Finite Group Databasebeta

← #25964561

Subgroups — #25964561

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#19147798C211yesmaximal, characteristic, complemented
3#19144586C213yesmaximal, complemented
4#19144575C213yesmaximal, complemented
5#19144565C213yesmaximal, complemented
6#19144565C213yesmaximal, complemented
7#19144544C213yesmaximal, complemented
8#19144528C213yesmaximal, complemented
9#19144510C213yesmaximal, complemented
10C2×#14583241C213yesmaximal, complemented
11#19143195C211yesmaximal, characteristic, complemented
12#19143190C211yesmaximal, characteristic, complemented
13#19143129C211yesmaximal, characteristic, complemented
14#19143129C211yesmaximal, characteristic, complemented
15C43×#2880C211yesmaximal, characteristic, complemented
16C2×#13063372C2211yescharacteristic
17Q8×C22⋊D43—21no—
18#14583556—21no—
19#14583548—23no—
20#14583543—23no—
21#14583477C2213yes—
22#14583470C2213yes—
23#14583410C2213yes—
24C2×#13063304C2213yes—
25#14583382C2211yescharacteristic
26#14583382C2211yescharacteristic
27#14583382C2211yescharacteristic
28#14583382C2213yes—
29#14583382C2213yes—
30#14583377—21no—
31#14583374—23no—
32#41×Dic43—21no—
33#41×Dic43—23no—
34C2×#13063284C2213yes—
35C2×#13063284C2213yes—
36#14583241C2213yes—
37#14583241C2216yes—
38#14583241C2213yes—
39#14583241C2216yescomplemented
40#14583241C2216yescomplemented
41#14583241C2216yescomplemented
42#14583235C2213yescomplemented
43#14583235C2216yescomplemented
44#14583230C2213yescomplemented
45#14583230C2216yescomplemented
46#14583224C2211yescharacteristic
47#14583224C2213yes—
48#14583224C2216yescomplemented
49#14583218C2213yescomplemented
50#14583213C2213yescomplemented
51#14582941C2213yescomplemented
52#14582941C2213yescomplemented
53#14582941C2213yescomplemented
54#14582941C2213yescomplemented
55#14582937C2213yescomplemented
56#14582937C2213yescomplemented
57C2×#13063259C2213yescomplemented
58C2×#13063257C2213yescomplemented
59#14582909C2213yescomplemented
60#14582909C2213yescomplemented
61#14582901C2213yescomplemented
62#14582901C2213yescomplemented
63#14582896C2213yescomplemented
64#14582896C2213yescomplemented
65C2×#13063250C2213yescomplemented
66C2×#13063250C2213yescomplemented
67C22×#41×C43C2211yescharacteristic
68C2×#131×C43C2211yescharacteristic
69C2×#131×C43C2211yescharacteristic
70C43×#408C2213yes—
71C43×#408C2213yes—
72C43×#407C2213yes—
73C2×C22⋊C8×C43C2213yes—
74#13063372—24no—
75#13063372—24no—
76C2×#10621898C2313yes—
77C2×#10621900—23no—
78C22×Dic86C2313yes—
79C2×Q8×D43—21no—
80#13063323—23no—
81#13063312—23no—
82#13063308—23no—
83#13063306—26no—
84#13063304—23no—
85#13063304—23no—
86#13063304C2313yes—
87#13063304C2316yes—
88#13063304C2313yes—
89#13063301—23no—
90#13063299C2311yescharacteristic
91#13063299C2313yes—
92#13063297—26no—
93#13063296—23no—
94#13063294—23no—
95Q8×Dic43—21no—
96Q8×Dic43—23no—
97Q8×Dic43—23no—
98Q8×Dic43—21no—
99Q8×Dic43—21no—
100D4×Dic43—23no—
101D4×Dic43—23no—
102D4×Dic43—26no—
103D4×Dic43—26no—
104D4×Dic43—23no—
105D4×Dic43—23no—
106D4×Dic43—23no—
107C4×C22⋊D43—23no—
108C4×C22⋊D43—23no—
109#13063284—23no—
110#13063284—23no—
111#13063284—23no—
112#13063284—23no—
113#13063284C2313yes—
114#13063284C2311yescharacteristic
115#13063284C2313yes—
116#13063284C2313yes—
117#13063284C2316yes—
118#13063284C2313yes—
119C2×C4⋊Dic43C2313yes—
120C2×C4⋊Dic43C2313yes—
121C2×C4⋊Dic43C2313yes—
122C2×C4⋊Dic43C2313yes—
123C2×C4⋊Dic43C2313yes—
124C2×Dic43⋊C4—23no—
125C2×C22⋊Dic43—23no—
126C2×C22⋊Dic43—23no—
127C2×C22⋊Dic43—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#13063250C2313yes—
141#13063250C2313yes—
142#13063250C2316yes—
143#13063250C2316yes—
144#13063250C2313yes—
145#13063250C2313yes—
146#13063247C2311yescharacteristic
147#13063247C2311yescharacteristic
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—
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×C43C2×D413yes—
187C22×C4×C43C2×D413yes—
188C22×C4×C43C2×D413yes—
189C22×C4×C43C2411yescharacteristic
190C22×C4×C43C2413yes—
191C22×C4×C43C2413yes—
192C2×C22⋊D43—21no—
193C2×C22⋊D43—23no—
194C2×C22⋊D43—23no—
195C22×Dic43—23no—
196C22×Dic43—23no—
197C22×Dic43—23no—
198C22×Dic43—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—
211M16×C43—26no—
212M16×C43—26no—
213C2×C8×C43—26no—
214C2×C8×C43—26no—
215C2×C8×C43C2411yescharacteristic
216C2×C8×C43C2411yescharacteristic
217C2×C8×C43C2413yes—
218C2×C8×C43C2413yes—
219C22⋊Dic43—23no—
220C22⋊Dic43—21no—
221C22⋊Dic43—23no—
222C22⋊Dic43—26no—
223C22⋊Dic43—23no—
224C22⋊Dic43—23no—
225C22⋊Dic43—26no—
226C22⋊Dic43—23no—
227C22⋊Dic43—23no—
228(C2×D43)⋊C4—21no—
229(C2×D43)⋊C4—23no—
230C4⋊Dic43—23no—
231C4⋊Dic43—23no—
232C4⋊Dic43—23no—
233C4⋊Dic43—23no—
234C4⋊Dic43—23no—
235C4⋊Dic43C2411yescharacteristic
236C4⋊Dic43C2413yes—
237C4⋊Dic43C2411yescharacteristic
238C4⋊Dic43C2413yes—
239C4⋊Dic43C2413yes—
240C4⋊Dic43C2411yescharacteristic
241Dic43⋊C4—23no—
242Dic43⋊C4—26no—
243Dic43⋊C4—23no—
244C4×Dic43—23no—
245C4×Dic43—21no—
246C4×Dic43—26no—
247C4×Dic43—23no—
248C4×Dic43—23no—
249C4×Dic43—23no—
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×C43C22×D411yescharacteristic
270C2×C4×C43C22×D413yes—
271C2×C4×C43C22×D413yes—
272C2×C4×C43C2×#4116yes—
273C2×C4×C43C2×#4116yes—
274C2×C4×C43C2511yescharacteristic
275C22⋊D43—42no—
276C22⋊D43—46no—
277C22⋊D43—83no—
278C2×Dic43—23no—
279C2×Dic43—21no—
280C2×Dic43—23no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—23no—
284C2×Dic43—23no—
285C2×Dic43—46no—
286C2×Dic43—83no—
287C2×Dic43—83no—
288C2×Dic43—83no—
289C2×Dic43—83no—
290C2×Dic43—83no—
291D172—21no—
292D172—21no—
293C4×D43—46no—
294Dic86—23no—
295Dic86—23no—
296Dic86—46no—
297C8×C43—21no—
298C8×C43—21no—
299C8×C43—23no—
300C8×C43—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×C43C2×#12316yes—
319C4×C43C22×#4111yescharacteristic
320C4×C43C22×#4111yescharacteristic
321Dic43—43no—
322Dic43—41no—
323Dic43—43no—
324Dic43—43no—
325Dic43—41no—
326Dic43—41no—
327Dic43—43no—
328#3489—431no—
329#3428—431no—
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#2880D4311yescharacteristic, complemented
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×#131C2×D4311yescharacteristic
353C2×#131C2×D4311yescharacteristic
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—433no—
363#520—433no—
364#520—431no—
365#520—431no—
366#520—431no—
367#519—861no—
368#518—863no—
369C4×#41—863no—
370C4×#41—861no—
371C2×#117—433no—
372C2×#117—433no—
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#408C2×D4313yes—
405#408C2×D4313yes—
406#407C2×D4313yes—
407C2×C22⋊C8C2×D4313yes—
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×#41D17213yes—
416C2×#41D17211yescharacteristic
417C2×#41C22×D4313yes—
418C2×#41C22×D4311yescharacteristic
419C22×Q8—433no—
420C22×Q8—861no—
421C22×Q8D17211yescharacteristic
422C22×D4D17213yes—
423C23×C4C22×D4313yes—
424#131—24no—
425#131—24no—
426C2×M16C22×D4313yes—
427C2×M16C22×D4313yes—
428C22×C8C22×D4313yes—
429C22×C8C22×D4313yes—
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—863no—
446C4×Q8—863no—
447C4×Q8—861no—
448C4×Q8—861no—
449C4×Q8—861no—
450C4×D4—866no—
451C4×D4—866no—
452C4×D4—863no—
453C4×D4—863no—
454C4×D4—863no—
455C4×D4—863no—
456C4×D4—863no—
457C4×D4—863no—
458C4×D4—863no—
459#117—433no—
460#117—431no—
461#117—433no—
462#117—433no—
463#117—436no—
464#117—433no—
465#117—863no—
466#117—863no—
467#117—863no—
468#117—863no—
469C2×C4⋊C4—433no—
470C2×C4⋊C4—433no—
471C2×C4⋊C4—433no—
472C2×C4⋊C4—433no—
473C2×C4⋊C4—433no—
474C2×C4⋊C4—863no—
475C2×C22⋊C4—863no—
476C2×C22⋊C4—863no—
477C2×C22⋊C4—863no—
478C2×C42—863no—
479C2×C42—863no—
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⋊C8C22×D4311yescharacteristic
501C22⋊C8C22×D4313yes—
502C22⋊C8C22×D4313yes—
503C22⋊C8C22×D4313yes—
504C22⋊C8C22×D4316yes—
505C24C2×D17213yes—
506#41—24no—
507#41—212no—
508#41—26no—
509#41—26no—
510#41—866no—
511#41—866no—
512#41—17212no—
513#41#1062190014yes—
514#41#1062190014yes—
515C2×Q8—24no—
516C2×Q8—433no—
517C2×Q8—863no—
518C2×Q8—866no—
519C2×Q8—866no—
520C2×Q8—1724no—
521C2×Q8C2×D17213yes—
522C2×Q8C2×D17211yescharacteristic
523C2×D4—212no—
524C2×D4—431no—
525C2×D4—863no—
526C2×D4—861no—
527C2×D4—863no—
528C2×D4C2×D17216yes—
529C2×D4C2×D17213yes—
530C2×D4C2×D17213yes—
531C22×C4—26no—
532C22×C4—26no—
533C22×C4—863no—
534C22×C4—863no—
535C22×C4—863no—
536C22×C4—863no—
537C22×C4—863no—
538C22×C4—863no—
539C22×C4—863no—
540C22×C4C2×D17213yes—
541C22×C4C2×D17213yes—
542C22×C4C2×D17213yes—
543C22×C4C23×D4313yes—
544C22×C4C23×D4311yescharacteristic
545C22×C4C23×D4313yes—
546M16—26no—
547M16—26no—
548C2×C8—26no—
549C2×C8—26no—
550C2×C8C23×D4311yescharacteristic
551C2×C8C23×D4313yes—
552C2×C8C23×D4313yes—
553C2×C8C23×D4311yescharacteristic
554C4⋊C4—431no—
555C4⋊C4—433no—
556C4⋊C4—431no—
557C4⋊C4—433no—
558C4⋊C4—433no—
559C4⋊C4—431no—
560C4⋊C4—863no—
561C4⋊C4—863no—
562C4⋊C4—863no—
563C4⋊C4—863no—
564C4⋊C4—863no—
565C4⋊C4—863no—
566C4⋊C4—866no—
567C4⋊C4—863no—
568C22⋊C4—863no—
569C22⋊C4—861no—
570C22⋊C4—863no—
571C22⋊C4—866no—
572C22⋊C4—863no—
573C22⋊C4—863no—
574C22⋊C4—866no—
575C22⋊C4—863no—
576C22⋊C4—863no—
577C22⋊C4—861no—
578C22⋊C4—863no—
579C42—863no—
580C42—861no—
581C42—866no—
582C42—863no—
583C42—863no—
584C42—863no—
585C23—26no—
586C23—43no—
587C23—43no—
588C23—861no—
589C23C22×D17211yescharacteristic
590C23C22×D17213yes—
591C23C22×D17213yes—
592Q8—26no—
593Q8—863no—
594Q8—863no—
595Q8—1726no—
596Q8#1306330914yes—
597D4—212no—
598D4—26no—
599D4—861no—
600D4—861no—
601D4—3443no—
602D4—1722no—
603D4—1726no—
604D4#13063309112yes—
605C2×C4—26no—
606C2×C4—26no—
607C2×C4—26no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—23no—
611C2×C4—23no—
612C2×C4—863no—
613C2×C4—861no—
614C2×C4—863no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—863no—
618C2×C4—863no—
619C2×C4—3443no—
620C2×C4—3443no—
621C2×C4—3443no—
622C2×C4—3443no—
623C2×C4—3443no—
624C2×C4—1726no—
625C2×C4—1726no—
626C2×C4C22×D17211yescharacteristic
627C2×C4C22×D17213yes—
628C2×C4C22×D17213yes—
629C2×C4C2×#1062190016yes—
630C2×C4C2×#1062190016yes—
631C2×C4C24×D4311yescharacteristic
632C8—21no—
633C8—21no—
634C8—23no—
635C8—23no—
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×#1306330916yes—
649C22C23×D17211yescharacteristic
650C4—21no—
651C4—23no—
652C4—1723no—
653C4—1723no—
654C4—1721no—
655C4—1723no—
656C4—1723no—
657C4—1721no—
658C4—1721no—
659C4C2×#1306330916yes—
660C4C22×#1062190011yescharacteristic
661C4C22×#1062190011yescharacteristic
662C2—26no—
663C2—41no—
664C2—43no—
665C2—3441no—
666C2C22×#1306330911yescharacteristic
667C2#1914936911yescharacteristic
668C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2880C2
socleC22×C43C23×D4
prime radical#19148275C2
hypercenter#2880D43
hypocenterC43#60524
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. #19144565C2semidirect
6. #19144565C2semidirect
7. #19144544C2semidirect
8. #19144528C2semidirect
9. #19144510C2semidirect
10. C2×#14583241C2semidirect
11. #19143195C2semidirect
12. #19143190C2semidirect
13. #19143129C2semidirect
14. #19143129C2semidirect
15. C43×#2880C2semidirect
39. #14583241C22semidirect
40. #14583241C22semidirect
41. #14583241C22semidirect
42. #14583235C22semidirect
43. #14583235C22semidirect
44. #14583230C22semidirect
45. #14583230C22semidirect
48. #14583224C22semidirect
49. #14583218C22semidirect
50. #14583213C22semidirect
51. #14582941C22semidirect
52. #14582941C22semidirect
53. #14582941C22semidirect
54. #14582941C22semidirect
55. #14582937C22semidirect
56. #14582937C22semidirect
57. C2×#13063259C22semidirect
58. C2×#13063257C22semidirect
59. #14582909C22semidirect
60. #14582909C22semidirect
61. #14582901C22semidirect
62. #14582901C22semidirect
63. #14582896C22semidirect
64. #14582896C22semidirect
65. C2×#13063250C22semidirect
66. C2×#13063250C22semidirect
342. #2880D43semidirect
408. C43#60524semidirect

Maximal subgroups

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

subgroupindex
#191482752
#191477982
#191445862
#191445752
#191445652
#191445442
#191445282
#191445102
C2×#145832412
#191431952
#191431902
#191431292
C43×#28802
#6052443