Finite Group Databasebeta

← #25964545

Subgroups — #25964545

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#19144584C213yesmaximal, complemented
3#19144573C213yesmaximal, complemented
4#19144553C213yesmaximal, complemented
5#19144553C213yesmaximal, complemented
6#19144535C213yesmaximal, complemented
7#19144526C213yesmaximal, complemented
8#19144508C213yesmaximal, complemented
9C2×#14583223C213yesmaximal, complemented
10#19143193C211yesmaximal, characteristic, complemented
11#19143188C211yesmaximal, characteristic, complemented
12#19143118C211yesmaximal, characteristic, complemented
13#19143118C211yesmaximal, characteristic, complemented
14#19143044C211yesmaximal, characteristic, complemented
15C43×#3428C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19#14583568—21no—
20#14583560—21no—
21#14583537—23no—
22D4×C22⋊D43—23no—
23#14583477C2213yes—
24#14583463C2213yes—
25#14583410C2213yes—
26C2×#13063299C2213yes—
27#14583382C2211yescharacteristic
28#14583240C2211yescharacteristic, complemented
29#14583240C2213yescomplemented
30#14583240C2216yescomplemented
31#14583234C2213yescomplemented
32#14583229C2213yescomplemented
33#14583223C2213yescomplemented
34#14583223C2216yescomplemented
35#14583223C2216yescomplemented
36#14583223C2216yescomplemented
37#14583223C2213yescomplemented
38#14583223C2216yescomplemented
39#14583217C2213yescomplemented
40#14583217C2216yescomplemented
41#14583212C2213yescomplemented
42#14583212C2216yescomplemented
43#14582942C2213yescomplemented
44#14582942C2213yescomplemented
45#14582939C2213yescomplemented
46#14582939C2213yescomplemented
47#14582935C2213yescomplemented
48#14582935C2213yescomplemented
49C2×#13063258C2213yescomplemented
50C2×#13063256C2213yescomplemented
51#14582903C2213yescomplemented
52#14582903C2213yescomplemented
53#14582898C2213yescomplemented
54#14582898C2213yescomplemented
55#14582893C2213yescomplemented
56#14582893C2213yescomplemented
57C2×#13063245C2213yescomplemented
58C2×#13063245C2213yescomplemented
59#14582866C2213yescomplemented
60#14582866C2213yescomplemented
61#14582863C2213yescomplemented
62C2×C22⋊(C43⋊C8)C2213yescomplemented
63C22×#41×C43C2211yescharacteristic
64C43×#520C2211yescharacteristic
65C43×#520C2211yescharacteristic
66C43×#520C2213yescomplemented
67C43×#520C2213yescomplemented
68C43×#519—21no—
69C43×#518—23no—
70C4×#41×C43—23no—
71C4×#41×C43—21no—
72C2×#117×C43C2213yescomplemented
73C2×#117×C43C2213yescomplemented
74#13063371—24no—
75#13063371—24no—
76C2×#10621902—21no—
77C2×#10621898C2313yes—
78C22×D172C2313yes—
79C22×C22⋊D43—23no—
80C2×D4×D43—23no—
81#13063332—24no—
82#13063332—24no—
83C2×#10621877C2313yes—
84C2×#10621877C2313yes—
85C22×C43⋊C8C2313yes—
86C22×C43⋊C8C2313yes—
87#13063321—23no—
88#13063314—23no—
89#13063308—23no—
90#13063304C2311yescharacteristic
91#13063304C2313yes—
92#13063301—23no—
93#13063299—23no—
94#13063299—23no—
95#13063299C2313yes—
96#13063299C2316yes—
97#13063299C2313yes—
98#13063297—26no—
99#13063296—23no—
100#13063294—23no—
101#13063293—26no—
102Q8×Dic43—21no—
103D4×Dic43—23no—
104C4×C22⋊D43—23no—
105C4×C22⋊D43—23no—
106#13063284C2313yes—
107C2×C4⋊Dic43C2313yes—
108C2×(C2×D43)⋊C4—23no—
109#13063258C2313yes—
110#13063258C2316yes—
111#13063258C2311yescharacteristic
112#13063258C2313yes—
113#13063258C2313yes—
114#13063256C2313yes—
115#13063256C2316yes—
116#13063256C2311yescharacteristic
117#13063256C2313yes—
118#13063256C2313yes—
119#13063248C2311yescharacteristic
120#13063248C2311yescharacteristic
121#13063248C2313yes—
122#13063248C2313yes—
123#13063245C2313yes—
124#13063245C2313yes—
125#13063245C2316yes—
126#13063245C2316yes—
127#13063245C2313yes—
128#13063245C2313yes—
129C22⋊(C43⋊C8)C2311yescharacteristic
130C22⋊(C43⋊C8)C2313yes—
131C22⋊(C43⋊C8)C2313yes—
132C22⋊(C43⋊C8)C2313yes—
133C22⋊(C43⋊C8)C2316yes—
134C2×#41×C43—24no—
135C2×#41×C43—24no—
136C2×#41×C43D411yescharacteristic
137C2×#41×C43D413yes—
138C2×#41×C43C2313yes—
139C2×#41×C43C2311yescharacteristic
140C22×Q8×C43D411yescharacteristic
141C22×D4×C43D413yes—
142C23×C4×C43C2313yes—
143C4×Q8×C43—21no—
144C4×Q8×C43—21no—
145C4×Q8×C43—23no—
146C4×Q8×C43—23no—
147C4×D4×C43—23no—
148C4×D4×C43—23no—
149C4×D4×C43—26no—
150C4×D4×C43—26no—
151C4×D4×C43—23no—
152C4×D4×C43—23no—
153#117×C43—23no—
154#117×C43—23no—
155#117×C43—23no—
156#117×C43—23no—
157#117×C43C2313yes—
158#117×C43C2311yescharacteristic
159#117×C43C2313yes—
160#117×C43C2313yes—
161#117×C43C2316yes—
162C2×C4⋊C4×C43C2313yes—
163C2×C4⋊C4×C43C2313yes—
164C2×C4⋊C4×C43C2313yes—
165C2×C4⋊C4×C43C2313yes—
166C2×C22⋊C4×C43—23no—
167C2×C22⋊C4×C43—23no—
168C2×C42×C43—23no—
169C2×C42×C43—23no—
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×C43—23no—
188C22×C4×C43—23no—
189C22×C4×C43—23no—
190C22×C4×C43—23no—
191C22×C4×C43C2×D413yes—
192C22×C4×C43C2×D413yes—
193C22×C4×C43C2×D413yes—
194C22×C4×C43C2413yes—
195C22×C4×C43C2411yescharacteristic
196C22×C4×C43C2413yes—
197C2×C22⋊D43—23no—
198C2×C22⋊D43—23no—
199C2×C22⋊D43—23no—
200C2×C22⋊D43—26no—
201C2×C22⋊D43—86no—
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
213C4⋊C4×C43—23no—
214C4⋊C4×C43—23no—
215C4⋊C4×C43—23no—
216C4⋊C4×C43—23no—
217C4⋊C4×C43C2413yes—
218C4⋊C4×C43C2411yescharacteristic
219C4⋊C4×C43C2413yes—
220C4⋊C4×C43C2411yescharacteristic
221C22⋊C4×C43—23no—
222C22⋊C4×C43—21no—
223C22⋊C4×C43—26no—
224C22⋊C4×C43—23no—
225C22⋊C4×C43—23no—
226C42×C43—23no—
227C42×C43—21no—
228C42×C43—26no—
229C42×C43—23no—
230C42×C43—23no—
231C22⋊Dic43—23no—
232C22⋊Dic43—21no—
233C22⋊Dic43—23no—
234(C2×D43)⋊C4—23no—
235(C2×D43)⋊C4—26no—
236(C2×D43)⋊C4—23no—
237C4⋊Dic43—23no—
238C4⋊Dic43C2413yes—
239C4⋊Dic43C2411yescharacteristic
240Dic43⋊C4—21no—
241Dic43⋊C4—23no—
242C4×Dic43—23no—
243#10621877—26no—
244#10621877—26no—
245C2×C43⋊C8—26no—
246C2×C43⋊C8—26no—
247C2×C43⋊C8C2411yescharacteristic
248C2×C43⋊C8C2413yes—
249C2×C43⋊C8C2413yes—
250C2×C43⋊C8C2411yescharacteristic
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×C43—23no—
274C2×C4×C43—21no—
275C2×C4×C43—23no—
276C2×C4×C43—21no—
277C2×C4×C43—83no—
278C2×C4×C43—83no—
279C2×C4×C43—83no—
280C2×C4×C43—83no—
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C22×D413yes—
283C2×C4×C43C22×D413yes—
284C2×C4×C43C2×#4116yes—
285C2×C4×C43C2×#4116yes—
286C2×C4×C43C2511yescharacteristic
287C22⋊D43—46no—
288C22⋊D43—46no—
289C22⋊D43—83no—
290C22⋊D43—86no—
291C2×Dic43—21no—
292C2×Dic43—23no—
293C2×Dic43—21no—
294C2×Dic43—83no—
295D172—23no—
296D172—23no—
297D172—46no—
298C4×D43—46no—
299Dic86—21no—
300Dic86—21no—
301C43⋊C8—21no—
302C43⋊C8—21no—
303C43⋊C8—23no—
304C43⋊C8—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×C43—43no—
324C4×C43—41no—
325C4×C43—43no—
326C4×C43—41no—
327C4×C43C2×#12316yes—
328C4×C43C22×#4111yescharacteristic
329C4×C43C22×#4111yescharacteristic
330Dic43—41no—
331Dic43—43no—
332Dic43—41no—
333#3488—431no—
334#3428D4311yescharacteristic, complemented
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#2880—431no—
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×#131—431no—
358C2×#131—431no—
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—431no—
368#520C2×D4311yescharacteristic
369#520C2×D4311yescharacteristic
370#520C2×D4313yescomplemented
371#520C2×D4313yescomplemented
372#519—21no—
373#518—23no—
374C4×#41—23no—
375C4×#41—21no—
376C2×#117C2×D4313yescomplemented
377C2×#117C2×D4313yescomplemented
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#408—433no—
410#408—433no—
411#407—433no—
412C2×C22⋊C8—433no—
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×#41C22⋊D4313yes—
421C2×#41C22⋊D4311yescharacteristic
422C2×#41C22×D4313yes—
423C2×#41C22×D4311yescharacteristic
424C22×Q8C22⋊D4311yescharacteristic
425C22×D4—433no—
426C22×D4—863no—
427C22×D4—863no—
428C22×D4C22⋊D4313yes—
429C23×C4C22×D4313yes—
430#131—864no—
431#131—864no—
432C2×M16—433no—
433C2×M16—433no—
434C22×C8—433no—
435C22×C8—433no—
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—21no—
452C4×Q8—21no—
453C4×Q8—23no—
454C4×Q8—23no—
455C4×Q8—861no—
456C4×D4—23no—
457C4×D4—23no—
458C4×D4—26no—
459C4×D4—26no—
460C4×D4—23no—
461C4×D4—23no—
462C4×D4—863no—
463C4×D4—863no—
464C4×D4—863no—
465#117—23no—
466#117—23no—
467#117—23no—
468#117—23no—
469#117—433no—
470#117C22×D4313yes—
471#117C22×D4311yescharacteristic
472#117C22×D4313yes—
473#117C22×D4313yes—
474#117C22×D4316yes—
475C2×C4⋊C4—433no—
476C2×C4⋊C4C22×D4313yes—
477C2×C4⋊C4C22×D4313yes—
478C2×C4⋊C4C22×D4313yes—
479C2×C4⋊C4C22×D4313yes—
480C2×C22⋊C4—23no—
481C2×C22⋊C4—23no—
482C2×C22⋊C4—863no—
483C2×C42—23no—
484C2×C42—23no—
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⋊C8—431no—
506C22⋊C8—433no—
507C22⋊C8—433no—
508C22⋊C8—433no—
509C22⋊C8—436no—
510C24—863no—
511C24C2×C22⋊D4313yes—
512#41—24no—
513#41—212no—
514#41—26no—
515#41—26no—
516#41—866no—
517#41—866no—
518#41—1724no—
519#41#1062189814yes—
520#41#1062189814yes—
521C2×Q8—24no—
522C2×Q8—431no—
523C2×Q8C2×C22⋊D4313yes—
524C2×Q8C2×C22⋊D4311yescharacteristic
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×C22⋊D4316yes—
537C2×D4C2×C22⋊D4313yes—
538C2×D4C2×C22⋊D4313yes—
539C22×C4—26no—
540C22×C4—26no—
541C22×C4—23no—
542C22×C4—23no—
543C22×C4—23no—
544C22×C4—23no—
545C22×C4—863no—
546C22×C4—863no—
547C22×C4C2×C22⋊D4313yes—
548C22×C4C2×C22⋊D4313yes—
549C22×C4C2×C22⋊D4313yes—
550C22×C4C23×D4313yes—
551C22×C4C23×D4311yescharacteristic
552C22×C4C23×D4313yes—
553M16—866no—
554M16—866no—
555C2×C8—431no—
556C2×C8—433no—
557C2×C8—433no—
558C2×C8—431no—
559C2×C8—866no—
560C2×C8—866no—
561C4⋊C4—23no—
562C4⋊C4—23no—
563C4⋊C4—23no—
564C4⋊C4—23no—
565C4⋊C4—433no—
566C4⋊C4—431no—
567C4⋊C4—863no—
568C4⋊C4—861no—
569C4⋊C4—863no—
570C4⋊C4C23×D4313yes—
571C4⋊C4C23×D4311yescharacteristic
572C4⋊C4C23×D4313yes—
573C4⋊C4C23×D4311yescharacteristic
574C22⋊C4—23no—
575C22⋊C4—21no—
576C22⋊C4—26no—
577C22⋊C4—23no—
578C22⋊C4—23no—
579C22⋊C4—863no—
580C22⋊C4—861no—
581C22⋊C4—863no—
582C22⋊C4—863no—
583C22⋊C4—866no—
584C22⋊C4—863no—
585C42—23no—
586C42—21no—
587C42—26no—
588C42—23no—
589C42—23no—
590C42—863no—
591C23—26no—
592C23—43no—
593C23—43no—
594C23—863no—
595C23—3443no—
596C23—3443no—
597C23—1726no—
598C23C22×C22⋊D4311yescharacteristic
599C23C22×C22⋊D4313yes—
600C23C22×C22⋊D4313yes—
601Q8—26no—
602Q8—861no—
603Q8—861no—
604Q8#1306330814yes—
605D4—212no—
606D4—26no—
607D4—863no—
608D4—863no—
609D4—3446no—
610D4—3443no—
611D4—1726no—
612D4—1726no—
613D4—1726no—
614D4#13063308112yes—
615C2×C4—26no—
616C2×C4—26no—
617C2×C4—26no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—23no—
621C2×C4—23no—
622C2×C4—23no—
623C2×C4—21no—
624C2×C4—23no—
625C2×C4—21no—
626C2×C4—83no—
627C2×C4—83no—
628C2×C4—83no—
629C2×C4—83no—
630C2×C4—861no—
631C2×C4—863no—
632C2×C4—861no—
633C2×C4—3443no—
634C2×C4—1726no—
635C2×C4C22×C22⋊D4311yescharacteristic
636C2×C4C22×C22⋊D4313yes—
637C2×C4C22×C22⋊D4313yes—
638C2×C4C2×#1062189816yes—
639C2×C4C2×#1062189816yes—
640C2×C4C24×D4311yescharacteristic
641C8—861no—
642C8—861no—
643C8—863no—
644C8—863no—
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×#1306330816yes—
659C22C23×C22⋊D4311yescharacteristic
660C4—21no—
661C4—23no—
662C4—43no—
663C4—41no—
664C4—43no—
665C4—41no—
666C4—1721no—
667C4—1721no—
668C4—1723no—
669C4C2×#1306330816yes—
670C4C22×#1062189811yescharacteristic
671C4C22×#1062189811yescharacteristic
672C2—26no—
673C2—41no—
674C2—43no—
675C2—3443no—
676C2C22×#1306330811yescharacteristic
677C2#1914936611yescharacteristic
678C2#1914937411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3428C2
socleC22×C43C23×D4
prime radical#19148264C2
hypercenter#3428D43
hypocenterC43#60523
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3428

Complements

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

NH ≅ G/Ntype
2. #19144584C2semidirect
3. #19144573C2semidirect
4. #19144553C2semidirect
5. #19144553C2semidirect
6. #19144535C2semidirect
7. #19144526C2semidirect
8. #19144508C2semidirect
9. C2×#14583223C2semidirect
10. #19143193C2semidirect
11. #19143188C2semidirect
12. #19143118C2semidirect
13. #19143118C2semidirect
14. #19143044C2semidirect
15. C43×#3428C2semidirect
28. #14583240C22semidirect
29. #14583240C22semidirect
30. #14583240C22semidirect
31. #14583234C22semidirect
32. #14583229C22semidirect
33. #14583223C22semidirect
34. #14583223C22semidirect
35. #14583223C22semidirect
36. #14583223C22semidirect
37. #14583223C22semidirect
38. #14583223C22semidirect
39. #14583217C22semidirect
40. #14583217C22semidirect
41. #14583212C22semidirect
42. #14583212C22semidirect
43. #14582942C22semidirect
44. #14582942C22semidirect
45. #14582939C22semidirect
46. #14582939C22semidirect
47. #14582935C22semidirect
48. #14582935C22semidirect
49. C2×#13063258C22semidirect
50. C2×#13063256C22semidirect
51. #14582903C22semidirect
52. #14582903C22semidirect
53. #14582898C22semidirect
54. #14582898C22semidirect
55. #14582893C22semidirect
56. #14582893C22semidirect
57. C2×#13063245C22semidirect
58. C2×#13063245C22semidirect
59. #14582866C22semidirect
60. #14582866C22semidirect
61. #14582863C22semidirect
62. C2×C22⋊(C43⋊C8)C22semidirect
66. C43×#520C22semidirect
67. C43×#520C22semidirect
72. C2×#117×C43C22semidirect
73. C2×#117×C43C22semidirect
334. #3428D43semidirect
370. #520C2×D43semidirect
371. #520C2×D43semidirect
376. C2×#117C2×D43semidirect
377. C2×#117C2×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
#191445842
#191445732
#191445532
#191445352
#191445262
#191445082
C2×#145832232
#191431932
#191431882
#191431182
#191430442
C43×#34282
#6052343