Finite Group Databasebeta

← #10579246

Subgroups — #10579246

Order 512.

6838 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62836C212yesmaximal, complemented
2#62434C2116yesmaximal, complemented
3#62427C218yesmaximal, complemented
4#62418C214yesmaximal, complemented
5#62417C214yesmaximal, complemented
6#61413C214yesmaximal, complemented
7#61090C214yesmaximal, complemented
8#61054C214yesmaximal, complemented
9#61051C214yesmaximal, complemented
10#60820C212yesmaximal, complemented
11#60818C212yesmaximal, complemented
12#60801C212yesmaximal, complemented
13#60715C211yesmaximal, characteristic, complemented
14#60714C211yesmaximal, characteristic, complemented
15#60673C211yesmaximal, characteristic, complemented
16#60648C211yesmaximal, characteristic, complemented
17#60647C211yesmaximal, characteristic, complemented
18C2×#3147C211yesmaximal, characteristic, complemented
19#60204C211yesmaximal, characteristic, complemented
20C2×#578C2214yescomplemented
21C2×#576C2214yes—
22C22×#135C2214yescomplemented
23#3562C22116yescomplemented
24#3554—24no—
25#3546—24no—
26#3542—28no—
27#3517—24no—
28#3514—24no—
29#3513—28no—
30#3511C2218yescomplemented
31#3510C2214yescomplemented
32#3509C2212yes—
33#3508C2218yescomplemented
34#3508C2212yescomplemented
35#3500C2214yes—
36#3499C2212yescomplemented
37#3498C2212yes—
38#3487C2214yescomplemented
39#3485C2214yes—
40#3444C2211yescharacteristic
41#3444C2212yescomplemented
42C2×#532C2212yescomplemented
43#3401C22132yescomplemented
44#3396C22116yescomplemented
45#3393C22116yescomplemented
46#3287C22116yescomplemented
47#3285C22116yescomplemented
48#3285C22116yescomplemented
49#3283C22116yescomplemented
50#3280C22116yescomplemented
51#3280C22116yescomplemented
52#3275C22132yescomplemented
53#3271C22132yescomplemented
54#3267C22132yescomplemented
55#3222C22116yescomplemented
56#3221C22116yescomplemented
57#3219C22116yescomplemented
58#3210C2218yescomplemented
59#3210C2218yescomplemented
60#3208C2218yescomplemented
61#3207C2218yescomplemented
62#3207C2218yescomplemented
63#3206C2218yescomplemented
64#3185C2214yescomplemented
65#3184C2214yescomplemented
66#3177C2218yescomplemented
67#3176C2218yescomplemented
68#3170C2212yescomplemented
69#3170C2214yescomplemented
70#3169C2212yescomplemented
71#3169C2214yescomplemented
72#3168C2218yescomplemented
73#3167C2214yescomplemented
74#3160C2211yescharacteristic, complemented
75#3156C2214yescomplemented
76#3156C2218yescomplemented
77#3155C2214yes—
78#3155C2218yescomplemented
79#3152C2212yescomplemented
80#3152C2214yescomplemented
81#3151C2212yes—
82#3151C2214yescomplemented
83#3147C2211yescharacteristic
84#3147C2212yescomplemented
85#3147C2214yescomplemented
86#3147C2212yescomplemented
87#3147C2214yescomplemented
88#3147C2218yescomplemented
89C2×#495C2214yescomplemented
90C2×#494C2211yescharacteristic, complemented
91C2×#494C2212yescomplemented
92C2×#493C2211yescharacteristic
93C2×#493C2212yescomplemented
94C2×#492C2212yescomplemented
95#3139C2212yescomplemented
96#3138C2212yescomplemented
97#3131C2212yescomplemented
98#3059C2214yes—
99#3058C2214yescomplemented
100#3050C2214yescomplemented
101#3043C2218yescomplemented
102#3042C2218yescomplemented
103#3040C2218yescomplemented
104#3010C2218yescomplemented
105#3009C2218yes—
106#3005C2218yescomplemented
107#2966C2218yescomplemented
108#2965C2214yescomplemented
109C8×#41C2214yescomplemented
110#2960C2212yescomplemented
111#2950C2214yescomplemented
112#2948C2214yescomplemented
113C4×#135C2214yescomplemented
114#2931C2212yes—
115#2929C2212yes—
116#2929C2212yescomplemented
117#2922C2211yescharacteristic
118#2922C2211yescharacteristic, complemented
119#2920C2211yescharacteristic, complemented
120C4×#131C2211yescharacteristic
121C4×#131C2211yescharacteristic, complemented
122C22×C4×C8C2211yescharacteristic, complemented
123C2×2−1+4C2314yes—
124C2×H(5,𝔽2)C2314yes—
125C22×#41C2314yes—
126#578—416no—
127#576—416no—
128C2×#137C2318yes—
129C2×#137C23116yes—
130C2×AGL(1,ℤ/8)C2318yes—
131C2×AGL(1,ℤ/8)C23116yes—
132C2×#135—416no—
133C2×#135C2314yes—
134C2×#135C23116yes—
135C2×#135C23116yes—
136C2×#135C2318yes—
137C2×#135C2318yes—
138C22×Q16C2314yes—
139C22×Q16C2318yes—
140C22×SD16C2318yes—
141C22×D8C2314yes—
142C22×D8C2318yes—
143C2×#131C2312yes—
144C2×#131C2312yes—
145C23×C8C2312yes—
146#562—216no—
147#560—216no—
148#559—28no—
149#559—24no—
150#559C23116yes—
151#557—24no—
152#556—24no—
153#556C23116yes—
154#555—28no—
155#554—28no—
156#553—216no—
157#553—28no—
158#553—28no—
159#552—28no—
160#551—216no—
161#551—216no—
162#550—28no—
163#550—24no—
164#550—28no—
165#550—24no—
166#550C23116yes—
167D4×Q8—24no—
168#548—28no—
169#548C23116yes—
170#548C23116yes—
171#547—28no—
172#547—28no—
173#547—24no—
174#547C23116yes—
175#546—28no—
176#546—216no—
177#546—28no—
178#546—28no—
179#546—28no—
180#546C23116yes—
181#546C23116yes—
182D42—28no—
183D42—24no—
184#542—28no—
185#542—28no—
186#542—28no—
187#541C2318yes—
188#540—216no—
189#540—28no—
190#540—28no—
191#540C2318yes—
192#539—216no—
193#538—216no—
194#538—216no—
195#537—28no—
196#536—24no—
197#536C2318yes—
198#536C2314yes—
199#536C2314yes—
200#535—28no—
201#535—24no—
202#535—28no—
203#535C2314yes—
204#535C2318yes—
205#535C2314yes—
206#534—28no—
207#533D412yes—
208#533C2314yes—
209#533C2318yes—
210#533C2312yes—
211#533C2311yescharacteristic
212#532—24no—
213#532—24no—
214#532—24no—
215#532D412yes—
216#532C2312yes—
217#532C2318yes—
218#532C2318yes—
219#532C2314yes—
220#532C2314yes—
221#532C2314yes—
222#532C2318yes—
223#532C2311yescharacteristic
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2314yes—
226C2×#127C2312yes—
227C2×#127C2314yes—
228#529—28no—
229#529—24no—
230#529—24no—
231#529D414yes—
232#529D412yes—
233#529D412yes—
234#529C2318yes—
235#529C2314yes—
236C2×#124—24no—
237C2×#124C2314yes—
238#525—24no—
239#525—28no—
240#525D414yes—
241#525C2314yes—
242#525C2311yescharacteristic
243#525C2311yescharacteristic
244C2×#123—28no—
245C2×#121—24no—
246#520—28no—
247#519C2314yes—
248#518—28no—
249#518C2314yes—
250C4×#41—24no—
251C4×#41C2314yes—
252C4×#41C2314yes—
253C4×#41C2311yescharacteristic
254C4×#41C2311yescharacteristic
255C2×C4×D4—24no—
256C22×C42C2311yescharacteristic
257#500C2312yes—
258#499C2314yes—
259#498C2312yes—
260#497C23116yes—
261#497C2318yes—
262#496C23116yes—
263#496C2318yes—
264#495C2318yes—
265#495C23116yes—
266#495C2318yes—
267#495C23116yes—
268#495C2314yes—
269#494C2318yes—
270#494C2311yescharacteristic
271#494C2312yes—
272#494C2312yes—
273#494C2314yes—
274#494C2314yes—
275#493C2318yes—
276#493C2312yes—
277#493C2312yes—
278#493C2314yes—
279#493C2311yescharacteristic
280#493C2314yes—
281#492C2318yes—
282#492C2318yes—
283#492C2312yes—
284#492C2314yes—
285#492C2314yes—
286#491C2318yes—
287#490C2318yes—
288#488C2318yes—
289#487C2314yes—
290#487C2318yes—
291#486C2314yes—
292#486C2318yes—
293#470C23116yes—
294#469C23116yes—
295#467C2318yes—
296#467C23116yes—
297#466C2318yes—
298#466C23116yes—
299#465C23116yes—
300#464C23132yes—
301#464C23132yes—
302#463C23132yes—
303#463C23132yes—
304#461C23132yes—
305#460C23132yes—
306#452C23132yes—
307#452C23132yes—
308#450C23132yes—
309#449C23132yes—
310#449C23132yes—
311#448C23132yes—
312#446C2318yes—
313C8×Q8C2318yes—
314#442C23116yes—
315#441C23116yes—
316C4×Q16C2318yes—
317C4×Q16C23116yes—
318C4×SD16C23116yes—
319C4×D8C23116yes—
320C4×D8C2318yes—
321#436C2318yes—
322#435C2318yes—
323#435C2318yes—
324C8×D4C2318yes—
325C8×D4C2318yes—
326C8×D4C2318yes—
327#433C2314yes—
328#433C2314yes—
329#432C2314yes—
330#431C2314yes—
331#431C2314yes—
332#431C2314yes—
333#427C2314yes—
334#424C2312yes—
335#424C2312yes—
336#423C2312yes—
337#419C2318yes—
338#418C2318yes—
339#416C2318yes—
340#408C2312yes—
341#408C2312yes—
342#407C2312yes—
343#405C2312yes—
344#405C2314yes—
345#405C2314yes—
346#405C2312yes—
347C4×M16C2311yescharacteristic
348C4×M16C2312yes—
349C4×M16C2311yescharacteristic
350C4×M16C2312yes—
351C2×C4×C8C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353C2×C4×C8C2312yes—
354C2×C4×C8C2312yes—
355C2×C4×C8C2314yes—
356C2×C4×C8C2312yes—
357C2×C4×C8C2312yes—
358C2×C4×C8C2312yes—
3592−1+4—416no—
360H(5,𝔽2)—416no—
361C2×#41—24no—
362C2×#41—28no—
363C2×#41—24no—
364C2×#41—24no—
365C2×#41—28no—
366C2×#41—28no—
367C2×#41—416no—
368C2×#41C2×D414yes—
369C2×#41C2414yes—
370C2×#41C24116yes—
371C2×#41C2418yes—
372C2×#41C2418yes—
373C2×#41C2411yescharacteristic
374C2×#41C2411yescharacteristic
375C22×Q8—24no—
376C22×Q8C2414yes—
377C22×Q8C2418yes—
378C22×D4—24no—
379C22×D4—28no—
380C22×D4—24no—
381C22×D4—24no—
382C22×D4—28no—
383C22×D4C2414yes—
384C22×D4C2418yes—
385C23×C4—24no—
386C23×C4C2×D412yes—
387C23×C4C2411yescharacteristic
388#137—432no—
389#137—416no—
390AGL(1,ℤ/8)—432no—
391AGL(1,ℤ/8)—416no—
392#135—216no—
393#135—432no—
394#135—432no—
395#135—416no—
396#135—416no—
397C2×Q16—216no—
398C2×Q16—416no—
399C2×Q16C2418yes—
400C2×Q16C2414yes—
401C2×Q16C2418yes—
402C2×Q16C24116yes—
403C2×SD16—416no—
404C2×SD16C2418yes—
405C2×SD16C24132yes—
406C2×SD16C24116yes—
407C2×SD16C24116yes—
408C2×D8—216no—
409C2×D8—416no—
410C2×D8C2418yes—
411C2×D8C2414yes—
412C2×D8C2418yes—
413C2×D8C24116yes—
414#131—28no—
415#131—28no—
416C2×M16C2412yes—
417C2×M16C2414yes—
418C2×M16C2412yes—
419C2×M16C2414yes—
420C22×C8—28no—
421C22×C8C2412yes—
422C22×C8C2414yes—
423C22×C8C2414yes—
424C22×C8C2414yes—
425C22×C8C2414yes—
426C22×C8C2412yes—
427C4⋊Q8—24no—
428C4⋊Q8—24no—
429C4⋊Q8—28no—
430C4⋊Q8C2×D412yes—
431C4⋊Q8C2×D411yescharacteristic
432C4⋊Q8C2414yes—
433C4⋊Q8C2412yes—
434C4⋊Q8C2414yes—
435C4⋊Q8C2418yes—
436C4⋊Q8C2414yes—
437#127—24no—
438#127—216no—
439#127—24no—
440#127—28no—
441#127C2×D411yescharacteristic
442#127C2414yes—
443#127C2412yes—
444#127C2414yes—
445#127C2418yes—
446#126—216no—
447#126—216no—
448#126—216no—
449#126—28no—
450#126C2×D414yes—
451#126C2×D414yes—
452#125—216no—
453#125—24no—
454#125—28no—
455#125C2×D412yes—
456#125C2×D414yes—
457#125C2414yes—
458#124—24no—
459#124—216no—
460#124—24no—
461#124—216no—
462#124—216no—
463#124—24no—
464#124—24no—
465#124—24no—
466#124—28no—
467#124C2×D411yescharacteristic
468#124C2×D411yescharacteristic
469#124C2×D414yes—
470#124C24116yes—
471#124C2414yes—
472#124C2418yes—
473#124C2418yes—
474#123—28no—
475#123—24no—
476#123—28no—
477#123—216no—
478#123—216no—
479#123—216no—
480#123—216no—
481#123—216no—
482#123—28no—
483#123—216no—
484#123—216no—
485#123—216no—
486#123C2×D412yes—
487#123C2×D412yes—
488#123C2×D414yes—
489#123C2×D414yes—
490C22⋊Q8—216no—
491C22⋊Q8—24no—
492C22⋊Q8—24no—
493C22⋊Q8—28no—
494C22⋊Q8—216no—
495C22⋊Q8—28no—
496C22⋊Q8—216no—
497C22⋊Q8—216no—
498C22⋊Q8C2×D414yes—
499C22⋊Q8C2×D414yes—
500C22⋊Q8C2×D412yes—
501C22⋊Q8C2×D412yes—
502C22⋊Q8C2418yes—
503C22⋊Q8C24116yes—
504#121—216no—
505#121—216no—
506#121—216no—
507#121—28no—
508#121—28no—
509#121—28no—
510#121—28no—
511#121—24no—
512#121—24no—
513#121—28no—
514#121—28no—
515#121—28no—
516#121—28no—
517#121—216no—
518#121—216no—
519#121—216no—
520#121—216no—
521#121—216no—
522#121—216no—
523#121C2×D414yes—
524#121C2×D414yes—
525#121C2×D412yes—
526#121C2×D412yes—
527#121C2418yes—
528#121C24116yes—
529#120—24no—
530#120—28no—
531#120—216no—
532#120—216no—
533#120—28no—
534#120—216no—
535#120C2×D412yes—
536#120C2×D412yes—
537C4×Q8—28no—
538C4×Q8—24no—
539C4×Q8—24no—
540C4×Q8—28no—
541C4×Q8C2×D412yes—
542C4×Q8C2×D412yes—
543C4×Q8C2×D414yes—
544C4×Q8C2418yes—
545C4×Q8C24116yes—
546C4×Q8C2414yes—
547C4×D4—28no—
548C4×D4—28no—
549C4×D4—28no—
550C4×D4—216no—
551C4×D4—216no—
552C4×D4—28no—
553C4×D4—216no—
554C4×D4—216no—
555C4×D4—28no—
556C4×D4—28no—
557C4×D4—28no—
558C4×D4—28no—
559C4×D4—24no—
560C4×D4—24no—
561C4×D4—28no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4C2×D414yes—
565C4×D4C2×D414yes—
566C4×D4C2×D414yes—
567C4×D4C2×D414yes—
568C4×D4C2×D412yes—
569C4×D4C2×D414yes—
570C4×D4C2×D412yes—
571C4×D4C2418yes—
572C4×D4C24116yes—
573C4×D4C2414yes—
574C4×D4C2414yes—
575C4×D4C2414yes—
576#117—24no—
577#117—28no—
578#117—216no—
579#117—28no—
580#117—28no—
581#117—24no—
582#117C2×D414yes—
583#117C2×D414yes—
584#117C2×D414yes—
585#117C2414yes—
586#117C2411yescharacteristic
587#117C2411yescharacteristic
588#117C2412yes—
589#117C2412yes—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—28no—
592C2×C4⋊C4—216no—
593C2×C22⋊C4—28no—
594C2×C22⋊C4—216no—
595C2×C22⋊C4—216no—
596C2×C22⋊C4—28no—
597C2×C42—24no—
598C2×C42C2×D412yes—
599C2×C42C2×D412yes—
600C2×C42C2×D412yes—
601C2×C42C2411yescharacteristic
602C2×C42C2412yes—
603C2×C42C2412yes—
604C2×C42C2411yescharacteristic
605C2×C42C2412yes—
606C2×C42C2412yes—
607#107C2418yes—
608#106C2418yes—
609C4⋊C8C2418yes—
610C4⋊C8C2418yes—
611C4⋊C8C2418yes—
612#103C24116yes—
613#103C24132yes—
614#102C24116yes—
615#102C24132yes—
616C22⋊C8C2418yes—
617C22⋊C8C2418yes—
618C22⋊C8C2418yes—
619#97C2412yes—
620#97C2412yes—
621#97C2414yes—
622#97C2414yes—
623C4×C8C2411yescharacteristic
624C4×C8C2411yescharacteristic
625C4×C8C2412yes—
626C4×C8C2412yes—
627C4×C8C2412yes—
628C4×C8C2414yes—
629C4×C8C2414yes—
630C4×C8C2412yes—
631C4×C8C2412yes—
632C4×C8C2414yes—
633C4×C8C2414yes—
634C24—24no—
635C24—28no—
636C24C22×D411yescharacteristic
637#41—24no—
638#41—24no—
639#41—216no—
640#41—48no—
641#41—432no—
642#41—416no—
643#41—416no—
644#41—88no—
645#41—816no—
646#41—816no—
647#41—816no—
648#41—88no—
649#41—88no—
650C2×Q8—24no—
651C2×Q8—24no—
652C2×Q8—28no—
653C2×Q8—216no—
654C2×Q8—416no—
655C2×Q8—88no—
656C2×Q8C22×D411yescharacteristic
657C2×Q8C22×D411yescharacteristic
658C2×Q8C22×D414yes—
659C2×Q8C2514yes—
660C2×Q8C2518yes—
661C2×D4—24no—
662C2×D4—28no—
663C2×D4—216no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—216no—
667C2×D4—28no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—28no—
671C2×D4—216no—
672C2×D4—28no—
673C2×D4—216no—
674C2×D4—416no—
675C2×D4—88no—
676C2×D4—816no—
677C2×D4—88no—
678C2×D4—88no—
679C2×D4—816no—
680C2×D4C22×D412yes—
681C2×D4C22×D412yes—
682C2×D4C22×D411yescharacteristic
683C2×D4C22×D411yescharacteristic
684C2×D4C22×D414yes—
685C2×D4C22×D414yes—
686C2×D4C22×D414yes—
687C2×D4C2518yes—
688C2×D4C2514yes—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—28no—
692C22×C4—24no—
693C22×C4—28no—
694C22×C4—216no—
695C22×C4—28no—
696C22×C4—216no—
697C22×C4—28no—
698C22×C4—44no—
699C22×C4—88no—
700C22×C4C22×D412yes—
701C22×C4C22×D411yescharacteristic
702C22×C4C22×D412yes—
703C22×C4C22×D412yes—
704C22×C4C22×D412yes—
705C22×C4C22×D414yes—
706C22×C4C22×D414yes—
707C22×C4C22×D412yes—
708C22×C4C22×D412yes—
709C22×C4C22×D412yes—
710C22×C4C2512yes—
711C22×C4C2512yes—
712C22×C4C2512yes—
713C22×C4C2511yescharacteristic
714Q16—216no—
715Q16—216no—
716Q16—28no—
717Q16—416no—
718SD16—216no—
719SD16—432no—
720SD16—416no—
721SD16—416no—
722D8—216no—
723D8—216no—
724D8—28no—
725D8—416no—
726M16—24no—
727M16—24no—
728M16—28no—
729M16—28no—
730C2×C8—24no—
731C2×C8—28no—
732C2×C8—28no—
733C2×C8—28no—
734C2×C8—28no—
735C2×C8H(5,𝔽2)18yes—
736C2×C8C2514yes—
737C2×C8C2514yes—
738C2×C8C2514yes—
739C2×C8C2512yes—
740C2×C8C2512yes—
741C4⋊C4—28no—
742C4⋊C4—24no—
743C4⋊C4—28no—
744C4⋊C4—216no—
745C4⋊C4—28no—
746C4⋊C4—216no—
747C4⋊C4—24no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—216no—
751C4⋊C4C22×D414yes—
752C4⋊C4C22×D414yes—
753C4⋊C4C22×D414yes—
754C4⋊C4C22×D414yes—
755C4⋊C4C22×D414yes—
756C4⋊C4C22×D414yes—
757C4⋊C4C22×D412yes—
758C4⋊C4C22×D412yes—
759C4⋊C4C22×D414yes—
760C4⋊C4C22×D414yes—
761C4⋊C4C2518yes—
762C22⋊C4—24no—
763C22⋊C4—216no—
764C22⋊C4—28no—
765C22⋊C4—216no—
766C22⋊C4—28no—
767C22⋊C4—216no—
768C22⋊C4—216no—
769C22⋊C4—216no—
770C22⋊C4—216no—
771C22⋊C4—216no—
772C22⋊C4—28no—
773C22⋊C4—28no—
774C22⋊C4C22×D414yes—
775C22⋊C4C22×D414yes—
776C22⋊C4C22×D412yes—
777C22⋊C4C22×D412yes—
778C22⋊C4C22×D414yes—
779C22⋊C4C22×D414yes—
780C22⋊C4C22×D414yes—
781C22⋊C4C22×D414yes—
782C22⋊C4C22×D414yes—
783C22⋊C4C22×D414yes—
784C42—28no—
785C42—24no—
786C42—216no—
787C42C22×D411yescharacteristic
788C42C22×D412yes—
789C42C22×D411yescharacteristic
790C42C22×D412yes—
791C42C22×D412yes—
792C42C22×D412yes—
793C42C22×D412yes—
794C42C22×D414yes—
795C42C22×D414yes—
796C42C2511yescharacteristic
797C42C2511yescharacteristic
798C42C2512yes—
799C42C2512yes—
800C42C2512yes—
801C23—22no—
802C23—24no—
803C23—28no—
804C23—42no—
805C23—48no—
806C23—88no—
807C23—88no—
808C23—816no—
809C23C23×D412yes—
810C23C23×D412yes—
811C23C23×D412yes—
812C23C23×D411yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—28no—
816Q8—216no—
817Q8—44no—
818Q8—48no—
819Q8—48no—
820Q8—88no—
821D4—24no—
822D4—24no—
823D4—216no—
824D4—28no—
825D4—22no—
826D4—22no—
827D4—44no—
828D4—44no—
829D4—44no—
830D4—48no—
831D4—416no—
832D4—48no—
833D4—48no—
834D4—88no—
835D4—88no—
836D4—816no—
837D4—88no—
838D4—816no—
839D4—88no—
840D4—88no—
841D4—816no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—28no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—28no—
853C2×C4—24no—
854C2×C4—28no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—48no—
859C2×C4—48no—
860C2×C4—816no—
861C2×C4—88no—
862C2×C4—88no—
863C2×C4—88no—
864C2×C4—816no—
865C2×C4—88no—
866C2×C4C23×D412yes—
867C2×C4C23×D414yes—
868C2×C4C23×D412yes—
869C2×C4C23×D412yes—
870C2×C4C23×D412yes—
871C2×C4C23×D412yes—
872C2×C4C23×D412yes—
873C2×C4C23×D414yes—
874C2×C4C23×D412yes—
875C2×C4C23×D411yescharacteristic
876C2×C4C2×H(5,𝔽2)14yes—
877C2×C4C2611yescharacteristic
878C8—24no—
879C8—24no—
880C8—24no—
881C8C2×H(5,𝔽2)14yes—
882C8C2×H(5,𝔽2)14yes—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—24no—
890C22—24no—
891C22—44no—
892C22—44no—
893C22—48no—
894C22—416no—
895C22—48no—
896C22—168no—
897C22—328no—
898C22#349812yes—
899C22C24×D411yescharacteristic
900C4—22no—
901C4—22no—
902C4—22no—
903C4—22no—
904C4—22no—
905C4—22no—
906C4—24no—
907C4—24no—
908C4—44no—
909C4—48no—
910C4—48no—
911C4#349812yes—
912C4#358414yes—
913C4C22×H(5,𝔽2)12yes—
914C2—22no—
915C2—42no—
916C2—42no—
917C2—42no—
918C2—88no—
919C2—84no—
920C2C2×#349811yescharacteristic
921C2C2×#358412yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3444 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62836C2semidirect
2. #62434C2semidirect
3. #62427C2semidirect
4. #62418C2semidirect
5. #62417C2semidirect
6. #61413C2semidirect
7. #61090C2semidirect
8. #61054C2semidirect
9. #61051C2semidirect
10. #60820C2semidirect
11. #60818C2semidirect
12. #60801C2semidirect
13. #60715C2semidirect
14. #60714C2semidirect
15. #60673C2semidirect
16. #60648C2semidirect
17. #60647C2semidirect
18. C2×#3147C2semidirect
19. #60204C2semidirect
20. C2×#578C22semidirect
22. C22×#135C22semidirect
23. #3562C22semidirect
30. #3511C22semidirect
31. #3510C22semidirect
33. #3508C22semidirect
34. #3508C22semidirect
36. #3499C22semidirect
38. #3487C22semidirect
41. #3444C22semidirect
42. C2×#532C22semidirect
43. #3401C22semidirect
44. #3396C22semidirect
45. #3393C22semidirect
46. #3287C22semidirect
47. #3285C22semidirect
48. #3285C22semidirect
49. #3283C22semidirect
50. #3280C22semidirect
51. #3280C22semidirect
52. #3275C22semidirect
53. #3271C22semidirect
54. #3267C22semidirect
55. #3222C22semidirect
56. #3221C22semidirect
57. #3219C22semidirect
58. #3210C22semidirect
59. #3210C22semidirect
60. #3208C22semidirect
61. #3207C22semidirect
62. #3207C22semidirect
63. #3206C22semidirect
64. #3185C22semidirect
65. #3184C22semidirect
66. #3177C22semidirect
67. #3176C22semidirect
68. #3170C22semidirect
69. #3170C22semidirect
70. #3169C22semidirect
71. #3169C22semidirect
72. #3168C22semidirect
73. #3167C22semidirect
74. #3160C22semidirect
75. #3156C22semidirect
76. #3156C22semidirect
78. #3155C22semidirect
79. #3152C22semidirect
80. #3152C22semidirect
82. #3151C22semidirect
84. #3147C22semidirect
85. #3147C22semidirect
86. #3147C22semidirect
87. #3147C22semidirect
88. #3147C22semidirect
89. C2×#495C22semidirect
90. C2×#494C22semidirect
91. C2×#494C22semidirect
93. C2×#493C22semidirect
94. C2×#492C22semidirect
95. #3139C22semidirect
96. #3138C22semidirect
97. #3131C22semidirect
99. #3058C22semidirect
100. #3050C22semidirect
101. #3043C22semidirect
102. #3042C22semidirect
103. #3040C22semidirect
104. #3010C22semidirect
106. #3005C22semidirect
107. #2966C22semidirect
108. #2965C22semidirect
109. C8×#41C22semidirect
110. #2960C22semidirect
111. #2950C22semidirect
112. #2948C22semidirect
113. C4×#135C22semidirect
116. #2929C22semidirect
118. #2922C22semidirect
119. #2920C22semidirect
121. C4×#131C22semidirect
122. C22×C4×C8C22semidirect

Maximal subgroups

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

subgroupindex
#628362
#624342
#624272
#624182
#624172
#614132
#610902
#610542
#610512
#608202
#608182
#608012
#607152
#607142
#606732
#606482
#606472
C2×#31472
#602042