Finite Group Databasebeta

← #10576733

Subgroups — #10576733

Order 512.

6691 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62860C211yesmaximal, characteristic, complemented
2#62845C211yesmaximal, characteristic, complemented
3#61424C218yesmaximal, complemented
4#61423C218yesmaximal, complemented
5#61422C218yesmaximal, complemented
6#61420C218yesmaximal, complemented
7#61416C214yesmaximal, complemented
8#61415C214yesmaximal, complemented
9#61408C214yesmaximal, complemented
10#61407C214yesmaximal, complemented
11#60645C212yesmaximal, complemented
12#60643C211yesmaximal, characteristic, complemented
13#60425C211yesmaximal, characteristic, complemented
14#60424C211yesmaximal, characteristic, complemented
15#60422C212yesmaximal, complemented
16C2×#3046C212yesmaximal, complemented
17#60193C211yesmaximal, characteristic, complemented
18#60170C212yesmaximal, complemented
19C2×#2947C211yesmaximal, characteristic, complemented
20C2×#575C2212yes—
21C2×#575C2212yes—
22C22×#137C2211yescharacteristic
23C22×#137C2212yes—
24C22×#135C2212yes—
25#3510C2218yescomplemented
26#3509C2218yescomplemented
27#3507C2214yescomplemented
28#3507C2218yescomplemented
29#3507C2214yescomplemented
30#3507C2214yescomplemented
31#3506C2214yescomplemented
32#3506C2218yescomplemented
33#3495—24no—
34#3495—24no—
35#3493—22no—
36#3493—24no—
37#3492—22no—
38#3492—24no—
39#3491—24no—
40#3461—22no—
41#3461—22no—
42#3459—24no—
43#3458C2211yescharacteristic
44#3449C2212yes—
45#3449C2211yescharacteristic
46#3449C2211yescharacteristic
47C2×#536C2212yes—
48#3428C2212yes—
49C2×#520C2211yescharacteristic
50C2×#520C2212yes—
51C2×#519C2211yescharacteristic
52#3403C22116yescomplemented
53#3402C22116yescomplemented
54#3402C22116yescomplemented
55#3401C22116yescomplemented
56#3401C22116yescomplemented
57#3401C22116yescomplemented
58#3400C2218yescomplemented
59#3400C2218yescomplemented
60#3400C22116yescomplemented
61#3399C2218yescomplemented
62#3398C2218yescomplemented
63#3398C22116yescomplemented
64#3398C22116yescomplemented
65#3397C22116yescomplemented
66#3396C2218yescomplemented
67#3395C2218yescomplemented
68#3394C22116yescomplemented
69#3394C2218yescomplemented
70#3393C22116yescomplemented
71#3392C2218yescomplemented
72#3156C2218yescomplemented
73#3156C2214yescomplemented
74#3156C2218yescomplemented
75#3155C2214yescomplemented
76#3154C2218yescomplemented
77#3154C2214yescomplemented
78#3154C2214yescomplemented
79#3154C2218yescomplemented
80#3153C2218yescomplemented
81#3152C2218yescomplemented
82#3150C2214yes—
83#3147C2214yes—
84#3046C2218yescomplemented
85#3046C2218yescomplemented
86#3046C2218yescomplemented
87#3046C2218yescomplemented
88#3046C2214yescomplemented
89#3046C2214yescomplemented
90#3046C2218yescomplemented
91#3045C2214yescomplemented
92#3045C2214yescomplemented
93#3045C2218yescomplemented
94#3044C2214yescomplemented
95#3044C2218yescomplemented
96#3043C2214yescomplemented
97#3043C2218yescomplemented
98#3042C2214yescomplemented
99#3041C2214yescomplemented
100#3037C2214yescomplemented
101#3037C2214yescomplemented
102#3037C2214yescomplemented
103#3036C2214yescomplemented
104#3035C2218yes—
105#3035C2218yes—
106C2×#464C2214yescomplemented
107C2×#462C2214yescomplemented
108C2×#463C2214yescomplemented
109C2×#461C2214yescomplemented
110#2962C2218yescomplemented
111#2962C2218yescomplemented
112#2961C2214yescomplemented
113#2960C2214yescomplemented
114#2952C2218yescomplemented
115#2951C2218yescomplemented
116#2947C2218yescomplemented
117#2947C2218yescomplemented
118#2947C2218yescomplemented
119#2946C2218yescomplemented
120C4×#137C2218yescomplemented
121C4×AGL(1,ℤ/8)C2218yescomplemented
122C2×#441C2212yescomplemented
123C2×#440C2212yescomplemented
124C2×C4×Q16C2212yescomplemented
125C2×C4×SD16C2212yescomplemented
126C2×#428C2211yescharacteristic
127#2905C2211yescharacteristic
128C2×#424C2212yes—
129#2896C2212yes—
130C2×#417C2212yes—
131C2×#416C2211yescharacteristic
132C22×#103C2211yescharacteristic
133#2873C2212yes—
134C2×#405C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C22×#41C2312yes—
137C22×#41C2312yes—
138C23×Q8C2311yescharacteristic
139#575—216no—
140#575—48no—
141C2×#137—28no—
142C2×#137—48no—
143C2×#137C2314yes—
144C2×#137C2318yes—
145C2×#137C2314yes—
146C2×#137C2314yes—
147C2×#137C2318yes—
148C2×#137C2318yes—
149C2×#137C2314yes—
150C2×AGL(1,ℤ/8)C2314yes—
151C2×AGL(1,ℤ/8)C2314yes—
152C2×AGL(1,ℤ/8)C2314yes—
153C2×AGL(1,ℤ/8)C2314yes—
154C2×#135—48no—
155C2×#135C2318yes—
156C2×#135C2314yes—
157C2×#135C2314yes—
158C2×#135C2314yes—
159C2×#135C2318yes—
160C2×#135C2314yes—
161C22×Q16C2312yes—
162C22×Q16C2312yes—
163C22×Q16C2314yes—
164C22×SD16C2312yes—
165C22×SD16C2312yes—
166C22×SD16C2314yes—
167C22×SD16C2312yes—
168C22×D8C2312yes—
169C22×M16C2312yes—
170C22×M16C2311yescharacteristic
171C23×C8C2311yescharacteristic
172#559C2318yes—
173#559C23116yes—
174#559C2318yes—
175#559C2318yes—
176#557C2318yes—
177#557C2318yes—
178#557C2318yes—
179#556—28no—
180#556—24no—
181#556—24no—
182#556—24no—
183#556C23116yes—
184#556C23116yes—
185#556C23116yes—
186#556C2318yes—
187#555—28no—
188#555—24no—
189#554—28no—
190#554—24no—
191#554—24no—
192#554—24no—
193#553—28no—
194#553—28no—
195#553—28no—
196#552—28no—
197#552—28no—
198#552—28no—
199#552—28no—
200#552—28no—
201#552—216no—
202#552—216no—
203#551—216no—
204#551—216no—
205#550C2318yes—
206#547—28no—
207#547—24no—
208#544D412yes—
209#544D412yes—
210#544D414yes—
211#544D414yes—
212#543D414yes—
213#542—28no—
214#542—28no—
215#541—28no—
216#541—28no—
217#539—28no—
218#539—216no—
219#539—28no—
220#539—28no—
221#538—28no—
222#538—216no—
223#537—21no—
224#537—21no—
225#537—21no—
226#537—22no—
227#537—21no—
228#537—22no—
229#536—24no—
230#536—24no—
231#536C2318yes—
232#536C2318yes—
233#536C2314yes—
234#536C2314yes—
235#536C2314yes—
236#536C2314yes—
237#535C2314yes—
238#535C2314yes—
239#535C2314yes—
240#535C2314yes—
241#534—22no—
242#534—24no—
243#534—22no—
244#533—28no—
245#533—28no—
246#533C2314yes—
247#533C2318yes—
248#532C2314yes—
249#532C2314yes—
250#532C2318yes—
251C2×C4⋊Q8C2314yes—
252#529—28no—
253#529—28no—
254#529—28no—
255#529—216no—
256#529—28no—
257#529—28no—
258C2×#124C2314yes—
259#525—28no—
260#525—216no—
261#525—24no—
262#525—24no—
263#525—24no—
264#525—24no—
265C2×#123—24no—
266C2×C22⋊Q8—22no—
267C2×C22⋊Q8—22no—
268#520—24no—
269#520—24no—
270#520—24no—
271#520—22no—
272#520—22no—
273#520C2318yes—
274#520C2318yes—
275#520C2318yes—
276#520C2314yes—
277#520C2314yes—
278#519—24no—
279#519C2318yes—
280#519C2314yes—
281#518—24no—
282#518C2314yes—
283C4×#41—24no—
284C4×#41C2318yes—
285C2×C4×Q8—21no—
286C2×C4×Q8—21no—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×D4—22no—
292C2×C4×D4—24no—
293C2×C4×D4C2312yes—
294C2×C4×D4C2314yes—
295C2×#117—24no—
296C2×#117—21no—
297C2×#117—22no—
298C2×#117—22no—
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C22×C4⋊C4—21no—
303C22×C4⋊C4—22no—
304C22×C4⋊C4C2311yescharacteristic
305#497C2318yes—
306#497C2318yes—
307#497C23116yes—
308#497C23116yes—
309#497C23116yes—
310#496C2318yes—
311#496C23116yes—
312#496C2318yes—
313#495C2318yes—
314#495C23116yes—
315#495C2318yes—
316#495C23116yes—
317#494C23116yes—
318#494C2314yes—
319#493C2314yes—
320#492C2314yes—
321#492C23116yes—
322#492C2314yes—
323#464C2318yes—
324#464C23116yes—
325#464C23116yes—
326#464C23116yes—
327#464C2318yes—
328#464C23116yes—
329#464C2318yes—
330#464C23116yes—
331#464C2318yes—
332#463C2318yes—
333#463C23116yes—
334#463C23116yes—
335#463C2318yes—
336#463C23116yes—
337#463C2318yes—
338#463C2318yes—
339#462C23116yes—
340#462C2318yes—
341#462C2318yes—
342#462C2318yes—
343#462C2318yes—
344#462C2318yes—
345#462C23116yes—
346#461C23116yes—
347#461C2318yes—
348#461C2318yes—
349#461C23116yes—
350#461C2318yes—
351#460C2318yes—
352#460C2318yes—
353#460C2318yes—
354#460C2318yes—
355#460C2318yes—
356#459C2318yes—
357#459C2318yes—
358#459C2318yes—
359#446C23116yes—
360#446C2318yes—
361#446C23116yes—
362#446C2318yes—
363C8×Q8C2318yes—
364C8×Q8C2318yes—
365#442C23116yes—
366#441C23116yes—
367#441C23116yes—
368#440C23116yes—
369#440C23116yes—
370#440C23116yes—
371C4×Q16C2318yes—
372C4×Q16C23116yes—
373C4×Q16C2318yes—
374C4×SD16C23116yes—
375C4×SD16C2318yes—
376C4×SD16C2318yes—
377C4×SD16C23116yes—
378C4×D8C23116yes—
379#428C2318yes—
380C2×#107C2312yes—
381C2×#106C2312yes—
382#424C2314yes—
383#424C2314yes—
384#424C2314yes—
385#424C2314yes—
386#424C2318yes—
387#423C2314yes—
388C2×C4⋊C8C2314yes—
389C2×C4⋊C8C2314yes—
390#419C2314yes—
391#418C2314yes—
392#417C2318yes—
393#417C2318yes—
394#417C2314yes—
395#417C2314yes—
396#416C2314yes—
397#416C2314yes—
398#416C2318yes—
399C2×#103C2312yes—
400C2×#103C2312yes—
401C2×#103C2314yes—
402C2×#103C2314yes—
403C2×#103C2311yescharacteristic
404C2×#103C2311yescharacteristic
405C2×#103C2314yes—
406C2×#102C2311yescharacteristic
407C2×#102C2311yescharacteristic
408C2×#102C2314yes—
409#405C2314yes—
410#405C2314yes—
411#405C2318yes—
412#405C2318yes—
413C4×M16C2318yes—
414C2×#97C2312yes—
415C2×C4×C8C2312yes—
416C2×#41—28no—
417C2×#41—22no—
418C2×#41—22no—
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—24no—
423C2×#41—28no—
424C2×#41—28no—
425C2×#41—28no—
426C2×#41—28no—
427C2×#41—24no—
428C2×#41C2414yes—
429C2×#41C2414yes—
430C2×#41C2414yes—
431C2×#41C2414yes—
432C2×#41C2414yes—
433C22×Q8—21no—
434C22×Q8—22no—
435C22×Q8—24no—
436C22×Q8—24no—
437C22×Q8C2412yes—
438C22×Q8C2412yes—
439C22×Q8C2411yescharacteristic
440C22×Q8C2414yes—
441C22×Q8C2412yes—
442C22×D4—21no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4C2412yes—
446C22×D4C2411yescharacteristic
447C22×D4C2412yes—
448C23×C4—21no—
449C23×C4—21no—
450C23×C4—21no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—24no—
455C23×C4C2411yescharacteristic
456#137—232no—
457#137—216no—
458#137—216no—
459#137—416no—
460#137—416no—
461#137—48no—
462#137—48no—
463AGL(1,ℤ/8)—216no—
464AGL(1,ℤ/8)—216no—
465AGL(1,ℤ/8)—48no—
466AGL(1,ℤ/8)—48no—
467#135—232no—
468#135—48no—
469#135—48no—
470#135—48no—
471#135—48no—
472#135—416no—
473C2×Q16—28no—
474C2×Q16—44no—
475C2×Q16—48no—
476C2×Q16C2418yes—
477C2×Q16C2418yes—
478C2×Q16C2414yes—
479C2×Q16C2414yes—
480C2×Q16C24116yes—
481C2×Q16C2418yes—
482C2×SD16—28no—
483C2×SD16—44no—
484C2×SD16—44no—
485C2×SD16—48no—
486C2×SD16C2418yes—
487C2×SD16C2418yes—
488C2×SD16C2418yes—
489C2×SD16C2414yes—
490C2×SD16C2414yes—
491C2×SD16C2414yes—
492C2×SD16C2414yes—
493C2×SD16C24116yes—
494C2×SD16C2418yes—
495C2×SD16C2418yes—
496C2×D8—44no—
497C2×D8C2418yes—
498C2×D8C2414yes—
499C2×D8C2414yes—
500C2×D8C2418yes—
501C2×M16—28no—
502C2×M16#4118yescomplemented
503C2×M16C2414yes—
504C2×M16C2414yes—
505C2×M16C2414yes—
506C22×C8—24no—
507C22×C8C2412yes—
508C22×C8C2412yes—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2414yes—
512C22×C8C2412yes—
513C4⋊Q8—28no—
514C4⋊Q8C2×D418yes—
515C4⋊Q8C2×D418yes—
516C4⋊Q8C2×D414yes—
517C4⋊Q8C2×D414yes—
518C4⋊Q8C24116yes—
519C4⋊Q8C2418yes—
520C4⋊Q8C2414yes—
521C4⋊Q8C2414yes—
522#127C2418yes—
523#127C2414yes—
524#127C2414yes—
525#126—216no—
526#126—216no—
527#126—216no—
528#126—216no—
529#126—216no—
530#126—216no—
531#126—216no—
532#125—216no—
533#125—28no—
534#125—28no—
535#125—28no—
536#125—216no—
537#125—216no—
538#125C2×D418yes—
539#125C2×D418yes—
540#125C2×D418yes—
541#124—216no—
542#124—28no—
543#124—28no—
544#124—28no—
545#124—28no—
546#124C24116yes—
547#124C2418yes—
548#124C2418yes—
549#124C2418yes—
550#124C2418yes—
551#123—216no—
552#123—216no—
553#123—216no—
554#123—216no—
555#123—216no—
556#123—216no—
557#123—216no—
558#123—28no—
559#123—28no—
560#123—28no—
561#123—28no—
562C22⋊Q8—216no—
563C22⋊Q8—28no—
564C22⋊Q8—216no—
565C22⋊Q8—216no—
566C22⋊Q8—28no—
567C22⋊Q8—28no—
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8—24no—
571C22⋊Q8—24no—
572C22⋊Q8—24no—
573C22⋊Q8—24no—
574C22⋊Q8—24no—
575C22⋊Q8—24no—
576C22⋊Q8—24no—
577C22⋊Q8—24no—
578C22⋊Q8C2×D418yes—
579C22⋊Q8C2×D4116yes—
580C22⋊Q8C2×D418yes—
581C22⋊Q8C2×D4116yes—
582#121—24no—
583#121—28no—
584#121—24no—
585#121—28no—
586#121—24no—
587#121—24no—
588#121—24no—
589#121—24no—
590#121—24no—
591#121—24no—
592#121—24no—
593#121—24no—
594#121—24no—
595#121—24no—
596#121—216no—
597#121—28no—
598#120—28no—
599#120—28no—
600#120—28no—
601#120—28no—
602C4×Q8—28no—
603C4×Q8—28no—
604C4×Q8—28no—
605C4×Q8—28no—
606C4×Q8—28no—
607C4×Q8—24no—
608C4×Q8—24no—
609C4×Q8—24no—
610C4×Q8—24no—
611C4×Q8—28no—
612C4×Q8—24no—
613C4×Q8C2418yes—
614C4×Q8C2418yes—
615C4×Q8C24116yes—
616C4×Q8C2418yes—
617C4×Q8C2418yes—
618C4×Q8C2418yes—
619C4×Q8C2418yes—
620C4×Q8C2418yes—
621C4×D4—28no—
622C4×D4—28no—
623C4×D4—24no—
624C4×D4—24no—
625C4×D4—216no—
626C4×D4—28no—
627C4×D4—28no—
628C4×D4—28no—
629C4×D4—216no—
630C4×D4—216no—
631C4×D4—216no—
632C4×D4—28no—
633C4×D4—28no—
634C4×D4—28no—
635C4×D4—24no—
636C4×D4—28no—
637C4×D4—24no—
638C4×D4—24no—
639C4×D4—24no—
640C4×D4—28no—
641C4×D4—24no—
642C4×D4C24116yes—
643C4×D4C2418yes—
644C4×D4C2418yes—
645C4×D4C2418yes—
646#117—22no—
647#117—24no—
648#117—24no—
649#117—28no—
650#117—28no—
651#117—28no—
652#117—216no—
653#117—28no—
654#117—216no—
655#117—216no—
656#117—28no—
657#117—216no—
658#117—28no—
659#117C2×D414yes—
660#117C2×D414yes—
661#117C2×D414yes—
662#117C2414yes—
663#117C2414yes—
664#117C2414yes—
665#117C2414yes—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—24no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—24no—
673C2×C4⋊C4—24no—
674C2×C4⋊C4—28no—
675C2×C4⋊C4—28no—
676C2×C4⋊C4—28no—
677C2×C4⋊C4—24no—
678C2×C4⋊C4—24no—
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D412yes—
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D412yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C22⋊C4—21no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—24no—
690C2×C22⋊C4—24no—
691C2×C22⋊C4—24no—
692C2×C22⋊C4—28no—
693C2×C22⋊C4C2×D412yes—
694C2×C22⋊C4C2×D414yes—
695C2×C42—22no—
696C2×C42—24no—
697C2×C42—22no—
698C2×C42—22no—
699C2×C42—21no—
700C2×C42—28no—
701C2×C42C2412yes—
702C2×C42C2414yes—
703#107C2418yes—
704#106C2418yes—
705C4⋊C8C2418yes—
706C4⋊C8C2418yes—
707C4⋊C8C2418yes—
708C4⋊C8C2418yes—
709C4⋊C8C2418yes—
710C4⋊C8C2418yes—
711#103C2414yes—
712#103C2414yes—
713#103C2418yes—
714#103C2412yes—
715#103C2412yes—
716#103C2414yes—
717#103C24116yes—
718#103C2418yes—
719#103C2418yes—
720#102C2412yes—
721#102C2412yes—
722#102C2414yes—
723#102C24116yes—
724#102C2418yes—
725#102C2418yes—
726#97C2418yes—
727#97C24116yes—
728C4×C8C2414yes—
729C4×C8C2414yes—
730C4×C8C24116yes—
731C24—22no—
732C24—22no—
733C24—21no—
734C24C22×D411yescharacteristic
735#41—28no—
736#41—28no—
737#41—28no—
738#41—28no—
739#41—28no—
740#41—28no—
741#41—28no—
742#41—28no—
743#41—28no—
744#41—28no—
745#41—48no—
746#41—48no—
747#41—48no—
748#41—48no—
749#41—48no—
750#41—168no—
751C2×Q8—22no—
752C2×Q8—22no—
753C2×Q8—21no—
754C2×Q8—24no—
755C2×Q8—22no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—28no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—28no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—48no—
767C2×Q8—44no—
768C2×Q8C22×D418yes—
769C2×Q8C22×D418yes—
770C2×Q8C2514yes—
771C2×Q8C2514yes—
772C2×Q8C2512yes—
773C2×Q8C2514yes—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—22no—
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—24no—
783C2×D4—28no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—28no—
788C2×D4—22no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—22no—
794C2×D4—44no—
795C2×D4—48no—
796C2×D4—48no—
797C2×D4C2514yes—
798C2×D4C2514yes—
799C2×D4C2512yes—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—24no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—24no—
808C22×C4—22no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—216no—
818C22×C4—44no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—44no—
822C22×C4—164no—
823C22×C4—162no—
824C22×C4—161no—
825C22×C4C22×D412yes—
826C22×C4C22×D414yes—
827C22×C4C22×D412yes—
828C22×C4C22×D414yes—
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D412yes—
831C22×C4C2×#4114yes—
832C22×C4H(5,𝔽2)14yes—
833C22×C4C2511yescharacteristic
834C22×C4C2512yes—
835Q16—216no—
836Q16—216no—
837Q16—44no—
838Q16—44no—
839Q16—416no—
840Q16—48no—
841SD16—216no—
842SD16—216no—
843SD16—216no—
844SD16—44no—
845SD16—44no—
846SD16—44no—
847SD16—44no—
848SD16—416no—
849SD16—48no—
850SD16—48no—
851D8—216no—
852D8—44no—
853D8—44no—
854D8—48no—
855M16—28no—
856M16—28no—
857M16C2×#41116yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—28no—
863C2×C8C2×#4118yes—
864C2×C8C2511yescharacteristic
865C2×C8C2511yescharacteristic
866C2×C8C2518yes—
867C2×C8C2512yes—
868C2×C8C2514yes—
869C4⋊C4—24no—
870C4⋊C4—22no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—28no—
874C4⋊C4—216no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—216no—
880C4⋊C4—216no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—28no—
887C4⋊C4C22×D414yes—
888C4⋊C4C22×D414yes—
889C4⋊C4C22×D414yes—
890C4⋊C4C22×D414yes—
891C4⋊C4C22×D414yes—
892C4⋊C4C22×D414yes—
893C4⋊C4C22×D4116yes—
894C4⋊C4C22×D418yes—
895C4⋊C4C22×D4116yes—
896C4⋊C4C22×D418yes—
897C4⋊C4C2512yes—
898C4⋊C4C2512yes—
899C4⋊C4C2514yes—
900C22⋊C4—24no—
901C22⋊C4—28no—
902C22⋊C4—216no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—216no—
906C22⋊C4—216no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4C22×D418yes—
916C22⋊C4C22×D418yes—
917C22⋊C4C22×D418yes—
918C42—24no—
919C42—28no—
920C42—216no—
921C42—28no—
922C42—28no—
923C42—28no—
924C42—28no—
925C42C22×D418yes—
926C42C22×D414yes—
927C42C2518yes—
928C42C2514yes—
929C23—24no—
930C23—24no—
931C23—22no—
932C23—41no—
933C23—41no—
934C23—44no—
935C23—42no—
936C23—44no—
937C23—81no—
938C23—82no—
939C23—81no—
940C23—82no—
941C23—82no—
942C23—82no—
943C23#55014yes—
944C23C23×D412yes—
945C23C23×D411yescharacteristic
946Q8—24no—
947Q8—24no—
948Q8—24no—
949Q8—22no—
950Q8—24no—
951Q8—24no—
952Q8—22no—
953Q8—24no—
954Q8—48no—
955Q8—48no—
956Q8—44no—
957Q8—48no—
958Q8—42no—
959Q8—44no—
960Q8—44no—
961D4—24no—
962D4—24no—
963D4—22no—
964D4—24no—
965D4—22no—
966D4—24no—
967D4—48no—
968D4—48no—
969D4—48no—
970D4—48no—
971D4—48no—
972D4—42no—
973D4—44no—
974D4—44no—
975D4—84no—
976D4—88no—
977D4—84no—
978D4—84no—
979D4—88no—
980D4—84no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—44no—
989C2×C4—42no—
990C2×C4—44no—
991C2×C4—42no—
992C2×C4—44no—
993C2×C4—44no—
994C2×C4—42no—
995C2×C4—48no—
996C2×C4—44no—
997C2×C4—48no—
998C2×C4—48no—
999C2×C4—48no—
1000C2×C4—48no—
1001C2×C4—48no—
1002C2×C4—88no—
1003C2×C4—88no—
1004C2×C4—816no—
1005C2×C4—88no—
1006C2×C4—81no—
1007C2×C4—81no—
1008C2×C4—82no—
1009C2×C4—84no—
1010C2×C4#55018yes—
1011C2×C4#55014yes—
1012C2×C4C23×D414yes—
1013C2×C4C23×D418yes—
1014C2×C4C23×D414yes—
1015C2×C4C23×D418yes—
1016C2×C4C23×D412yes—
1017C2×C4C23×D411yescharacteristic
1018C2×C4C22×#4112yes—
1019C2×C4C22×#4114yes—
1020C2×C4C2×H(5,𝔽2)14yes—
1021C2×C4C2×H(5,𝔽2)12yes—
1022C2×C4C2611yescharacteristic
1023C8—21no—
1024C8—22no—
1025C8—21no—
1026C8—28no—
1027C8C22×#4118yes—
1028C22—21no—
1029C22—22no—
1030C22—21no—
1031C22—22no—
1032C22—44no—
1033C22—44no—
1034C22—42no—
1035C22—44no—
1036C22—44no—
1037C22—42no—
1038C22—44no—
1039C22—44no—
1040C22—42no—
1041C22—44no—
1042C22—88no—
1043C22—84no—
1044C22—164no—
1045C22C2×#55014yes—
1046C22C2×#55012yes—
1047C22C24×D411yescharacteristic
1048C4—28no—
1049C4—24no—
1050C4—28no—
1051C4—24no—
1052C4—42no—
1053C4—44no—
1054C4—42no—
1055C4—44no—
1056C4—42no—
1057C4—44no—
1058C4—44no—
1059C4C2×#55012yes—
1060C4C2×#55014yes—
1061C4C23×#4111yescharacteristic
1062C4C22×H(5,𝔽2)11yescharacteristic
1063C2—24no—
1064C2—22no—
1065C2—84no—
1066C2—82no—
1067C2—84no—
1068C2C22×#55011yescharacteristic
1069C2#6309211yescharacteristic
1070C2#6309311yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
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
1. #62860C2semidirect
2. #62845C2semidirect
3. #61424C2semidirect
4. #61423C2semidirect
5. #61422C2semidirect
6. #61420C2semidirect
7. #61416C2semidirect
8. #61415C2semidirect
9. #61408C2semidirect
10. #61407C2semidirect
11. #60645C2semidirect
12. #60643C2semidirect
13. #60425C2semidirect
14. #60424C2semidirect
15. #60422C2semidirect
16. C2×#3046C2semidirect
17. #60193C2semidirect
18. #60170C2semidirect
19. C2×#2947C2semidirect
25. #3510C22semidirect
26. #3509C22semidirect
27. #3507C22semidirect
28. #3507C22semidirect
29. #3507C22semidirect
30. #3507C22semidirect
31. #3506C22semidirect
32. #3506C22semidirect
52. #3403C22semidirect
53. #3402C22semidirect
54. #3402C22semidirect
55. #3401C22semidirect
56. #3401C22semidirect
57. #3401C22semidirect
58. #3400C22semidirect
59. #3400C22semidirect
60. #3400C22semidirect
61. #3399C22semidirect
62. #3398C22semidirect
63. #3398C22semidirect
64. #3398C22semidirect
65. #3397C22semidirect
66. #3396C22semidirect
67. #3395C22semidirect
68. #3394C22semidirect
69. #3394C22semidirect
70. #3393C22semidirect
71. #3392C22semidirect
72. #3156C22semidirect
73. #3156C22semidirect
74. #3156C22semidirect
75. #3155C22semidirect
76. #3154C22semidirect
77. #3154C22semidirect
78. #3154C22semidirect
79. #3154C22semidirect
80. #3153C22semidirect
81. #3152C22semidirect
84. #3046C22semidirect
85. #3046C22semidirect
86. #3046C22semidirect
87. #3046C22semidirect
88. #3046C22semidirect
89. #3046C22semidirect
90. #3046C22semidirect
91. #3045C22semidirect
92. #3045C22semidirect
93. #3045C22semidirect
94. #3044C22semidirect
95. #3044C22semidirect
96. #3043C22semidirect
97. #3043C22semidirect
98. #3042C22semidirect
99. #3041C22semidirect
100. #3037C22semidirect
101. #3037C22semidirect
102. #3037C22semidirect
103. #3036C22semidirect
106. C2×#464C22semidirect
107. C2×#462C22semidirect
108. C2×#463C22semidirect
109. C2×#461C22semidirect
110. #2962C22semidirect
111. #2962C22semidirect
112. #2961C22semidirect
113. #2960C22semidirect
114. #2952C22semidirect
115. #2951C22semidirect
116. #2947C22semidirect
117. #2947C22semidirect
118. #2947C22semidirect
119. #2946C22semidirect
120. C4×#137C22semidirect
121. C4×AGL(1,ℤ/8)C22semidirect
122. C2×#441C22semidirect
123. C2×#440C22semidirect
124. C2×C4×Q16C22semidirect
125. C2×C4×SD16C22semidirect
502. C2×M16#41semidirect

Maximal subgroups

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

subgroupindex
#628602
#628452
#614242
#614232
#614222
#614202
#614162
#614152
#614082
#614072
#606452
#606432
#604252
#604242
#604222
C2×#30462
#601932
#601702
C2×#29472