Finite Group Databasebeta

← #25964546

Subgroups — #25964546

Order 11008.

2184 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148264C211yesmaximal, characteristic
2#19147798C211yesmaximal, characteristic, complemented
3#19144586C213yesmaximal, complemented
4#19144575C213yesmaximal, complemented
5#19144554C213yesmaximal, complemented
6#19144554C213yesmaximal, complemented
7#19144536C213yesmaximal, complemented
8#19144528C213yesmaximal, complemented
9#19144510C213yesmaximal, complemented
10C2×#14583224C213yesmaximal, complemented
11#19143195C211yesmaximal, characteristic, complemented
12#19143190C211yesmaximal, characteristic, complemented
13#19143122C211yesmaximal, characteristic, complemented
14#19143122C211yesmaximal, characteristic, complemented
15C43×#2880C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17#14583568—21no—
18#14583560—21no—
19#14583537—23no—
20D4×C22⋊D43—23no—
21#14583477C2213yes—
22#14583463C2213yes—
23#14583410C2213yes—
24C2×#13063299C2213yes—
25#14583382C2211yescharacteristic
26#14583382C2211yescharacteristic
27#14583382C2211yescharacteristic
28#14583382C2213yescomplemented
29#14583382C2213yescomplemented
30#14583377—21no—
31#14583374—23no—
32#41×Dic43—21no—
33#41×Dic43—23no—
34C2×#13063284C2213yescomplemented
35C2×#13063284C2213yescomplemented
36#14583241C2211yescharacteristic, complemented
37#14583241C2213yescomplemented
38#14583241C2216yescomplemented
39#14583235C2213yescomplemented
40#14583230C2213yescomplemented
41#14583224C2213yescomplemented
42#14583224C2216yescomplemented
43#14583224C2216yescomplemented
44#14583224C2216yescomplemented
45#14583224C2213yescomplemented
46#14583224C2216yescomplemented
47#14583218C2213yescomplemented
48#14583218C2216yescomplemented
49#14583213C2213yescomplemented
50#14583213C2216yescomplemented
51#14582941C2213yescomplemented
52#14582941C2213yescomplemented
53#14582941C2213yescomplemented
54#14582941C2213yescomplemented
55#14582937C2213yescomplemented
56#14582937C2213yescomplemented
57C2×#13063259C2213yescomplemented
58C2×#13063257C2213yescomplemented
59#14582905C2213yescomplemented
60#14582905C2213yescomplemented
61#14582901C2213yescomplemented
62#14582901C2213yescomplemented
63#14582896C2213yescomplemented
64#14582896C2213yescomplemented
65C2×#13063247C2213yescomplemented
66C2×#13063247C2213yescomplemented
67C22×#41×C43C2211yescharacteristic
68C2×#131×C43C2211yescharacteristic
69C2×#131×C43C2211yescharacteristic
70C43×#408C2213yescomplemented
71C43×#408C2213yescomplemented
72C43×#407C2213yescomplemented
73C2×C22⋊C8×C43C2213yescomplemented
74#13063371—24no—
75#13063371—24no—
76C2×#10621902—21no—
77C2×#10621898C2313yes—
78C22×D172C2313yes—
79C22×C22⋊D43—23no—
80C2×D4×D43—23no—
81#13063321—23no—
82#13063314—23no—
83#13063308—23no—
84#13063304C2311yescharacteristic
85#13063304C2313yes—
86#13063301—23no—
87#13063299—23no—
88#13063299—23no—
89#13063299C2313yes—
90#13063299C2316yes—
91#13063299C2313yes—
92#13063297—26no—
93#13063296—23no—
94#13063294—23no—
95#13063293—26no—
96Q8×Dic43—21no—
97Q8×Dic43—21no—
98Q8×Dic43—21no—
99Q8×Dic43—23no—
100Q8×Dic43—23no—
101D4×Dic43—23no—
102D4×Dic43—23no—
103D4×Dic43—26no—
104D4×Dic43—26no—
105D4×Dic43—23no—
106D4×Dic43—23no—
107D4×Dic43—23no—
108C4×C22⋊D43—23no—
109C4×C22⋊D43—23no—
110#13063284—23no—
111#13063284—23no—
112#13063284—23no—
113#13063284—23no—
114#13063284C2313yes—
115#13063284C2311yescharacteristic
116#13063284C2313yes—
117#13063284C2313yes—
118#13063284C2316yes—
119#13063284C2313yes—
120C2×C4⋊Dic43C2313yes—
121C2×C4⋊Dic43C2313yes—
122C2×C4⋊Dic43C2313yes—
123C2×C4⋊Dic43C2313yes—
124C2×C4⋊Dic43C2313yes—
125C2×C22⋊Dic43—23no—
126C2×C22⋊Dic43—23no—
127C2×(C2×D43)⋊C4—23no—
128C2×C4×Dic43—23no—
129C2×C4×Dic43—23no—
130#13063259C2313yes—
131#13063259C2316yes—
132#13063259C2311yescharacteristic
133#13063259C2313yes—
134#13063259C2313yes—
135#13063257C2313yes—
136#13063257C2316yes—
137#13063257C2311yescharacteristic
138#13063257C2313yes—
139#13063257C2313yes—
140#13063250C2311yescharacteristic
141#13063250C2311yescharacteristic
142#13063250C2313yes—
143#13063250C2313yes—
144#13063247C2313yes—
145#13063247C2313yes—
146#13063247C2316yes—
147#13063247C2316yes—
148#13063247C2313yes—
149#13063247C2313yes—
150C2×#41×C43—24no—
151C2×#41×C43—24no—
152C2×#41×C43D411yescharacteristic
153C2×#41×C43D413yes—
154C2×#41×C43C2313yes—
155C2×#41×C43C2311yescharacteristic
156C22×Q8×C43D411yescharacteristic
157C22×D4×C43D413yes—
158C23×C4×C43C2313yes—
159#131×C43—24no—
160#131×C43—24no—
161C2×M16×C43C2313yes—
162C2×M16×C43C2313yes—
163C22×C8×C43C2313yes—
164C22×C8×C43C2313yes—
165C22⋊C8×C43C2311yescharacteristic
166C22⋊C8×C43C2313yes—
167C22⋊C8×C43C2313yes—
168C22⋊C8×C43C2313yes—
169C22⋊C8×C43C2316yes—
170C24×C43C2×D413yes—
171C23×D43—23no—
172#41×C43—24no—
173#41×C43—212no—
174#41×C43—26no—
175#41×C43—26no—
176#41×C43#4114yes—
177#41×C43#4114yes—
178C2×Q8×C43—24no—
179C2×Q8×C43C2×D413yes—
180C2×Q8×C43C2×D411yescharacteristic
181C2×D4×C43—212no—
182C2×D4×C43C2×D416yes—
183C2×D4×C43C2×D413yes—
184C2×D4×C43C2×D413yes—
185C22×C4×C43—26no—
186C22×C4×C43—26no—
187C22×C4×C43C2×D413yes—
188C22×C4×C43C2×D413yes—
189C22×C4×C43C2×D413yes—
190C22×C4×C43C2411yescharacteristic
191C22×C4×C43C2413yes—
192C22×C4×C43C2413yes—
193C2×C22⋊D43—23no—
194C2×C22⋊D43—23no—
195C2×C22⋊D43—23no—
196C2×C22⋊D43—26no—
197C2×C22⋊D43—86no—
198C22×Dic43—23no—
199C22×Dic43—23no—
200C22×Dic43—23no—
201C22×Dic43—23no—
202C22×Dic43—23no—
203#10621902—44no—
204D4×D43—412no—
205#10621898—26no—
206#10621898—26no—
207C2×D172—23no—
208C2×D172—26no—
209C2×D172—26no—
210C2×D172C2413yes—
211C2×C4×D43—23no—
212C2×Dic86C2411yescharacteristic
213M16×C43—26no—
214M16×C43—26no—
215C2×C8×C43—26no—
216C2×C8×C43—26no—
217C2×C8×C43C2411yescharacteristic
218C2×C8×C43C2411yescharacteristic
219C2×C8×C43C2413yes—
220C2×C8×C43C2413yes—
221C22⋊Dic43—23no—
222C22⋊Dic43—21no—
223C22⋊Dic43—26no—
224C22⋊Dic43—23no—
225C22⋊Dic43—23no—
226C22⋊Dic43—23no—
227C22⋊Dic43—21no—
228C22⋊Dic43—23no—
229(C2×D43)⋊C4—23no—
230(C2×D43)⋊C4—26no—
231(C2×D43)⋊C4—23no—
232C4⋊Dic43—23no—
233C4⋊Dic43—23no—
234C4⋊Dic43—23no—
235C4⋊Dic43—23no—
236C4⋊Dic43—23no—
237C4⋊Dic43C2413yes—
238C4⋊Dic43C2411yescharacteristic
239C4⋊Dic43C2413yes—
240C4⋊Dic43C2411yescharacteristic
241C4⋊Dic43C2413yes—
242C4⋊Dic43C2411yescharacteristic
243Dic43⋊C4—21no—
244Dic43⋊C4—23no—
245C4×Dic43—23no—
246C4×Dic43—21no—
247C4×Dic43—26no—
248C4×Dic43—23no—
249C4×Dic43—23no—
250C4×Dic43—23no—
251C23×C43—26no—
252C23×C43—43no—
253C23×C43—43no—
254C23×C43C22×D411yescharacteristic
255C23×C43C22×D413yes—
256C23×C43C22×D413yes—
257C22×D43—23no—
258C22×D43—46no—
259C22×D43—83no—
260C22×D43—83no—
261Q8×C43—26no—
262Q8×C43#12314yes—
263D4×C43—212no—
264D4×C43—26no—
265D4×C43#123112yes—
266C2×C4×C43—26no—
267C2×C4×C43—26no—
268C2×C4×C43—26no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—23no—
272C2×C4×C43—23no—
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×D413yes—
275C2×C4×C43C22×D413yes—
276C2×C4×C43C2×#4116yes—
277C2×C4×C43C2×#4116yes—
278C2×C4×C43C2511yescharacteristic
279C22⋊D43—46no—
280C22⋊D43—46no—
281C22⋊D43—83no—
282C22⋊D43—86no—
283C2×Dic43—23no—
284C2×Dic43—21no—
285C2×Dic43—23no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—23no—
289C2×Dic43—21no—
290C2×Dic43—83no—
291C2×Dic43—83no—
292C2×Dic43—83no—
293C2×Dic43—83no—
294C2×Dic43—83no—
295D172—23no—
296D172—23no—
297D172—46no—
298C4×D43—46no—
299Dic86—21no—
300Dic86—21no—
301C8×C43—21no—
302C8×C43—21no—
303C8×C43—23no—
304C8×C43—23no—
305#60523—431nomaximal, Sylow
306C22×C43—23no—
307C22×C43—23no—
308C22×C43—21no—
309C22×C43—23no—
310C22×C43—21no—
311C22×C43—23no—
312C22×C43—21no—
313C22×C43—23no—
314C22×C43—86no—
315C22×C43C2×#12316yes—
316C22×C43C23×D411yescharacteristic
317C2×D43—43no—
318C2×D43—43no—
319C2×D43—43no—
320C2×D43—166no—
321C4×C43—21no—
322C4×C43—23no—
323C4×C43C2×#12316yes—
324C4×C43C22×#4111yescharacteristic
325C4×C43C22×#4111yescharacteristic
326Dic43—43no—
327Dic43—41no—
328Dic43—41no—
329Dic43—43no—
330Dic43—41no—
331Dic43—43no—
332Dic43—41no—
333#3488—431no—
334#3428—431no—
335#3099—433no—
336#3098—433no—
337#3096—433no—
338#3096—433no—
339#3094—433no—
340#3093—433no—
341#3091—433no—
342C2×#482—433no—
343#2913—431no—
344#2912—431no—
345#2897—431no—
346#2897—431no—
347#2880D4311yescharacteristic, complemented
348C2×C43—26no—
349C2×C43—43no—
350C2×C43—41no—
351C2×C43C22×#12311yescharacteristic
352C2×C43#358411yescharacteristic
353C2×C43#358511yescharacteristic
354D43—83no—
355C2×H(5,𝔽2)—431no—
356C22×#41C2×D4311yescharacteristic
357C2×#131C2×D4311yescharacteristic
358C2×#131C2×D4311yescharacteristic
359#550—861no—
360#548—861no—
361#546—863no—
362D42—863no—
363#537—433no—
364#535—433no—
365#525—433no—
366C2×#121—433no—
367#520—433no—
368#520—433no—
369#520—431no—
370#520—431no—
371#520—431no—
372#519—861no—
373#518—863no—
374C4×#41—863no—
375C4×#41—861no—
376C2×#117—433no—
377C2×#117—433no—
378#485—431no—
379#485—433no—
380#485—436no—
381#484—433no—
382#483—433no—
383#482—433no—
384#482—436no—
385#482—436no—
386#482—436no—
387#482—433no—
388#482—436no—
389#481—433no—
390#481—436no—
391#480—433no—
392#480—436no—
393#428—433no—
394#428—433no—
395#428—433no—
396#428—433no—
397#427—433no—
398#427—433no—
399C2×#107—433no—
400C2×#106—433no—
401#418—433no—
402#418—433no—
403#417—433no—
404#417—433no—
405#416—433no—
406#416—433no—
407C2×#102—433no—
408C2×#102—433no—
409#408C2×D4313yescomplemented
410#408C2×D4313yescomplemented
411#407C2×D4313yescomplemented
412C2×C22⋊C8C2×D4313yescomplemented
413C43#6052311yescharacteristic, complemented, Sylow
414H(5,𝔽2)—864no—
415H(5,𝔽2)—864no—
416C2×#41—24no—
417C2×#41—24no—
418C2×#41—433no—
419C2×#41—861no—
420C2×#41D17213yes—
421C2×#41D17211yescharacteristic
422C2×#41C22×D4313yes—
423C2×#41C22×D4311yescharacteristic
424C22×Q8D17211yescharacteristic
425C22×D4—433no—
426C22×D4—863no—
427C22×D4—863no—
428C22×D4D17213yes—
429C23×C4C22×D4313yes—
430#131—24no—
431#131—24no—
432C2×M16C22×D4313yes—
433C2×M16C22×D4313yes—
434C22×C8C22×D4313yes—
435C22×C8C22×D4313yes—
436#127—863no—
437#124—863no—
438#123—863no—
439C22⋊Q8—431no—
440C22⋊Q8—433no—
441C22⋊Q8—863no—
442#121—433no—
443#121—436no—
444#121—433no—
445#121—866no—
446#121—863no—
447#121—863no—
448#121—863no—
449#120—863no—
450#120—866no—
451C4×Q8—863no—
452C4×Q8—863no—
453C4×Q8—861no—
454C4×Q8—861no—
455C4×Q8—861no—
456C4×D4—866no—
457C4×D4—866no—
458C4×D4—863no—
459C4×D4—863no—
460C4×D4—863no—
461C4×D4—863no—
462C4×D4—863no—
463C4×D4—863no—
464C4×D4—863no—
465#117—433no—
466#117—431no—
467#117—433no—
468#117—433no—
469#117—436no—
470#117—433no—
471#117—863no—
472#117—863no—
473#117—863no—
474#117—863no—
475C2×C4⋊C4—433no—
476C2×C4⋊C4—433no—
477C2×C4⋊C4—433no—
478C2×C4⋊C4—433no—
479C2×C4⋊C4—433no—
480C2×C22⋊C4—863no—
481C2×C22⋊C4—863no—
482C2×C22⋊C4—863no—
483C2×C42—863no—
484C2×C42—863no—
485#107—433no—
486#107—436no—
487#107—431no—
488#107—433no—
489#107—433no—
490#106—433no—
491#106—436no—
492#106—431no—
493#106—433no—
494#106—433no—
495#103—431no—
496#103—431no—
497#103—433no—
498#103—433no—
499#102—433no—
500#102—433no—
501#102—436no—
502#102—436no—
503#102—433no—
504#102—433no—
505C22⋊C8C22×D4311yescharacteristic
506C22⋊C8C22×D4313yes—
507C22⋊C8C22×D4313yes—
508C22⋊C8C22×D4313yes—
509C22⋊C8C22×D4316yes—
510C24—863no—
511C24C2×D17213yes—
512#41—24no—
513#41—212no—
514#41—26no—
515#41—26no—
516#41—866no—
517#41—866no—
518#41—1724no—
519#41#1062190014yes—
520#41#1062190014yes—
521C2×Q8—24no—
522C2×Q8—431no—
523C2×Q8C2×D17213yes—
524C2×Q8C2×D17211yescharacteristic
525C2×D4—212no—
526C2×D4—433no—
527C2×D4—863no—
528C2×D4—866no—
529C2×D4—863no—
530C2×D4—863no—
531C2×D4—863no—
532C2×D4—866no—
533C2×D4—866no—
534C2×D4—3446no—
535C2×D4—17212no—
536C2×D4C2×D17216yes—
537C2×D4C2×D17213yes—
538C2×D4C2×D17213yes—
539C22×C4—26no—
540C22×C4—26no—
541C22×C4—863no—
542C22×C4—863no—
543C22×C4—863no—
544C22×C4—863no—
545C22×C4—863no—
546C22×C4—863no—
547C22×C4C2×D17213yes—
548C22×C4C2×D17213yes—
549C22×C4C2×D17213yes—
550C22×C4C23×D4313yes—
551C22×C4C23×D4311yescharacteristic
552C22×C4C23×D4313yes—
553M16—26no—
554M16—26no—
555C2×C8—26no—
556C2×C8—26no—
557C2×C8C23×D4311yescharacteristic
558C2×C8C23×D4313yes—
559C2×C8C23×D4313yes—
560C2×C8C23×D4311yescharacteristic
561C4⋊C4—433no—
562C4⋊C4—431no—
563C4⋊C4—433no—
564C4⋊C4—431no—
565C4⋊C4—433no—
566C4⋊C4—431no—
567C4⋊C4—863no—
568C4⋊C4—863no—
569C4⋊C4—863no—
570C4⋊C4—863no—
571C4⋊C4—863no—
572C4⋊C4—861no—
573C4⋊C4—863no—
574C22⋊C4—863no—
575C22⋊C4—861no—
576C22⋊C4—866no—
577C22⋊C4—863no—
578C22⋊C4—863no—
579C22⋊C4—863no—
580C22⋊C4—861no—
581C22⋊C4—863no—
582C22⋊C4—863no—
583C22⋊C4—866no—
584C22⋊C4—863no—
585C42—863no—
586C42—861no—
587C42—866no—
588C42—863no—
589C42—863no—
590C42—863no—
591C23—26no—
592C23—43no—
593C23—43no—
594C23—863no—
595C23—3443no—
596C23—3443no—
597C23—1726no—
598C23C22×D17211yescharacteristic
599C23C22×D17213yes—
600C23C22×D17213yes—
601Q8—26no—
602Q8—861no—
603Q8—861no—
604Q8#1306330914yes—
605D4—212no—
606D4—26no—
607D4—863no—
608D4—863no—
609D4—3446no—
610D4—3443no—
611D4—1726no—
612D4—1726no—
613D4—1726no—
614D4#13063309112yes—
615C2×C4—26no—
616C2×C4—26no—
617C2×C4—26no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—23no—
621C2×C4—23no—
622C2×C4—863no—
623C2×C4—861no—
624C2×C4—863no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—863no—
628C2×C4—861no—
629C2×C4—3443no—
630C2×C4—3443no—
631C2×C4—3443no—
632C2×C4—3443no—
633C2×C4—3443no—
634C2×C4—1726no—
635C2×C4C22×D17211yescharacteristic
636C2×C4C22×D17213yes—
637C2×C4C22×D17213yes—
638C2×C4C2×#1062190016yes—
639C2×C4C2×#1062190016yes—
640C2×C4C24×D4311yescharacteristic
641C8—21no—
642C8—21no—
643C8—23no—
644C8—23no—
645C22—23no—
646C22—23no—
647C22—21no—
648C22—23no—
649C22—23no—
650C22—21no—
651C22—23no—
652C22—21no—
653C22—86no—
654C22—1723no—
655C22—1723no—
656C22—1723no—
657C22—6886no—
658C22C2×#1306330916yes—
659C22C23×D17211yescharacteristic
660C4—21no—
661C4—23no—
662C4—1721no—
663C4—1723no—
664C4—1721no—
665C4—1721no—
666C4—1723no—
667C4—1721no—
668C4—1723no—
669C4C2×#1306330916yes—
670C4C22×#1062190011yescharacteristic
671C4C22×#1062190011yescharacteristic
672C2—26no—
673C2—41no—
674C2—43no—
675C2—3443no—
676C2C22×#1306330911yescharacteristic
677C2#1914936911yescharacteristic
678C2#1914937611yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2880C2
socleC22×C43C23×D4
prime radical#19148264C2
hypercenter#2880D43
hypocenterC43#60523
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×#41 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. #19147798C2semidirect
3. #19144586C2semidirect
4. #19144575C2semidirect
5. #19144554C2semidirect
6. #19144554C2semidirect
7. #19144536C2semidirect
8. #19144528C2semidirect
9. #19144510C2semidirect
10. C2×#14583224C2semidirect
11. #19143195C2semidirect
12. #19143190C2semidirect
13. #19143122C2semidirect
14. #19143122C2semidirect
15. C43×#2880C2semidirect
28. #14583382C22semidirect
29. #14583382C22semidirect
34. C2×#13063284C22semidirect
35. C2×#13063284C22semidirect
36. #14583241C22semidirect
37. #14583241C22semidirect
38. #14583241C22semidirect
39. #14583235C22semidirect
40. #14583230C22semidirect
41. #14583224C22semidirect
42. #14583224C22semidirect
43. #14583224C22semidirect
44. #14583224C22semidirect
45. #14583224C22semidirect
46. #14583224C22semidirect
47. #14583218C22semidirect
48. #14583218C22semidirect
49. #14583213C22semidirect
50. #14583213C22semidirect
51. #14582941C22semidirect
52. #14582941C22semidirect
53. #14582941C22semidirect
54. #14582941C22semidirect
55. #14582937C22semidirect
56. #14582937C22semidirect
57. C2×#13063259C22semidirect
58. C2×#13063257C22semidirect
59. #14582905C22semidirect
60. #14582905C22semidirect
61. #14582901C22semidirect
62. #14582901C22semidirect
63. #14582896C22semidirect
64. #14582896C22semidirect
65. C2×#13063247C22semidirect
66. C2×#13063247C22semidirect
70. C43×#408C22semidirect
71. C43×#408C22semidirect
72. C43×#407C22semidirect
73. C2×C22⋊C8×C43C22semidirect
347. #2880D43semidirect
409. #408C2×D43semidirect
410. #408C2×D43semidirect
411. #407C2×D43semidirect
412. C2×C22⋊C8C2×D43semidirect
413. C43#60523semidirect

Maximal subgroups

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

subgroupindex
#191482642
#191477982
#191445862
#191445752
#191445542
#191445362
#191445282
#191445102
C2×#145832242
#191431952
#191431902
#191431222
C43×#28802
#6052343