Finite Group Databasebeta

← #25964560

Subgroups — #25964560

Order 11008.

2116 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148275C211yesmaximal, characteristic
2#19144584C213yesmaximal, complemented
3#19144573C213yesmaximal, complemented
4#19144564C213yesmaximal, complemented
5#19144564C213yesmaximal, complemented
6#19144543C213yesmaximal, complemented
7#19144526C213yesmaximal, complemented
8#19144508C213yesmaximal, complemented
9C2×#14583240C213yesmaximal, complemented
10#19143193C211yesmaximal, characteristic, complemented
11#19143188C211yesmaximal, characteristic, complemented
12#19143125C211yesmaximal, characteristic, complemented
13#19143125C211yesmaximal, characteristic, complemented
14#19143044C211yesmaximal, characteristic, complemented
15C43×#3428C211yesmaximal, characteristic, complemented
16C2×#13063372C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19Q8×C22⋊D43—21no—
20#14583556—21no—
21#14583548—23no—
22#14583543—23no—
23#14583477C2213yes—
24#14583470C2213yes—
25#14583410C2213yes—
26C2×#13063304C2213yes—
27#14583382C2211yescharacteristic
28#14583240C2213yes—
29#14583240C2216yes—
30#14583240C2213yes—
31#14583240C2216yescomplemented
32#14583240C2216yescomplemented
33#14583240C2216yescomplemented
34#14583234C2213yescomplemented
35#14583234C2216yescomplemented
36#14583229C2213yescomplemented
37#14583229C2216yescomplemented
38#14583223C2211yescharacteristic
39#14583223C2213yes—
40#14583223C2216yescomplemented
41#14583217C2213yescomplemented
42#14583212C2213yescomplemented
43#14582942C2213yescomplemented
44#14582942C2213yescomplemented
45#14582939C2213yescomplemented
46#14582939C2213yescomplemented
47#14582935C2213yescomplemented
48#14582935C2213yescomplemented
49C2×#13063258C2213yescomplemented
50C2×#13063256C2213yescomplemented
51#14582907C2213yescomplemented
52#14582907C2213yescomplemented
53#14582898C2213yescomplemented
54#14582898C2213yescomplemented
55#14582893C2213yescomplemented
56#14582893C2213yescomplemented
57C2×#13063248C2213yescomplemented
58C2×#13063248C2213yescomplemented
59#14582866C2213yes—
60#14582866C2213yes—
61#14582863C2213yes—
62C2×C22⋊(C43⋊C8)C2213yes—
63C22×#41×C43C2211yescharacteristic
64C43×#520C2211yescharacteristic
65C43×#520C2211yescharacteristic
66C43×#520C2213yes—
67C43×#520C2213yes—
68C43×#519—21no—
69C43×#518—23no—
70C4×#41×C43—21no—
71C4×#41×C43—23no—
72C2×#117×C43C2213yes—
73C2×#117×C43C2213yes—
74#13063372—24no—
75#13063372—24no—
76C2×#10621898C2313yes—
77C2×#10621900—23no—
78C22×Dic86C2313yes—
79C2×Q8×D43—21no—
80#13063332—24no—
81#13063332—24no—
82C2×#10621877C2313yes—
83C2×#10621877C2313yes—
84C22×C43⋊C8C2313yes—
85C22×C43⋊C8C2313yes—
86#13063323—23no—
87#13063312—23no—
88#13063308—23no—
89#13063306—26no—
90#13063304—23no—
91#13063304—23no—
92#13063304C2313yes—
93#13063304C2316yes—
94#13063304C2313yes—
95#13063301—23no—
96#13063299C2311yescharacteristic
97#13063299C2313yes—
98#13063297—26no—
99#13063296—23no—
100#13063294—23no—
101Q8×Dic43—21no—
102D4×Dic43—23no—
103C4×C22⋊D43—23no—
104C4×C22⋊D43—23no—
105#13063284C2313yes—
106C2×C4⋊Dic43C2313yes—
107C2×Dic43⋊C4—23no—
108C2×C22⋊Dic43—23no—
109#13063258C2313yes—
110#13063258C2316yes—
111#13063258C2311yescharacteristic
112#13063258C2313yes—
113#13063258C2313yes—
114#13063256C2313yes—
115#13063256C2316yes—
116#13063256C2311yescharacteristic
117#13063256C2313yes—
118#13063256C2313yes—
119#13063248C2313yes—
120#13063248C2313yes—
121#13063248C2316yes—
122#13063248C2316yes—
123#13063248C2313yes—
124#13063248C2313yes—
125#13063245C2311yescharacteristic
126#13063245C2311yescharacteristic
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—23no—
144C4×Q8×C43—23no—
145C4×Q8×C43—21no—
146C4×Q8×C43—21no—
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—
171#41×C43—24no—
172#41×C43—212no—
173#41×C43—26no—
174#41×C43—26no—
175#41×C43#4114yes—
176#41×C43#4114yes—
177C2×Q8×C43—24no—
178C2×Q8×C43C2×D413yes—
179C2×Q8×C43C2×D411yescharacteristic
180C2×D4×C43—212no—
181C2×D4×C43C2×D413yes—
182C2×D4×C43C2×D416yes—
183C2×D4×C43C2×D413yes—
184C22×C4×C43—26no—
185C22×C4×C43—26no—
186C22×C4×C43—23no—
187C22×C4×C43—23no—
188C22×C4×C43—23no—
189C22×C4×C43—23no—
190C22×C4×C43C2×D413yes—
191C22×C4×C43C2×D413yes—
192C22×C4×C43C2×D413yes—
193C22×C4×C43C2413yes—
194C22×C4×C43C2411yescharacteristic
195C22×C4×C43C2413yes—
196C2×C22⋊D43—21no—
197C2×C22⋊D43—23no—
198C2×C22⋊D43—23no—
199C22×Dic43—23no—
200C22×Dic43—23no—
201Q8×D43—44no—
202#10621900—412no—
203#10621898—26no—
204#10621898—26no—
205C2×D172C2411yescharacteristic
206C2×C4×D43—23no—
207C2×Dic86—26no—
208C2×Dic86—26no—
209C2×Dic86—23no—
210C2×Dic86C2413yes—
211C4⋊C4×C43—23no—
212C4⋊C4×C43—23no—
213C4⋊C4×C43—23no—
214C4⋊C4×C43—23no—
215C4⋊C4×C43C2413yes—
216C4⋊C4×C43C2411yescharacteristic
217C4⋊C4×C43C2413yes—
218C4⋊C4×C43C2411yescharacteristic
219C22⋊C4×C43—23no—
220C22⋊C4×C43—21no—
221C22⋊C4×C43—26no—
222C22⋊C4×C43—23no—
223C22⋊C4×C43—23no—
224C42×C43—23no—
225C42×C43—21no—
226C42×C43—26no—
227C42×C43—23no—
228C42×C43—23no—
229C22⋊Dic43—23no—
230C22⋊Dic43—26no—
231C22⋊Dic43—23no—
232C22⋊Dic43—23no—
233(C2×D43)⋊C4—21no—
234(C2×D43)⋊C4—23no—
235C4⋊Dic43—23no—
236C4⋊Dic43C2413yes—
237C4⋊Dic43C2411yescharacteristic
238Dic43⋊C4—23no—
239Dic43⋊C4—26no—
240Dic43⋊C4—23no—
241C4×Dic43—23no—
242#10621877—26no—
243#10621877—26no—
244C2×C43⋊C8—26no—
245C2×C43⋊C8—26no—
246C2×C43⋊C8C2411yescharacteristic
247C2×C43⋊C8C2413yes—
248C2×C43⋊C8C2413yes—
249C2×C43⋊C8C2411yescharacteristic
250C23×C43—26no—
251C23×C43—43no—
252C23×C43—43no—
253C23×C43C22×D411yescharacteristic
254C23×C43C22×D413yes—
255C23×C43C22×D413yes—
256C22×D43—21no—
257Q8×C43—26no—
258Q8×C43#12314yes—
259D4×C43—212no—
260D4×C43—26no—
261D4×C43#123112yes—
262C2×C4×C43—26no—
263C2×C4×C43—26no—
264C2×C4×C43—26no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—23no—
268C2×C4×C43—23no—
269C2×C4×C43—23no—
270C2×C4×C43—21no—
271C2×C4×C43—23no—
272C2×C4×C43—21no—
273C2×C4×C43—83no—
274C2×C4×C43—83no—
275C2×C4×C43—83no—
276C2×C4×C43—83no—
277C2×C4×C43C22×D411yescharacteristic
278C2×C4×C43C22×D413yes—
279C2×C4×C43C22×D413yes—
280C2×C4×C43C2×#4116yes—
281C2×C4×C43C2×#4116yes—
282C2×C4×C43C2511yescharacteristic
283C22⋊D43—42no—
284C22⋊D43—46no—
285C22⋊D43—83no—
286C2×Dic43—21no—
287C2×Dic43—23no—
288C2×Dic43—23no—
289C2×Dic43—46no—
290C2×Dic43—83no—
291D172—21no—
292D172—21no—
293C4×D43—46no—
294Dic86—23no—
295Dic86—23no—
296Dic86—46no—
297C43⋊C8—21no—
298C43⋊C8—21no—
299C43⋊C8—23no—
300C43⋊C8—23no—
301#60524—431nomaximal, Sylow
302C22×C43—23no—
303C22×C43—23no—
304C22×C43—21no—
305C22×C43—23no—
306C22×C43—21no—
307C22×C43—23no—
308C22×C43—21no—
309C22×C43—23no—
310C22×C43—86no—
311C22×C43C2×#12316yes—
312C22×C43C23×D411yescharacteristic
313C2×D43—41no—
314C2×D43—41no—
315C2×D43—41no—
316C4×C43—21no—
317C4×C43—23no—
318C4×C43—43no—
319C4×C43—41no—
320C4×C43—43no—
321C4×C43—41no—
322C4×C43C2×#12316yes—
323C4×C43C22×#4111yescharacteristic
324C4×C43C22×#4111yescharacteristic
325Dic43—43no—
326Dic43—41no—
327Dic43—43no—
328#3489—431no—
329#3428D4311yescharacteristic, complemented
330#3099—433no—
331#3098—433no—
332#3097—433no—
333#3097—433no—
334#3095—433no—
335#3093—433no—
336#3091—433no—
337C2×#485—433no—
338#2913—431no—
339#2912—431no—
340#2898—431no—
341#2898—431no—
342#2880—431no—
343C2×C43—26no—
344C2×C43—43no—
345C2×C43—41no—
346C2×C43C22×#12311yescharacteristic
347C2×C43#358411yescharacteristic
348C2×C43#358611yescharacteristic
349D43—81no—
350C2×2−1+4—431no—
351C22×#41C2×D4311yescharacteristic
352C2×#131—431no—
353C2×#131—431no—
354D4×Q8—861no—
355#548—861no—
356#547—863no—
357#546—863no—
358#537—433no—
359#536—433no—
360#525—433no—
361C2×C22⋊Q8—433no—
362#520—431no—
363#520C2×D4313yes—
364#520C2×D4313yes—
365#520C2×D4311yescharacteristic
366#520C2×D4311yescharacteristic
367#519—21no—
368#518—23no—
369C4×#41—23no—
370C4×#41—21no—
371C2×#117C2×D4313yes—
372C2×#117C2×D4313yes—
373#485—433no—
374#485—436no—
375#485—436no—
376#485—436no—
377#485—433no—
378#485—436no—
379#484—433no—
380#484—436no—
381#483—433no—
382#483—436no—
383#482—431no—
384#482—433no—
385#482—436no—
386#481—433no—
387#480—433no—
388#428—433no—
389#428—433no—
390#428—433no—
391#428—433no—
392#427—433no—
393#427—433no—
394C2×#107—433no—
395C2×#106—433no—
396#419—433no—
397#419—433no—
398#417—433no—
399#417—433no—
400#416—433no—
401#416—433no—
402C2×#103—433no—
403C2×#103—433no—
404#408—433no—
405#408—433no—
406#407—433no—
407C2×C22⋊C8—433no—
408C43#6052411yescharacteristic, complemented, Sylow
4092−1+4—864no—
4102−1+4—864no—
411C2×#41—24no—
412C2×#41—24no—
413C2×#41—433no—
414C2×#41—863no—
415C2×#41C22⋊D4313yes—
416C2×#41C22⋊D4311yescharacteristic
417C2×#41C22×D4313yes—
418C2×#41C22×D4311yescharacteristic
419C22×Q8—433no—
420C22×Q8—861no—
421C22×Q8C22⋊D4311yescharacteristic
422C22×D4C22⋊D4313yes—
423C23×C4C22×D4313yes—
424#131—864no—
425#131—864no—
426C2×M16—433no—
427C2×M16—433no—
428C22×C8—433no—
429C22×C8—433no—
430C4⋊Q8—863no—
431#124—863no—
432#123—866no—
433#123—863no—
434C22⋊Q8—433no—
435C22⋊Q8—436no—
436C22⋊Q8—433no—
437C22⋊Q8—863no—
438C22⋊Q8—863no—
439C22⋊Q8—863no—
440#121—431no—
441#121—433no—
442#121—866no—
443#121—863no—
444#120—863no—
445C4×Q8—23no—
446C4×Q8—23no—
447C4×Q8—21no—
448C4×Q8—21no—
449C4×Q8—861no—
450C4×D4—26no—
451C4×D4—26no—
452C4×D4—23no—
453C4×D4—23no—
454C4×D4—23no—
455C4×D4—23no—
456C4×D4—863no—
457C4×D4—863no—
458C4×D4—863no—
459#117—23no—
460#117—23no—
461#117—23no—
462#117—23no—
463#117—433no—
464#117C22×D4313yes—
465#117C22×D4311yescharacteristic
466#117C22×D4313yes—
467#117C22×D4313yes—
468#117C22×D4316yes—
469C2×C4⋊C4—433no—
470C2×C4⋊C4—863no—
471C2×C4⋊C4C22×D4313yes—
472C2×C4⋊C4C22×D4313yes—
473C2×C4⋊C4C22×D4313yes—
474C2×C4⋊C4C22×D4313yes—
475C2×C22⋊C4—23no—
476C2×C22⋊C4—23no—
477C2×C22⋊C4—863no—
478C2×C42—23no—
479C2×C42—23no—
480#107—433no—
481#107—436no—
482#107—431no—
483#107—433no—
484#107—433no—
485#106—433no—
486#106—436no—
487#106—431no—
488#106—433no—
489#106—433no—
490#103—433no—
491#103—433no—
492#103—436no—
493#103—436no—
494#103—433no—
495#103—433no—
496#102—431no—
497#102—431no—
498#102—433no—
499#102—433no—
500C22⋊C8—431no—
501C22⋊C8—433no—
502C22⋊C8—433no—
503C22⋊C8—433no—
504C22⋊C8—436no—
505C24C2×C22⋊D4313yes—
506#41—24no—
507#41—212no—
508#41—26no—
509#41—26no—
510#41—866no—
511#41—866no—
512#41—17212no—
513#41#1062189814yes—
514#41#1062189814yes—
515C2×Q8—24no—
516C2×Q8—433no—
517C2×Q8—863no—
518C2×Q8—866no—
519C2×Q8—866no—
520C2×Q8—1724no—
521C2×Q8C2×C22⋊D4313yes—
522C2×Q8C2×C22⋊D4311yescharacteristic
523C2×D4—212no—
524C2×D4—431no—
525C2×D4—863no—
526C2×D4—861no—
527C2×D4—863no—
528C2×D4C2×C22⋊D4316yes—
529C2×D4C2×C22⋊D4313yes—
530C2×D4C2×C22⋊D4313yes—
531C22×C4—26no—
532C22×C4—26no—
533C22×C4—23no—
534C22×C4—23no—
535C22×C4—23no—
536C22×C4—23no—
537C22×C4—863no—
538C22×C4—863no—
539C22×C4—863no—
540C22×C4C2×C22⋊D4313yes—
541C22×C4C2×C22⋊D4313yes—
542C22×C4C2×C22⋊D4313yes—
543C22×C4C23×D4313yes—
544C22×C4C23×D4311yescharacteristic
545C22×C4C23×D4313yes—
546M16—866no—
547M16—866no—
548C2×C8—431no—
549C2×C8—433no—
550C2×C8—433no—
551C2×C8—431no—
552C2×C8—866no—
553C2×C8—866no—
554C4⋊C4—23no—
555C4⋊C4—23no—
556C4⋊C4—23no—
557C4⋊C4—23no—
558C4⋊C4—433no—
559C4⋊C4—431no—
560C4⋊C4—863no—
561C4⋊C4—863no—
562C4⋊C4—866no—
563C4⋊C4—863no—
564C4⋊C4C23×D4311yescharacteristic
565C4⋊C4C23×D4313yes—
566C4⋊C4C23×D4311yescharacteristic
567C4⋊C4C23×D4313yes—
568C22⋊C4—23no—
569C22⋊C4—21no—
570C22⋊C4—26no—
571C22⋊C4—23no—
572C22⋊C4—23no—
573C22⋊C4—863no—
574C22⋊C4—866no—
575C22⋊C4—863no—
576C22⋊C4—863no—
577C22⋊C4—861no—
578C22⋊C4—863no—
579C42—23no—
580C42—21no—
581C42—26no—
582C42—23no—
583C42—23no—
584C42—863no—
585C23—26no—
586C23—43no—
587C23—43no—
588C23—861no—
589C23C22×C22⋊D4311yescharacteristic
590C23C22×C22⋊D4313yes—
591C23C22×C22⋊D4313yes—
592Q8—26no—
593Q8—863no—
594Q8—863no—
595Q8—1726no—
596Q8#1306330814yes—
597D4—212no—
598D4—26no—
599D4—861no—
600D4—861no—
601D4—3443no—
602D4—1722no—
603D4—1726no—
604D4#13063308112yes—
605C2×C4—26no—
606C2×C4—26no—
607C2×C4—26no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—23no—
611C2×C4—23no—
612C2×C4—23no—
613C2×C4—21no—
614C2×C4—23no—
615C2×C4—21no—
616C2×C4—83no—
617C2×C4—83no—
618C2×C4—83no—
619C2×C4—83no—
620C2×C4—861no—
621C2×C4—863no—
622C2×C4—863no—
623C2×C4—3443no—
624C2×C4—1726no—
625C2×C4—1726no—
626C2×C4C22×C22⋊D4311yescharacteristic
627C2×C4C22×C22⋊D4313yes—
628C2×C4C22×C22⋊D4313yes—
629C2×C4C2×#1062189816yes—
630C2×C4C2×#1062189816yes—
631C2×C4C24×D4311yescharacteristic
632C8—861no—
633C8—861no—
634C8—863no—
635C8—863no—
636C22—23no—
637C22—23no—
638C22—21no—
639C22—23no—
640C22—23no—
641C22—21no—
642C22—23no—
643C22—21no—
644C22—86no—
645C22—1721no—
646C22—1721no—
647C22—1721no—
648C22C2×#1306330816yes—
649C22C23×C22⋊D4311yescharacteristic
650C4—21no—
651C4—23no—
652C4—43no—
653C4—41no—
654C4—43no—
655C4—41no—
656C4—1723no—
657C4—1723no—
658C4—1721no—
659C4C2×#1306330816yes—
660C4C22×#1062189811yescharacteristic
661C4C22×#1062189811yescharacteristic
662C2—26no—
663C2—41no—
664C2—43no—
665C2—3441no—
666C2C22×#1306330811yescharacteristic
667C2#1914936611yescharacteristic
668C2#1914938111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3428C2
socleC22×C43C23×D4
prime radical#19148275C2
hypercenter#3428D43
hypocenterC43#60524
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. #19144564C2semidirect
5. #19144564C2semidirect
6. #19144543C2semidirect
7. #19144526C2semidirect
8. #19144508C2semidirect
9. C2×#14583240C2semidirect
10. #19143193C2semidirect
11. #19143188C2semidirect
12. #19143125C2semidirect
13. #19143125C2semidirect
14. #19143044C2semidirect
15. C43×#3428C2semidirect
31. #14583240C22semidirect
32. #14583240C22semidirect
33. #14583240C22semidirect
34. #14583234C22semidirect
35. #14583234C22semidirect
36. #14583229C22semidirect
37. #14583229C22semidirect
40. #14583223C22semidirect
41. #14583217C22semidirect
42. #14583212C22semidirect
43. #14582942C22semidirect
44. #14582942C22semidirect
45. #14582939C22semidirect
46. #14582939C22semidirect
47. #14582935C22semidirect
48. #14582935C22semidirect
49. C2×#13063258C22semidirect
50. C2×#13063256C22semidirect
51. #14582907C22semidirect
52. #14582907C22semidirect
53. #14582898C22semidirect
54. #14582898C22semidirect
55. #14582893C22semidirect
56. #14582893C22semidirect
57. C2×#13063248C22semidirect
58. C2×#13063248C22semidirect
329. #3428D43semidirect
408. C43#60524semidirect

Maximal subgroups

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

subgroupindex
#191482752
#191445842
#191445732
#191445642
#191445432
#191445262
#191445082
C2×#145832402
#191431932
#191431882
#191431252
#191430442
C43×#34282
#6052443