Finite Group Databasebeta

← #25966294

Subgroups — #25966294

Order 11008.

1790 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148419C211yesmaximal, characteristic
2#19148411C211yesmaximal, characteristic
3#19145146C212yesmaximal, complemented
4#19145144C211yesmaximal, characteristic, complemented
5#19145140C212yesmaximal, complemented
6#19145137C211yesmaximal, characteristic, complemented
7#19145131C212yesmaximal, complemented
8#19145130C214yesmaximal, complemented
9#19145123C212yesmaximal, complemented
10#19145122C214yesmaximal, complemented
11#19145119C211yesmaximal, characteristic, complemented
12#19145116C212yesmaximal, complemented
13#501×D43C212yesmaximal, complemented
14#19143191C212yesmaximal
15#19143186C212yesmaximal
16#19143020C211yesmaximal, characteristic
17C2×C43×#501C211yesmaximal, characteristic, complemented
18C2×#13063331C2212yes—
19#14583629—21no—
20#14583626—21no—
21#14583626—21no—
22#14583624—21no—
23#14583610—21no—
24#14583605—21no—
25#14583605—21no—
26#14583604—22no—
27#14583604—22no—
28#14583604—22no—
29#14583564—21no—
30Q8×C22⋊D43—22no—
31#14583530C2212yes—
32#14583530C2211yescharacteristic
33#14583530C2211yescharacteristic
34#14583529C2212yes—
35#14583529C2212yes—
36#14583526C2214yes—
37#14583456C2211yescharacteristic
38#14583456C2211yescharacteristic
39#14583455C2212yes—
40#14583454C2212yes—
41C4⋊Q8×D43C2212yes—
42#125×D43C2212yes—
43#14583380C2211yescharacteristic
44#14583380C2212yes—
45#14583380C2211yescharacteristic
46C4×#10621898C2211yescharacteristic
47#14583309C2212yes—
48#14583309C2212yes—
49#14583308C2211yescharacteristic
50#14583308C2211yescharacteristic
51#14583308C2212yes—
52#14583308C2212yes—
53#14583308C2211yescharacteristic
54#14583308C2211yescharacteristic
55#14583307C2214yes—
56#14583307C2214yes—
57#14583306C2214yes—
58#14583306C2214yes—
59#14583305C2212yes—
60#14583305C2212yes—
61#14583303C2214yes—
62#14583302C2212yes—
63#14583300C2214yes—
64#14583299C2214yes—
65#14583298C2214yes—
66#14583296C2214yes—
67#14583295C2212yes—
68#14582940C2214yes—
69#14582940C2214yes—
70#14582939C2212yes—
71#14582939C2212yes—
72#14582939C2212yes—
73#14582939C2212yes—
74#14582938C2214yes—
75#14582938C2214yes—
76#14582937C2212yes—
77#14582937C2212yes—
78#14582936C2214yes—
79#14582934C2214yes—
80#107×D43C2214yes—
81#106×D43C2214yes—
82#14582856C2214yes—
83#14582854C2212yes—
84C4×#10621877C2211yescharacteristic
85#14582851C2212yes—
86#97×D43C2212yes—
87C2×C4⋊Q8×C43C2211yescharacteristic
88C2×#125×C43C2211yescharacteristic
89C43×#501C2212yes—
90C43×#501C2214yes—
91C43×#501C2212yes—
92C2×#107×C43C2212yes—
93C2×#106×C43C2212yes—
94C2×#97×C43C2211yescharacteristic
95C2×#10621898C2311yescharacteristic
96C2×Q8×D43—22no—
97#13063331Q8116yescomplemented
98C2×#10621877C2312yes—
99C2×#10621872C2314yes—
100C2×C8×D43C2314yes—
101#13063325C2311yescharacteristic
102#13063325C2311yescharacteristic
103#13063325C2311yescharacteristic
104#13063325C2311yescharacteristic
105#13063324—22no—
106#13063324—21no—
107#13063324—21no—
108#13063324—22no—
109#13063324—22no—
110#13063324—22no—
111#13063324C2312yes—
112#13063324C2314yes—
113#13063324C2312yes—
114#13063323—24no—
115#13063323—22no—
116#13063317C2312yes—
117#13063317C2311yescharacteristic
118#13063317C2311yescharacteristic
119#13063316—21no—
120#13063316—21no—
121#13063316—22no—
122#13063316C2312yes—
123#13063316C2314yes—
124#13063316C2312yes—
125#13063315—24no—
126#13063315—22no—
127#13063315—22no—
128#13063315—22no—
129#13063315—22no—
130#13063305—22no—
131#13063305—22no—
132#13063305—22no—
133#13063304—21no—
134#13063304—21no—
135#13063304—21no—
136#13063304—21no—
137#13063304—24no—
138#13063304—22no—
139#13063304—22no—
140#13063303—22no—
141#13063303—22no—
142#13063303—24no—
143#13063303—22no—
144#13063303—22no—
145#13063301—22no—
146#13063301—24no—
147Q8×Dic43—22no—
148C4×Dic86—21no—
149C4×Dic86—21no—
150C4×Dic86—21no—
151C4×Dic86—21no—
152C4×Dic86D411yescharacteristic
153C4×Dic86D411yescharacteristic
154#13063290—22no—
155#13063290—21no—
156#13063290—21no—
157#13063290—22no—
158#13063290—22no—
159#13063290—22no—
160C4×D172D411yescharacteristic
161C4×D172D411yescharacteristic
162#13063287—22no—
163#13063287—21no—
164#13063287—21no—
165C4×C22⋊D43—24no—
166C4×C22⋊D43—22no—
167C4×C22⋊D43—22no—
168C4×C22⋊D43D412yes—
169C4×C22⋊D43D412yes—
170#13063284C2311yescharacteristic
171#13063284C2311yescharacteristic
172#13063284C2312yes—
173#13063284C2311yescharacteristic
174#13063283C2312yes—
175#13063283C2314yes—
176#13063283C2312yes—
177#13063282C2312yes—
178C4⋊C4×D43—22no—
179C4⋊C4×D43—22no—
180C4⋊C4×D43—22no—
181C4⋊C4×D43C2312yes—
182C4⋊C4×D43C2312yes—
183C4⋊C4×D43C2314yes—
184C42×D43C2312yes—
185#13063259C2312yes—
186#13063259C2312yes—
187#13063259C2312yes—
188#13063259C2312yes—
189#13063258C2314yes—
190#13063258C2314yes—
191#13063258C2314yes—
192#13063258C2314yes—
193#13063257C2312yes—
194#13063257C2312yes—
195#13063257C2312yes—
196#13063257C2312yes—
197#13063256C2314yes—
198#13063256C2314yes—
199#13063256C2314yes—
200#13063256C2314yes—
201#13063236C2312yes—
202#13063235C2314yes—
203C4×C43⋊C8C2312yes—
204C8×Dic43C2314yes—
205C22×Q8×C43—21no—
206C22×C8×C43C2312yes—
207C4⋊Q8×C43—21no—
208C4⋊Q8×C43—21no—
209C4⋊Q8×C43C2312yes—
210C4⋊Q8×C43C2312yes—
211#125×C43—21no—
212#125×C43—21no—
213#125×C43C2312yes—
214#125×C43C2312yes—
215C2×C4⋊C4×C43—21no—
216C2×C4⋊C4×C43—21no—
217C2×C4⋊C4×C43—21no—
218C2×C4⋊C4×C43C2311yescharacteristic
219C2×C4⋊C4×C43C2311yescharacteristic
220C2×C4⋊C4×C43C2312yes—
221C2×C42×C43C2311yescharacteristic
222#107×C43C2314yes—
223#107×C43C2314yes—
224#106×C43C2314yes—
225#106×C43C2314yes—
226#97×C43C2311yescharacteristic
227#97×C43C2311yescharacteristic
228#97×C43C2312yes—
229C2×Q8×C43—22no—
230C2×Q8×C43—22no—
231C2×Q8×C43—82no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—22no—
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2411yescharacteristic
238C2×C22⋊D43C2×D412yes—
239Q8×D43—84no—
240#10621898C2×Q818yes—
241C2×D172C2×D411yescharacteristic
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43—24no—
245C2×C4×D43C2×D412yes—
246C2×C4×D43C2×D412yes—
247C2×C4×D43C2412yes—
248C2×Dic86—21no—
249C2×Dic86—21no—
250C2×Dic86—21no—
251C2×Dic86—21no—
252C2×Dic86—22no—
253C2×Dic86—22no—
254C2×Dic86—24no—
255C2×Dic86C2×D411yescharacteristic
256C2×C8×C43C2×Q818yescomplemented
257C2×C8×C43C2412yes—
258C2×C8×C43C2412yes—
259C4⋊C4×C43—22no—
260C4⋊C4×C43—22no—
261C4⋊C4×C43—22no—
262C4⋊C4×C43—22no—
263C4⋊C4×C43—22no—
264C4⋊C4×C43—22no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—22no—
268C4⋊C4×C43C2412yes—
269C4⋊C4×C43C2414yes—
270C4⋊C4×C43C2412yes—
271C42×C43C2×D411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C42×C43C2411yescharacteristic
274C42×C43C2411yescharacteristic
275C22⋊Dic43—22no—
276C22⋊Dic43—21no—
277C22⋊Dic43—21no—
278C22⋊Dic43C2×D412yes—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4—22no—
281(C2×D43)⋊C4—22no—
282(C2×D43)⋊C4C2×D412yes—
283(C2×D43)⋊C4C2×D412yes—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—22no—
289C4⋊Dic43—22no—
290C4⋊Dic43—24no—
291C4⋊Dic43C2×D411yescharacteristic
292C4⋊Dic43C2×D411yescharacteristic
293C4⋊Dic43C2411yescharacteristic
294C4⋊Dic43C2411yescharacteristic
295C4⋊Dic43C2412yes—
296C4⋊Dic43C2412yes—
297C4⋊Dic43C2411yescharacteristic
298C4⋊Dic43C2411yescharacteristic
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—22no—
304Dic43⋊C4—22no—
305Dic43⋊C4—24no—
306Dic43⋊C4—22no—
307Dic43⋊C4—22no—
308Dic43⋊C4—22no—
309Dic43⋊C4—22no—
310Dic43⋊C4—24no—
311Dic43⋊C4—24no—
312Dic43⋊C4—22no—
313Dic43⋊C4—22no—
314Dic43⋊C4C2×D412yes—
315Dic43⋊C4C2×D412yes—
316C4×Dic43—22no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—22no—
320C4×Dic43—22no—
321C4×Dic43—24no—
322C4×Dic43C2×D412yes—
323C4×Dic43C2×D412yes—
324C4×Dic43C2412yes—
325#10621877C2×Q818yescomplemented
326C2×C43⋊C8C2414yes—
327#10621872C2×Q8116yescomplemented
328C8×D43C2×Q8116yescomplemented
329C23×C43C22×D411yescharacteristic
330C22×D43C22×D412yes—
331Q8×C43—44no—
332Q8×C43—82no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—24no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—81no—
339C2×C4×C43—81no—
340C2×C4×C43—82no—
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×Q814yes—
347C2×C4×C43C2511yescharacteristic
348C22⋊D43C4⋊Q818yes—
349C2×Dic43—22no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—22no—
355C2×Dic43C22×D412yes—
356C2×Dic43C22×D412yes—
357C2×Dic43C22×D412yes—
358D172C4⋊Q814yes—
359C4×D43—42no—
360C4×D43—42no—
361C4×D43—82no—
362C4×D43—82no—
363C4×D43—84no—
364C4×D43C22×Q818yes—
365Dic86—42no—
366Dic86—42no—
367Dic86—82no—
368Dic86—82no—
369Dic86—84no—
370Dic86—81no—
371Dic86—81no—
372Dic86C4⋊Q814yes—
373C8×C43C22×Q814yes—
374C8×C43C22×Q814yes—
375C43⋊C8C22×Q818yes—
376#60668—431nomaximal, Sylow
377C22×C43—21no—
378C22×C43—21no—
379C22×C43C2×C4⋊Q812yes—
380C22×C43C23×D411yescharacteristic
381C2×D43—22no—
382C2×D43—22no—
383C2×D43C2×C4⋊Q814yes—
384C4×C43—21no—
385C4×C43—21no—
386C4×C43—21no—
387C4×C43—21no—
388C4×C43—42no—
389C4×C43—44no—
390C4×C43—42no—
391C4×C43C2×C4⋊Q812yes—
392C4×C43C23×Q812yes—
393Dic43—22no—
394Dic43—22no—
395Dic43—42no—
396Dic43—41no—
397Dic43—41no—
398Dic43—42no—
399Dic43—41no—
400Dic43—41no—
401Dic43C2×C4⋊Q814yes—
402#3504—431no—
403#3503—431no—
404#3166—432no—
405#3166—431no—
406#3165—432no—
407#3165—431no—
408#3164—434no—
409#3164—432no—
410#3163—434no—
411#3163—432no—
412#3162—432no—
413#3162—431no—
414C2×#501—432no—
415C2×#501D4311yescharacteristic, complemented
416#2913—432no—
417#2912—432no—
418#2875—431no—
419C2×C43—22no—
420C2×C43C22×C4⋊Q811yescharacteristic
421C2×C43#358511yescharacteristic
422C2×C43#358611yescharacteristic
423D43—24no—
424C2×#131—432no—
425Q82—861no—
426#557—861no—
427#557—861no—
428#557—861no—
429#554—862no—
430#554—862no—
431#554—862no—
432#554—861no—
433#554—861no—
434#554—861no—
435D4×Q8—861no—
436D4×Q8—862no—
437#544—434no—
438#544—432no—
439#544—432no—
440#544—431no—
441#544—432no—
442#544—431no—
443#533—432no—
444#533—432no—
445#533—431no—
446#533—431no—
447C2×C4⋊Q8—432no—
448C2×C4⋊Q8C2×D4311yescharacteristic
449C2×#125—432no—
450C2×#125C2×D4311yescharacteristic
451#520—431no—
452#520—432no—
453#520—431no—
454C4×#41—431no—
455#501—432no—
456#501—432no—
457#501—432no—
458#501—432no—
459#501—434no—
460#501—434no—
461#501—434no—
462#501—434no—
463#501—431no—
464#501—431no—
465#501—432no—
466#501—432no—
467#501—431no—
468#501—431no—
469#501C2×D4312yes—
470#501C2×D4314yes—
471#501C2×D4312yes—
472#500—432no—
473#500—434no—
474#499—434no—
475#499—434no—
476#499—434no—
477#498—432no—
478#498—434no—
479#428—432no—
480#428—432no—
481#428—432no—
482#428—432no—
483#428—434no—
484#428—434no—
485#428—434no—
486#428—434no—
487#427—432no—
488#427—432no—
489#427—434no—
490#427—434no—
491C2×#107—434no—
492C2×#107C2×D4312yes—
493C2×#106—434no—
494C2×#106C2×D4312yes—
495#405—432no—
496#405—434no—
497C4×M16—431no—
498C4×M16—432no—
499C2×#97—432no—
500C2×#97C2×D4311yescharacteristic
501C43#6066811yescharacteristic, complemented, Sylow
502C2×#41—431no—
503C22×Q8—21no—
504C22×Q8—862no—
505#131—4316no—
506C2×M16—432no—
507C2×M16—434no—
508C22×C8—434no—
509C22×C8C22×D4312yes—
510C4⋊Q8—21no—
511C4⋊Q8—21no—
512C4⋊Q8—434no—
513C4⋊Q8—432no—
514C4⋊Q8—432no—
515C4⋊Q8—431no—
516C4⋊Q8—431no—
517C4⋊Q8—431no—
518C4⋊Q8—431no—
519C4⋊Q8—862no—
520C4⋊Q8—862no—
521C4⋊Q8—862no—
522C4⋊Q8—862no—
523C4⋊Q8—862no—
524C4⋊Q8—861no—
525C4⋊Q8—861no—
526C4⋊Q8—864no—
527C4⋊Q8C22×D4312yes—
528C4⋊Q8C22×D4312yes—
529#125—21no—
530#125—21no—
531#125—432no—
532#125—432no—
533#125—434no—
534#125—431no—
535#125—431no—
536#125—432no—
537#125—862no—
538#125—862no—
539#125—862no—
540#125—862no—
541#125—864no—
542#125—861no—
543#125—861no—
544#125—862no—
545#125C22×D4312yes—
546#125C22×D4312yes—
547C22⋊Q8—864no—
548C22⋊Q8—862no—
549C22⋊Q8—862no—
550C22⋊Q8—862no—
551C22⋊Q8—862no—
552C22⋊Q8—864no—
553C22⋊Q8—862no—
554C22⋊Q8—862no—
555C22⋊Q8—864no—
556C22⋊Q8—862no—
557C22⋊Q8—862no—
558C22⋊Q8—862no—
559C22⋊Q8—862no—
560C22⋊Q8—861no—
561C22⋊Q8—861no—
562C22⋊Q8—861no—
563C22⋊Q8—861no—
564C4×Q8—431no—
565C4×Q8—431no—
566C4×Q8—862no—
567C4×Q8—862no—
568C4×Q8—862no—
569C4×Q8—862no—
570C4×Q8—861no—
571C4×Q8—861no—
572C4×Q8—862no—
573C4×Q8—861no—
574C4×Q8—861no—
575C4×Q8—861no—
576C4×Q8—861no—
577C4×D4—432no—
578C4×D4—432no—
579C4×D4—431no—
580C4×D4—431no—
581C4×D4—862no—
582C4×D4—861no—
583C4×D4—861no—
584C4×D4—864no—
585C4×D4—862no—
586C4×D4—862no—
587#117—431no—
588#117—432no—
589#117—431no—
590#117—431no—
591#117—432no—
592#117—432no—
593#117—434no—
594#117—432no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—432no—
599C2×C4⋊C4—432no—
600C2×C4⋊C4—434no—
601C2×C4⋊C4—862no—
602C2×C4⋊C4—862no—
603C2×C4⋊C4—862no—
604C2×C4⋊C4C22×D4311yescharacteristic
605C2×C4⋊C4C22×D4311yescharacteristic
606C2×C4⋊C4C22×D4312yes—
607C2×C42—432no—
608C2×C42C22×D4311yescharacteristic
609#107—432no—
610#107—432no—
611#107—432no—
612#107—432no—
613#107—434no—
614#107—434no—
615#107—434no—
616#107—434no—
617#107C22×D4314yes—
618#107C22×D4314yes—
619#106—432no—
620#106—432no—
621#106—432no—
622#106—432no—
623#106—434no—
624#106—434no—
625#106—434no—
626#106—434no—
627#106C22×D4314yes—
628#106C22×D4314yes—
629#97—434no—
630#97—432no—
631#97C22×D4311yescharacteristic
632#97C22×D4311yescharacteristic
633#97C22×D4312yes—
634C4×C8—434no—
635C4×C8—432no—
636#41—438no—
637C2×Q8—22no—
638C2×Q8—22no—
639C2×Q8—82no—
640C2×Q8—431no—
641C2×Q8—862no—
642C2×Q8—862no—
643C2×Q8—864no—
644C2×Q8—861no—
645C2×Q8—861no—
646C2×Q8—861no—
647C2×Q8—861no—
648C2×Q8—3444no—
649C2×D4—432no—
650C2×D4—431no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—22no—
654C22×C4—432no—
655C22×C4—432no—
656C22×C4—432no—
657C22×C4—862no—
658C22×C4—862no—
659C22×C4—864no—
660C22×C4D4×D4311yescharacteristic
661C22×C4D4×D4311yescharacteristic
662C22×C4C23×D4311yescharacteristic
663M16—438no—
664M16—4316no—
665C2×C8—434no—
666C2×C8—4316no—
667C2×C8Q8×D4318yescomplemented
668C2×C8C23×D4312yes—
669C2×C8C23×D4312yes—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—22no—
679C4⋊C4—432no—
680C4⋊C4—431no—
681C4⋊C4—432no—
682C4⋊C4—431no—
683C4⋊C4—431no—
684C4⋊C4—431no—
685C4⋊C4—432no—
686C4⋊C4—432no—
687C4⋊C4—431no—
688C4⋊C4—431no—
689C4⋊C4—862no—
690C4⋊C4—862no—
691C4⋊C4—864no—
692C4⋊C4—862no—
693C4⋊C4—862no—
694C4⋊C4—862no—
695C4⋊C4—862no—
696C4⋊C4—864no—
697C4⋊C4—864no—
698C4⋊C4—864no—
699C4⋊C4—862no—
700C4⋊C4—862no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—862no—
708C4⋊C4—862no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4C23×D4312yes—
712C4⋊C4C23×D4314yes—
713C4⋊C4C23×D4312yes—
714C22⋊C4—432no—
715C22⋊C4—432no—
716C22⋊C4—432no—
717C22⋊C4—862no—
718C22⋊C4—862no—
719C22⋊C4—864no—
720C22⋊C4—862no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C42—432no—
724C42—432no—
725C42—432no—
726C42—862no—
727C42—862no—
728C42—864no—
729C42—862no—
730C42—861no—
731C42—861no—
732C42D4×D4311yescharacteristic
733C42D4×D4311yescharacteristic
734C42C23×D4311yescharacteristic
735C42C23×D4311yescharacteristic
736C23—432no—
737C23C2×D4×D4311yescharacteristic
738Q8—44no—
739Q8—82no—
740Q8—434no—
741Q8—3441no—
742Q8—3441no—
743Q8—3444no—
744Q8—3442no—
745Q8—3442no—
746Q8—1722no—
747Q8—1722no—
748D4—438no—
749D4—434no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—82no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—432no—
759C2×C4—438no—
760C2×C4—432no—
761C2×C4—432no—
762C2×C4—862no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—861no—
766C2×C4—861no—
767C2×C4—862no—
768C2×C4—3444no—
769C2×C4—3442no—
770C2×C4—3442no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4C2×D4×D4311yescharacteristic
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4C2×D4×D4311yescharacteristic
776C2×C4C2×D4×D4311yescharacteristic
777C2×C4C2×D4×D4311yescharacteristic
778C2×C4C2×Q8×D4314yes—
779C2×C4C24×D4311yescharacteristic
780C8—438no—
781C8C2×Q8×D4314yes—
782C8C2×Q8×D4314yes—
783C22—21no—
784C22—21no—
785C22—434no—
786C22—862no—
787C22—862no—
788C22C4⋊Q8×D4312yes—
789C22C22×D4×D4311yescharacteristic
790C4—21no—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—44no—
795C4—42no—
796C4—42no—
797C4—434no—
798C4—862no—
799C4—862no—
800C4—1722no—
801C4—1721no—
802C4—1721no—
803C4—1721no—
804C4—1721no—
805C4—1722no—
806C4C4⋊Q8×D4312yes—
807C4C22×Q8×D4312yes—
808C2—22no—
809C2—864no—
810C2C2×C4⋊Q8×D4311yescharacteristic
811C2#1914937111yescharacteristic
812C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#501C2
socleC22×C43C23×D4
prime radicalC2×#10621898C23
hypercenterC2×#501D43
hypocenterC43#60668
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #19145146C2semidirect
4. #19145144C2semidirect
5. #19145140C2semidirect
6. #19145137C2semidirect
7. #19145131C2semidirect
8. #19145130C2semidirect
9. #19145123C2semidirect
10. #19145122C2semidirect
11. #19145119C2semidirect
12. #19145116C2semidirect
13. #501×D43C2semidirect
17. C2×C43×#501C2semidirect
97. #13063331Q8semidirect
256. C2×C8×C43C2×Q8semidirect
325. #10621877C2×Q8semidirect
327. #10621872C2×Q8semidirect
328. C8×D43C2×Q8semidirect
415. C2×#501D43semidirect
501. C43#60668semidirect
667. C2×C8Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#191484192
#191484112
#191451462
#191451442
#191451402
#191451372
#191451312
#191451302
#191451232
#191451222
#191451192
#191451162
#501×D432
#191431912
#191431862
#191430202
C2×C43×#5012
#6066843