Finite Group Databasebeta

← #25964569

Subgroups — #25964569

Order 11008.

2234 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148257C211yesmaximal, characteristic
2#520×D43C211yesmaximal, characteristic, complemented
3#19144583C213yesmaximal, complemented
4#19144582C213yesmaximal, complemented
5#19144551C213yesmaximal, complemented
6#19144549C213yesmaximal, complemented
7#19144533C213yesmaximal, complemented
8#19144516C213yesmaximal, complemented
9#19144506C213yesmaximal, complemented
10C2×#14583216C213yesmaximal, complemented
11#19143190C211yesmaximal, characteristic, complemented
12#19143188C211yesmaximal, characteristic, complemented
13#19143121C211yesmaximal, characteristic, complemented
14#19143042C211yesmaximal, characteristic, complemented
15C43×#2897C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#14583568—21no—
19#14583556—21no—
20#14583543—23no—
21D4×C22⋊D43—23no—
22#14583477C2213yes—
23#14583466C2213yes—
24#14583406C2213yes—
25C2×#13063296C2213yes—
26#14583382C2211yescharacteristic
27#14583382C2211yescharacteristic
28#14583381—21no—
29#14583380C2213yescomplemented
30#14583379C2213yescomplemented
31#14583378—23no—
32C4×Q8×D43—21no—
33C4×D4×D43—23no—
34#117×D43C2213yescomplemented
35C2×C4⋊C4×D43C2213yescomplemented
36#14583239C2213yescomplemented
37#14583238C2213yescomplemented
38#14583233C2213yescomplemented
39#14583228C2211yescharacteristic, complemented
40#14583228C2216yescomplemented
41#14583222C2213yescomplemented
42#14583222C2216yescomplemented
43#14583221C2213yescomplemented
44#14583221C2216yescomplemented
45#14583216C2213yescomplemented
46#14583216C2216yescomplemented
47#14583216C2216yescomplemented
48#14583216C2216yescomplemented
49#14583211C2213yescomplemented
50#14583211C2216yescomplemented
51#14582942C2213yescomplemented
52#14582941C2213yescomplemented
53#14582941C2213yescomplemented
54#14582939C2213yescomplemented
55#14582937C2213yescomplemented
56#14582935C2213yescomplemented
57C2×#13063257C2213yescomplemented
58C2×#13063256C2213yescomplemented
59#14582904C2213yescomplemented
60#14582900C2213yescomplemented
61#14582895C2213yescomplemented
62C2×#13063246C2213yescomplemented
63#14582867C2213yescomplemented
64#14582865C2213yescomplemented
65#14582862C2213yescomplemented
66C2×(C2×D43)⋊C8C2213yescomplemented
67C2×H(5,𝔽2)×C43C2211yescharacteristic
68C2×#131×C43C2211yescharacteristic
69C43×#520C2211yescharacteristic
70C43×#418C2213yescomplemented
71C43×#417C2213yescomplemented
72C43×#416C2213yescomplemented
73C2×#102×C43C2213yescomplemented
74C2×#10621902D411yescharacteristic
75C2×#10621898C2313yes—
76C2×#10621900D413yes—
77#41×D43—24no—
78#41×D43—24no—
79C2×Q8×D43D411yescharacteristic
80C22×C22⋊D43—23no—
81C2×D4×D43D413yes—
82C22×C4×D43—23no—
83C22×C4×D43C2313yes—
84#13063332—24no—
85C2×#10621877C2313yes—
86C22×C43⋊C8C2313yes—
87#13063321—23no—
88#13063312—23no—
89#13063306—23no—
90#13063304—23no—
91#13063301C2311yescharacteristic
92#13063301C2313yes—
93#13063299—23no—
94#13063297—26no—
95#13063296—23no—
96#13063296—23no—
97#13063296C2313yes—
98#13063296C2316yes—
99#13063296C2313yes—
100#13063294—26no—
101#13063293—23no—
102Q8×Dic43—21no—
103Q8×Dic43—21no—
104C4×Dic86—23no—
105#13063290—23no—
106C4×D172—23no—
107D4×Dic43—23no—
108D4×Dic43—23no—
109#13063287—23no—
110C4×C22⋊D43—26no—
111C4×C22⋊D43—23no—
112C4×C22⋊D43—23no—
113(C22⋊D43)⋊C4—26no—
114#13063284C2313yes—
115#13063284C2313yes—
116#13063283C2313yes—
117#13063283C2313yes—
118#13063282—23no—
119#13063281—23no—
120C2×C4⋊Dic43C2313yes—
121C2×C4⋊Dic43C2313yes—
122C2×Dic43⋊C4—23no—
123C4⋊C4×D43—23no—
124C4⋊C4×D43—23no—
125C4⋊C4×D43C2313yes—
126C4⋊C4×D43C2316yes—
127C4⋊C4×D43C2311yescharacteristic
128C2×C22⋊Dic43—23no—
129C22⋊C4×D43—23no—
130C42×D43—23no—
131#13063259C2313yes—
132#13063259C2313yes—
133#13063258C2313yes—
134#13063258C2313yes—
135#13063257C2313yes—
136#13063257C2316yes—
137#13063257C2311yescharacteristic
138#13063256C2313yes—
139#13063256C2316yes—
140#13063256C2311yescharacteristic
141#13063249C2311yescharacteristic
142#13063249C2313yes—
143#13063246C2313yes—
144#13063246C2316yes—
145#13063246C2313yes—
146(C2×D43)⋊C8C2311yescharacteristic
147(C2×D43)⋊C8C2313yes—
148(C2×D43)⋊C8C2313yes—
149(C2×D43)⋊C8C2313yes—
150(C2×D43)⋊C8C2316yes—
151H(5,𝔽2)×C43—24no—
152H(5,𝔽2)×C43—24no—
153C2×#41×C43—21no—
154C2×#41×C43C2313yes—
155C2×#41×C43C2311yescharacteristic
156C22×D4×C43—23no—
157C22×D4×C43C2313yes—
158#131×C43—24no—
159C2×M16×C43C2313yes—
160C22×C8×C43C2313yes—
161C4×Q8×C43—21no—
162C4×D4×C43—23no—
163#117×C43C2313yes—
164C2×C4⋊C4×C43C2313yes—
165#103×C43C2311yescharacteristic
166#103×C43C2313yes—
167#102×C43C2316yes—
168#102×C43C2313yes—
169#102×C43C2313yes—
170C24×C43—23no—
171C23×D43C2×D413yes—
172#41×C43—26no—
173#41×C43—26no—
174#41×C43—44no—
175#41×C43#4114yes—
176#41×C43#4114yes—
177C2×Q8×C43C2×D411yescharacteristic
178C2×Q8×C43C2411yescharacteristic
179C2×D4×C43—23no—
180C2×D4×C43—23no—
181C2×D4×C43—26no—
182C2×D4×C43—26no—
183C2×D4×C43—412no—
184C2×D4×C43C2×D413yes—
185C2×D4×C43C2413yes—
186C22×C4×C43—23no—
187C22×C4×C43—23no—
188C22×C4×C43C2413yes—
189C2×C22⋊D43—23no—
190C2×C22⋊D43—23no—
191C2×C22⋊D43—26no—
192C2×C22⋊D43—86no—
193C2×C22⋊D43C2×D416yes—
194C22×Dic43—23no—
195C22×Dic43—23no—
196C22×Dic43C2×D413yes—
197#10621902—24no—
198Q8×D43—24no—
199#10621900—212no—
200D4×D43—212no—
201#10621898—26no—
202#10621898—26no—
203C2×D172C2×D413yes—
204C2×C4×D43—26no—
205C2×C4×D43—26no—
206C2×C4×D43—21no—
207C2×C4×D43—23no—
208C2×C4×D43—26no—
209C2×C4×D43—86no—
210C2×C4×D43C2×D413yes—
211C2×C4×D43C2×D413yes—
212C2×C4×D43C2411yescharacteristic
213C2×C4×D43C2413yes—
214C2×Dic86C2×D413yes—
215M16×C43—26no—
216C2×C8×C43—26no—
217C2×C8×C43C2411yescharacteristic
218C2×C8×C43C2413yes—
219C4⋊C4×C43—23no—
220C4⋊C4×C43C2413yes—
221C4⋊C4×C43C2411yescharacteristic
222C22⋊C4×C43—23no—
223C42×C43—23no—
224C22⋊Dic43—23no—
225C22⋊Dic43—26no—
226C22⋊Dic43—23no—
227C22⋊Dic43—23no—
228C22⋊Dic43—23no—
229(C2×D43)⋊C4—23no—
230(C2×D43)⋊C4—23no—
231(C2×D43)⋊C4—21no—
232(C2×D43)⋊C4—23no—
233C4⋊Dic43—23no—
234C4⋊Dic43—23no—
235C4⋊Dic43C2413yes—
236C4⋊Dic43C2411yescharacteristic
237C4⋊Dic43C2413yes—
238C4⋊Dic43C2411yescharacteristic
239Dic43⋊C4—23no—
240Dic43⋊C4—26no—
241Dic43⋊C4—21no—
242Dic43⋊C4—21no—
243Dic43⋊C4—23no—
244C4×Dic43—23no—
245C4×Dic43—23no—
246C4×Dic43—23no—
247C4×Dic43—23no—
248#10621877—26no—
249C2×C43⋊C8—26no—
250C2×C43⋊C8C2411yescharacteristic
251C2×C43⋊C8C2413yes—
252C23×C43—23no—
253C23×C43—46no—
254C23×C43—83no—
255C23×C43—83no—
256C23×C43C22×D413yes—
257C22×D43—26no—
258C22×D43—26no—
259C22×D43—43no—
260C22×D43C22×D413yes—
261C22×D43C22×D411yescharacteristic
262Q8×C43—21no—
263Q8×C43—21no—
264Q8×C43#12314yes—
265D4×C43—23no—
266D4×C43—23no—
267D4×C43—46no—
268D4×C43—46no—
269D4×C43#123112yes—
270C2×C4×C43—21no—
271C2×C4×C43—23no—
272C2×C4×C43—21no—
273C2×C4×C43—46no—
274C2×C4×C43—83no—
275C2×C4×C43C22×D413yes—
276C2×C4×C43C2×#4116yes—
277C2×C4×C43C2×#4116yes—
278C2×C4×C43C2511yescharacteristic
279C22⋊D43—212no—
280C22⋊D43—46no—
281C22⋊D43—83no—
282C22⋊D43—86no—
283C2×Dic43—26no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—23no—
287C2×Dic43—23no—
288C2×Dic43—83no—
289C2×Dic43—83no—
290C2×Dic43C22×D413yes—
291C2×Dic43C22×D411yescharacteristic
292D172—26no—
293C4×D43—26no—
294C4×D43—26no—
295C4×D43—21no—
296C4×D43—21no—
297C4×D43—23no—
298C4×D43—23no—
299C4×D43—46no—
300C4×D43—42no—
301C4×D43—86no—
302Dic86—26no—
303C8×C43—21no—
304C8×C43—23no—
305C43⋊C8—21no—
306C43⋊C8—23no—
307#60525—431nomaximal, Sylow
308C22×C43—23no—
309C22×C43—23no—
310C22×C43—43no—
311C22×C43—43no—
312C22×C43—43no—
313C22×C43—166no—
314C22×C43C2×#12316yes—
315C22×C43C23×D411yescharacteristic
316C2×D43—21no—
317C2×D43—21no—
318C2×D43—23no—
319C2×D43—23no—
320C2×D43—23no—
321C2×D43—412no—
322C2×D43#57712yes—
323C4×C43—43no—
324C4×C43—41no—
325C4×C43—41no—
326C4×C43C2×#12316yes—
327C4×C43C22×#4111yescharacteristic
328C4×C43C22×#4111yescharacteristic
329Dic43—23no—
330Dic43—21no—
331Dic43—43no—
332Dic43—41no—
333Dic43—41no—
334Dic43—43no—
335#3488—431no—
336C2×#520—431no—
337#3099—433no—
338#3099—433no—
339#3096—433no—
340#3096—433no—
341#3094—433no—
342#3092—433no—
343#3091—433no—
344C2×#481—433no—
345#2912—431no—
346#2912—431no—
347#2897—431no—
348#2897D4311yescharacteristic, complemented
349#2880—431no—
350C2×C43—26no—
351C2×C43—83no—
352C2×C43C22×#12311yescharacteristic
353C2×C43C2×#57711yescharacteristic
354C2×C43#358511yescharacteristic
355D43—22no—
356D43—43no—
357C2×H(5,𝔽2)C2×D4311yescharacteristic
358C22×#41—431no—
359C2×#131—431no—
360C2×#131C2×D4311yescharacteristic
361#550—861no—
362#548—861no—
363#546—863no—
364D42—863no—
365#537—433no—
366#535—433no—
367#525—433no—
368C2×#121—433no—
369#520—431no—
370#520—431no—
371#520—433no—
372#520—433no—
373#520—863no—
374#520—861no—
375#520C2×D4311yescharacteristic
376C2×C4×Q8—861no—
377C2×C4×D4—863no—
378C2×#117—433no—
379C22×C4⋊C4—433no—
380#485—433no—
381#485—433no—
382#484—433no—
383#483—431no—
384#483—436no—
385#482—433no—
386#482—433no—
387#482—436no—
388#482—436no—
389#481—433no—
390#481—436no—
391#481—436no—
392#481—436no—
393#480—433no—
394#480—436no—
395#428—433no—
396#428—433no—
397#428—433no—
398#428—433no—
399#427—433no—
400#427—433no—
401C2×#106—433no—
402C2×#106—433no—
403#418—433no—
404#418C2×D4313yescomplemented
405#417—433no—
406#417C2×D4313yescomplemented
407#416—433no—
408#416C2×D4313yescomplemented
409C2×#102—433no—
410C2×#102C2×D4313yescomplemented
411#408—433no—
412#408—433no—
413#407—433no—
414C2×C22⋊C8—433no—
415C43#6052511yescharacteristic, complemented, Sylow
416H(5,𝔽2)—24no—
417H(5,𝔽2)—24no—
418C2×#41—21no—
419C2×#41—431no—
420C2×#41—433no—
421C2×#41—433no—
422C2×#41—864no—
423C2×#41—864no—
424C2×#41C22×D4313yes—
425C2×#41C22×D4311yescharacteristic
426C22×Q8—431no—
427C22×D4—23no—
428C22×D4—433no—
429C22×D4—863no—
430C22×D4C22×D4313yes—
431C23×C4—433no—
432C23×C4—863no—
433#131—24no—
434#131—864no—
435C2×M16—433no—
436C2×M16C22×D4313yes—
437C22×C8—433no—
438C22×C8C22×D4313yes—
439#127—863no—
440#124—863no—
441#123—863no—
442C22⋊Q8—431no—
443C22⋊Q8—433no—
444C22⋊Q8—863no—
445#121—433no—
446#121—436no—
447#121—433no—
448#121—863no—
449#121—863no—
450#121—863no—
451#121—866no—
452#120—863no—
453#120—866no—
454C4×Q8—21no—
455C4×Q8—863no—
456C4×Q8—863no—
457C4×Q8—861no—
458C4×Q8—861no—
459C4×D4—23no—
460C4×D4—863no—
461C4×D4—866no—
462C4×D4—863no—
463C4×D4—863no—
464C4×D4—863no—
465C4×D4—866no—
466C4×D4—863no—
467C4×D4—863no—
468#117—433no—
469#117—433no—
470#117—433no—
471#117—433no—
472#117—863no—
473#117—863no—
474#117C22×D4313yes—
475C2×C4⋊C4—433no—
476C2×C4⋊C4—433no—
477C2×C4⋊C4—433no—
478C2×C4⋊C4—436no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—863no—
481C2×C4⋊C4—863no—
482C2×C4⋊C4—863no—
483C2×C4⋊C4C22×D4313yes—
484C2×C22⋊C4—863no—
485C2×C22⋊C4—863no—
486C2×C42—863no—
487#107—433no—
488#107—433no—
489#107—433no—
490#107—433no—
491#106—433no—
492#106—436no—
493#106—431no—
494#106—433no—
495#106—436no—
496#106—431no—
497#103—431no—
498#103—433no—
499#103C22×D4311yescharacteristic
500#103C22×D4313yes—
501#102—433no—
502#102—436no—
503#102—433no—
504#102C22×D4313yes—
505#102C22×D4316yes—
506#102C22×D4313yes—
507C22⋊C8—431no—
508C22⋊C8—433no—
509C22⋊C8—433no—
510C22⋊C8—433no—
511C22⋊C8—436no—
512C24—23no—
513C24—433no—
514#41—26no—
515#41—26no—
516#41—44no—
517#41—864no—
518#41—8612no—
519#41—866no—
520#41—866no—
521#41#1062189814yes—
522#41#1062190014yes—
523C2×Q8—433no—
524C2×Q8—864no—
525C2×Q8D4×D4311yescharacteristic
526C2×Q8C23×D4311yescharacteristic
527C2×D4—23no—
528C2×D4—23no—
529C2×D4—26no—
530C2×D4—26no—
531C2×D4—412no—
532C2×D4—436no—
533C2×D4—433no—
534C2×D4—8612no—
535C2×D4—863no—
536C2×D4—866no—
537C2×D4—863no—
538C2×D4—3446no—
539C2×D4D4×D4313yes—
540C2×D4C23×D4313yes—
541C22×C4—23no—
542C22×C4—23no—
543C22×C4—433no—
544C22×C4—433no—
545C22×C4—433no—
546C22×C4—431no—
547C22×C4—433no—
548C22×C4—866no—
549C22×C4—861no—
550C22×C4—863no—
551C22×C4—866no—
552C22×C4—866no—
553C22×C4—863no—
554C22×C4—863no—
555C22×C4—3446no—
556C22×C4C23×D4313yes—
557M16—26no—
558M16—866no—
559C2×C8—26no—
560C2×C8—431no—
561C2×C8—433no—
562C2×C8—866no—
563C2×C8C23×D4311yescharacteristic
564C2×C8C23×D4313yes—
565C4⋊C4—23no—
566C4⋊C4—433no—
567C4⋊C4—431no—
568C4⋊C4—433no—
569C4⋊C4—431no—
570C4⋊C4—863no—
571C4⋊C4—866no—
572C4⋊C4—861no—
573C4⋊C4—861no—
574C4⋊C4—863no—
575C4⋊C4—863no—
576C4⋊C4—863no—
577C4⋊C4C23×D4313yes—
578C4⋊C4C23×D4311yescharacteristic
579C22⋊C4—23no—
580C22⋊C4—863no—
581C22⋊C4—863no—
582C22⋊C4—861no—
583C22⋊C4—863no—
584C22⋊C4—863no—
585C22⋊C4—866no—
586C22⋊C4—863no—
587C22⋊C4—863no—
588C22⋊C4—863no—
589C42—23no—
590C42—863no—
591C42—863no—
592C42—863no—
593C42—863no—
594C23—23no—
595C23—46no—
596C23—83no—
597C23—83no—
598C23—431no—
599C23—433no—
600C23—866no—
601C23—866no—
602C23—1723no—
603C23C2×D4×D4313yes—
604Q8—21no—
605Q8—21no—
606Q8—866no—
607Q8#1306330714yes—
608D4—23no—
609D4—23no—
610D4—46no—
611D4—46no—
612D4—8612no—
613D4—866no—
614D4—3446no—
615D4—3443no—
616D4—1726no—
617D4#13063307112yes—
618C2×C4—21no—
619C2×C4—23no—
620C2×C4—21no—
621C2×C4—46no—
622C2×C4—83no—
623C2×C4—433no—
624C2×C4—431no—
625C2×C4—866no—
626C2×C4—866no—
627C2×C4—866no—
628C2×C4—861no—
629C2×C4—863no—
630C2×C4—861no—
631C2×C4—863no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—863no—
635C2×C4—863no—
636C2×C4—3446no—
637C2×C4—3443no—
638C2×C4—3443no—
639C2×C4—1722no—
640C2×C4—1726no—
641C2×C4C2×D4×D4313yes—
642C2×C4C2×#1062190016yes—
643C2×C4C2×#1062189816yes—
644C2×C4C24×D4311yescharacteristic
645C8—21no—
646C8—23no—
647C8—861no—
648C8—863no—
649C22—23no—
650C22—23no—
651C22—43no—
652C22—43no—
653C22—43no—
654C22—166no—
655C22—432no—
656C22—861no—
657C22—861no—
658C22—863no—
659C22—863no—
660C22—863no—
661C22—17212no—
662C22C2×#1306330716yes—
663C22C22×D4×D4311yescharacteristic
664C4—41no—
665C4—41no—
666C4—43no—
667C4—861no—
668C4—863no—
669C4—1723no—
670C4—1721no—
671C4—1723no—
672C4—1721no—
673C4C2×#1306330716yes—
674C4C22×#1062190011yescharacteristic
675C4C22×#1062189811yescharacteristic
676C2—26no—
677C2—83no—
678C2—862no—
679C2—1723no—
680C2C22×#1306330711yescharacteristic
681C2#577×D4311yescharacteristic
682C2#1914937011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2897C2
socleC22×C43C23×D4
prime radical#19148257C2
hypercenter#2897D43
hypocenterC43#60525
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2897

Complements

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

NH ≅ G/Ntype
2. #520×D43C2semidirect
3. #19144583C2semidirect
4. #19144582C2semidirect
5. #19144551C2semidirect
6. #19144549C2semidirect
7. #19144533C2semidirect
8. #19144516C2semidirect
9. #19144506C2semidirect
10. C2×#14583216C2semidirect
11. #19143190C2semidirect
12. #19143188C2semidirect
13. #19143121C2semidirect
14. #19143042C2semidirect
15. C43×#2897C2semidirect
29. #14583380C22semidirect
30. #14583379C22semidirect
34. #117×D43C22semidirect
35. C2×C4⋊C4×D43C22semidirect
36. #14583239C22semidirect
37. #14583238C22semidirect
38. #14583233C22semidirect
39. #14583228C22semidirect
40. #14583228C22semidirect
41. #14583222C22semidirect
42. #14583222C22semidirect
43. #14583221C22semidirect
44. #14583221C22semidirect
45. #14583216C22semidirect
46. #14583216C22semidirect
47. #14583216C22semidirect
48. #14583216C22semidirect
49. #14583211C22semidirect
50. #14583211C22semidirect
51. #14582942C22semidirect
52. #14582941C22semidirect
53. #14582941C22semidirect
54. #14582939C22semidirect
55. #14582937C22semidirect
56. #14582935C22semidirect
57. C2×#13063257C22semidirect
58. C2×#13063256C22semidirect
59. #14582904C22semidirect
60. #14582900C22semidirect
61. #14582895C22semidirect
62. C2×#13063246C22semidirect
63. #14582867C22semidirect
64. #14582865C22semidirect
65. #14582862C22semidirect
66. C2×(C2×D43)⋊C8C22semidirect
70. C43×#418C22semidirect
71. C43×#417C22semidirect
72. C43×#416C22semidirect
73. C2×#102×C43C22semidirect
348. #2897D43semidirect
404. #418C2×D43semidirect
406. #417C2×D43semidirect
408. #416C2×D43semidirect
410. C2×#102C2×D43semidirect
415. C43#60525semidirect

Maximal subgroups

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

subgroupindex
#191482572
#520×D432
#191445832
#191445822
#191445512
#191445492
#191445332
#191445162
#191445062
C2×#145832162
#191431902
#191431882
#191431212
#191430422
C43×#28972
#6052543