Finite Group Databasebeta

← #10578629

Subgroups — #10578629

Order 512.

6526 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62788C211yesmaximal, characteristic, complemented
2C22×#559C211yesmaximal, characteristic, complemented
3#61904C218yesmaximal, complemented
4#61898C218yesmaximal, complemented
5#61895C218yesmaximal, complemented
6#61892C212yesmaximal, complemented
7#61891C212yesmaximal, complemented
8#61885C214yesmaximal, complemented
9#61405C218yesmaximal, complemented
10#61324C218yesmaximal, complemented
11#60799C214yesmaximal, complemented
12#60798C212yesmaximal, complemented
13#60560C212yesmaximal, complemented
14#60558C214yesmaximal, complemented
15#60248C211yesmaximal, characteristic, complemented
16#3523C2214yescomplemented
17#3522C2214yescomplemented
18#3516—24no—
19#3507C2212yescomplemented
20#3507C2214yescomplemented
21#3502C2211yescharacteristic, complemented
22#3497C2211yescharacteristic, complemented
23#3492—21no—
24#3492—22no—
25#3486—21no—
26#3482—24no—
27#3480C2214yescomplemented
28C2×#559—21no—
29C2×#559—21no—
30C2×#559—22no—
31C2×#559—24no—
32C2×#559—24no—
33C2×#559C2218yes—
34C2×#559C2212yes—
35C2×#559C2212yes—
36C2×#559C2214yes—
37C2×#559C2218yes—
38Q8×#41C2214yescomplemented
39#3461—22no—
40#3461—21no—
41#3444C2212yes—
42#3444C2214yes—
43C22×#127C2211yescharacteristic
44C22×#124—21no—
45C22×#124C2212yes—
46C22×#123—22no—
47C4×2−1+4—21no—
48C22×C4×Q8C2211yescharacteristic
49C22×C4×Q8C2211yescharacteristic
50C22×C4×D4—21no—
51C22×C4×D4C2212yes—
52#3403C22132yescomplemented
53#3401C22132yescomplemented
54#3400C22116yescomplemented
55#3399C22116yescomplemented
56#3396C22116yescomplemented
57#3394C22116yescomplemented
58#3375C22116yescomplemented
59#3373C22116yescomplemented
60#3371C22132yescomplemented
61#3370C22132yescomplemented
62#3365C22116yescomplemented
63#3361C22116yescomplemented
64#3217C2218yes—
65#3217C2218yes—
66#3215C2218yescomplemented
67#3215C2218yescomplemented
68#3213C2218yescomplemented
69#3213C2218yescomplemented
70#3211C22116yescomplemented
71#3211C22116yescomplemented
72#3208C2214yes—
73#3208C2214yes—
74#3205C2214yes—
75#3205C2214yes—
76#3153C2218yescomplemented
77#3151C2214yes—
78#3140C2218yescomplemented
79#3138C2214yes—
80#3117C2218yescomplemented
81#3114C22116yescomplemented
82#3113C2214yescomplemented
83#3112C2214yescomplemented
84#3110C2218yescomplemented
85#3109C2218yescomplemented
86#3108C2218yescomplemented
87#3105C22116yescomplemented
88#3104C2214yescomplemented
89#3103C2214yescomplemented
90#3101C2218yescomplemented
91#3100C2218yescomplemented
92#3092C2214yes—
93#3078C2214yescomplemented
94#3077C2218yescomplemented
95#3040C22116yescomplemented
96#3038C2218yes—
97#3037C2214yescomplemented
98#3036C2218yescomplemented
99#3004C2214yes—
100#3003C2218yes—
101#2984C2218yescomplemented
102#2983C2212yescomplemented
103#2983C2214yescomplemented
104#2982C2212yescomplemented
105Q8×M16C2218yescomplemented
106C4×#137C2218yescomplemented
107C4×AGL(1,ℤ/8)C22116yescomplemented
108#2920C2212yes—
109#2920C2214yes—
110C2×2−1+4—21no—
111C23×Q8D411yescharacteristic
112C23×Q8C2311yescharacteristic
113C23×D4—21no—
114C23×D4—21no—
115C23×D4C2312yes—
116C24×C4—22no—
117C2×#137C2318yes—
118C2×AGL(1,ℤ/8)C23116yes—
119#559—28no—
120#559—28no—
121#559—28no—
122#559—216no—
123#559—28no—
124#559—216no—
125#559—28no—
126#559—28no—
127#559—216no—
128#559C23116yes—
129#559C23132yes—
130#559C23116yes—
131#559C2314yescomplemented
132#559C2318yescomplemented
133Q82C2314yescomplemented
134#557—24no—
135#557C2314yescomplemented
136#557C2314yescomplemented
137#557C2318yescomplemented
138#556—24no—
139#556—28no—
140#556C2314yescomplemented
141#556C2318yescomplemented
142#554—24no—
143#554—28no—
144#554C2314yescomplemented
145#554C2318yescomplemented
146#553—24no—
147#553—28no—
148#552—24no—
149#552—28no—
150#552—24no—
151#552—28no—
152#550C2314yescomplemented
153D4×Q8—24no—
154D4×Q8—24no—
155D4×Q8C2314yescomplemented
156#548—24no—
157#548—24no—
158#548—24no—
159#547—24no—
160#547—28no—
161#544—21no—
162#544—22no—
163#542—28no—
164#542—24no—
165#541—28no—
166#541—24no—
167#539—24no—
168#539—24no—
169#539—24no—
170#537—21no—
171#537—22no—
172#536—22no—
173#536—24no—
174#533—28no—
175#533—24no—
176#533C2314yes—
177#533C2312yes—
178#533C2314yes—
179#533C2312yes—
180#533C2314yes—
181#533C2312yes—
182#532C2312yes—
183#532C2314yes—
184#532C2314yes—
185#532C2312yes—
186#532C2314yes—
187#532C2312yes—
188C2×#127—21no—
189C2×#127—22no—
190C2×#127—21no—
191C2×#127—22no—
192C2×#127C2314yes—
193C2×#127C2312yes—
194C2×#127C2314yes—
195C2×#127C2312yes—
196#529—28no—
197#529—24no—
198#529—24no—
199#529—22no—
200#529—24no—
201#529—22no—
202#529—24no—
203#529—24no—
204#529—22no—
205#529—22no—
206#529C2318yes—
207#529C2314yes—
208#529C2318yes—
209#529C2314yes—
210C2×#124—22no—
211C2×#124—22no—
212C2×#124—24no—
213C2×#124—28no—
214C2×#124—28no—
215C2×#124—22no—
216C2×#124—24no—
217C2×#124—22no—
218C2×#124—24no—
219C2×#124C2318yes—
220C2×#124C2314yes—
221C2×#124C2318yes—
222C2×#124C2314yes—
223#525—22no—
224#525—24no—
225#525—24no—
226#525—22no—
227#525C2314yes—
228C2×#123—24no—
229C2×#123—24no—
230C2×#123—24no—
231C2×#123—24no—
232C2×#123—216no—
233C2×#123—216no—
234#520—24no—
235#520—22no—
236#520—24no—
237#519—21no—
238#519—24no—
239C4×#41—24no—
240C4×#41—24no—
241C4×#41—22no—
242C4×#41—24no—
243C4×#41—22no—
244C4×#41C2318yes—
245C4×#41C2314yes—
246C2×C4×Q8—24no—
247C2×C4×Q8—21no—
248C2×C4×Q8—22no—
249C2×C4×Q8—22no—
250C2×C4×Q8—21no—
251C2×C4×Q8D411yescharacteristic
252C2×C4×Q8D412yes—
253C2×C4×Q8D411yescharacteristic
254C2×C4×Q8D414yes—
255C2×C4×Q8D414yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2314yes—
265C2×C4×D4—22no—
266C2×C4×D4—22no—
267C2×C4×D4—24no—
268C2×C4×D4—28no—
269C2×C4×D4—28no—
270C2×C4×D4—22no—
271C2×C4×D4—24no—
272C2×C4×D4—22no—
273C2×C4×D4—24no—
274C2×C4×D4C2318yes—
275C2×C4×D4C2318yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C22×C4⋊C4—21no—
279C22×C4⋊C4D411yescharacteristic
280C22×C4⋊C4D412yes—
281C22×C4⋊C4C2311yescharacteristic
282C22×C22⋊C4—22no—
283C22×C22⋊C4—22no—
284C22×C22⋊C4—22no—
285C22×C42—21no—
286C22×C42C2312yes—
287C22×C42C2311yescharacteristic
288#497C23116yescomplemented
289#496C23116yes—
290#496C23116yescomplemented
291#495C23132yescomplemented
292#493C2318yes—
293#492C2318yes—
294#490C23116yes—
295#489C23116yescomplemented
296#489C23116yescomplemented
297#488C23132yescomplemented
298#486C2318yes—
299#486C2318yes—
300#484C2318yes—
301#483C2318yes—
302#481C2318yes—
303#480C2318yes—
304#479C23116yescomplemented
305#478C23132yescomplemented
306#477C2318yescomplemented
307#476C23116yescomplemented
308#475C2318yescomplemented
309#474C23116yescomplemented
310#464C23116yescomplemented
311#464C23132yescomplemented
312#464C23132yescomplemented
313#463C23132yescomplemented
314#463C23132yescomplemented
315#463C23132yescomplemented
316#462C2318yescomplemented
317#461C23116yescomplemented
318#460C23116yes—
319#460C23116yes—
320#460C2318yescomplemented
321#459C23116yes—
322#459C23116yes—
323#459C23116yescomplemented
324#451C2318yes—
325#451C2318yes—
326#450C23116yes—
327#450C23116yes—
328#448C2318yes—
329#448C2318yes—
330#447C23116yes—
331#447C23116yes—
332#446C23132yescomplemented
333#446C23116yescomplemented
334C8×Q8C23116yescomplemented
335#442C23132yescomplemented
336#441C23116yescomplemented
337#440C23132yescomplemented
338#440C23116yescomplemented
339C4×Q16C23116yescomplemented
340C4×SD16C23132yescomplemented
341C4×SD16C23116yescomplemented
342C4×D8C23132yescomplemented
343#432C2318yes—
344#432C2314yes—
345#432C2318yes—
346#432C2314yes—
347#431C2318yes—
348#431C2314yes—
349#431C2318yes—
350#431C2314yes—
351#428C2318yes—
352#423C2318yes—
353#423C2314yes—
354#419C2318yes—
355#418C23116yes—
356#417C2318yes—
357#407C2314yes—
358C4×M16C2314yes—
359C4×M16C2318yes—
360C25—22no—
3612−1+4—48no—
362C2×#41—24no—
363C2×#41—24no—
364C2×#41—22no—
365C2×#41—24no—
366C2×#41—22no—
367C2×#41C2414yes—
368C22×Q8—24no—
369C22×Q8—21no—
370C22×Q8—21no—
371C22×Q8—21no—
372C22×Q8—44no—
373C22×Q8—44no—
374C22×Q8C2×D411yescharacteristic
375C22×Q8C2×D411yescharacteristic
376C22×Q8C2×D412yes—
377C22×Q8C2×D414yes—
378C22×Q8C2×D414yes—
379C22×Q8C2412yes—
380C22×Q8C2412yes—
381C22×Q8C2412yes—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—24no—
386C22×D4—24no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—24no—
390C22×D4—22no—
391C22×D4—24no—
392C22×D4—22no—
393C22×D4—48no—
394C22×D4—48no—
395C22×D4—84no—
396C22×D4C2414yes—
397C22×D4C2414yes—
398C22×D4C2414yes—
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—28no—
402C23×C4—24no—
403C23×C4—28no—
404C23×C4—24no—
405C23×C4—88no—
406C23×C4C2×D411yescharacteristic
407C23×C4C2×D412yes—
408C23×C4C2×D412yes—
409C23×C4C2×D411yescharacteristic
410C23×C4C2411yescharacteristic
411#137—416no—
412AGL(1,ℤ/8)—432no—
413C2×Q16C24116yes—
414C2×SD16C24132yes—
415C2×SD16C24116yes—
416C2×D8C24132yes—
417C2×M16C2418yes—
418C4⋊Q8—24no—
419C4⋊Q8—28no—
420C4⋊Q8—24no—
421C4⋊Q8—28no—
422C4⋊Q8C2414yes—
423C4⋊Q8C2412yes—
424C4⋊Q8C2412yes—
425C4⋊Q8C2414yes—
426C4⋊Q8C2414yes—
427C4⋊Q8C2412yes—
428#127—24no—
429#127—24no—
430#127—24no—
431#127—24no—
432#127—24no—
433#127—24no—
434#127C2418yes—
435#127C2418yes—
436#127C2414yes—
437#127C2412yes—
438#126—28no—
439#126—28no—
440#126—28no—
441#126—28no—
442#126—24no—
443#126—28no—
444#126—24no—
445#125—24no—
446#125—28no—
447#125—28no—
448#125—28no—
449#125—28no—
450#125—24no—
451#125—22no—
452#125—24no—
453#125—22no—
454#125C2418yes—
455#125C2414yes—
456#124—216no—
457#124—216no—
458#124—232no—
459#124—24no—
460#124—28no—
461#124—28no—
462#124—28no—
463#124—28no—
464#124—28no—
465#124—28no—
466#124—28no—
467#124—24no—
468#124—22no—
469#124—24no—
470#124—22no—
471#124C24116yes—
472#124C24116yes—
473#124C2418yes—
474#124C2414yes—
475#123—24no—
476#123—28no—
477#123—28no—
478#123—24no—
479#123—24no—
480#123—232no—
481#123—232no—
482#123—232no—
483#123—232no—
484#123—28no—
485#123—28no—
486#123—28no—
487C22⋊Q8—24no—
488C22⋊Q8—28no—
489C22⋊Q8—24no—
490C22⋊Q8—28no—
491C22⋊Q8—24no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—24no—
495C22⋊Q8—22no—
496C22⋊Q8—24no—
497C22⋊Q8—24no—
498C22⋊Q8—22no—
499C22⋊Q8—24no—
500C22⋊Q8—28no—
501C22⋊Q8—28no—
502C22⋊Q8—28no—
503C22⋊Q8—28no—
504C22⋊Q8C2414yes—
505C22⋊Q8C2414yes—
506#121—24no—
507#121—22no—
508#121—22no—
509#121—24no—
510#121—22no—
511#121—24no—
512#121—24no—
513#121—22no—
514#121—24no—
515#121—28no—
516#121C2414yes—
517#121C2414yes—
518#120—24no—
519C4×Q8—24no—
520C4×Q8—24no—
521C4×Q8—24no—
522C4×Q8—28no—
523C4×Q8—24no—
524C4×Q8—24no—
525C4×Q8—24no—
526C4×Q8—24no—
527C4×Q8—24no—
528C4×Q8—24no—
529C4×Q8—24no—
530C4×Q8—22no—
531C4×Q8—24no—
532C4×Q8—22no—
533C4×Q8—24no—
534C4×Q8—22no—
535C4×Q8—24no—
536C4×Q8—22no—
537C4×Q8C2×D414yes—
538C4×Q8C2×D414yes—
539C4×Q8C2×D418yes—
540C4×Q8C2×D414yes—
541C4×Q8C2×D418yes—
542C4×Q8C2×D414yes—
543C4×Q8C2×D414yes—
544C4×Q8C2×D414yes—
545C4×Q8C2×D418yes—
546C4×Q8C2418yes—
547C4×Q8C2418yes—
548C4×Q8C2418yes—
549C4×Q8C2414yes—
550C4×Q8C2414yes—
551C4×Q8C2418yes—
552C4×Q8C2414yes—
553C4×Q8C2414yes—
554C4×Q8C2418yes—
555C4×D4—24no—
556C4×D4—24no—
557C4×D4—28no—
558C4×D4—24no—
559C4×D4—24no—
560C4×D4—28no—
561C4×D4—24no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4—24no—
565C4×D4—216no—
566C4×D4—216no—
567C4×D4—232no—
568C4×D4—24no—
569C4×D4—28no—
570C4×D4—28no—
571C4×D4—28no—
572C4×D4—28no—
573C4×D4—28no—
574C4×D4—28no—
575C4×D4—28no—
576C4×D4—24no—
577C4×D4—22no—
578C4×D4—24no—
579C4×D4—22no—
580C4×D4—24no—
581C4×D4—22no—
582C4×D4—24no—
583C4×D4—22no—
584C4×D4C24116yes—
585C4×D4C24116yes—
586C4×D4C2414yes—
587C4×D4C2418yes—
588C4×D4C2418yes—
589C4×D4C2414yes—
590#117—24no—
591#117—22no—
592#117—24no—
593#117—22no—
594#117—24no—
595#117—28no—
596#117—28no—
597#117—24no—
598#117—28no—
599#117—24no—
600#117—28no—
601#117—24no—
602#117C2414yes—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—28no—
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D412yes—
615C2×C4⋊C4C2×D414yes—
616C2×C4⋊C4C2×D414yes—
617C2×C4⋊C4C2×D412yes—
618C2×C4⋊C4C2×D412yes—
619C2×C4⋊C4C2×D412yes—
620C2×C4⋊C4C2×D412yes—
621C2×C4⋊C4C2×D418yes—
622C2×C4⋊C4C2×D418yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C22⋊C4—28no—
627C2×C22⋊C4—24no—
628C2×C22⋊C4—28no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—28no—
633C2×C22⋊C4—28no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—28no—
637C2×C22⋊C4—28no—
638C2×C42—24no—
639C2×C42—24no—
640C2×C42—22no—
641C2×C42—22no—
642C2×C42—28no—
643C2×C42—24no—
644C2×C42C2×D412yes—
645C2×C42C2×D414yes—
646C2×C42C2×D412yes—
647C2×C42C2×D414yes—
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D412yes—
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D412yes—
652C2×C42C2414yes—
653C2×C42C2412yes—
654C2×C42C2414yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2411yescharacteristic
658C2×C42C2412yes—
659C2×C42C2411yescharacteristic
660#107C24116yes—
661#106C24116yes—
662C4⋊C8C2418yes—
663C4⋊C8C24116yes—
664C4⋊C8C2418yes—
665C4⋊C8C24116yes—
666#103C24116yes—
667#103C24116yes—
668#103C24116yes—
669#102C24116yes—
670#102C24132yes—
671#102C24132yes—
672C22⋊C8C2418yes—
673C22⋊C8C2418yes—
674#97C2418yes—
675#97C24116yes—
676C4×C8C24116yes—
677C4×C8C2418yes—
678C24—24no—
679C24—24no—
680C24—24no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24C22×D411yescharacteristic
685#41—216no—
686#41—416no—
687#41—416no—
688#41—48no—
689#41—88no—
690#41—84no—
691C2×Q8—24no—
692C2×Q8—24no—
693C2×Q8—24no—
694C2×Q8—22no—
695C2×Q8—22no—
696C2×Q8—22no—
697C2×Q8—22no—
698C2×Q8—24no—
699C2×Q8—22no—
700C2×Q8—28no—
701C2×Q8—44no—
702C2×Q8—48no—
703C2×Q8—48no—
704C2×Q8—44no—
705C2×Q8—44no—
706C2×Q8—44no—
707C2×Q8—44no—
708C2×Q8—44no—
709C2×Q8—416no—
710C2×Q8C22×D414yes—
711C2×Q8C22×D414yes—
712C2×Q8C22×D418yes—
713C2×Q8C2514yes—
714C2×Q8C2514yes—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—22no—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—24no—
726C2×D4—22no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—216no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—416no—
737C2×D4—416no—
738C2×D4—48no—
739C2×D4—88no—
740C2×D4—84no—
741C2×D4—88no—
742C2×D4—84no—
743C2×D4C2518yes—
744C2×D4C2514yes—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—24no—
754C22×C4—28no—
755C22×C4—24no—
756C22×C4—28no—
757C22×C4—24no—
758C22×C4—216no—
759C22×C4—216no—
760C22×C4—44no—
761C22×C4—42no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—816no—
766C22×C4—88no—
767C22×C4—816no—
768C22×C4—88no—
769C22×C4C22×D412yes—
770C22×C4C22×D412yes—
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D412yes—
776C22×C4C22×D412yes—
777C22×C4C22×D414yes—
778C22×C4C22×D412yes—
779C22×C4C22×D414yes—
780C22×C4C22×D414yes—
781C22×C4C22×D412yes—
782C22×C4C22×D414yes—
783C22×C4C22×D412yes—
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D412yes—
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791Q16—416no—
792SD16—432no—
793SD16—416no—
794D8—432no—
795M16—216no—
796C2×C8C25116yes—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—22no—
802C4⋊C4—24no—
803C4⋊C4—22no—
804C4⋊C4—28no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—22no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—22no—
812C4⋊C4—24no—
813C4⋊C4—22no—
814C4⋊C4—24no—
815C4⋊C4—28no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—24no—
820C4⋊C4C22×D414yes—
821C4⋊C4C22×D418yes—
822C4⋊C4C22×D414yes—
823C4⋊C4C22×D418yes—
824C4⋊C4C22×D418yes—
825C4⋊C4C22×D418yes—
826C4⋊C4C22×D418yes—
827C4⋊C4C2514yes—
828C4⋊C4C2514yes—
829C4⋊C4C2514yes—
830C22⋊C4—24no—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—216no—
834C22⋊C4—216no—
835C22⋊C4—216no—
836C22⋊C4—216no—
837C22⋊C4—216no—
838C22⋊C4—216no—
839C22⋊C4—28no—
840C22⋊C4—24no—
841C22⋊C4—24no—
842C22⋊C4—24no—
843C22⋊C4—24no—
844C22⋊C4—28no—
845C22⋊C4—28no—
846C22⋊C4—24no—
847C22⋊C4—24no—
848C22⋊C4—28no—
849C42—24no—
850C42—28no—
851C42—28no—
852C42—28no—
853C42—24no—
854C42—28no—
855C42—24no—
856C42C22×D414yes—
857C42C22×D412yes—
858C42C22×D414yes—
859C42C22×D414yes—
860C42C22×D414yes—
861C42C22×D412yes—
862C42C22×D412yes—
863C42C22×D412yes—
864C42C22×D414yes—
865C42C22×D414yes—
866C42C22×D412yes—
867C42C22×D412yes—
868C42C2514yes—
869C42C2512yes—
870C42C2514yes—
871C42C2512yes—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—24no—
876C23—28no—
877C23—48no—
878C23—48no—
879C23—48no—
880C23—48no—
881C23—48no—
882C23—48no—
883C23—48no—
884C23—48no—
885C23—48no—
886C23—832no—
887C23C23×D411yescharacteristic
888C23C23×D411yescharacteristic
889C23C23×D411yescharacteristic
890Q8—28no—
891Q8—28no—
892Q8—28no—
893Q8—28no—
894Q8—48no—
895Q8—44no—
896Q8—44no—
897Q8—48no—
898Q8—44no—
899Q8—44no—
900Q8—84no—
901Q8—82no—
902D4—28no—
903D4—216no—
904D4—48no—
905D4—48no—
906D4—416no—
907D4—48no—
908D4—48no—
909D4—48no—
910D4—48no—
911D4—48no—
912D4—416no—
913D4—44no—
914D4—88no—
915D4—88no—
916D4—84no—
917D4—82no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—42no—
936C2×C4—44no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—41no—
941C2×C4—44no—
942C2×C4—44no—
943C2×C4—416no—
944C2×C4—44no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—44no—
949C2×C4—44no—
950C2×C4—48no—
951C2×C4—48no—
952C2×C4—816no—
953C2×C4—816no—
954C2×C4—88no—
955C2×C4—84no—
956C2×C4#57514yes—
957C2×C4C23×D412yes—
958C2×C4C23×D414yes—
959C2×C4C23×D414yes—
960C2×C4C23×D412yes—
961C2×C4C23×D411yescharacteristic
962C2×C4C23×D411yescharacteristic
963C2×C4C23×D414yes—
964C2×C4C23×D414yes—
965C2×C4C23×D412yes—
966C2×C4C23×D411yescharacteristic
967C2×C4C23×D412yes—
968C2×C4#58514yes—
969C2×C4C2611yescharacteristic
970C8—216no—
971C22—28no—
972C22—21no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—21no—
977C22—21no—
978C22—44no—
979C22—48no—
980C22—44no—
981C22—48no—
982C22—48no—
983C22—44no—
984C22—816no—
985C22—816no—
986C22—816no—
987C22#348712yes—
988C22C2×#57512yes—
989C22#358512yes—
990C22C24×D411yescharacteristic
991C4—21no—
992C4—21no—
993C4—22no—
994C4—24no—
995C4—24no—
996C4—24no—
997C4—24no—
998C4—22no—
999C4—22no—
1000C4—44no—
1001C4—44no—
1002C4—44no—
1003C4—44no—
1004C4—44no—
1005C4#348712yes—
1006C4C2×#57514yes—
1007C4C2×#58512yes—
1008C2—22no—
1009C2—22no—
1010C2—22no—
1011C2—84no—
1012C2—88no—
1013C2C2×#348711yescharacteristic
1014C2C22×#57511yescharacteristic
1015C2C2×#358511yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62788C2semidirect
2. C22×#559C2semidirect
3. #61904C2semidirect
4. #61898C2semidirect
5. #61895C2semidirect
6. #61892C2semidirect
7. #61891C2semidirect
8. #61885C2semidirect
9. #61405C2semidirect
10. #61324C2semidirect
11. #60799C2semidirect
12. #60798C2semidirect
13. #60560C2semidirect
14. #60558C2semidirect
15. #60248C2semidirect
16. #3523C22semidirect
17. #3522C22semidirect
19. #3507C22semidirect
20. #3507C22semidirect
21. #3502C22semidirect
22. #3497C22semidirect
27. #3480C22semidirect
38. Q8×#41C22semidirect
52. #3403C22semidirect
53. #3401C22semidirect
54. #3400C22semidirect
55. #3399C22semidirect
56. #3396C22semidirect
57. #3394C22semidirect
58. #3375C22semidirect
59. #3373C22semidirect
60. #3371C22semidirect
61. #3370C22semidirect
62. #3365C22semidirect
63. #3361C22semidirect
66. #3215C22semidirect
67. #3215C22semidirect
68. #3213C22semidirect
69. #3213C22semidirect
70. #3211C22semidirect
71. #3211C22semidirect
76. #3153C22semidirect
78. #3140C22semidirect
80. #3117C22semidirect
81. #3114C22semidirect
82. #3113C22semidirect
83. #3112C22semidirect
84. #3110C22semidirect
85. #3109C22semidirect
86. #3108C22semidirect
87. #3105C22semidirect
88. #3104C22semidirect
89. #3103C22semidirect
90. #3101C22semidirect
91. #3100C22semidirect
93. #3078C22semidirect
94. #3077C22semidirect
95. #3040C22semidirect
97. #3037C22semidirect
98. #3036C22semidirect
101. #2984C22semidirect
102. #2983C22semidirect
103. #2983C22semidirect
104. #2982C22semidirect
105. Q8×M16C22semidirect
106. C4×#137C22semidirect
107. C4×AGL(1,ℤ/8)C22semidirect
131. #559C23semidirect
132. #559C23semidirect
133. Q82C23semidirect
135. #557C23semidirect
136. #557C23semidirect
137. #557C23semidirect
140. #556C23semidirect
141. #556C23semidirect
144. #554C23semidirect
145. #554C23semidirect
152. #550C23semidirect
155. D4×Q8C23semidirect
288. #497C23semidirect
290. #496C23semidirect
291. #495C23semidirect
295. #489C23semidirect
296. #489C23semidirect
297. #488C23semidirect
304. #479C23semidirect
305. #478C23semidirect
306. #477C23semidirect
307. #476C23semidirect
308. #475C23semidirect
309. #474C23semidirect
310. #464C23semidirect
311. #464C23semidirect
312. #464C23semidirect
313. #463C23semidirect
314. #463C23semidirect
315. #463C23semidirect
316. #462C23semidirect
317. #461C23semidirect
320. #460C23semidirect
323. #459C23semidirect
332. #446C23semidirect
333. #446C23semidirect
334. C8×Q8C23semidirect
335. #442C23semidirect
336. #441C23semidirect
337. #440C23semidirect
338. #440C23semidirect
339. C4×Q16C23semidirect
340. C4×SD16C23semidirect
341. C4×SD16C23semidirect
342. C4×D8C23semidirect

Maximal subgroups

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

subgroupindex
#627882
C22×#5592
#619042
#618982
#618952
#618922
#618912
#618852
#614052
#613242
#607992
#607982
#605602
#605582
#602482