Finite Group Databasebeta

← #6393862

Subgroups — #6393862

Order 512.

3245 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3514C211yesmaximal, characteristic
2#60263C211yesmaximal, characteristic, complemented
3M16×#41C211yesmaximal, characteristic, complemented
4#22539C212yesmaximal, complemented
5#22537C212yesmaximal, complemented
6#22410C214yesmaximal, complemented
7D4×#101C212yesmaximal, complemented
8#22408C214yesmaximal, complemented
9D4×#100C212yesmaximal, complemented
10#21880C211yesmaximal, characteristic, complemented
11#21880C212yesmaximal, complemented
12#21800C211yesmaximal, characteristic, complemented
13#21798C212yesmaximal, complemented
14#21426C211yesmaximal, characteristic, complemented
15#21426C212yesmaximal, complemented
16#21218C211yesmaximal, characteristic, complemented
17C2×#1967C212yesmaximal, complemented
18#3514—21no—
19#3514—22no—
20#3514—21no—
21#3514—21no—
22#3514—22no—
23#3514—21no—
24#3514—21no—
25#3514—22no—
26#3514—21no—
27#3514—21no—
28#3514—22no—
29#3514—21no—
30C2×#559C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#555C412yes—
33C2×#551C414yes—
34C2×D4×Q8C2211yescharacteristic
35C2×#548C2212yes—
36C2×#546C412yes—
37C2×#546C2212yes—
38C2×D42C2211yescharacteristic
39C2×#542C412yes—
40C2×#538C414yes—
41C2×#532C2211yescharacteristic
42C2×#529C2211yescharacteristic
43C2×#529C2212yes—
44C22×#124C2212yes—
45C2×#518C412yes—
46C2×C4×#41C2211yescharacteristic
47#2991—21no—
48#2990—21no—
49#2990—22no—
50#2989—22no—
51#2989—21no—
52#2988—21no—
53#2971—21no—
54#2970—21no—
55#2970—22no—
56#2965—22no—
57#2965—21no—
58C8×#41—21no—
59Q8×M16C2212yescomplemented
60Q8×M16C2212yescomplemented
61D4×M16C2212yes—
62D4×M16C2212yes—
63D4×M16C2214yescomplemented
64D4×M16C2214yescomplemented
65#2920C2212yescomplemented
66#2920C2212yescomplemented
67#2920C2211yescharacteristic, complemented
68#2920C2211yescharacteristic, complemented
69C2×#423C2212yescomplemented
70C2×#423C2211yescharacteristic, complemented
71C2×#413C2214yescomplemented
72C22×#101C2214yescomplemented
73C22×#100C2214yes—
74C2×C4×M16C2212yescomplemented
75C2×C4×M16C2211yescharacteristic, complemented
76#1998C2212yescomplemented
77#1998C2211yescharacteristic, complemented
78#1998C2211yescharacteristic, complemented
79#1967C2214yes—
80#1967C2214yes—
81#1967C2211yescharacteristic
82#1967C2212yes—
83#1967C2211yescharacteristic
84#1967C2214yescomplemented
85#1967C2214yescomplemented
86#1967C2212yescomplemented
87#1967C2212yescomplemented
88#1967C2212yescomplemented
89#1967C2212yescomplemented
90#1966C2212yescomplemented
91#1966C2212yescomplemented
92#1965C2212yes—
93#1965C2212yes—
94#1901C2214yescomplemented
95#1901C2212yescomplemented
96#1901C2214yescomplemented
97#1901C2212yescomplemented
98#1900C2214yes—
99#1900C2212yes—
100#1900C2214yes—
101#1900C2212yes—
102#1801C2214yescomplemented
103#1801C2212yescomplemented
104#1800C2212yes—
105#1800C2214yescomplemented
106#1785C2214yescomplemented
107#1784C2214yescomplemented
108#1783C2214yes—
109C4×#101C2214yescomplemented
110C4×#101C2212yescomplemented
111C4×#100C2212yes—
112C4×#100C2214yescomplemented
113C22×#41C2×C411yescharacteristic
114C22×#41C2312yes—
115C23×Q8C2312yes—
116C23×D4C2×C412yes—
117C23×D4C2312yes—
118C22×M16C2314yes—
119C22×M16C2312yes—
120C22×M16C2314yes—
121C22×M16C2312yes—
122#559—21no—
123#559—21no—
124#559—22no—
125#559—22no—
126#559—21no—
127#559—21no—
128#556—21no—
129#556—21no—
130#556—21no—
131#556—21no—
132#556—22no—
133#556—22no—
134#555—22no—
135#555—22no—
136#555—22no—
137#555—22no—
138#555—24no—
139#555—24no—
140#551—24no—
141#551—24no—
142#551—24no—
143#551—24no—
144#551—24no—
145#551—24no—
146#551—24no—
147#551—24no—
148D4×Q8—21no—
149D4×Q8—21no—
150D4×Q8—22no—
151D4×Q8—22no—
152D4×Q8—21no—
153D4×Q8—21no—
154#548—22no—
155#548—22no—
156#548—22no—
157#548—22no—
158#548—22no—
159#548—22no—
160#548—22no—
161#548—22no—
162#546—22no—
163#546—22no—
164#546—24no—
165#546—24no—
166#546—22no—
167#546—22no—
168#546—22no—
169#546—22no—
170#546—22no—
171#546—22no—
172#546—22no—
173#546—22no—
174#546—22no—
175#546—22no—
176D42—21no—
177D42—21no—
178D42—22no—
179D42—22no—
180D42—21no—
181D42—21no—
182#542—22no—
183#542—22no—
184#542—22no—
185#542—22no—
186#542—24no—
187#542—24no—
188#538—24no—
189#538—24no—
190#538—24no—
191#538—24no—
192#538—24no—
193#538—24no—
194#538—24no—
195#538—24no—
196#532—21no—
197#532—21no—
198#532—21no—
199#532—21no—
200#532—21no—
201#532—21no—
202#532—21no—
203#532—21no—
204C2×C4⋊Q8C2×C412yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×#127C2311yescharacteristic
207#529—22no—
208#529—22no—
209#529—22no—
210#529—22no—
211#529—22no—
212#529—22no—
213#529—22no—
214#529—22no—
215#529—21no—
216#529—21no—
217#529—21no—
218#529—21no—
219#529—21no—
220#529—21no—
221#529—21no—
222#529—21no—
223C2×#126C2×C414yes—
224C2×#126C2×C412yes—
225C2×#126C2×C414yes—
226C2×#125C2311yescharacteristic
227C2×#124—22no—
228C2×#124—22no—
229C2×#124—22no—
230C2×#124—22no—
231C2×#124—22no—
232C2×#124—22no—
233C2×#124—22no—
234C2×#124—22no—
235C2×#124C2×C414yes—
236C2×#124C2×C414yes—
237C2×#124C2×C414yes—
238C2×#124C2×C412yes—
239C2×#124C2311yescharacteristic
240C2×#124C2312yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#123C2×C412yes—
244C2×#123C2×C414yes—
245C2×#123C2×C414yes—
246C2×#123C2×C414yes—
247C2×C22⋊Q8C2×C414yes—
248C2×C22⋊Q8C2×C412yes—
249C2×C22⋊Q8C2×C414yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2311yescharacteristic
252C2×#121C2×C412yes—
253C2×#121C2×C412yes—
254C2×#121C2×C414yes—
255C2×#121C2×C414yes—
256C2×#121C2×C412yes—
257C2×#121C2312yes—
258C2×#121C2311yescharacteristic
259C2×#120C2×C414yes—
260C2×#120C2×C414yes—
261#518—22no—
262#518—24no—
263#518—24no—
264#518—22no—
265#518—22no—
266#518—22no—
267C4×#41D411yescharacteristic
268C4×#41D412yes—
269C4×#41D411yescharacteristic
270C4×#41D411yescharacteristic
271C4×#41D412yes—
272C4×#41D411yescharacteristic
273C4×#41D411yescharacteristic
274C4×#41D412yes—
275C4×#41D411yescharacteristic
276C4×#41D411yescharacteristic
277C4×#41D412yes—
278C4×#41D411yescharacteristic
279C2×C4×Q8C2×C411yescharacteristic
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×D4C2×C414yes—
284C2×C4×D4C2×C412yes—
285C2×C4×D4C2×C412yes—
286C2×C4×D4C2×C414yes—
287C2×C4×D4C2×C412yes—
288C2×C4×D4C2×C412yes—
289C2×C4×D4C2×C412yes—
290C2×C4×D4C2×C411yescharacteristic
291C2×C4×D4C2×C412yes—
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2312yes—
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2312yes—
296C2×#117C2×C412yes—
297C2×#117C2×C412yes—
298C2×#117C2×C414yes—
299C2×#117C2×C412yes—
300C2×#117C2×C411yescharacteristic
301C22×C22⋊C4C2×C414yes—
302C22×C22⋊C4C2×C414yes—
303C22×C22⋊C4C2×C414yes—
304C22×C42C2312yes—
305C22×C42C2311yescharacteristic
306#446—24no—
307#446—22no—
308#446—24no—
309#446—22no—
310C8×Q8—22no—
311C8×Q8—22no—
312#436—22no—
313#436—22no—
314#436—24no—
315#436—24no—
316#435—24no—
317#435—24no—
318#435—24no—
319#435—24no—
320#435—24no—
321#435—24no—
322C8×D4—22no—
323C8×D4—22no—
324C8×D4—24no—
325C8×D4—24no—
326#432—22no—
327#432—21no—
328#432—22no—
329#432—21no—
330#432—22no—
331#432—21no—
332#432—22no—
333#432—21no—
334#431—22no—
335#431—21no—
336#431—22no—
337#431—21no—
338#431—22no—
339#431—21no—
340#431—22no—
341#431—21no—
342#423—22no—
343#423—21no—
344#423—22no—
345#423—21no—
346#423C2312yes—
347#423C2312yes—
348#423C2314yes—
349#423C2314yes—
350#423C2311yescharacteristic
351#423C2312yes—
352#423C2311yescharacteristic
353C2×C4⋊C8—22no—
354C2×C4⋊C8—21no—
355C2×C4⋊C8—22no—
356C2×C4⋊C8—21no—
357#413—48no—
358C2×#101—48no—
359C2×#101C2312yes—
360C2×#101C2314yes—
361C2×#101C2314yes—
362C2×#101C2314yes—
363C2×#101C2314yes—
364C2×#101C2314yes—
365C2×#101C2312yes—
366C2×#100—48no—
367C2×#100C2312yes—
368C2×#100C2314yes—
369C2×#100C2314yes—
370C2×#100C2314yes—
371C2×#100C2314yes—
372C2×#100C2314yes—
373C2×#100C2312yes—
374#407C2314yes—
375#407C2314yes—
376#407C2312yes—
377#407C2312yes—
378C4×M16—22no—
379C4×M16—21no—
380C4×M16—22no—
381C4×M16—21no—
382C4×M16C2311yescharacteristic
383C4×M16C2312yes—
384C4×M16C2311yescharacteristic
385C4×M16C2312yes—
386C4×M16C2314yes—
387C4×M16C2312yes—
388C4×M16C2314yes—
389C2×#97—22no—
390C2×#97—21no—
391C2×C4×C8—22no—
392C2×C4×C8—21no—
393#343C2314yes—
394#343C2312yes—
395#343C2314yes—
396#343C2312yes—
397#343C2312yes—
398#343C2312yes—
399C25C22×C414yes—
400C2×#41—22no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—22no—
404C2×#41—44no—
405C2×#41—44no—
406C2×#41—44no—
407C2×#41C22⋊C411yescharacteristic
408C2×#41C22⋊C411yescharacteristic
409C2×#41C22⋊C412yes—
410C2×#41C22⋊C412yes—
411C2×#41C22⋊C411yescharacteristic
412C2×#41C22⋊C411yescharacteristic
413C22×Q8—22no—
414C22×Q8—22no—
415C22×Q8—22no—
416C22×Q8—22no—
417C22×Q8—44no—
418C22×Q8—44no—
419C22×Q8C22×C414yes—
420C22×Q8C22×C411yescharacteristic
421C22×Q8C2411yescharacteristic
422C22×Q8C2412yes—
423C22×D4—24no—
424C22×D4—22no—
425C22×D4—22no—
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—44no—
431C22×D4—44no—
432C22×D4—48no—
433C22×D4C22×C411yescharacteristic
434C22×D4C22×C414yes—
435C22×D4C22×C412yes—
436C22×D4C22×C414yes—
437C22×D4C22×C414yes—
438C22×D4C22×C412yes—
439C22×D4C22×C412yes—
440C22×D4C22×C412yes—
441C22×D4C2411yescharacteristic
442C22×D4C2412yes—
443C23×C4C22×C414yes—
444C23×C4C22×C414yes—
445C23×C4C22×C412yes—
446C23×C4C22×C414yes—
447C23×C4C22×C412yes—
448C23×C4C22×C411yescharacteristic
449C23×C4C22×C412yes—
450C23×C4C22×C411yescharacteristic
451C23×C4C2412yes—
452C23×C4C2411yescharacteristic
453C2×M16—24no—
454C2×M16—22no—
455C2×M16—24no—
456C2×M16—22no—
457C2×M16—28no—
458C2×M16—24no—
459C2×M16—44no—
460C2×M16—42no—
461C2×M16—44no—
462C2×M16—44no—
463C2×M16—44no—
464C2×M16C2412yes—
465C2×M16C2414yes—
466C2×M16C2414yes—
467C2×M16C2412yes—
468C2×M16C2412yes—
469C2×M16C2412yes—
470C22×C8—24no—
471C22×C8—22no—
472C22×C8—24no—
473C22×C8—22no—
474C4⋊Q8—24no—
475C4⋊Q8—22no—
476C4⋊Q8—22no—
477C4⋊Q8—21no—
478C4⋊Q8—21no—
479C4⋊Q8—21no—
480C4⋊Q8—21no—
481#127—21no—
482#127—21no—
483#127—21no—
484#127—21no—
485#126—24no—
486#126—24no—
487#126—24no—
488#126—24no—
489#126—24no—
490#126—24no—
491#126—24no—
492#126—24no—
493#126—22no—
494#126—22no—
495#126—22no—
496#126—22no—
497#125—21no—
498#125—21no—
499#125—21no—
500#125—21no—
501#124—22no—
502#124—22no—
503#124—24no—
504#124—24no—
505#124—24no—
506#124—24no—
507#124—24no—
508#124—24no—
509#124—24no—
510#124—24no—
511#124—24no—
512#124—24no—
513#124—24no—
514#124—24no—
515#124—24no—
516#124—21no—
517#124—21no—
518#124—21no—
519#124—21no—
520#124—22no—
521#124—22no—
522#124—22no—
523#124—22no—
524#124—22no—
525#124—22no—
526#124—22no—
527#124—22no—
528#124—22no—
529#124—22no—
530#124—22no—
531#124—22no—
532#123—22no—
533#123—22no—
534#123—22no—
535#123—22no—
536#123—24no—
537#123—24no—
538#123—24no—
539#123—24no—
540#123—24no—
541#123—24no—
542#123—24no—
543#123—24no—
544#123—24no—
545#123—24no—
546#123—24no—
547#123—24no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—24no—
551C22⋊Q8—22no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—22no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—24no—
560C22⋊Q8—24no—
561C22⋊Q8—24no—
562C22⋊Q8—24no—
563C22⋊Q8—24no—
564C22⋊Q8—24no—
565C22⋊Q8—24no—
566C22⋊Q8—24no—
567#121—24no—
568#121—24no—
569#121—24no—
570#121—24no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—24no—
588#121—22no—
589#121—22no—
590#121—24no—
591#121—24no—
592#121—24no—
593#121—24no—
594#120—24no—
595#120—24no—
596#120—24no—
597#120—24no—
598#120—24no—
599#120—24no—
600#120—24no—
601#120—24no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—21no—
607C4×Q8—21no—
608C4×Q8—21no—
609C4×Q8—21no—
610C4×Q8C22⋊C411yescharacteristic
611C4×Q8C22⋊C411yescharacteristic
612C4×Q8C22⋊C411yescharacteristic
613C4×Q8C22⋊C411yescharacteristic
614C4×Q8C22⋊C412yes—
615C4×Q8C22⋊C412yes—
616C4×Q8C2×D411yescharacteristic
617C4×Q8C2×D411yescharacteristic
618C4×Q8C2×D412yes—
619C4×Q8C2×D412yes—
620C4×Q8C2×D411yescharacteristic
621C4×Q8C2×D411yescharacteristic
622C4×D4—24no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—24no—
626C4×D4—24no—
627C4×D4—24no—
628C4×D4—24no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—24no—
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—24no—
637C4×D4—24no—
638C4×D4—24no—
639C4×D4—24no—
640C4×D4—22no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C4×D4—22no—
656C4×D4C22⋊C412yes—
657C4×D4C22⋊C411yescharacteristic
658C4×D4C22⋊C412yes—
659C4×D4C22⋊C411yescharacteristic
660C4×D4C22⋊C411yescharacteristic
661C4×D4C22⋊C411yescharacteristic
662C4×D4C22⋊C412yes—
663C4×D4C22⋊C412yes—
664C4×D4C22⋊C412yes—
665C4×D4C22⋊C412yes—
666C4×D4C22⋊C412yes—
667C4×D4C22⋊C412yes—
668C4×D4C22⋊C412yes—
669C4×D4C22⋊C412yes—
670C4×D4C2×D411yescharacteristic
671C4×D4C2×D411yescharacteristic
672C4×D4C2×D412yes—
673C4×D4C2×D412yes—
674C4×D4C2×D411yescharacteristic
675C4×D4C2×D411yescharacteristic
676C4×D4C2×D412yes—
677C4×D4C2×D412yes—
678C4×D4C2×D412yes—
679C4×D4C2×D412yes—
680C4×D4C2×D412yes—
681C4×D4C2×D412yes—
682C4×D4C2×D412yes—
683C4×D4C2×D412yes—
684#117—24no—
685#117—22no—
686#117—22no—
687#117—22no—
688#117—22no—
689#117—22no—
690#117—22no—
691#117—24no—
692#117—24no—
693#117—24no—
694#117—24no—
695#117C22⋊C412yes—
696#117C22⋊C412yes—
697#117C22⋊C412yes—
698#117C22⋊C412yes—
699#117C22⋊C412yes—
700#117C22⋊C412yes—
701#117C22⋊C412yes—
702#117C22⋊C412yes—
703#117C22⋊C411yescharacteristic
704#117C22⋊C411yescharacteristic
705#117C22⋊C411yescharacteristic
706#117C22⋊C411yescharacteristic
707#117C22⋊C412yes—
708#117C22⋊C412yes—
709C2×C4⋊C4C22×C412yes—
710C2×C4⋊C4C22×C412yes—
711C2×C4⋊C4C22×C412yes—
712C2×C4⋊C4C22×C412yes—
713C2×C4⋊C4C22×C414yes—
714C2×C4⋊C4C22×C412yes—
715C2×C4⋊C4C22×C414yes—
716C2×C4⋊C4C22×C412yes—
717C2×C4⋊C4C22×C411yescharacteristic
718C2×C4⋊C4C22×C412yes—
719C2×C4⋊C4C22×C411yescharacteristic
720C2×C4⋊C4C22×C412yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C22⋊C4—24no—
724C2×C22⋊C4—24no—
725C2×C22⋊C4—24no—
726C2×C22⋊C4—24no—
727C2×C22⋊C4—24no—
728C2×C22⋊C4—24no—
729C2×C22⋊C4—24no—
730C2×C22⋊C4—24no—
731C2×C22⋊C4—24no—
732C2×C22⋊C4—24no—
733C2×C22⋊C4—24no—
734C2×C22⋊C4—24no—
735C2×C22⋊C4C22×C414yes—
736C2×C22⋊C4C22×C412yes—
737C2×C22⋊C4C22×C412yes—
738C2×C22⋊C4C22×C412yes—
739C2×C22⋊C4C22×C414yes—
740C2×C22⋊C4C22×C414yes—
741C2×C22⋊C4C22×C414yes—
742C2×C22⋊C4C22×C414yes—
743C2×C22⋊C4C22×C414yes—
744C2×C22⋊C4C22×C414yes—
745C2×C22⋊C4C22×C414yes—
746C2×C22⋊C4C22×C412yes—
747C2×C22⋊C4C22×C412yes—
748C2×C22⋊C4C22×C414yes—
749C2×C22⋊C4C22×C412yes—
750C2×C22⋊C4C22×C412yes—
751C2×C22⋊C4C22×C412yes—
752C2×C42C22×C414yes—
753C2×C42C22×C412yes—
754C2×C42C22×C412yes—
755C2×C42C22×C411yescharacteristic
756C2×C42C22×C411yescharacteristic
757C2×C42C22×C412yes—
758C2×C42C2×D412yes—
759C2×C42C2×D412yes—
760C2×C42C2×D412yes—
761C2×C42C2×D412yes—
762C2×C42C2×D412yes—
763C2×C42C2×D412yes—
764C2×C42C2×D412yes—
765C2×C42C2×D412yes—
766C2×C42C2×D411yescharacteristic
767C2×C42C2×D411yescharacteristic
768C2×C42C2×D411yescharacteristic
769C2×C42C2×D411yescharacteristic
770C2×C42C2×D411yescharacteristic
771C2×C42C2×D411yescharacteristic
772C2×C42C2×D411yescharacteristic
773C2×C42C2×D411yescharacteristic
774C2×C42C2412yes—
775C2×C42C2411yescharacteristic
776C2×C42C2411yescharacteristic
777C4⋊C8—21no—
778C4⋊C8—22no—
779C4⋊C8—21no—
780C4⋊C8—22no—
781C4⋊C8—24no—
782C4⋊C8—22no—
783C4⋊C8—24no—
784C4⋊C8—22no—
785C4⋊C8—21no—
786C4⋊C8—21no—
787C4⋊C8—24no—
788C4⋊C8—22no—
789C4⋊C8—24no—
790C4⋊C8—22no—
791#101—24no—
792#101—28no—
793#101—44no—
794#101—44no—
795#101—42no—
796#101—44no—
797#101—44no—
798#100—24no—
799#100—28no—
800#100—44no—
801#100—44no—
802#100—44no—
803#100—42no—
804#100—44no—
805C22⋊C8—24no—
806C22⋊C8—22no—
807C22⋊C8—24no—
808C22⋊C8—22no—
809C22⋊C8—24no—
810C22⋊C8—22no—
811C22⋊C8—24no—
812C22⋊C8—22no—
813#97—21no—
814#97—22no—
815#97—21no—
816#97—24no—
817#97—22no—
818#97—24no—
819#97—22no—
820C4×C8—21no—
821C4×C8—22no—
822C4×C8—21no—
823C4×C8—24no—
824C4×C8—22no—
825C4×C8—24no—
826C4×C8—22no—
827C24—24no—
828C24—24no—
829C24—48no—
830C24—48no—
831C24—84no—
832C24C23×C412yes—
833C24C23×C412yes—
834C24C23×C414yes—
835C24C23×C411yescharacteristic
836#41—24no—
837#41—24no—
838#41—44no—
839#41—44no—
840#41—42no—
841#41—42no—
842#41—84no—
843#41—84no—
844#41—82no—
845#41—82no—
846#41—82no—
847#41—82no—
848C2×Q8—24no—
849C2×Q8—24no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—22no—
853C2×Q8—22no—
854C2×Q8—22no—
855C2×Q8—24no—
856C2×Q8—22no—
857C2×Q8—24no—
858C2×Q8—48no—
859C2×Q8—42no—
860C2×Q8—84no—
861C2×Q8—84no—
862C2×Q8—82no—
863C2×Q8—82no—
864C2×Q8—82no—
865C2×Q8—82no—
866C2×Q8C2×C22⋊C411yescharacteristic
867C2×Q8C2×C22⋊C411yescharacteristic
868C2×Q8C2×C22⋊C412yes—
869C2×D4—24no—
870C2×D4—24no—
871C2×D4—24no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—24no—
881C2×D4—24no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—24no—
888C2×D4—22no—
889C2×D4—24no—
890C2×D4—44no—
891C2×D4—48no—
892C2×D4—48no—
893C2×D4—44no—
894C2×D4—416no—
895C2×D4—48no—
896C2×D4—48no—
897C2×D4—48no—
898C2×D4—84no—
899C2×D4—84no—
900C2×D4—82no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4C2×C22⋊C412yes—
907C2×D4C2×C22⋊C411yescharacteristic
908C2×D4C2×C22⋊C412yes—
909C2×D4C2×C22⋊C412yes—
910C2×D4C2×C22⋊C412yes—
911C2×D4C2×C22⋊C412yes—
912C2×D4C2×C22⋊C411yescharacteristic
913C22×C4—24no—
914C22×C4—22no—
915C22×C4—24no—
916C22×C4—22no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—42no—
926C22×C4—44no—
927C22×C4—48no—
928C22×C4—48no—
929C22×C4—44no—
930C22×C4—82no—
931C22×C4—81no—
932C22×C4—84no—
933C22×C4C2×C22⋊C412yes—
934C22×C4C2×C22⋊C412yes—
935C22×C4C2×C22⋊C411yescharacteristic
936C22×C4C2×C22⋊C411yescharacteristic
937C22×C4C2×C22⋊C412yes—
938C22×C4C2×C22⋊C412yes—
939C22×C4C2×C22⋊C412yes—
940C22×C4C2×C22⋊C412yes—
941C22×C4C2×C22⋊C412yes—
942C22×C4C2×C22⋊C412yes—
943C22×C4C2×C22⋊C411yescharacteristic
944C22×C4C2×C22⋊C411yescharacteristic
945C22×C4C2×C22⋊C411yescharacteristic
946C22×C4C2×C22⋊C411yescharacteristic
947C22×C4C2×C22⋊C411yescharacteristic
948C22×C4C2×C22⋊C411yescharacteristic
949C22×C4C23×C412yes—
950C22×C4C23×C414yes—
951C22×C4C23×C411yescharacteristic
952C22×C4C23×C411yescharacteristic
953C22×C4C23×C412yes—
954C22×C4C23×C412yes—
955C22×C4C23×C412yes—
956C22×C4C23×C411yescharacteristic
957C22×C4C23×C412yes—
958C22×C4C23×C411yescharacteristic
959C22×C4C23×C412yes—
960C22×C4C23×C411yescharacteristic
961C22×C4C22×D412yes—
962C22×C4C22×D412yes—
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D412yes—
966C22×C4C22×D412yes—
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C2511yescharacteristic
970M16—22no—
971M16—22no—
972M16—24no—
973M16—24no—
974M16—22no—
975M16—24no—
976M16—22no—
977M16—22no—
978M16—22no—
979M16—24no—
980M16—22no—
981M16—48no—
982M16—44no—
983M16—84no—
984M16—82no—
985M16H(5,𝔽2)14yes—
986C2×C8—22no—
987C2×C8—22no—
988C2×C8—24no—
989C2×C8—22no—
990C2×C8—22no—
991C2×C8—24no—
992C2×C8—48no—
993C2×C8—44no—
994C2×C8—84no—
995C2×C8—82no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
1003C4⋊C4—22no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4C2×C22⋊C412yes—
1017C4⋊C4C2×C22⋊C411yescharacteristic
1018C4⋊C4C2×C22⋊C411yescharacteristic
1019C4⋊C4C2×C22⋊C412yes—
1020C4⋊C4C2×C22⋊C412yes—
1021C4⋊C4C2×C22⋊C412yes—
1022C4⋊C4C2×C22⋊C412yes—
1023C4⋊C4C2×C22⋊C412yes—
1024C4⋊C4C2×C22⋊C411yescharacteristic
1025C4⋊C4C2×C22⋊C411yescharacteristic
1026C4⋊C4C2×C22⋊C412yes—
1027C4⋊C4C2×C22⋊C412yes—
1028C4⋊C4C2×C22⋊C412yes—
1029C4⋊C4C2×C22⋊C412yes—
1030C22⋊C4—24no—
1031C22⋊C4—24no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—24no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—24no—
1046C22⋊C4—24no—
1047C22⋊C4—24no—
1048C22⋊C4—24no—
1049C22⋊C4—24no—
1050C22⋊C4—24no—
1051C22⋊C4—24no—
1052C22⋊C4—24no—
1053C22⋊C4—24no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—24no—
1057C22⋊C4—24no—
1058C22⋊C4C2×C22⋊C412yes—
1059C22⋊C4C2×C22⋊C412yes—
1060C22⋊C4C2×C22⋊C412yes—
1061C22⋊C4C2×C22⋊C412yes—
1062C22⋊C4C2×C22⋊C412yes—
1063C22⋊C4C2×C22⋊C412yes—
1064C22⋊C4C2×C22⋊C412yes—
1065C22⋊C4C2×C22⋊C412yes—
1066C22⋊C4C2×C22⋊C412yes—
1067C22⋊C4C2×C22⋊C412yes—
1068C22⋊C4C2×C22⋊C412yes—
1069C22⋊C4C2×C22⋊C412yes—
1070C42—24no—
1071C42—24no—
1072C42—22no—
1073C42—22no—
1074C42C2×C22⋊C412yes—
1075C42C2×C22⋊C412yes—
1076C42C2×C22⋊C412yes—
1077C42C2×C22⋊C412yes—
1078C42C2×C22⋊C411yescharacteristic
1079C42C2×C22⋊C411yescharacteristic
1080C42C2×C22⋊C411yescharacteristic
1081C42C2×C22⋊C411yescharacteristic
1082C42C2×C22⋊C411yescharacteristic
1083C42C2×C22⋊C411yescharacteristic
1084C42C2×C22⋊C411yescharacteristic
1085C42C2×C22⋊C411yescharacteristic
1086C42C2×C22⋊C412yes—
1087C42C2×C22⋊C412yes—
1088C42C2×C22⋊C412yes—
1089C42C2×C22⋊C412yes—
1090C42C22×D411yescharacteristic
1091C42C22×D412yes—
1092C42C22×D412yes—
1093C42C22×D411yescharacteristic
1094C42C22×D411yescharacteristic
1095C42C22×D411yescharacteristic
1096C42C22×D412yes—
1097C42C22×D412yes—
1098C42C22×D411yescharacteristic
1099C42C22×D411yescharacteristic
1100C42C22×D411yescharacteristic
1101C42C22×D411yescharacteristic
1102C23—24no—
1103C23—24no—
1104C23—22no—
1105C23—22no—
1106C23—24no—
1107C23—28no—
1108C23—24no—
1109C23—42no—
1110C23—41no—
1111C23—41no—
1112C23—48no—
1113C23—42no—
1114C23—44no—
1115C23—44no—
1116C23—42no—
1117C23—48no—
1118C23—84no—
1119C23—84no—
1120C23—84no—
1121C23—84no—
1122C23—1616no—
1123C23C22×C22⋊C412yes—
1124C23C22×C22⋊C411yescharacteristic
1125C23C22×C22⋊C411yescharacteristic
1126C23C22×C22⋊C412yes—
1127C23C24×C411yescharacteristic
1128Q8—22no—
1129Q8—22no—
1130Q8—42no—
1131Q8—42no—
1132Q8—44no—
1133Q8—41no—
1134Q8—42no—
1135Q8—41no—
1136Q8—42no—
1137Q8—84no—
1138Q8—84no—
1139D4—24no—
1140D4—24no—
1141D4—24no—
1142D4—22no—
1143D4—42no—
1144D4—42no—
1145D4—44no—
1146D4—48no—
1147D4—48no—
1148D4—44no—
1149D4—42no—
1150D4—44no—
1151D4—41no—
1152D4—42no—
1153D4—41no—
1154D4—42no—
1155D4—84no—
1156D4—84no—
1157D4—82no—
1158D4—82no—
1159D4—84no—
1160D4—84no—
1161D4—82no—
1162D4—82no—
1163D4#41314yescomplemented
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—28no—
1188C2×C4—24no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—44no—
1207C2×C4—44no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4C22×C22⋊C412yes—
1217C2×C4C22×C22⋊C412yes—
1218C2×C4C22×C22⋊C411yescharacteristic
1219C2×C4C22×C22⋊C411yescharacteristic
1220C2×C4C22×C22⋊C411yescharacteristic
1221C2×C4C22×C22⋊C411yescharacteristic
1222C2×C4C22×C22⋊C411yescharacteristic
1223C2×C4C22×C22⋊C411yescharacteristic
1224C2×C4C22×C22⋊C411yescharacteristic
1225C2×C4C22×C22⋊C412yes—
1226C2×C4C22×C22⋊C412yes—
1227C2×C4C22×C22⋊C412yes—
1228C2×C4C22×C22⋊C412yes—
1229C2×C4C22×C22⋊C411yescharacteristic
1230C2×C4C22×C22⋊C411yescharacteristic
1231C2×C4C22×C22⋊C411yescharacteristic
1232C2×C4C23×D411yescharacteristic
1233C2×C4C23×D411yescharacteristic
1234C2×C4C2×H(5,𝔽2)12yes—
1235C2×C4#58512yes—
1236C8—24no—
1237C8—44no—
1238C8—42no—
1239C8—42no—
1240C8—44no—
1241C8—42no—
1242C22—21no—
1243C22—21no—
1244C22—22no—
1245C22—22no—
1246C22—21no—
1247C22—21no—
1248C22—22no—
1249C22—21no—
1250C22—21no—
1251C22—22no—
1252C22—22no—
1253C22—21no—
1254C22—21no—
1255C22—48no—
1256C22—42no—
1257C22—44no—
1258C22—44no—
1259C22—42no—
1260C22—44no—
1261C22—42no—
1262C22—82no—
1263C22—88no—
1264C22—84no—
1265C22—168no—
1266C22—168no—
1267C22C2×#41314yes—
1268C22C23×C22⋊C411yescharacteristic
1269C22C4×H(5,𝔽2)12yes—
1270C4—21no—
1271C4—21no—
1272C4—21no—
1273C4—22no—
1274C4—22no—
1275C4—21no—
1276C4—21no—
1277C4—22no—
1278C4—22no—
1279C4—21no—
1280C4—21no—
1281C4—21no—
1282C4—21no—
1283C4—22no—
1284C4—22no—
1285C4—42no—
1286C4—42no—
1287C4—44no—
1288C4—42no—
1289C4C2×#41312yes—
1290C4#348812yes—
1291C4#349811yescharacteristic
1292C4#350011yescharacteristic
1293C2—22no—
1294C2—24no—
1295C2—42no—
1296C2—41no—
1297C2—41no—
1298C2—84no—
1299C2—82no—
1300C2#3425811yescharacteristic
1301C2C22×#41311yescharacteristic
1302C2#6007611yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3514C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60263C2semidirect
3. M16×#41C2semidirect
4. #22539C2semidirect
5. #22537C2semidirect
6. #22410C2semidirect
7. D4×#101C2semidirect
8. #22408C2semidirect
9. D4×#100C2semidirect
10. #21880C2semidirect
11. #21880C2semidirect
12. #21800C2semidirect
13. #21798C2semidirect
14. #21426C2semidirect
15. #21426C2semidirect
16. #21218C2semidirect
17. C2×#1967C2semidirect
59. Q8×M16C22semidirect
60. Q8×M16C22semidirect
63. D4×M16C22semidirect
64. D4×M16C22semidirect
65. #2920C22semidirect
66. #2920C22semidirect
67. #2920C22semidirect
68. #2920C22semidirect
69. C2×#423C22semidirect
70. C2×#423C22semidirect
71. C2×#413C22semidirect
72. C22×#101C22semidirect
74. C2×C4×M16C22semidirect
75. C2×C4×M16C22semidirect
76. #1998C22semidirect
77. #1998C22semidirect
78. #1998C22semidirect
84. #1967C22semidirect
85. #1967C22semidirect
86. #1967C22semidirect
87. #1967C22semidirect
88. #1967C22semidirect
89. #1967C22semidirect
90. #1966C22semidirect
91. #1966C22semidirect
94. #1901C22semidirect
95. #1901C22semidirect
96. #1901C22semidirect
97. #1901C22semidirect
102. #1801C22semidirect
103. #1801C22semidirect
105. #1800C22semidirect
106. #1785C22semidirect
107. #1784C22semidirect
109. C4×#101C22semidirect
110. C4×#101C22semidirect
112. C4×#100C22semidirect
1163. D4#413semidirect

Maximal subgroups

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

subgroupindex
C2×#35142
#602632
M16×#412
#225392
#225372
#224102
D4×#1012
#224082
D4×#1002
#218802
#218002
#217982
#214262
#212182
C2×#19672