Finite Group Databasebeta

← #6343163

Subgroups — #6343163

Order 512.

2863 conjugacy classes of subgroups.

The subgroup lattice has 1143 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62793C211yesmaximal, characteristic
2#60295C211yesmaximal, characteristic, complemented
3#60210C211yesmaximal, characteristic, complemented
4#17526C212yesmaximal, complemented
5#17525C212yesmaximal, complemented
6#17520C212yesmaximal, complemented
7#17519C212yesmaximal, complemented
8#17516C214yesmaximal, complemented
9#17510C214yesmaximal, complemented
10#17505C214yesmaximal, complemented
11#17503C211yesmaximal, characteristic, complemented
12#17489C211yesmaximal, characteristic, complemented
13#17454C214yesmaximal, complemented
14#17447C211yesmaximal, characteristic, complemented
15#17443C211yesmaximal, characteristic, complemented
16#3524—22no—
17#3524C414yes—
18#3518—21no—
19#3518C412yes—
20#3517—21no—
21#3517C412yes—
22#3506—22no—
23#3506C411yescharacteristic
24#3506C411yescharacteristic
25#3502C411yescharacteristic
26#3497C411yescharacteristic
27#3493—22no—
28#3493C412yes—
29#3487C412yes—
30#3483—21no—
31#3483C2212yes—
32#3482—21no—
33#3482C2212yes—
34#3480—22no—
35#3480C2214yes—
36#3460—22no—
37#3460C2212yes—
38#3444—22no—
39#3444C2211yescharacteristic
40#3444C2211yescharacteristic
41C4×2−1+4C2212yes—
42C2×C4×#41C2211yescharacteristic
43#2991C2212yescomplemented
44#2990C2212yescomplemented
45#2989C2214yes—
46#2985—21no—
47#2981—21no—
48#2978—22no—
49#2969—22no—
50#2969—22no—
51#2968—22no—
52#2967—22no—
53#2965C2214yes—
54#2965C2212yescomplemented
55C8×#41C2212yescomplemented
56#2962—21no—
57#2935—21no—
58#2933—22no—
59#2925C2214yescomplemented
60#2922C2212yescomplemented
61#2920C2211yescharacteristic
62#2920C2211yescharacteristic
63C2×#431C2211yescharacteristic
64C4×#131C2212yescomplemented
65C2×C4×M16C2211yescharacteristic
66#1496C2214yescomplemented
67#1495C2214yescomplemented
68#1494C2214yescomplemented
69#1494C2214yescomplemented
70#1493C2212yescomplemented
71#1492C2212yescomplemented
72#1492C2214yescomplemented
73#1491C2212yes—
74#1491C2214yescomplemented
75#1490C2212yes—
76#1489C2212yes—
77#1489C2212yes—
78#1489C2214yes—
79#1489C2214yescomplemented
80#1488C2212yes—
81#1488C2212yes—
82#1488C2214yes—
83#1488C2214yescomplemented
84#1487C2212yes—
85#1487C2214yescomplemented
86#1486C2212yes—
87#1485C2211yescharacteristic, complemented
88#1485C2211yescharacteristic, complemented
89#1484C2211yescharacteristic, complemented
90#1484C2211yescharacteristic, complemented
91#1484C2214yescomplemented
92#1483C2214yescomplemented
93#1482C2212yescomplemented
94#1482C2212yescomplemented
95#1482C2214yescomplemented
96#1480C2214yescomplemented
97#1479C2214yescomplemented
98#1477C2214yescomplemented
99#1476C2212yes—
100#1476C2212yes—
101#1476C2214yes—
102#1476C2214yescomplemented
103C2×Q8⋊C8C2214yescomplemented
104C2×2−1+4C2×C412yes—
105C22×#41C2×C411yescharacteristic
106C2×#131—22no—
107C22×M16—21no—
108#559—22no—
109#559—24no—
110#559—24no—
111#559C2×C414yes—
112Q82—21no—
113Q82C2×C412yes—
114#557—21no—
115#557—22no—
116#557C2×C414yes—
117#557C2×C412yes—
118#556—21no—
119#556—24no—
120#556—22no—
121#556—22no—
122#556—24no—
123#556—22no—
124#556C2×C412yes—
125#556C2×C414yes—
126#555—21no—
127#555—24no—
128#555—22no—
129#555—22no—
130#555—24no—
131#555—22no—
132#555C2×C414yes—
133#555C2×C412yes—
134#553—24no—
135#553—22no—
136#553—24no—
137#553—22no—
138#553—24no—
139#553—24no—
140#553C2×C414yes—
141#553C2×C414yes—
142#552—24no—
143#552—22no—
144#552—24no—
145#552C2×C414yes—
146#550—22no—
147#550—21no—
148#550—21no—
149#550—22no—
150#550—22no—
151#550—22no—
152#550C2×C414yes—
153#550C2×C414yes—
154#550C2×C412yes—
155#550C2×C412yes—
156D4×Q8—21no—
157D4×Q8C2×C412yes—
158#548—22no—
159#548—22no—
160#548—22no—
161#548C2×C414yes—
162#548C2×C414yes—
163#548C2×C414yes—
164#547—22no—
165#547—21no—
166#547—22no—
167#547C2×C412yes—
168#544—22no—
169#544C2×C412yes—
170#542—24no—
171#542—24no—
172#542—22no—
173#542C2×C414yes—
174#540—24no—
175#540—24no—
176#540—22no—
177#540C2×C414yes—
178#538—22no—
179#538—22no—
180#538—24no—
181#538—24no—
182#537—22no—
183#537C2×C412yes—
184#535—24no—
185#535C2×C412yes—
186#535C2×C412yes—
187#533—22no—
188#533—22no—
189#533—22no—
190#533C2×C411yescharacteristic
191#533C2×C411yescharacteristic
192#533C2×C411yescharacteristic
193#533D411yescharacteristic
194#533D411yescharacteristic
195#533C2311yescharacteristic
196#532—24no—
197#532—22no—
198#532—22no—
199#532—22no—
200#532—24no—
201#532—22no—
202#532C2×C411yescharacteristic
203#532C2×C411yescharacteristic
204#532C2×C411yescharacteristic
205#532D411yescharacteristic
206#532D411yescharacteristic
207#532C2311yescharacteristic
208#532C2314yes—
209#529—24no—
210#529—24no—
211#529—22no—
212#529—22no—
213#529—24no—
214#529—22no—
215#529—24no—
216#529—24no—
217#529—24no—
218#529—21no—
219#529—21no—
220#529—21no—
221#529—21no—
222#529C2×C412yes—
223#529C2×C412yes—
224#529C2×C412yes—
225#529D412yes—
226#529D412yes—
227#529D412yes—
228#529D412yes—
229#529C2312yes—
230#529C2314yes—
231#525—21no—
232#525—21no—
233#525—24no—
234#525—22no—
235#525—22no—
236#525—24no—
237#525C2×C412yes—
238#525C2×C412yes—
239#525D412yes—
240#525D412yes—
241#520—24no—
242#520—22no—
243#520C2×C412yes—
244#520C2×C414yes—
245#520C2×C412yes—
246#519—22no—
247#519C2×C412yes—
248#519C2×C414yes—
249C4×#41—22no—
250C4×#41—24no—
251C4×#41—22no—
252C4×#41—22no—
253C4×#41—24no—
254C4×#41—21no—
255C4×#41—21no—
256C4×#41—21no—
257C4×#41—21no—
258C4×#41—21no—
259C4×#41—21no—
260C4×#41C2×C412yes—
261C4×#41C2×C412yes—
262C4×#41C2312yes—
263C4×#41C2312yes—
264C4×#41C2312yes—
265C4×#41C2314yes—
266C4×#41C2312yes—
267C4×#41C2312yes—
268C4×#41C2312yes—
269C2×C4×Q8—22no—
270C2×C4×Q8C2×C411yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2314yes—
273C2×C4×D4—21no—
274C2×C4×D4—21no—
275C2×C4×D4C2×C411yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×#117—21no—
278C2×#117C2×C411yescharacteristic
279C22×C42—21no—
280C22×C42C2311yescharacteristic
281#446—24no—
282#446—22no—
283#446—24no—
284#446—22no—
285C8×Q8—22no—
286C8×Q8—22no—
287#436—24no—
288#436—22no—
289#436—24no—
290#436—24no—
291#436—22no—
292#435—24no—
293#435—24no—
294#435—24no—
295#435—24no—
296#435—24no—
297#435—24no—
298C8×D4—24no—
299C8×D4—22no—
300C8×D4—22no—
301#433—24no—
302#433—24no—
303#433—24no—
304#432—21no—
305#432—21no—
306#432C2312yes—
307#432C2312yes—
308#432C2314yes—
309#431—21no—
310#431—21no—
311#431—21no—
312#431—21no—
313#431C2312yes—
314#431C2311yescharacteristic
315#431C2311yescharacteristic
316#431C2314yes—
317#431C2311yescharacteristic
318#431C2312yes—
319#431C2311yescharacteristic
320#431C2314yes—
321#431C2314yes—
322#424—22no—
323#423C2312yes—
324#423C2312yes—
325#423C2314yes—
326C2×C4⋊C8—21no—
327C2×C4⋊C8C2314yes—
328#408—22no—
329#408—24no—
330#407—21no—
331#407—21no—
332C2×C22⋊C8—21no—
333#405—22no—
334#405—24no—
335#405—24no—
336C4×M16—21no—
337C4×M16—21no—
338C4×M16—21no—
339C4×M16—21no—
340C4×M16C2311yescharacteristic
341C4×M16C2311yescharacteristic
342C4×M16C2312yes—
343C4×M16C2314yes—
344C2×#97—21no—
345C2×C4×C8C2312yes—
346C2×C4×C8C2312yes—
347C2×C4×C8C2314yes—
348Q8⋊C8C2312yes—
349Q8⋊C8C2314yes—
350Q8⋊C8C2314yes—
351Q8⋊C8C2314yes—
352Q8⋊C8C2312yes—
353Q8⋊C8C2312yes—
354Q8⋊C8C2314yes—
355Q8⋊C8C2312yes—
356Q8⋊C8C2314yes—
357Q8⋊C8C2314yes—
358D4⋊C8C2312yes—
359D4⋊C8C2314yes—
360D4⋊C8C2312yes—
361D4⋊C8C2312yes—
362D4⋊C8C2314yes—
363D4⋊C8C2312yes—
364D4⋊C8C2314yes—
365D4⋊C8C2314yes—
366D4⋊C8C2314yes—
367D4⋊C8C2314yes—
3682−1+4—48no—
369C2×#41—22no—
370C2×#41—24no—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41—24no—
378C2×#41—44no—
379C2×#41C22×C412yes—
380C2×#41C22×C412yes—
381C2×#41C22×C414yes—
382C2×#41C22×C412yes—
383C2×#41C22×C412yes—
384C2×#41C2×D412yes—
385C2×#41C2×D412yes—
386C22×Q8—22no—
387C22×Q8C22×C411yescharacteristic
388C22×Q8C22×C414yes—
389C22×D4—21no—
390C22×D4C22×C411yescharacteristic
391C23×C4—21no—
392C23×C4—21no—
393C23×C4—21no—
394C23×C4C22×C411yescharacteristic
395C23×C4C2×D411yescharacteristic
396C23×C4C2×D411yescharacteristic
397#131—48no—
398C2×M16—21no—
399C2×M16—21no—
400C2×M16—22no—
401C2×M16—24no—
402C2×M16—22no—
403C2×M16—22no—
404C2×M16—24no—
405C2×M16—44no—
406C22×C8—22no—
407C22×C8—22no—
408C22×C8—24no—
409C22×C8—24no—
410C4⋊Q8—22no—
411C4⋊Q8—24no—
412C4⋊Q8—22no—
413C4⋊Q8—22no—
414C4⋊Q8—24no—
415C4⋊Q8—22no—
416C4⋊Q8C22⋊C411yescharacteristic
417C4⋊Q8C22⋊C411yescharacteristic
418C4⋊Q8C22⋊C411yescharacteristic
419C4⋊Q8C22×C411yescharacteristic
420C4⋊Q8C22×C411yescharacteristic
421C4⋊Q8C22×C411yescharacteristic
422C4⋊Q8C22×C414yes—
423#127—22no—
424#127—24no—
425#127—24no—
426#127—22no—
427#127C22⋊C411yescharacteristic
428#127C22×C411yescharacteristic
429#127C22×C414yes—
430#126—24no—
431#126—24no—
432#126—24no—
433#126—24no—
434#126—24no—
435#126—24no—
436#126—24no—
437#126—22no—
438#126—22no—
439#126—24no—
440#126C22⋊C414yes—
441#126C22⋊C414yes—
442#125—24no—
443#125—24no—
444#125—24no—
445#125—24no—
446#125—22no—
447#125—21no—
448#125—21no—
449#125C22⋊C412yes—
450#125C22⋊C412yes—
451#125C22⋊C412yes—
452#125C22×C412yes—
453#125C22×C414yes—
454#124—22no—
455#124—24no—
456#124—24no—
457#124—24no—
458#124—24no—
459#124—24no—
460#124—24no—
461#124—24no—
462#124—24no—
463#124—24no—
464#124—21no—
465#124—21no—
466#124—24no—
467#124C22⋊C412yes—
468#124C22⋊C412yes—
469#124C22⋊C412yes—
470#124C22×C412yes—
471#124C22×C414yes—
472#123—24no—
473#123—22no—
474#123—22no—
475#123—22no—
476#123—24no—
477#123—24no—
478#123—24no—
479#123—24no—
480#123—24no—
481#123—24no—
482#123—24no—
483#123—24no—
484#123—24no—
485#123C22⋊C414yes—
486#123C22⋊C414yes—
487#123C22⋊C414yes—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—24no—
495C22⋊Q8—22no—
496C22⋊Q8—24no—
497C22⋊Q8—24no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8C22⋊C412yes—
502C22⋊Q8C22⋊C412yes—
503C22⋊Q8C22⋊C412yes—
504C22⋊Q8C22⋊C412yes—
505C22⋊Q8C22⋊C412yes—
506C22⋊Q8C22⋊C412yes—
507C22⋊Q8C22×C412yes—
508C22⋊Q8C22×C412yes—
509C22⋊Q8C22×C414yes—
510#121—24no—
511#121—22no—
512#121—24no—
513#121—24no—
514#121—24no—
515#121—22no—
516#121—24no—
517#121—24no—
518#121—24no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—24no—
524#121—22no—
525#121—22no—
526#121—22no—
527#121—24no—
528#121—24no—
529#121—24no—
530#121—24no—
531#121—24no—
532#121—24no—
533#121—24no—
534#121—24no—
535#121C22⋊C412yes—
536#121C22⋊C412yes—
537#121C22⋊C412yes—
538#121C22⋊C412yes—
539#121C22⋊C412yes—
540#121C22⋊C412yes—
541#121C22×C412yes—
542#121C22×C412yes—
543#121C22×C414yes—
544#121C22×C414yes—
545#121C22×C414yes—
546#120—22no—
547#120—24no—
548#120—24no—
549#120C22⋊C414yes—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—24no—
554C4×Q8—24no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—24no—
558C4×Q8—24no—
559C4×Q8—21no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—21no—
563C4×Q8—21no—
564C4×Q8—21no—
565C4×Q8—24no—
566C4×Q8—21no—
567C4×Q8—24no—
568C4×Q8—21no—
569C4×Q8C22×C412yes—
570C4×Q8C22×C412yes—
571C4×Q8C22×C412yes—
572C4×Q8C22×C414yes—
573C4×Q8C22×C414yes—
574C4×Q8C22×C412yes—
575C4×Q8C22×C414yes—
576C4×Q8C22×C412yes—
577C4×Q8C22×C412yes—
578C4×Q8C2×D412yes—
579C4×Q8C2×D412yes—
580C4×Q8C2×D412yes—
581C4×Q8C2×D412yes—
582C4×Q8C2412yes—
583C4×Q8C2412yes—
584C4×D4—24no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—24no—
600C4×D4—22no—
601C4×D4—24no—
602C4×D4—22no—
603C4×D4—24no—
604C4×D4—24no—
605C4×D4—24no—
606C4×D4—24no—
607C4×D4—22no—
608C4×D4—24no—
609C4×D4—24no—
610C4×D4—24no—
611C4×D4—24no—
612C4×D4—24no—
613C4×D4—24no—
614C4×D4—24no—
615C4×D4—24no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4—21no—
624C4×D4—24no—
625C4×D4C22×C412yes—
626C4×D4C22×C412yes—
627C4×D4C22×C412yes—
628C4×D4C22×C412yes—
629C4×D4C22×C414yes—
630C4×D4C22×C414yes—
631C4×D4C22×C414yes—
632C4×D4C22×C412yes—
633C4×D4C22×C412yes—
634C4×D4C2×D414yes—
635C4×D4C2×D412yes—
636C4×D4C2×D412yes—
637C4×D4C2×D414yes—
638C4×D4C2×D412yes—
639C4×D4C2×D414yes—
640C4×D4C2×D414yes—
641C4×D4C2×D412yes—
642C4×D4C2412yes—
643C4×D4C2412yes—
644#117—21no—
645#117—21no—
646#117—21no—
647#117—21no—
648#117—24no—
649#117—22no—
650#117—22no—
651#117—22no—
652#117—24no—
653#117—24no—
654#117—24no—
655#117—24no—
656#117—24no—
657#117—22no—
658#117—22no—
659#117—22no—
660#117—22no—
661#117—22no—
662#117—22no—
663#117—24no—
664#117—22no—
665#117—24no—
666#117C22×C412yes—
667#117C22×C412yes—
668#117C22×C412yes—
669#117C22×C414yes—
670#117C22×C412yes—
671#117C22×C414yes—
672#117C2×D414yes—
673#117C2×D412yes—
674#117C2×D412yes—
675#117C2×D414yes—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—24no—
679C2×C4⋊C4—24no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4C22×C411yescharacteristic
682C2×C4⋊C4C22×C411yescharacteristic
683C2×C4⋊C4C22×C414yes—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—24no—
691C2×C42—22no—
692C2×C42—22no—
693C2×C42—22no—
694C2×C42—24no—
695C2×C42—22no—
696C2×C42—22no—
697C2×C42C22×C411yescharacteristic
698C2×C42C22×C411yescharacteristic
699C2×C42C22×C411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2414yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C4⋊C8—21no—
711C4⋊C8—22no—
712C4⋊C8—21no—
713C4⋊C8—24no—
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—24no—
717C4⋊C8—24no—
718C4⋊C8—24no—
719C4⋊C8C2412yes—
720C4⋊C8C2414yes—
721C4⋊C8C2412yes—
722C22⋊C8—21no—
723C22⋊C8—21no—
724C22⋊C8—22no—
725C22⋊C8—22no—
726C22⋊C8—22no—
727C22⋊C8—22no—
728C22⋊C8—21no—
729C22⋊C8—21no—
730C22⋊C8—24no—
731C22⋊C8—24no—
732C22⋊C8—24no—
733C22⋊C8—24no—
734#97—21no—
735#97—21no—
736#97—22no—
737#97—22no—
738#97—22no—
739#97—24no—
740#97—24no—
741C4×C8—22no—
742C4×C8—22no—
743C4×C8—24no—
744C4×C8—22no—
745C4×C8—21no—
746C4×C8—21no—
747C4×C8—24no—
748C4×C8C2412yes—
749C4×C8C2412yes—
750C4×C8C2412yes—
751C4×C8C2412yes—
752C24—21no—
753C24C2×C22⋊C411yescharacteristic
754#41—24no—
755#41—24no—
756#41—28no—
757#41—44no—
758#41—44no—
759#41—44no—
760#41—42no—
761#41—42no—
762#41—44no—
763#41—44no—
764#41—416no—
765#41—44no—
766#41—44no—
767#41—48no—
768#41—84no—
769#41—82no—
770#41—84no—
771#41—82no—
772#41—84no—
773#41—84no—
774C2×Q8—24no—
775C2×Q8—21no—
776C2×Q8—24no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—44no—
782C2×Q8—48no—
783C2×Q8C2×C22⋊C412yes—
784C2×Q8C2×C22⋊C412yes—
785C2×Q8C2×C22⋊C412yes—
786C2×Q8C23×C412yes—
787C2×Q8C23×C412yes—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—22no—
794C2×D4—24no—
795C2×D4—22no—
796C2×D4—24no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—21no—
802C2×D4—42no—
803C2×D4—44no—
804C2×D4C2×C22⋊C412yes—
805C2×D4C2×C22⋊C414yes—
806C2×D4C2×C22⋊C412yes—
807C2×D4C2×C22⋊C414yes—
808C2×D4C2×C22⋊C414yes—
809C2×D4C2×C22⋊C412yes—
810C2×D4C23×C412yes—
811C2×D4C23×C412yes—
812C22×C4—21no—
813C22×C4—24no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—24no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—24no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—24no—
827C22×C4—22no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—44no—
832C22×C4—82no—
833C22×C4—82no—
834C22×C4C2×C22⋊C411yescharacteristic
835C22×C4C2×C22⋊C411yescharacteristic
836C22×C4C2×C22⋊C411yescharacteristic
837C22×C4C2×C22⋊C411yescharacteristic
838C22×C4C2×C22⋊C411yescharacteristic
839C22×C4C2×C22⋊C411yescharacteristic
840C22×C4C2×C22⋊C411yescharacteristic
841C22×C4C2×C22⋊C411yescharacteristic
842C22×C4C2×C22⋊C411yescharacteristic
843C22×C4C23×C411yescharacteristic
844C22×C4C23×C411yescharacteristic
845C22×C4C23×C411yescharacteristic
846C22×C4C23×C414yes—
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D414yes—
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D414yes—
855M16—24no—
856M16—44no—
857M16—48no—
858M16—42no—
859M16—82no—
860M16—82no—
861M16—84no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—22no—
865C2×C8—22no—
866C2×C8—22no—
867C2×C8—24no—
868C2×C8—22no—
869C2×C8—44no—
870C2×C8—48no—
871C2×C8—44no—
872C2×C8—84no—
873C4⋊C4—22no—
874C4⋊C4—21no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—22no—
883C4⋊C4—21no—
884C4⋊C4—24no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—22no—
890C4⋊C4—24no—
891C4⋊C4—21no—
892C4⋊C4—24no—
893C4⋊C4—21no—
894C4⋊C4—24no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4C2×C22⋊C412yes—
898C4⋊C4C2×C22⋊C414yes—
899C4⋊C4C2×C22⋊C412yes—
900C4⋊C4C2×C22⋊C414yes—
901C4⋊C4C2×C22⋊C412yes—
902C4⋊C4C2×C22⋊C414yes—
903C4⋊C4C2×C22⋊C412yes—
904C4⋊C4C2×C22⋊C414yes—
905C4⋊C4C2×C22⋊C414yes—
906C4⋊C4C2×C22⋊C412yes—
907C4⋊C4C2×C22⋊C414yes—
908C4⋊C4C2×C22⋊C412yes—
909C4⋊C4C23×C412yes—
910C4⋊C4C23×C412yes—
911C4⋊C4C23×C412yes—
912C4⋊C4C23×C412yes—
913C22⋊C4—22no—
914C22⋊C4—22no—
915C22⋊C4—22no—
916C22⋊C4—24no—
917C22⋊C4—22no—
918C22⋊C4—22no—
919C22⋊C4—24no—
920C22⋊C4—22no—
921C22⋊C4—22no—
922C22⋊C4—22no—
923C22⋊C4—22no—
924C22⋊C4—22no—
925C22⋊C4—24no—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—24no—
931C22⋊C4—24no—
932C22⋊C4—22no—
933C22⋊C4—24no—
934C22⋊C4—22no—
935C22⋊C4—22no—
936C22⋊C4C2×C22⋊C414yes—
937C22⋊C4C2×C22⋊C414yes—
938C22⋊C4C2×C22⋊C414yes—
939C22⋊C4C2×C22⋊C414yes—
940C22⋊C4C2×C22⋊C414yes—
941C22⋊C4C2×C22⋊C414yes—
942C22⋊C4C2×C22⋊C414yes—
943C22⋊C4C2×C22⋊C414yes—
944C22⋊C4C2×C22⋊C414yes—
945C42—22no—
946C42—22no—
947C42—22no—
948C42—22no—
949C42—22no—
950C42—24no—
951C42—22no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—22no—
956C42—22no—
957C42—22no—
958C42C2×C22⋊C411yescharacteristic
959C42C2×C22⋊C411yescharacteristic
960C42C2×C22⋊C411yescharacteristic
961C42C2×C22⋊C411yescharacteristic
962C42C2×C22⋊C411yescharacteristic
963C42C2×C22⋊C411yescharacteristic
964C42C23×C411yescharacteristic
965C42C23×C411yescharacteristic
966C42C23×C411yescharacteristic
967C42C23×C414yes—
968C42C22×D411yescharacteristic
969C42C22×D411yescharacteristic
970C42C22×D414yes—
971C42C22×D411yescharacteristic
972C42C22×D411yescharacteristic
973C42C22×D411yescharacteristic
974C42C22×D414yes—
975C42C22×D411yescharacteristic
976C42C2511yescharacteristic
977C23—22no—
978C23—22no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—42no—
983C23—81no—
984C23—81no—
985C23C22×C22⋊C411yescharacteristic
986C23C22×C22⋊C411yescharacteristic
987C23C22×C22⋊C414yes—
988C23C22×C22⋊C411yescharacteristic
989Q8—24no—
990Q8—24no—
991Q8—22no—
992Q8—24no—
993Q8—42no—
994Q8—42no—
995Q8—48no—
996Q8—42no—
997Q8—81no—
998Q8—84no—
999Q8#56814yes—
1000D4—24no—
1001D4—22no—
1002D4—22no—
1003D4—24no—
1004D4—42no—
1005D4—44no—
1006D4—44no—
1007D4—42no—
1008D4—44no—
1009D4—44no—
1010D4—44no—
1011D4—48no—
1012D4—42no—
1013D4—44no—
1014D4—42no—
1015D4—81no—
1016D4—84no—
1017D4—84no—
1018D4—84no—
1019D4—82no—
1020D4—84no—
1021D4—82no—
1022D4—84no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—41no—
1044C2×C4—44no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4—44no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—44no—
1061C2×C4—44no—
1062C2×C4—82no—
1063C2×C4—82no—
1064C2×C4—82no—
1065C2×C4—84no—
1066C2×C4—81no—
1067C2×C4—81no—
1068C2×C4—84no—
1069C2×C4C22×C22⋊C411yescharacteristic
1070C2×C4C22×C22⋊C411yescharacteristic
1071C2×C4C22×C22⋊C411yescharacteristic
1072C2×C4C22×C22⋊C411yescharacteristic
1073C2×C4C22×C22⋊C411yescharacteristic
1074C2×C4C22×C22⋊C411yescharacteristic
1075C2×C4C22×C22⋊C414yes—
1076C2×C4C22×C22⋊C414yes—
1077C2×C4C22×C22⋊C414yes—
1078C2×C4C22×C22⋊C411yescharacteristic
1079C2×C4C22×C22⋊C411yescharacteristic
1080C2×C4C22×C22⋊C411yescharacteristic
1081C2×C4C24×C411yescharacteristic
1082C2×C4C23×D411yescharacteristic
1083C2×C4C23×D411yescharacteristic
1084C8—24no—
1085C8—42no—
1086C8—42no—
1087C8—42no—
1088C8—42no—
1089C8—44no—
1090C8—42no—
1091C22—21no—
1092C22—24no—
1093C22—21no—
1094C22—21no—
1095C22—21no—
1096C22—21no—
1097C22—21no—
1098C22—24no—
1099C22—21no—
1100C22—21no—
1101C22—21no—
1102C22—24no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—82no—
1110C22—84no—
1111C22C23×C22⋊C411yescharacteristic
1112C4—24no—
1113C4—21no—
1114C4—21no—
1115C4—21no—
1116C4—24no—
1117C4—21no—
1118C4—21no—
1119C4—21no—
1120C4—24no—
1121C4—21no—
1122C4—21no—
1123C4—21no—
1124C4—24no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4#290112yes—
1131C4C2×#56812yes—
1132C4#358412yes—
1133C2—44no—
1134C2—41no—
1135C2—41no—
1136C2—41no—
1137C2—82no—
1138C2—82no—
1139C2#6006411yescharacteristic
1140C2#6008611yescharacteristic
1141C2C2×#290111yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62793C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ #3444 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60295C2semidirect
3. #60210C2semidirect
4. #17526C2semidirect
5. #17525C2semidirect
6. #17520C2semidirect
7. #17519C2semidirect
8. #17516C2semidirect
9. #17510C2semidirect
10. #17505C2semidirect
11. #17503C2semidirect
12. #17489C2semidirect
13. #17454C2semidirect
14. #17447C2semidirect
15. #17443C2semidirect
43. #2991C22semidirect
44. #2990C22semidirect
54. #2965C22semidirect
55. C8×#41C22semidirect
59. #2925C22semidirect
60. #2922C22semidirect
64. C4×#131C22semidirect
66. #1496C22semidirect
67. #1495C22semidirect
68. #1494C22semidirect
69. #1494C22semidirect
70. #1493C22semidirect
71. #1492C22semidirect
72. #1492C22semidirect
74. #1491C22semidirect
79. #1489C22semidirect
83. #1488C22semidirect
85. #1487C22semidirect
87. #1485C22semidirect
88. #1485C22semidirect
89. #1484C22semidirect
90. #1484C22semidirect
91. #1484C22semidirect
92. #1483C22semidirect
93. #1482C22semidirect
94. #1482C22semidirect
95. #1482C22semidirect
96. #1480C22semidirect
97. #1479C22semidirect
98. #1477C22semidirect
102. #1476C22semidirect
103. C2×Q8⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#627932
#602952
#602102
#175262
#175252
#175202
#175192
#175162
#175102
#175052
#175032
#174892
#174542
#174472
#174432