Finite Group Databasebeta

← #10578337

Subgroups — #10578337

Order 512.

5782 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62889C211yesmaximal, characteristic
2#62849C211yesmaximal, characteristic, complemented
3#61875C218yesmaximal, complemented
4#61866C218yesmaximal, complemented
5#61856C218yesmaximal, complemented
6#61852C218yesmaximal, complemented
7#61386C214yesmaximal, complemented
8#61379C212yesmaximal, complemented
9#61372C212yesmaximal, complemented
10#61342C214yesmaximal, complemented
11#61335C212yesmaximal, complemented
12#61328C212yesmaximal, complemented
13#60876C214yesmaximal, complemented
14#60869C211yesmaximal, characteristic, complemented
15#60859C211yesmaximal, characteristic
16#60583C214yesmaximal, complemented
17#60566C211yesmaximal, characteristic
18C2×#3127C211yesmaximal, characteristic, complemented
19#60252C211yesmaximal, characteristic, complemented
20#3564—24no—
21#3563—24no—
22#3563—24no—
23#3557C2214yes—
24#3556C2214yes—
25#3555—24no—
26#3555C2218yes—
27#3509C2212yes—
28#3507C2212yes—
29#3504C2212yes—
30#3502—24no—
31#3502—24no—
32#3502—24no—
33#3502C2212yes—
34#3502C2212yes—
35#3502C2218yes—
36#3502C2214yes—
37#3502C2218yes—
38#3502C2212yes—
39#3495C2214yes—
40#3458—24no—
41#3458C2211yescharacteristic
42#3458C2212yes—
43#3458C2211yescharacteristic
44#3455C2211yescharacteristic
45C2×#541C2211yescharacteristic
46C2×#519C2211yescharacteristic
47C2×#519C2212yes—
48#3390C2218yescomplemented
49#3390C2218yescomplemented
50#3390C2218yescomplemented
51#3390C2218yescomplemented
52#3390C2218yescomplemented
53#3388C2218yescomplemented
54#3388C2218yescomplemented
55#3387C2218yescomplemented
56#3387C2218yescomplemented
57#3387C2218yescomplemented
58#3387C2214yescomplemented
59#3387C2214yescomplemented
60#3385C2218yescomplemented
61#3383C2218yescomplemented
62#3383C2218yescomplemented
63#3383C2214yescomplemented
64Q8×Q16C2214yescomplemented
65#3381C2218yescomplemented
66#3377C2218yescomplemented
67#3377C2218yescomplemented
68#3377C2218yescomplemented
69#3377C2218yescomplemented
70#3375C2214yescomplemented
71#3374C2214yescomplemented
72#3374C2218yescomplemented
73#3374C2218yescomplemented
74#3374C2218yescomplemented
75#3374C2218yescomplemented
76#3371C2218yescomplemented
77#3369C2218yescomplemented
78#3369C2218yescomplemented
79#3365C2214yescomplemented
80#3364C2218yescomplemented
81#3364C2218yescomplemented
82#3363C2214yescomplemented
83#3363C2218yescomplemented
84#3244C2218yes—
85#3244C2214yes—
86#3243C2218yes—
87#3243C2214yes—
88#3242C2214yes—
89#3242C2218yes—
90#3242C2218yes—
91#3242C2218yes—
92#3242C2218yes—
93#3241C2214yes—
94#3240C2218yes—
95#3237C2218yes—
96#3233C2218yes—
97#3231C2218yes—
98#3166C2212yes—
99#3164C2214yes—
100#3163C2214yes—
101#3162C2211yescharacteristic
102#3160C2211yescharacteristic
103#3139C2212yes—
104#3137C2214yes—
105#3137C2214yes—
106#3135C2211yescharacteristic
107#3131C2211yescharacteristic
108#3127C2218yes—
109#3127C2214yes—
110#3127C2214yes—
111#3127C2214yes—
112#3127C2218yes—
113#3127C2218yes—
114#3126C2214yes—
115#3121C2218yes—
116#3121C2218yes—
117#3121C2218yes—
118#3117C2218yes—
119#3113C2218yes—
120#3108C2218yes—
121#3104C2218yes—
122#3095C2214yes—
123#3093C2212yes—
124#3091C2214yes—
125C2×#485C2212yes—
126#3084C2214yes—
127#3083C2214yes—
128#3082C2214yes—
129#3082C2214yes—
130#3082C2214yes—
131#3082C2214yes—
132#3078C2212yes—
133#3078C2212yes—
134#3078C2212yes—
135#3076C2214yes—
136C2×#479C2212yes—
137#3044C2214yes—
138#3044C2214yes—
139#3037C2212yes—
140C2×#462C2212yes—
141#3004C2212yes—
142C2×#451C2212yes—
143#2987C2214yes—
144#2986C2214yes—
145#2985C2218yes—
146#2962C2214yes—
147#2961C2212yes—
148#2960C2212yes—
149#2950C2214yes—
150#2950C2214yes—
151#2947C2214yes—
152#2947C2214yes—
153C4×#137C2214yes—
154C2×#441C2212yes—
155C2×C4×Q16C2212yes—
156#2924C2214yes—
157#2921C2211yescharacteristic
158C2×#433C2211yescharacteristic
159C23×Q8C2311yescharacteristic
160C2×#137C2314yes—
161C22×Q16C2312yes—
162C22×Q16C2312yes—
163#564—28no—
164#563—28no—
165#563—28no—
166#563—28no—
167#559C2314yes—
168Q82—24no—
169Q82—28no—
170Q82—22no—
171Q82—22no—
172Q82—28no—
173Q82—22no—
174Q82C2318yes—
175Q82C2314yes—
176Q82C2314yes—
177Q82C2314yes—
178#557—24no—
179#557—28no—
180#557—22no—
181#557—22no—
182#557—28no—
183#557—22no—
184#557—28no—
185#557—24no—
186#557—24no—
187#557—28no—
188#557—28no—
189#557—24no—
190#557—24no—
191#557—28no—
192#557—28no—
193#557—24no—
194#557C2314yes—
195#557C2318yes—
196#557C2318yes—
197#557C2318yes—
198#557C2314yes—
199#557C2318yes—
200#557C2318yes—
201#557C2318yes—
202#557C2314yes—
203#557C2314yes—
204#557C2318yes—
205#557C2318yes—
206#556—22no—
207#556—28no—
208#556—24no—
209#556C2318yes—
210#556C2318yes—
211#554—22no—
212#554—28no—
213#554—24no—
214#554C2318yes—
215#552—24no—
216#552—28no—
217#552—28no—
218#552—28no—
219#552—28no—
220#552—24no—
221#552—24no—
222#551—28no—
223#544—24no—
224#544—28no—
225#544—24no—
226#544—24no—
227#544—28no—
228#544—28no—
229#544—28no—
230#544—28no—
231#544—28no—
232#544—24no—
233#544—22no—
234#544—24no—
235#544D414yes—
236#544D414yes—
237#544D414yes—
238#544C2314yes—
239#544C2314yes—
240#544C2314yes—
241#544C2314yes—
242#544C2314yes—
243#544C2318yes—
244#543—22no—
245#543—24no—
246#543D414yes—
247#542—28no—
248#542C2314yes—
249#542C2318yes—
250#541—28no—
251#541—22no—
252#541—22no—
253#541—28no—
254#541—28no—
255#541—28no—
256#541—28no—
257#541—24no—
258#541C2314yes—
259#541C2314yes—
260#541C2312yes—
261#541C2318yes—
262#540C2312yes—
263#539—24no—
264#539—28no—
265#539—22no—
266#538—22no—
267#536C2314yes—
268#533—24no—
269#533—22no—
270#533—24no—
271#533—24no—
272#533—28no—
273#533—28no—
274#533—28no—
275#533—28no—
276#533—28no—
277#533—24no—
278#533—24no—
279#533—24no—
280#533—22no—
281#533—22no—
282#533C2318yes—
283#533C2312yes—
284#533C2311yescharacteristic
285#533C2311yescharacteristic
286#533C2311yescharacteristic
287#533C2318yes—
288#533C2312yes—
289#533C2312yes—
290#533C2314yes—
291#533C2314yes—
292#532C2311yescharacteristic
293C2×C4⋊Q8C2311yescharacteristic
294#529—24no—
295#529—24no—
296#529C2318yes—
297C2×#126—22no—
298C2×#125—22no—
299C2×#125—22no—
300C2×#125C2311yescharacteristic
301#525C2312yes—
302C2×C22⋊Q8C2312yes—
303#520C2314yes—
304#519—24no—
305#519—24no—
306#519—22no—
307#519—22no—
308#519C2314yes—
309#519C2314yes—
310#519C2314yes—
311#519C2314yes—
312#519C2318yes—
313#519C2314yes—
314C4×#41C2312yes—
315C2×C4×Q8—22no—
316C2×C4×Q8—24no—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2318yes—
321C2×#117—22no—
322C2×#117—24no—
323C2×#117C2311yescharacteristic
324C2×#117C2312yes—
325C2×#117C2311yescharacteristic
326C2×#117C2312yes—
327#501C2318yes—
328#501C2318yes—
329#501C2318yes—
330#501C2314yes—
331#501C2314yes—
332#501C2318yes—
333#501C2318yes—
334#500C2312yes—
335#500C2318yes—
336#499C2318yes—
337#499C2318yes—
338#499C2314yes—
339#499C2318yes—
340#498C2318yes—
341#498C2312yes—
342#491C2312yes—
343#491C2318yes—
344#491C2318yes—
345#491C2318yes—
346#490C2312yes—
347#489C2318yes—
348#489C2314yes—
349#489C2318yes—
350#488C2312yes—
351#488C2318yes—
352#488C2318yes—
353#488C2312yes—
354#487C2318yes—
355#487C2312yes—
356#487C2318yes—
357#487C2318yes—
358#486C2312yes—
359#485C2318yes—
360#485C2318yes—
361#485C2314yes—
362#485C2314yes—
363#485C2318yes—
364#485C2318yes—
365#485C2318yes—
366#484C2314yes—
367#484C2318yes—
368#483C2314yes—
369#483C2318yes—
370#482C2314yes—
371#482C2314yes—
372#482C2318yes—
373#481C2314yes—
374#480C2314yes—
375#479C2318yes—
376#479C2318yes—
377#479C2314yes—
378#479C2314yes—
379#479C2318yes—
380#479C2318yes—
381#479C2318yes—
382#479C2318yes—
383#479C2318yes—
384#479C2318yes—
385#479C2318yes—
386#479C2318yes—
387#479C2318yes—
388#479C2318yes—
389#479C2318yes—
390#479C2318yes—
391#479C2318yes—
392#478C2314yes—
393#478C2314yes—
394#478C2318yes—
395#478C2318yes—
396#477C2314yes—
397#477C2314yes—
398#477C2314yes—
399#477C2314yes—
400#477C2318yes—
401#477C2318yes—
402#477C2318yes—
403#477C2318yes—
404#477C2318yes—
405#476C2314yes—
406#476C2318yes—
407#475C2314yes—
408#475C2314yes—
409#475C2314yes—
410#475C2314yes—
411#475C2318yes—
412#475C2318yes—
413#475C2318yes—
414#475C2318yes—
415#475C2318yes—
416#474C2314yes—
417#474C2318yes—
418#464C2318yes—
419#464C2318yes—
420#464C2318yes—
421#464C2318yes—
422#464C2318yes—
423#462C2318yes—
424#462C2318yes—
425#462C2318yes—
426#462C2318yes—
427#462C2318yes—
428#462C2314yes—
429#462C2318yes—
430#460C2314yes—
431#451C2318yes—
432#451C2318yes—
433#451C2318yes—
434#448C2318yes—
435#446C2318yes—
436#446C2318yes—
437#446C2318yes—
438#446C2314yes—
439#446C2318yes—
440#446C2318yes—
441#446C2314yes—
442C8×Q8C2318yes—
443C8×Q8C2314yes—
444C8×Q8C2314yes—
445#441C2318yes—
446#441C2318yes—
447#441C2318yes—
448#441C2318yes—
449#441C2318yes—
450#441C2318yes—
451#441C2318yes—
452#441C2318yes—
453#441C2318yes—
454#440C2318yes—
455#440C2318yes—
456#440C2318yes—
457C4×Q16C2318yes—
458C4×Q16C2318yes—
459C4×Q16C2318yes—
460C4×Q16C2318yes—
461C4×Q16C2318yes—
462C4×Q16C2314yes—
463C4×Q16C2318yes—
464C4×Q16C2318yes—
465C4×Q16C2314yes—
466C4×Q16C2314yes—
467C4×Q16C2314yes—
468C4×SD16C2318yes—
469C4×SD16C2318yes—
470C4×SD16C2318yes—
471#433C2314yes—
472#433C2318yes—
473#433C2318yes—
474#433C2314yes—
475#433C2314yes—
476#433C2312yes—
477#433C2312yes—
478#432C2318yes—
479#431C2318yes—
480#428C2314yes—
481#428C2314yes—
482#428C2314yes—
483#427C2314yes—
484#427C2314yes—
485C2×#107C2312yes—
486C2×#106C2312yes—
487#424C2314yes—
488#424C2314yes—
489#423C2312yes—
490C2×C4⋊C8C2312yes—
491#419C2314yes—
492#419C2314yes—
493#419C2314yes—
494#417C2314yes—
495#416C2314yes—
496#416C2314yes—
497C2×#103C2312yes—
498C2×#103C2312yes—
499C2×#103C2312yes—
500C2×#103C2312yes—
501#407C2312yes—
502C2×C22⋊C8C2312yes—
503#405C2314yes—
504#405C2314yes—
505C4×M16C2312yes—
506C2×#97C2311yescharacteristic
507C2×C4×C8C2311yescharacteristic
508C2×#41C2412yes—
509C22×Q8—28no—
510C22×Q8—21no—
511C22×Q8—22no—
512C22×Q8C2414yes—
513C22×Q8C2412yes—
514C22×Q8C2412yes—
515C23×C4—21no—
516C23×C4C2411yescharacteristic
517#137—216no—
518C2×Q16—28no—
519C2×Q16—28no—
520C2×Q16C2414yes—
521C2×Q16C2414yes—
522C2×Q16C2418yes—
523C2×Q16C2418yes—
524C2×SD16C2418yes—
525C2×M16C2414yes—
526C22×C8C2412yes—
527C22×C8C2412yes—
528C4⋊Q8—28no—
529C4⋊Q8—28no—
530C4⋊Q8—28no—
531C4⋊Q8—28no—
532C4⋊Q8—24no—
533C4⋊Q8—24no—
534C4⋊Q8—28no—
535C4⋊Q8—24no—
536C4⋊Q8—28no—
537C4⋊Q8—28no—
538C4⋊Q8—24no—
539C4⋊Q8—28no—
540C4⋊Q8—28no—
541C4⋊Q8—28no—
542C4⋊Q8—24no—
543C4⋊Q8—28no—
544C4⋊Q8—28no—
545C4⋊Q8—24no—
546C4⋊Q8—24no—
547C4⋊Q8—24no—
548C4⋊Q8—24no—
549C4⋊Q8—28no—
550C4⋊Q8—24no—
551C4⋊Q8—24no—
552C4⋊Q8—28no—
553C4⋊Q8—22no—
554C4⋊Q8C2×D414yes—
555C4⋊Q8C2×D418yes—
556C4⋊Q8C2×D412yes—
557C4⋊Q8C2×D412yes—
558C4⋊Q8C2×D418yes—
559C4⋊Q8C2414yes—
560C4⋊Q8C2411yescharacteristic
561C4⋊Q8C2418yes—
562C4⋊Q8C2412yes—
563C4⋊Q8C2418yes—
564C4⋊Q8C2414yes—
565C4⋊Q8C2418yes—
566C4⋊Q8C2418yes—
567C4⋊Q8C2412yes—
568C4⋊Q8C2412yes—
569#127C2411yescharacteristic
570#126—24no—
571#126—28no—
572#126—28no—
573#126—28no—
574#126—28no—
575#126—28no—
576#126—28no—
577#126—28no—
578#126—24no—
579#126—28no—
580#126—28no—
581#126—28no—
582#125—28no—
583#125—28no—
584#125—28no—
585#125—24no—
586#125—24no—
587#125—24no—
588#125—28no—
589#125—28no—
590#125—28no—
591#125—28no—
592#125—28no—
593#125—28no—
594#125—28no—
595#125—28no—
596#125—28no—
597#125—28no—
598#125—28no—
599#125—28no—
600#125—28no—
601#125—28no—
602#125—24no—
603#125—24no—
604#125—28no—
605#125—24no—
606#125—24no—
607#125—28no—
608#125—28no—
609#125—28no—
610#125—28no—
611#125—28no—
612#125—28no—
613#125—28no—
614#125—28no—
615#125—22no—
616#125—28no—
617#125C2×D412yes—
618#125C2×D412yes—
619#125C2×D418yes—
620#125C2×D414yes—
621#125C2×D418yes—
622#125C2414yes—
623#125C2418yes—
624#125C2412yes—
625#125C2414yes—
626#125C2418yes—
627#125C2418yes—
628#125C2412yes—
629#125C2412yes—
630#124—24no—
631#124—24no—
632#124—28no—
633#124C2418yes—
634#124C2412yes—
635#123—22no—
636#123—28no—
637#123—24no—
638#123—28no—
639#123—28no—
640#123—24no—
641#123—28no—
642C22⋊Q8—28no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—24no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—24no—
650C22⋊Q8—28no—
651C22⋊Q8—28no—
652C22⋊Q8—28no—
653C22⋊Q8—24no—
654C22⋊Q8—24no—
655C22⋊Q8—24no—
656C22⋊Q8—28no—
657C22⋊Q8—28no—
658C22⋊Q8—28no—
659C22⋊Q8—28no—
660C22⋊Q8—28no—
661C22⋊Q8—24no—
662C22⋊Q8—24no—
663C22⋊Q8—28no—
664C22⋊Q8—24no—
665C22⋊Q8—24no—
666C22⋊Q8—28no—
667C22⋊Q8—28no—
668C22⋊Q8C2×D414yes—
669C22⋊Q8C2×D414yes—
670C22⋊Q8C2×D418yes—
671C22⋊Q8C2×D418yes—
672C22⋊Q8C2×D418yes—
673C22⋊Q8C2×D418yes—
674C22⋊Q8C2×D418yes—
675C22⋊Q8C2418yes—
676C22⋊Q8C2414yes—
677#121—22no—
678#121—24no—
679#121C2414yes—
680#120—22no—
681C4×Q8—24no—
682C4×Q8—28no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—28no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—28no—
692C4×Q8—28no—
693C4×Q8—28no—
694C4×Q8—28no—
695C4×Q8—24no—
696C4×Q8—24no—
697C4×Q8—28no—
698C4×Q8—28no—
699C4×Q8—28no—
700C4×Q8—24no—
701C4×Q8—28no—
702C4×Q8—28no—
703C4×Q8—24no—
704C4×Q8—28no—
705C4×Q8—24no—
706C4×Q8—28no—
707C4×Q8—24no—
708C4×Q8—28no—
709C4×Q8—22no—
710C4×Q8—22no—
711C4×Q8—28no—
712C4×Q8—22no—
713C4×Q8—22no—
714C4×Q8—22no—
715C4×Q8—24no—
716C4×Q8—28no—
717C4×Q8—22no—
718C4×Q8—22no—
719C4×Q8—28no—
720C4×Q8—28no—
721C4×Q8C2418yes—
722C4×Q8C2418yes—
723C4×Q8C2418yes—
724C4×Q8C2418yes—
725C4×Q8C2418yes—
726C4×Q8C2414yes—
727C4×Q8C2414yes—
728C4×Q8C2414yes—
729C4×Q8C2414yes—
730C4×Q8C2414yes—
731C4×Q8C2418yes—
732C4×Q8C2418yes—
733C4×Q8C2418yes—
734C4×Q8C2418yes—
735C4×Q8C2414yes—
736C4×Q8C2414yes—
737C4×D4—24no—
738C4×D4—24no—
739C4×D4—28no—
740C4×D4—24no—
741C4×D4—28no—
742C4×D4—22no—
743C4×D4C2414yes—
744C4×D4C2418yes—
745#117—22no—
746#117—22no—
747#117—22no—
748#117—28no—
749#117—24no—
750#117—28no—
751#117—28no—
752#117—28no—
753#117—28no—
754#117—28no—
755#117—28no—
756#117—28no—
757#117—28no—
758#117—28no—
759#117—22no—
760#117—28no—
761#117C2×D414yes—
762#117C2×D412yes—
763#117C2×D414yes—
764#117C2×D412yes—
765#117C2412yes—
766#117C2412yes—
767#117C2414yes—
768#117C2414yes—
769#117C2412yes—
770#117C2414yes—
771#117C2412yes—
772#117C2412yes—
773#117C2414yes—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—22no—
776C2×C4⋊C4—28no—
777C2×C4⋊C4—22no—
778C2×C4⋊C4—22no—
779C2×C4⋊C4—22no—
780C2×C4⋊C4—22no—
781C2×C4⋊C4—24no—
782C2×C4⋊C4—28no—
783C2×C4⋊C4C2×D412yes—
784C2×C4⋊C4C2×D414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C22⋊C4—21no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4C2×D412yes—
792C2×C22⋊C4C2×D414yes—
793C2×C42—22no—
794C2×C42—22no—
795C2×C42—28no—
796C2×C42—21no—
797C2×C42—22no—
798C2×C42—22no—
799C2×C42—22no—
800C2×C42C2411yescharacteristic
801C2×C42C2411yescharacteristic
802C2×C42C2414yes—
803#107C2414yes—
804#107C2414yes—
805#107C2414yes—
806#107C2414yes—
807#107C2414yes—
808#107C2414yes—
809#107C2418yes—
810#107C2418yes—
811#107C2418yes—
812#106C2418yes—
813#106C2414yes—
814#106C2414yes—
815#106C2414yes—
816#106C2414yes—
817#106C2418yes—
818#106C2418yes—
819#106C2418yes—
820C4⋊C8C2414yes—
821C4⋊C8C2414yes—
822C4⋊C8C2414yes—
823C4⋊C8C2414yes—
824C4⋊C8C2418yes—
825C4⋊C8C2418yes—
826C4⋊C8C2418yes—
827C4⋊C8C2418yes—
828#103C2414yes—
829#103C2418yes—
830#103C2414yes—
831#103C2414yes—
832#103C2414yes—
833#103C2418yes—
834#103C2414yes—
835#103C2414yes—
836#103C2414yes—
837#103C2414yes—
838#103C2418yes—
839#103C2418yes—
840#103C2418yes—
841#103C2418yes—
842#103C2418yes—
843#103C2418yes—
844#103C2418yes—
845#102C2414yes—
846#102C2414yes—
847#102C2414yes—
848#102C2414yes—
849#102C2418yes—
850C22⋊C8C2414yes—
851C22⋊C8C2414yes—
852C22⋊C8C2418yes—
853#97C2412yes—
854#97C2412yes—
855#97C2414yes—
856#97C2418yes—
857#97C2418yes—
858C4×C8C2411yescharacteristic
859C4×C8C2412yes—
860C4×C8C2411yescharacteristic
861C4×C8C2414yes—
862C4×C8C2418yes—
863C4×C8C2418yes—
864C24C22×D411yescharacteristic
865#41—28no—
866C2×Q8—216no—
867C2×Q8—28no—
868C2×Q8—216no—
869C2×Q8—24no—
870C2×Q8—22no—
871C2×Q8—22no—
872C2×Q8—28no—
873C2×Q8—22no—
874C2×Q8—28no—
875C2×Q8—22no—
876C2×Q8—22no—
877C2×Q8—24no—
878C2×Q8—28no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—24no—
882C2×Q8C22×D414yes—
883C2×Q8C22×D418yes—
884C2×Q8C22×D414yes—
885C2×Q82−1+418yes—
886C2×Q8C2514yes—
887C2×Q8C2512yes—
888C2×Q8C2514yes—
889C2×D4—22no—
890C2×D4—24no—
891C2×D4—22no—
892C2×D4C2512yes—
893C22×C4—28no—
894C22×C4—24no—
895C22×C4—22no—
896C22×C4—24no—
897C22×C4—22no—
898C22×C4—24no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—24no—
903C22×C4—28no—
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D412yes—
906C22×C4C22×D412yes—
907C22×C4C22×D412yes—
908C22×C4C22×D418yes—
909C22×C4C2512yes—
910C22×C4C2511yescharacteristic
911Q16—28no—
912Q16—28no—
913Q16—216no—
914Q16—216no—
915SD16—216no—
916M16—28no—
917C2×C8—24no—
918C2×C8—24no—
919C2×C8C2512yes—
920C2×C8C2518yes—
921C2×C8C2512yes—
922C2×C8C2514yes—
923C4⋊C4—22no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—28no—
930C4⋊C4—28no—
931C4⋊C4—28no—
932C4⋊C4—28no—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—22no—
941C4⋊C4—28no—
942C4⋊C4—24no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—22no—
946C4⋊C4—28no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—28no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—24no—
953C4⋊C4—28no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—24no—
960C4⋊C4—28no—
961C4⋊C4—28no—
962C4⋊C4—28no—
963C4⋊C4—22no—
964C4⋊C4C22×D414yes—
965C4⋊C4C22×D418yes—
966C4⋊C4C22×D414yes—
967C4⋊C4C22×D414yes—
968C4⋊C4C22×D418yes—
969C4⋊C4C22×D414yes—
970C4⋊C4C22×D418yes—
971C4⋊C4C22×D418yes—
972C4⋊C4C22×D414yes—
973C4⋊C4C22×D418yes—
974C4⋊C4C22×D418yes—
975C4⋊C4C22×D414yes—
976C4⋊C4C2514yes—
977C4⋊C4C2514yes—
978C4⋊C4C2514yes—
979C4⋊C4C2514yes—
980C4⋊C4C2514yes—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—28no—
986C22⋊C4—22no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—28no—
991C22⋊C4—28no—
992C22⋊C4—24no—
993C22⋊C4—28no—
994C22⋊C4C22×D418yes—
995C22⋊C4C22×D414yes—
996C22⋊C4C22×D414yes—
997C22⋊C4C22×D414yes—
998C22⋊C4C22×D414yes—
999C42—28no—
1000C42—28no—
1001C42—24no—
1002C42—24no—
1003C42—28no—
1004C42—28no—
1005C42—28no—
1006C42—24no—
1007C42—22no—
1008C42—24no—
1009C42—24no—
1010C42—22no—
1011C42—22no—
1012C42—24no—
1013C42—24no—
1014C42—28no—
1015C42—28no—
1016C42—28no—
1017C42C22×D412yes—
1018C42C22×D414yes—
1019C42C22×D412yes—
1020C42C22×D414yes—
1021C42C2512yes—
1022C42C2518yes—
1023C42C2511yescharacteristic
1024C42C2511yescharacteristic
1025C23—22no—
1026C23—22no—
1027C23—42no—
1028C23C23×D412yes—
1029C23C23×D411yescharacteristic
1030Q8—216no—
1031Q8—24no—
1032Q8—28no—
1033Q8—24no—
1034Q8—24no—
1035Q8—24no—
1036Q8—44no—
1037Q8—48no—
1038Q8—44no—
1039Q8—44no—
1040Q8—84no—
1041Q8—88no—
1042Q8—82no—
1043Q8—88no—
1044Q8—82no—
1045Q8—88no—
1046Q8—82no—
1047Q8C2×2−1+418yes—
1048D4—24no—
1049D4—44no—
1050D4—82no—
1051D4—84no—
1052C2×C4—216no—
1053C2×C4—24no—
1054C2×C4—28no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—42no—
1066C2×C4—48no—
1067C2×C4—42no—
1068C2×C4—44no—
1069C2×C4—44no—
1070C2×C4—88no—
1071C2×C4—84no—
1072C2×C4—82no—
1073C2×C4—82no—
1074C2×C4—84no—
1075C2×C4C23×D412yes—
1076C2×C4C23×D412yes—
1077C2×C4C23×D418yes—
1078C2×C4C23×D412yes—
1079C2×C4C23×D414yes—
1080C2×C4C23×D418yes—
1081C2×C4C23×D411yescharacteristic
1082C2×C4C2×2−1+414yes—
1083C2×C4C2611yescharacteristic
1084C8—22no—
1085C8—22no—
1086C8—24no—
1087C8—28no—
1088C22—22no—
1089C22—22no—
1090C22—24no—
1091C22—42no—
1092C22—44no—
1093C22—82no—
1094C22#348612yes—
1095C22C24×D411yescharacteristic
1096C4—28no—
1097C4—22no—
1098C4—24no—
1099C4—28no—
1100C4—22no—
1101C4—28no—
1102C4—22no—
1103C4—42no—
1104C4—44no—
1105C4—44no—
1106C4—44no—
1107C4—44no—
1108C4—44no—
1109C4—44no—
1110C4#348612yes—
1111C4C22×2−1+412yes—
1112C2—22no—
1113C2—42no—
1114C2—82no—
1115C2C2×#348611yescharacteristic
1116C2#6309312yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#3455C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3458 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #62849C2semidirect
3. #61875C2semidirect
4. #61866C2semidirect
5. #61856C2semidirect
6. #61852C2semidirect
7. #61386C2semidirect
8. #61379C2semidirect
9. #61372C2semidirect
10. #61342C2semidirect
11. #61335C2semidirect
12. #61328C2semidirect
13. #60876C2semidirect
14. #60869C2semidirect
16. #60583C2semidirect
18. C2×#3127C2semidirect
19. #60252C2semidirect
48. #3390C22semidirect
49. #3390C22semidirect
50. #3390C22semidirect
51. #3390C22semidirect
52. #3390C22semidirect
53. #3388C22semidirect
54. #3388C22semidirect
55. #3387C22semidirect
56. #3387C22semidirect
57. #3387C22semidirect
58. #3387C22semidirect
59. #3387C22semidirect
60. #3385C22semidirect
61. #3383C22semidirect
62. #3383C22semidirect
63. #3383C22semidirect
64. Q8×Q16C22semidirect
65. #3381C22semidirect
66. #3377C22semidirect
67. #3377C22semidirect
68. #3377C22semidirect
69. #3377C22semidirect
70. #3375C22semidirect
71. #3374C22semidirect
72. #3374C22semidirect
73. #3374C22semidirect
74. #3374C22semidirect
75. #3374C22semidirect
76. #3371C22semidirect
77. #3369C22semidirect
78. #3369C22semidirect
79. #3365C22semidirect
80. #3364C22semidirect
81. #3364C22semidirect
82. #3363C22semidirect
83. #3363C22semidirect

Maximal subgroups

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

subgroupindex
#628892
#628492
#618752
#618662
#618562
#618522
#613862
#613792
#613722
#613422
#613352
#613282
#608762
#608692
#608592
#605832
#605662
C2×#31272
#602522