Finite Group Databasebeta

← #25968954

Subgroups — #25968954

Order 11008.

1754 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148000C211yesmaximal, characteristic, complemented
2C2×#14583502C211yesmaximal, characteristic
3#19145854C214yesmaximal, complemented
4#19145852C214yesmaximal, complemented
5#19145846C214yesmaximal, complemented
6#19145844C214yesmaximal, complemented
7#19145145C212yesmaximal, complemented
8#19144967C212yesmaximal, complemented
9#19144536C211yesmaximal, characteristic, complemented
10#19144535C211yesmaximal, characteristic, complemented
11#19144531C211yesmaximal, characteristic, complemented
12#19144391C212yesmaximal, complemented
13#19144389C212yesmaximal, complemented
14#19143230C211yesmaximal, characteristic, complemented
15C43×#3094C211yesmaximal, characteristic, complemented
16#14583530C2212yescomplemented
17#14583530C2212yescomplemented
18#14583527—21no—
19#14583527—21no—
20#14583527C2212yescomplemented
21#14583527C2212yescomplemented
22#14583525—21no—
23#14583525—21no—
24#14583502—22no—
25#14583502—22no—
26#14583502C2214yes—
27#14583502C2214yes—
28#14583456—22no—
29#14583452—22no—
30#14583452C2212yes—
31#14583452C2212yes—
32C2×#13063321C2211yescharacteristic
33C2×#13063316C2211yescharacteristic
34C2×#13063309—21no—
35C2×#13063307—21no—
36C2×#13063299C2211yescharacteristic
37C2×#13063297—21no—
38C2×#13063296—21no—
39C2×D4×Dic43C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×#13063284C2211yescharacteristic
42C2×#13063284C2211yescharacteristic
43#14583307C2214yescomplemented
44#14583306C2214yescomplemented
45#14583300C2214yescomplemented
46#14583299C2214yescomplemented
47#14583262C2214yescomplemented
48#14583262C2214yescomplemented
49#14583244C2214yescomplemented
50#14583244C2214yescomplemented
51#14583224C2214yescomplemented
52#14583223C2214yescomplemented
53#14583220C2214yescomplemented
54#14583218C2212yescomplemented
55#14583217C2212yescomplemented
56#14583215C2212yescomplemented
57#14583213C2212yescomplemented
58#14583212C2212yescomplemented
59#14583210C2212yescomplemented
60#14583202C2214yescomplemented
61#14583201C2214yescomplemented
62#14583198C2214yescomplemented
63#14583197C2214yescomplemented
64#14583188C2214yescomplemented
65#14583187C2214yescomplemented
66#14583178C2214yescomplemented
67#14583177C2214yescomplemented
68#14582957C2214yescomplemented
69#14582957C2214yescomplemented
70#14582942C2212yes—
71#14582941C2212yes—
72#14582939C2212yes—
73#14582922C2212yes—
74#14582905C2212yes—
75#14582904C2212yes—
76#14582903C2212yes—
77#14582863C2211yescharacteristic
78M16×Dic43C2212yes—
79C2×#121×C43C2211yescharacteristic
80C2×#117×C43C2211yescharacteristic
81C43×#482C2214yescomplemented
82C43×#481C2212yescomplemented
83C43×#480C2212yescomplemented
84C43×#428C2212yes—
85C43×#418C2212yes—
86C43×#407C2211yescharacteristic
87C22×D172C2311yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C2×#10621877C2312yes—
94#13063325—22no—
95#13063325—22no—
96#13063324—22no—
97#13063324—22no—
98#13063324C2312yes—
99#13063324C2312yes—
100#13063324C2312yes—
101#13063324C2312yes—
102#13063321—22no—
103#13063321C2314yes—
104#13063317—22no—
105#13063317—22no—
106#13063316—22no—
107#13063316—22no—
108#13063316—22no—
109#13063316C2312yes—
110#13063316C2314yes—
111#13063316C2312yes—
112#13063316C2312yes—
113#13063316C2312yes—
114#13063309—24no—
115#13063309—24no—
116#13063307—24no—
117#13063307—24no—
118#13063304—22no—
119#13063304—22no—
120#13063304—22no—
121#13063304—22no—
122#13063302—22no—
123#13063302—22no—
124#13063302—22no—
125#13063302—22no—
126#13063302—22no—
127#13063302—22no—
128#13063302—22no—
129#13063302—22no—
130#13063299—21no—
131#13063299—21no—
132#13063299C2312yes—
133#13063299C2312yes—
134#13063297—24no—
135#13063297—24no—
136#13063296—24no—
137#13063296—24no—
138C4×Dic86—22no—
139C4×Dic86—22no—
140C4×Dic86—22no—
141C4×Dic86—22no—
142D4×Dic43—22no—
143D4×Dic43C2314yes—
144#13063287—22no—
145#13063287C2314yes—
146#13063284—21no—
147#13063284—21no—
148#13063284D412yes—
149#13063284D412yes—
150#13063284C2312yes—
151#13063284C2312yes—
152#13063284C2312yes—
153#13063284C2312yes—
154C2×C4⋊Dic43—21no—
155C2×C4⋊Dic43D411yescharacteristic
156C2×C4⋊Dic43D411yescharacteristic
157C2×C4⋊Dic43C2311yescharacteristic
158C2×C4⋊Dic43C2311yescharacteristic
159C2×C4⋊Dic43C2311yescharacteristic
160C2×Dic43⋊C4—21no—
161C2×C22⋊Dic43—21no—
162C2×C22⋊Dic43—21no—
163C2×C22⋊Dic43D411yescharacteristic
164C2×C22⋊Dic43D411yescharacteristic
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—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#13063247C2314yes—
179#13063247C2314yes—
180#13063246C2314yes—
181#13063246C2314yes—
182#13063245C2314yes—
183#13063245C2314yes—
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
214C23×D43—21no—
215C2×D4×C43—21no—
216C2×D4×C43—22no—
217C2×D4×C43—22no—
218C2×D4×C43—24no—
219C2×D4×C43—82no—
220C2×D4×C43C2412yes—
221C22×C4×C43—24no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C22×C4×C43C2411yescharacteristic
231C2×C22⋊D43—24no—
232C2×C22⋊D43—24no—
233C2×C22⋊D43—22no—
234C2×C22⋊D43—22no—
235C2×C22⋊D43—82no—
236C2×C22⋊D43—82no—
237C2×C22⋊D43—82no—
238C22×Dic43—24no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—82no—
243C22×Dic43C2×D411yescharacteristic
244C22×Dic43C2×D411yescharacteristic
245C22×Dic43C2×D411yescharacteristic
246C22×Dic43C2×D411yescharacteristic
247C2×D172—21no—
248C2×D172—24no—
249C2×D172C2412yes—
250C2×C4×D43—24no—
251C2×C4×D43—82no—
252C2×Dic86—22no—
253C2×Dic86—22no—
254C2×Dic86—22no—
255C2×Dic86—22no—
256M16×C43—24no—
257C2×C8×C43C2414yes—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43C2412yes—
262C4⋊C4×C43C2412yes—
263C4⋊C4×C43C2412yes—
264C22⋊C4×C43—22no—
265C22⋊C4×C43—22no—
266C22⋊C4×C43—22no—
267C22⋊C4×C43—22no—
268C42×C43—22no—
269C42×C43—22no—
270C22⋊Dic43—24no—
271C22⋊Dic43—22no—
272C22⋊Dic43—22no—
273C22⋊Dic43C2×D412yes—
274C22⋊Dic43C2×D412yes—
275C22⋊Dic43C2×D412yes—
276C22⋊Dic43C2×D412yes—
277(C2×D43)⋊C4—22no—
278(C2×D43)⋊C4—22no—
279(C2×D43)⋊C4—24no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—24no—
284C4⋊Dic43—22no—
285C4⋊Dic43—22no—
286C4⋊Dic43—22no—
287C4⋊Dic43—22no—
288C4⋊Dic43C2×D412yes—
289C4⋊Dic43C2×D412yes—
290C4⋊Dic43C2×D412yes—
291C4⋊Dic43C2×D412yes—
292C4⋊Dic43C2412yes—
293C4⋊Dic43C2412yes—
294C4⋊Dic43C2412yes—
295Dic43⋊C4—24no—
296Dic43⋊C4—22no—
297Dic43⋊C4—22no—
298Dic43⋊C4—22no—
299Dic43⋊C4—22no—
300Dic43⋊C4—22no—
301Dic43⋊C4—22no—
302Dic43⋊C4—22no—
303Dic43⋊C4—22no—
304C4×Dic43—22no—
305C4×Dic43—22no—
306C4×Dic43C2×D412yes—
307C4×Dic43C2×D412yes—
308C4×Dic43C2412yes—
309C4×Dic43C2412yes—
310#10621877—24no—
311C2×C43⋊C8C2414yes—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—42no—
317C23×C43—42no—
318C23×C43—42no—
319C23×C43C22×D411yescharacteristic
320C23×C43C22×D411yescharacteristic
321C23×C43C22×D411yescharacteristic
322C22×D43—22no—
323C22×D43—42no—
324C22×D43—42no—
325C22×D43—42no—
326D4×C43—24no—
327D4×C43—42no—
328D4×C43—82no—
329D4×C43—82no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—42no—
339C2×C4×C43—81no—
340C2×C4×C43—81no—
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C432−1+414yes—
345C2×C4×C43C2511yescharacteristic
346C22⋊D43—84no—
347C22⋊D43—84no—
348C22⋊D43—82no—
349C22⋊D43—82no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—42no—
358C2×Dic43—84no—
359C2×Dic43—81no—
360C2×Dic43—81no—
361C2×Dic43C22×D412yes—
362C2×Dic43C22×D412yes—
363C2×Dic43C22×D412yes—
364C2×Dic43C22×D412yes—
365D172—24no—
366D172—42no—
367C4×D43—84no—
368Dic86—82no—
369Dic86—82no—
370Dic86—82no—
371Dic86—82no—
372C8×C43—24no—
373C43⋊C8—24no—
374#60868—431nomaximal, Sylow
375C22×C43—21no—
376C22×C43—21no—
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—82no—
387C22×C43—84no—
388C22×C43#53612yes—
389C22×C43C23×D411yescharacteristic
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—84no—
394C4×C43—21no—
395C4×C43—21no—
396C4×C43—42no—
397C4×C43—42no—
398C4×C43—42no—
399C4×C43#53612yes—
400C4×C43C2×2−1+412yes—
401Dic43—22no—
402Dic43—22no—
403Dic43—22no—
404Dic43—22no—
405Dic43—42no—
406Dic43—42no—
407Dic43—42no—
408#3458—431no—
409C2×#540—431no—
410#3241—434no—
411#3241—434no—
412#3241—434no—
413#3241—434no—
414#3166—432no—
415#3138—432no—
416#3094—431no—
417#3094—431no—
418#3094—431no—
419#3094D4311yescharacteristic, complemented
420#3077—432no—
421#3077—432no—
422#2921—431no—
423C2×C43—22no—
424C2×C43—41no—
425C2×C43—41no—
426C2×C43—82no—
427C2×C43C2×#53611yescharacteristic
428C2×C43#358511yescharacteristic
429C2×C43#358511yescharacteristic
430D43—82no—
431#544—432no—
432#544—432no—
433#544—432no—
434#544—432no—
435#544—861no—
436#544—861no—
437#543—861no—
438#543—861no—
439#540—434no—
440#540—434no—
441#540—862no—
442#540—862no—
443#533—432no—
444#533—432no—
445#533—862no—
446#533—862no—
447C2×#127—431no—
448C2×#125—431no—
449C2×#123—861no—
450C2×#123—861no—
451C2×#121—431no—
452C2×#121—861no—
453C2×#121—861no—
454C2×#121C2×D4311yescharacteristic
455C2×C4×D4—431no—
456C2×C4×D4—431no—
457C2×#117—431no—
458C2×#117—431no—
459C2×#117C2×D4311yescharacteristic
460#501—434no—
461#501—434no—
462#499—434no—
463#499—434no—
464#490—434no—
465#490—434no—
466#486—434no—
467#486—434no—
468#482—434no—
469#482—434no—
470#482—434no—
471#482C2×D4314yescomplemented
472#481—432no—
473#481—432no—
474#481—432no—
475#481C2×D4312yescomplemented
476#480—432no—
477#480—432no—
478#480—432no—
479#480C2×D4312yescomplemented
480#478—434no—
481#478—434no—
482#478—434no—
483#478—434no—
484#476—434no—
485#476—434no—
486#474—434no—
487#474—434no—
488#433—434no—
489#433—434no—
490#428—432no—
491#428—432no—
492#428—432no—
493#428C2×D4312yes—
494#423—432no—
495#418—432no—
496#418—432no—
497#418—432no—
498#418C2×D4312yes—
499#407—431no—
500#407C2×D4311yescharacteristic
501C4×M16—432no—
502C43#6086811yescharacteristic, complemented, Sylow
503C22×D4—21no—
504C22×D4—431no—
505C22×D4—861no—
506C22×D4—861no—
507C22×D4—861no—
508C22×D4C22×D4311yescharacteristic
509C23×C4—861no—
510C23×C4—861no—
511C23×C4C22×D4311yescharacteristic
512C2×M16—432no—
513C2×M16C22×D4312yes—
514C4⋊Q8—432no—
515C4⋊Q8—432no—
516C4⋊Q8—432no—
517C4⋊Q8—432no—
518C4⋊Q8—862no—
519C4⋊Q8—862no—
520C4⋊Q8—862no—
521C4⋊Q8—862no—
522#127—434no—
523#127—862no—
524#125—434no—
525#125—432no—
526#125—432no—
527#125—432no—
528#125—432no—
529#125—862no—
530#125—862no—
531#125—862no—
532#125—862no—
533#125—862no—
534#123—864no—
535#123—864no—
536#123—864no—
537#123—864no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540C22⋊Q8—862no—
541C22⋊Q8—862no—
542C22⋊Q8—862no—
543C22⋊Q8—862no—
544C22⋊Q8—862no—
545C22⋊Q8—862no—
546C22⋊Q8—862no—
547C22⋊Q8—862no—
548C22⋊Q8—862no—
549C22⋊Q8—862no—
550#121—21no—
551#121—21no—
552#121—432no—
553#121—432no—
554#121—864no—
555#121—864no—
556#121—864no—
557#121—864no—
558#121—861no—
559#121—861no—
560#121C22×D4312yes—
561#121C22×D4312yes—
562C4×Q8—862no—
563C4×Q8—862no—
564C4×Q8—862no—
565C4×Q8—862no—
566C4×D4—434no—
567C4×D4—434no—
568C4×D4—862no—
569C4×D4—862no—
570#117—21no—
571#117—21no—
572#117—432no—
573#117—432no—
574#117—432no—
575#117—432no—
576#117—432no—
577#117—432no—
578#117—861no—
579#117—861no—
580#117C22×D4312yes—
581#117C22×D4312yes—
582C2×C4⋊C4—431no—
583C2×C4⋊C4—431no—
584C2×C4⋊C4—431no—
585C2×C4⋊C4—431no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—861no—
588C2×C4⋊C4—861no—
589C2×C4⋊C4C22×D4311yescharacteristic
590C2×C4⋊C4C22×D4311yescharacteristic
591C2×C4⋊C4C22×D4311yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—431no—
595C2×C22⋊C4—431no—
596C2×C22⋊C4—861no—
597C2×C22⋊C4—861no—
598C2×C22⋊C4—861no—
599C2×C22⋊C4—861no—
600C2×C42—21no—
601C2×C42—431no—
602C2×C42—431no—
603C2×C42—861no—
604#107—434no—
605#107—434no—
606#107—434no—
607#107C22×D4314yes—
608#106—434no—
609#106—434no—
610#106—434no—
611#106C22×D4314yes—
612C4⋊C8—434no—
613C4⋊C8—434no—
614#102—434no—
615#102—434no—
616#102—434no—
617#102—434no—
618#102—434no—
619#102—434no—
620#102C22×D4314yes—
621#102C22×D4314yes—
622C22⋊C8—432no—
623C22⋊C8—432no—
624C22⋊C8C22×D4312yes—
625C22⋊C8C22×D4312yes—
626#97—434no—
627C4×C8—434no—
628C24—21no—
629C24—861no—
630C24D4×D4311yescharacteristic
631C2×Q8—862no—
632C2×Q8—862no—
633C2×Q8—862no—
634C2×Q8—862no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—24no—
639C2×D4—82no—
640C2×D4—432no—
641C2×D4—864no—
642C2×D4—864no—
643C2×D4—862no—
644C2×D4—862no—
645C2×D4—861no—
646C2×D4—864no—
647C2×D4—3442no—
648C2×D4—3442no—
649C2×D4—3442no—
650C2×D4C23×D4312yes—
651C22×C4—24no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—864no—
660C22×C4—864no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—3442no—
665C22×C4—3442no—
666C22×C4D4×D4311yescharacteristic
667C22×C4D4×D4311yescharacteristic
668C22×C4D4×D4311yescharacteristic
669C22×C4C23×D4311yescharacteristic
670C22×C4C23×D4311yescharacteristic
671C22×C4C23×D4311yescharacteristic
672M16—24no—
673M16—864no—
674C2×C8—434no—
675C2×C8C23×D4314yes—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—432no—
680C4⋊C4—432no—
681C4⋊C4—432no—
682C4⋊C4—432no—
683C4⋊C4—432no—
684C4⋊C4—432no—
685C4⋊C4—432no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—862no—
689C4⋊C4—862no—
690C4⋊C4—862no—
691C4⋊C4—862no—
692C4⋊C4—862no—
693C4⋊C4—862no—
694C4⋊C4—862no—
695C4⋊C4—862no—
696C4⋊C4—862no—
697C4⋊C4—862no—
698C4⋊C4—862no—
699C4⋊C4—862no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4C23×D4312yes—
704C4⋊C4C23×D4312yes—
705C4⋊C4C23×D4312yes—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—432no—
711C22⋊C4—432no—
712C22⋊C4—432no—
713C22⋊C4—432no—
714C22⋊C4—864no—
715C22⋊C4—864no—
716C22⋊C4—862no—
717C22⋊C4—862no—
718C22⋊C4—862no—
719C22⋊C4—862no—
720C42—22no—
721C42—22no—
722C42—432no—
723C42—432no—
724C42—432no—
725C42—432no—
726C42—862no—
727C42—862no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—862no—
736C23—1722no—
737C23—1722no—
738C23—1722no—
739C23C2×D4×D4311yescharacteristic
740C23C2×D4×D4311yescharacteristic
741C23C2×D4×D4311yescharacteristic
742Q8—3442no—
743Q8—3442no—
744Q8—3442no—
745Q8—3442no—
746D4—24no—
747D4—42no—
748D4—82no—
749D4—82no—
750D4—864no—
751D4—3444no—
752D4—3444no—
753D4—3442no—
754D4—3442no—
755D4—1722no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—42no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—432no—
768C2×C4—432no—
769C2×C4—432no—
770C2×C4—432no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—3444no—
775C2×C4—3444no—
776C2×C4—3441no—
777C2×C4—3441no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1722no—
783C2×C4C2×D4×D4311yescharacteristic
784C2×C4C2×D4×D4311yescharacteristic
785C2×C4C2×D4×D4311yescharacteristic
786C2×C4#1306337214yes—
787C2×C4C24×D4311yescharacteristic
788C8—24no—
789C8—864no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—82no—
802C22—84no—
803C22—3444no—
804C22—1722no—
805C22—1722no—
806C22—1722no—
807C22#1458347112yes—
808C22C22×D4×D4311yescharacteristic
809C4—21no—
810C4—21no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—862no—
815C4—862no—
816C4—862no—
817C4—862no—
818C4—1722no—
819C4—1722no—
820C4—1722no—
821C4#1458347112yes—
822C4C2×#1306337212yes—
823C2—22no—
824C2—41no—
825C2—41no—
826C2—82no—
827C2—3442no—
828C2C2×#1458347111yescharacteristic
829C2#1914937111yescharacteristic
830C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3094C2
socleC22×C43C23×D4
prime radicalC2×#14583502C2
hypercenter#3094D43
hypocenterC43#60868
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. #19145854C2semidirect
4. #19145852C2semidirect
5. #19145846C2semidirect
6. #19145844C2semidirect
7. #19145145C2semidirect
8. #19144967C2semidirect
9. #19144536C2semidirect
10. #19144535C2semidirect
11. #19144531C2semidirect
12. #19144391C2semidirect
13. #19144389C2semidirect
14. #19143230C2semidirect
15. C43×#3094C2semidirect
16. #14583530C22semidirect
17. #14583530C22semidirect
20. #14583527C22semidirect
21. #14583527C22semidirect
43. #14583307C22semidirect
44. #14583306C22semidirect
45. #14583300C22semidirect
46. #14583299C22semidirect
47. #14583262C22semidirect
48. #14583262C22semidirect
49. #14583244C22semidirect
50. #14583244C22semidirect
51. #14583224C22semidirect
52. #14583223C22semidirect
53. #14583220C22semidirect
54. #14583218C22semidirect
55. #14583217C22semidirect
56. #14583215C22semidirect
57. #14583213C22semidirect
58. #14583212C22semidirect
59. #14583210C22semidirect
60. #14583202C22semidirect
61. #14583201C22semidirect
62. #14583198C22semidirect
63. #14583197C22semidirect
64. #14583188C22semidirect
65. #14583187C22semidirect
66. #14583178C22semidirect
67. #14583177C22semidirect
68. #14582957C22semidirect
69. #14582957C22semidirect
81. C43×#482C22semidirect
82. C43×#481C22semidirect
83. C43×#480C22semidirect
419. #3094D43semidirect
471. #482C2×D43semidirect
475. #481C2×D43semidirect
479. #480C2×D43semidirect
502. C43#60868semidirect

Maximal subgroups

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

subgroupindex
#191480002
C2×#145835022
#191458542
#191458522
#191458462
#191458442
#191451452
#191449672
#191445362
#191445352
#191445312
#191443912
#191443892
#191432302
C43×#30942
#6086843