Finite Group Databasebeta

← #10575145

Subgroups — #10575145

Order 512.

7738 conjugacy classes of subgroups.

The subgroup lattice has 1097 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62814C211yesmaximal, characteristic, complemented
2C22×#520C211yesmaximal, characteristic, complemented
3#60589C218yesmaximal, complemented
4#60588C218yesmaximal, complemented
5#60585C218yesmaximal, complemented
6#60584C218yesmaximal, complemented
7#60565C218yesmaximal, complemented
8#60560C214yesmaximal, complemented
9#60558C214yesmaximal, complemented
10C2×#3092C212yesmaximal, complemented
11#60492C212yesmaximal, complemented
12#60425C212yesmaximal, complemented
13#60359C212yesmaximal, complemented
14#60170C214yesmaximal, complemented
15#60124C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C2×#575C2214yes—
18#3495C2214yescomplemented
19#3495C2214yescomplemented
20#3494C2214yescomplemented
21#3494C2214yescomplemented
22#3493—21no—
23#3493—21no—
24#3492—21no—
25#3492—21no—
26#3491—22no—
27#3490—22no—
28#3475—24no—
29#3475—24no—
30#3458C2211yescharacteristic, complemented
31#3455C2214yescomplemented
32#3449C2211yescharacteristic, complemented
33#3444C2214yes—
34C2×#525C2212yes—
35#3428C2212yescomplemented
36C2×#520—21no—
37C2×#520—21no—
38C2×#520—24no—
39C2×#520—24no—
40C2×#520—22no—
41C2×#520C2212yes—
42C2×#520C2212yes—
43C2×#520C2214yescomplemented
44C2×#520C2218yescomplemented
45C2×#520C2218yescomplemented
46C22×C4×Q8C2212yescomplemented
47C22×C4×D4—22no—
48C22×C4×D4C2212yescomplemented
49C22×#117—21no—
50C22×#117C2211yescharacteristic
51C23×C4⋊C4—21no—
52C23×C4⋊C4C2211yescharacteristic
53#3125C22132yescomplemented
54#3124C22132yescomplemented
55#3120C22132yescomplemented
56#3119C22132yescomplemented
57#3117C22116yescomplemented
58#3114C22116yescomplemented
59#3113C2218yescomplemented
60#3112C2218yescomplemented
61#3110C2218yescomplemented
62#3109C2218yescomplemented
63#3108C22116yescomplemented
64#3105C22116yescomplemented
65#3104C2218yescomplemented
66#3103C2218yescomplemented
67#3101C2218yescomplemented
68#3100C2218yescomplemented
69#3092C2218yescomplemented
70#3092C2218yescomplemented
71#3092C2218yescomplemented
72#3092C2218yescomplemented
73C2×#484C2214yescomplemented
74C2×#481C2214yescomplemented
75C2×#483C2214yescomplemented
76C2×#480C2214yescomplemented
77#3084C22116yescomplemented
78#3083C22116yescomplemented
79#3078C2218yescomplemented
80#3077C2218yescomplemented
81#3046C22116yescomplemented
82#3045C22116yescomplemented
83#3037C2218yescomplemented
84#3036C2218yescomplemented
85#3007C2214yescomplemented
86#3007C2214yescomplemented
87#3006C2214yescomplemented
88#3006C2214yescomplemented
89#3005C2218yescomplemented
90#3004C2214yescomplemented
91#3003C2214yescomplemented
92#3002C2218yes—
93#3002C2218yes—
94#2952C22116yescomplemented
95#2951C22116yescomplemented
96#2947C22116yescomplemented
97#2946C22116yescomplemented
98C4×#137C22116yescomplemented
99C4×AGL(1,ℤ/8)C22116yescomplemented
100#2924C2218yescomplemented
101#2924C2218yescomplemented
102#2921C2214yescomplemented
103#2920C2214yescomplemented
104C2×#428C2214yescomplemented
105#2905C2212yescomplemented
106#2896C2214yes—
107C2×#417C2214yescomplemented
108C2×#407C2212yes—
109#2873C2212yescomplemented
110C22×#41—216no—
111C22×#41—22no—
112C22×#41—22no—
113C22×#41—21no—
114C22×#41—21no—
115C22×#41C2314yes—
116C22×#41C2314yes—
117C22×#41C2312yes—
118C22×#41C2312yes—
119C22×#41C2312yes—
120C23×Q8C2311yescharacteristic
121C23×D4—21no—
122C23×D4C2311yescharacteristic
123C24×C4—21no—
124C24×C4—21no—
125C24×C4—22no—
126C24×C4C2311yescharacteristic
127#575—232no—
128C2×#137C2318yes—
129C2×#137C2318yes—
130C2×AGL(1,ℤ/8)C2318yes—
131C2×AGL(1,ℤ/8)C2318yes—
132C2×#135C23116yes—
133C22×M16C2314yes—
134#556—24no—
135#556—24no—
136#555—24no—
137#555—24no—
138#554—24no—
139#554—24no—
140#553—24no—
141#553—24no—
142#553—24no—
143#553—24no—
144#552—28no—
145#552—28no—
146#552—24no—
147#552—24no—
148#552—24no—
149#552—24no—
150#551—28no—
151#551—28no—
152#551—28no—
153#551—28no—
154#547—24no—
155#547—24no—
156#546—28no—
157#546—28no—
158#544—21no—
159#544—21no—
160#544C2314yescomplemented
161#544C2314yescomplemented
162#543—22no—
163#542C2318yescomplemented
164#542C2318yescomplemented
165#541C2318yescomplemented
166#540C2318yescomplemented
167#539—24no—
168#539—24no—
169#538—24no—
170#538—24no—
171#537—21no—
172#537—21no—
173#536C2314yescomplemented
174#535C2314yescomplemented
175#534—22no—
176#533—24no—
177#533C2314yes—
178#533C2314yes—
179#533C2314yes—
180#532C2314yes—
181#532C2314yes—
182#532C2314yes—
183#529—28no—
184#529—28no—
185#529—24no—
186#529—24no—
187#529—24no—
188#529—24no—
189#529C2318yes—
190#529C2318yes—
191#525—22no—
192#525—22no—
193#525—22no—
194#525—22no—
195#525—24no—
196#525—24no—
197#525—24no—
198#525C2314yes—
199#525C2314yes—
200#525C2314yes—
201#525C2314yes—
202C2×#123—22no—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2312yes—
205C2×#121C2312yes—
206C2×#121C2312yes—
207C2×#120—22no—
208#520—28no—
209#520—28no—
210#520—216no—
211#520—216no—
212#520—216no—
213#520—28no—
214#520—28no—
215#520—28no—
216#520—28no—
217#520—22no—
218#520—22no—
219#520C23116yes—
220#520C23132yes—
221#520C23116yes—
222#520C2314yescomplemented
223#520C2314yescomplemented
224#519C2314yescomplemented
225#518—24no—
226#518C2314yescomplemented
227C4×#41—24no—
228C4×#41—24no—
229C4×#41—24no—
230C4×#41C2318yes—
231C2×C4×Q8—24no—
232C2×C4×Q8—24no—
233C2×C4×Q8—22no—
234C2×C4×Q8—22no—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2318yes—
237C2×C4×Q8C2318yes—
238C2×C4×Q8C2314yes—
239C2×C4×D4—22no—
240C2×C4×D4—22no—
241C2×C4×D4—24no—
242C2×C4×D4—24no—
243C2×C4×D4—24no—
244C2×C4×D4—24no—
245C2×C4×D4—216no—
246C2×C4×D4—216no—
247C2×C4×D4—24no—
248C2×C4×D4—24no—
249C2×C4×D4—22no—
250C2×C4×D4—22no—
251C2×C4×D4C2314yes—
252C2×C4×D4C2318yes—
253C2×C4×D4C2318yes—
254C2×C4×D4C2314yes—
255C2×#117—24no—
256C2×#117—22no—
257C2×#117—22no—
258C2×#117—24no—
259C2×#117—28no—
260C2×#117—28no—
261C2×#117D414yes—
262C2×#117D414yes—
263C2×#117D412yes—
264C2×#117D411yescharacteristic
265C2×#117D411yescharacteristic
266C2×#117C2312yes—
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2312yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C22×C4⋊C4—21no—
273C22×C4⋊C4—22no—
274C22×C4⋊C4—22no—
275C22×C4⋊C4—22no—
276C22×C4⋊C4—21no—
277C22×C4⋊C4—21no—
278C22×C4⋊C4—22no—
279C22×C4⋊C4—22no—
280C22×C4⋊C4—24no—
281C22×C4⋊C4—28no—
282C22×C4⋊C4—28no—
283C22×C4⋊C4D411yescharacteristic
284C22×C4⋊C4D411yescharacteristic
285C22×C4⋊C4C2314yes—
286C22×C4⋊C4C2314yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C22⋊C4—22no—
291C22×C22⋊C4D412yes—
292C22×C42—22no—
293C22×C42C2312yes—
294#484C23116yes—
295#484C23116yescomplemented
296#483C23116yes—
297#483C23116yescomplemented
298#481C23116yes—
299#481C23116yescomplemented
300#480C23116yes—
301#480C23116yescomplemented
302#479C23132yescomplemented
303#478C23132yescomplemented
304#477C23116yescomplemented
305#476C23116yescomplemented
306#475C23116yescomplemented
307#474C23116yescomplemented
308#464C23132yescomplemented
309#463C23132yescomplemented
310#462C23116yescomplemented
311#461C23116yescomplemented
312#460C23116yescomplemented
313#459C23116yescomplemented
314#452C23116yes—
315#452C23116yes—
316#451C2318yes—
317#451C2318yes—
318#450C2318yes—
319#450C2318yes—
320#449C23116yes—
321#449C23116yes—
322#448C2318yes—
323#448C2318yes—
324#447C2318yes—
325#447C2318yes—
326#442C23132yescomplemented
327#441C23132yescomplemented
328#440C23132yescomplemented
329#440C23132yescomplemented
330C4×Q16C23132yescomplemented
331C4×SD16C23132yescomplemented
332C4×SD16C23132yescomplemented
333C4×D8C23132yescomplemented
334#433C23132yescomplemented
335#432C2318yes—
336#432C2318yes—
337#431C2318yes—
338#431C2318yes—
339#428C23116yes—
340#428C23116yescomplemented
341C2×#107C2318yescomplemented
342C2×#106C2318yescomplemented
343#424C23116yescomplemented
344#423C2318yes—
345#419C2318yes—
346#418C2318yes—
347#417C2318yes—
348#417C2318yes—
349#417C23116yes—
350#417C23116yescomplemented
351#416C23116yes—
352C2×#103C2318yescomplemented
353C2×#102C2318yescomplemented
354#407C2314yes—
355#407C2314yes—
356#407C2314yes—
357#407C2314yes—
358C2×C22⋊C8C2314yes—
359C2×C22⋊C8C2314yes—
360#405C23116yescomplemented
361C4×M16C2318yes—
362C25—21no—
363C25C2×D411yescharacteristic
364C2×#41—216no—
365C2×#41—232no—
366C2×#41—232no—
367C2×#41—216no—
368C2×#41—232no—
369C2×#41—232no—
370C2×#41—28no—
371C2×#41—28no—
372C2×#41—24no—
373C2×#41—24no—
374C2×#41—24no—
375C2×#41—24no—
376C2×#41—24no—
377C2×#41—24no—
378C2×#41—22no—
379C2×#41—22no—
380C2×#41—24no—
381C2×#41—24no—
382C2×#41—28no—
383C2×#41—216no—
384C2×#41#41116yescomplemented
385C2×#41C2414yes—
386C2×#41C2418yes—
387C2×#41C2414yes—
388C2×#41C2418yes—
389C22×Q8—28no—
390C22×Q8—21no—
391C22×Q8—21no—
392C22×Q8—21no—
393C22×Q8C2412yes—
394C22×Q8C2412yes—
395C22×Q8C2412yes—
396C22×Q8C2412yes—
397C22×D4—216no—
398C22×D4—24no—
399C22×D4—24no—
400C22×D4—22no—
401C22×D4—22no—
402C22×D4—28no—
403C22×D4—22no—
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—21no—
407C22×D4—21no—
408C22×D4—21no—
409C22×D4C2412yes—
410C22×D4C2412yes—
411C22×D4C2412yes—
412C22×D4C2412yes—
413C23×C4—216no—
414C23×C4—21no—
415C23×C4—24no—
416C23×C4—24no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—28no—
420C23×C4—22no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—22no—
424C23×C4—22no—
425C23×C4—22no—
426C23×C4—28no—
427C23×C4—24no—
428C23×C4—28no—
429C23×C4—24no—
430C23×C4—88no—
431C23×C4—84no—
432C23×C4C2×D411yescharacteristic
433C23×C4C2×D412yes—
434C23×C4C2×D412yes—
435C23×C4C2×D411yescharacteristic
436C23×C4C2×D411yescharacteristic
437C23×C4C2×D412yes—
438C23×C4C2×D412yes—
439C23×C4C2412yes—
440C23×C4C2412yes—
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444#137—232no—
445#137—232no—
446AGL(1,ℤ/8)—232no—
447AGL(1,ℤ/8)—232no—
448#135—264no—
449C2×Q16C24116yes—
450C2×SD16C24116yes—
451C2×SD16C24116yes—
452C2×D8C24116yes—
453C2×M16—216no—
454C2×M16C2418yes—
455C2×M16C2418yes—
456C22×C8C2418yes—
457C4⋊Q8—24no—
458C4⋊Q8—24no—
459C4⋊Q8C2414yes—
460C4⋊Q8C2414yes—
461C4⋊Q8C2414yes—
462#127C2414yes—
463#126—28no—
464#126—28no—
465#126—28no—
466#126—28no—
467#126—28no—
468#126—28no—
469#125—28no—
470#125—28no—
471#125—24no—
472#125—24no—
473#125—24no—
474#125—24no—
475#125C2418yes—
476#124—28no—
477#124—28no—
478#124—24no—
479#124—24no—
480#124C2418yes—
481#123—24no—
482#123—24no—
483#123—24no—
484#123—24no—
485#123—28no—
486#123—28no—
487#123—28no—
488#123—28no—
489#123—28no—
490#123—28no—
491#123—28no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—24no—
497C22⋊Q8—24no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—24no—
502C22⋊Q8—28no—
503C22⋊Q8—28no—
504C22⋊Q8—28no—
505C22⋊Q8—28no—
506C22⋊Q8C2414yes—
507C22⋊Q8C2414yes—
508C22⋊Q8C2414yes—
509C22⋊Q8C2414yes—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—24no—
515#121—24no—
516#121—24no—
517#121—24no—
518#121—24no—
519#121—24no—
520#121—28no—
521#121—28no—
522#121C2414yes—
523#121C2414yes—
524#121C2414yes—
525#121C2414yes—
526#120—24no—
527#120—24no—
528#120—24no—
529#120—24no—
530#120—28no—
531C4×Q8—24no—
532C4×Q8—24no—
533C4×Q8—28no—
534C4×Q8—28no—
535C4×Q8—28no—
536C4×Q8—28no—
537C4×Q8—28no—
538C4×Q8—28no—
539C4×Q8—24no—
540C4×Q8—24no—
541C4×Q8—24no—
542C4×Q8—24no—
543C4×Q8C24116yes—
544C4×Q8C24116yes—
545C4×Q8C2418yes—
546C4×Q8C2418yes—
547C4×D4—24no—
548C4×D4—24no—
549C4×D4—24no—
550C4×D4—24no—
551C4×D4—24no—
552C4×D4—24no—
553C4×D4—24no—
554C4×D4—24no—
555C4×D4—28no—
556C4×D4—28no—
557C4×D4—28no—
558C4×D4—28no—
559C4×D4—24no—
560C4×D4—24no—
561C4×D4—232no—
562C4×D4—232no—
563C4×D4—232no—
564C4×D4—232no—
565C4×D4—28no—
566C4×D4—28no—
567C4×D4—28no—
568C4×D4—28no—
569C4×D4—28no—
570C4×D4—28no—
571C4×D4—28no—
572C4×D4—28no—
573C4×D4—24no—
574C4×D4—24no—
575C4×D4—24no—
576C4×D4—24no—
577C4×D4C24116yes—
578C4×D4C24116yes—
579C4×D4C2418yes—
580C4×D4C2418yes—
581#117—22no—
582#117—22no—
583#117—24no—
584#117—24no—
585#117—216no—
586#117—216no—
587#117—232no—
588#117—24no—
589#117—24no—
590#117—28no—
591#117—28no—
592#117—28no—
593#117—28no—
594#117C2×D414yes—
595#117C2×D414yes—
596#117C2×D418yes—
597#117C2×D418yes—
598#117C2×D418yes—
599#117C2×D414yes—
600#117C2×D414yes—
601#117C2×D414yes—
602#117C2×D414yes—
603#117C2414yes—
604#117C2414yes—
605#117C2414yes—
606#117C2414yes—
607#117C2418yes—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—28no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—28no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—22no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—24no—
620C2×C4⋊C4—24no—
621C2×C4⋊C4—24no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—216no—
628C2×C4⋊C4—216no—
629C2×C4⋊C4—232no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—24no—
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D412yes—
635C2×C4⋊C4C2×D414yes—
636C2×C4⋊C4C2×D414yes—
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D412yes—
640C2×C4⋊C4C2×D414yes—
641C2×C4⋊C4C2×D414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—28no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—28no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—28no—
659C2×C22⋊C4C2×D412yes—
660C2×C22⋊C4C2×D412yes—
661C2×C22⋊C4C2×D412yes—
662C2×C22⋊C4C2×D412yes—
663C2×C22⋊C4C2×D418yes—
664C2×C22⋊C4C2×D418yes—
665C2×C42—28no—
666C2×C42—24no—
667C2×C42—28no—
668C2×C42—24no—
669C2×C42—22no—
670C2×C42—28no—
671C2×C42C2×D414yes—
672C2×C42C2×D414yes—
673C2×C42C2×D412yes—
674C2×C42C2×D412yes—
675C2×C42C2412yes—
676C2×C42C2414yes—
677C2×C42C2414yes—
678C2×C42C2412yes—
679#107C24132yes—
680#106C24132yes—
681C4⋊C8C24116yes—
682C4⋊C8C24116yes—
683#103C24132yes—
684#103C24116yes—
685#103C24116yes—
686#102C24132yes—
687#102C24116yes—
688#102C24116yes—
689C22⋊C8C2418yes—
690C22⋊C8C2418yes—
691C22⋊C8C2418yes—
692C22⋊C8C2418yes—
693#97C24116yes—
694C4×C8C24116yes—
695C24—28no—
696C24—24no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—42no—
702C24—42no—
703C24—44no—
704C24—44no—
705C24C22×D411yescharacteristic
706C24C22×D412yes—
707C24C22×D412yes—
708C24C22×D411yescharacteristic
709C24C22×D411yescharacteristic
710#41—232no—
711#41—232no—
712#41—232no—
713#41—232no—
714#41—232no—
715#41—216no—
716#41—216no—
717#41—232no—
718#41—216no—
719#41—216no—
720#41—216no—
721#41—48no—
722#41—48no—
723#41—88no—
724#41—88no—
725#41C2×#41132yes—
726C2×Q8—28no—
727C2×Q8—28no—
728C2×Q8—28no—
729C2×Q8—28no—
730C2×Q8—28no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—22no—
734C2×Q8—22no—
735C2×Q8—24no—
736C2×Q8—24no—
737C2×Q8—24no—
738C2×Q8—28no—
739C2×Q8C2×#4118yes—
740C2×Q8C2514yes—
741C2×Q8C2514yes—
742C2×D4—232no—
743C2×D4—232no—
744C2×D4—216no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—216no—
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—24no—
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—28no—
767C2×D4—48no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4C2×#4118yes—
771C2×D4C2514yes—
772C2×D4C2514yes—
773C22×C4—28no—
774C22×C4—232no—
775C22×C4—232no—
776C22×C4—216no—
777C22×C4—24no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—24no—
782C22×C4—216no—
783C22×C4—24no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—216no—
805C22×C4—216no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—816no—
811C22×C4—88no—
812C22×C4—88no—
813C22×C4—816no—
814C22×C4—88no—
815C22×C4—84no—
816C22×C4—88no—
817C22×C4—84no—
818C22×C4C22×D414yes—
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D414yes—
823C22×C4C22×D412yes—
824C22×C4C22×D412yes—
825C22×C4C22×D412yes—
826C22×C4C22×D412yes—
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D412yes—
829C22×C4C22×D412yes—
830C22×C4C22×D412yes—
831C22×C4C22×D412yes—
832C22×C4C22×D414yes—
833C22×C4C22×D412yes—
834C22×C4C22×D412yes—
835C22×C4C22×D414yes—
836C22×C4C22×D412yes—
837C22×C4C22×D412yes—
838C22×C4C22×D411yescharacteristic
839C22×C4C2×#4118yes—
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2512yes—
843C22×C4C2511yescharacteristic
844C22×C4C2512yes—
845Q16—232no—
846SD16—232no—
847SD16—232no—
848D8—232no—
849M16—216no—
850M16—216no—
851C2×C8—216no—
852C2×C8C25116yes—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—216no—
856C4⋊C4—216no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4C22×D414yes—
875C4⋊C4C22×D414yes—
876C4⋊C4C22×D418yes—
877C4⋊C4C22×D414yes—
878C4⋊C4C22×D414yes—
879C4⋊C4C22×D418yes—
880C4⋊C4C2514yes—
881C4⋊C4C2518yes—
882C4⋊C4C2514yes—
883C22⋊C4—24no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—216no—
890C22⋊C4—216no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4C22×D418yes—
900C22⋊C4C22×D418yes—
901C22⋊C4C22×D418yes—
902C22⋊C4C22×D418yes—
903C42—216no—
904C42—216no—
905C42—24no—
906C42—28no—
907C42—28no—
908C42—24no—
909C42C22×D414yes—
910C42C22×D414yes—
911C42C22×D414yes—
912C42C22×D414yes—
913C42C22×D414yes—
914C42C22×D414yes—
915C42C2514yes—
916C42C2514yes—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—28no—
921C23—28no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—22no—
928C23—28no—
929C23—24no—
930C23—41no—
931C23—42no—
932C23—41no—
933C23—41no—
934C23—42no—
935C23—41no—
936C23—44no—
937C23—44no—
938C23—416no—
939C23—432no—
940C23—44no—
941C23—44no—
942C23—44no—
943C23—44no—
944C23—44no—
945C23—82no—
946C23—82no—
947C23#52514yes—
948C23C23×D412yes—
949C23C23×D411yescharacteristic
950C23C23×D411yescharacteristic
951C23C23×D411yescharacteristic
952C23C23×D412yes—
953Q8—28no—
954Q8—28no—
955Q8—24no—
956Q8—28no—
957Q8—28no—
958Q8—44no—
959Q8—84no—
960Q8—84no—
961Q8C22×#4118yes—
962D4—232no—
963D4—28no—
964D4—28no—
965D4—232no—
966D4—24no—
967D4—28no—
968D4—28no—
969D4—48no—
970D4—48no—
971D4—48no—
972D4—48no—
973D4—44no—
974D4—84no—
975D4—84no—
976D4—84no—
977D4—84no—
978D4C22×#4118yes—
979C2×C4—28no—
980C2×C4—28no—
981C2×C4—232no—
982C2×C4—28no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—28no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—232no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—28no—
1005C2×C4—42no—
1006C2×C4—44no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—44no—
1010C2×C4—42no—
1011C2×C4—48no—
1012C2×C4—48no—
1013C2×C4—48no—
1014C2×C4—44no—
1015C2×C4—48no—
1016C2×C4—48no—
1017C2×C4—816no—
1018C2×C4—816no—
1019C2×C4—88no—
1020C2×C4—88no—
1021C2×C4—88no—
1022C2×C4—88no—
1023C2×C4—82no—
1024C2×C4—82no—
1025C2×C4#52514yes—
1026C2×C4#52518yes—
1027C2×C4C23×D414yes—
1028C2×C4C23×D414yes—
1029C2×C4C23×D414yes—
1030C2×C4C23×D411yescharacteristic
1031C2×C4C23×D411yescharacteristic
1032C2×C4C23×D414yes—
1033C2×C4C23×D412yes—
1034C2×C4C23×D411yescharacteristic
1035C2×C4C23×D412yes—
1036C2×C4C22×#4118yes—
1037C2×C4C22×#4114yes—
1038C2×C4C2611yescharacteristic
1039C8—216no—
1040C22—28no—
1041C22—21no—
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—21no—
1046C22—22no—
1047C22—21no—
1048C22—21no—
1049C22—22no—
1050C22—22no—
1051C22—22no—
1052C22—28no—
1053C22—44no—
1054C22—48no—
1055C22—48no—
1056C22—416no—
1057C22—416no—
1058C22—44no—
1059C22—416no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—164no—
1066C22C2×#52512yes—
1067C22C2×#52514yes—
1068C22#358512yes—
1069C22#358612yes—
1070C22C24×D411yescharacteristic
1071C4—24no—
1072C4—24no—
1073C4—24no—
1074C4—24no—
1075C4—22no—
1076C4—28no—
1077C4—21no—
1078C4—21no—
1079C4—48no—
1080C4—44no—
1081C4—44no—
1082C4—44no—
1083C4C2×#52514yes—
1084C4C2×#52512yes—
1085C4C23×#4112yes—
1086C2—22no—
1087C2—22no—
1088C2—22no—
1089C2—24no—
1090C2—42no—
1091C2—48no—
1092C2—84no—
1093C2C22×#52511yescharacteristic
1094C2C2×#358511yescharacteristic
1095C2C2×#358611yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×#117 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62814C2semidirect
2. C22×#520C2semidirect
3. #60589C2semidirect
4. #60588C2semidirect
5. #60585C2semidirect
6. #60584C2semidirect
7. #60565C2semidirect
8. #60560C2semidirect
9. #60558C2semidirect
10. C2×#3092C2semidirect
11. #60492C2semidirect
12. #60425C2semidirect
13. #60359C2semidirect
14. #60170C2semidirect
15. #60124C2semidirect
18. #3495C22semidirect
19. #3495C22semidirect
20. #3494C22semidirect
21. #3494C22semidirect
30. #3458C22semidirect
31. #3455C22semidirect
32. #3449C22semidirect
35. #3428C22semidirect
43. C2×#520C22semidirect
44. C2×#520C22semidirect
45. C2×#520C22semidirect
46. C22×C4×Q8C22semidirect
48. C22×C4×D4C22semidirect
53. #3125C22semidirect
54. #3124C22semidirect
55. #3120C22semidirect
56. #3119C22semidirect
57. #3117C22semidirect
58. #3114C22semidirect
59. #3113C22semidirect
60. #3112C22semidirect
61. #3110C22semidirect
62. #3109C22semidirect
63. #3108C22semidirect
64. #3105C22semidirect
65. #3104C22semidirect
66. #3103C22semidirect
67. #3101C22semidirect
68. #3100C22semidirect
69. #3092C22semidirect
70. #3092C22semidirect
71. #3092C22semidirect
72. #3092C22semidirect
73. C2×#484C22semidirect
74. C2×#481C22semidirect
75. C2×#483C22semidirect
76. C2×#480C22semidirect
77. #3084C22semidirect
78. #3083C22semidirect
79. #3078C22semidirect
80. #3077C22semidirect
81. #3046C22semidirect
82. #3045C22semidirect
83. #3037C22semidirect
84. #3036C22semidirect
85. #3007C22semidirect
86. #3007C22semidirect
87. #3006C22semidirect
88. #3006C22semidirect
89. #3005C22semidirect
90. #3004C22semidirect
91. #3003C22semidirect
94. #2952C22semidirect
95. #2951C22semidirect
96. #2947C22semidirect
97. #2946C22semidirect
98. C4×#137C22semidirect
99. C4×AGL(1,ℤ/8)C22semidirect
100. #2924C22semidirect
101. #2924C22semidirect
102. #2921C22semidirect
103. #2920C22semidirect
104. C2×#428C22semidirect
105. #2905C22semidirect
107. C2×#417C22semidirect
109. #2873C22semidirect
160. #544C23semidirect
161. #544C23semidirect
163. #542C23semidirect
164. #542C23semidirect
165. #541C23semidirect
166. #540C23semidirect
173. #536C23semidirect
174. #535C23semidirect
222. #520C23semidirect
223. #520C23semidirect
224. #519C23semidirect
226. #518C23semidirect
295. #484C23semidirect
297. #483C23semidirect
299. #481C23semidirect
301. #480C23semidirect
302. #479C23semidirect
303. #478C23semidirect
304. #477C23semidirect
305. #476C23semidirect
306. #475C23semidirect
307. #474C23semidirect
308. #464C23semidirect
309. #463C23semidirect
310. #462C23semidirect
311. #461C23semidirect
312. #460C23semidirect
313. #459C23semidirect
326. #442C23semidirect
327. #441C23semidirect
328. #440C23semidirect
329. #440C23semidirect
330. C4×Q16C23semidirect
331. C4×SD16C23semidirect
332. C4×SD16C23semidirect
333. C4×D8C23semidirect
334. #433C23semidirect
340. #428C23semidirect
341. C2×#107C23semidirect
342. C2×#106C23semidirect
343. #424C23semidirect
350. #417C23semidirect
352. C2×#103C23semidirect
353. C2×#102C23semidirect
360. #405C23semidirect
384. C2×#41#41semidirect

Maximal subgroups

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

subgroupindex
#628142
C22×#5202
#605892
#605882
#605852
#605842
#605652
#605602
#605582
C2×#30922
#604922
#604252
#603592
#601702
#601242