Finite Group Databasebeta

← #6343213

Subgroups — #6343213

Order 512.

2886 conjugacy classes of subgroups.

The subgroup lattice has 1073 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62748C211yesmaximal, characteristic
2#60294C211yesmaximal, characteristic, complemented
3#60205C211yesmaximal, characteristic, complemented
4#17521C214yesmaximal, complemented
5#17517C214yesmaximal, complemented
6#17516C214yesmaximal, complemented
7#17511C214yesmaximal, complemented
8#17505C214yesmaximal, complemented
9#17502C211yesmaximal, characteristic, complemented
10#17495C211yesmaximal, characteristic, complemented
11#17468C214yesmaximal, complemented
12#17465C211yesmaximal, characteristic, complemented
13C2×#1484C211yesmaximal, characteristic, complemented
14#3562—22no—
15#3561—21no—
16#3560—22no—
17#3559C412yes—
18#3558—21no—
19#3558C412yes—
20#3554C412yes—
21#3552C412yes—
22#3546C412yes—
23#3543C412yes—
24#3537C412yes—
25#3536C412yes—
26#3534—22no—
27#3529—22no—
28#3481C2214yes—
29#3480C2212yes—
30D4×#41—22no—
31D4×#41C2212yes—
32#3460C2214yes—
33#3459—22no—
34#3455—21no—
35#3449—21no—
36#3444C2211yescharacteristic
37C2×#532C2211yescharacteristic
38C2×#529C2211yescharacteristic
39#2990C2214yescomplemented
40#2989C2212yescomplemented
41#2988C2212yescomplemented
42#2985—21no—
43#2981—21no—
44#2977—22no—
45#2968—22no—
46#2967—22no—
47#2967—22no—
48#2966—22no—
49#2965C2214yescomplemented
50#2965C2214yescomplemented
51#2961—21no—
52#2932—21no—
53#2930—22no—
54#2925C2214yescomplemented
55#2922C2212yescomplemented
56#2920C2211yescharacteristic, complemented
57C2×#432C2211yescharacteristic, complemented
58C2×#431C2211yescharacteristic, complemented
59C4×#131C2212yescomplemented
60C2×C4×M16C2211yescharacteristic, complemented
61#1496C2214yescomplemented
62#1496C2214yescomplemented
63#1495C2214yescomplemented
64#1494C2212yescomplemented
65#1494C2212yescomplemented
66#1494C2214yescomplemented
67#1492C2214yescomplemented
68#1491C2212yescomplemented
69#1490C2214yescomplemented
70#1490C2212yescomplemented
71#1490C2214yescomplemented
72#1489C2214yescomplemented
73#1488C2214yescomplemented
74#1486C2214yescomplemented
75#1484C2212yescomplemented
76#1484C2212yescomplemented
77#1484C2214yescomplemented
78#1484C2214yescomplemented
79#1483C2214yescomplemented
80#1483C2214yescomplemented
81#1483C2214yescomplemented
82#1482C2212yescomplemented
83#1482C2212yescomplemented
84#1482C2214yescomplemented
85#1480C2214yescomplemented
86#1480C2214yescomplemented
87#1479C2212yescomplemented
88#1478C2212yescomplemented
89#1478C2214yescomplemented
90#1477C2214yescomplemented
91#1476C2214yescomplemented
92C2×D4⋊C8C2212yescomplemented
93C2×D4⋊C8C2212yescomplemented
94C2×D4⋊C8C2214yescomplemented
95C22×#41—22no—
96C22×#41—21no—
97C2×#131—22no—
98C22×M16—21no—
99#563—24no—
100#563—22no—
101#562—22no—
102#562—22no—
103#562—24no—
104#562—24no—
105H(3,𝔽4)—22no—
106#560—24no—
107#560—24no—
108#560—24no—
109#559—22no—
110#559C2×C412yes—
111#559C2×C414yes—
112#557C2×C412yes—
113#556—22no—
114#556C2×C412yes—
115#554C2×C414yes—
116#554C2×C414yes—
117#553—24no—
118#553—24no—
119#553C2×C414yes—
120#553C2×C414yes—
121#553C2×C414yes—
122#551—24no—
123#551—24no—
124#550—22no—
125#550C2×C412yes—
126#550C2×C412yes—
127D4×Q8—22no—
128D4×Q8C2×C412yes—
129#548—22no—
130#548—22no—
131#548—22no—
132#548C2×C414yes—
133#547—24no—
134#547—22no—
135#547C2×C414yes—
136#547C2×C412yes—
137#546—24no—
138#546—24no—
139#546—22no—
140#546—22no—
141#546—24no—
142#546—24no—
143#546—22no—
144#546C2×C414yes—
145#546C2×C414yes—
146D42—22no—
147D42—24no—
148D42C2×C414yes—
149D42C2×C412yes—
150D42C2×C414yes—
151#544C2×C414yes—
152#543—22no—
153#542—22no—
154#542—22no—
155#542—24no—
156#542C2×C414yes—
157#542C2×C414yes—
158#541—22no—
159#540—22no—
160#540—24no—
161#540C2×C414yes—
162#540C2×C414yes—
163#539—24no—
164#539—24no—
165#539—24no—
166#539—22no—
167#539—22no—
168#538—24no—
169#538—24no—
170#538—22no—
171#538—22no—
172#538—22no—
173#538—22no—
174#538—24no—
175#538—24no—
176#537—22no—
177#537—22no—
178#537C2×C414yes—
179#536—22no—
180#536—22no—
181#535—22no—
182#535—22no—
183#535C2×C414yes—
184#535C2×C414yes—
185#534—24no—
186#534—22no—
187#534—22no—
188#534—22no—
189#533C2×C411yescharacteristic
190#533D411yescharacteristic
191#533D411yescharacteristic
192#532—22no—
193#532—24no—
194#532—21no—
195#532—21no—
196#532—21no—
197#532—21no—
198#532C2×C412yes—
199#532C2×C412yes—
200#532C2×C411yescharacteristic
201#532D411yescharacteristic
202#532D411yescharacteristic
203#532C2312yes—
204#532C2312yes—
205#532C2314yes—
206C2×C4⋊Q8C2×C411yescharacteristic
207C2×#127C2×C411yescharacteristic
208#529—24no—
209#529—24no—
210#529—24no—
211#529—21no—
212#529—21no—
213#529—21no—
214#529—21no—
215#529C2×C412yes—
216#529C2×C412yes—
217#529C2×C412yes—
218#529C2×C412yes—
219#529D412yes—
220#529D412yes—
221#529D412yes—
222#529D412yes—
223#529C2312yes—
224#529C2312yes—
225#529C2314yes—
226C2×#126—21no—
227C2×#125C2×C411yescharacteristic
228C2×#124—21no—
229C2×#124C2×C411yescharacteristic
230#525—24no—
231#525—24no—
232#525—24no—
233#525—24no—
234#525—22no—
235#525—24no—
236#525C2×C412yes—
237#525D412yes—
238#525D412yes—
239C2×#123—21no—
240C2×C22⋊Q8C2×C411yescharacteristic
241C2×#121—21no—
242C2×#121C2×C411yescharacteristic
243C2×#121C2×C412yes—
244C4×#41—22no—
245C4×#41C2314yes—
246C4×#41C2312yes—
247C4×#41C2312yes—
248C4×#41C2312yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4—21no—
251C2×C4×D4—24no—
252C2×C4×D4—21no—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×#117—21no—
257C22×C42C2311yescharacteristic
258#446—24no—
259#446—24no—
260#446—22no—
261#446—24no—
262C8×Q8—22no—
263#436—24no—
264#436—24no—
265#436—22no—
266#435—24no—
267#435—24no—
268#435—24no—
269#435—24no—
270#435—24no—
271#435—24no—
272#435—24no—
273C8×D4—24no—
274C8×D4—22no—
275C8×D4—24no—
276#433—24no—
277#433—24no—
278#433—24no—
279#432—21no—
280#432—21no—
281#432—21no—
282#432—21no—
283#432C2312yes—
284#432C2312yes—
285#432C2314yes—
286#431—21no—
287#431—21no—
288#431C2312yes—
289#431C2311yescharacteristic
290#431C2311yescharacteristic
291#431C2314yes—
292#431C2312yes—
293#431C2312yes—
294#431C2314yes—
295#431C2314yes—
296#424—22no—
297#423—21no—
298#423C2314yes—
299C2×C4⋊C8C2312yes—
300C2×C4⋊C8C2312yes—
301C2×C4⋊C8C2314yes—
302#408—22no—
303#408—24no—
304#407—21no—
305C2×C22⋊C8—21no—
306C2×C22⋊C8—21no—
307#405—22no—
308#405—24no—
309#405—24no—
310C4×M16—21no—
311C4×M16—21no—
312C4×M16C2312yes—
313C4×M16C2312yes—
314C4×M16C2312yes—
315C4×M16C2314yes—
316C2×#97—21no—
317C2×#97—21no—
318C2×C4×C8—21no—
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2314yes—
322Q8⋊C8C2314yes—
323Q8⋊C8C2314yes—
324Q8⋊C8C2314yes—
325Q8⋊C8C2314yes—
326D4⋊C8C2314yes—
327D4⋊C8C2314yes—
328D4⋊C8C2314yes—
329D4⋊C8C2314yes—
330D4⋊C8C2314yes—
331D4⋊C8C2314yes—
332D4⋊C8C2314yes—
333D4⋊C8C2314yes—
334D4⋊C8C2314yes—
335D4⋊C8C2314yes—
336D4⋊C8C2314yes—
337D4⋊C8C2314yes—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—24no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—24no—
345C2×#41—22no—
346C2×#41—84no—
347C2×#41—88no—
348C2×#41C22×C414yes—
349C2×#41C22×C412yes—
350C2×#41C2×D412yes—
351C2×#41C2×D412yes—
352C22×Q8—22no—
353C22×Q8—21no—
354C22×Q8C22×C411yescharacteristic
355C22×D4—21no—
356C22×D4—22no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—22no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4C22×C411yescharacteristic
363C22×D4C22×C412yes—
364C22×D4C22×C414yes—
365C23×C4—21no—
366C23×C4—22no—
367C23×C4—24no—
368C23×C4C22×C411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D411yescharacteristic
371#131—48no—
372C2×M16—22no—
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—24no—
376C2×M16—24no—
377C2×M16—44no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—24no—
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—24no—
384C4⋊Q8—22no—
385C4⋊Q8—24no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8C22⋊C411yescharacteristic
389C4⋊Q8C22⋊C411yescharacteristic
390C4⋊Q8C22⋊C411yescharacteristic
391C4⋊Q8C22×C412yes—
392C4⋊Q8C22×C412yes—
393C4⋊Q8C22×C414yes—
394#127—22no—
395#127—24no—
396#127—21no—
397#127—21no—
398#127C22⋊C411yescharacteristic
399#127C22×C412yes—
400#127C22×C412yes—
401#127C22×C414yes—
402#126—24no—
403#126—24no—
404#126—24no—
405#126—24no—
406#126—24no—
407#126—24no—
408#126—22no—
409#126—22no—
410#126—22no—
411#126—22no—
412#126—24no—
413#126C22⋊C414yes—
414#126C22⋊C414yes—
415#125—24no—
416#125—24no—
417#125—24no—
418#125—21no—
419#125—21no—
420#125C22⋊C412yes—
421#125C22⋊C412yes—
422#125C22⋊C412yes—
423#125C22×C412yes—
424#125C22×C412yes—
425#125C22×C414yes—
426#124—24no—
427#124—24no—
428#124—22no—
429#124—22no—
430#124—24no—
431#124—24no—
432#124—24no—
433#124—22no—
434#124—22no—
435#124—21no—
436#124—21no—
437#124—22no—
438#124—22no—
439#124—24no—
440#124C22⋊C412yes—
441#124C22⋊C412yes—
442#124C22⋊C412yes—
443#124C22×C412yes—
444#124C22×C412yes—
445#124C22×C414yes—
446#123—22no—
447#123—22no—
448#123—22no—
449#123—22no—
450#123—24no—
451#123—24no—
452#123—24no—
453#123—24no—
454#123—24no—
455#123—24no—
456#123—24no—
457#123—24no—
458#123—24no—
459#123—24no—
460#123—24no—
461#123—24no—
462#123—24no—
463#123—24no—
464#123—24no—
465#123—24no—
466#123—24no—
467#123—24no—
468#123C22⋊C414yes—
469#123C22⋊C414yes—
470#123C22⋊C414yes—
471C22⋊Q8—24no—
472C22⋊Q8—24no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—24no—
476C22⋊Q8—24no—
477C22⋊Q8—24no—
478C22⋊Q8—24no—
479C22⋊Q8—24no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8—24no—
483C22⋊Q8—24no—
484C22⋊Q8—24no—
485C22⋊Q8—24no—
486C22⋊Q8—24no—
487C22⋊Q8—24no—
488C22⋊Q8C22⋊C412yes—
489C22⋊Q8C22⋊C412yes—
490C22⋊Q8C22⋊C412yes—
491C22⋊Q8C22⋊C412yes—
492C22⋊Q8C22⋊C412yes—
493C22⋊Q8C22⋊C412yes—
494C22⋊Q8C22×C412yes—
495C22⋊Q8C22×C412yes—
496C22⋊Q8C22×C414yes—
497#121—24no—
498#121—24no—
499#121—24no—
500#121—24no—
501#121—24no—
502#121—24no—
503#121—24no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—21no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—24no—
513#121—24no—
514#121—24no—
515#121—22no—
516#121—22no—
517#121—24no—
518#121—24no—
519#121—24no—
520#121—24no—
521#121—24no—
522#121—24no—
523#121—24no—
524#121—24no—
525#121—24no—
526#121—24no—
527#121C22⋊C412yes—
528#121C22⋊C412yes—
529#121C22⋊C412yes—
530#121C22⋊C412yes—
531#121C22⋊C412yes—
532#121C22⋊C412yes—
533#121C22×C412yes—
534#121C22×C412yes—
535#121C22×C414yes—
536#121C22×C414yes—
537#121C22×C414yes—
538#121C22×C414yes—
539#121C22×C414yes—
540#120—24no—
541#120—24no—
542#120—24no—
543#120—24no—
544#120—24no—
545#120—24no—
546#120—24no—
547#120—24no—
548#120—24no—
549#120—24no—
550#120—24no—
551#120C22⋊C414yes—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—21no—
555C4×Q8—21no—
556C4×Q8C22×C412yes—
557C4×Q8C22×C414yes—
558C4×Q8C22×C412yes—
559C4×Q8C22×C412yes—
560C4×Q8C2×D412yes—
561C4×Q8C2×D412yes—
562C4×Q8C2×D412yes—
563C4×Q8C2×D412yes—
564C4×Q8C2412yes—
565C4×D4—24no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—24no—
570C4×D4—22no—
571C4×D4—24no—
572C4×D4—24no—
573C4×D4—24no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—24no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—24no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—24no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—21no—
586C4×D4—24no—
587C4×D4—22no—
588C4×D4—21no—
589C4×D4—22no—
590C4×D4—24no—
591C4×D4C22×C412yes—
592C4×D4C22×C414yes—
593C4×D4C22×C414yes—
594C4×D4C22×C414yes—
595C4×D4C22×C414yes—
596C4×D4C22×C414yes—
597C4×D4C22×C414yes—
598C4×D4C22×C412yes—
599C4×D4C22×C412yes—
600C4×D4C2×D414yes—
601C4×D4C2×D412yes—
602C4×D4C2×D412yes—
603C4×D4C2×D414yes—
604C4×D4C2×D414yes—
605C4×D4C2×D414yes—
606C4×D4C2×D412yes—
607C4×D4C2×D412yes—
608C4×D4C2412yes—
609C4×D4C2414yes—
610#117—22no—
611#117—22no—
612#117—22no—
613#117—22no—
614#117—24no—
615#117—24no—
616#117C22×C414yes—
617#117C22×C412yes—
618#117C22×C414yes—
619#117C2×D412yes—
620#117C2×D414yes—
621#117C2×D412yes—
622#117C2×D414yes—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4C22×C412yes—
630C2×C4⋊C4C22×C411yescharacteristic
631C2×C4⋊C4C22×C414yes—
632C2×C4⋊C4C22×C411yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C42—21no—
644C2×C42—24no—
645C2×C42C22×C411yescharacteristic
646C2×C42C22×C411yescharacteristic
647C2×C42C22×C411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2414yes—
657C2×C42C2411yescharacteristic
658C4⋊C8—22no—
659C4⋊C8—22no—
660C4⋊C8—24no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—24no—
664C4⋊C8—24no—
665C4⋊C8—24no—
666C4⋊C8C2412yes—
667C4⋊C8C2414yes—
668C4⋊C8C2412yes—
669C22⋊C8—22no—
670C22⋊C8—22no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8—22no—
674C22⋊C8—22no—
675C22⋊C8—22no—
676C22⋊C8—24no—
677C22⋊C8—24no—
678C22⋊C8—24no—
679C22⋊C8—24no—
680#97—22no—
681#97—22no—
682#97—22no—
683#97—22no—
684#97—22no—
685#97—24no—
686#97—24no—
687C4×C8—22no—
688C4×C8—21no—
689C4×C8—21no—
690C4×C8—21no—
691C4×C8—21no—
692C4×C8—24no—
693C4×C8—24no—
694C4×C8C2412yes—
695C4×C8C2412yes—
696C4×C8C2414yes—
697C24—21no—
698C24—22no—
699C24—24no—
700C24C2×C22⋊C411yescharacteristic
701#41—44no—
702#41—44no—
703#41—44no—
704#41—48no—
705#41—48no—
706#41—84no—
707#41—84no—
708#41—84no—
709#41—84no—
710#41—88no—
711#41—84no—
712#41—84no—
713#41—84no—
714C2×Q8—22no—
715C2×Q8—21no—
716C2×Q8—24no—
717C2×Q8—22no—
718C2×Q8—42no—
719C2×Q8—82no—
720C2×Q8—84no—
721C2×Q8C2×C22⋊C412yes—
722C2×Q8C2×C22⋊C412yes—
723C2×Q8C2×C22⋊C412yes—
724C2×Q8C23×C412yes—
725C2×D4—22no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—22no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—22no—
734C2×D4—21no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—24no—
741C2×D4—22no—
742C2×D4—44no—
743C2×D4—42no—
744C2×D4—48no—
745C2×D4—82no—
746C2×D4—82no—
747C2×D4—84no—
748C2×D4—88no—
749C2×D4—82no—
750C2×D4—88no—
751C2×D4—84no—
752C2×D4C2×C22⋊C414yes—
753C2×D4C2×C22⋊C412yes—
754C2×D4C2×C22⋊C414yes—
755C2×D4C2×C22⋊C412yes—
756C2×D4C2×C22⋊C412yes—
757C2×D4C2×C22⋊C414yes—
758C2×D4C23×C412yes—
759C2×D4C23×C414yes—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—24no—
765C22×C4—22no—
766C22×C4—24no—
767C22×C4—22no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—44no—
777C22×C4—82no—
778C22×C4—82no—
779C22×C4—84no—
780C22×C4—84no—
781C22×C4C2×C22⋊C411yescharacteristic
782C22×C4C2×C22⋊C411yescharacteristic
783C22×C4C2×C22⋊C411yescharacteristic
784C22×C4C2×C22⋊C411yescharacteristic
785C22×C4C2×C22⋊C411yescharacteristic
786C22×C4C2×C22⋊C411yescharacteristic
787C22×C4C2×C22⋊C411yescharacteristic
788C22×C4C2×C22⋊C411yescharacteristic
789C22×C4C2×C22⋊C411yescharacteristic
790C22×C4C23×C411yescharacteristic
791C22×C4C23×C411yescharacteristic
792C22×C4C23×C411yescharacteristic
793C22×C4C23×C414yes—
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D414yes—
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D414yes—
802M16—44no—
803M16—44no—
804M16—48no—
805M16—44no—
806M16—84no—
807C2×C8—24no—
808C2×C8—22no—
809C2×C8—22no—
810C2×C8—24no—
811C2×C8—22no—
812C2×C8—22no—
813C2×C8—24no—
814C2×C8—48no—
815C2×C8—42no—
816C2×C8—84no—
817C2×C8—82no—
818C2×C8—82no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—24no—
827C4⋊C4—22no—
828C4⋊C4—24no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—24no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—22no—
838C4⋊C4C2×C22⋊C414yes—
839C4⋊C4C2×C22⋊C414yes—
840C4⋊C4C2×C22⋊C414yes—
841C4⋊C4C2×C22⋊C412yes—
842C4⋊C4C2×C22⋊C412yes—
843C4⋊C4C2×C22⋊C412yes—
844C4⋊C4C2×C22⋊C412yes—
845C4⋊C4C2×C22⋊C414yes—
846C4⋊C4C2×C22⋊C414yes—
847C4⋊C4C2×C22⋊C412yes—
848C4⋊C4C2×C22⋊C414yes—
849C4⋊C4C2×C22⋊C412yes—
850C4⋊C4C23×C412yes—
851C4⋊C4C23×C414yes—
852C4⋊C4C23×C412yes—
853C22⋊C4—22no—
854C22⋊C4—24no—
855C22⋊C4—22no—
856C22⋊C4—24no—
857C22⋊C4—22no—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—22no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—22no—
876C22⋊C4—24no—
877C22⋊C4C2×C22⋊C414yes—
878C22⋊C4C2×C22⋊C414yes—
879C22⋊C4C2×C22⋊C414yes—
880C22⋊C4C2×C22⋊C414yes—
881C22⋊C4C2×C22⋊C414yes—
882C22⋊C4C2×C22⋊C414yes—
883C22⋊C4C2×C22⋊C414yes—
884C22⋊C4C2×C22⋊C414yes—
885C22⋊C4C2×C22⋊C414yes—
886C42—22no—
887C42—24no—
888C42—24no—
889C42—22no—
890C42C2×C22⋊C411yescharacteristic
891C42C2×C22⋊C411yescharacteristic
892C42C2×C22⋊C411yescharacteristic
893C42C2×C22⋊C411yescharacteristic
894C42C2×C22⋊C411yescharacteristic
895C42C2×C22⋊C411yescharacteristic
896C42C23×C411yescharacteristic
897C42C23×C411yescharacteristic
898C42C23×C411yescharacteristic
899C42C23×C414yes—
900C42C22×D411yescharacteristic
901C42C22×D414yes—
902C42C22×D411yescharacteristic
903C42C22×D411yescharacteristic
904C42C22×D411yescharacteristic
905C42C22×D411yescharacteristic
906C42C22×D414yes—
907C42C22×D411yescharacteristic
908C42C2511yescharacteristic
909C23—22no—
910C23—22no—
911C23—24no—
912C23—41no—
913C23—41no—
914C23—42no—
915C23—44no—
916C23—82no—
917C23—84no—
918C23—82no—
919C23—81no—
920C23—84no—
921C23—81no—
922C23—84no—
923C23C22×C22⋊C414yes—
924C23C22×C22⋊C411yescharacteristic
925C23C22×C22⋊C411yescharacteristic
926C23C22×C22⋊C411yescharacteristic
927Q8—24no—
928Q8—42no—
929Q8—42no—
930Q8—42no—
931Q8—44no—
932Q8—81no—
933Q8—82no—
934Q8—84no—
935D4—28no—
936D4—24no—
937D4—28no—
938D4—42no—
939D4—44no—
940D4—42no—
941D4—44no—
942D4—42no—
943D4—44no—
944D4—48no—
945D4—44no—
946D4—82no—
947D4—81no—
948D4—84no—
949D4—82no—
950D4—82no—
951D4—84no—
952D4—82no—
953D4—84no—
954D4—82no—
955D4—84no—
956D4—84no—
957D4—84no—
958D4—84no—
959D4—84no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—28no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—44no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—44no—
987C2×C4—42no—
988C2×C4—44no—
989C2×C4—44no—
990C2×C4—44no—
991C2×C4—84no—
992C2×C4—84no—
993C2×C4—84no—
994C2×C4—84no—
995C2×C4—84no—
996C2×C4—82no—
997C2×C4—84no—
998C2×C4—81no—
999C2×C4—81no—
1000C2×C4C22×C22⋊C411yescharacteristic
1001C2×C4C22×C22⋊C414yes—
1002C2×C4C22×C22⋊C414yes—
1003C2×C4C22×C22⋊C411yescharacteristic
1004C2×C4C22×C22⋊C411yescharacteristic
1005C2×C4C22×C22⋊C411yescharacteristic
1006C2×C4C22×C22⋊C411yescharacteristic
1007C2×C4C22×C22⋊C411yescharacteristic
1008C2×C4C22×C22⋊C411yescharacteristic
1009C2×C4C22×C22⋊C411yescharacteristic
1010C2×C4C22×C22⋊C411yescharacteristic
1011C2×C4C22×C22⋊C414yes—
1012C2×C4C24×C411yescharacteristic
1013C2×C4C23×D411yescharacteristic
1014C2×C4C23×D411yescharacteristic
1015C8—24no—
1016C8—44no—
1017C8—42no—
1018C8—42no—
1019C8—44no—
1020C8—42no—
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—24no—
1026C22—21no—
1027C22—21no—
1028C22—24no—
1029C22—21no—
1030C22—21no—
1031C22—24no—
1032C22—44no—
1033C22—42no—
1034C22—42no—
1035C22—44no—
1036C22—44no—
1037C22—42no—
1038C22—82no—
1039C22—164no—
1040C22—162no—
1041C22—168no—
1042C22#290112yes—
1043C22C23×C22⋊C411yescharacteristic
1044C4—21no—
1045C4—21no—
1046C4—21no—
1047C4—24no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—24no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—21no—
1056C4—24no—
1057C4—42no—
1058C4—42no—
1059C4—44no—
1060C4—42no—
1061C4#357312yes—
1062C4#358512yes—
1063C2—22no—
1064C2—41no—
1065C2—41no—
1066C2—44no—
1067C2—84no—
1068C2—82no—
1069C2#6006511yescharacteristic
1070C2#6008711yescharacteristic
1071C2C2×#290111yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62748C2
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. #60294C2semidirect
3. #60205C2semidirect
4. #17521C2semidirect
5. #17517C2semidirect
6. #17516C2semidirect
7. #17511C2semidirect
8. #17505C2semidirect
9. #17502C2semidirect
10. #17495C2semidirect
11. #17468C2semidirect
12. #17465C2semidirect
13. C2×#1484C2semidirect
39. #2990C22semidirect
40. #2989C22semidirect
41. #2988C22semidirect
49. #2965C22semidirect
50. #2965C22semidirect
54. #2925C22semidirect
55. #2922C22semidirect
56. #2920C22semidirect
57. C2×#432C22semidirect
58. C2×#431C22semidirect
59. C4×#131C22semidirect
60. C2×C4×M16C22semidirect
61. #1496C22semidirect
62. #1496C22semidirect
63. #1495C22semidirect
64. #1494C22semidirect
65. #1494C22semidirect
66. #1494C22semidirect
67. #1492C22semidirect
68. #1491C22semidirect
69. #1490C22semidirect
70. #1490C22semidirect
71. #1490C22semidirect
72. #1489C22semidirect
73. #1488C22semidirect
74. #1486C22semidirect
75. #1484C22semidirect
76. #1484C22semidirect
77. #1484C22semidirect
78. #1484C22semidirect
79. #1483C22semidirect
80. #1483C22semidirect
81. #1483C22semidirect
82. #1482C22semidirect
83. #1482C22semidirect
84. #1482C22semidirect
85. #1480C22semidirect
86. #1480C22semidirect
87. #1479C22semidirect
88. #1478C22semidirect
89. #1478C22semidirect
90. #1477C22semidirect
91. #1476C22semidirect
92. C2×D4⋊C8C22semidirect
93. C2×D4⋊C8C22semidirect
94. C2×D4⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#627482
#602942
#602052
#175212
#175172
#175162
#175112
#175052
#175022
#174952
#174682
#174652
C2×#14842