Finite Group Databasebeta

← #6354041

Subgroups — #6354041

Order 512.

1639 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60950C211yesmaximal, characteristic, complemented
2#60949C211yesmaximal, characteristic
3C2×#3131C211yesmaximal, characteristic, complemented
4C2×#2966C211yesmaximal, characteristic, complemented
5#19367C214yesmaximal, complemented
6#19366C214yesmaximal, complemented
7#19365C212yesmaximal, complemented
8#19364C212yesmaximal, complemented
9#19363C212yesmaximal, complemented
10#19362C212yesmaximal, complemented
11#19155C212yesmaximal, complemented
12#19142C212yesmaximal, complemented
13#19123C212yesmaximal, complemented
14#19110C212yesmaximal, complemented
15#17793C211yesmaximal, characteristic, complemented
16#17734C211yesmaximal, characteristic, complemented
17#17731C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×#529C2211yescharacteristic
21#3252C2214yescomplemented
22#3251C2214yes—
23#3239C2212yes—
24#3238C2212yes—
25#3236—21no—
26#3234—21no—
27#3218C2212yes—
28#3217C2212yes—
29#3215—21no—
30#3213—21no—
31#3195—21no—
32#3193—21no—
33#3193—21no—
34#3192—21no—
35#3172—22no—
36#3171—22no—
37#3131—21no—
38#3131—21no—
39#3131—21no—
40#3131—21no—
41#3131C2212yes—
42#3131C2212yes—
43#3131C2212yescomplemented
44#3131C2212yescomplemented
45C2×#488—21no—
46C2×#488—21no—
47C2×#487C2211yescharacteristic, complemented
48C2×#487C2211yescharacteristic, complemented
49C2×#486C2211yescharacteristic, complemented
50C2×#486C2211yescharacteristic, complemented
51#3108—22no—
52#3105—22no—
53#3104C2212yescomplemented
54#3103C2212yes—
55#3101C2212yescomplemented
56#3100C2212yes—
57#2966—21no—
58#2966—21no—
59#2966—21no—
60#2966—21no—
61#2966C2212yes—
62#2966C2212yes—
63#2966C2212yescomplemented
64#2966C2212yescomplemented
65C2×#446C2211yescharacteristic, complemented
66C2×C8×Q8C2211yescharacteristic, complemented
67C2×#436C2211yescharacteristic, complemented
68C2×#435—21no—
69C2×C8×D4—21no—
70C2×C8×D4C2211yescharacteristic, complemented
71#2920C2211yescharacteristic
72#2920C2211yescharacteristic
73C2×#433—21no—
74C2×#432C2211yescharacteristic
75C2×#416—21no—
76C2×#416—21no—
77C2×#405—21no—
78C22×C4×C8C2211yescharacteristic
79#1704C2214yescomplemented
80#1703C2214yescomplemented
81#1702C2214yescomplemented
82#1701C2214yescomplemented
83#1700C2214yescomplemented
84#1699C2214yescomplemented
85#1698C2214yescomplemented
86#1697C2214yescomplemented
87#1684C2214yescomplemented
88#1683C2214yescomplemented
89#1682C2214yescomplemented
90#1681C2214yescomplemented
91#1680C2214yescomplemented
92#1679C2214yescomplemented
93#1678C2214yescomplemented
94#1677C2214yescomplemented
95#1568C2212yescomplemented
96#1568C2212yescomplemented
97#1567C2212yescomplemented
98#1566C2212yescomplemented
99#1564C2212yescomplemented
100#1564C2212yescomplemented
101#1559C2214yescomplemented
102#1558C2212yescomplemented
103#1557C2214yescomplemented
104#1556C2212yescomplemented
105#1556C2212yescomplemented
106#1555C2212yescomplemented
107#1542C2212yescomplemented
108#1542C2212yescomplemented
109#1540C2212yes—
110#1540C2212yes—
111C22×#41—21no—
112C22×M16—21no—
113C23×C8—21no—
114C23×C8D411yescharacteristic
115C23×C8D411yescharacteristic
116#533—21no—
117#533—21no—
118#533—21no—
119#533—21no—
120#533—21no—
121#533—21no—
122#533C2312yes—
123#533C2312yes—
124#532—21no—
125#532—21no—
126#532—21no—
127#532—21no—
128#532—21no—
129#532—21no—
130#532C2312yes—
131#532C2312yes—
132C2×C4⋊Q8C2311yescharacteristic
133C2×C4⋊Q8C2311yescharacteristic
134C2×C4⋊Q8C2311yescharacteristic
135C2×#127C2311yescharacteristic
136#529—21no—
137#529—21no—
138#529—21no—
139#529—21no—
140#529D412yes—
141#529D412yes—
142#529C2312yes—
143#529C2312yes—
144C2×#126—21no—
145C2×#125—21no—
146C2×#125D411yescharacteristic
147C2×#124—21no—
148C2×#124D411yescharacteristic
149C2×#123—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8D411yescharacteristic
153C2×#121—21no—
154C2×#121—21no—
155C2×#121D411yescharacteristic
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8C2311yescharacteristic
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4—21no—
162C2×C4×D4C2311yescharacteristic
163C2×#117—21no—
164C2×#117—21no—
165C22×C42C2311yescharacteristic
166#501—22no—
167#501—22no—
168#497—22no—
169#496—22no—
170#491—22no—
171#490—22no—
172#489—22no—
173#489—22no—
174#488—22no—
175#488—22no—
176#488—22no—
177#488—22no—
178#488—22no—
179#488—22no—
180#488—22no—
181#488—22no—
182#487—21no—
183#487—21no—
184#487—21no—
185#487—21no—
186#487C2312yes—
187#487C2312yes—
188#487C2312yes—
189#487C2312yes—
190#486—21no—
191#486—21no—
192#486—21no—
193#486—21no—
194#486C2312yes—
195#486C2312yes—
196#486C2312yes—
197#486C2312yes—
198#484—22no—
199#484—22no—
200#483—22no—
201#483—22no—
202#481—22no—
203#481—22no—
204#480—22no—
205#480—22no—
206#479—24no—
207#478—24no—
208#477C2314yes—
209#476C2314yes—
210#475C2314yes—
211#474C2314yes—
212#470—24no—
213#469—24no—
214#468—24no—
215#468—24no—
216#464—24no—
217#463—24no—
218#462C2314yes—
219#461C2314yes—
220#460C2314yes—
221#459C2314yes—
222#451—22no—
223#451—22no—
224#450—22no—
225#450—22no—
226#448—22no—
227#448—22no—
228#447—22no—
229#447—22no—
230#446—21no—
231#446—21no—
232#446C2312yes—
233#446C2312yes—
234C8×Q8—21no—
235C8×Q8—21no—
236C8×Q8C2312yes—
237C8×Q8C2312yes—
238C4×Q16—24no—
239C4×SD16—24no—
240C4×SD16—24no—
241C4×D8—24no—
242#436—21no—
243#436—21no—
244#436C2312yes—
245#436C2312yes—
246#435—22no—
247#435—22no—
248#435—22no—
249#435—22no—
250C8×D4—22no—
251C8×D4—22no—
252C8×D4—22no—
253C8×D4—22no—
254C8×D4—21no—
255C8×D4—21no—
256C8×D4C2312yes—
257C8×D4C2312yes—
258#433—22no—
259#433—22no—
260#433—22no—
261#433—22no—
262#432—21no—
263#432—21no—
264#432—21no—
265#432—21no—
266#432C2312yes—
267#432C2312yes—
268#432C2312yes—
269#432C2312yes—
270#431—21no—
271#431—21no—
272#431C2312yes—
273#431C2312yes—
274#423C2312yes—
275#423C2312yes—
276C2×C4⋊C8—21no—
277C2×C4⋊C8—21no—
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280#416—22no—
281#416—22no—
282#416—22no—
283#416—22no—
284#416—22no—
285#416—22no—
286#416—22no—
287#416—22no—
288C2×#103—21no—
289C2×#103—21no—
290C2×#103—21no—
291C2×#103—21no—
292C2×#102—21no—
293C2×#102—21no—
294C2×#102—21no—
295C2×#102—21no—
296#407—21no—
297#407—21no—
298C2×C22⋊C8—21no—
299C2×C22⋊C8—21no—
300C2×C22⋊C8—21no—
301#405—22no—
302#405—22no—
303#405—22no—
304#405—22no—
305C4×M16—21no—
306C4×M16—21no—
307C2×#97—21no—
308C2×#97—21no—
309C2×C4×C8—21no—
310C2×C4×C8D411yescharacteristic
311C2×C4×C8D411yescharacteristic
312C2×C4×C8D411yescharacteristic
313C2×C4×C8D411yescharacteristic
314C2×C4×C8D411yescharacteristic
315C2×C4×C8D411yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#335C2314yes—
323#335C2314yes—
324#334C2314yes—
325#334C2314yes—
326#333C2314yes—
327#333C2314yes—
328#332C2314yes—
329#332C2314yes—
330#332C2314yes—
331#332C2314yes—
332#331C2314yes—
333#331C2314yes—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—44no—
337C2×#41—44no—
338C2×#41—41no—
339C2×#41—41no—
340C22×Q8—21no—
341C22×Q8—21no—
342C22×Q8—21no—
343C22×Q8C2×D411yescharacteristic
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—41no—
349C22×D4C2×D411yescharacteristic
350C23×C4—21no—
351C23×C4—41no—
352C23×C4C2×D411yescharacteristic
353C23×C4C2×D411yescharacteristic
354C23×C4#4111yescharacteristic
355C2×Q16—24no—
356C2×SD16—24no—
357C2×SD16—24no—
358C2×D8—24no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—44no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—42no—
369C22×C8—42no—
370C22×C8—44no—
371C22×C8C2×D411yescharacteristic
372C22×C8C2×D411yescharacteristic
373C22×C8C2×D411yescharacteristic
374C22×C8C2×D411yescharacteristic
375C22×C8C2×D411yescharacteristic
376C22×C8C2×D411yescharacteristic
377C22×C8C2×D411yescharacteristic
378C22×C8C2×D411yescharacteristic
379C22×C8C2×D411yescharacteristic
380C22×C8C2×D411yescharacteristic
381C22×C8C2×D411yescharacteristic
382C22×C8C2×D411yescharacteristic
383C4⋊Q8—21no—
384C4⋊Q8—21no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8—21no—
391C4⋊Q8—21no—
392C4⋊Q8C2412yes—
393C4⋊Q8C2412yes—
394C4⋊Q8C2412yes—
395#127—21no—
396#127—21no—
397#127—21no—
398#127C2412yes—
399#126—22no—
400#126—22no—
401#126—22no—
402#126—22no—
403#125—21no—
404#125—21no—
405#125—22no—
406#125—22no—
407#125—41no—
408#125—41no—
409#125C2×D412yes—
410#125C2×D412yes—
411#124—21no—
412#124—21no—
413#124—22no—
414#124—22no—
415#124—41no—
416#124—41no—
417#124C2×D412yes—
418#124C2×D412yes—
419#123—22no—
420#123—22no—
421#123—22no—
422#123—22no—
423C22⋊Q8—21no—
424C22⋊Q8—21no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—41no—
430C22⋊Q8—41no—
431C22⋊Q8—41no—
432C22⋊Q8—41no—
433C22⋊Q8C2×D412yes—
434C22⋊Q8C2×D412yes—
435#121—21no—
436#121—21no—
437#121—22no—
438#121—22no—
439#121—22no—
440#121—22no—
441#121—41no—
442#121—41no—
443#121—41no—
444#121—41no—
445#121C2×D412yes—
446#121C2×D412yes—
447C4×Q8—21no—
448C4×Q8—21no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8—22no—
453C4×Q8—41no—
454C4×Q8—41no—
455C4×Q8—41no—
456C4×Q8—41no—
457C4×Q8C2×D412yes—
458C4×Q8C2412yes—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—21no—
464C4×D4—22no—
465C4×D4—22no—
466C4×D4—21no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—41no—
470C4×D4—41no—
471C4×D4—41no—
472C4×D4—41no—
473C4×D4C2×D412yes—
474C4×D4C2412yes—
475#117—22no—
476#117—22no—
477#117—22no—
478#117—22no—
479#117—22no—
480#117—22no—
481#117—41no—
482#117—41no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—41no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4C2×D411yescharacteristic
496C2×C4⋊C4C2×D411yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C42—21no—
506C2×C42—41no—
507C2×C42C2×D411yescharacteristic
508C2×C42C2×D411yescharacteristic
509C2×C42C2×D411yescharacteristic
510C2×C42C2×D411yescharacteristic
511C2×C42C2×D411yescharacteristic
512C2×C42C2×D411yescharacteristic
513C2×C42#4111yescharacteristic
514C2×C42#4111yescharacteristic
515C2×C42#4111yescharacteristic
516C2×C42C2411yescharacteristic
517C2×C42C2411yescharacteristic
518C2×C42C2411yescharacteristic
519#107—24no—
520#107—24no—
521#106—24no—
522#106—24no—
523C4⋊C8—22no—
524C4⋊C8—22no—
525C4⋊C8—22no—
526C4⋊C8—22no—
527C4⋊C8—21no—
528C4⋊C8—21no—
529C4⋊C8—22no—
530C4⋊C8—22no—
531C4⋊C8C2412yes—
532C4⋊C8C2412yes—
533C4⋊C8C2414yes—
534C4⋊C8C2414yes—
535#103—24no—
536#103—24no—
537#103—22no—
538#103—22no—
539#103—22no—
540#103—22no—
541#103—22no—
542#103—22no—
543#103—22no—
544#103—22no—
545#103—24no—
546#103—24no—
547#102—24no—
548#102—24no—
549#102—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—22no—
555#102—22no—
556#102—22no—
557#102—24no—
558#102—24no—
559C22⋊C8—22no—
560C22⋊C8—22no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564C22⋊C8—22no—
565C22⋊C8—22no—
566C22⋊C8—22no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569#97—22no—
570#97—22no—
571#97—22no—
572#97—22no—
573#97—22no—
574#97—22no—
575C4×C8—22no—
576C4×C8—22no—
577C4×C8—22no—
578C4×C8—22no—
579C4×C8C2×D411yescharacteristic
580C4×C8C2×D411yescharacteristic
581C4×C8C2×D411yescharacteristic
582C4×C8C2×D411yescharacteristic
583C4×C8C2×D411yescharacteristic
584C4×C8C2×D411yescharacteristic
585C4×C8C2×D411yescharacteristic
586C4×C8C2×D411yescharacteristic
587C4×C8C2×D411yescharacteristic
588C4×C8C2×D411yescharacteristic
589C4×C8C2×D411yescharacteristic
590C4×C8C2×D411yescharacteristic
591C4×C8C2411yescharacteristic
592C4×C8C2411yescharacteristic
593C4×C8C2411yescharacteristic
594C4×C8C2411yescharacteristic
595C24—21no—
596C24—41no—
597C24#12111yescharacteristic
598#41—44no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—84no—
603#41—84no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—42no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8—41no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—82no—
615C2×Q8—82no—
616C2×Q8C22×D412yes—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—44no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—82no—
633C2×D4—82no—
634C2×D4—84no—
635C2×D4C22×D412yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—84no—
653C22×C4#12111yescharacteristic
654C22×C4#12111yescharacteristic
655C22×C4#12111yescharacteristic
656C22×C4#12111yescharacteristic
657C22×C4#12111yescharacteristic
658C22×C4#12111yescharacteristic
659C22×C4#12111yescharacteristic
660C22×C4#12111yescharacteristic
661C22×C4#12111yescharacteristic
662C22×C4C22×D411yescharacteristic
663C22×C4C22×D411yescharacteristic
664C22×C4C22×D411yescharacteristic
665C22×C4C22×D411yescharacteristic
666C22×C4C22×D411yescharacteristic
667C22×C4C22×D411yescharacteristic
668C22×C4C2×#4111yescharacteristic
669C22×C4C2×#4111yescharacteristic
670C22×C4C2×#4111yescharacteristic
671Q16—84no—
672SD16—84no—
673SD16—84no—
674D8—84no—
675M16—44no—
676M16—44no—
677M16—82no—
678M16—82no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—24no—
685C2×C8—24no—
686C2×C8—22no—
687C2×C8—41no—
688C2×C8—41no—
689C2×C8—41no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—44no—
696C2×C8—44no—
697C2×C8—42no—
698C2×C8—42no—
699C2×C8C22×D411yescharacteristic
700C2×C8C22×D411yescharacteristic
701C2×C8C22×D411yescharacteristic
702C2×C8C22×D411yescharacteristic
703C2×C8C22×D411yescharacteristic
704C2×C8C22×D411yescharacteristic
705C2×C8C22×D411yescharacteristic
706C2×C8C22×D411yescharacteristic
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—22no—
722C4⋊C4—22no—
723C4⋊C4—41no—
724C4⋊C4—41no—
725C4⋊C4—41no—
726C4⋊C4—41no—
727C4⋊C4—41no—
728C4⋊C4—41no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C4⋊C4—42no—
732C4⋊C4—42no—
733C4⋊C4C22×D412yes—
734C4⋊C4C22×D412yes—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C42—22no—
752C42—22no—
753C42—42no—
754C42—42no—
755C42#12111yescharacteristic
756C42#12111yescharacteristic
757C42#12111yescharacteristic
758C42#12111yescharacteristic
759C42#12111yescharacteristic
760C42#12111yescharacteristic
761C42C22×D411yescharacteristic
762C42C22×D411yescharacteristic
763C42C22×D411yescharacteristic
764C42C22×D411yescharacteristic
765C42C22×D411yescharacteristic
766C42C22×D411yescharacteristic
767C42C2×#4111yescharacteristic
768C42C2×#4111yescharacteristic
769C42C2×#4111yescharacteristic
770C42C2511yescharacteristic
771C23—22no—
772C23—22no—
773C23—22no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—82no—
780C23—82no—
781C23—82no—
782C23C2×#12111yescharacteristic
783C23C2×#12111yescharacteristic
784C23C2×#12111yescharacteristic
785Q8—24no—
786Q8—42no—
787Q8—44no—
788Q8—42no—
789Q8—42no—
790Q8—82no—
791Q8—82no—
792Q8—82no—
793Q8—82no—
794D4—24no—
795D4—42no—
796D4—44no—
797D4—44no—
798D4—44no—
799D4—42no—
800D4—42no—
801D4—82no—
802D4—82no—
803D4—82no—
804D4—82no—
805D4—84no—
806D4—84no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—84no—
839C2×C4—82no—
840C2×C4—82no—
841C2×C4—82no—
842C2×C4—84no—
843C2×C4C2×#12111yescharacteristic
844C2×C4C2×#12111yescharacteristic
845C2×C4C2×#12111yescharacteristic
846C2×C4C2×#12111yescharacteristic
847C2×C4C2×#12111yescharacteristic
848C2×C4C2×#12111yescharacteristic
849C2×C4C2×#12111yescharacteristic
850C2×C4C2×#12111yescharacteristic
851C2×C4C2×#12111yescharacteristic
852C2×C4#57512yes—
853C2×C4#57512yes—
854C2×C4C23×D411yescharacteristic
855C2×C4C23×D411yescharacteristic
856C2×C4C22×#4111yescharacteristic
857C8—21no—
858C8—21no—
859C8—21no—
860C8—21no—
861C8—21no—
862C8—21no—
863C8—21no—
864C8—21no—
865C8—44no—
866C8—44no—
867C8—42no—
868C8—42no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—44no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—84no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22—164no—
885C22#304012yes—
886C22#306712yes—
887C22C22×#12111yescharacteristic
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—21no—
893C4—21no—
894C4—21no—
895C4—21no—
896C4—21no—
897C4—42no—
898C4—42no—
899C4—42no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4#304012yes—
904C4C2×#57511yescharacteristic
905C4C2×#57511yescharacteristic
906C4#358412yes—
907C2—22no—
908C2—22no—
909C2—41no—
910C2—82no—
911C2—162no—
912C2C2×#304011yescharacteristic
913C2#6045011yescharacteristic
914C2C2×#306711yescharacteristic
subgroupG/H
centerC2×C4C2×#121
commutator, Frattini, cosocleC42C25
socleC22C22×#121
prime radical#60949C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60950C2semidirect
3. C2×#3131C2semidirect
4. C2×#2966C2semidirect
5. #19367C2semidirect
6. #19366C2semidirect
7. #19365C2semidirect
8. #19364C2semidirect
9. #19363C2semidirect
10. #19362C2semidirect
11. #19155C2semidirect
12. #19142C2semidirect
13. #19123C2semidirect
14. #19110C2semidirect
15. #17793C2semidirect
16. #17734C2semidirect
17. #17731C2semidirect
21. #3252C22semidirect
43. #3131C22semidirect
44. #3131C22semidirect
47. C2×#487C22semidirect
48. C2×#487C22semidirect
49. C2×#486C22semidirect
50. C2×#486C22semidirect
53. #3104C22semidirect
55. #3101C22semidirect
63. #2966C22semidirect
64. #2966C22semidirect
65. C2×#446C22semidirect
66. C2×C8×Q8C22semidirect
67. C2×#436C22semidirect
70. C2×C8×D4C22semidirect
79. #1704C22semidirect
80. #1703C22semidirect
81. #1702C22semidirect
82. #1701C22semidirect
83. #1700C22semidirect
84. #1699C22semidirect
85. #1698C22semidirect
86. #1697C22semidirect
87. #1684C22semidirect
88. #1683C22semidirect
89. #1682C22semidirect
90. #1681C22semidirect
91. #1680C22semidirect
92. #1679C22semidirect
93. #1678C22semidirect
94. #1677C22semidirect
95. #1568C22semidirect
96. #1568C22semidirect
97. #1567C22semidirect
98. #1566C22semidirect
99. #1564C22semidirect
100. #1564C22semidirect
101. #1559C22semidirect
102. #1558C22semidirect
103. #1557C22semidirect
104. #1556C22semidirect
105. #1556C22semidirect
106. #1555C22semidirect
107. #1542C22semidirect
108. #1542C22semidirect

Maximal subgroups

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

subgroupindex
#609502
#609492
C2×#31312
C2×#29662
#193672
#193662
#193652
#193642
#193632
#193622
#191552
#191422
#191232
#191102
#177932
#177342
#177312