Finite Group Databasebeta

← #6343028

Subgroups — #6343028

Order 512.

3050 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3460C211yesmaximal, characteristic
2#60278C211yesmaximal, characteristic, complemented
3#60263C211yesmaximal, characteristic, complemented
4#17505C218yesmaximal, complemented
5#17492C212yesmaximal, complemented
6#17490C212yesmaximal, complemented
7#17487C212yesmaximal, complemented
8#17485C212yesmaximal, complemented
9#17483C214yesmaximal, complemented
10#17468C214yesmaximal, complemented
11#17451C211yesmaximal, characteristic, complemented
12#17448C211yesmaximal, characteristic, complemented
13#17443C211yesmaximal, characteristic, complemented
14C2×#1486C211yesmaximal, 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#2991—21no—
45#2991—21no—
46#2990—22no—
47#2990—21no—
48#2990—22no—
49#2990—21no—
50#2989C2212yescomplemented
51#2989C2214yescomplemented
52#2988C2212yescomplemented
53#2984—21no—
54#2974—22no—
55#2974—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×#431C2211yescharacteristic
67C2×#431C2212yescomplemented
68C2×#423C2211yescharacteristic
69C2×#423C2212yescomplemented
70#1496C2218yescomplemented
71#1495C2218yescomplemented
72#1494C2218yescomplemented
73#1492C2218yescomplemented
74#1490C2214yescomplemented
75#1489C2214yescomplemented
76#1488C2214yescomplemented
77#1487C2211yescharacteristic, complemented
78#1487C2211yescharacteristic, complemented
79#1487C2212yescomplemented
80#1486C2212yes—
81#1486C2212yes—
82#1486C2212yes—
83#1486C2212yes—
84#1486C2214yescomplemented
85#1486C2211yescharacteristic, complemented
86#1486C2211yescharacteristic, complemented
87#1486C2212yescomplemented
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—21no—
310#432—22no—
311#432—22no—
312#432—22no—
313#432C2312yes—
314#432C2314yescomplemented
315#431—21no—
316#431—21no—
317#431—22no—
318#431—22no—
319#431—21no—
320#431—22no—
321#431C2312yes—
322#431C2311yescharacteristic
323#431C2311yescharacteristic
324#431C2312yes—
325#431C2312yes—
326#431C2312yes—
327#431C2314yescomplemented
328#431C2314yescomplemented
329#431C2314yescomplemented
330#423—21no—
331#423—21no—
332#423—22no—
333#423—22no—
334#423—21no—
335#423—22no—
336#423C2312yes—
337#423C2312yes—
338#423C2311yescharacteristic
339#423C2311yescharacteristic
340#423C2314yescomplemented
341C2×C4⋊C8—21no—
342C2×C4⋊C8—22no—
343C2×C4⋊C8—21no—
344C2×C4⋊C8—22no—
345C2×C4⋊C8C2312yes—
346C2×C4⋊C8C2314yescomplemented
347#407—21no—
348#407—21no—
349#407—22no—
350#407—22no—
351C2×C22⋊C8—21no—
352C2×C22⋊C8—22no—
353C4×M16—21no—
354C4×M16—22no—
355C4×M16C2312yes—
356C4×M16C2314yescomplemented
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—84no—
379C2×#41—84no—
380C2×#41C22⋊C412yes—
381C2×#41C22⋊C411yescharacteristic
382C2×#41C22⋊C411yescharacteristic
383C2×#41C22×C412yes—
384C2×#41C22×C412yes—
385C2×#41C22×C411yescharacteristic
386C2×#41C22×C411yescharacteristic
387C2×#41C22×C412yes—
388C22×Q8—22no—
389C22×Q8C22⋊C411yescharacteristic
390C22×Q8C22×C411yescharacteristic
391C22×D4—21no—
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—22no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—44no—
401C22×D4C22⋊C412yes—
402C22×D4C22⋊C411yescharacteristic
403C22×D4C22×C412yes—
404C22×D4C22×C412yes—
405C22×D4C22×C411yescharacteristic
406C22×D4C22×C412yes—
407C23×C4—21no—
408C23×C4—21no—
409C23×C4—22no—
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—82no—
418C23×C4—82no—
419C23×C4C22×C411yescharacteristic
420C23×C4C22×C412yes—
421C23×C4C2×D411yescharacteristic
422C23×C4C2×D412yes—
423C23×C4C2×D411yescharacteristic
424C23×C4C2×D412yes—
425C2×M16—22no—
426C2×M16—21no—
427C2×M16—21no—
428C2×M16—22no—
429C2×M16—24no—
430C2×M16—22no—
431C2×M16—24no—
432C2×M16—82no—
433C2×M16—84no—
434C22×C8—22no—
435C22×C8—24no—
436C22×C8—22no—
437C22×C8—24no—
438C4⋊Q8—24no—
439C4⋊Q8—22no—
440C4⋊Q8—22no—
441C4⋊Q8—22no—
442C4⋊Q8—22no—
443C4⋊Q8C22×C414yes—
444C4⋊Q8C22×C414yes—
445#127—22no—
446#127—22no—
447#127—24no—
448#127—22no—
449#127—22no—
450#127C22×C414yes—
451#127C22×C414yes—
452#126—24no—
453#126—24no—
454#126—24no—
455#126—24no—
456#126—24no—
457#126—24no—
458#126—24no—
459#126—24no—
460#125—24no—
461#125—22no—
462#125—22no—
463#125—22no—
464#125—22no—
465#125C22×C414yes—
466#125C22×C414yes—
467#124—22no—
468#124—22no—
469#124—24no—
470#124—24no—
471#124—24no—
472#124—24no—
473#124—24no—
474#124—24no—
475#124—24no—
476#124—22no—
477#124—22no—
478#124—24no—
479#124—24no—
480#124C22×C414yes—
481#124C22×C414yes—
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—
496#123—24no—
497#123—24no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—24no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—24no—
510C22⋊Q8—24no—
511C22⋊Q8C22×C414yes—
512C22⋊Q8C22×C414yes—
513#121—24no—
514#121—24no—
515#121—24no—
516#121—24no—
517#121—22no—
518#121—22no—
519#121—24no—
520#121—24no—
521#121—24no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—22no—
526#121—22no—
527#121—22no—
528#121—24no—
529#121—24no—
530#121—24no—
531#121—22no—
532#121—22no—
533#121—24no—
534#121—22no—
535#121—22no—
536#121—24no—
537#121—24no—
538#121—24no—
539#121—24no—
540#121—24no—
541#121—24no—
542#121—24no—
543#121—24no—
544#121C22×C414yes—
545#121C22×C414yes—
546#121C22×C414yes—
547#121C22×C414yes—
548#121C22×C414yes—
549#121C22×C414yes—
550#120—24no—
551#120—24no—
552#120—24no—
553#120—24no—
554#120—24no—
555#120—24no—
556#120—24no—
557#120—24no—
558C4×Q8—21no—
559C4×Q8—21no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8C22⋊C411yescharacteristic
563C4×Q8C22⋊C411yescharacteristic
564C4×Q8C22⋊C412yes—
565C4×Q8C22⋊C411yescharacteristic
566C4×Q8C22⋊C411yescharacteristic
567C4×Q8C22⋊C412yes—
568C4×Q8C22×C412yes—
569C4×Q8C22×C412yes—
570C4×Q8C22×C412yes—
571C4×Q8C2×D411yescharacteristic
572C4×Q8C2×D411yescharacteristic
573C4×Q8C2×D412yes—
574C4×Q8C2×D411yescharacteristic
575C4×Q8C2×D411yescharacteristic
576C4×Q8C2×D412yes—
577C4×Q8C2412yes—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—24no—
607C4×D4—24no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4C22⋊C412yes—
611C4×D4C22⋊C412yes—
612C4×D4C22⋊C412yes—
613C4×D4C22⋊C412yes—
614C4×D4C22⋊C411yescharacteristic
615C4×D4C22⋊C411yescharacteristic
616C4×D4C22⋊C412yes—
617C4×D4C22⋊C412yes—
618C4×D4C22⋊C412yes—
619C4×D4C22⋊C412yes—
620C4×D4C22⋊C412yes—
621C4×D4C22⋊C411yescharacteristic
622C4×D4C22⋊C411yescharacteristic
623C4×D4C22⋊C412yes—
624C4×D4C22×C414yes—
625C4×D4C22×C414yes—
626C4×D4C22×C414yes—
627C4×D4C22×C412yes—
628C4×D4C22×C412yes—
629C4×D4C22×C412yes—
630C4×D4C2×D412yes—
631C4×D4C2×D412yes—
632C4×D4C2×D412yes—
633C4×D4C2×D412yes—
634C4×D4C2×D411yescharacteristic
635C4×D4C2×D412yes—
636C4×D4C2×D411yescharacteristic
637C4×D4C2×D412yes—
638C4×D4C2×D412yes—
639C4×D4C2×D412yes—
640C4×D4C2×D412yes—
641C4×D4C2×D411yescharacteristic
642C4×D4C2×D412yes—
643C4×D4C2×D411yescharacteristic
644C4×D4C2414yes—
645C4×D4C2412yes—
646#117—21no—
647#117—21no—
648#117—22no—
649#117—22no—
650#117—24no—
651#117—24no—
652#117—22no—
653#117—22no—
654#117—24no—
655#117—24no—
656#117C22⋊C411yescharacteristic
657#117C22⋊C412yes—
658#117C22⋊C411yescharacteristic
659#117C22⋊C412yes—
660#117C22⋊C412yes—
661#117C22⋊C412yes—
662#117C22⋊C412yes—
663#117C22×C412yes—
664#117C22×C412yes—
665#117C22×C412yes—
666#117C22×C411yescharacteristic
667#117C22×C411yescharacteristic
668#117C22×C412yes—
669#117C22×C412yes—
670#117C22×C412yes—
671#117C22×C412yes—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4C22⋊C411yescharacteristic
682C2×C4⋊C4C22⋊C411yescharacteristic
683C2×C4⋊C4C22⋊C412yes—
684C2×C4⋊C4C22⋊C412yes—
685C2×C4⋊C4C22×C412yes—
686C2×C4⋊C4C22×C412yes—
687C2×C4⋊C4C22×C412yes—
688C2×C4⋊C4C22×C411yescharacteristic
689C2×C4⋊C4C22×C411yescharacteristic
690C2×C22⋊C4—21no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—21no—
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—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4C22⋊C412yes—
706C2×C22⋊C4C22⋊C412yes—
707C2×C22⋊C4C22⋊C412yes—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—22no—
714C2×C42—22no—
715C2×C42C22×C411yescharacteristic
716C2×C42C22×C412yes—
717C2×C42C22×C411yescharacteristic
718C2×C42C22×C411yescharacteristic
719C2×C42C22×C412yes—
720C2×C42C22×C412yes—
721C2×C42C2×D412yes—
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2×D411yescharacteristic
727C2×C42C2×D411yescharacteristic
728C2×C42C2×D412yes—
729C2×C42C2×D412yes—
730C2×C42C2×D412yes—
731C2×C42C2×D412yes—
732C2×C42C2×D412yes—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2412yes—
737C2×C42C2412yes—
738C4⋊C8—21no—
739C4⋊C8—22no—
740C4⋊C8—21no—
741C4⋊C8—21no—
742C4⋊C8—22no—
743C4⋊C8—22no—
744C4⋊C8—24no—
745C4⋊C8—22no—
746C4⋊C8—24no—
747C4⋊C8—22no—
748C4⋊C8—24no—
749C4⋊C8—22no—
750C4⋊C8—24no—
751C4⋊C8—21no—
752C4⋊C8C2414yes—
753C4⋊C8C2412yes—
754C4⋊C8C2412yes—
755C22⋊C8—21no—
756C22⋊C8—21no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—24no—
760C22⋊C8—22no—
761C22⋊C8—24no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—24no—
765C22⋊C8—24no—
766#97—22no—
767#97—24no—
768#97—22no—
769#97—24no—
770C4×C8—22no—
771C4×C8—24no—
772C4×C8—22no—
773C4×C8—24no—
774C4×C8C2412yes—
775C4×C8C2412yes—
776C4×C8C2414yes—
777C24—22no—
778C24—21no—
779C24—22no—
780C24—22no—
781C24—44no—
782C24—82no—
783C24—82no—
784C24C2×C22⋊C411yescharacteristic
785C24C2×C22⋊C412yes—
786#41—24no—
787#41—24no—
788#41—28no—
789#41—44no—
790#41—44no—
791#41—42no—
792#41—42no—
793#41—44no—
794#41—44no—
795#41—44no—
796#41—88no—
797#41—88no—
798#41—84no—
799#41—84no—
800#41—84no—
801#41—84no—
802C2×Q8—21no—
803C2×Q8—24no—
804C2×Q8—24no—
805C2×Q8—42no—
806C2×Q8—42no—
807C2×Q8—84no—
808C2×Q8C2×C22⋊C411yescharacteristic
809C2×Q8C2×C22⋊C411yescharacteristic
810C2×Q8C2×C22⋊C412yes—
811C2×Q8C23×C412yes—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—21no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—28no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—84no—
839C2×D4—84no—
840C2×D4—84no—
841C2×D4—84no—
842C2×D4—84no—
843C2×D4C2×C22⋊C412yes—
844C2×D4C2×C22⋊C412yes—
845C2×D4C2×C22⋊C411yescharacteristic
846C2×D4C2×C22⋊C411yescharacteristic
847C2×D4C2×C22⋊C412yes—
848C2×D4C2×C22⋊C412yes—
849C2×D4C2×C22⋊C412yes—
850C2×D4C23×C414yes—
851C2×D4C23×C412yes—
852C22×C4—24no—
853C22×C4—22no—
854C22×C4—24no—
855C22×C4—22no—
856C22×C4—24no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—24no—
867C22×C4—22no—
868C22×C4—24no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—42no—
877C22×C4—44no—
878C22×C4—42no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—82no—
882C22×C4—82no—
883C22×C4—82no—
884C22×C4—82no—
885C22×C4—84no—
886C22×C4—81no—
887C22×C4—82no—
888C22×C4—82no—
889C22×C4—82no—
890C22×C4C2×C22⋊C411yescharacteristic
891C22×C4C2×C22⋊C411yescharacteristic
892C22×C4C2×C22⋊C412yes—
893C22×C4C2×C22⋊C411yescharacteristic
894C22×C4C2×C22⋊C411yescharacteristic
895C22×C4C2×C22⋊C412yes—
896C22×C4C2×C22⋊C412yes—
897C22×C4C2×C22⋊C411yescharacteristic
898C22×C4C2×C22⋊C411yescharacteristic
899C22×C4C2×C22⋊C411yescharacteristic
900C22×C4C2×C22⋊C411yescharacteristic
901C22×C4C2×C22⋊C411yescharacteristic
902C22×C4C2×C22⋊C412yes—
903C22×C4C2×C22⋊C412yes—
904C22×C4C2×C22⋊C412yes—
905C22×C4C2×C22⋊C412yes—
906C22×C4C2×C22⋊C412yes—
907C22×C4C2×C22⋊C412yes—
908C22×C4C23×C411yescharacteristic
909C22×C4C23×C411yescharacteristic
910C22×C4C23×C412yes—
911C22×C4C23×C412yes—
912C22×C4C23×C411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D412yes—
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D412yes—
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D412yes—
921C22×C4C22×D412yes—
922C22×C4C22×D411yescharacteristic
923M16—44no—
924M16—42no—
925M16—42no—
926M16—82no—
927M16—84no—
928M16—82no—
929M16—84no—
930C2×C8—22no—
931C2×C8—22no—
932C2×C8—24no—
933C2×C8—22no—
934C2×C8—22no—
935C2×C8—24no—
936C2×C8—82no—
937C2×C8—84no—
938C2×C8—82no—
939C2×C8—84no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—22no—
957C4⋊C4C2×C22⋊C412yes—
958C4⋊C4C2×C22⋊C411yescharacteristic
959C4⋊C4C2×C22⋊C411yescharacteristic
960C4⋊C4C2×C22⋊C412yes—
961C4⋊C4C2×C22⋊C411yescharacteristic
962C4⋊C4C2×C22⋊C411yescharacteristic
963C4⋊C4C2×C22⋊C412yes—
964C4⋊C4C2×C22⋊C412yes—
965C4⋊C4C2×C22⋊C412yes—
966C4⋊C4C2×C22⋊C412yes—
967C4⋊C4C2×C22⋊C412yes—
968C4⋊C4C2×C22⋊C412yes—
969C4⋊C4C2×C22⋊C412yes—
970C4⋊C4C2×C22⋊C412yes—
971C4⋊C4C23×C414yes—
972C4⋊C4C23×C412yes—
973C4⋊C4C23×C412yes—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—24no—
977C22⋊C4—24no—
978C22⋊C4—24no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—22no—
996C22⋊C4C2×C22⋊C412yes—
997C22⋊C4C2×C22⋊C412yes—
998C22⋊C4C2×C22⋊C412yes—
999C22⋊C4C2×C22⋊C412yes—
1000C22⋊C4C2×C22⋊C412yes—
1001C22⋊C4C2×C22⋊C412yes—
1002C22⋊C4C2×C22⋊C412yes—
1003C22⋊C4C2×C22⋊C412yes—
1004C22⋊C4C2×C22⋊C412yes—
1005C22⋊C4C2×C22⋊C412yes—
1006C22⋊C4C2×C22⋊C412yes—
1007C22⋊C4C2×C22⋊C412yes—
1008C42—22no—
1009C42—22no—
1010C42—22no—
1011C42—22no—
1012C42—22no—
1013C42—22no—
1014C42C2×C22⋊C411yescharacteristic
1015C42C2×C22⋊C411yescharacteristic
1016C42C2×C22⋊C411yescharacteristic
1017C42C2×C22⋊C411yescharacteristic
1018C42C2×C22⋊C412yes—
1019C42C2×C22⋊C412yes—
1020C42C2×C22⋊C411yescharacteristic
1021C42C2×C22⋊C411yescharacteristic
1022C42C2×C22⋊C412yes—
1023C42C2×C22⋊C412yes—
1024C42C2×C22⋊C412yes—
1025C42C2×C22⋊C412yes—
1026C42C23×C411yescharacteristic
1027C42C23×C411yescharacteristic
1028C42C23×C411yescharacteristic
1029C42C23×C412yes—
1030C42C23×C412yes—
1031C42C22×D411yescharacteristic
1032C42C22×D412yes—
1033C42C22×D411yescharacteristic
1034C42C22×D412yes—
1035C42C22×D411yescharacteristic
1036C42C22×D411yescharacteristic
1037C42C22×D412yes—
1038C42C22×D411yescharacteristic
1039C42C22×D412yes—
1040C42C22×D411yescharacteristic
1041C42C2511yescharacteristic
1042C23—22no—
1043C23—22no—
1044C23—24no—
1045C23—24no—
1046C23—22no—
1047C23—41no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—44no—
1053C23—44no—
1054C23—44no—
1055C23—44no—
1056C23—44no—
1057C23—42no—
1058C23—82no—
1059C23—82no—
1060C23—82no—
1061C23—82no—
1062C23—816no—
1063C23C22×C22⋊C411yescharacteristic
1064C23C22×C22⋊C412yes—
1065C23C22×C22⋊C412yes—
1066C23C22×C22⋊C411yescharacteristic
1067C23C22×C22⋊C411yescharacteristic
1068Q8—22no—
1069Q8—22no—
1070Q8—24no—
1071Q8—42no—
1072Q8—42no—
1073Q8—84no—
1074Q8—84no—
1075D4—24no—
1076D4—24no—
1077D4—22no—
1078D4—22no—
1079D4—28no—
1080D4—24no—
1081D4—42no—
1082D4—42no—
1083D4—42no—
1084D4—44no—
1085D4—44no—
1086D4—42no—
1087D4—44no—
1088D4—44no—
1089D4—44no—
1090D4—84no—
1091D4—84no—
1092D4—84no—
1093D4—84no—
1094D4—84no—
1095D4—84no—
1096D4—84no—
1097D4—84no—
1098D4—84no—
1099D4—84no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—41no—
1126C2×C4—42no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—44no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—44no—
1143C2×C4—42no—
1144C2×C4—44no—
1145C2×C4—48no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—42no—
1149C2×C4—44no—
1150C2×C4—42no—
1151C2×C4—82no—
1152C2×C4—82no—
1153C2×C4—84no—
1154C2×C4—84no—
1155C2×C4—82no—
1156C2×C4—82no—
1157C2×C4C22×C22⋊C411yescharacteristic
1158C2×C4C22×C22⋊C411yescharacteristic
1159C2×C4C22×C22⋊C411yescharacteristic
1160C2×C4C22×C22⋊C411yescharacteristic
1161C2×C4C22×C22⋊C411yescharacteristic
1162C2×C4C22×C22⋊C412yes—
1163C2×C4C22×C22⋊C412yes—
1164C2×C4C22×C22⋊C411yescharacteristic
1165C2×C4C22×C22⋊C411yescharacteristic
1166C2×C4C22×C22⋊C412yes—
1167C2×C4C22×C22⋊C412yes—
1168C2×C4C22×C22⋊C412yes—
1169C2×C4C22×C22⋊C412yes—
1170C2×C4C22×C22⋊C411yescharacteristic
1171C2×C4C22×C22⋊C411yescharacteristic
1172C2×C4#56814yes—
1173C2×C4#57612yes—
1174C2×C4#57712yes—
1175C2×C4C24×C411yescharacteristic
1176C2×C4C23×D411yescharacteristic
1177C2×C4C23×D411yescharacteristic
1178C8—42no—
1179C8—42no—
1180C8—44no—
1181C8—42no—
1182C8—44no—
1183C8—42no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—22no—
1190C22—22no—
1191C22—21no—
1192C22—22no—
1193C22—22no—
1194C22—22no—
1195C22—22no—
1196C22—21no—
1197C22—44no—
1198C22—42no—
1199C22—44no—
1200C22—44no—
1201C22—42no—
1202C22—42no—
1203C22—44no—
1204C22—84no—
1205C22—84no—
1206C22—88no—
1207C22—88no—
1208C22—88no—
1209C22#287912yes—
1210C22#289712yes—
1211C22C23×C22⋊C411yescharacteristic
1212C4—21no—
1213C4—21no—
1214C4—22no—
1215C4—22no—
1216C4—21no—
1217C4—21no—
1218C4—22no—
1219C4—22no—
1220C4—21no—
1221C4—21no—
1222C4—21no—
1223C4—21no—
1224C4—22no—
1225C4—22no—
1226C4—42no—
1227C4—44no—
1228C4—42no—
1229C4—42no—
1230C4#287912yes—
1231C4#289712yes—
1232C4C2×#56812yes—
1233C4C2×#57611yescharacteristic
1234C4C2×#57711yescharacteristic
1235C2—22no—
1236C2—22no—
1237C2—41no—
1238C2—42no—
1239C2—42no—
1240C2—82no—
1241C2—84no—
1242C2C2×#287911yescharacteristic
1243C2C2×#289711yescharacteristic
1244C2#6009311yescharacteristic
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. #60278C2semidirect
3. #60263C2semidirect
4. #17505C2semidirect
5. #17492C2semidirect
6. #17490C2semidirect
7. #17487C2semidirect
8. #17485C2semidirect
9. #17483C2semidirect
10. #17468C2semidirect
11. #17451C2semidirect
12. #17448C2semidirect
13. #17443C2semidirect
14. C2×#1486C2semidirect
50. #2989C22semidirect
51. #2989C22semidirect
52. #2988C22semidirect
56. #2965C22semidirect
57. #2965C22semidirect
58. C8×#41C22semidirect
64. #2920C22semidirect
65. #2920C22semidirect
67. C2×#431C22semidirect
69. C2×#423C22semidirect
70. #1496C22semidirect
71. #1495C22semidirect
72. #1494C22semidirect
73. #1492C22semidirect
74. #1490C22semidirect
75. #1489C22semidirect
76. #1488C22semidirect
77. #1487C22semidirect
78. #1487C22semidirect
79. #1487C22semidirect
84. #1486C22semidirect
85. #1486C22semidirect
86. #1486C22semidirect
87. #1486C22semidirect
88. #1484C22semidirect
89. #1483C22semidirect
90. #1482C22semidirect
91. #1480C22semidirect
92. #1478C22semidirect
93. #1477C22semidirect
94. #1476C22semidirect
95. C2×D4⋊C8C22semidirect
314. #432C23semidirect
327. #431C23semidirect
328. #431C23semidirect
329. #431C23semidirect
340. #423C23semidirect
346. C2×C4⋊C8C23semidirect
356. 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
#602782
#602632
#175052
#174922
#174902
#174872
#174852
#174832
#174682
#174512
#174482
#174432
C2×#14862