Finite Group Databasebeta

← #10578302

Subgroups — #10578302

Order 512.

5892 conjugacy classes of subgroups.

The subgroup lattice has 1297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62837C211yesmaximal, characteristic
2C2×#3502C211yesmaximal, characteristic, complemented
3#61866C218yesmaximal, complemented
4#61854C214yesmaximal, complemented
5#61852C214yesmaximal, complemented
6#61842C218yesmaximal, complemented
7#61830C212yesmaximal, complemented
8#61829C212yesmaximal, complemented
9#61822C212yesmaximal, complemented
10#61821C212yesmaximal, complemented
11#61384C214yesmaximal, complemented
12#61372C214yesmaximal, complemented
13#61342C214yesmaximal, complemented
14#61328C214yesmaximal, complemented
15#60874C214yesmaximal, complemented
16#60865C211yesmaximal, characteristic, complemented
17#60846C211yesmaximal, characteristic
18#60583C214yesmaximal, complemented
19#60560C211yesmaximal, characteristic
20C2×#3104C211yesmaximal, characteristic, complemented
21#60250C211yesmaximal, characteristic, complemented
22#3563—22no—
23#3563—22no—
24#3556C2212yes—
25#3555—22no—
26#3555C2214yes—
27#3550C2212yes—
28#3538—22no—
29#3523—22no—
30#3523C2214yes—
31#3509—22no—
32#3509—21no—
33#3509C2212yes—
34#3507C2212yes—
35#3507C2212yes—
36#3503—21no—
37#3503C2212yes—
38#3502—22no—
39#3502—22no—
40#3502—22no—
41#3502—22no—
42#3502C2212yes—
43#3502C2214yes—
44#3502C2214yes—
45#3502C2214yes—
46#3502C2214yes—
47#3502C2212yes—
48#3495—22no—
49#3495C2214yes—
50C2×Q82—21no—
51C2×Q82C2212yes—
52C2×#557—21no—
53C2×#557—22no—
54C2×#557C2212yes—
55C2×#557C2214yes—
56C2×#544—22no—
57C2×#544C2212yes—
58#3444C2211yescharacteristic
59C2×#533—22no—
60C2×#533C2211yescharacteristic
61C2×#533C2211yescharacteristic
62C2×#533C2211yescharacteristic
63C2×#519C2212yes—
64C22×C4×Q8C2211yescharacteristic
65#3390C22116yescomplemented
66#3390C22116yescomplemented
67#3387C2218yescomplemented
68#3387C2218yescomplemented
69#3387C2218yescomplemented
70#3386C22116yescomplemented
71#3385C2218yescomplemented
72#3383C2218yescomplemented
73#3383C22116yescomplemented
74Q8×Q16C2218yescomplemented
75Q8×Q16C2218yescomplemented
76#3381C2218yescomplemented
77#3377C22116yescomplemented
78#3377C22116yescomplemented
79#3375C2218yescomplemented
80#3374C2218yescomplemented
81#3374C2218yescomplemented
82#3374C22116yescomplemented
83#3369C2218yescomplemented
84#3365C2218yescomplemented
85#3364C2218yescomplemented
86#3364C22116yescomplemented
87#3363C2218yescomplemented
88#3363C2218yescomplemented
89#3243C22116yes—
90#3242C22116yes—
91#3239C2218yes—
92#3237C2214yes—
93#3236C2218yes—
94#3236C2214yes—
95#3233C2214yes—
96#3232C2218yes—
97#3232C2214yes—
98#3231C2212yes—
99#3231C2214yes—
100#3230C2211yescharacteristic
101#3230C2212yes—
102#3230C2218yes—
103#3229C2212yes—
104#3229C2211yescharacteristic
105#3228C2212yes—
106#3227C2211yescharacteristic
107#3226C2211yescharacteristic
108#3165C2212yes—
109#3164C2218yes—
110#3160C2212yes—
111#3139C2212yes—
112#3137C2218yes—
113#3131C2212yes—
114#3127C22116yes—
115#3121C22116yes—
116#3117C2218yes—
117#3117C2214yes—
118#3113C2218yes—
119#3113C2212yes—
120#3112C2212yes—
121#3108C2218yes—
122#3108C2214yes—
123#3104C2212yes—
124#3104C2212yes—
125#3104C2214yes—
126#3104C2214yes—
127#3104C2214yes—
128#3104C2212yes—
129#3104C2218yes—
130#3103C2212yes—
131#3095C2214yes—
132#3092C2212yes—
133#3091C2214yes—
134C2×#484C2212yes—
135#3083C2218yes—
136#3082C2218yes—
137#3082C2218yes—
138#3078C2212yes—
139#3078C2214yes—
140#3076C2214yes—
141C2×#477C2212yes—
142#3044C2218yes—
143#3037C2212yes—
144C2×#462C2212yes—
145#3004C2212yes—
146C2×#451C2212yes—
147#2986C2214yes—
148#2985C2214yes—
149#2984C2214yes—
150#2983C2212yes—
151#2982C2212yes—
152#2962C2214yes—
153#2960C2214yes—
154#2950C2218yes—
155#2947C2218yes—
156C4×#137C2214yes—
157C2×C4×Q16C2214yes—
158#2924C2214yes—
159#2920C2211yescharacteristic
160C2×#431C2211yescharacteristic
161C23×Q8C2311yescharacteristic
162C2×#137C2314yes—
163C22×Q16C2314yes—
164#564—24no—
165#563—24no—
166#563—28no—
167#559C2314yes—
168Q82—24no—
169Q82—24no—
170Q82—24no—
171Q82—24no—
172Q82—22no—
173Q82—24no—
174Q82—24no—
175Q82C2318yes—
176Q82C2318yes—
177Q82C2314yes—
178Q82C2314yes—
179#557—24no—
180#557—24no—
181#557—24no—
182#557—24no—
183#557—22no—
184#557—22no—
185#557—22no—
186#557—28no—
187#557—28no—
188#557—28no—
189#557—28no—
190#557—24no—
191#557—28no—
192#557—28no—
193#557—24no—
194#557—24no—
195#557—24no—
196#557—24no—
197#557C2314yes—
198#557C2314yes—
199#557C2314yes—
200#557C2318yes—
201#557C23116yes—
202#557C2318yes—
203#557C23116yes—
204#557C2314yes—
205#557C2318yes—
206#557C2314yes—
207#556—22no—
208#556—22no—
209#556—24no—
210#556—24no—
211#556—24no—
212#556C2314yes—
213#556C2318yes—
214#556C2314yes—
215#554—22no—
216#554—24no—
217#554—24no—
218#554C2314yes—
219#552—24no—
220#552—24no—
221#552—24no—
222#552—24no—
223#552—24no—
224#552—24no—
225#552—28no—
226#552—28no—
227#552—24no—
228#552—24no—
229#551—28no—
230D4×Q8—24no—
231D4×Q8—22no—
232D4×Q8—24no—
233D4×Q8C2314yes—
234#544—24no—
235#544—24no—
236#544—28no—
237#544—28no—
238#544—28no—
239#544—28no—
240#544—24no—
241#544—24no—
242#544—24no—
243#544—22no—
244#544—24no—
245#544C2314yes—
246#544C2318yes—
247#544C2318yes—
248#542—24no—
249#542C2318yes—
250#541—24no—
251#541—24no—
252#541—28no—
253#541—24no—
254#541—24no—
255#541—24no—
256#541—28no—
257#541C2318yes—
258#539—24no—
259#539—24no—
260#536—22no—
261#536—24no—
262#536C2314yes—
263#533—22no—
264#533—22no—
265#533—22no—
266#533—28no—
267#533—28no—
268#533—28no—
269#533—28no—
270#533—24no—
271#533—21no—
272#533—21no—
273#533—21no—
274#533—21no—
275#533—21no—
276#533—21no—
277#533—21no—
278#533—21no—
279#533D412yes—
280#533D412yes—
281#533D412yes—
282#533D412yes—
283#533C2312yes—
284#533C2312yes—
285#533C2312yes—
286#533C2312yes—
287#533C2311yescharacteristic
288#533C2318yes—
289#533C2311yescharacteristic
290#533C2312yes—
291#533C2312yes—
292#533C2311yescharacteristic
293#533C2312yes—
294#533C2312yes—
295#533C2312yes—
296#533C2312yes—
297#533C2312yes—
298#533C2312yes—
299#532C2311yescharacteristic
300#532C2311yescharacteristic
301#532C2311yescharacteristic
302C2×C4⋊Q8—22no—
303C2×C4⋊Q8—24no—
304C2×C4⋊Q8—22no—
305C2×C4⋊Q8—22no—
306C2×C4⋊Q8—24no—
307C2×C4⋊Q8—22no—
308C2×C4⋊Q8D411yescharacteristic
309C2×C4⋊Q8D411yescharacteristic
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2314yes—
315#529—24no—
316#529—21no—
317#529—21no—
318#529—21no—
319#529—21no—
320#529C2312yes—
321#529C2318yes—
322#529C2312yes—
323C2×#125—24no—
324C2×#125—24no—
325C2×#125—24no—
326C2×#125—22no—
327C2×#125—21no—
328C2×#125D412yes—
329C2×#125C2312yes—
330C2×#125C2314yes—
331#525—21no—
332#525—21no—
333#525C2312yes—
334C2×C22⋊Q8—21no—
335C2×C22⋊Q8—21no—
336C2×C22⋊Q8—21no—
337C2×C22⋊Q8—24no—
338C2×C22⋊Q8D412yes—
339C2×C22⋊Q8D412yes—
340C2×C22⋊Q8C2312yes—
341#520—22no—
342#520C2314yes—
343#519—22no—
344#519—24no—
345#519—24no—
346#519—24no—
347#519C2314yes—
348#519C2318yes—
349#519C2318yes—
350C4×#41—21no—
351C4×#41—21no—
352C4×#41C2312yes—
353C2×C4×Q8—22no—
354C2×C4×Q8—22no—
355C2×C4×Q8—22no—
356C2×C4×Q8—24no—
357C2×C4×Q8—22no—
358C2×C4×Q8—21no—
359C2×C4×Q8—21no—
360C2×C4×Q8—21no—
361C2×C4×Q8—21no—
362C2×C4×Q8—21no—
363C2×C4×Q8—21no—
364C2×C4×Q8—21no—
365C2×C4×Q8—21no—
366C2×C4×Q8—21no—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2312yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2312yes—
372C2×C4×Q8C2312yes—
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2314yes—
375C2×C4×Q8C2314yes—
376C2×C4×Q8C2312yes—
377C2×C4×Q8C2312yes—
378C2×#117—21no—
379C2×#117—24no—
380C2×#117C2312yes—
381C2×#117C2312yes—
382C22×C4⋊C4—21no—
383C22×C4⋊C4C2311yescharacteristic
384C22×C42—21no—
385C22×C42C2311yescharacteristic
386#501C23116yes—
387#501C2318yes—
388#501C23116yes—
389#500C2312yes—
390#500C23116yes—
391#500C2314yes—
392#500C2312yes—
393#499C23116yes—
394#499C2318yes—
395#498C2314yes—
396#498C2312yes—
397#498C2312yes—
398#491C23116yes—
399#491C2318yes—
400#489C23116yes—
401#488C23116yes—
402#488C2318yes—
403#487C2312yes—
404#487C23116yes—
405#487C2314yes—
406#487C2314yes—
407#487C2312yes—
408#486C2312yes—
409#486C2312yes—
410#485C2318yes—
411#485C23116yes—
412#484C2314yes—
413#484C2314yes—
414#484C2318yes—
415#484C2314yes—
416#484C2314yes—
417#484C2318yes—
418#483C2314yes—
419#483C2314yes—
420#483C2318yes—
421#482C2318yes—
422#481C2314yes—
423#481C2314yes—
424#480C2314yes—
425#480C2314yes—
426#479C2318yes—
427#479C2318yes—
428#479C23116yes—
429#479C23116yes—
430#479C23116yes—
431#479C23116yes—
432#479C23116yes—
433#479C23116yes—
434#478C2318yes—
435#478C23116yes—
436#477C2314yes—
437#477C2314yes—
438#477C2318yes—
439#477C2314yes—
440#477C2314yes—
441#477C2318yes—
442#477C23116yes—
443#477C23116yes—
444#477C23116yes—
445#476C2314yes—
446#475C2314yes—
447#475C2314yes—
448#475C2318yes—
449#475C23116yes—
450#475C23116yes—
451#474C2314yes—
452#474C23116yes—
453#464C2318yes—
454#464C23116yes—
455#464C23116yes—
456#462C2314yes—
457#462C2314yes—
458#462C2318yes—
459#462C2314yes—
460#462C23116yes—
461#462C23116yes—
462#460C2314yes—
463#451C2314yes—
464#451C2314yes—
465#451C2314yes—
466#451C2318yes—
467#451C2314yes—
468#448C2314yes—
469#448C2314yes—
470#446C2318yes—
471#446C2318yes—
472#446C23116yes—
473#446C2318yes—
474C8×Q8C2318yes—
475C8×Q8C2318yes—
476C8×Q8C2318yes—
477#441C2318yes—
478#441C23116yes—
479#441C23116yes—
480#441C23116yes—
481#440C2318yes—
482#440C23116yes—
483C4×Q16C2318yes—
484C4×Q16C2318yes—
485C4×Q16C2318yes—
486C4×Q16C2318yes—
487C4×Q16C2318yes—
488C4×Q16C23116yes—
489C4×Q16C23116yes—
490C4×Q16C23116yes—
491C4×SD16C2318yes—
492C4×SD16C23116yes—
493#433C23116yes—
494#432C2312yes—
495#432C2318yes—
496#432C2312yes—
497#431C2312yes—
498#431C2311yescharacteristic
499#431C2311yescharacteristic
500#431C2312yes—
501#431C2312yes—
502#431C2312yes—
503#431C2318yes—
504#431C2312yes—
505#428C2314yes—
506#428C2318yes—
507#427C2318yes—
508C2×#107C2314yes—
509#424C2318yes—
510#423C2312yes—
511C2×C4⋊C8C2312yes—
512#419C2314yes—
513#419C2318yes—
514#417C2314yes—
515#416C2318yes—
516C2×#103C2314yes—
517C2×#103C2314yes—
518#407C2312yes—
519C2×C22⋊C8C2312yes—
520#405C2318yes—
521C4×M16C2312yes—
522C2×C4×C8C2312yes—
523C2×#41—21no—
524C2×#41—21no—
525C2×#41C2412yes—
526C22×Q8—28no—
527C22×Q8—24no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8—21no—
531C22×Q8—21no—
532C22×Q8—21no—
533C22×Q8—24no—
534C22×Q8—21no—
535C22×Q8C2×D412yes—
536C22×Q8C2×D412yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2412yes—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C2×D411yescharacteristic
544C23×C4C2×D411yescharacteristic
545C23×C4C2411yescharacteristic
546#137—216no—
547C2×Q16—216no—
548C2×Q16C2418yes—
549C2×Q16C2418yes—
550C2×Q16C2418yes—
551C2×SD16C2418yes—
552C2×M16C2414yes—
553C22×C8C2414yes—
554C4⋊Q8—28no—
555C4⋊Q8—28no—
556C4⋊Q8—24no—
557C4⋊Q8—216no—
558C4⋊Q8—216no—
559C4⋊Q8—24no—
560C4⋊Q8—28no—
561C4⋊Q8—28no—
562C4⋊Q8—28no—
563C4⋊Q8—24no—
564C4⋊Q8—216no—
565C4⋊Q8—216no—
566C4⋊Q8—24no—
567C4⋊Q8—28no—
568C4⋊Q8—28no—
569C4⋊Q8—24no—
570C4⋊Q8—28no—
571C4⋊Q8—28no—
572C4⋊Q8—21no—
573C4⋊Q8—21no—
574C4⋊Q8—21no—
575C4⋊Q8—21no—
576C4⋊Q8—21no—
577C4⋊Q8—21no—
578C4⋊Q8—21no—
579C4⋊Q8—21no—
580C4⋊Q8—28no—
581C4⋊Q8C2×D412yes—
582C4⋊Q8C2×D412yes—
583C4⋊Q8C2×D412yes—
584C4⋊Q8C2×D412yes—
585C4⋊Q8C2×D412yes—
586C4⋊Q8C2×D412yes—
587C4⋊Q8C2×D412yes—
588C4⋊Q8C2×D412yes—
589C4⋊Q8C2412yes—
590C4⋊Q8C2412yes—
591C4⋊Q8C2411yescharacteristic
592C4⋊Q8C2418yes—
593C4⋊Q8C2412yes—
594C4⋊Q8C2412yes—
595C4⋊Q8C2412yes—
596C4⋊Q8C2412yes—
597C4⋊Q8C2412yes—
598C4⋊Q8C2412yes—
599C4⋊Q8C24116yes—
600C4⋊Q8C2411yescharacteristic
601C4⋊Q8C2411yescharacteristic
602C4⋊Q8C2418yes—
603#127C2411yescharacteristic
604#126—28no—
605#126—28no—
606#126—28no—
607#126—28no—
608#126—28no—
609#126—28no—
610#126—28no—
611#126—22no—
612#126—22no—
613#126—28no—
614#125—216no—
615#125—216no—
616#125—216no—
617#125—216no—
618#125—216no—
619#125—216no—
620#125—28no—
621#125—28no—
622#125—24no—
623#125—28no—
624#125—24no—
625#125—24no—
626#125—24no—
627#125—28no—
628#125—28no—
629#125—28no—
630#125—28no—
631#125—28no—
632#125—28no—
633#125—28no—
634#125—28no—
635#125—22no—
636#125—22no—
637#125—22no—
638#125—22no—
639#125—22no—
640#125—22no—
641#125—28no—
642#125—21no—
643#125—21no—
644#125—28no—
645#125C2×D414yes—
646#125C2×D414yes—
647#125C2×D414yes—
648#125C2×D414yes—
649#125C2414yes—
650#125C2414yes—
651#125C24116yes—
652#125C2412yes—
653#125C2418yes—
654#124—24no—
655#124—28no—
656#124—21no—
657#124—21no—
658#124C2412yes—
659#124C2418yes—
660#123—22no—
661#123—22no—
662#123—22no—
663#123—28no—
664#123—28no—
665#123—28no—
666#123—28no—
667C22⋊Q8—24no—
668C22⋊Q8—24no—
669C22⋊Q8—24no—
670C22⋊Q8—28no—
671C22⋊Q8—22no—
672C22⋊Q8—22no—
673C22⋊Q8—22no—
674C22⋊Q8—22no—
675C22⋊Q8—22no—
676C22⋊Q8—22no—
677C22⋊Q8—22no—
678C22⋊Q8—22no—
679C22⋊Q8—22no—
680C22⋊Q8—22no—
681C22⋊Q8—22no—
682C22⋊Q8—22no—
683C22⋊Q8—22no—
684C22⋊Q8—22no—
685C22⋊Q8—21no—
686C22⋊Q8—21no—
687C22⋊Q8—21no—
688C22⋊Q8—21no—
689C22⋊Q8—28no—
690C22⋊Q8—24no—
691C22⋊Q8—24no—
692C22⋊Q8—24no—
693C22⋊Q8—28no—
694C22⋊Q8—28no—
695C22⋊Q8—28no—
696C22⋊Q8—216no—
697C22⋊Q8—216no—
698C22⋊Q8—28no—
699C22⋊Q8C2×D414yes—
700C22⋊Q8C2×D414yes—
701C22⋊Q8C2×D414yes—
702C22⋊Q8C2×D414yes—
703C22⋊Q8C2×D414yes—
704C22⋊Q8C2×D414yes—
705C22⋊Q8C2×D414yes—
706C22⋊Q8C2×D414yes—
707C22⋊Q8C2414yes—
708C22⋊Q8C2414yes—
709C22⋊Q8C2412yes—
710C22⋊Q8C2412yes—
711#121—21no—
712#121—21no—
713#121—21no—
714#121—21no—
715#121C2412yes—
716#121C2412yes—
717#120—22no—
718C4×Q8—28no—
719C4×Q8—28no—
720C4×Q8—24no—
721C4×Q8—24no—
722C4×Q8—24no—
723C4×Q8—24no—
724C4×Q8—24no—
725C4×Q8—28no—
726C4×Q8—28no—
727C4×Q8—28no—
728C4×Q8—28no—
729C4×Q8—216no—
730C4×Q8—216no—
731C4×Q8—28no—
732C4×Q8—28no—
733C4×Q8—24no—
734C4×Q8—28no—
735C4×Q8—24no—
736C4×Q8—24no—
737C4×Q8—24no—
738C4×Q8—22no—
739C4×Q8—22no—
740C4×Q8—22no—
741C4×Q8—22no—
742C4×Q8—22no—
743C4×Q8—22no—
744C4×Q8—22no—
745C4×Q8—22no—
746C4×Q8—22no—
747C4×Q8—22no—
748C4×Q8—22no—
749C4×Q8—22no—
750C4×Q8—22no—
751C4×Q8—22no—
752C4×Q8—22no—
753C4×Q8—22no—
754C4×Q8—22no—
755C4×Q8—22no—
756C4×Q8—22no—
757C4×Q8—22no—
758C4×Q8—22no—
759C4×Q8—22no—
760C4×Q8—22no—
761C4×Q8—22no—
762C4×Q8—28no—
763C4×Q8—28no—
764C4×Q8—22no—
765C4×Q8—22no—
766C4×Q8—21no—
767C4×Q8—21no—
768C4×Q8—21no—
769C4×Q8—21no—
770C4×Q8—28no—
771C4×Q8C2×D414yes—
772C4×Q8C2×D414yes—
773C4×Q8C2×D414yes—
774C4×Q8C2×D414yes—
775C4×Q8C2414yes—
776C4×Q8C2414yes—
777C4×Q8C2414yes—
778C4×Q8C2414yes—
779C4×Q8C24116yes—
780C4×Q8C24116yes—
781C4×Q8C2414yes—
782C4×Q8C2414yes—
783C4×Q8C2412yes—
784C4×Q8C2412yes—
785C4×Q8C2418yes—
786C4×Q8C2418yes—
787C4×Q8C2418yes—
788C4×Q8C2414yes—
789C4×Q8C2414yes—
790C4×Q8C2414yes—
791C4×Q8C2414yes—
792C4×D4—22no—
793C4×D4—22no—
794C4×D4—22no—
795C4×D4—22no—
796C4×D4—22no—
797C4×D4—22no—
798C4×D4—28no—
799C4×D4—24no—
800C4×D4—28no—
801C4×D4—21no—
802C4×D4—21no—
803C4×D4—21no—
804C4×D4—21no—
805C4×D4C2412yes—
806C4×D4C2412yes—
807C4×D4C2418yes—
808#117—22no—
809#117—22no—
810#117—22no—
811#117—22no—
812#117—22no—
813#117—22no—
814#117—21no—
815#117—21no—
816#117—28no—
817#117—28no—
818#117—24no—
819#117—24no—
820#117—24no—
821#117—216no—
822#117—216no—
823#117—28no—
824#117—22no—
825#117—22no—
826#117—22no—
827#117—28no—
828#117C2×D414yes—
829#117C2×D414yes—
830#117C2414yes—
831#117C2414yes—
832#117C2412yes—
833#117C2414yes—
834#117C2414yes—
835C2×C4⋊C4—22no—
836C2×C4⋊C4—22no—
837C2×C4⋊C4—22no—
838C2×C4⋊C4—22no—
839C2×C4⋊C4—22no—
840C2×C4⋊C4—22no—
841C2×C4⋊C4—21no—
842C2×C4⋊C4—21no—
843C2×C4⋊C4—21no—
844C2×C4⋊C4—24no—
845C2×C4⋊C4—24no—
846C2×C4⋊C4—21no—
847C2×C4⋊C4—21no—
848C2×C4⋊C4—22no—
849C2×C4⋊C4—21no—
850C2×C4⋊C4—21no—
851C2×C4⋊C4—24no—
852C2×C4⋊C4—24no—
853C2×C4⋊C4—22no—
854C2×C4⋊C4—24no—
855C2×C4⋊C4—21no—
856C2×C4⋊C4—22no—
857C2×C4⋊C4—22no—
858C2×C4⋊C4—24no—
859C2×C4⋊C4—24no—
860C2×C4⋊C4C2×D412yes—
861C2×C4⋊C4C2×D412yes—
862C2×C4⋊C4C2×D412yes—
863C2×C4⋊C4C2×D414yes—
864C2×C4⋊C4C2×D412yes—
865C2×C4⋊C4C2×D414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C22⋊C4—22no—
873C2×C22⋊C4—22no—
874C2×C22⋊C4C2×D414yes—
875C2×C42—24no—
876C2×C42—24no—
877C2×C42—22no—
878C2×C42—22no—
879C2×C42—22no—
880C2×C42—22no—
881C2×C42—22no—
882C2×C42—22no—
883C2×C42—22no—
884C2×C42—22no—
885C2×C42—22no—
886C2×C42C2×D411yescharacteristic
887C2×C42C2×D411yescharacteristic
888C2×C42C2×D411yescharacteristic
889C2×C42C2×D411yescharacteristic
890C2×C42C2×D411yescharacteristic
891C2×C42C2×D411yescharacteristic
892C2×C42C2414yes—
893C2×C42C2411yescharacteristic
894C2×C42C2411yescharacteristic
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899#107C2418yes—
900#107C2418yes—
901#107C2418yes—
902#107C2418yes—
903#107C24116yes—
904#107C2418yes—
905#106C2418yes—
906#106C2418yes—
907#106C2418yes—
908#106C24116yes—
909C4⋊C8C2412yes—
910C4⋊C8C2412yes—
911C4⋊C8C2414yes—
912C4⋊C8C2414yes—
913C4⋊C8C2414yes—
914C4⋊C8C24116yes—
915C4⋊C8C24116yes—
916#103C2418yes—
917#103C2418yes—
918#103C2418yes—
919#103C2418yes—
920#103C2418yes—
921#103C2418yes—
922#103C2418yes—
923#103C2418yes—
924#103C2418yes—
925#103C24116yes—
926#103C24116yes—
927#102C2418yes—
928#102C2418yes—
929#102C2418yes—
930C22⋊C8C2412yes—
931C22⋊C8C2412yes—
932C22⋊C8C2414yes—
933C22⋊C8C2414yes—
934C22⋊C8C2414yes—
935#97C2414yes—
936#97C24116yes—
937C4×C8C2412yes—
938C4×C8C2414yes—
939C4×C8C2412yes—
940C4×C8C2414yes—
941C4×C8C24116yes—
942C24C22×D411yescharacteristic
943#41—28no—
944#41—44no—
945#41—82no—
946C2×Q8—28no—
947C2×Q8—28no—
948C2×Q8—28no—
949C2×Q8—28no—
950C2×Q8—28no—
951C2×Q8—28no—
952C2×Q8—22no—
953C2×Q8—22no—
954C2×Q8—22no—
955C2×Q8—22no—
956C2×Q8—21no—
957C2×Q8—22no—
958C2×Q8—22no—
959C2×Q8—22no—
960C2×Q8—22no—
961C2×Q8—28no—
962C2×Q8—21no—
963C2×Q8—22no—
964C2×Q8—22no—
965C2×Q8—216no—
966C2×Q8—24no—
967C2×Q8—28no—
968C2×Q8—44no—
969C2×Q8—82no—
970C2×Q8—82no—
971C2×Q8—88no—
972C2×Q8—82no—
973C2×Q8—88no—
974C2×Q8C22×D414yes—
975C2×Q8C22×D414yes—
976C2×Q8C22×D414yes—
977C2×Q8C22×D414yes—
978C2×Q82−1+418yes—
979C2×Q8C2514yes—
980C2×Q8C2512yes—
981C2×Q8C2514yes—
982C2×D4—22no—
983C2×D4—22no—
984C2×D4—22no—
985C2×D4—21no—
986C2×D4—21no—
987C2×D4C2512yes—
988C22×C4—28no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—28no—
1005C22×C4—81no—
1006C22×C4—82no—
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D414yes—
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C22×D414yes—
1017C22×C4C22×D411yescharacteristic
1018C22×C4C22×D411yescharacteristic
1019C22×C4C22×D411yescharacteristic
1020C22×C4C22×D411yescharacteristic
1021C22×C4C22×D411yescharacteristic
1022C22×C4C22×D411yescharacteristic
1023C22×C4C22×D411yescharacteristic
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027Q16—216no—
1028Q16—216no—
1029Q16—216no—
1030SD16—216no—
1031M16—28no—
1032C2×C8—28no—
1033C2×C8C2514yes—
1034C2×C8C2518yes—
1035C2×C8C2514yes—
1036C4⋊C4—22no—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—22no—
1044C4⋊C4—22no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—24no—
1048C4⋊C4—216no—
1049C4⋊C4—216no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—24no—
1059C4⋊C4—22no—
1060C4⋊C4—22no—
1061C4⋊C4—216no—
1062C4⋊C4—216no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—216no—
1066C4⋊C4—22no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—22no—
1070C4⋊C4—22no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—21no—
1076C4⋊C4—21no—
1077C4⋊C4—22no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—22no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4C22×D414yes—
1088C4⋊C4C22×D414yes—
1089C4⋊C4C22×D414yes—
1090C4⋊C4C22×D418yes—
1091C4⋊C4C22×D414yes—
1092C4⋊C4C22×D414yes—
1093C4⋊C4C22×D414yes—
1094C4⋊C4C22×D414yes—
1095C4⋊C4C22×D418yes—
1096C4⋊C4C22×D418yes—
1097C4⋊C4C22×D418yes—
1098C4⋊C4C22×D414yes—
1099C4⋊C4C2514yes—
1100C4⋊C4C2514yes—
1101C4⋊C4C2514yes—
1102C4⋊C4C2512yes—
1103C4⋊C4C2514yes—
1104C4⋊C4C2512yes—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—24no—
1108C22⋊C4—24no—
1109C22⋊C4—22no—
1110C22⋊C4—22no—
1111C22⋊C4—22no—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—28no—
1115C22⋊C4—22no—
1116C22⋊C4—22no—
1117C22⋊C4—28no—
1118C22⋊C4—22no—
1119C22⋊C4—22no—
1120C22⋊C4—28no—
1121C22⋊C4C22×D418yes—
1122C22⋊C4C22×D418yes—
1123C42—24no—
1124C42—24no—
1125C42—24no—
1126C42—24no—
1127C42—24no—
1128C42—22no—
1129C42—22no—
1130C42—24no—
1131C42—216no—
1132C42—216no—
1133C42—22no—
1134C42—24no—
1135C42—24no—
1136C42—28no—
1137C42—28no—
1138C42—28no—
1139C42C22×D411yescharacteristic
1140C42C22×D411yescharacteristic
1141C42C22×D411yescharacteristic
1142C42C22×D411yescharacteristic
1143C42C22×D411yescharacteristic
1144C42C22×D411yescharacteristic
1145C42C22×D411yescharacteristic
1146C42C22×D411yescharacteristic
1147C42C22×D411yescharacteristic
1148C42C22×D411yescharacteristic
1149C42C22×D411yescharacteristic
1150C42C22×D411yescharacteristic
1151C42C22×D418yes—
1152C42C2511yescharacteristic
1153C42C2511yescharacteristic
1154C42C2511yescharacteristic
1155C42C2518yes—
1156C42C2511yescharacteristic
1157C23—22no—
1158C23—22no—
1159C23—22no—
1160C23—41no—
1161C23C23×D411yescharacteristic
1162C23C23×D411yescharacteristic
1163C23C23×D411yescharacteristic
1164Q8—28no—
1165Q8—28no—
1166Q8—24no—
1167Q8—28no—
1168Q8—28no—
1169Q8—28no—
1170Q8—28no—
1171Q8—24no—
1172Q8—44no—
1173Q8—44no—
1174Q8—44no—
1175Q8—44no—
1176Q8—44no—
1177Q8—44no—
1178Q8—42no—
1179Q8—82no—
1180Q8—82no—
1181Q8—82no—
1182Q8—816no—
1183Q8—88no—
1184Q8—81no—
1185Q8C2×2−1+418yes—
1186D4—24no—
1187D4—44no—
1188D4—44no—
1189D4—42no—
1190D4—81no—
1191D4—82no—
1192C2×C4—28no—
1193C2×C4—28no—
1194C2×C4—24no—
1195C2×C4—28no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—28no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—44no—
1222C2×C4—44no—
1223C2×C4—44no—
1224C2×C4—44no—
1225C2×C4—44no—
1226C2×C4—44no—
1227C2×C4—44no—
1228C2×C4—44no—
1229C2×C4—88no—
1230C2×C4—82no—
1231C2×C4—82no—
1232C2×C4—82no—
1233C2×C4#57814yes—
1234C2×C4C23×D411yescharacteristic
1235C2×C4C23×D411yescharacteristic
1236C2×C4C23×D411yescharacteristic
1237C2×C4C23×D418yes—
1238C2×C4C23×D418yes—
1239C2×C4C23×D411yescharacteristic
1240C2×C4C23×D411yescharacteristic
1241C2×C4C23×D411yescharacteristic
1242C2×C4C23×D411yescharacteristic
1243C2×C4C23×D411yescharacteristic
1244C2×C4C23×D411yescharacteristic
1245C2×C4C23×D411yescharacteristic
1246C2×C4C23×D411yescharacteristic
1247C2×C4C2×2−1+414yes—
1248C2×C4C2611yescharacteristic
1249C8—24no—
1250C8—24no—
1251C8—28no—
1252C22—21no—
1253C22—21no—
1254C22—21no—
1255C22—21no—
1256C22—21no—
1257C22—21no—
1258C22—21no—
1259C22—44no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22#348612yes—
1264C22C2×#57812yes—
1265C22C24×D411yescharacteristic
1266C4—28no—
1267C4—21no—
1268C4—21no—
1269C4—21no—
1270C4—21no—
1271C4—28no—
1272C4—21no—
1273C4—21no—
1274C4—21no—
1275C4—21no—
1276C4—28no—
1277C4—42no—
1278C4—44no—
1279C4—42no—
1280C4—44no—
1281C4—44no—
1282C4—42no—
1283C4—44no—
1284C4—44no—
1285C4#348612yes—
1286C4C2×#57812yes—
1287C4C2×#57812yes—
1288C4C22×2−1+412yes—
1289C2—22no—
1290C2—22no—
1291C2—41no—
1292C2—82no—
1293C2C2×#348611yescharacteristic
1294C2C22×#57811yescharacteristic
1295C2#6309011yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#3444C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#533 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3502C2semidirect
3. #61866C2semidirect
4. #61854C2semidirect
5. #61852C2semidirect
6. #61842C2semidirect
7. #61830C2semidirect
8. #61829C2semidirect
9. #61822C2semidirect
10. #61821C2semidirect
11. #61384C2semidirect
12. #61372C2semidirect
13. #61342C2semidirect
14. #61328C2semidirect
15. #60874C2semidirect
16. #60865C2semidirect
18. #60583C2semidirect
20. C2×#3104C2semidirect
21. #60250C2semidirect
65. #3390C22semidirect
66. #3390C22semidirect
67. #3387C22semidirect
68. #3387C22semidirect
69. #3387C22semidirect
70. #3386C22semidirect
71. #3385C22semidirect
72. #3383C22semidirect
73. #3383C22semidirect
74. Q8×Q16C22semidirect
75. Q8×Q16C22semidirect
76. #3381C22semidirect
77. #3377C22semidirect
78. #3377C22semidirect
79. #3375C22semidirect
80. #3374C22semidirect
81. #3374C22semidirect
82. #3374C22semidirect
83. #3369C22semidirect
84. #3365C22semidirect
85. #3364C22semidirect
86. #3364C22semidirect
87. #3363C22semidirect
88. #3363C22semidirect

Maximal subgroups

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

subgroupindex
#628372
C2×#35022
#618662
#618542
#618522
#618422
#618302
#618292
#618222
#618212
#613842
#613722
#613422
#613282
#608742
#608652
#608462
#605832
#605602
C2×#31042
#602502