Finite Group Databasebeta

← #25966757

Subgroups — #25966757

Order 11008.

1910 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147984C211yesmaximal, characteristic, complemented
2C2×#14583523C211yesmaximal, characteristic, complemented
3#19145285C214yesmaximal, complemented
4#19145270C214yesmaximal, complemented
5#19145233C214yesmaximal, complemented
6#19145211C214yesmaximal, complemented
7#19145137C211yesmaximal, characteristic, complemented
8#19145063C211yesmaximal, characteristic, complemented
9#19144982C211yesmaximal, characteristic, complemented
10#19144228C212yesmaximal, complemented
11#19144217C212yesmaximal, complemented
12#19143419C212yesmaximal, complemented
13#19143408C212yesmaximal, complemented
14#19143012C211yesmaximal, characteristic, complemented
15C43×#3141C211yesmaximal, characteristic, complemented
16C2×#13063355C2212yes—
17C2×#13063350C2212yes—
18C2×M16×D43C2212yes—
19#14583523—22no—
20#14583523—22no—
21#14583523C2214yes—
22#14583523C2214yes—
23#14583518C2212yescomplemented
24#14583518C2212yescomplemented
25#14583510C2212yescomplemented
26#14583503C2212yescomplemented
27#14583494—21no—
28#14583494—21no—
29#14583486—21no—
30#14583486—21no—
31#14583456C2211yescharacteristic
32#14583429—22no—
33#14583429—22no—
34C2×#13063320—21no—
35C2×#13063314—21no—
36C2×#13063313C2211yescharacteristic
37#14583406C2212yes—
38C2×#13063310—21no—
39C2×#13063305C2211yescharacteristic
40C2×#13063301—21no—
41C2×#13063300C2211yescharacteristic
42#41×Dic43C2212yes—
43C2×#13063290C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063282C2211yescharacteristic
46#14583305C2214yescomplemented
47#14583302C2212yescomplemented
48#14583295C2212yescomplemented
49#14583291C2212yescomplemented
50#14583286C2212yescomplemented
51#14583281C2214yescomplemented
52#14583259C2212yescomplemented
53#14583259C2212yescomplemented
54#14583254C2214yescomplemented
55#14583156C2214yescomplemented
56#14583151C2214yes—
57#14583148C2214yes—
58#14583144C2214yescomplemented
59#14583139C2214yescomplemented
60#14583134C2214yes—
61#14583131C2214yes—
62#14583127C2214yescomplemented
63#14583008C2214yescomplemented
64#14583003C2214yescomplemented
65#14583002C2214yescomplemented
66#14582996C2214yescomplemented
67#14582991C2214yescomplemented
68#14582990C2214yescomplemented
69#14582984C2214yescomplemented
70#14582979C2214yescomplemented
71#14582939C2212yes—
72#14582939C2212yes—
73#14582909C2212yes—
74#14582905C2212yes—
75#14582856C2214yescomplemented
76#14582853C2214yescomplemented
77C4×#10621877C2211yescharacteristic
78M16×Dic43C2212yes—
79C43×#532C2211yescharacteristic
80C2×C4⋊Q8×C43C2211yescharacteristic
81C43×#489C2214yescomplemented
82C43×#487C2212yescomplemented
83C43×#486C2212yescomplemented
84C43×#417C2212yes—
85C43×#417C2212yes—
86C4×M16×C43C2211yescharacteristic
87C22×Dic86C2311yescharacteristic
88C22×D172—21no—
89C22×D172C2311yescharacteristic
90C22×C4×D43—21no—
91C22×C4×D43C2311yescharacteristic
92#13063355—28no—
93#13063350—28no—
94C2×#10621885C2314yes—
95C2×#10621883C2314yes—
96C2×#10621884C2314yes—
97C2×#10621882C2314yes—
98C2×#10621877C2312yes—
99C2×#10621872C2314yes—
100M16×D43—28no—
101C2×C8×D43C2314yes—
102#13063325C2311yescharacteristic
103#13063325C2311yescharacteristic
104#13063320—22no—
105#13063320—22no—
106#13063320—24no—
107#13063320—24no—
108#13063318—22no—
109#13063318—22no—
110#13063317C2312yes—
111#13063315—22no—
112#13063315—22no—
113#13063314—24no—
114#13063314—24no—
115#13063313—21no—
116#13063313—21no—
117#13063313C2312yes—
118#13063313C2312yes—
119#13063311—22no—
120#13063311—22no—
121#13063310—24no—
122#13063310—24no—
123#13063309—22no—
124#13063309—22no—
125#13063306—22no—
126#13063306—22no—
127#13063306—22no—
128#13063305—22no—
129#13063305C2314yes—
130#13063304—21no—
131#13063304—21no—
132#13063302—22no—
133#13063302—22no—
134#13063301—24no—
135#13063301—24no—
136#13063301C2312yes—
137#13063301C2312yes—
138#13063300—22no—
139#13063300C2314yes—
140#13063297—22no—
141#13063297—22no—
142#13063296C2312yes—
143#13063296C2312yes—
144#13063293—22no—
145Q8×Dic43C2312yes—
146Q8×Dic43C2312yes—
147C4×Dic86—21no—
148C4×Dic86—21no—
149#13063290—22no—
150#13063290C2314yes—
151D4×Dic43—22no—
152D4×Dic43—22no—
153D4×Dic43C2312yes—
154D4×Dic43C2312yes—
155#13063287—22no—
156#13063287C2314yes—
157C4×C22⋊D43—22no—
158C4×C22⋊D43—22no—
159#13063284—22no—
160#13063284C2312yes—
161#13063282D412yes—
162#13063282D412yes—
163#13063282C2312yes—
164#13063282C2312yes—
165C2×C4⋊Dic43—21no—
166C2×Dic43⋊C4—21no—
167C2×Dic43⋊C4D411yescharacteristic
168C2×Dic43⋊C4D411yescharacteristic
169C2×(C2×D43)⋊C4—21no—
170C2×(C2×D43)⋊C4—21no—
171C2×(C2×D43)⋊C4—21no—
172C2×(C2×D43)⋊C4—21no—
173C2×(C2×D43)⋊C4—21no—
174C2×(C2×D43)⋊C4D411yescharacteristic
175C2×(C2×D43)⋊C4D411yescharacteristic
176C2×C4×Dic43—21no—
177C2×C4×Dic43—22no—
178C2×C4×Dic43C2311yescharacteristic
179#13063258C2314yes—
180#13063258C2314yes—
181#13063256C2314yes—
182#13063256C2314yes—
183#13063250C2314yes—
184#13063250C2314yes—
185#13063247C2314yes—
186#13063247C2314yes—
187#13063236C2312yes—
188#13063235C2314yes—
189C4×C43⋊C8C2312yes—
190C8×Dic43C2314yes—
191C2×#41×C43C2312yes—
192C22×Q8×C43—21no—
193C2×M16×C43C2312yes—
194C4⋊Q8×C43—21no—
195C4⋊Q8×C43—21no—
196C4⋊Q8×C43C2311yescharacteristic
197C4⋊Q8×C43C2312yes—
198C4⋊Q8×C43C2312yes—
199#127×C43C2311yescharacteristic
200#124×C43C2312yes—
201#121×C43—21no—
202#121×C43—21no—
203C4×D4×C43—21no—
204C4×D4×C43—21no—
205C2×C4⋊C4×C43—21no—
206C2×C4⋊C4×C43C2311yescharacteristic
207C2×C4⋊C4×C43C2311yescharacteristic
208C2×C42×C43C2311yescharacteristic
209#103×C43C2314yes—
210#103×C43C2314yes—
211#102×C43C2314yes—
212#102×C43C2314yes—
213#97×C43C2312yes—
214C4×C8×C43C2312yes—
215C23×D43—21no—
216C23×D43C2×D411yescharacteristic
217#41×C43—24no—
218#41×C43—24no—
219C2×Q8×C43—22no—
220C2×Q8×C43—22no—
221C2×Q8×C43—82no—
222C2×Q8×C43C2412yes—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—22no—
226C2×D4×C43C2412yes—
227C22×C4×C43—22no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2411yescharacteristic
233C2×C22⋊D43—22no—
234C2×C22⋊D43—22no—
235C22×Dic43—22no—
236C22×Dic43—22no—
237C22×Dic43—21no—
238C22×Dic43C2×D411yescharacteristic
239C22×Dic43C2×D411yescharacteristic
240C22×Dic43C2×D411yescharacteristic
241C2×D172—21no—
242C2×D172—24no—
243C2×D172—24no—
244C2×D172—82no—
245C2×D172C2412yes—
246C2×C4×D43—24no—
247C2×C4×D43—24no—
248C2×C4×D43—82no—
249C2×C4×D43C2×D412yes—
250C2×C4×D43C2412yes—
251C2×Dic86—24no—
252C2×Dic86—21no—
253C2×Dic86—21no—
254C2×Dic86—21no—
255C2×Dic86C2412yes—
256M16×C43—24no—
257C2×C8×C43C2414yes—
258C4⋊C4×C43—22no—
259C4⋊C4×C43—22no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43C2412yes—
265C4⋊C4×C43C2412yes—
266C22⋊C4×C43—22no—
267C22⋊C4×C43—22no—
268C42×C43C2×D411yescharacteristic
269C42×C43C2×D411yescharacteristic
270C42×C43C2411yescharacteristic
271C42×C43C2411yescharacteristic
272C22⋊Dic43—22no—
273C22⋊Dic43—22no—
274C22⋊Dic43—22no—
275C22⋊Dic43—22no—
276C22⋊Dic43—22no—
277#10621885—28no—
278#10621884—28no—
279#10621883—28no—
280#10621882—28no—
281(C2×D43)⋊C4—22no—
282(C2×D43)⋊C4—22no—
283(C2×D43)⋊C4—22no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4C2×D412yes—
291(C2×D43)⋊C4C2×D412yes—
292(C2×D43)⋊C4C2×D412yes—
293(C2×D43)⋊C4C2×D412yes—
294C4⋊Dic43—21no—
295C4⋊Dic43—21no—
296C4⋊Dic43—24no—
297C4⋊Dic43—22no—
298C4⋊Dic43—22no—
299C4⋊Dic43C2412yes—
300C4⋊Dic43C2412yes—
301Dic43⋊C4—22no—
302Dic43⋊C4—22no—
303Dic43⋊C4—24no—
304Dic43⋊C4—22no—
305Dic43⋊C4—22no—
306Dic43⋊C4C2×D412yes—
307Dic43⋊C4C2×D412yes—
308Dic43⋊C4C2×D412yes—
309Dic43⋊C4C2×D412yes—
310C4×Dic43—22no—
311C4×Dic43—22no—
312C4×Dic43—22no—
313C4×Dic43—24no—
314C4×Dic43C2×D412yes—
315C4×Dic43C2412yes—
316#10621877#4118yes—
317C2×C43⋊C8C2414yes—
318#10621872—28no—
319C8×D43—28no—
320C23×C43—22no—
321C23×C43C22×D411yescharacteristic
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—41no—
325C22×D43—41no—
326C22×D43—42no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43C22×D412yes—
330Q8×C43—22no—
331Q8×C43—22no—
332Q8×C43—82no—
333Q8×C43—82no—
334D4×C43—22no—
335D4×C43—22no—
336D4×C43—44no—
337D4×C43—81no—
338D4×C43—81no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—42no—
345C2×C4×C43—42no—
346C2×C4×C43—44no—
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C2×#4114yes—
353C2×C4×C43C2511yescharacteristic
354C22⋊D43—82no—
355C22⋊D43—82no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—42no—
363C2×Dic43—82no—
364C2×Dic43—82no—
365C2×Dic43C22×D412yes—
366C2×Dic43C22×D412yes—
367C2×Dic43C22×D412yes—
368D172—24no—
369D172—42no—
370D172—84no—
371C4×D43—24no—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—84no—
375Dic86—24no—
376Dic86—42no—
377Dic86—81no—
378Dic86—81no—
379C8×C43—24no—
380C43⋊C8C2×#4118yes—
381#60703—431nomaximal, Sylow
382C22×C43—21no—
383C22×C43—21no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43#53212yes—
388C22×C43C23×D411yescharacteristic
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—82no—
396C2×D43—84no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43#53212yes—
405C4×C43C22×#4112yes—
406Dic43—22no—
407Dic43—22no—
408Dic43—22no—
409Dic43—42no—
410Dic43—42no—
411Dic43—42no—
412#3455—431no—
413C2×#542—431no—
414#3179—434no—
415#3178—434no—
416#3175—434no—
417#3173—434no—
418#3165—431no—
419#3153—431no—
420#3141D4311yescharacteristic, complemented
421#3140—431no—
422#3056—432no—
423#3055—432no—
424C4×#137—432no—
425C4×AGL(1,ℤ/8)—432no—
426#2873—431no—
427C2×C43—22no—
428C2×C43—82no—
429C2×C43C2×#53211yescharacteristic
430C2×C43#358511yescharacteristic
431C2×C43#358611yescharacteristic
432D43—42no—
433D43—82no—
434C2×#137—432no—
435C2×AGL(1,ℤ/8)—432no—
436C22×M16—432no—
437#542—434no—
438#542—434no—
439#542—432no—
440#542—432no—
441#542—862no—
442#542—862no—
443#541—432no—
444#540—432no—
445#539—861no—
446#539—861no—
447#538—861no—
448#538—861no—
449#533—431no—
450#532C2×D4311yescharacteristic
451C2×C4⋊Q8C2×D4311yescharacteristic
452#529—862no—
453#529—862no—
454C2×#126—861no—
455C2×#124—431no—
456C2×#124—861no—
457#525—432no—
458C2×#123—861no—
459C2×C22⋊Q8—431no—
460C2×C22⋊Q8—861no—
461C2×#121—431no—
462C4×#41—432no—
463C2×C4×Q8—431no—
464C2×C4×D4—431no—
465C2×#117—431no—
466#501—434no—
467#500—432no—
468#498—432no—
469#497—432no—
470#496—432no—
471#495—434no—
472#489—432no—
473#489—432no—
474#489C2×D4314yescomplemented
475#488—434no—
476#487C2×D4312yescomplemented
477#486C2×D4312yescomplemented
478#470—434no—
479#469—434no—
480#468—434no—
481#468—434no—
482#467—434no—
483#466—434no—
484#465—434no—
485#465—434no—
486#442—434no—
487#441—434no—
488#440—434no—
489#440—434no—
490C4×Q16—434no—
491C4×SD16—434no—
492C4×SD16—434no—
493C4×D8—434no—
494#428—432no—
495#428—432no—
496#419—432no—
497#418—432no—
498#417C2×D4312yes—
499#417C2×D4312yes—
500#405—434no—
501#405—434no—
502C4×M16—432no—
503C4×M16—431no—
504C4×M16C2×D4311yescharacteristic
505C43#6070311yescharacteristic, complemented, Sylow
506C2×#41C22×D4312yes—
507C22×Q8—21no—
508C22×Q8—431no—
509C22×D4—431no—
510C22×D4—861no—
511C23×C4—431no—
512C23×C4—861no—
513#137—868no—
514AGL(1,ℤ/8)—868no—
515C2×Q16—434no—
516C2×SD16—434no—
517C2×SD16—434no—
518C2×D8—434no—
519C2×M16—432no—
520C2×M16—434no—
521C2×M16—868no—
522C2×M16C22×D4312yes—
523C22×C8—434no—
524C4⋊Q8—21no—
525C4⋊Q8—21no—
526C4⋊Q8—431no—
527C4⋊Q8—431no—
528C4⋊Q8C22×D4311yescharacteristic
529C4⋊Q8C22×D4312yes—
530C4⋊Q8C22×D4312yes—
531#127C22×D4311yescharacteristic
532#126—862no—
533#126—862no—
534#126—862no—
535#126—862no—
536#126—864no—
537#126—864no—
538#125—432no—
539#125—862no—
540#125—862no—
541#124—432no—
542#124—432no—
543#124—862no—
544#124—862no—
545#124—864no—
546#124—864no—
547#124—861no—
548#124—861no—
549#124C22×D4312yes—
550#123—862no—
551#123—862no—
552#123—864no—
553#123—864no—
554#123—862no—
555#123—862no—
556#123—862no—
557C22⋊Q8—432no—
558C22⋊Q8—432no—
559C22⋊Q8—434no—
560C22⋊Q8—862no—
561C22⋊Q8—862no—
562C22⋊Q8—862no—
563C22⋊Q8—864no—
564C22⋊Q8—864no—
565C22⋊Q8—861no—
566C22⋊Q8—861no—
567#121—21no—
568#121—21no—
569#121—432no—
570#121—432no—
571#121—434no—
572#121—862no—
573#121—862no—
574#121—862no—
575#120—862no—
576C4×Q8—432no—
577C4×Q8—432no—
578C4×Q8—434no—
579C4×Q8—862no—
580C4×Q8—861no—
581C4×Q8—861no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—432no—
585C4×D4—432no—
586C4×D4—434no—
587C4×D4—862no—
588C4×D4—862no—
589C4×D4—862no—
590C4×D4—862no—
591C4×D4—862no—
592#117—432no—
593#117—432no—
594#117—432no—
595#117—432no—
596#117—432no—
597#117—862no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4C22×D4311yescharacteristic
604C2×C4⋊C4C22×D4311yescharacteristic
605C2×C22⋊C4—431no—
606C2×C22⋊C4—431no—
607C2×C22⋊C4—861no—
608C2×C22⋊C4—861no—
609C2×C22⋊C4—861no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C42—431no—
613C2×C42—862no—
614C2×C42—861no—
615C2×C42C22×D4311yescharacteristic
616#107—434no—
617#107—434no—
618#106—434no—
619#106—434no—
620#103—434no—
621#103—434no—
622#103C22×D4314yes—
623#103C22×D4314yes—
624#102—434no—
625#102—434no—
626#102C22×D4314yes—
627#102C22×D4314yes—
628#97—434no—
629#97—432no—
630#97C22×D4312yes—
631C4×C8—434no—
632C4×C8—432no—
633C4×C8C22×D4312yes—
634C24—431no—
635C24—861no—
636#41—24no—
637#41—24no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—82no—
641C2×Q8—432no—
642C2×Q8—861no—
643C2×Q8—861no—
644C2×Q8—861no—
645C2×Q8—864no—
646C2×Q8C23×D4312yes—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—432no—
651C2×D4—864no—
652C2×D4—862no—
653C2×D4—862no—
654C2×D4—861no—
655C2×D4—864no—
656C2×D4—3442no—
657C2×D4C23×D4312yes—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—432no—
665C22×C4—432no—
666C22×C4—864no—
667C22×C4—862no—
668C22×C4—862no—
669C22×C4—864no—
670C22×C4—861no—
671C22×C4—3442no—
672C22×C4D4×D4311yescharacteristic
673C22×C4D4×D4311yescharacteristic
674C22×C4C23×D4311yescharacteristic
675Q16—868no—
676SD16—868no—
677SD16—868no—
678D8—868no—
679M16—24no—
680M16—438no—
681M16—868no—
682C2×C8—434no—
683C2×C8—868no—
684C2×C8C23×D4314yes—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—432no—
692C4⋊C4—432no—
693C4⋊C4—432no—
694C4⋊C4—432no—
695C4⋊C4—432no—
696C4⋊C4—432no—
697C4⋊C4—864no—
698C4⋊C4—864no—
699C4⋊C4—862no—
700C4⋊C4—862no—
701C4⋊C4—862no—
702C4⋊C4—862no—
703C4⋊C4—862no—
704C4⋊C4—862no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4C23×D4312yes—
708C4⋊C4C23×D4312yes—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—432no—
712C22⋊C4—432no—
713C22⋊C4—432no—
714C22⋊C4—432no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—862no—
719C22⋊C4—862no—
720C22⋊C4—862no—
721C22⋊C4—862no—
722C22⋊C4—862no—
723C22⋊C4—862no—
724C22⋊C4—862no—
725C22⋊C4—862no—
726C22⋊C4—862no—
727C22⋊C4—862no—
728C22⋊C4—862no—
729C42—432no—
730C42—432no—
731C42—862no—
732C42—862no—
733C42—864no—
734C42—862no—
735C42D4×D4311yescharacteristic
736C42D4×D4311yescharacteristic
737C42C23×D4311yescharacteristic
738C42C23×D4311yescharacteristic
739C23—22no—
740C23—432no—
741C23—862no—
742C23—862no—
743C23—1721no—
744C23—1721no—
745C23—1722no—
746C23—1722no—
747C23—1722no—
748C23C2×D4×D4311yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—82no—
752Q8—82no—
753Q8—864no—
754Q8—3441no—
755Q8—3441no—
756Q8—1722no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—81no—
761D4—81no—
762D4—864no—
763D4—3444no—
764D4—3442no—
765D4—3442no—
766D4—1722no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—432no—
776C2×C4—432no—
777C2×C4—432no—
778C2×C4—862no—
779C2×C4—864no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—3444no—
786C2×C4—3442no—
787C2×C4—3442no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1722no—
791C2×C4C2×D4×D4311yescharacteristic
792C2×C4C2×D4×D4311yescharacteristic
793C2×C4C2×D4×D4311yescharacteristic
794C2×C4C2×D4×D4311yescharacteristic
795C2×C4C2×D4×D4311yescharacteristic
796C2×C4#41×D4314yes—
797C2×C4C24×D4311yescharacteristic
798C8—24no—
799C8—438no—
800C22—21no—
801C22—21no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—862no—
806C22—862no—
807C22—862no—
808C22—3444no—
809C22—3442no—
810C22—1722no—
811C22—1722no—
812C22—1722no—
813C22#1458344812yes—
814C22C22×D4×D4311yescharacteristic
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—862no—
823C4—862no—
824C4—862no—
825C4—1722no—
826C4—1722no—
827C4—1722no—
828C4#1458344812yes—
829C4C2×#41×D4312yes—
830C2—22no—
831C2—82no—
832C2—3442no—
833C2—1722no—
834C2C2×#1458344811yescharacteristic
835C2#1914937111yescharacteristic
836C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3141C2
socleC22×C43C23×D4
hypercenter#3141D43
hypocenterC43#60703
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
1. #19147984C2semidirect
2. C2×#14583523C2semidirect
3. #19145285C2semidirect
4. #19145270C2semidirect
5. #19145233C2semidirect
6. #19145211C2semidirect
7. #19145137C2semidirect
8. #19145063C2semidirect
9. #19144982C2semidirect
10. #19144228C2semidirect
11. #19144217C2semidirect
12. #19143419C2semidirect
13. #19143408C2semidirect
14. #19143012C2semidirect
15. C43×#3141C2semidirect
23. #14583518C22semidirect
24. #14583518C22semidirect
25. #14583510C22semidirect
26. #14583503C22semidirect
46. #14583305C22semidirect
47. #14583302C22semidirect
48. #14583295C22semidirect
49. #14583291C22semidirect
50. #14583286C22semidirect
51. #14583281C22semidirect
52. #14583259C22semidirect
53. #14583259C22semidirect
54. #14583254C22semidirect
55. #14583156C22semidirect
58. #14583144C22semidirect
59. #14583139C22semidirect
62. #14583127C22semidirect
63. #14583008C22semidirect
64. #14583003C22semidirect
65. #14583002C22semidirect
66. #14582996C22semidirect
67. #14582991C22semidirect
68. #14582990C22semidirect
69. #14582984C22semidirect
70. #14582979C22semidirect
75. #14582856C22semidirect
76. #14582853C22semidirect
81. C43×#489C22semidirect
82. C43×#487C22semidirect
83. C43×#486C22semidirect
420. #3141D43semidirect
474. #489C2×D43semidirect
476. #487C2×D43semidirect
477. #486C2×D43semidirect
505. C43#60703semidirect

Maximal subgroups

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

subgroupindex
#191479842
C2×#145835232
#191452852
#191452702
#191452332
#191452112
#191451372
#191450632
#191449822
#191442282
#191442172
#191434192
#191434082
#191430122
C43×#31412
#6070343