Finite Group Databasebeta

← #10578336

Subgroups — #10578336

Order 512.

5888 conjugacy classes of subgroups.

The subgroup lattice has 1139 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62881C211yesmaximal, characteristic
2#62849C211yesmaximal, characteristic, complemented
3#61874C218yesmaximal, complemented
4#61865C218yesmaximal, complemented
5#61856C218yesmaximal, complemented
6#61851C218yesmaximal, complemented
7#61386C214yesmaximal, complemented
8#61377C212yesmaximal, complemented
9#61371C212yesmaximal, complemented
10#61341C214yesmaximal, complemented
11#61334C212yesmaximal, complemented
12#61327C212yesmaximal, complemented
13#60875C214yesmaximal, complemented
14#60868C211yesmaximal, characteristic, complemented
15#60859C211yesmaximal, characteristic, complemented
16#60582C214yesmaximal, complemented
17#60566C211yesmaximal, characteristic, complemented
18C2×#3126C211yesmaximal, characteristic, complemented
19#60252C211yesmaximal, characteristic, complemented
20#3559—24no—
21#3557C2214yes—
22#3554C2218yes—
23#3548C2214yes—
24#3547—24no—
25#3536—24no—
26#3535—24no—
27#3508C2212yes—
28#3506C2212yes—
29#3504C2212yes—
30#3502—24no—
31#3502—24no—
32#3502—24no—
33#3502C2212yes—
34#3502C2212yes—
35#3502C2214yes—
36#3502C2218yescomplemented
37#3502C2218yescomplemented
38#3501C2212yes—
39#3494C2214yes—
40#3458—24no—
41#3458C2211yescharacteristic
42#3458C2212yes—
43#3458C2211yescharacteristic
44#3455C2211yescharacteristic
45C2×#540C2211yescharacteristic
46C2×#519C2211yescharacteristic
47C2×#519C2212yes—
48#3390C2218yescomplemented
49#3390C2218yescomplemented
50#3388C2218yescomplemented
51#3388C2218yescomplemented
52#3388C2218yescomplemented
53#3388C2218yescomplemented
54#3388C2218yescomplemented
55#3387C2218yescomplemented
56#3386C2218yescomplemented
57#3386C2214yescomplemented
58#3385C2218yescomplemented
59#3385C2218yescomplemented
60#3385C2214yescomplemented
61#3383C2218yescomplemented
62#3381C2218yescomplemented
63#3381C2218yescomplemented
64#3381C2214yescomplemented
65Q8×SD16C2214yescomplemented
66#3377C2218yescomplemented
67#3375C2218yescomplemented
68#3375C2218yescomplemented
69#3371C2218yescomplemented
70#3371C2218yescomplemented
71#3371C2218yescomplemented
72#3371C2218yescomplemented
73#3369C2214yescomplemented
74#3368C2214yescomplemented
75#3368C2218yescomplemented
76#3368C2218yescomplemented
77#3368C2218yescomplemented
78#3368C2218yescomplemented
79#3365C2218yescomplemented
80#3365C2218yescomplemented
81#3364C2214yescomplemented
82#3362C2214yescomplemented
83#3362C2218yescomplemented
84#3244C2218yescomplemented
85#3244C2214yescomplemented
86#3243C2218yescomplemented
87#3243C2214yescomplemented
88#3242C2214yescomplemented
89#3241C2218yes—
90#3241C2218yes—
91#3241C2214yescomplemented
92#3241C2218yescomplemented
93#3241C2218yescomplemented
94#3240C2218yescomplemented
95#3235C2218yescomplemented
96#3233C2218yescomplemented
97#3228C2218yescomplemented
98#3166C2212yes—
99#3164C2214yes—
100#3163C2214yes—
101#3162C2211yescharacteristic
102#3160C2211yescharacteristic
103#3138C2212yes—
104#3136C2214yes—
105#3136C2214yes—
106#3135C2211yescharacteristic
107#3131C2211yescharacteristic
108#3127C2214yescomplemented
109#3126C2218yes—
110#3126C2214yes—
111#3126C2214yes—
112#3126C2214yescomplemented
113#3126C2218yescomplemented
114#3126C2218yescomplemented
115#3121C2218yescomplemented
116#3121C2218yescomplemented
117#3121C2218yescomplemented
118#3117C2218yescomplemented
119#3112C2218yescomplemented
120#3108C2218yescomplemented
121#3103C2218yescomplemented
122#3094C2214yes—
123#3093C2212yes—
124#3091C2214yes—
125C2×#482C2212yes—
126#3084C2214yes—
127#3083C2214yes—
128#3082C2214yes—
129#3082C2214yes—
130#3081C2214yes—
131#3081C2214yes—
132#3078C2212yes—
133#3077C2212yes—
134#3077C2212yes—
135#3076C2214yes—
136C2×#479C2212yes—
137#3043C2214yes—
138#3043C2214yes—
139#3037C2212yes—
140C2×#460C2212yes—
141#3004C2212yes—
142C2×#448C2212yes—
143#2987C2214yescomplemented
144#2986C2214yescomplemented
145#2985C2218yescomplemented
146#2962C2214yes—
147#2961C2212yes—
148#2960C2212yes—
149#2949C2214yes—
150#2949C2214yes—
151#2947C2214yes—
152#2947C2214yes—
153C4×#137C2214yes—
154C2×#440C2212yes—
155C2×C4×SD16C2212yes—
156#2924C2214yes—
157#2921C2211yescharacteristic
158C2×#433C2211yescharacteristic
159C23×Q8C2311yescharacteristic
160C2×#137C2314yes—
161C22×SD16C2312yes—
162C22×SD16C2312yes—
163#563—28no—
164#562—28no—
165#562—28no—
166#562—28no—
167#559C2318yes—
168#559C2318yes—
169Q82—24no—
170Q82—22no—
171Q82—22no—
172Q82—28no—
173Q82—28no—
174Q82C2314yes—
175Q82C2318yes—
176Q82C2314yes—
177#557—24no—
178#557—22no—
179#557—22no—
180#557—28no—
181#557—28no—
182#557—24no—
183#557—24no—
184#557—24no—
185#557—24no—
186#557—28no—
187#557—28no—
188#557—28no—
189#557—28no—
190#557C2314yes—
191#557C2318yes—
192#557C2318yes—
193#557C2318yes—
194#557C2318yes—
195#557C2318yes—
196#557C2314yes—
197#557C2318yes—
198#556C2314yes—
199#555—22no—
200#555—24no—
201#554—22no—
202#554—24no—
203#554—28no—
204#554C2318yes—
205#554C2314yes—
206#554C2318yes—
207#553—24no—
208#553—24no—
209#553—24no—
210#552—28no—
211#551—28no—
212#550C2314yes—
213#550C2318yes—
214D4×Q8—22no—
215D4×Q8C2314yes—
216#548—28no—
217#547—22no—
218#547—28no—
219#547—28no—
220#547—24no—
221#546—28no—
222#546—28no—
223#544—24no—
224#544—24no—
225#544—24no—
226#544—28no—
227#544—28no—
228#544—28no—
229#544—28no—
230#544—28no—
231#544—22no—
232#544—24no—
233#544D414yes—
234#544D414yes—
235#544D414yes—
236#544C2314yes—
237#544C2314yes—
238#544C2314yes—
239#544C2314yes—
240#544C2314yes—
241#544C2318yes—
242#543—24no—
243#543—22no—
244#543—24no—
245#543D414yes—
246#542—28no—
247#542—28no—
248#542C2314yes—
249#542C2318yes—
250#541C2312yes—
251#540—22no—
252#540—22no—
253#540—24no—
254#540C2314yes—
255#540C2314yes—
256#540C2312yes—
257#540C2318yes—
258#539—28no—
259#539—28no—
260#539—28no—
261#539—22no—
262#538—24no—
263#538—22no—
264#537—28no—
265#537—28no—
266#536—28no—
267#535C2314yes—
268#533—22no—
269#533—24no—
270#533—24no—
271#533—28no—
272#533—28no—
273#533—28no—
274#533—28no—
275#533—28no—
276#533—24no—
277#533—24no—
278#533—22no—
279#533—22no—
280#533C2312yes—
281#533C2311yescharacteristic
282#533C2311yescharacteristic
283#533C2311yescharacteristic
284#533C2318yes—
285#533C2312yes—
286#533C2312yes—
287#533C2314yes—
288#533C2314yes—
289#532—24no—
290#532C2311yescharacteristic
291#532C2318yes—
292C2×#127C2311yescharacteristic
293#529—24no—
294#529C2318yes—
295C2×#125—22no—
296C2×#125C2311yescharacteristic
297#525—24no—
298#525C2312yes—
299C2×#123—22no—
300C2×C22⋊Q8—24no—
301C2×#121—22no—
302C2×#121C2312yes—
303#520C2314yes—
304#519—24no—
305#519—24no—
306#519—22no—
307#519—22no—
308#519C2314yes—
309#519C2314yes—
310#519C2314yes—
311#519C2318yes—
312#519C2314yes—
313#518C2314yes—
314C4×#41C2312yes—
315C2×C4×Q8—22no—
316C2×C4×Q8—24no—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2318yes—
320C2×C4×D4C2312yes—
321C2×#117—22no—
322C2×#117—24no—
323C2×#117C2311yescharacteristic
324C2×#117C2312yes—
325C2×#117C2311yescharacteristic
326C2×#117C2312yes—
327#501C2314yes—
328#501C2318yes—
329#501C2318yes—
330#501C2318yes—
331#501C2314yes—
332#501C2318yes—
333#501C2318yes—
334#500C2318yes—
335#500C2312yes—
336#499C2318yes—
337#499C2314yes—
338#499C2318yes—
339#499C2318yes—
340#498C2312yes—
341#498C2318yes—
342#491C2312yes—
343#490C2312yes—
344#490C2318yes—
345#490C2318yes—
346#490C2318yes—
347#489C2318yes—
348#489C2314yes—
349#489C2318yes—
350#488C2318yes—
351#488C2312yes—
352#488C2318yes—
353#488C2312yes—
354#487C2312yes—
355#486C2318yes—
356#486C2312yes—
357#486C2318yes—
358#486C2318yes—
359#485C2314yes—
360#485C2314yes—
361#485C2318yes—
362#484C2314yes—
363#483C2314yes—
364#482C2318yes—
365#482C2318yes—
366#482C2314yes—
367#482C2314yes—
368#482C2318yes—
369#482C2318yes—
370#482C2318yes—
371#481C2314yes—
372#481C2318yes—
373#480C2314yes—
374#480C2318yes—
375#479C2318yes—
376#479C2318yes—
377#479C2314yes—
378#479C2314yes—
379#479C2318yes—
380#479C2318yes—
381#479C2318yes—
382#479C2318yes—
383#479C2318yes—
384#479C2318yes—
385#479C2318yes—
386#478C2314yes—
387#478C2314yes—
388#478C2318yes—
389#478C2318yes—
390#478C2318yes—
391#478C2318yes—
392#478C2318yes—
393#478C2318yes—
394#478C2318yes—
395#478C2318yes—
396#477C2314yes—
397#477C2314yes—
398#477C2318yes—
399#477C2318yes—
400#477C2318yes—
401#476C2314yes—
402#476C2314yes—
403#476C2314yes—
404#476C2318yes—
405#476C2318yes—
406#476C2318yes—
407#475C2314yes—
408#475C2314yes—
409#475C2318yes—
410#475C2318yes—
411#475C2318yes—
412#474C2314yes—
413#474C2314yes—
414#474C2314yes—
415#474C2318yes—
416#474C2318yes—
417#474C2318yes—
418#464C2318yes—
419#464C2318yes—
420#464C2318yes—
421#464C2318yes—
422#464C2318yes—
423#462C2314yes—
424#460C2318yes—
425#460C2318yes—
426#460C2318yes—
427#460C2318yes—
428#460C2318yes—
429#460C2314yes—
430#460C2318yes—
431#451C2318yes—
432#448C2318yes—
433#448C2318yes—
434#448C2318yes—
435#446C2314yes—
436#446C2318yes—
437#446C2318yes—
438#446C2318yes—
439#446C2318yes—
440#446C2314yes—
441#446C2318yes—
442C8×Q8C2314yes—
443C8×Q8C2318yes—
444C8×Q8C2314yes—
445#441C2318yes—
446#441C2318yes—
447#441C2318yes—
448#440C2318yes—
449#440C2318yes—
450#440C2318yes—
451#440C2318yes—
452#440C2318yes—
453#440C2318yes—
454#440C2318yes—
455#440C2318yes—
456#440C2318yes—
457C4×Q16C2318yes—
458C4×Q16C2318yes—
459C4×Q16C2318yes—
460C4×SD16C2318yes—
461C4×SD16C2318yes—
462C4×SD16C2318yes—
463C4×SD16C2318yes—
464C4×SD16C2318yes—
465C4×SD16C2314yes—
466C4×SD16C2318yes—
467C4×SD16C2318yes—
468C4×SD16C2314yes—
469C4×SD16C2314yes—
470C4×SD16C2314yes—
471#433C2314yes—
472#433C2318yes—
473#433C2318yes—
474#433C2314yes—
475#433C2312yes—
476#433C2312yes—
477#433C2314yes—
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#418C2314yes—
493#418C2314yes—
494#417C2314yes—
495#416C2314yes—
496#416C2314yes—
497C2×#103C2312yes—
498C2×#103C2312yes—
499C2×#102C2312yes—
500C2×#102C2312yes—
501#407C2312yes—
502C2×C22⋊C8C2312yes—
503#405C2314yes—
504#405C2314yes—
505C4×M16C2312yes—
506C2×#97C2311yescharacteristic
507C2×C4×C8C2311yescharacteristic
508C2×#41—24no—
509C2×#41—28no—
510C2×#41—28no—
511C2×#41C2412yes—
512C22×Q8—28no—
513C22×Q8—24no—
514C22×Q8—21no—
515C22×Q8—22no—
516C22×Q8C2414yes—
517C22×Q8C2412yes—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4C2412yes—
521C23×C4—21no—
522C23×C4—22no—
523C23×C4C2411yescharacteristic
524#137—216no—
525C2×Q16C2418yes—
526C2×SD16—28no—
527C2×SD16—28no—
528C2×SD16C2414yes—
529C2×SD16C2414yes—
530C2×SD16C2418yes—
531C2×SD16C2418yes—
532C2×M16C2414yes—
533C22×C8C2412yes—
534C22×C8C2412yes—
535C4⋊Q8—24no—
536C4⋊Q8—28no—
537C4⋊Q8—24no—
538C4⋊Q8—28no—
539C4⋊Q8—28no—
540C4⋊Q8—28no—
541C4⋊Q8—28no—
542C4⋊Q8—28no—
543C4⋊Q8—28no—
544C4⋊Q8—28no—
545C4⋊Q8—24no—
546C4⋊Q8—24no—
547C4⋊Q8—28no—
548C4⋊Q8—28no—
549C4⋊Q8—28no—
550C4⋊Q8—24no—
551C4⋊Q8—24no—
552C4⋊Q8—24no—
553C4⋊Q8—24no—
554C4⋊Q8—28no—
555C4⋊Q8—24no—
556C4⋊Q8C2×D414yes—
557C4⋊Q8C2×D418yes—
558C4⋊Q8C2×D412yes—
559C4⋊Q8C2×D418yes—
560C4⋊Q8C2×D412yes—
561C4⋊Q8C2411yescharacteristic
562C4⋊Q8C2418yes—
563C4⋊Q8C2412yes—
564C4⋊Q8C2412yes—
565C4⋊Q8C2412yes—
566C4⋊Q8C2418yes—
567C4⋊Q8C2418yes—
568C4⋊Q8C2414yes—
569#127—22no—
570#127C2414yes—
571#127C2418yes—
572#127C2411yescharacteristic
573#126—24no—
574#126—28no—
575#126—28no—
576#126—24no—
577#126—28no—
578#125—28no—
579#125—24no—
580#125—24no—
581#125—28no—
582#125—28no—
583#125—28no—
584#125—28no—
585#125—28no—
586#125—28no—
587#125—28no—
588#125—28no—
589#125—28no—
590#125—28no—
591#125—28no—
592#125—28no—
593#125—24no—
594#125—24no—
595#125—24no—
596#125—28no—
597#125—24no—
598#125—28no—
599#125—22no—
600#125C2×D412yes—
601#125C2×D412yes—
602#125C2×D418yes—
603#125C2×D418yes—
604#125C2×D414yes—
605#125C2414yes—
606#125C2418yes—
607#125C2412yes—
608#125C2412yes—
609#125C2412yes—
610#125C2418yes—
611#125C2418yes—
612#125C2414yes—
613#124—28no—
614#124—28no—
615#124—24no—
616#124—28no—
617#124—28no—
618#124C2418yes—
619#124C2412yes—
620#123—22no—
621#123—28no—
622#123—28no—
623#123—28no—
624#123—28no—
625#123—24no—
626#123—28no—
627#123—28no—
628#123—28no—
629#123—28no—
630#123—28no—
631#123—24no—
632#123—28no—
633C22⋊Q8—24no—
634C22⋊Q8—24no—
635C22⋊Q8—28no—
636C22⋊Q8—28no—
637C22⋊Q8—22no—
638C22⋊Q8—22no—
639C22⋊Q8—22no—
640C22⋊Q8—24no—
641C22⋊Q8—28no—
642C22⋊Q8—28no—
643C22⋊Q8—28no—
644C22⋊Q8—24no—
645C22⋊Q8—24no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—28no—
651C22⋊Q8—28no—
652C22⋊Q8—28no—
653C22⋊Q8—28no—
654C22⋊Q8—28no—
655C22⋊Q8—24no—
656C22⋊Q8—24no—
657C22⋊Q8—28no—
658C22⋊Q8—24no—
659C22⋊Q8—24no—
660C22⋊Q8—28no—
661C22⋊Q8C2×D414yes—
662C22⋊Q8C2×D414yes—
663C22⋊Q8C2×D418yes—
664C22⋊Q8C2×D418yes—
665C22⋊Q8C2×D418yes—
666C22⋊Q8C2×D418yes—
667C22⋊Q8C2×D418yes—
668C22⋊Q8C2414yes—
669#121—24no—
670#121—22no—
671#121—28no—
672#121—24no—
673#121—24no—
674#121—24no—
675#121—28no—
676#121—28no—
677#121—28no—
678#121—28no—
679#121—28no—
680#121—28no—
681#121—24no—
682#121—28no—
683#121—28no—
684#121C2418yes—
685#121C2414yes—
686#120—22no—
687#120—28no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—28no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—28no—
696C4×Q8—28no—
697C4×Q8—28no—
698C4×Q8—28no—
699C4×Q8—28no—
700C4×Q8—28no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—28no—
704C4×Q8—28no—
705C4×Q8—28no—
706C4×Q8—28no—
707C4×Q8—24no—
708C4×Q8—28no—
709C4×Q8—22no—
710C4×Q8—22no—
711C4×Q8—28no—
712C4×Q8—22no—
713C4×Q8—24no—
714C4×Q8—28no—
715C4×Q8—22no—
716C4×Q8—22no—
717C4×Q8—28no—
718C4×Q8C2414yes—
719C4×Q8C2414yes—
720C4×Q8C2418yes—
721C4×Q8C2418yes—
722C4×Q8C2418yes—
723C4×Q8C2418yes—
724C4×Q8C2418yes—
725C4×Q8C2414yes—
726C4×Q8C2418yes—
727C4×Q8C2414yes—
728C4×Q8C2414yes—
729C4×Q8C2418yes—
730C4×D4—24no—
731C4×D4—24no—
732C4×D4—28no—
733C4×D4—24no—
734C4×D4—24no—
735C4×D4—28no—
736C4×D4—28no—
737C4×D4—28no—
738C4×D4—22no—
739C4×D4—22no—
740C4×D4—22no—
741C4×D4—28no—
742C4×D4C2414yes—
743C4×D4C2414yes—
744C4×D4C2414yes—
745C4×D4C2418yes—
746C4×D4C2418yes—
747C4×D4C2418yes—
748#117—22no—
749#117—22no—
750#117—22no—
751#117—24no—
752#117—24no—
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×D414yes—
763#117C2×D412yes—
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—24no—
779C2×C4⋊C4—28no—
780C2×C4⋊C4—24no—
781C2×C4⋊C4—28no—
782C2×C4⋊C4C2×D412yes—
783C2×C4⋊C4C2×D414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C22⋊C4—21no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—28no—
792C2×C22⋊C4C2×D412yes—
793C2×C22⋊C4C2×D414yes—
794C2×C42—22no—
795C2×C42—22no—
796C2×C42—28no—
797C2×C42—21no—
798C2×C42—22no—
799C2×C42—22no—
800C2×C42C2411yescharacteristic
801C2×C42C2411yescharacteristic
802C2×C42C2414yes—
803#107C2418yes—
804#107C2414yes—
805#107C2414yes—
806#107C2414yes—
807#107C2414yes—
808#107C2418yes—
809#107C2418yes—
810#107C2418yes—
811#106C2414yes—
812#106C2414yes—
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#103C2414yes—
830#103C2418yes—
831#103C2414yes—
832#103C2414yes—
833#103C2414yes—
834#103C2414yes—
835#103C2418yes—
836#103C2418yes—
837#103C2418yes—
838#102C2414yes—
839#102C2414yes—
840#102C2418yes—
841#102C2414yes—
842#102C2414yes—
843#102C2414yes—
844#102C2414yes—
845#102C2418yes—
846#102C2418yes—
847#102C2418yes—
848#102C2418yes—
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—
864C24—22no—
865C24C22×D411yescharacteristic
866#41—28no—
867#41—168no—
868#41—164no—
869#41—168no—
870C2×Q8—216no—
871C2×Q8—28no—
872C2×Q8—216no—
873C2×Q8—24no—
874C2×Q8—22no—
875C2×Q8—28no—
876C2×Q8—24no—
877C2×Q8—22no—
878C2×Q8—22no—
879C2×Q8—28no—
880C2×Q8—22no—
881C2×Q8—28no—
882C2×Q8—24no—
883C2×Q8—164no—
884C2×Q8C22×D414yes—
885C2×Q8C22×D414yes—
886C2×Q8C22×D418yes—
887C2×Q82−1+418yes—
888C2×Q8C2512yes—
889C2×Q8C2514yes—
890C2×D4—22no—
891C2×D4—24no—
892C2×D4—28no—
893C2×D4—22no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—22no—
897C2×D4—28no—
898C2×D4—24no—
899C2×D4—24no—
900C2×D4—162no—
901C2×D4—162no—
902C2×D4C2514yes—
903C2×D4C2512yes—
904C22×C4—28no—
905C22×C4—24no—
906C22×C4—22no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—24no—
913C22×C4—28no—
914C22×C4—28no—
915C22×C4—28no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—162no—
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D412yes—
921C22×C4C22×D412yes—
922C22×C4C22×D412yes—
923C22×C4C22×D418yes—
924C22×C4C2512yes—
925C22×C4C2511yescharacteristic
926Q16—216no—
927SD16—28no—
928SD16—28no—
929SD16—216no—
930SD16—216no—
931M16—28no—
932C2×C8—24no—
933C2×C8—24no—
934C2×C8C2512yes—
935C2×C8C2518yes—
936C2×C8C2512yes—
937C2×C8C2514yes—
938C4⋊C4—22no—
939C4⋊C4—28no—
940C4⋊C4—28no—
941C4⋊C4—28no—
942C4⋊C4—24no—
943C4⋊C4—22no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—28no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—28no—
953C4⋊C4—24no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—28no—
959C4⋊C4—24no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—28no—
963C4⋊C4—28no—
964C4⋊C4—28no—
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—24no—
968C4⋊C4—24no—
969C4⋊C4—28no—
970C4⋊C4—28no—
971C4⋊C4C22×D414yes—
972C4⋊C4C22×D418yes—
973C4⋊C4C22×D418yes—
974C4⋊C4C22×D414yes—
975C4⋊C4C22×D414yes—
976C4⋊C4C22×D418yes—
977C4⋊C4C22×D414yes—
978C4⋊C4C22×D414yes—
979C4⋊C4C22×D414yes—
980C4⋊C4C22×D418yes—
981C4⋊C4C22×D418yes—
982C4⋊C4C22×D418yes—
983C4⋊C4C2514yes—
984C4⋊C4C2514yes—
985C4⋊C4C2514yes—
986C4⋊C4C2514yes—
987C4⋊C4C2514yes—
988C22⋊C4—22no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—24no—
994C22⋊C4—28no—
995C22⋊C4—24no—
996C22⋊C4—28no—
997C22⋊C4—28no—
998C22⋊C4—24no—
999C22⋊C4—28no—
1000C22⋊C4—24no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—24no—
1004C22⋊C4—24no—
1005C22⋊C4C22×D418yes—
1006C22⋊C4C22×D414yes—
1007C22⋊C4C22×D414yes—
1008C22⋊C4C22×D414yes—
1009C22⋊C4C22×D414yes—
1010C42—28no—
1011C42—28no—
1012C42—28no—
1013C42—24no—
1014C42—24no—
1015C42—28no—
1016C42—28no—
1017C42—22no—
1018C42—24no—
1019C42—24no—
1020C42—22no—
1021C42—22no—
1022C42—24no—
1023C42—28no—
1024C42C22×D412yes—
1025C42C22×D414yes—
1026C42C22×D412yes—
1027C42C22×D414yes—
1028C42C2511yescharacteristic
1029C42C2511yescharacteristic
1030C42C2518yes—
1031C42C2512yes—
1032C23—22no—
1033C23—24no—
1034C23—22no—
1035C23—42no—
1036C23—44no—
1037C23—82no—
1038C23—82no—
1039C23C23×D412yes—
1040C23C23×D411yescharacteristic
1041Q8—216no—
1042Q8—24no—
1043Q8—28no—
1044Q8—24no—
1045Q8—44no—
1046Q8—44no—
1047Q8—48no—
1048Q8—82no—
1049Q8—88no—
1050Q8—82no—
1051Q8—84no—
1052Q8—88no—
1053Q8—82no—
1054Q8—88no—
1055Q8C2×2−1+418yes—
1056D4—24no—
1057D4—24no—
1058D4—24no—
1059D4—44no—
1060D4—44no—
1061D4—88no—
1062D4—88no—
1063D4—82no—
1064D4—88no—
1065D4—88no—
1066D4—84no—
1067C2×C4—216no—
1068C2×C4—24no—
1069C2×C4—28no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—42no—
1080C2×C4—42no—
1081C2×C4—48no—
1082C2×C4—44no—
1083C2×C4—84no—
1084C2×C4—84no—
1085C2×C4—88no—
1086C2×C4—88no—
1087C2×C4—88no—
1088C2×C4—84no—
1089C2×C4—82no—
1090C2×C4—84no—
1091C2×C4—82no—
1092C2×C4C23×D412yes—
1093C2×C4C23×D418yes—
1094C2×C4C23×D414yes—
1095C2×C4C23×D412yes—
1096C2×C4C23×D412yes—
1097C2×C4C23×D418yes—
1098C2×C4C23×D411yescharacteristic
1099C2×C4C2×2−1+414yes—
1100C2×C4C2611yescharacteristic
1101C8—22no—
1102C8—22no—
1103C8—24no—
1104C8—28no—
1105C22—22no—
1106C22—22no—
1107C22—24no—
1108C22—42no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—44no—
1113C22—82no—
1114C22—164no—
1115C22#348612yes—
1116C22C24×D411yescharacteristic
1117C4—28no—
1118C4—22no—
1119C4—22no—
1120C4—28no—
1121C4—22no—
1122C4—24no—
1123C4—28no—
1124C4—42no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4—44no—
1130C4#348612yes—
1131C4C22×2−1+412yes—
1132C2—22no—
1133C2—42no—
1134C2—82no—
1135C2—84no—
1136C2C2×#348611yescharacteristic
1137C2#6309212yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#62881C2
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. #61874C2semidirect
4. #61865C2semidirect
5. #61856C2semidirect
6. #61851C2semidirect
7. #61386C2semidirect
8. #61377C2semidirect
9. #61371C2semidirect
10. #61341C2semidirect
11. #61334C2semidirect
12. #61327C2semidirect
13. #60875C2semidirect
14. #60868C2semidirect
15. #60859C2semidirect
16. #60582C2semidirect
17. #60566C2semidirect
18. C2×#3126C2semidirect
19. #60252C2semidirect
36. #3502C22semidirect
37. #3502C22semidirect
48. #3390C22semidirect
49. #3390C22semidirect
50. #3388C22semidirect
51. #3388C22semidirect
52. #3388C22semidirect
53. #3388C22semidirect
54. #3388C22semidirect
55. #3387C22semidirect
56. #3386C22semidirect
57. #3386C22semidirect
58. #3385C22semidirect
59. #3385C22semidirect
60. #3385C22semidirect
61. #3383C22semidirect
62. #3381C22semidirect
63. #3381C22semidirect
64. #3381C22semidirect
65. Q8×SD16C22semidirect
66. #3377C22semidirect
67. #3375C22semidirect
68. #3375C22semidirect
69. #3371C22semidirect
70. #3371C22semidirect
71. #3371C22semidirect
72. #3371C22semidirect
73. #3369C22semidirect
74. #3368C22semidirect
75. #3368C22semidirect
76. #3368C22semidirect
77. #3368C22semidirect
78. #3368C22semidirect
79. #3365C22semidirect
80. #3365C22semidirect
81. #3364C22semidirect
82. #3362C22semidirect
83. #3362C22semidirect
84. #3244C22semidirect
85. #3244C22semidirect
86. #3243C22semidirect
87. #3243C22semidirect
88. #3242C22semidirect
91. #3241C22semidirect
92. #3241C22semidirect
93. #3241C22semidirect
94. #3240C22semidirect
95. #3235C22semidirect
96. #3233C22semidirect
97. #3228C22semidirect
108. #3127C22semidirect
112. #3126C22semidirect
113. #3126C22semidirect
114. #3126C22semidirect
115. #3121C22semidirect
116. #3121C22semidirect
117. #3121C22semidirect
118. #3117C22semidirect
119. #3112C22semidirect
120. #3108C22semidirect
121. #3103C22semidirect
143. #2987C22semidirect
144. #2986C22semidirect
145. #2985C22semidirect

Maximal subgroups

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

subgroupindex
#628812
#628492
#618742
#618652
#618562
#618512
#613862
#613772
#613712
#613412
#613342
#613272
#608752
#608682
#608592
#605822
#605662
C2×#31262
#602522