Finite Group Databasebeta

← #10580918

Subgroups — #10580918

Order 512.

6240 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62781C212yesmaximal, complemented
2#62547C218yesmaximal, complemented
3#62484C214yesmaximal, complemented
4#62428C214yesmaximal, complemented
5#62367C214yesmaximal, complemented
6#62261C214yesmaximal, complemented
7#62254C214yesmaximal, complemented
8#62253C214yesmaximal, complemented
9#61446C214yesmaximal, complemented
10#61445C218yesmaximal, complemented
11#61444C214yesmaximal, complemented
12#60945C212yesmaximal, complemented
13#60942C214yesmaximal, complemented
14#60702C214yesmaximal, complemented
15C2×#3168C212yesmaximal, complemented
16C2×#2965C211yesmaximal, characteristic, complemented
17#3521—28no—
18#3515C2218yescomplemented
19#3514C2218yescomplemented
20#3507C2214yescomplemented
21#3505C2214yes—
22#3505C2214yescomplemented
23#3501C2212yescomplemented
24#3496C2212yescomplemented
25#3493—22no—
26#3491—22no—
27#3491—22no—
28#3485—22no—
29#3482C2218yescomplemented
30#3481C2218yescomplemented
31#3475—28no—
32#3461—22no—
33#3459—22no—
34#3459—22no—
35#3444C2214yescomplemented
36C2×#529C2214yescomplemented
37C2×#529C2214yescomplemented
38C4×H(5,𝔽2)—22no—
39C2×C4×#41C2211yescharacteristic
40#3403C2214yescomplemented
41#3402C2214yescomplemented
42#3401C2218yescomplemented
43#3390C2214yescomplemented
44#3389C2214yescomplemented
45#3388C2218yescomplemented
46#3377C2218yescomplemented
47#3376C2218yescomplemented
48#3371C2218yescomplemented
49#3370C2218yescomplemented
50#3355C2214yescomplemented
51#3352C2214yescomplemented
52#3351C2218yescomplemented
53#3346C2218yescomplemented
54#3345C2218yescomplemented
55#3344C2218yescomplemented
56#3343C2218yescomplemented
57#3327C2218yescomplemented
58#3326C2218yescomplemented
59#3323C2218yescomplemented
60#3322C2218yescomplemented
61#3320C2218yescomplemented
62#3318C2218yescomplemented
63#3316C2218yescomplemented
64#3314C2218yescomplemented
65#3312C2218yescomplemented
66#3310C2218yescomplemented
67#3308C2218yescomplemented
68#3306C2218yescomplemented
69#3277C2214yescomplemented
70#3275C2218yescomplemented
71#3273C2214yescomplemented
72#3270C2218yescomplemented
73#3266C2218yescomplemented
74#3265C2218yescomplemented
75#3264C2218yescomplemented
76#3250C2218yescomplemented
77#3248C2218yescomplemented
78#3247C2218yescomplemented
79#3233C2218yescomplemented
80#3232C2218yescomplemented
81#3232C2218yescomplemented
82#3212C2218yescomplemented
83#3211C2218yescomplemented
84#3211C2218yescomplemented
85#3190C2218yescomplemented
86#3189C2212yescomplemented
87#3188C2218yescomplemented
88#3187C2214yescomplemented
89#3186C2212yes—
90#3183C2218yescomplemented
91#3183C2218yescomplemented
92#3181C2218yescomplemented
93#3180C2218yescomplemented
94#3172C2218yescomplemented
95#3171C2218yescomplemented
96#3168C2214yescomplemented
97#3168C2214yescomplemented
98#3168C2214yescomplemented
99#3168C2218yescomplemented
100#3168C2214yescomplemented
101#3168C2214yescomplemented
102#3168C2214yescomplemented
103#3168C2214yescomplemented
104#3168C2214yescomplemented
105#3166C2214yescomplemented
106C2×#499C2212yescomplemented
107#3153C2214yescomplemented
108C2×#495C2212yescomplemented
109#3142C2214yescomplemented
110#3140C2214yescomplemented
111C2×#488C2214yescomplemented
112#3108C2218yescomplemented
113#3105C2218yescomplemented
114#3104C2214yescomplemented
115#3103C2214yescomplemented
116#3102C2218yescomplemented
117#3102C2218yescomplemented
118#3101C2214yescomplemented
119#3100C2214yescomplemented
120#3056C2218yescomplemented
121#3055C2218yescomplemented
122C2×#467C2212yescomplemented
123C2×#466C2212yes—
124C2×#465C2214yescomplemented
125#2965C2214yescomplemented
126#2965C2214yescomplemented
127#2965C2214yescomplemented
128#2965C2214yescomplemented
129C2×#446C2212yescomplemented
130C4×#137C2218yescomplemented
131C4×AGL(1,ℤ/8)C2218yescomplemented
132C2×C4×Q16C2212yescomplemented
133C2×C4×SD16C2214yescomplemented
134C2×C4×D8C2212yescomplemented
135C2×#436C2212yescomplemented
136C2×#435C2214yescomplemented
137C2×#431C2212yescomplemented
138C2×#431C2211yescharacteristic, complemented
139C2×C4×M16C2212yescomplemented
140C22×C4×C8C2211yescharacteristic, complemented
141C2×H(5,𝔽2)—22no—
142C22×#41D411yescharacteristic
143C2×#137C2318yes—
144C2×AGL(1,ℤ/8)C2318yes—
145C22×Q16C2312yes—
146C22×SD16C2314yes—
147C22×D8C2312yes—
148C22×M16C2314yes—
149C23×C8C2312yes—
150#559C2318yes—
151#557C2318yes—
152#556—28no—
153#556—28no—
154#556C2318yes—
155#555—28no—
156#554—28no—
157#554C2318yes—
158#554C2318yes—
159#553—28no—
160#553—28no—
161#553—28no—
162#553C2318yes—
163#553C2318yes—
164#552—28no—
165#552—28no—
166#552—28no—
167#552—28no—
168#552—28no—
169#552—28no—
170#552C2318yes—
171#552C2318yes—
172#551—28no—
173#551—28no—
174#551—28no—
175#551—28no—
176#551—28no—
177#551—28no—
178D4×Q8C2318yes—
179#548C2318yes—
180#548C2318yes—
181#547—28no—
182#547—28no—
183#547C2318yes—
184#546—28no—
185#546—28no—
186#546—28no—
187#546C2318yes—
188#546C2318yes—
189D42C2318yes—
190#544—22no—
191#543—22no—
192#543—22no—
193#542—28no—
194#541—28no—
195#539—28no—
196#539—28no—
197#539—24no—
198#539—24no—
199#539—24no—
200#539—24no—
201#538—28no—
202#538—28no—
203#538—24no—
204#538—24no—
205#537—22no—
206#536—24no—
207#534—24no—
208#534—24no—
209#534—22no—
210#534—22no—
211#533—28no—
212#533C2314yes—
213#533C2314yes—
214#533C2314yes—
215#532C2314yes—
216#532C2314yes—
217#532C2314yes—
218#529—28no—
219#529—28no—
220#529—28no—
221#529—24no—
222#529—24no—
223#529—24no—
224#529—24no—
225#529—24no—
226#529—24no—
227#529—24no—
228#529—24no—
229#529—24no—
230#529—24no—
231#529—24no—
232#529—24no—
233#529C2318yes—
234#529C2318yes—
235#529C2318yes—
236#529C2318yes—
237#529C2318yes—
238#529C2318yes—
239#529C2318yes—
240#529C2318yes—
241C2×#126—24no—
242C2×#126—24no—
243C2×#125C2314yes—
244C2×#125C2314yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247#525—24no—
248#525—24no—
249#525—28no—
250#525—28no—
251#525C2318yes—
252C2×#123—24no—
253C2×#123—24no—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×#121C2314yes—
257C2×#121C2314yes—
258#520—28no—
259#520—24no—
260#518—22no—
261#518—28no—
262#518—24no—
263#518—24no—
264C4×#41—28no—
265C4×#41—24no—
266C4×#41—24no—
267C4×#41D414yes—
268C4×#41D414yes—
269C4×#41C2318yes—
270C4×#41C2314yes—
271C4×#41C2314yes—
272C2×C4×Q8D411yescharacteristic
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2314yes—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×D4—24no—
277C2×C4×D4—24no—
278C2×C4×D4—28no—
279C2×C4×D4D412yes—
280C2×C4×D4D411yescharacteristic
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2311yescharacteristic
285C2×#117—24no—
286C2×#117—24no—
287C2×#117D411yescharacteristic
288C2×#117D412yes—
289C22×C42C2311yescharacteristic
290C22×C42C2312yes—
291#501C2318yes—
292#501C2318yes—
293#499C2314yes—
294#499C2314yes—
295#499C2314yes—
296#499C2314yes—
297#499C2318yes—
298#497C2318yes—
299#496C2318yes—
300#495C2314yes—
301#495C2314yes—
302#495C2314yes—
303#495C2314yes—
304#495C2318yes—
305#491C2318yes—
306#490C2318yes—
307#489C2318yes—
308#489C2318yes—
309#488C2318yes—
310#488C2318yes—
311#488C2318yes—
312#488C2318yes—
313#488C2318yes—
314#488C2318yes—
315#485C2318yes—
316#485C2318yes—
317#484C2318yes—
318#484C2318yes—
319#483C2318yes—
320#483C2318yes—
321#482C2318yes—
322#482C2318yes—
323#481C2318yes—
324#481C2318yes—
325#480C2318yes—
326#480C2318yes—
327#479C2318yes—
328#479C2318yes—
329#479C2318yes—
330#479C2318yes—
331#478C2318yes—
332#478C2318yes—
333#478C2318yes—
334#478C2318yes—
335#477C2318yes—
336#476C2318yes—
337#475C2318yes—
338#474C2318yes—
339#470C2318yes—
340#470C2318yes—
341#469C2318yes—
342#469C2318yes—
343#468C2318yes—
344#468C2318yes—
345#468C2318yes—
346#468C2318yes—
347#467C2314yes—
348#467C2314yes—
349#467C2314yes—
350#467C2314yes—
351#467C2318yes—
352#466C2314yes—
353#466C2314yes—
354#466C2314yes—
355#466C2314yes—
356#466C2318yes—
357#465C2318yes—
358#465C2318yes—
359#465C2318yes—
360#465C2318yes—
361#465C2318yes—
362#465C2318yes—
363#464C2318yes—
364#464C2318yes—
365#464C2318yes—
366#464C2318yes—
367#463C2318yes—
368#463C2318yes—
369#463C2318yes—
370#463C2318yes—
371#462C2318yes—
372#461C2318yes—
373#460C2318yes—
374#459C2318yes—
375#452C2318yes—
376#452C2318yes—
377#451C2318yes—
378#451C2318yes—
379#450C2318yes—
380#450C2318yes—
381#449C2318yes—
382#449C2318yes—
383#448C2318yes—
384#448C2318yes—
385#447C2318yes—
386#447C2318yes—
387#446C2314yes—
388#446C2314yes—
389#446C2314yes—
390#446C2314yes—
391#442C2318yes—
392#442C2318yes—
393#441C2318yes—
394#441C2318yes—
395#440C2318yes—
396#440C2318yes—
397#440C2318yes—
398#440C2318yes—
399C4×Q16C2314yes—
400C4×Q16C2314yes—
401C4×Q16C2318yes—
402C4×Q16C2314yes—
403C4×Q16C2314yes—
404C4×SD16C2318yes—
405C4×SD16C2318yes—
406C4×SD16C2318yes—
407C4×SD16C2318yes—
408C4×SD16C2318yes—
409C4×SD16C2318yes—
410C4×D8C2314yes—
411C4×D8C2314yes—
412C4×D8C2318yes—
413C4×D8C2314yes—
414C4×D8C2314yes—
415#436C2314yes—
416#436C2314yes—
417#436C2314yes—
418#436C2314yes—
419#435C2318yes—
420#435C2318yes—
421#435C2318yes—
422#435C2318yes—
423#431C2314yes—
424#431C2314yes—
425#431C2314yes—
426#431C2314yes—
427#431C2318yes—
428#428C2318yes—
429#428C2318yes—
430C2×#107C2312yes—
431C2×#107C2312yes—
432C2×#106C2314yes—
433C2×C4⋊C8C2314yes—
434C2×C4⋊C8C2312yes—
435#419C2318yes—
436#418C2318yes—
437#417C2318yes—
438#417C2318yes—
439C2×#103C2314yes—
440C2×#103C2314yes—
441C2×#102C2314yes—
442C2×#102C2314yes—
443C2×C22⋊C8C2312yes—
444C2×C22⋊C8C2314yes—
445C4×M16C2314yes—
446C4×M16C2314yes—
447C4×M16C2318yes—
448C2×#97C2314yes—
449C2×C4×C8C2311yescharacteristic
450C2×C4×C8C2312yes—
451C2×C4×C8C2312yes—
452C2×C4×C8C2311yescharacteristic
453C2×C4×C8C2312yes—
454C2×C4×C8C2312yes—
455C2×C4×C8C2312yes—
456C2×C4×C8C2312yes—
457H(5,𝔽2)—416no—
458C2×#41—28no—
459C2×#41—24no—
460C2×#41—24no—
461C2×#41—44no—
462C2×#41C2×D414yes—
463C2×#41C2×D414yes—
464C2×#41C2418yes—
465C22×Q8C2×D411yescharacteristic
466C22×Q8C2414yes—
467C22×Q8C2414yes—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—28no—
471C22×D4C2×D412yes—
472C22×D4C2×D411yescharacteristic
473C22×D4C2414yes—
474C22×D4C2414yes—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4C2×D411yescharacteristic
478C23×C4C2×D412yes—
479C23×C4C2×D411yescharacteristic
480C23×C4C2×D412yes—
481C23×C4C2411yescharacteristic
482C23×C4C2412yes—
483#137—416no—
484AGL(1,ℤ/8)—416no—
485C2×Q16—44no—
486C2×Q16C2414yes—
487C2×Q16C2414yes—
488C2×Q16C2418yes—
489C2×SD16—48no—
490C2×SD16C2418yes—
491C2×SD16C2418yes—
492C2×SD16C2418yes—
493C2×SD16C2418yes—
494C2×D8—44no—
495C2×D8C2414yes—
496C2×D8C2414yes—
497C2×D8C2418yes—
498C2×M16—48no—
499C2×M16C2418yes—
500C2×M16C2418yes—
501C22×C8—44no—
502C22×C8C2412yes—
503C22×C8C2412yes—
504C22×C8C2412yes—
505C22×C8C2412yes—
506C22×C8C2412yes—
507C22×C8C2412yes—
508C22×C8C2414yes—
509C4⋊Q8—28no—
510C4⋊Q8—28no—
511C4⋊Q8C2414yes—
512C4⋊Q8C2414yes—
513C4⋊Q8C2414yes—
514#127C2414yes—
515#126—28no—
516#126—28no—
517#126—28no—
518#126—28no—
519#126—28no—
520#126—28no—
521#126—28no—
522#126—28no—
523#126—28no—
524#126—28no—
525#126—28no—
526#126—28no—
527#126—28no—
528#126—28no—
529#125—28no—
530#125—28no—
531#125—28no—
532#125—28no—
533#125—28no—
534#125—24no—
535#125—24no—
536#125—24no—
537#125—24no—
538#125—24no—
539#125—24no—
540#125C2418yes—
541#125C2418yes—
542#125C2418yes—
543#124—28no—
544#124—28no—
545#124—28no—
546#124—24no—
547#124—24no—
548#124—24no—
549#124—24no—
550#124—24no—
551#124—24no—
552#124C2418yes—
553#124C2418yes—
554#124C2418yes—
555#123—28no—
556#123—28no—
557#123—28no—
558#123—28no—
559#123—28no—
560#123—28no—
561#123—28no—
562#123—28no—
563#123—28no—
564#123—28no—
565#123—28no—
566#123—28no—
567#123—28no—
568#123—28no—
569#123—28no—
570#123—28no—
571#123—28no—
572#123—28no—
573#123—28no—
574C22⋊Q8—28no—
575C22⋊Q8—28no—
576C22⋊Q8—24no—
577C22⋊Q8—24no—
578C22⋊Q8—24no—
579C22⋊Q8—24no—
580C22⋊Q8—24no—
581C22⋊Q8—24no—
582C22⋊Q8—24no—
583C22⋊Q8—24no—
584C22⋊Q8—28no—
585C22⋊Q8—28no—
586C22⋊Q8—28no—
587C22⋊Q8—28no—
588C22⋊Q8—28no—
589C22⋊Q8—28no—
590C22⋊Q8—28no—
591C22⋊Q8—28no—
592C22⋊Q8—28no—
593C22⋊Q8C2418yes—
594C22⋊Q8C2418yes—
595C22⋊Q8C2418yes—
596C22⋊Q8C2418yes—
597#121—28no—
598#121—28no—
599#121—28no—
600#121—28no—
601#121—24no—
602#121—24no—
603#121—24no—
604#121—24no—
605#121—24no—
606#121—24no—
607#121—24no—
608#121—24no—
609#121—28no—
610#121—28no—
611#121—28no—
612#121C2418yes—
613#121C2418yes—
614#121C2418yes—
615#121C2418yes—
616#120—28no—
617#120—28no—
618#120—28no—
619#120—28no—
620#120—28no—
621C4×Q8—28no—
622C4×Q8—24no—
623C4×Q8—24no—
624C4×Q8—24no—
625C4×Q8—24no—
626C4×Q8—24no—
627C4×Q8—24no—
628C4×Q8—24no—
629C4×Q8—24no—
630C4×Q8C2×D414yes—
631C4×Q8C2×D414yes—
632C4×Q8C2×D414yes—
633C4×Q8C2418yes—
634C4×Q8C2418yes—
635C4×Q8C2418yes—
636C4×Q8C2418yes—
637C4×Q8C2414yes—
638C4×D4—28no—
639C4×D4—28no—
640C4×D4—28no—
641C4×D4—28no—
642C4×D4—28no—
643C4×D4—28no—
644C4×D4—28no—
645C4×D4—28no—
646C4×D4—28no—
647C4×D4—28no—
648C4×D4—28no—
649C4×D4—28no—
650C4×D4—28no—
651C4×D4—28no—
652C4×D4—28no—
653C4×D4—28no—
654C4×D4—28no—
655C4×D4—28no—
656C4×D4—28no—
657C4×D4—24no—
658C4×D4—24no—
659C4×D4—24no—
660C4×D4—24no—
661C4×D4—24no—
662C4×D4—24no—
663C4×D4—24no—
664C4×D4—24no—
665C4×D4C2×D418yes—
666C4×D4C2×D418yes—
667C4×D4C2×D414yes—
668C4×D4C2×D414yes—
669C4×D4C2×D418yes—
670C4×D4C2×D414yes—
671C4×D4C2418yes—
672C4×D4C2418yes—
673C4×D4C2418yes—
674C4×D4C2418yes—
675C4×D4C2418yes—
676C4×D4C2414yes—
677#117—24no—
678#117—24no—
679#117—28no—
680#117—28no—
681#117—28no—
682#117—28no—
683#117—28no—
684#117—28no—
685#117—28no—
686#117—28no—
687#117—28no—
688#117—28no—
689#117—28no—
690#117—28no—
691#117C2×D414yes—
692#117C2×D414yes—
693#117C2×D418yes—
694#117C2×D418yes—
695#117C2418yes—
696C2×C4⋊C4—24no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—24no—
699C2×C4⋊C4—24no—
700C2×C4⋊C4—24no—
701C2×C4⋊C4—24no—
702C2×C4⋊C4—24no—
703C2×C4⋊C4—24no—
704C2×C4⋊C4—28no—
705C2×C4⋊C4C2×D412yes—
706C2×C4⋊C4C2×D411yescharacteristic
707C2×C4⋊C4C2×D412yes—
708C2×C4⋊C4C2×D411yescharacteristic
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C22⋊C4—24no—
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—24no—
717C2×C22⋊C4—24no—
718C2×C22⋊C4—24no—
719C2×C22⋊C4—24no—
720C2×C22⋊C4—24no—
721C2×C22⋊C4—24no—
722C2×C22⋊C4—24no—
723C2×C22⋊C4—28no—
724C2×C22⋊C4—28no—
725C2×C22⋊C4C2×D412yes—
726C2×C22⋊C4C2×D412yes—
727C2×C22⋊C4C2×D412yes—
728C2×C42—24no—
729C2×C42—24no—
730C2×C42—28no—
731C2×C42C2×D412yes—
732C2×C42C2×D414yes—
733C2×C42C2×D411yescharacteristic
734C2×C42C2×D412yes—
735C2×C42C2×D412yes—
736C2×C42C2×D411yescharacteristic
737C2×C42C2×D412yes—
738C2×C42C2×D414yes—
739C2×C42C2412yes—
740C2×C42C2414yes—
741C2×C42C2411yescharacteristic
742C2×C42C2412yes—
743C2×C42C2412yes—
744C2×C42C2414yes—
745C2×C42C2411yescharacteristic
746#107C2414yes—
747#107C2414yes—
748#107C2414yes—
749#107C2414yes—
750#107C2418yes—
751#107C2418yes—
752#106C2418yes—
753#106C2418yes—
754#106C2418yes—
755#106C2418yes—
756C4⋊C8C2418yes—
757C4⋊C8C2418yes—
758C4⋊C8C2414yes—
759C4⋊C8C2414yes—
760#103C2418yes—
761#103C2418yes—
762#103C2418yes—
763#103C2418yes—
764#103C2418yes—
765#103C2418yes—
766#103C2418yes—
767#103C2418yes—
768#102C2418yes—
769#102C2418yes—
770#102C2418yes—
771#102C2418yes—
772#102C2418yes—
773#102C2418yes—
774#102C2418yes—
775#102C2418yes—
776C22⋊C8C2418yes—
777C22⋊C8C2418yes—
778C22⋊C8C2418yes—
779#97C2418yes—
780#97C2418yes—
781C4×C8C2412yes—
782C4×C8C2411yescharacteristic
783C4×C8C2411yescharacteristic
784C4×C8C2411yescharacteristic
785C4×C8C2411yescharacteristic
786C4×C8C2412yes—
787C4×C8C2412yes—
788C4×C8C2412yes—
789C4×C8C2412yes—
790C4×C8C2412yes—
791C4×C8C2414yes—
792C4×C8C2414yes—
793C24—24no—
794C24—24no—
795C24C22×D412yes—
796C24C22×D411yescharacteristic
797#41—48no—
798#41—48no—
799#41—416no—
800#41—48no—
801#41—48no—
802#41—432no—
803#41—88no—
804C2×Q8—24no—
805C2×Q8—24no—
806C2×Q8—24no—
807C2×Q8—24no—
808C2×Q8—42no—
809C2×Q8—44no—
810C2×Q8—44no—
811C2×Q8—48no—
812C2×Q8C22×D414yes—
813C2×Q8C2518yes—
814C2×D4—28no—
815C2×D4—28no—
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—48no—
827C2×D4—42no—
828C2×D4—432no—
829C2×D4—416no—
830C2×D4—416no—
831C2×D4C22×D418yes—
832C2×D4C22×D414yes—
833C2×D4C2518yes—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—28no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—42no—
847C22×C4—44no—
848C22×C4—42no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—88no—
852C22×C4—88no—
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D412yes—
855C22×C4C22×D412yes—
856C22×C4C22×D412yes—
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D412yes—
859C22×C4C22×D414yes—
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D412yes—
862C22×C4C22×D414yes—
863C22×C4C22×D412yes—
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D412yes—
866C22×C4C22×D414yes—
867C22×C4C22×D414yes—
868C22×C4C22×D414yes—
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D412yes—
871C22×C4C2512yes—
872C22×C4C2514yes—
873C22×C4C2511yescharacteristic
874Q16—28no—
875Q16—44no—
876Q16—48no—
877SD16—216no—
878SD16—48no—
879SD16—48no—
880SD16—48no—
881D8—28no—
882D8—44no—
883D8—48no—
884M16—216no—
885M16—48no—
886C2×C8—24no—
887C2×C8—24no—
888C2×C8—24no—
889C2×C8—42no—
890C2×C8—42no—
891C2×C8—42no—
892C2×C8—44no—
893C2×C8C2512yes—
894C2×C8C2512yes—
895C2×C8C2512yes—
896C2×C8C2518yes—
897C2×C8C2512yes—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—28no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—28no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—28no—
920C4⋊C4C22×D418yes—
921C4⋊C4C22×D414yes—
922C4⋊C4C22×D418yes—
923C4⋊C4C22×D414yes—
924C4⋊C4C2518yes—
925C4⋊C4C2518yes—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4C22×D418yes—
946C22⋊C4C22×D418yes—
947C22⋊C4C22×D418yes—
948C42—28no—
949C42—28no—
950C42—28no—
951C42—28no—
952C42—28no—
953C42C22×D411yescharacteristic
954C42C22×D412yes—
955C42C22×D412yes—
956C42C22×D414yes—
957C42C22×D414yes—
958C42C22×D414yes—
959C42C22×D414yes—
960C42C22×D412yes—
961C42C22×D412yes—
962C42C22×D414yes—
963C42C22×D411yescharacteristic
964C42C22×D412yes—
965C42C2511yescharacteristic
966C42C2512yes—
967C42C2514yes—
968C42C2511yescharacteristic
969C23—24no—
970C23—28no—
971C23—41no—
972C23—41no—
973C23—42no—
974C23—42no—
975C23—48no—
976C23—48no—
977C23—84no—
978C23—84no—
979C23—84no—
980C23—84no—
981C23#57514yes—
982C23C23×D414yes—
983C23C23×D411yescharacteristic
984C23C23×D412yes—
985Q8—28no—
986Q8—28no—
987Q8—44no—
988Q8—48no—
989Q8—84no—
990Q8—84no—
991Q8—84no—
992D4—216no—
993D4—28no—
994D4—28no—
995D4—44no—
996D4—48no—
997D4—416no—
998D4—416no—
999D4—416no—
1000D4—84no—
1001D4—84no—
1002D4—84no—
1003D4—88no—
1004D4—88no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—28no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—28no—
1017C2×C4—28no—
1018C2×C4—28no—
1019C2×C4—28no—
1020C2×C4—44no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—41no—
1024C2×C4—42no—
1025C2×C4—44no—
1026C2×C4—41no—
1027C2×C4—42no—
1028C2×C4—44no—
1029C2×C4—44no—
1030C2×C4—416no—
1031C2×C4—48no—
1032C2×C4—48no—
1033C2×C4—416no—
1034C2×C4—88no—
1035C2×C4—88no—
1036C2×C4—88no—
1037C2×C4—84no—
1038C2×C4—84no—
1039C2×C4—84no—
1040C2×C4—84no—
1041C2×C4C23×D412yes—
1042C2×C4C23×D414yes—
1043C2×C4C23×D414yes—
1044C2×C4C23×D414yes—
1045C2×C4C23×D411yescharacteristic
1046C2×C4C23×D411yescharacteristic
1047C2×C4C23×D411yescharacteristic
1048C2×C4C23×D411yescharacteristic
1049C2×C4C23×D412yes—
1050C2×C4C23×D412yes—
1051C2×C4C23×D411yescharacteristic
1052C2×C4C2611yescharacteristic
1053C8—22no—
1054C8—22no—
1055C8—22no—
1056C8—28no—
1057C8#58514yes—
1058C22—21no—
1059C22—22no—
1060C22—21no—
1061C22—22no—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—44no—
1066C22—48no—
1067C22—48no—
1068C22—48no—
1069C22—84no—
1070C22—168no—
1071C22—168no—
1072C22C2×#57512yes—
1073C22C2×#57514yes—
1074C22C24×D411yescharacteristic
1075C4—21no—
1076C4—24no—
1077C4—22no—
1078C4—21no—
1079C4—21no—
1080C4—22no—
1081C4—24no—
1082C4—21no—
1083C4—22no—
1084C4—24no—
1085C4—48no—
1086C4—48no—
1087C4—48no—
1088C4#358412yes—
1089C4C2×#58512yes—
1090C2—22no—
1091C2—24no—
1092C2—44no—
1093C2—88no—
1094C2#6281211yescharacteristic
1095C2C22×#57511yescharacteristic
1096C2C2×#358411yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutator, Frattini, cosocleC2×C4C26
socleC22C24×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62781C2semidirect
2. #62547C2semidirect
3. #62484C2semidirect
4. #62428C2semidirect
5. #62367C2semidirect
6. #62261C2semidirect
7. #62254C2semidirect
8. #62253C2semidirect
9. #61446C2semidirect
10. #61445C2semidirect
11. #61444C2semidirect
12. #60945C2semidirect
13. #60942C2semidirect
14. #60702C2semidirect
15. C2×#3168C2semidirect
16. C2×#2965C2semidirect
18. #3515C22semidirect
19. #3514C22semidirect
20. #3507C22semidirect
22. #3505C22semidirect
23. #3501C22semidirect
24. #3496C22semidirect
29. #3482C22semidirect
30. #3481C22semidirect
35. #3444C22semidirect
36. C2×#529C22semidirect
37. C2×#529C22semidirect
40. #3403C22semidirect
41. #3402C22semidirect
42. #3401C22semidirect
43. #3390C22semidirect
44. #3389C22semidirect
45. #3388C22semidirect
46. #3377C22semidirect
47. #3376C22semidirect
48. #3371C22semidirect
49. #3370C22semidirect
50. #3355C22semidirect
51. #3352C22semidirect
52. #3351C22semidirect
53. #3346C22semidirect
54. #3345C22semidirect
55. #3344C22semidirect
56. #3343C22semidirect
57. #3327C22semidirect
58. #3326C22semidirect
59. #3323C22semidirect
60. #3322C22semidirect
61. #3320C22semidirect
62. #3318C22semidirect
63. #3316C22semidirect
64. #3314C22semidirect
65. #3312C22semidirect
66. #3310C22semidirect
67. #3308C22semidirect
68. #3306C22semidirect
69. #3277C22semidirect
70. #3275C22semidirect
71. #3273C22semidirect
72. #3270C22semidirect
73. #3266C22semidirect
74. #3265C22semidirect
75. #3264C22semidirect
76. #3250C22semidirect
77. #3248C22semidirect
78. #3247C22semidirect
79. #3233C22semidirect
80. #3232C22semidirect
81. #3232C22semidirect
82. #3212C22semidirect
83. #3211C22semidirect
84. #3211C22semidirect
85. #3190C22semidirect
86. #3189C22semidirect
87. #3188C22semidirect
88. #3187C22semidirect
90. #3183C22semidirect
91. #3183C22semidirect
92. #3181C22semidirect
93. #3180C22semidirect
94. #3172C22semidirect
95. #3171C22semidirect
96. #3168C22semidirect
97. #3168C22semidirect
98. #3168C22semidirect
99. #3168C22semidirect
100. #3168C22semidirect
101. #3168C22semidirect
102. #3168C22semidirect
103. #3168C22semidirect
104. #3168C22semidirect
105. #3166C22semidirect
106. C2×#499C22semidirect
107. #3153C22semidirect
108. C2×#495C22semidirect
109. #3142C22semidirect
110. #3140C22semidirect
111. C2×#488C22semidirect
112. #3108C22semidirect
113. #3105C22semidirect
114. #3104C22semidirect
115. #3103C22semidirect
116. #3102C22semidirect
117. #3102C22semidirect
118. #3101C22semidirect
119. #3100C22semidirect
120. #3056C22semidirect
121. #3055C22semidirect
122. C2×#467C22semidirect
124. C2×#465C22semidirect
125. #2965C22semidirect
126. #2965C22semidirect
127. #2965C22semidirect
128. #2965C22semidirect
129. C2×#446C22semidirect
130. C4×#137C22semidirect
131. C4×AGL(1,ℤ/8)C22semidirect
132. C2×C4×Q16C22semidirect
133. C2×C4×SD16C22semidirect
134. C2×C4×D8C22semidirect
135. C2×#436C22semidirect
136. C2×#435C22semidirect
137. C2×#431C22semidirect
138. C2×#431C22semidirect
139. C2×C4×M16C22semidirect
140. C22×C4×C8C22semidirect

Maximal subgroups

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

subgroupindex
#627812
#625472
#624842
#624282
#623672
#622612
#622542
#622532
#614462
#614452
#614442
#609452
#609422
#607022
C2×#31682
C2×#29652