Finite Group Databasebeta

← #25964536

Subgroups — #25964536

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#19147798C211yesmaximal, characteristic, complemented
2#19144580C213yesmaximal, complemented
3#19144569C213yesmaximal, complemented
4#19144547C213yesmaximal, complemented
5#19144547C213yesmaximal, complemented
6#19144531C213yesmaximal, complemented
7#19144524C213yesmaximal, complemented
8#19144504C213yesmaximal, complemented
9C2×#14583220C213yesmaximal, complemented
10#19143193C211yesmaximal, characteristic, complemented
11#19143188C211yesmaximal, characteristic, complemented
12#19143121C211yesmaximal, characteristic, complemented
13#19143121C211yesmaximal, characteristic, complemented
14#19143044C211yesmaximal, characteristic, complemented
15C43×#3488C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583382C2213yescomplemented
21#14583382C2213yescomplemented
22#14583377—21no—
23#14583374—23no—
24#41×Dic43—23no—
25#41×Dic43—21no—
26C2×#13063284C2213yescomplemented
27C2×#13063284C2213yescomplemented
28#14583237C2211yescharacteristic, complemented
29#14583237C2213yescomplemented
30#14583237C2216yescomplemented
31#14583232C2213yescomplemented
32#14583227C2213yescomplemented
33#14583220C2213yescomplemented
34#14583220C2216yescomplemented
35#14583220C2216yescomplemented
36#14583220C2216yescomplemented
37#14583220C2213yescomplemented
38#14583220C2216yescomplemented
39#14583215C2213yescomplemented
40#14583215C2216yescomplemented
41#14583210C2213yescomplemented
42#14583210C2216yescomplemented
43#14582942C2213yescomplemented
44#14582942C2213yescomplemented
45#14582939C2213yescomplemented
46#14582939C2213yescomplemented
47#14582935C2213yescomplemented
48#14582935C2213yescomplemented
49C2×#13063258C2213yescomplemented
50C2×#13063256C2213yescomplemented
51#14582904C2213yescomplemented
52#14582904C2213yescomplemented
53#14582900C2213yescomplemented
54#14582900C2213yescomplemented
55#14582895C2213yescomplemented
56#14582895C2213yescomplemented
57C2×#13063246C2213yescomplemented
58C2×#13063246C2213yescomplemented
59#14582866C2213yescomplemented
60#14582866C2213yescomplemented
61#14582863C2213yescomplemented
62C2×C22⋊(C43⋊C8)C2213yescomplemented
63C2×H(5,𝔽2)×C43C2211yescharacteristic
64C22×#41×C43C2211yescharacteristic
65C43×#550—21no—
66C43×#548—21no—
67C43×#546—23no—
68D42×C43—23no—
69C43×#537C2213yes—
70C43×#535C2213yes—
71C43×#525C2213yes—
72C2×#121×C43C2213yes—
73C43×#520C2211yescharacteristic
74#13063332—24no—
75#13063332—24no—
76C2×#10621877C2313yes—
77C2×#10621877C2313yes—
78C22×C43⋊C8C2313yes—
79C22×C43⋊C8C2313yes—
80Q8×Dic43—21no—
81Q8×Dic43—21no—
82Q8×Dic43—23no—
83Q8×Dic43—23no—
84D4×Dic43—23no—
85D4×Dic43—23no—
86D4×Dic43—26no—
87D4×Dic43—26no—
88D4×Dic43—23no—
89D4×Dic43—23no—
90#13063284—23no—
91#13063284—23no—
92#13063284—23no—
93#13063284—23no—
94#13063284C2313yes—
95#13063284C2311yescharacteristic
96#13063284C2313yes—
97#13063284C2313yes—
98#13063284C2316yes—
99C2×C4⋊Dic43C2313yes—
100C2×C4⋊Dic43C2313yes—
101C2×C4⋊Dic43C2313yes—
102C2×C4⋊Dic43C2313yes—
103C2×C22⋊Dic43—23no—
104C2×C22⋊Dic43—23no—
105C2×C4×Dic43—23no—
106C2×C4×Dic43—23no—
107#13063258C2313yes—
108#13063258C2316yes—
109#13063258C2311yescharacteristic
110#13063258C2313yes—
111#13063258C2313yes—
112#13063256C2313yes—
113#13063256C2316yes—
114#13063256C2311yescharacteristic
115#13063256C2313yes—
116#13063256C2313yes—
117#13063249C2311yescharacteristic
118#13063249C2311yescharacteristic
119#13063249C2313yes—
120#13063249C2313yes—
121#13063246C2313yes—
122#13063246C2313yes—
123#13063246C2316yes—
124#13063246C2316yes—
125#13063246C2313yes—
126#13063246C2313yes—
127C22⋊(C43⋊C8)C2311yescharacteristic
128C22⋊(C43⋊C8)C2313yes—
129C22⋊(C43⋊C8)C2313yes—
130C22⋊(C43⋊C8)C2313yes—
131C22⋊(C43⋊C8)C2316yes—
132H(5,𝔽2)×C43—24no—
133H(5,𝔽2)×C43—24no—
134C2×#41×C43—24no—
135C2×#41×C43—24no—
136C2×#41×C43—21no—
137C2×#41×C43D413yes—
138C2×#41×C43D411yescharacteristic
139C2×#41×C43C2313yes—
140C2×#41×C43C2313yes—
141C2×#41×C43C2311yescharacteristic
142C22×Q8×C43D411yescharacteristic
143C22×D4×C43—23no—
144C22×D4×C43—23no—
145C22×D4×C43D413yes—
146C22×D4×C43C2313yes—
147C23×C4×C43C2313yes—
148#127×C43—23no—
149#124×C43—23no—
150#123×C43—23no—
151C22⋊Q8×C43—23no—
152C22⋊Q8×C43C2311yescharacteristic
153C22⋊Q8×C43C2313yes—
154#121×C43—26no—
155#121×C43—23no—
156#121×C43—23no—
157#121×C43—23no—
158#121×C43C2313yes—
159#121×C43C2316yes—
160#121×C43C2313yes—
161#120×C43—23no—
162#120×C43—26no—
163C4×Q8×C43—21no—
164C4×D4×C43—23no—
165C4×D4×C43—23no—
166C4×D4×C43—23no—
167#117×C43C2313yes—
168C2×C4⋊C4×C43C2313yes—
169C2×C22⋊C4×C43—23no—
170C24×C43—23no—
171C24×C43C2×D413yes—
172#41×C43—24no—
173#41×C43—212no—
174#41×C43—26no—
175#41×C43—26no—
176#41×C43—26no—
177#41×C43—26no—
178#41×C43—44no—
179#41×C43#4114yes—
180#41×C43#4114yes—
181C2×Q8×C43—24no—
182C2×Q8×C43C2×D413yes—
183C2×Q8×C43C2×D411yescharacteristic
184C2×Q8×C43C2411yescharacteristic
185C2×D4×C43—212no—
186C2×D4×C43—23no—
187C2×D4×C43—23no—
188C2×D4×C43—23no—
189C2×D4×C43—23no—
190C2×D4×C43—26no—
191C2×D4×C43—26no—
192C2×D4×C43—26no—
193C2×D4×C43—412no—
194C2×D4×C43—86no—
195C2×D4×C43C2×D416yes—
196C2×D4×C43C2×D413yes—
197C2×D4×C43C2×D413yes—
198C2×D4×C43C2413yes—
199C22×C4×C43—26no—
200C22×C4×C43—26no—
201C22×C4×C43—23no—
202C22×C4×C43—23no—
203C22×C4×C43C2×D413yes—
204C22×C4×C43C2×D413yes—
205C22×C4×C43C2×D413yes—
206C22×C4×C43C2411yescharacteristic
207C22×C4×C43C2413yes—
208C22×C4×C43C2413yes—
209C22×Dic43—23no—
210C22×Dic43—23no—
211C22×Dic43—23no—
212C22×Dic43—23no—
213C4⋊C4×C43—23no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—23no—
216C4⋊C4×C43C2413yes—
217C4⋊C4×C43C2411yescharacteristic
218C22⋊C4×C43—23no—
219C22⋊C4×C43—26no—
220C22⋊C4×C43—23no—
221C22⋊C4×C43—23no—
222C22⋊C4×C43—21no—
223C22⋊C4×C43—23no—
224C42×C43—23no—
225C22⋊Dic43—23no—
226C22⋊Dic43—21no—
227C22⋊Dic43—26no—
228C22⋊Dic43—23no—
229C22⋊Dic43—23no—
230C4⋊Dic43—23no—
231C4⋊Dic43—23no—
232C4⋊Dic43—23no—
233C4⋊Dic43—23no—
234C4⋊Dic43C2413yes—
235C4⋊Dic43C2411yescharacteristic
236C4⋊Dic43C2413yes—
237C4⋊Dic43C2411yescharacteristic
238C4×Dic43—23no—
239C4×Dic43—21no—
240C4×Dic43—26no—
241C4×Dic43—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—23no—
253C23×C43—43no—
254C23×C43—43no—
255C23×C43—46no—
256C23×C43—83no—
257C23×C43—83no—
258C23×C43C22×D411yescharacteristic
259C23×C43C22×D413yes—
260C23×C43C22×D413yes—
261Q8×C43—26no—
262Q8×C43—21no—
263Q8×C43—21no—
264Q8×C43#12314yes—
265D4×C43—212no—
266D4×C43—26no—
267D4×C43—23no—
268D4×C43—23no—
269D4×C43—46no—
270D4×C43—46no—
271D4×C43—46no—
272D4×C43—83no—
273D4×C43—86no—
274D4×C43#123112yes—
275C2×C4×C43—26no—
276C2×C4×C43—26no—
277C2×C4×C43—26no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—23no—
281C2×C4×C43—23no—
282C2×C4×C43—21no—
283C2×C4×C43—23no—
284C2×C4×C43—21no—
285C2×C4×C43—46no—
286C2×C4×C43—83no—
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C22×D413yes—
289C2×C4×C43C22×D413yes—
290C2×C4×C43C2×#4116yes—
291C2×C4×C43C2×#4116yes—
292C2×C4×C43C2511yescharacteristic
293C2×Dic43—23no—
294C2×Dic43—21no—
295C2×Dic43—23no—
296C2×Dic43—21no—
297C2×Dic43—83no—
298C2×Dic43—83no—
299C2×Dic43—83no—
300C2×Dic43—83no—
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—43no—
315C22×C43—43no—
316C22×C43—43no—
317C22×C43—86no—
318C22×C43—166no—
319C22×C43C2×#12316yes—
320C22×C43C23×D411yescharacteristic
321C4×C43—21no—
322C4×C43—23no—
323C4×C43—41no—
324C4×C43—43no—
325C4×C43—41no—
326C4×C43C2×#12316yes—
327C4×C43C22×#4111yescharacteristic
328C4×C43C22×#4111yescharacteristic
329Dic43—43no—
330Dic43—41no—
331Dic43—43no—
332Dic43—41no—
333#3488D4311yescharacteristic
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#2880—431no—
348C2×C43—26no—
349C2×C43—43no—
350C2×C43—41no—
351C2×C43—83no—
352C2×C43C22×#12311yescharacteristic
353C2×C43#358411yescharacteristic
354C2×C43#358511yescharacteristic
355C2×H(5,𝔽2)C2×D4311yescharacteristic
356C22×#41C2×D4311yescharacteristic
357C2×#131—431no—
358C2×#131—431no—
359#550—21no—
360#548—21no—
361#546—23no—
362D42—23no—
363#537C2×D4313yes—
364#535C2×D4313yes—
365#525C2×D4313yes—
366C2×#121C2×D4313yes—
367#520—433no—
368#520—433no—
369#520—431no—
370#520—431no—
371#520C2×D4311yescharacteristic
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#408—433no—
410#408—433no—
411#407—433no—
412C2×C22⋊C8—433no—
413C43#6052311yescharacteristic, complemented, Sylow
414H(5,𝔽2)—24no—
415H(5,𝔽2)—24no—
416C2×#41—24no—
417C2×#41—24no—
418C2×#41—21no—
419C2×#41C22⋊D4313yes—
420C2×#41C22⋊D4311yescharacteristic
421C2×#41C22×D4313yes—
422C2×#41C22×D4313yes—
423C2×#41C22×D4311yescharacteristic
424C22×Q8C22⋊D4311yescharacteristic
425C22×D4—23no—
426C22×D4—23no—
427C22×D4C22⋊D4313yes—
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—23no—
437#124—23no—
438#123—23no—
439C22⋊Q8—23no—
440C22⋊Q8C22×D4311yescharacteristic
441C22⋊Q8C22×D4313yes—
442#121—26no—
443#121—23no—
444#121—23no—
445#121—23no—
446#121C22×D4313yes—
447#121C22×D4316yes—
448#121C22×D4313yes—
449#120—23no—
450#120—26no—
451C4×Q8—21no—
452C4×Q8—863no—
453C4×Q8—863no—
454C4×Q8—861no—
455C4×Q8—861no—
456C4×D4—23no—
457C4×D4—23no—
458C4×D4—23no—
459C4×D4—866no—
460C4×D4—866no—
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—863no—
471#117—863no—
472#117—863no—
473#117—863no—
474#117C22×D4313yes—
475C2×C4⋊C4—433no—
476C2×C4⋊C4—433no—
477C2×C4⋊C4—433no—
478C2×C4⋊C4—433no—
479C2×C4⋊C4C22×D4313yes—
480C2×C22⋊C4—23no—
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⋊C8—431no—
506C22⋊C8—433no—
507C22⋊C8—433no—
508C22⋊C8—433no—
509C22⋊C8—436no—
510C24—23no—
511C24C2×C22⋊D4313yes—
512#41—24no—
513#41—212no—
514#41—26no—
515#41—26no—
516#41—26no—
517#41—26no—
518#41—44no—
519#41#1062190014yes—
520#41#1062190014yes—
521C2×Q8—24no—
522C2×Q8C2×C22⋊D4313yes—
523C2×Q8C2×C22⋊D4311yescharacteristic
524C2×Q8C23×D4311yescharacteristic
525C2×D4—212no—
526C2×D4—23no—
527C2×D4—23no—
528C2×D4—23no—
529C2×D4—26no—
530C2×D4—23no—
531C2×D4—26no—
532C2×D4—26no—
533C2×D4—412no—
534C2×D4—86no—
535C2×D4C2×C22⋊D4316yes—
536C2×D4C2×C22⋊D4313yes—
537C2×D4C2×C22⋊D4313yes—
538C2×D4C23×D4313yes—
539C22×C4—26no—
540C22×C4—26no—
541C22×C4—23no—
542C22×C4—23no—
543C22×C4—863no—
544C22×C4—863no—
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—21no—
563C4⋊C4—23no—
564C4⋊C4—433no—
565C4⋊C4—431no—
566C4⋊C4—433no—
567C4⋊C4—431no—
568C4⋊C4—863no—
569C4⋊C4—863no—
570C4⋊C4—863no—
571C4⋊C4—863no—
572C4⋊C4C23×D4313yes—
573C4⋊C4C23×D4311yescharacteristic
574C22⋊C4—23no—
575C22⋊C4—21no—
576C22⋊C4—23no—
577C22⋊C4—23no—
578C22⋊C4—26no—
579C22⋊C4—23no—
580C22⋊C4—863no—
581C22⋊C4—861no—
582C22⋊C4—866no—
583C22⋊C4—863no—
584C22⋊C4—863no—
585C42—23no—
586C42—863no—
587C42—861no—
588C42—866no—
589C42—863no—
590C42—863no—
591C23—26no—
592C23—23no—
593C23—43no—
594C23—43no—
595C23—46no—
596C23—83no—
597C23—83no—
598C23C22×C22⋊D4311yescharacteristic
599C23C22×C22⋊D4313yes—
600C23C22×C22⋊D4313yes—
601Q8—26no—
602Q8—21no—
603Q8—21no—
604Q8#1306330614yes—
605D4—212no—
606D4—26no—
607D4—23no—
608D4—23no—
609D4—46no—
610D4—46no—
611D4—46no—
612D4—86no—
613D4—83no—
614D4#13063306112yes—
615C2×C4—26no—
616C2×C4—26no—
617C2×C4—26no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—23no—
621C2×C4—23no—
622C2×C4—21no—
623C2×C4—23no—
624C2×C4—21no—
625C2×C4—46no—
626C2×C4—83no—
627C2×C4—863no—
628C2×C4—861no—
629C2×C4—863no—
630C2×C4—861no—
631C2×C4—3443no—
632C2×C4—3443no—
633C2×C4—3443no—
634C2×C4—3443no—
635C2×C4C22×C22⋊D4311yescharacteristic
636C2×C4C22×C22⋊D4313yes—
637C2×C4C22×C22⋊D4313yes—
638C2×C4C2×#1062190016yes—
639C2×C4C2×#1062190016yes—
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—43no—
654C22—43no—
655C22—43no—
656C22—86no—
657C22—166no—
658C22C2×#1306330616yes—
659C22C23×C22⋊D4311yescharacteristic
660C4—21no—
661C4—23no—
662C4—41no—
663C4—41no—
664C4—43no—
665C4—1723no—
666C4—1721no—
667C4—1723no—
668C4—1721no—
669C4C2×#1306330616yes—
670C4C22×#1062190011yescharacteristic
671C4C22×#1062190011yescharacteristic
672C2—26no—
673C2—41no—
674C2—43no—
675C2—83no—
676C2C22×#1306330611yescharacteristic
677C2#1914936611yescharacteristic
678C2#1914937511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
Fitting, prime radicalC43×#3488C2
socleC22×C43C23×D4
hypercenter#3488D43
hypocenterC43#60523
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #19147798C2semidirect
2. #19144580C2semidirect
3. #19144569C2semidirect
4. #19144547C2semidirect
5. #19144547C2semidirect
6. #19144531C2semidirect
7. #19144524C2semidirect
8. #19144504C2semidirect
9. C2×#14583220C2semidirect
10. #19143193C2semidirect
11. #19143188C2semidirect
12. #19143121C2semidirect
13. #19143121C2semidirect
14. #19143044C2semidirect
20. #14583382C22semidirect
21. #14583382C22semidirect
26. C2×#13063284C22semidirect
27. C2×#13063284C22semidirect
28. #14583237C22semidirect
29. #14583237C22semidirect
30. #14583237C22semidirect
31. #14583232C22semidirect
32. #14583227C22semidirect
33. #14583220C22semidirect
34. #14583220C22semidirect
35. #14583220C22semidirect
36. #14583220C22semidirect
37. #14583220C22semidirect
38. #14583220C22semidirect
39. #14583215C22semidirect
40. #14583215C22semidirect
41. #14583210C22semidirect
42. #14583210C22semidirect
43. #14582942C22semidirect
44. #14582942C22semidirect
45. #14582939C22semidirect
46. #14582939C22semidirect
47. #14582935C22semidirect
48. #14582935C22semidirect
49. C2×#13063258C22semidirect
50. C2×#13063256C22semidirect
51. #14582904C22semidirect
52. #14582904C22semidirect
53. #14582900C22semidirect
54. #14582900C22semidirect
55. #14582895C22semidirect
56. #14582895C22semidirect
57. C2×#13063246C22semidirect
58. C2×#13063246C22semidirect
59. #14582866C22semidirect
60. #14582866C22semidirect
61. #14582863C22semidirect
62. C2×C22⋊(C43⋊C8)C22semidirect
413. C43#60523semidirect

Maximal subgroups

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

subgroupindex
#191477982
#191445802
#191445692
#191445472
#191445312
#191445242
#191445042
C2×#145832202
#191431932
#191431882
#191431212
#191430442
C43×#34882
#6052343