⋊D43—22no—
292C22⋊D43—41no—
293C22⋊D43—41no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—42no—
299C2×Dic43—41no—
300D172—21no—
301D172—21no—
302D172—21no—
303D172C4×D412yes—
304C4×D43—22no—
305C4×D43—22no—
306C4×D43—44no—
307C4×D43—41no—
308C4×D43—41no—
309Dic86—21no—
310Dic86—21no—
311Dic86—21no—
312Dic86C4×D412yes—
313C8×C43—22no—
314C8×C43—22no—
315C8×C43—41no—
316C8×C43#12111yescharacteristic
317C8×C43#12111yescharacteristic
318C8×C43#12111yescharacteristic
319C8×C43#12111yescharacteristic
320C43⋊C8—22no—
321C43⋊C8—22no—
322C43⋊C8—41no—
323C43⋊C8C4×D411yescharacteristic
324C43⋊C8C4×D411yescharacteristic
325C43⋊C8C4×D411yescharacteristic
326C43⋊C8C4×D411yescharacteristic
327#21558—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—42no—
339C4×C43—41no—
340C4×C43—81no—
341C4×C43C2×C4×D411yescharacteristic
342C4×C43C2×C4×D411yescharacteristic
343C4×C43C2×#12111yescharacteristic
344C4×C43#52911yescharacteristic
345Dic43—22no—
346Dic43—22no—
347Dic43—41no—
348Dic43—41no—
349Dic43—81no—
350#3067—431no—
351#2955—431no—
352#2955—431no—
353C2×#443—431no—
354C4×#131—431no—
355#1976—431no—
356#1953—431no—
357#1932—431no—
358#1932—431no—
359#1906—431no—
360#1906—431no—
361#1814—431no—
362#1772—431no—
363#1757—431no—
364#1757D4311yescharacteristic, complemented
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×#131C2×D4311yescharacteristic
379C4×#41—431no—
380#473—432no—
381#472—432no—
382#471—432no—
383#471—432no—
384#444—862no—
385#444—862no—
386#443—862no—
387#443—861no—
388#443—861no—
389#443—861no—
390#443—861no—
391#443—862no—
392#430—431no—
393#430—431no—
394C2×#108—431no—
395C2×#108—431no—
396#427—431no—
397#421—431no—
398#421—431no—
399#421—431no—
400#421—431no—
401C2×#104—431no—
402C2×#104—431no—
403#413—431no—
404#413C2×D4311yescharacteristic
405#410—431no—
406#410C2×D4311yescharacteristic
407#405—431no—
408#405—431no—
409#405—861no—
410#405—861no—
411#405C2×D4311yescharacteristic
412#405C2×D4311yescharacteristic
413C4×M16—431no—
414C4×M16—861no—
415C2×C4×C8—431no—
416C2×C4×C8—861no—
417#344—431no—
418#344—431no—
419#344C2×D4311yescharacteristic
420#344C2×D4311yescharacteristic
421#339—431no—
422#339—431no—
423C43#2155811yescharacteristic, 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—21no—
446#131—21no—
447#131—21no—
448#131—21no—
449#131—432no—
450#131—432no—
451#131—432no—
452#131—432no—
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—21no—
462C2×M16—431no—
463C2×M16—431no—
464C2×M16—431no—
465C2×M16—861no—
466C2×M16—861no—
467C2×M16—861no—
468C2×M16C22×D4311yescharacteristic
469C2×M16C22×D4311yescharacteristic
470C2×M16C22×D4311yescharacteristic
471C22×C8—21no—
472C22×C8—431no—
473C22×C8—861no—
474C22×C8—861no—
475C22×C8—861no—
476C22×C8C22×D4311yescharacteristic
477C4×Q8—861no—
478C4×D4—861no—
479C4×D4—862no—
480#117—431no—
481#117—861no—
482#117C22×D4311yescharacteristic
483#117C22×D4311yescharacteristic
484C2×C42—431no—
485C2×C42—861no—
486#108—432no—
487#108—432no—
488#108—862no—
489#108—861no—
490#108—861no—
491#108—862no—
492#107—861no—
493#106—861no—
494#104—862no—
495#104—862no—
496#104—861no—
497#104—861no—
498#104—861no—
499#104—861no—
500#104—862no—
501#104—862no—
502#101—432no—
503#101C4×D4312yescomplemented
504#100—432no—
505#100C4×D4312yescomplemented
506#99—22no—
507#99—862no—
508#97—21no—
509#97—21no—
510#97—861no—
511#97—861no—
512#97—861no—
513C4×C8—21no—
514C4×C8—21no—
515C4×C8—431no—
516C4×C8—431no—
517C4×C8—431no—
518C4×C8—431no—
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—862no—
545C22×C4—861no—
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—41no—
570M16—41no—
571M16—432no—
572M16—432no—
573M16—862no—
574M16—862no—
575M16—861no—
576M16—861no—
577M16—862no—
578M16—862no—
579M16—861no—
580M16—861no—
581M16—1721no—
582M16—1721no—
583M16C2×C4×D4312yes—
584M16C2×C4×D4312yes—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—431no—
591C2×C8—431no—
592C2×C8—431no—
593C2×C8—431no—
594C2×C8—431no—
595C2×C8—431no—
596C2×C8—862no—
597C2×C8—862no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—862no—
601C2×C8—862no—
602C2×C8—861no—
603C2×C8—1721no—
604C2×C8—1721no—
605C2×C8#1062189811yescharacteristic
606C2×C8#1062189811yescharacteristic
607C2×C8D4×D4311yescharacteristic
608C2×C8D4×D4311yescharacteristic
609C2×C8D4×D4311yescharacteristic
610C2×C8D4×D4311yescharacteristic
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—862no—
614C4⋊C4—861no—
615C22⋊C4—21no—
616C22⋊C4—862no—
617C22⋊C4—861no—
618C22⋊C4#1062189812yes—
619C42—21no—
620C42—21no—
621C42—431no—
622C42—431no—
623C42—862no—
624C42—861no—
625C42—861no—
626C23—21no—
627C23—861no—
628C23—861no—
629C23C2×#1062189811yescharacteristic
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—22no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—861no—
654C2×C4—861no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—1724no—
660C2×C4—1722no—
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×C4C2×#1062189811yescharacteristic
670C8—22no—
671C8—22no—
672C8—41no—
673C8—431no—
674C8—431no—
675C8—431no—
676C8—431no—
677C8—862no—
678C8—862no—
679C8—1721no—
680C8#1306329811yescharacteristic
681C8#1306329811yescharacteristic
682C8#1306329811yescharacteristic
683C8#1306329811yescharacteristic
684C22—41no—
685C22—41no—
686C22—81no—
687C22—862no—
688C22—3441no—
689C22—1722no—
690C22—1721no—
691C22C4×#1062189811yescharacteristic
692C22#1458340811yescharacteristic
693C22#1458344611yescharacteristic
694C4—42no—
695C4—41no—
696C4—81no—
697C4—862no—
698C4—862no—
699C4—3441no—
700C4—1721no—
701C4—1721no—
702C4C4×D4×D4311yescharacteristic
703C4C4×D4×D4311yescharacteristic
704C4C2×#1306329811yescharacteristic
705C4#1458342711yescharacteristic
706C2—21no—
707C2—21no—
708C2—21no—
709C2—81no—
710C2—3441no—
711C2—1722no—
712C2C4×#1306329811yescharacteristic
subgroupG/H
centerC8#13063298
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1757C2
socleC2×C43C4×#121
prime radical#19144314C2
cosocleC22×C4×C43C24
hypercenter#1757D43
hypocenterC43#21558
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C22×C8 ◁ #1757

Complements

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

NH ≅ G/Ntype
2. #19143499C2semidirect
3. #19143496C2semidirect
4. C2×#14583014C2semidirect
5. #19143017C2semidirect
6. #19135490C2semidirect
7. #19135384C2semidirect
8. #19135266C2semidirect
9. #19135262C2semidirect
10. #19135097C2semidirect
11. #19135093C2semidirect
12. #19134648C2semidirect
13. #19134475C2semidirect
14. #19134396C2semidirect
15. C43×#1757C2semidirect
23. #14583173C4semidirect
24. #14583168C4semidirect
25. #14583165C4semidirect
26. #14583161C4semidirect
83. C2×#10621885C2×C4semidirect
84. C2×#10621883C2×C4semidirect
85. C2×#10621884C2×C4semidirect
86. C2×#10621882C2×C4semidirect
120. #13063260C2×C4semidirect
121. #13063260C2×C4semidirect
132. #13063243C2×C4semidirect
133. #13063241C2×C4semidirect
158. #101×C43C2×C4semidirect
159. #100×C43C2×C4semidirect
364. #1757D43semidirect
423. C43#21558semidirect
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
#191434992
#191434962
C2×#145830142
#191430172
#191354902
#191353842
#191352662
#191352622
#191350972
#191350932
#191346482
#191344752
#191343962
C43×#17572
#2155843