Finite Group Databasebeta

← #25968971

Subgroups — #25968971

Order 11008.

1690 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148000C211yesmaximal, characteristic, complemented
2C2×#14583516C211yesmaximal, characteristic
3#19145891C214yesmaximal, complemented
4#19145889C214yesmaximal, complemented
5#19145876C214yesmaximal, complemented
6#19145874C214yesmaximal, complemented
7#19145139C212yesmaximal, complemented
8#19144979C212yesmaximal, complemented
9#19144544C211yesmaximal, characteristic, complemented
10#19144543C211yesmaximal, characteristic, complemented
11#19144531C211yesmaximal, characteristic
12#19144399C212yesmaximal, complemented
13#19144389C212yesmaximal, complemented
14#19143230C211yesmaximal, characteristic, complemented
15C43×#3094C211yesmaximal, characteristic
16#14583530C2212yescomplemented
17#14583530C2212yescomplemented
18#14583527—21no—
19#14583527—21no—
20#14583527C2212yescomplemented
21#14583527C2212yescomplemented
22#14583525—21no—
23#14583525—21no—
24#14583516—22no—
25#14583516—22no—
26#14583516C2214yes—
27#14583516C2214yes—
28#14583456—22no—
29#14583452—22no—
30#14583452C2212yes—
31#14583452C2212yes—
32C2×#13063324C2211yescharacteristic
33C2×#13063318—21no—
34C2×#13063312—21no—
35C2×#13063312C2211yescharacteristic
36C2×#13063306—21no—
37C2×#13063304C2211yescharacteristic
38C2×#13063302—21no—
39C2×#13063290C2211yescharacteristic
40C2×D4×Dic43C2211yescharacteristic
41C2×#13063284C2211yescharacteristic
42C2×#13063284C2211yescharacteristic
43#14583307C2214yescomplemented
44#14583306C2214yescomplemented
45#14583303C2214yescomplemented
46#14583296C2214yescomplemented
47#14583257C2214yescomplemented
48#14583257C2214yescomplemented
49#14583252C2214yescomplemented
50#14583252C2214yescomplemented
51#14583241C2214yescomplemented
52#14583240C2214yescomplemented
53#14583235C2212yescomplemented
54#14583234C2212yescomplemented
55#14583230C2212yescomplemented
56#14583229C2212yescomplemented
57#14583220C2214yes—
58#14583215C2212yes—
59#14583210C2212yes—
60#14583209C2214yescomplemented
61#14583205C2214yescomplemented
62#14583201C2214yescomplemented
63#14583197C2214yescomplemented
64#14583193C2214yescomplemented
65#14583187C2214yescomplemented
66#14583183C2214yescomplemented
67#14583177C2214yescomplemented
68#14582957C2214yescomplemented
69#14582957C2214yescomplemented
70#14582942C2212yes—
71#14582941C2212yes—
72#14582939C2212yes—
73#14582922C2212yes—
74#14582909C2212yes—
75#14582907C2212yes—
76#14582904C2212yes—
77#14582863C2211yescharacteristic
78M16×Dic43C2212yes—
79C2×#121×C43C2211yescharacteristic
80C2×#117×C43C2211yescharacteristic
81C43×#482C2214yes—
82C43×#481C2212yes—
83C43×#480C2212yes—
84C43×#428C2212yes—
85C43×#418C2212yes—
86C43×#407C2211yescharacteristic
87C22×Dic86—21no—
88C22×Dic86C2311yescharacteristic
89C23×Dic43—21no—
90C2×#10621877C2312yes—
91#13063325—22no—
92#13063325—22no—
93#13063324—22no—
94#13063324—22no—
95#13063324—22no—
96#13063324C2312yes—
97#13063324C2314yes—
98#13063324C2312yes—
99#13063324C2312yes—
100#13063324C2312yes—
101#13063318—24no—
102#13063318—24no—
103#13063317—22no—
104#13063317—22no—
105#13063316—22no—
106#13063316—22no—
107#13063316C2312yes—
108#13063316C2312yes—
109#13063316C2312yes—
110#13063316C2312yes—
111#13063312—24no—
112#13063312—24no—
113#13063312—22no—
114#13063312C2314yes—
115#13063306—24no—
116#13063306—24no—
117#13063304—21no—
118#13063304—21no—
119#13063304—22no—
120#13063304—22no—
121#13063304—22no—
122#13063304—22no—
123#13063304C2312yes—
124#13063304C2312yes—
125#13063302—22no—
126#13063302—22no—
127#13063302—22no—
128#13063302—22no—
129#13063302—22no—
130#13063302—22no—
131#13063302—22no—
132#13063302—22no—
133#13063302—24no—
134#13063302—24no—
135C4×Dic86—22no—
136C4×Dic86—22no—
137C4×Dic86—22no—
138C4×Dic86—22no—
139#13063290—22no—
140#13063290C2314yes—
141D4×Dic43—22no—
142D4×Dic43C2314yes—
143#13063284—21no—
144#13063284—21no—
145#13063284D412yes—
146#13063284D412yes—
147#13063284C2312yes—
148#13063284C2312yes—
149#13063284C2312yes—
150#13063284C2312yes—
151C2×C4⋊Dic43D411yescharacteristic
152C2×C4⋊Dic43D411yescharacteristic
153C2×C4⋊Dic43C2311yescharacteristic
154C2×C4⋊Dic43C2311yescharacteristic
155C2×C4⋊Dic43C2311yescharacteristic
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C2×C22⋊Dic43—21no—
160C2×C22⋊Dic43—21no—
161C2×C22⋊Dic43—21no—
162C2×C22⋊Dic43—21no—
163C2×C22⋊Dic43—21no—
164C2×C22⋊Dic43D411yescharacteristic
165C2×C22⋊Dic43D411yescharacteristic
166C2×C4×Dic43—21no—
167C2×C4×Dic43—21no—
168C2×C4×Dic43C2311yescharacteristic
169C2×C4×Dic43C2311yescharacteristic
170#13063259C2314yes—
171#13063258C2314yes—
172#13063258C2314yes—
173#13063257C2314yes—
174#13063256C2314yes—
175#13063256C2314yes—
176Dic43⋊C8C2314yes—
177Dic43⋊C8C2314yes—
178#13063250C2314yes—
179#13063250C2314yes—
180#13063248C2314yes—
181#13063248C2314yes—
182#13063246C2314yes—
183#13063246C2314yes—
184C22⋊(C43⋊C8)C2312yes—
185C22⋊(C43⋊C8)C2312yes—
186#13063235C2314yes—
187C8×Dic43C2314yes—
188C22×D4×C43—21no—
189C22×D4×C43C2311yescharacteristic
190C23×C4×C43C2311yescharacteristic
191C2×M16×C43C2312yes—
192#121×C43—21no—
193#121×C43—21no—
194#121×C43C2312yes—
195#121×C43C2312yes—
196#117×C43—21no—
197#117×C43—21no—
198#117×C43C2312yes—
199#117×C43C2312yes—
200C2×C4⋊C4×C43C2311yescharacteristic
201C2×C4⋊C4×C43C2311yescharacteristic
202C2×C4⋊C4×C43C2311yescharacteristic
203C2×C22⋊C4×C43—21no—
204C2×C22⋊C4×C43—21no—
205C2×C42×C43—21no—
206#107×C43C2314yes—
207#106×C43C2314yes—
208#102×C43C2314yes—
209#102×C43C2314yes—
210C22⋊C8×C43C2312yes—
211C22⋊C8×C43C2312yes—
212C24×C43—21no—
213C24×C43C2×D411yescharacteristic
214C2×D4×C43—21no—
215C2×D4×C43—22no—
216C2×D4×C43—22no—
217C2×D4×C43—24no—
218C2×D4×C43—82no—
219C2×D4×C43C2412yes—
220C22×C4×C43—24no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C22×Dic43—24no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—82no—
236C22×Dic43C2×D411yescharacteristic
237C22×Dic43C2×D411yescharacteristic
238C22×Dic43C2×D411yescharacteristic
239C22×Dic43C2×D411yescharacteristic
240C2×Dic86—24no—
241C2×Dic86—21no—
242C2×Dic86—22no—
243C2×Dic86—22no—
244C2×Dic86—22no—
245C2×Dic86—22no—
246C2×Dic86—24no—
247C2×Dic86—82no—
248C2×Dic86C2412yes—
249M16×C43—24no—
250C2×C8×C43C2414yes—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43C2412yes—
255C4⋊C4×C43C2412yes—
256C4⋊C4×C43C2412yes—
257C22⋊C4×C43—22no—
258C22⋊C4×C43—22no—
259C22⋊C4×C43—22no—
260C22⋊C4×C43—22no—
261C42×C43—22no—
262C42×C43—22no—
263C22⋊Dic43—24no—
264C22⋊Dic43—24no—
265C22⋊Dic43—24no—
266C22⋊Dic43—22no—
267C22⋊Dic43—22no—
268C22⋊Dic43—22no—
269C22⋊Dic43—22no—
270C22⋊Dic43C2×D412yes—
271C22⋊Dic43C2×D412yes—
272C22⋊Dic43C2×D412yes—
273C22⋊Dic43C2×D412yes—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—22no—
278C4⋊Dic43—22no—
279C4⋊Dic43—22no—
280C4⋊Dic43—22no—
281C4⋊Dic43C2×D412yes—
282C4⋊Dic43C2×D412yes—
283C4⋊Dic43C2×D412yes—
284C4⋊Dic43C2×D412yes—
285C4⋊Dic43C2412yes—
286C4⋊Dic43C2412yes—
287C4⋊Dic43C2412yes—
288Dic43⋊C4—22no—
289Dic43⋊C4—22no—
290Dic43⋊C4—24no—
291Dic43⋊C4—24no—
292Dic43⋊C4—22no—
293Dic43⋊C4—22no—
294Dic43⋊C4—22no—
295Dic43⋊C4—22no—
296Dic43⋊C4—22no—
297Dic43⋊C4—22no—
298Dic43⋊C4—22no—
299Dic43⋊C4—22no—
300C4×Dic43—22no—
301C4×Dic43—22no—
302C4×Dic43—24no—
303C4×Dic43C2×D412yes—
304C4×Dic43C2×D412yes—
305C4×Dic43C2412yes—
306C4×Dic43C2412yes—
307#10621877—24no—
308C2×C43⋊C8C2414yes—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43—42no—
316C23×C43C22×D411yescharacteristic
317C23×C43C22×D411yescharacteristic
318C23×C43C22×D411yescharacteristic
319D4×C43—24no—
320D4×C43—42no—
321D4×C43—82no—
322D4×C43—82no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—42no—
332C2×C4×C43—81no—
333C2×C4×C43—81no—
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C432−1+414yes—
338C2×C4×C43C2511yescharacteristic
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—42no—
348C2×Dic43—42no—
349C2×Dic43—84no—
350C2×Dic43—81no—
351C2×Dic43—81no—
352C2×Dic43C22×D412yes—
353C2×Dic43C22×D412yes—
354C2×Dic43C22×D412yes—
355C2×Dic43C22×D412yes—
356Dic86—24no—
357Dic86—42no—
358Dic86—82no—
359Dic86—82no—
360Dic86—82no—
361Dic86—82no—
362Dic86—84no—
363C8×C43—24no—
364C43⋊C8—24no—
365#60870—431nomaximal, Sylow
366C22×C43—21no—
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—21no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—82no—
378C22×C43—84no—
379C22×C43#53612yes—
380C22×C43C23×D411yescharacteristic
381C4×C43—21no—
382C4×C43—21no—
383C4×C43—42no—
384C4×C43—42no—
385C4×C43—42no—
386C4×C43#53612yes—
387C4×C43C2×2−1+412yes—
388Dic43—22no—
389Dic43—22no—
390Dic43—22no—
391Dic43—22no—
392Dic43—42no—
393Dic43—42no—
394Dic43—42no—
395Dic43—42no—
396#3458—431no—
397C2×#542—431no—
398#3244—434no—
399#3244—434no—
400#3243—434no—
401#3243—434no—
402#3165—432no—
403#3140—432no—
404#3095—431no—
405#3095—431no—
406#3094—431no—
407#3094D4311yescharacteristic
408#3078—432no—
409#3077—432no—
410#2921—431no—
411C2×C43—22no—
412C2×C43—41no—
413C2×C43—41no—
414C2×C43—82no—
415C2×C43C2×#53611yescharacteristic
416C2×C43#358511yescharacteristic
417C2×C43#358611yescharacteristic
418#544—432no—
419#544—432no—
420#544—432no—
421#544—432no—
422#544—861no—
423#544—861no—
424#543—861no—
425#543—861no—
426#542—434no—
427#542—434no—
428#542—862no—
429#542—862no—
430#533—432no—
431#533—432no—
432#533—862no—
433#533—862no—
434C2×C4⋊Q8—431no—
435C2×#126—861no—
436C2×#124—431no—
437C2×#124—861no—
438C2×#123—861no—
439C2×C22⋊Q8—431no—
440C2×C22⋊Q8—861no—
441C2×#121C2×D4311yescharacteristic
442C2×C4×Q8—431no—
443C2×C4×D4—431no—
444C2×#117—431no—
445C2×#117—431no—
446C2×#117C2×D4311yescharacteristic
447#501—434no—
448#501—434no—
449#500—434no—
450#498—434no—
451#489—434no—
452#489—434no—
453#488—434no—
454#488—434no—
455#485—434no—
456#485—434no—
457#484—432no—
458#484—432no—
459#483—432no—
460#483—432no—
461#482—434no—
462#482C2×D4314yes—
463#481—432no—
464#481C2×D4312yes—
465#480—432no—
466#480C2×D4312yes—
467#479—434no—
468#479—434no—
469#478—434no—
470#478—434no—
471#477—434no—
472#476—434no—
473#475—434no—
474#474—434no—
475#433—434no—
476#433—434no—
477#428—432no—
478#428—432no—
479#428—432no—
480#428C2×D4312yes—
481#423—432no—
482#419—432no—
483#419—432no—
484#418—432no—
485#418C2×D4312yes—
486#407—431no—
487#407C2×D4311yescharacteristic
488C4×M16—432no—
489C43#6087011yescharacteristic, complemented, Sylow
490C22×Q8—431no—
491C22×Q8—861no—
492C22×D4—21no—
493C22×D4C22×D4311yescharacteristic
494C23×C4—861no—
495C23×C4C22×D4311yescharacteristic
496C2×M16—432no—
497C2×M16C22×D4312yes—
498C4⋊Q8—434no—
499C4⋊Q8—432no—
500C4⋊Q8—432no—
501C4⋊Q8—432no—
502C4⋊Q8—432no—
503C4⋊Q8—862no—
504C4⋊Q8—862no—
505C4⋊Q8—862no—
506C4⋊Q8—862no—
507C4⋊Q8—862no—
508#126—864no—
509#126—864no—
510#125—432no—
511#125—432no—
512#125—432no—
513#125—432no—
514#125—862no—
515#125—862no—
516#125—862no—
517#125—862no—
518#124—434no—
519#124—862no—
520#124—864no—
521#124—864no—
522#123—864no—
523#123—864no—
524C22⋊Q8—432no—
525C22⋊Q8—432no—
526C22⋊Q8—862no—
527C22⋊Q8—862no—
528C22⋊Q8—862no—
529C22⋊Q8—862no—
530C22⋊Q8—864no—
531C22⋊Q8—864no—
532C22⋊Q8—862no—
533C22⋊Q8—862no—
534C22⋊Q8—862no—
535C22⋊Q8—862no—
536C22⋊Q8—862no—
537C22⋊Q8—862no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540C22⋊Q8—861no—
541C22⋊Q8—861no—
542#121—21no—
543#121—21no—
544#121C22×D4312yes—
545#121C22×D4312yes—
546C4×Q8—434no—
547C4×Q8—862no—
548C4×Q8—862no—
549C4×Q8—862no—
550C4×Q8—862no—
551C4×Q8—862no—
552C4×D4—434no—
553C4×D4—862no—
554#117—21no—
555#117—21no—
556#117—432no—
557#117—432no—
558#117—432no—
559#117—432no—
560#117—432no—
561#117—432no—
562#117—861no—
563#117—861no—
564#117C22×D4312yes—
565#117C22×D4312yes—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—431no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4C22×D4311yescharacteristic
575C2×C4⋊C4C22×D4311yescharacteristic
576C2×C4⋊C4C22×D4311yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—431no—
580C2×C22⋊C4—431no—
581C2×C22⋊C4—861no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C42—21no—
587C2×C42—431no—
588C2×C42—431no—
589C2×C42—861no—
590C2×C42—861no—
591#107—434no—
592#107—434no—
593#107—434no—
594#107C22×D4314yes—
595#106—434no—
596#106—434no—
597#106—434no—
598#106C22×D4314yes—
599C4⋊C8—434no—
600C4⋊C8—434no—
601#103—434no—
602#103—434no—
603#103—434no—
604#103—434no—
605#102—434no—
606#102—434no—
607#102C22×D4314yes—
608#102C22×D4314yes—
609C22⋊C8—432no—
610C22⋊C8—432no—
611C22⋊C8C22×D4312yes—
612C22⋊C8C22×D4312yes—
613#97—434no—
614C4×C8—434no—
615C24—21no—
616C24D4×D4311yescharacteristic
617C2×Q8—432no—
618C2×Q8—862no—
619C2×Q8—862no—
620C2×Q8—862no—
621C2×Q8—862no—
622C2×Q8—864no—
623C2×Q8—861no—
624C2×Q8—864no—
625C2×Q8—3442no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—21no—
629C2×D4—24no—
630C2×D4—82no—
631C2×D4C23×D4312yes—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—864no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—3442no—
646C22×C4D4×D4311yescharacteristic
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4311yescharacteristic
649C22×C4C23×D4311yescharacteristic
650C22×C4C23×D4311yescharacteristic
651C22×C4C23×D4311yescharacteristic
652M16—24no—
653M16—864no—
654C2×C8—434no—
655C2×C8C23×D4314yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—432no—
660C4⋊C4—432no—
661C4⋊C4—432no—
662C4⋊C4—432no—
663C4⋊C4—432no—
664C4⋊C4—432no—
665C4⋊C4—432no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—862no—
669C4⋊C4—862no—
670C4⋊C4—862no—
671C4⋊C4—862no—
672C4⋊C4—862no—
673C4⋊C4—862no—
674C4⋊C4—862no—
675C4⋊C4—862no—
676C4⋊C4—862no—
677C4⋊C4—862no—
678C4⋊C4—862no—
679C4⋊C4—862no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4—861no—
683C4⋊C4—862no—
684C4⋊C4—862no—
685C4⋊C4C23×D4312yes—
686C4⋊C4C23×D4312yes—
687C4⋊C4C23×D4312yes—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—432no—
693C22⋊C4—432no—
694C22⋊C4—432no—
695C22⋊C4—432no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—862no—
700C22⋊C4—862no—
701C22⋊C4—862no—
702C22⋊C4—862no—
703C42—22no—
704C42—22no—
705C42—432no—
706C42—432no—
707C42—432no—
708C42—432no—
709C42—864no—
710C42—862no—
711C42—862no—
712C23—22no—
713C23—22no—
714C23—41no—
715C23—41no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23C2×D4×D4311yescharacteristic
720C23C2×D4×D4311yescharacteristic
721C23C2×D4×D4311yescharacteristic
722Q8—864no—
723Q8—3444no—
724Q8—3442no—
725Q8—3442no—
726Q8—3442no—
727Q8—3442no—
728Q8—1722no—
729D4—24no—
730D4—42no—
731D4—82no—
732D4—82no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—432no—
745C2×C4—432no—
746C2×C4—432no—
747C2×C4—432no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—3444no—
753C2×C4—3441no—
754C2×C4—3441no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4C2×D4×D4311yescharacteristic
762C2×C4C2×D4×D4311yescharacteristic
763C2×C4C2×D4×D4311yescharacteristic
764C2×C4#1306337214yes—
765C2×C4C24×D4311yescharacteristic
766C8—24no—
767C8—864no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—82no—
780C22—84no—
781C22#1458347112yes—
782C22C22×D4×D4311yescharacteristic
783C4—21no—
784C4—21no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—862no—
789C4—862no—
790C4—862no—
791C4—862no—
792C4—1722no—
793C4—1722no—
794C4—1722no—
795C4—1722no—
796C4#1458347112yes—
797C4C2×#1306337212yes—
798C2—22no—
799C2—41no—
800C2—41no—
801C2—82no—
802C2C2×#1458347111yescharacteristic
803C2#1914937111yescharacteristic
804C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3094C2
socleC22×C43C23×D4
prime radicalC2×#121×C43C22
hypercenter#3094D43
hypocenterC43#60870
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. #19148000C2semidirect
3. #19145891C2semidirect
4. #19145889C2semidirect
5. #19145876C2semidirect
6. #19145874C2semidirect
7. #19145139C2semidirect
8. #19144979C2semidirect
9. #19144544C2semidirect
10. #19144543C2semidirect
12. #19144399C2semidirect
13. #19144389C2semidirect
14. #19143230C2semidirect
16. #14583530C22semidirect
17. #14583530C22semidirect
20. #14583527C22semidirect
21. #14583527C22semidirect
43. #14583307C22semidirect
44. #14583306C22semidirect
45. #14583303C22semidirect
46. #14583296C22semidirect
47. #14583257C22semidirect
48. #14583257C22semidirect
49. #14583252C22semidirect
50. #14583252C22semidirect
51. #14583241C22semidirect
52. #14583240C22semidirect
53. #14583235C22semidirect
54. #14583234C22semidirect
55. #14583230C22semidirect
56. #14583229C22semidirect
60. #14583209C22semidirect
61. #14583205C22semidirect
62. #14583201C22semidirect
63. #14583197C22semidirect
64. #14583193C22semidirect
65. #14583187C22semidirect
66. #14583183C22semidirect
67. #14583177C22semidirect
68. #14582957C22semidirect
69. #14582957C22semidirect
489. C43#60870semidirect

Maximal subgroups

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

subgroupindex
#191480002
C2×#145835162
#191458912
#191458892
#191458762
#191458742
#191451392
#191449792
#191445442
#191445432
#191445312
#191443992
#191443892
#191432302
C43×#30942
#6087043