Finite Group Databasebeta

← #6343031

Subgroups — #6343031

Order 512.

3061 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3460C211yesmaximal, characteristic
2#60283C211yesmaximal, characteristic, complemented
3M16×#41C211yesmaximal, characteristic, complemented
4#17505C218yesmaximal, complemented
5#17502C212yesmaximal, complemented
6#17500C212yesmaximal, complemented
7#17497C212yesmaximal, complemented
8#17495C212yesmaximal, complemented
9#17483C214yesmaximal, complemented
10#17468C214yesmaximal, complemented
11#17452C211yesmaximal, characteristic, complemented
12#17448C211yesmaximal, characteristic, complemented
13#17447C211yesmaximal, characteristic, complemented
14C2×#1490C211yesmaximal, characteristic, complemented
15#3460—22no—
16#3460—21no—
17#3460—22no—
18#3460—21no—
19#3460—21no—
20#3460—21no—
21#3460C412yes—
22#3460C412yes—
23#3460C414yes—
24#3460C2212yes—
25#3460C2212yes—
26#3460C2214yes—
27C2×#544C411yescharacteristic
28C2×#542—21no—
29C2×#542C412yes—
30C2×#540—21no—
31C2×#540C412yes—
32C2×#538—22no—
33C2×#537C411yescharacteristic
34C2×#535C411yescharacteristic
35C2×#535C411yescharacteristic
36C2×#532—21no—
37C2×#532C2212yes—
38C2×#529—21no—
39C2×#529C2212yes—
40C2×#525—22no—
41C2×C4×#41C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C22×C4×D4C2211yescharacteristic
44#2989C2212yescomplemented
45#2989C2214yescomplemented
46#2988C2212yescomplemented
47#2984—21no—
48#2974—22no—
49#2974—21no—
50#2971—21no—
51#2971—21no—
52#2970—22no—
53#2970—21no—
54#2970—22no—
55#2970—21no—
56#2965C2212yescomplemented
57#2965C2214yescomplemented
58C8×#41C2212yescomplemented
59Q8×M16—21no—
60D4×M16—22no—
61D4×M16—21no—
62#2920C2211yescharacteristic
63#2920C2211yescharacteristic
64#2920C2212yescomplemented
65#2920C2212yescomplemented
66C2×#432C2211yescharacteristic
67C2×#432C2212yescomplemented
68C2×C4×M16C2211yescharacteristic
69C2×C4×M16C2212yescomplemented
70#1496C2218yescomplemented
71#1495C2218yescomplemented
72#1494C2218yescomplemented
73#1492C2218yescomplemented
74#1491C2211yescharacteristic, complemented
75#1491C2211yescharacteristic, complemented
76#1491C2212yescomplemented
77#1490C2212yes—
78#1490C2212yes—
79#1490C2212yes—
80#1490C2212yes—
81#1490C2214yescomplemented
82#1490C2211yescharacteristic, complemented
83#1490C2211yescharacteristic, complemented
84#1490C2212yescomplemented
85#1489C2214yescomplemented
86#1488C2214yescomplemented
87#1486C2214yescomplemented
88#1484C2218yescomplemented
89#1483C2218yescomplemented
90#1482C2218yescomplemented
91#1480C2218yescomplemented
92#1478C2214yescomplemented
93#1477C2214yescomplemented
94#1476C2214yescomplemented
95C2×D4⋊C8C2214yescomplemented
96C22×#41—22no—
97C22×#41C2×C411yescharacteristic
98C22×#41C2×C411yescharacteristic
99C23×D4C2×C411yescharacteristic
100C24×C4—21no—
101C22×M16—21no—
102C22×M16—22no—
103#544—22no—
104#544—21no—
105#544—21no—
106#544C2×C412yes—
107#544C2×C412yes—
108#544C2×C414yes—
109#542—22no—
110#542—22no—
111#542—24no—
112#542—22no—
113#542—22no—
114#542—24no—
115#542—22no—
116#542—22no—
117#542—22no—
118#542—22no—
119#542C2×C414yes—
120#542C2×C414yes—
121#542C2×C414yes—
122#542C2×C414yes—
123#540—22no—
124#540—22no—
125#540—24no—
126#540—22no—
127#540—24no—
128#540—22no—
129#540—22no—
130#540—22no—
131#540—22no—
132#540—22no—
133#540C2×C414yes—
134#540C2×C414yes—
135#540C2×C414yes—
136#540C2×C414yes—
137#538—24no—
138#538—24no—
139#538—24no—
140#538—24no—
141#538—24no—
142#538—24no—
143#538—24no—
144#538—24no—
145#537—22no—
146#537—21no—
147#537—21no—
148#537C2×C412yes—
149#537C2×C412yes—
150#537C2×C414yes—
151#535—22no—
152#535—21no—
153#535—21no—
154#535—21no—
155#535—22no—
156#535—21no—
157#535C2×C412yes—
158#535C2×C412yes—
159#535C2×C414yes—
160#535C2×C412yes—
161#535C2×C412yes—
162#535C2×C414yes—
163#532—22no—
164#532—22no—
165#532—24no—
166#532—22no—
167#532—24no—
168#532—22no—
169#532—22no—
170#532—22no—
171#532—22no—
172#532—22no—
173#532C2×C414yes—
174#532C2×C414yes—
175#532C2314yes—
176#532C2314yes—
177C2×C4⋊Q8—21no—
178C2×C4⋊Q8C2×C412yes—
179C2×#127—21no—
180C2×#127C2×C412yes—
181#529—22no—
182#529—22no—
183#529—24no—
184#529—22no—
185#529—22no—
186#529—24no—
187#529—22no—
188#529—22no—
189#529—22no—
190#529—22no—
191#529C2×C414yes—
192#529C2×C414yes—
193#529C2314yes—
194#529C2314yes—
195C2×#126—22no—
196C2×#126—22no—
197C2×#125—21no—
198C2×#125C2×C412yes—
199C2×#124—21no—
200C2×#124—22no—
201C2×#124—22no—
202C2×#124C2×C412yes—
203#525—24no—
204#525—24no—
205#525—24no—
206#525—24no—
207#525—24no—
208#525—24no—
209#525—24no—
210#525—24no—
211C2×#123—22no—
212C2×#123—22no—
213C2×#123—22no—
214C2×#123—22no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—22no—
217C2×C22⋊Q8—22no—
218C2×C22⋊Q8C2×C412yes—
219C2×#121—22no—
220C2×#121—21no—
221C2×#121—22no—
222C2×#121—21no—
223C2×#121—21no—
224C2×#121—22no—
225C2×#121—22no—
226C2×#121C2×C412yes—
227C2×#121C2×C412yes—
228C2×#121C2×C412yes—
229C2×#120—22no—
230C2×#120—22no—
231C4×#41—21no—
232C4×#41—21no—
233C4×#41—21no—
234C4×#41—21no—
235C4×#41C2×C412yes—
236C4×#41C2×C412yes—
237C4×#41C2×C411yescharacteristic
238C4×#41C2×C411yescharacteristic
239C4×#41C2×C412yes—
240C4×#41D412yes—
241C4×#41D412yes—
242C4×#41D411yescharacteristic
243C4×#41D411yescharacteristic
244C4×#41D411yescharacteristic
245C4×#41D411yescharacteristic
246C4×#41C2312yes—
247C4×#41C2312yes—
248C4×#41C2311yescharacteristic
249C4×#41C2311yescharacteristic
250C4×#41C2312yes—
251C2×C4×Q8C2×C411yescharacteristic
252C2×C4×Q8D411yescharacteristic
253C2×C4×Q8D411yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4—22no—
258C2×C4×D4—21no—
259C2×C4×D4—21no—
260C2×C4×D4—21no—
261C2×C4×D4—21no—
262C2×C4×D4—21no—
263C2×C4×D4—21no—
264C2×C4×D4—22no—
265C2×C4×D4C2×C412yes—
266C2×C4×D4C2×C412yes—
267C2×C4×D4C2×C412yes—
268C2×C4×D4C2×C411yescharacteristic
269C2×C4×D4D412yes—
270C2×C4×D4D411yescharacteristic
271C2×C4×D4D412yes—
272C2×C4×D4D411yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2311yescharacteristic
277C2×#117—21no—
278C2×#117—22no—
279C2×#117C2×C411yescharacteristic
280C2×#117C2×C411yescharacteristic
281C2×#117C2×C412yes—
282C22×C4⋊C4C2×C411yescharacteristic
283C22×C22⋊C4—21no—
284C22×C42—21no—
285C22×C42C2311yescharacteristic
286C22×C42C2312yes—
287#446—22no—
288#446—24no—
289#446—22no—
290#446—24no—
291C8×Q8—22no—
292C8×Q8—22no—
293#436—22no—
294#436—24no—
295#436—22no—
296#436—24no—
297#435—24no—
298#435—24no—
299#435—24no—
300#435—24no—
301#435—24no—
302#435—24no—
303C8×D4—22no—
304C8×D4—24no—
305C8×D4—22no—
306C8×D4—24no—
307#432—21no—
308#432—21no—
309#432—22no—
310#432—22no—
311#432—21no—
312#432—21no—
313#432—21no—
314#432—22no—
315#432—22no—
316#432—22no—
317#432C2312yes—
318#432C2312yes—
319#432C2311yescharacteristic
320#432C2311yescharacteristic
321#432C2314yescomplemented
322#431—21no—
323#431—22no—
324#431C2312yes—
325#431C2312yes—
326#431C2312yes—
327#431C2314yescomplemented
328#431C2314yescomplemented
329#431C2314yescomplemented
330#423—21no—
331#423—22no—
332#423C2312yes—
333#423C2314yescomplemented
334C2×C4⋊C8C2312yes—
335C2×C4⋊C8C2314yescomplemented
336#407—21no—
337#407—21no—
338#407—22no—
339#407—22no—
340C2×C22⋊C8—21no—
341C2×C22⋊C8—22no—
342C4×M16—21no—
343C4×M16—21no—
344C4×M16—22no—
345C4×M16—22no—
346C4×M16—21no—
347C4×M16—22no—
348C4×M16C2311yescharacteristic
349C4×M16C2311yescharacteristic
350C4×M16C2312yes—
351C4×M16C2312yes—
352C4×M16C2314yescomplemented
353C2×#97—21no—
354C2×#97—22no—
355C2×#97—21no—
356C2×#97—22no—
357C2×C4×C8C2312yes—
358C2×C4×C8C2314yescomplemented
359Q8⋊C8C2314yescomplemented
360Q8⋊C8C2314yescomplemented
361Q8⋊C8C2318yescomplemented
362D4⋊C8C2318yes—
363D4⋊C8C2318yes—
364D4⋊C8C2318yes—
365D4⋊C8C2318yes—
366D4⋊C8C2314yescomplemented
367D4⋊C8C2314yescomplemented
368D4⋊C8C2318yescomplemented
369C25—21no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—24no—
373C2×#41—24no—
374C2×#41—24no—
375C2×#41—24no—
376C2×#41—44no—
377C2×#41—44no—
378C2×#41—88no—
379C2×#41C22⋊C412yes—
380C2×#41C22⋊C411yescharacteristic
381C2×#41C22⋊C411yescharacteristic
382C2×#41C22×C412yes—
383C2×#41C22×C412yes—
384C2×#41C22×C411yescharacteristic
385C2×#41C22×C411yescharacteristic
386C2×#41C22×C412yes—
387C22×Q8—22no—
388C22×Q8C22⋊C411yescharacteristic
389C22×Q8C22×C411yescharacteristic
390C22×D4—21no—
391C22×D4—22no—
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—22no—
398C22×D4—22no—
399C22×D4—44no—
400C22×D4C22⋊C412yes—
401C22×D4C22⋊C411yescharacteristic
402C22×D4C22×C412yes—
403C22×D4C22×C412yes—
404C22×D4C22×C411yescharacteristic
405C22×D4C22×C412yes—
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—22no—
409C23×C4—21no—
410C23×C4—21no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—84no—
417C23×C4C22×C411yescharacteristic
418C23×C4C22×C412yes—
419C23×C4C2×D411yescharacteristic
420C23×C4C2×D411yescharacteristic
421C23×C4C2×D412yes—
422C23×C4C2×D412yes—
423C2×M16—21no—
424C2×M16—21no—
425C2×M16—22no—
426C2×M16—22no—
427C2×M16—24no—
428C2×M16—22no—
429C2×M16—24no—
430C2×M16—44no—
431C2×M16—48no—
432C22×C8—22no—
433C22×C8—24no—
434C22×C8—22no—
435C22×C8—24no—
436C4⋊Q8—24no—
437C4⋊Q8—22no—
438C4⋊Q8—22no—
439C4⋊Q8—22no—
440C4⋊Q8—22no—
441C4⋊Q8C22×C414yes—
442C4⋊Q8C22×C414yes—
443#127—22no—
444#127—22no—
445#127—24no—
446#127—22no—
447#127—22no—
448#127C22×C414yes—
449#127C22×C414yes—
450#126—24no—
451#126—24no—
452#126—24no—
453#126—24no—
454#126—24no—
455#126—24no—
456#126—24no—
457#126—24no—
458#125—24no—
459#125—22no—
460#125—22no—
461#125—22no—
462#125—22no—
463#125C22×C414yes—
464#125C22×C414yes—
465#124—22no—
466#124—22no—
467#124—24no—
468#124—24no—
469#124—24no—
470#124—24no—
471#124—24no—
472#124—24no—
473#124—24no—
474#124—22no—
475#124—22no—
476#124—24no—
477#124—24no—
478#124C22×C414yes—
479#124C22×C414yes—
480#123—24no—
481#123—24no—
482#123—24no—
483#123—24no—
484#123—24no—
485#123—24no—
486#123—24no—
487#123—24no—
488#123—24no—
489#123—24no—
490#123—24no—
491#123—24no—
492#123—24no—
493#123—24no—
494#123—24no—
495#123—24no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8—24no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—24no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8C22×C414yes—
510C22⋊Q8C22×C414yes—
511#121—24no—
512#121—24no—
513#121—24no—
514#121—24no—
515#121—22no—
516#121—22no—
517#121—24no—
518#121—24no—
519#121—24no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—22no—
526#121—24no—
527#121—24no—
528#121—24no—
529#121—22no—
530#121—22no—
531#121—24no—
532#121—22no—
533#121—22no—
534#121—24no—
535#121—24no—
536#121—24no—
537#121—24no—
538#121—24no—
539#121—24no—
540#121—24no—
541#121—24no—
542#121C22×C414yes—
543#121C22×C414yes—
544#121C22×C414yes—
545#121C22×C414yes—
546#121C22×C414yes—
547#121C22×C414yes—
548#120—24no—
549#120—24no—
550#120—24no—
551#120—24no—
552#120—24no—
553#120—24no—
554#120—24no—
555#120—24no—
556C4×Q8—21no—
557C4×Q8—21no—
558C4×Q8—21no—
559C4×Q8—21no—
560C4×Q8C22⋊C411yescharacteristic
561C4×Q8C22⋊C411yescharacteristic
562C4×Q8C22⋊C412yes—
563C4×Q8C22⋊C411yescharacteristic
564C4×Q8C22⋊C411yescharacteristic
565C4×Q8C22⋊C412yes—
566C4×Q8C22×C412yes—
567C4×Q8C22×C412yes—
568C4×Q8C22×C412yes—
569C4×Q8C2×D411yescharacteristic
570C4×Q8C2×D411yescharacteristic
571C4×Q8C2×D412yes—
572C4×Q8C2×D411yescharacteristic
573C4×Q8C2×D411yescharacteristic
574C4×Q8C2×D412yes—
575C4×Q8C2412yes—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—24no—
605C4×D4—24no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4C22⋊C412yes—
609C4×D4C22⋊C412yes—
610C4×D4C22⋊C412yes—
611C4×D4C22⋊C412yes—
612C4×D4C22⋊C411yescharacteristic
613C4×D4C22⋊C411yescharacteristic
614C4×D4C22⋊C412yes—
615C4×D4C22⋊C412yes—
616C4×D4C22⋊C412yes—
617C4×D4C22⋊C412yes—
618C4×D4C22⋊C412yes—
619C4×D4C22⋊C411yescharacteristic
620C4×D4C22⋊C411yescharacteristic
621C4×D4C22⋊C412yes—
622C4×D4C22×C414yes—
623C4×D4C22×C414yes—
624C4×D4C22×C414yes—
625C4×D4C22×C412yes—
626C4×D4C22×C412yes—
627C4×D4C22×C412yes—
628C4×D4C2×D412yes—
629C4×D4C2×D412yes—
630C4×D4C2×D412yes—
631C4×D4C2×D412yes—
632C4×D4C2×D411yescharacteristic
633C4×D4C2×D412yes—
634C4×D4C2×D411yescharacteristic
635C4×D4C2×D412yes—
636C4×D4C2×D412yes—
637C4×D4C2×D412yes—
638C4×D4C2×D412yes—
639C4×D4C2×D411yescharacteristic
640C4×D4C2×D412yes—
641C4×D4C2×D411yescharacteristic
642C4×D4C2414yes—
643C4×D4C2412yes—
644#117—21no—
645#117—21no—
646#117—22no—
647#117—22no—
648#117—24no—
649#117—24no—
650#117—22no—
651#117—22no—
652#117—24no—
653#117—24no—
654#117C22⋊C411yescharacteristic
655#117C22⋊C412yes—
656#117C22⋊C411yescharacteristic
657#117C22⋊C412yes—
658#117C22⋊C412yes—
659#117C22⋊C412yes—
660#117C22⋊C412yes—
661#117C22×C412yes—
662#117C22×C412yes—
663#117C22×C412yes—
664#117C22×C411yescharacteristic
665#117C22×C411yescharacteristic
666#117C22×C412yes—
667#117C22×C412yes—
668#117C22×C412yes—
669#117C22×C412yes—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4C22⋊C411yescharacteristic
680C2×C4⋊C4C22⋊C411yescharacteristic
681C2×C4⋊C4C22⋊C412yes—
682C2×C4⋊C4C22⋊C412yes—
683C2×C4⋊C4C22×C412yes—
684C2×C4⋊C4C22×C412yes—
685C2×C4⋊C4C22×C412yes—
686C2×C4⋊C4C22×C411yescharacteristic
687C2×C4⋊C4C22×C411yescharacteristic
688C2×C22⋊C4—21no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4C22⋊C412yes—
704C2×C22⋊C4C22⋊C412yes—
705C2×C22⋊C4C22⋊C412yes—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42C22×C411yescharacteristic
714C2×C42C22×C412yes—
715C2×C42C22×C411yescharacteristic
716C2×C42C22×C411yescharacteristic
717C2×C42C22×C412yes—
718C2×C42C22×C412yes—
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D412yes—
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2×D412yes—
727C2×C42C2×D412yes—
728C2×C42C2×D412yes—
729C2×C42C2×D412yes—
730C2×C42C2×D412yes—
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2412yes—
735C2×C42C2412yes—
736C4⋊C8—22no—
737C4⋊C8—24no—
738C4⋊C8—22no—
739C4⋊C8—22no—
740C4⋊C8—24no—
741C4⋊C8—24no—
742C4⋊C8—22no—
743C4⋊C8—24no—
744C4⋊C8C2414yes—
745C4⋊C8C2412yes—
746C4⋊C8C2412yes—
747C22⋊C8—22no—
748C22⋊C8—21no—
749C22⋊C8—22no—
750C22⋊C8—24no—
751C22⋊C8—21no—
752C22⋊C8—22no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—24no—
756C22⋊C8—24no—
757C22⋊C8—24no—
758#97—21no—
759#97—22no—
760#97—21no—
761#97—21no—
762#97—22no—
763#97—22no—
764#97—24no—
765#97—22no—
766#97—24no—
767#97—21no—
768C4×C8—22no—
769C4×C8—24no—
770C4×C8—22no—
771C4×C8—24no—
772C4×C8C2412yes—
773C4×C8C2412yes—
774C4×C8C2414yes—
775C24—22no—
776C24—21no—
777C24—22no—
778C24—22no—
779C24—44no—
780C24—82no—
781C24—82no—
782C24C2×C22⋊C411yescharacteristic
783C24C2×C22⋊C412yes—
784#41—24no—
785#41—24no—
786#41—28no—
787#41—44no—
788#41—44no—
789#41—42no—
790#41—42no—
791#41—44no—
792#41—44no—
793#41—44no—
794#41—88no—
795#41—88no—
796#41—88no—
797#41—88no—
798C2×Q8—21no—
799C2×Q8—24no—
800C2×Q8—24no—
801C2×Q8—42no—
802C2×Q8—42no—
803C2×Q8—84no—
804C2×Q8C2×C22⋊C411yescharacteristic
805C2×Q8C2×C22⋊C411yescharacteristic
806C2×Q8C2×C22⋊C412yes—
807C2×Q8C23×C412yes—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—21no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—28no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—84no—
835C2×D4—84no—
836C2×D4—84no—
837C2×D4—84no—
838C2×D4—84no—
839C2×D4C2×C22⋊C412yes—
840C2×D4C2×C22⋊C412yes—
841C2×D4C2×C22⋊C411yescharacteristic
842C2×D4C2×C22⋊C411yescharacteristic
843C2×D4C2×C22⋊C412yes—
844C2×D4C2×C22⋊C412yes—
845C2×D4C2×C22⋊C412yes—
846C2×D4C23×C414yes—
847C2×D4C23×C412yes—
848C22×C4—24no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—24no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—42no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—42no—
869C22×C4—44no—
870C22×C4—48no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—82no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—82no—
880C22×C4C2×C22⋊C411yescharacteristic
881C22×C4C2×C22⋊C411yescharacteristic
882C22×C4C2×C22⋊C412yes—
883C22×C4C2×C22⋊C411yescharacteristic
884C22×C4C2×C22⋊C411yescharacteristic
885C22×C4C2×C22⋊C411yescharacteristic
886C22×C4C2×C22⋊C411yescharacteristic
887C22×C4C2×C22⋊C411yescharacteristic
888C22×C4C2×C22⋊C412yes—
889C22×C4C2×C22⋊C411yescharacteristic
890C22×C4C2×C22⋊C411yescharacteristic
891C22×C4C2×C22⋊C412yes—
892C22×C4C2×C22⋊C412yes—
893C22×C4C2×C22⋊C412yes—
894C22×C4C2×C22⋊C412yes—
895C22×C4C2×C22⋊C412yes—
896C22×C4C2×C22⋊C412yes—
897C22×C4C2×C22⋊C412yes—
898C22×C4C23×C411yescharacteristic
899C22×C4C23×C411yescharacteristic
900C22×C4C23×C412yes—
901C22×C4C23×C412yes—
902C22×C4C23×C411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D412yes—
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D412yes—
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D412yes—
912C22×C4C22×D412yes—
913M16—24no—
914M16—44no—
915M16—48no—
916M16—42no—
917M16—44no—
918M16—82no—
919M16—84no—
920C2×C8—22no—
921C2×C8—22no—
922C2×C8—24no—
923C2×C8—22no—
924C2×C8—22no—
925C2×C8—24no—
926C2×C8—44no—
927C2×C8—48no—
928C2×C8—82no—
929C2×C8—84no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—22no—
947C4⋊C4C2×C22⋊C412yes—
948C4⋊C4C2×C22⋊C411yescharacteristic
949C4⋊C4C2×C22⋊C411yescharacteristic
950C4⋊C4C2×C22⋊C412yes—
951C4⋊C4C2×C22⋊C411yescharacteristic
952C4⋊C4C2×C22⋊C411yescharacteristic
953C4⋊C4C2×C22⋊C412yes—
954C4⋊C4C2×C22⋊C412yes—
955C4⋊C4C2×C22⋊C412yes—
956C4⋊C4C2×C22⋊C412yes—
957C4⋊C4C2×C22⋊C412yes—
958C4⋊C4C2×C22⋊C412yes—
959C4⋊C4C2×C22⋊C412yes—
960C4⋊C4C2×C22⋊C412yes—
961C4⋊C4C23×C414yes—
962C4⋊C4C23×C412yes—
963C4⋊C4C23×C412yes—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—24no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—24no—
975C22⋊C4—24no—
976C22⋊C4—24no—
977C22⋊C4—24no—
978C22⋊C4—24no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—22no—
986C22⋊C4C2×C22⋊C412yes—
987C22⋊C4C2×C22⋊C412yes—
988C22⋊C4C2×C22⋊C412yes—
989C22⋊C4C2×C22⋊C412yes—
990C22⋊C4C2×C22⋊C412yes—
991C22⋊C4C2×C22⋊C412yes—
992C22⋊C4C2×C22⋊C412yes—
993C22⋊C4C2×C22⋊C412yes—
994C22⋊C4C2×C22⋊C412yes—
995C22⋊C4C2×C22⋊C412yes—
996C22⋊C4C2×C22⋊C412yes—
997C22⋊C4C2×C22⋊C412yes—
998C42—22no—
999C42—22no—
1000C42—22no—
1001C42—22no—
1002C42—22no—
1003C42—22no—
1004C42C2×C22⋊C411yescharacteristic
1005C42C2×C22⋊C411yescharacteristic
1006C42C2×C22⋊C412yes—
1007C42C2×C22⋊C412yes—
1008C42C2×C22⋊C411yescharacteristic
1009C42C2×C22⋊C411yescharacteristic
1010C42C2×C22⋊C411yescharacteristic
1011C42C2×C22⋊C411yescharacteristic
1012C42C2×C22⋊C412yes—
1013C42C2×C22⋊C412yes—
1014C42C2×C22⋊C412yes—
1015C42C2×C22⋊C412yes—
1016C42C23×C411yescharacteristic
1017C42C23×C411yescharacteristic
1018C42C23×C411yescharacteristic
1019C42C23×C412yes—
1020C42C23×C412yes—
1021C42C22×D411yescharacteristic
1022C42C22×D412yes—
1023C42C22×D411yescharacteristic
1024C42C22×D411yescharacteristic
1025C42C22×D412yes—
1026C42C22×D411yescharacteristic
1027C42C22×D412yes—
1028C42C22×D411yescharacteristic
1029C42C22×D411yescharacteristic
1030C42C22×D412yes—
1031C42C2511yescharacteristic
1032C23—22no—
1033C23—22no—
1034C23—24no—
1035C23—24no—
1036C23—22no—
1037C23—41no—
1038C23—42no—
1039C23—42no—
1040C23—44no—
1041C23—42no—
1042C23—42no—
1043C23—44no—
1044C23—44no—
1045C23—44no—
1046C23—42no—
1047C23—44no—
1048C23—82no—
1049C23—82no—
1050C23—82no—
1051C23—82no—
1052C23—816no—
1053C23C22×C22⋊C411yescharacteristic
1054C23C22×C22⋊C412yes—
1055C23C22×C22⋊C412yes—
1056C23C22×C22⋊C411yescharacteristic
1057C23C22×C22⋊C411yescharacteristic
1058Q8—22no—
1059Q8—22no—
1060Q8—24no—
1061Q8—42no—
1062Q8—42no—
1063Q8—84no—
1064Q8—84no—
1065D4—24no—
1066D4—24no—
1067D4—22no—
1068D4—22no—
1069D4—28no—
1070D4—24no—
1071D4—42no—
1072D4—42no—
1073D4—42no—
1074D4—44no—
1075D4—44no—
1076D4—42no—
1077D4—44no—
1078D4—44no—
1079D4—44no—
1080D4—84no—
1081D4—84no—
1082D4—84no—
1083D4—84no—
1084D4—84no—
1085D4—84no—
1086D4—84no—
1087D4—84no—
1088D4—84no—
1089D4—84no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—41no—
1110C2×C4—42no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—48no—
1127C2×C4—44no—
1128C2×C4—44no—
1129C2×C4—44no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—48no—
1134C2×C4—44no—
1135C2×C4—44no—
1136C2×C4—82no—
1137C2×C4—82no—
1138C2×C4—84no—
1139C2×C4—84no—
1140C2×C4—82no—
1141C2×C4—82no—
1142C2×C4C22×C22⋊C411yescharacteristic
1143C2×C4C22×C22⋊C411yescharacteristic
1144C2×C4C22×C22⋊C411yescharacteristic
1145C2×C4C22×C22⋊C411yescharacteristic
1146C2×C4C22×C22⋊C411yescharacteristic
1147C2×C4C22×C22⋊C411yescharacteristic
1148C2×C4C22×C22⋊C412yes—
1149C2×C4C22×C22⋊C412yes—
1150C2×C4C22×C22⋊C411yescharacteristic
1151C2×C4C22×C22⋊C411yescharacteristic
1152C2×C4C22×C22⋊C412yes—
1153C2×C4C22×C22⋊C412yes—
1154C2×C4C22×C22⋊C412yes—
1155C2×C4C22×C22⋊C412yes—
1156C2×C4C22×C22⋊C411yescharacteristic
1157C2×C4#56814yes—
1158C2×C4C24×C411yescharacteristic
1159C2×C4C23×D411yescharacteristic
1160C2×C4C23×D411yescharacteristic
1161C8—24no—
1162C8—42no—
1163C8—44no—
1164C8—42no—
1165C8—44no—
1166C8—42no—
1167C22—21no—
1168C22—21no—
1169C22—21no—
1170C22—21no—
1171C22—21no—
1172C22—22no—
1173C22—22no—
1174C22—21no—
1175C22—22no—
1176C22—22no—
1177C22—22no—
1178C22—22no—
1179C22—21no—
1180C22—44no—
1181C22—42no—
1182C22—44no—
1183C22—44no—
1184C22—42no—
1185C22—42no—
1186C22—44no—
1187C22—84no—
1188C22—84no—
1189C22—88no—
1190C22—88no—
1191C22—88no—
1192C22#287912yes—
1193C22#290112yes—
1194C22C23×C22⋊C411yescharacteristic
1195C4—21no—
1196C4—21no—
1197C4—22no—
1198C4—22no—
1199C4—21no—
1200C4—21no—
1201C4—21no—
1202C4—22no—
1203C4—22no—
1204C4—21no—
1205C4—21no—
1206C4—21no—
1207C4—21no—
1208C4—22no—
1209C4—22no—
1210C4—42no—
1211C4—44no—
1212C4—42no—
1213C4—42no—
1214C4#287912yes—
1215C4C2×#56812yes—
1216C4#358512yes—
1217C2—22no—
1218C2—22no—
1219C2—41no—
1220C2—42no—
1221C2—42no—
1222C2—82no—
1223C2—84no—
1224C2C2×#287911yescharacteristic
1225C2#6008711yescharacteristic
1226C2C2×#290111yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radicalC2×#3460C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60283C2semidirect
3. M16×#41C2semidirect
4. #17505C2semidirect
5. #17502C2semidirect
6. #17500C2semidirect
7. #17497C2semidirect
8. #17495C2semidirect
9. #17483C2semidirect
10. #17468C2semidirect
11. #17452C2semidirect
12. #17448C2semidirect
13. #17447C2semidirect
14. C2×#1490C2semidirect
44. #2989C22semidirect
45. #2989C22semidirect
46. #2988C22semidirect
56. #2965C22semidirect
57. #2965C22semidirect
58. C8×#41C22semidirect
64. #2920C22semidirect
65. #2920C22semidirect
67. C2×#432C22semidirect
69. C2×C4×M16C22semidirect
70. #1496C22semidirect
71. #1495C22semidirect
72. #1494C22semidirect
73. #1492C22semidirect
74. #1491C22semidirect
75. #1491C22semidirect
76. #1491C22semidirect
81. #1490C22semidirect
82. #1490C22semidirect
83. #1490C22semidirect
84. #1490C22semidirect
85. #1489C22semidirect
86. #1488C22semidirect
87. #1486C22semidirect
88. #1484C22semidirect
89. #1483C22semidirect
90. #1482C22semidirect
91. #1480C22semidirect
92. #1478C22semidirect
93. #1477C22semidirect
94. #1476C22semidirect
95. C2×D4⋊C8C22semidirect
321. #432C23semidirect
327. #431C23semidirect
328. #431C23semidirect
329. #431C23semidirect
333. #423C23semidirect
335. C2×C4⋊C8C23semidirect
352. C4×M16C23semidirect
358. C2×C4×C8C23semidirect
359. Q8⋊C8C23semidirect
360. Q8⋊C8C23semidirect
361. Q8⋊C8C23semidirect
366. D4⋊C8C23semidirect
367. D4⋊C8C23semidirect
368. D4⋊C8C23semidirect

Maximal subgroups

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

subgroupindex
C2×#34602
#602832
M16×#412
#175052
#175022
#175002
#174972
#174952
#174832
#174682
#174522
#174482
#174472
C2×#14902