Finite Group Databasebeta

← #6343122

Subgroups — #6343122

Order 512.

3256 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3481C211yesmaximal, characteristic
2#60263C211yesmaximal, characteristic, complemented
3#60127C211yesmaximal, characteristic, complemented
4#17522C214yesmaximal, complemented
5#17521C218yesmaximal, complemented
6#17517C214yesmaximal, complemented
7#17492C212yesmaximal, complemented
8#17490C211yesmaximal, characteristic, complemented
9#17487C212yesmaximal, complemented
10#17485C211yesmaximal, characteristic, complemented
11#17451C211yesmaximal, characteristic, complemented
12#17448C212yesmaximal, complemented
13#17443C211yesmaximal, characteristic, complemented
14C2×#1486C212yesmaximal, complemented
15#3481—21no—
16#3481—22no—
17#3481—21no—
18#3481—21no—
19#3481—22no—
20#3481—21no—
21#3481C412yes—
22#3481C414yes—
23#3481C412yes—
24#3481C2212yes—
25#3481C2214yes—
26#3481C2212yes—
27C2×#559C411yescharacteristic
28C2×#554C411yescharacteristic
29C2×#554C411yescharacteristic
30C2×#553—21no—
31C2×#553C412yes—
32C2×#551—22no—
33C2×#546—21no—
34C2×#546C412yes—
35C2×D42C411yescharacteristic
36C2×#532C2211yescharacteristic
37C2×#529—21no—
38C2×#529C2212yes—
39C2×#525—22no—
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42C22×C4×D4—21no—
43C22×C4×D4C2212yes—
44#2991C2212yescomplemented
45#2990C2212yescomplemented
46#2990C2214yescomplemented
47#2989—22no—
48#2989—21no—
49#2988—21no—
50Q8×M16—21no—
51D4×M16—21no—
52D4×M16—22no—
53#2925—22no—
54#2925—21no—
55#2924—22no—
56#2924—21no—
57#2922C2214yescomplemented
58#2922C2212yescomplemented
59#2920C2211yescharacteristic, complemented
60#2920C2212yescomplemented
61#2920C2212yescomplemented
62#2920C2211yescharacteristic, complemented
63C2×#431C2212yescomplemented
64C2×#431C2211yescharacteristic, complemented
65#2906—21no—
66C2×#423C2212yescomplemented
67C2×#423C2211yescharacteristic, complemented
68#2880—21no—
69C4×#131C2212yescomplemented
70#1496C2214yescomplemented
71#1495C2218yescomplemented
72#1494C2218yescomplemented
73#1492C2214yescomplemented
74#1490C2218yescomplemented
75#1489C2214yescomplemented
76#1488C2214yescomplemented
77#1487C2211yescharacteristic, complemented
78#1487C2211yescharacteristic, complemented
79#1487C2212yescomplemented
80#1486C2211yescharacteristic
81#1486C2212yes—
82#1486C2211yescharacteristic
83#1486C2218yescomplemented
84#1486C2212yescomplemented
85#1486C2212yescomplemented
86#1486C2212yescomplemented
87#1486C2212yescomplemented
88#1484C2214yescomplemented
89#1483C2218yescomplemented
90#1482C2218yescomplemented
91#1480C2214yescomplemented
92#1478C2218yescomplemented
93#1477C2214yescomplemented
94#1476C2214yescomplemented
95C2×D4⋊C8C2218yescomplemented
96C22×#41—21no—
97C22×#41C2×C411yescharacteristic
98C22×#41D411yescharacteristic
99C23×D4—21no—
100C23×D4C2×C412yes—
101C24×C4—22no—
102C2×#131—22no—
103C22×M16—22no—
104C22×M16—21no—
105#559—21no—
106#559—21no—
107#559—22no—
108#559C2×C412yes—
109#559C2×C414yes—
110#559C2×C412yes—
111#554—21no—
112#554—21no—
113#554—22no—
114#554—21no—
115#554—22no—
116#554—21no—
117#554C2×C412yes—
118#554C2×C414yes—
119#554C2×C412yes—
120#554C2×C412yes—
121#554C2×C414yes—
122#554C2×C412yes—
123#553—22no—
124#553—22no—
125#553—22no—
126#553—22no—
127#553—22no—
128#553—22no—
129#553—24no—
130#553—22no—
131#553—22no—
132#553—24no—
133#553C2×C414yes—
134#553C2×C414yes—
135#553C2×C414yes—
136#553C2×C414yes—
137#551—24no—
138#551—24no—
139#551—24no—
140#551—24no—
141#551—24no—
142#551—24no—
143#551—24no—
144#551—24no—
145#546—22no—
146#546—24no—
147#546—22no—
148#546—22no—
149#546—24no—
150#546—22no—
151#546—22no—
152#546—22no—
153#546—22no—
154#546—22no—
155#546C2×C414yes—
156#546C2×C414yes—
157#546C2×C414yes—
158#546C2×C414yes—
159D42—22no—
160D42—21no—
161D42—21no—
162D42C2×C412yes—
163D42C2×C414yes—
164D42C2×C412yes—
165#532—21no—
166#532—21no—
167#532—21no—
168#532—21no—
169#532C2×C412yes—
170#532C2×C412yes—
171#532C2312yes—
172#532C2312yes—
173C2×C4⋊Q8C2×C411yescharacteristic
174C2×#127C2×C411yescharacteristic
175#529—22no—
176#529—22no—
177#529—24no—
178#529—22no—
179#529—22no—
180#529—24no—
181#529—22no—
182#529—22no—
183#529—22no—
184#529—22no—
185#529C2×C414yes—
186#529C2×C414yes—
187#529C2314yes—
188#529C2314yes—
189C2×#126—22no—
190C2×#126—22no—
191C2×#125—21no—
192C2×#125C2×C412yes—
193C2×#124—21no—
194C2×#124—21no—
195C2×#124C2×C412yes—
196#525—24no—
197#525—24no—
198#525—24no—
199#525—24no—
200#525—24no—
201#525—24no—
202#525—24no—
203#525—24no—
204C2×#123—22no—
205C2×#123—22no—
206C2×#123—22no—
207C2×#123—22no—
208C2×C22⋊Q8—21no—
209C2×C22⋊Q8—22no—
210C2×C22⋊Q8—22no—
211C2×C22⋊Q8C2×C412yes—
212C2×#121—22no—
213C2×#121—21no—
214C2×#121—21no—
215C2×#121—22no—
216C2×#121C2×C412yes—
217C2×#121C2×C412yes—
218C2×#120—22no—
219C2×#120—22no—
220C4×#41—21no—
221C4×#41—21no—
222C4×#41—21no—
223C4×#41—21no—
224C4×#41C2×C412yes—
225C4×#41C2×C412yes—
226C4×#41C2×C411yescharacteristic
227C4×#41C2×C412yes—
228C4×#41C2×C411yescharacteristic
229C4×#41D411yescharacteristic
230C4×#41D412yes—
231C4×#41D411yescharacteristic
232C4×#41D411yescharacteristic
233C4×#41D412yes—
234C4×#41D411yescharacteristic
235C4×#41C2312yes—
236C4×#41C2312yes—
237C4×#41C2311yescharacteristic
238C4×#41C2312yes—
239C4×#41C2311yescharacteristic
240C2×C4×Q8C2×C411yescharacteristic
241C2×C4×Q8C2×C411yescharacteristic
242C2×C4×Q8D411yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—22no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—24no—
249C2×C4×D4—22no—
250C2×C4×D4—22no—
251C2×C4×D4—22no—
252C2×C4×D4—24no—
253C2×C4×D4—22no—
254C2×C4×D4—21no—
255C2×C4×D4—22no—
256C2×C4×D4—21no—
257C2×C4×D4—22no—
258C2×C4×D4—22no—
259C2×C4×D4—22no—
260C2×C4×D4—22no—
261C2×C4×D4—22no—
262C2×C4×D4—22no—
263C2×C4×D4C2×C412yes—
264C2×C4×D4C2×C412yes—
265C2×C4×D4C2×C414yes—
266C2×C4×D4C2×C414yes—
267C2×C4×D4C2×C411yescharacteristic
268C2×C4×D4C2×C411yescharacteristic
269C2×C4×D4C2×C412yes—
270C2×C4×D4D411yescharacteristic
271C2×C4×D4D412yes—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×#117—21no—
277C2×#117—22no—
278C2×#117C2×C411yescharacteristic
279C2×#117D412yes—
280C2×#117D411yescharacteristic
281C22×C4⋊C4—21no—
282C22×C4⋊C4C2×C412yes—
283C22×C22⋊C4—22no—
284C22×C22⋊C4—22no—
285C22×C42—21no—
286C22×C42C2312yes—
287C22×C42C2311yescharacteristic
288#446—22no—
289#446—24no—
290C8×Q8—22no—
291#436—22no—
292#436—24no—
293#435—24no—
294#435—24no—
295#435—24no—
296C8×D4—22no—
297C8×D4—24no—
298#433—24no—
299#433—24no—
300#433—24no—
301#432—21no—
302#432—22no—
303#432—22no—
304#432—21no—
305#432—22no—
306#432—21no—
307#432C2312yescomplemented
308#432C2314yescomplemented
309#431—21no—
310#431—22no—
311#431—22no—
312#431—21no—
313#431—22no—
314#431—21no—
315#431C2311yescharacteristic
316#431C2312yes—
317#431C2311yescharacteristic
318#431C2312yescomplemented
319#431C2314yescomplemented
320#431C2312yescomplemented
321#431C2314yescomplemented
322#431C2312yescomplemented
323#431C2314yescomplemented
324#424—24no—
325#424—22no—
326#423—22no—
327#423—21no—
328#423—22no—
329#423—21no—
330#423—22no—
331#423—21no—
332#423C2311yescharacteristic
333#423C2312yes—
334#423C2311yescharacteristic
335#423C2314yescomplemented
336#423C2312yescomplemented
337C2×C4⋊C8—22no—
338C2×C4⋊C8—21no—
339C2×C4⋊C8—22no—
340C2×C4⋊C8—21no—
341C2×C4⋊C8C2314yescomplemented
342C2×C4⋊C8C2312yescomplemented
343#408—24no—
344#408—22no—
345#407—22no—
346#407—21no—
347#407—22no—
348#407—21no—
349C2×C22⋊C8—22no—
350C2×C22⋊C8—21no—
351#405—24no—
352#405—22no—
353C4×M16—22no—
354C4×M16—21no—
355C4×M16C2314yescomplemented
356C4×M16C2312yescomplemented
357C2×C4×C8C2314yescomplemented
358C2×C4×C8C2312yescomplemented
359Q8⋊C8C2314yescomplemented
360Q8⋊C8C2314yescomplemented
361Q8⋊C8C2318yescomplemented
362D4⋊C8C2314yes—
363D4⋊C8C2318yes—
364D4⋊C8C2314yes—
365D4⋊C8C2318yescomplemented
366D4⋊C8C2318yescomplemented
367D4⋊C8C2318yescomplemented
368D4⋊C8C2318yescomplemented
369C25—22no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—44no—
377C2×#41—44no—
378C2×#41—82no—
379C2×#41—82no—
380C2×#41C22⋊C411yescharacteristic
381C2×#41C22⋊C412yes—
382C2×#41C22⋊C411yescharacteristic
383C2×#41C22×C412yes—
384C2×#41C22×C412yes—
385C2×#41C2×D411yescharacteristic
386C2×#41C2×D412yes—
387C2×#41C2×D411yescharacteristic
388C22×Q8—21no—
389C22×Q8C22⋊C411yescharacteristic
390C22×Q8C22×C411yescharacteristic
391C22×D4—21no—
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—24no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—21no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—21no—
402C22×D4—48no—
403C22×D4—48no—
404C22×D4C22⋊C411yescharacteristic
405C22×D4C22⋊C412yes—
406C22×D4C22×C411yescharacteristic
407C22×D4C22×C414yes—
408C22×D4C22×C414yes—
409C22×D4C22×C412yes—
410C23×C4—22no—
411C23×C4—21no—
412C23×C4—21no—
413C23×C4—22no—
414C23×C4—21no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—24no—
418C23×C4—24no—
419C23×C4—24no—
420C23×C4—24no—
421C23×C4—84no—
422C23×C4—84no—
423C23×C4C22×C412yes—
424C23×C4C22×C411yescharacteristic
425C23×C4C2×D412yes—
426C23×C4C2×D411yescharacteristic
427C23×C4C2×D412yes—
428C23×C4C2×D411yescharacteristic
429#131—48no—
430C2×M16—21no—
431C2×M16—22no—
432C2×M16—24no—
433C2×M16—22no—
434C2×M16—21no—
435C2×M16—24no—
436C2×M16—22no—
437C2×M16—84no—
438C2×M16—82no—
439C22×C8—24no—
440C22×C8—22no—
441C22×C8—24no—
442C22×C8—22no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8C22×C412yes—
446C4⋊Q8C22×C412yes—
447#127—21no—
448#127—21no—
449#127C22×C412yes—
450#127C22×C412yes—
451#126—24no—
452#126—24no—
453#126—24no—
454#126—24no—
455#126—24no—
456#126—24no—
457#126—24no—
458#126—24no—
459#125—24no—
460#125—22no—
461#125—22no—
462#125—22no—
463#125—22no—
464#125C22×C414yes—
465#125C22×C414yes—
466#124—22no—
467#124—22no—
468#124—24no—
469#124—22no—
470#124—22no—
471#124—22no—
472#124—22no—
473#124—22no—
474#124—22no—
475#124C22×C414yes—
476#124C22×C414yes—
477#123—24no—
478#123—24no—
479#123—24no—
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—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—24no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—24no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8C22×C414yes—
507C22⋊Q8C22×C414yes—
508#121—24no—
509#121—24no—
510#121—24no—
511#121—24no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—24no—
521#121—22no—
522#121—22no—
523#121—24no—
524#121—24no—
525#121—24no—
526#121—24no—
527#121C22×C414yes—
528#121C22×C414yes—
529#121C22×C414yes—
530#121C22×C414yes—
531#120—24no—
532#120—24no—
533#120—24no—
534#120—24no—
535#120—24no—
536#120—24no—
537#120—24no—
538#120—24no—
539C4×Q8—21no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—21no—
543C4×Q8C22⋊C411yescharacteristic
544C4×Q8C22⋊C411yescharacteristic
545C4×Q8C22⋊C412yes—
546C4×Q8C22⋊C411yescharacteristic
547C4×Q8C22⋊C411yescharacteristic
548C4×Q8C22⋊C412yes—
549C4×Q8C22×C412yes—
550C4×Q8C22×C412yes—
551C4×Q8C22×C412yes—
552C4×Q8C22×C411yescharacteristic
553C4×Q8C22×C411yescharacteristic
554C4×Q8C22×C412yes—
555C4×Q8C2×D411yescharacteristic
556C4×Q8C2×D411yescharacteristic
557C4×Q8C2×D412yes—
558C4×Q8C2412yes—
559C4×D4—24no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—24no—
563C4×D4—24no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—24no—
569C4×D4—24no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—24no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4C22⋊C412yes—
604C4×D4C22⋊C411yescharacteristic
605C4×D4C22⋊C411yescharacteristic
606C4×D4C22⋊C412yes—
607C4×D4C22⋊C411yescharacteristic
608C4×D4C22⋊C411yescharacteristic
609C4×D4C22⋊C412yes—
610C4×D4C22⋊C412yes—
611C4×D4C22⋊C412yes—
612C4×D4C22⋊C412yes—
613C4×D4C22⋊C412yes—
614C4×D4C22⋊C412yes—
615C4×D4C22⋊C412yes—
616C4×D4C22⋊C412yes—
617C4×D4C22×C412yes—
618C4×D4C22×C414yes—
619C4×D4C22×C414yes—
620C4×D4C22×C414yes—
621C4×D4C22×C414yes—
622C4×D4C22×C414yes—
623C4×D4C22×C412yes—
624C4×D4C22×C412yes—
625C4×D4C22×C412yes—
626C4×D4C22×C411yescharacteristic
627C4×D4C22×C411yescharacteristic
628C4×D4C22×C412yes—
629C4×D4C22×C412yes—
630C4×D4C22×C412yes—
631C4×D4C22×C412yes—
632C4×D4C2×D411yescharacteristic
633C4×D4C2×D412yes—
634C4×D4C2×D411yescharacteristic
635C4×D4C2×D412yes—
636C4×D4C2×D412yes—
637C4×D4C2×D412yes—
638C4×D4C2×D412yes—
639C4×D4C2412yes—
640C4×D4C2414yes—
641#117—21no—
642#117—21no—
643#117—22no—
644#117—22no—
645#117—24no—
646#117—24no—
647#117—22no—
648#117—22no—
649#117—24no—
650#117—24no—
651#117C22⋊C412yes—
652#117C22⋊C412yes—
653#117C22⋊C412yes—
654#117C22⋊C412yes—
655#117C22⋊C411yescharacteristic
656#117C22⋊C411yescharacteristic
657#117C22⋊C412yes—
658#117C22×C412yes—
659#117C22×C412yes—
660#117C2×D412yes—
661#117C2×D412yes—
662#117C2×D412yes—
663#117C2×D412yes—
664#117C2×D411yescharacteristic
665#117C2×D411yescharacteristic
666#117C2×D412yes—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—24no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4C22⋊C411yescharacteristic
680C2×C4⋊C4C22⋊C411yescharacteristic
681C2×C4⋊C4C22⋊C412yes—
682C2×C4⋊C4C22⋊C412yes—
683C2×C4⋊C4C22×C411yescharacteristic
684C2×C4⋊C4C22×C412yes—
685C2×C4⋊C4C22×C414yes—
686C2×C4⋊C4C22×C414yes—
687C2×C4⋊C4C22×C411yescharacteristic
688C2×C22⋊C4—22no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—24no—
695C2×C22⋊C4—24no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—24no—
702C2×C22⋊C4—24no—
703C2×C22⋊C4—24no—
704C2×C22⋊C4—24no—
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4C22⋊C412yes—
708C2×C22⋊C4C22⋊C412yes—
709C2×C22⋊C4C22⋊C412yes—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—22no—
714C2×C42—22no—
715C2×C42—22no—
716C2×C42—22no—
717C2×C42C22×C412yes—
718C2×C42C22×C411yescharacteristic
719C2×C42C22×C412yes—
720C2×C42C22×C412yes—
721C2×C42C22×C411yescharacteristic
722C2×C42C22×C411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D412yes—
725C2×C42C2×D412yes—
726C2×C42C2×D411yescharacteristic
727C2×C42C2×D412yes—
728C2×C42C2×D412yes—
729C2×C42C2×D412yes—
730C2×C42C2×D412yes—
731C2×C42C2×D411yescharacteristic
732C2×C42C2×D411yescharacteristic
733C2×C42C2×D411yescharacteristic
734C2×C42C2×D411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2412yes—
737C2×C42C2412yes—
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C4⋊C8—21no—
741C4⋊C8—21no—
742C4⋊C8—22no—
743C4⋊C8—22no—
744C4⋊C8—21no—
745C4⋊C8—22no—
746C4⋊C8—24no—
747C4⋊C8—22no—
748C4⋊C8—24no—
749C4⋊C8—22no—
750C4⋊C8—24no—
751C4⋊C8—22no—
752C4⋊C8—24no—
753C4⋊C8—21no—
754C4⋊C8C2412yes—
755C4⋊C8C2414yes—
756C4⋊C8C2412yes—
757C22⋊C8—21no—
758C22⋊C8—22no—
759C22⋊C8—21no—
760C22⋊C8—24no—
761C22⋊C8—22no—
762C22⋊C8—24no—
763C22⋊C8—22no—
764C22⋊C8—24no—
765C22⋊C8—22no—
766C22⋊C8—24no—
767C22⋊C8—22no—
768#97—22no—
769#97—24no—
770#97—22no—
771#97—24no—
772C4×C8—22no—
773C4×C8—24no—
774C4×C8—22no—
775C4×C8—24no—
776C4×C8C2412yes—
777C4×C8C2414yes—
778C4×C8C2412yes—
779C24—21no—
780C24—22no—
781C24—24no—
782C24—24no—
783C24—48no—
784C24—48no—
785C24—84no—
786C24C2×C22⋊C412yes—
787C24C2×C22⋊C411yescharacteristic
788#41—24no—
789#41—24no—
790#41—24no—
791#41—24no—
792#41—44no—
793#41—44no—
794#41—42no—
795#41—42no—
796#41—42no—
797#41—42no—
798#41—44no—
799#41—44no—
800#41—84no—
801#41—84no—
802#41—82no—
803#41—82no—
804#41—82no—
805#41—82no—
806C2×Q8—21no—
807C2×Q8—22no—
808C2×Q8—22no—
809C2×Q8—42no—
810C2×Q8—42no—
811C2×Q8—82no—
812C2×Q8C2×C22⋊C411yescharacteristic
813C2×Q8C2×C22⋊C411yescharacteristic
814C2×Q8C2×C22⋊C412yes—
815C2×Q8C23×C412yes—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—21no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—22no—
832C2×D4—22no—
833C2×D4—22no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—48no—
840C2×D4—48no—
841C2×D4—416no—
842C2×D4—48no—
843C2×D4—48no—
844C2×D4—48no—
845C2×D4—44no—
846C2×D4—48no—
847C2×D4—82no—
848C2×D4—84no—
849C2×D4C2×C22⋊C412yes—
850C2×D4C2×C22⋊C411yescharacteristic
851C2×D4C2×C22⋊C412yes—
852C2×D4C2×C22⋊C412yes—
853C2×D4C2×C22⋊C412yes—
854C2×D4C2×C22⋊C412yes—
855C2×D4C2×C22⋊C411yescharacteristic
856C2×D4C23×C414yes—
857C2×D4C23×C412yes—
858C22×C4—24no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—22no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—22no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—24no—
874C22×C4—22no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—44no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—42no—
887C22×C4—44no—
888C22×C4—42no—
889C22×C4—44no—
890C22×C4—88no—
891C22×C4—88no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4—84no—
896C22×C4—84no—
897C22×C4—84no—
898C22×C4—84no—
899C22×C4C2×C22⋊C411yescharacteristic
900C22×C4C2×C22⋊C412yes—
901C22×C4C2×C22⋊C412yes—
902C22×C4C2×C22⋊C411yescharacteristic
903C22×C4C2×C22⋊C411yescharacteristic
904C22×C4C2×C22⋊C412yes—
905C22×C4C2×C22⋊C412yes—
906C22×C4C2×C22⋊C411yescharacteristic
907C22×C4C2×C22⋊C411yescharacteristic
908C22×C4C2×C22⋊C411yescharacteristic
909C22×C4C2×C22⋊C412yes—
910C22×C4C2×C22⋊C412yes—
911C22×C4C2×C22⋊C411yescharacteristic
912C22×C4C2×C22⋊C412yes—
913C22×C4C2×C22⋊C412yes—
914C22×C4C2×C22⋊C412yes—
915C22×C4C2×C22⋊C411yescharacteristic
916C22×C4C2×C22⋊C411yescharacteristic
917C22×C4C23×C411yescharacteristic
918C22×C4C23×C412yes—
919C22×C4C23×C412yes—
920C22×C4C23×C411yescharacteristic
921C22×C4C23×C411yescharacteristic
922C22×C4C22×D412yes—
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D412yes—
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D412yes—
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D412yes—
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932M16—48no—
933M16—44no—
934M16—42no—
935M16—44no—
936M16—42no—
937M16—84no—
938M16—82no—
939C2×C8—22no—
940C2×C8—22no—
941C2×C8—24no—
942C2×C8—22no—
943C2×C8—22no—
944C2×C8—24no—
945C2×C8—48no—
946C2×C8—44no—
947C2×C8—84no—
948C2×C8—82no—
949C4⋊C4—21no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—22no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—21no—
965C4⋊C4—22no—
966C4⋊C4C2×C22⋊C412yes—
967C4⋊C4C2×C22⋊C411yescharacteristic
968C4⋊C4C2×C22⋊C411yescharacteristic
969C4⋊C4C2×C22⋊C412yes—
970C4⋊C4C2×C22⋊C411yescharacteristic
971C4⋊C4C2×C22⋊C411yescharacteristic
972C4⋊C4C2×C22⋊C412yes—
973C4⋊C4C2×C22⋊C412yes—
974C4⋊C4C2×C22⋊C412yes—
975C4⋊C4C2×C22⋊C412yes—
976C4⋊C4C2×C22⋊C412yes—
977C4⋊C4C2×C22⋊C412yes—
978C4⋊C4C2×C22⋊C412yes—
979C4⋊C4C2×C22⋊C412yes—
980C4⋊C4C23×C412yes—
981C4⋊C4C23×C414yes—
982C4⋊C4C23×C412yes—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—24no—
1000C22⋊C4—24no—
1001C22⋊C4—24no—
1002C22⋊C4—24no—
1003C22⋊C4—22no—
1004C22⋊C4—24no—
1005C22⋊C4C2×C22⋊C412yes—
1006C22⋊C4C2×C22⋊C412yes—
1007C22⋊C4C2×C22⋊C412yes—
1008C22⋊C4C2×C22⋊C412yes—
1009C22⋊C4C2×C22⋊C412yes—
1010C22⋊C4C2×C22⋊C412yes—
1011C22⋊C4C2×C22⋊C412yes—
1012C22⋊C4C2×C22⋊C412yes—
1013C22⋊C4C2×C22⋊C412yes—
1014C22⋊C4C2×C22⋊C412yes—
1015C22⋊C4C2×C22⋊C412yes—
1016C22⋊C4C2×C22⋊C412yes—
1017C42—22no—
1018C42—22no—
1019C42—22no—
1020C42—22no—
1021C42—22no—
1022C42—22no—
1023C42C2×C22⋊C411yescharacteristic
1024C42C2×C22⋊C411yescharacteristic
1025C42C2×C22⋊C411yescharacteristic
1026C42C2×C22⋊C411yescharacteristic
1027C42C2×C22⋊C412yes—
1028C42C2×C22⋊C412yes—
1029C42C2×C22⋊C412yes—
1030C42C2×C22⋊C412yes—
1031C42C2×C22⋊C412yes—
1032C42C2×C22⋊C412yes—
1033C42C2×C22⋊C411yescharacteristic
1034C42C2×C22⋊C411yescharacteristic
1035C42C23×C411yescharacteristic
1036C42C23×C412yes—
1037C42C23×C412yes—
1038C42C23×C411yescharacteristic
1039C42C23×C411yescharacteristic
1040C42C22×D411yescharacteristic
1041C42C22×D412yes—
1042C42C22×D411yescharacteristic
1043C42C22×D411yescharacteristic
1044C42C22×D412yes—
1045C42C22×D411yescharacteristic
1046C42C22×D412yes—
1047C42C22×D411yescharacteristic
1048C42C22×D412yes—
1049C42C22×D411yescharacteristic
1050C42C2511yescharacteristic
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—22no—
1055C23—22no—
1056C23—24no—
1057C23—42no—
1058C23—41no—
1059C23—41no—
1060C23—48no—
1061C23—48no—
1062C23—42no—
1063C23—44no—
1064C23—44no—
1065C23—48no—
1066C23—42no—
1067C23—44no—
1068C23—48no—
1069C23—84no—
1070C23—84no—
1071C23—832no—
1072C23C22×C22⋊C412yes—
1073C23C22×C22⋊C411yescharacteristic
1074C23C22×C22⋊C411yescharacteristic
1075C23C22×C22⋊C411yescharacteristic
1076C23C22×C22⋊C412yes—
1077Q8—22no—
1078Q8—22no—
1079Q8—22no—
1080Q8—22no—
1081Q8—42no—
1082Q8—42no—
1083Q8—82no—
1084Q8—82no—
1085D4—24no—
1086D4—24no—
1087D4—24no—
1088D4—24no—
1089D4—22no—
1090D4—22no—
1091D4—24no—
1092D4—24no—
1093D4—42no—
1094D4—42no—
1095D4—48no—
1096D4—48no—
1097D4—44no—
1098D4—44no—
1099D4—44no—
1100D4—44no—
1101D4—48no—
1102D4—48no—
1103D4—44no—
1104D4—82no—
1105D4—82no—
1106D4—84no—
1107D4—84no—
1108D4#42114yes—
1109D4#56814yes—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—44no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—44no—
1157C2×C4—44no—
1158C2×C4—48no—
1159C2×C4—44no—
1160C2×C4—42no—
1161C2×C4—44no—
1162C2×C4—42no—
1163C2×C4—44no—
1164C2×C4—84no—
1165C2×C4—84no—
1166C2×C4—84no—
1167C2×C4—84no—
1168C2×C4—84no—
1169C2×C4—84no—
1170C2×C4C22×C22⋊C411yescharacteristic
1171C2×C4C22×C22⋊C411yescharacteristic
1172C2×C4C22×C22⋊C411yescharacteristic
1173C2×C4C22×C22⋊C411yescharacteristic
1174C2×C4C22×C22⋊C411yescharacteristic
1175C2×C4C22×C22⋊C412yes—
1176C2×C4C22×C22⋊C412yes—
1177C2×C4C22×C22⋊C412yes—
1178C2×C4C22×C22⋊C412yes—
1179C2×C4C22×C22⋊C411yescharacteristic
1180C2×C4C22×C22⋊C411yescharacteristic
1181C2×C4C22×C22⋊C412yes—
1182C2×C4C22×C22⋊C412yes—
1183C2×C4C22×C22⋊C411yescharacteristic
1184C2×C4C22×C22⋊C411yescharacteristic
1185C2×C4#57612yes—
1186C2×C4#57712yes—
1187C2×C4C24×C411yescharacteristic
1188C2×C4C23×D411yescharacteristic
1189C2×C4C23×D411yescharacteristic
1190C8—42no—
1191C8—44no—
1192C8—42no—
1193C8—42no—
1194C8—44no—
1195C8—42no—
1196C22—21no—
1197C22—22no—
1198C22—22no—
1199C22—21no—
1200C22—21no—
1201C22—21no—
1202C22—22no—
1203C22—24no—
1204C22—22no—
1205C22—21no—
1206C22—21no—
1207C22—21no—
1208C22—21no—
1209C22—22no—
1210C22—48no—
1211C22—48no—
1212C22—42no—
1213C22—42no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—82no—
1218C22—816no—
1219C22—88no—
1220C22—816no—
1221C22#289712yes—
1222C22C2×#42114yes—
1223C22C23×C22⋊C411yescharacteristic
1224C4—21no—
1225C4—21no—
1226C4—21no—
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—21no—
1232C4—21no—
1233C4—21no—
1234C4—21no—
1235C4—21no—
1236C4—22no—
1237C4—22no—
1238C4—42no—
1239C4—42no—
1240C4—44no—
1241C4—42no—
1242C4#289712yes—
1243C4C2×#42112yes—
1244C4C2×#56812yes—
1245C4C2×#57611yescharacteristic
1246C4C2×#57711yescharacteristic
1247C2—22no—
1248C2—24no—
1249C2—42no—
1250C2—41no—
1251C2—41no—
1252C2—44no—
1253C2—84no—
1254C2#6006411yescharacteristic
1255C2C2×#289711yescharacteristic
1256C2C22×#42111yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radicalC2×#3481C2
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. #60263C2semidirect
3. #60127C2semidirect
4. #17522C2semidirect
5. #17521C2semidirect
6. #17517C2semidirect
7. #17492C2semidirect
8. #17490C2semidirect
9. #17487C2semidirect
10. #17485C2semidirect
11. #17451C2semidirect
12. #17448C2semidirect
13. #17443C2semidirect
14. C2×#1486C2semidirect
44. #2991C22semidirect
45. #2990C22semidirect
46. #2990C22semidirect
57. #2922C22semidirect
58. #2922C22semidirect
59. #2920C22semidirect
60. #2920C22semidirect
61. #2920C22semidirect
62. #2920C22semidirect
63. C2×#431C22semidirect
64. C2×#431C22semidirect
66. C2×#423C22semidirect
67. C2×#423C22semidirect
69. C4×#131C22semidirect
70. #1496C22semidirect
71. #1495C22semidirect
72. #1494C22semidirect
73. #1492C22semidirect
74. #1490C22semidirect
75. #1489C22semidirect
76. #1488C22semidirect
77. #1487C22semidirect
78. #1487C22semidirect
79. #1487C22semidirect
83. #1486C22semidirect
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
307. #432C23semidirect
308. #432C23semidirect
318. #431C23semidirect
319. #431C23semidirect
320. #431C23semidirect
321. #431C23semidirect
322. #431C23semidirect
323. #431C23semidirect
335. #423C23semidirect
336. #423C23semidirect
341. C2×C4⋊C8C23semidirect
342. C2×C4⋊C8C23semidirect
355. C4×M16C23semidirect
356. C4×M16C23semidirect
357. C2×C4×C8C23semidirect
358. C2×C4×C8C23semidirect
359. Q8⋊C8C23semidirect
360. Q8⋊C8C23semidirect
361. Q8⋊C8C23semidirect
365. D4⋊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×#34812
#602632
#601272
#175222
#175212
#175172
#174922
#174902
#174872
#174852
#174512
#174482
#174432
C2×#14862