Finite Group Databasebeta

← #6343131

Subgroups — #6343131

Order 512.

3037 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3480C211yesmaximal, characteristic
2M16×#41C211yesmaximal, characteristic, complemented
3#60128C211yesmaximal, characteristic, complemented
4#17516C218yesmaximal, complemented
5#17515C214yesmaximal, complemented
6#17510C214yesmaximal, complemented
7#17502C212yesmaximal, complemented
8#17500C211yesmaximal, characteristic, complemented
9#17497C212yesmaximal, complemented
10#17495C211yesmaximal, characteristic, complemented
11#17452C212yesmaximal, complemented
12#17449C211yesmaximal, characteristic, complemented
13#17447C212yesmaximal, complemented
14C2×#1491C211yesmaximal, characteristic, complemented
15#3480—22no—
16#3480—21no—
17#3480—21no—
18#3480—21no—
19#3480—21no—
20#3480—22no—
21#3480C414yes—
22#3480C412yes—
23#3480C412yes—
24#3480C2212yes—
25#3480C2212yes—
26#3480C2214yes—
27C2×#559—21no—
28C2×#559C411yescharacteristic
29C2×#557C411yescharacteristic
30C2×#556—21no—
31C2×#556C411yescharacteristic
32C2×#553—22no—
33C2×#553C412yes—
34C2×#550C411yescharacteristic
35C2×#548C412yes—
36C2×#532—21no—
37C2×#532C2211yescharacteristic
38C2×#529—22no—
39C2×#529C2212yes—
40C2×C4×#41—21no—
41C2×C4×#41C2212yes—
42C2×C4×#41C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44#2971—21no—
45#2970—22no—
46#2970—21no—
47#2965C2212yescomplemented
48#2965C2214yescomplemented
49C8×#41C2212yescomplemented
50Q8×M16—21no—
51D4×M16—22no—
52D4×M16—21no—
53#2925C2212yescomplemented
54#2925C2214yescomplemented
55#2924—21no—
56#2924—22no—
57#2923—21no—
58#2923—22no—
59#2920C2212yes—
60#2920C2211yescharacteristic
61#2920C2211yescharacteristic
62#2920C2212yes—
63C2×#432C2211yescharacteristic
64C2×#432C2212yes—
65#2906C2212yescomplemented
66#2880—21no—
67#2875—21no—
68C2×C4×M16C2211yescharacteristic
69C2×C4×M16C2212yes—
70#1496C2214yescomplemented
71#1495C2218yescomplemented
72#1494C2218yescomplemented
73#1492C2214yescomplemented
74#1491C2211yescharacteristic
75#1491C2211yescharacteristic
76#1491C2211yescharacteristic
77#1491C2211yescharacteristic
78#1491C2212yes—
79#1491C2212yes—
80#1491C2214yescomplemented
81#1490C2212yes—
82#1490C2212yes—
83#1490C2212yes—
84#1490C2212yes—
85#1489C2218yescomplemented
86#1488C2218yescomplemented
87#1487C2214yescomplemented
88#1484C2214yescomplemented
89#1483C2218yescomplemented
90#1482C2218yescomplemented
91#1480C2214yescomplemented
92#1479C2214yescomplemented
93#1477C2218yescomplemented
94#1476C2218yescomplemented
95C2×Q8⋊C8C2214yescomplemented
96C22×#41—21no—
97C22×#41C2×C412yes—
98C22×#41D411yescharacteristic
99C23×Q8C2×C411yescharacteristic
100C2×#131—22no—
101C22×M16—21no—
102C22×M16—22no—
103#559—21no—
104#559—21no—
105#559—22no—
106#559—22no—
107#559—22no—
108#559—24no—
109#559—22no—
110#559—24no—
111#559—22no—
112#559C2×C412yes—
113#559C2×C412yes—
114#559C2×C414yes—
115#557—21no—
116#557—21no—
117#557—22no—
118#557C2×C412yes—
119#557C2×C412yes—
120#557C2×C414yes—
121#556—22no—
122#556—22no—
123#556—24no—
124#556—22no—
125#556—22no—
126#556—24no—
127#556—21no—
128#556—21no—
129#556—22no—
130#556C2×C412yes—
131#556C2×C412yes—
132#556C2×C414yes—
133#553—24no—
134#553—24no—
135#553—24no—
136#553—24no—
137#553—22no—
138#553—22no—
139#553—22no—
140#553—22no—
141#553—24no—
142#553—24no—
143#553—24no—
144#553—24no—
145#553C2×C414yes—
146#553C2×C414yes—
147#553C2×C414yes—
148#553C2×C414yes—
149#550—21no—
150#550—21no—
151#550—22no—
152#550C2×C412yes—
153#550C2×C412yes—
154#550C2×C414yes—
155#548—22no—
156#548—22no—
157#548—22no—
158#548—22no—
159#548C2×C414yes—
160#548C2×C414yes—
161#548C2×C414yes—
162#548C2×C414yes—
163#532—24no—
164#532—22no—
165#532—22no—
166#532—22no—
167#532—22no—
168#532—24no—
169#532—21no—
170#532—21no—
171#532—21no—
172#532—21no—
173#532C2×C412yes—
174#532C2×C412yes—
175#532C2312yes—
176#532C2312yes—
177C2×C4⋊Q8—21no—
178C2×C4⋊Q8C2×C411yescharacteristic
179C2×#127—21no—
180C2×#127C2×C411yescharacteristic
181#529—24no—
182#529—24no—
183#529—24no—
184#529—24no—
185#529—24no—
186#529—24no—
187#529—24no—
188#529—24no—
189#529—22no—
190#529—22no—
191#529—22no—
192#529—22no—
193#529C2×C414yes—
194#529C2×C414yes—
195#529C2314yes—
196#529C2314yes—
197C2×#126—22no—
198C2×#126—22no—
199C2×#126—22no—
200C2×#125—22no—
201C2×#125C2×C412yes—
202C2×#124—21no—
203C2×#124—21no—
204C2×#124—22no—
205C2×#124—21no—
206C2×#124C2×C412yes—
207C2×#123—22no—
208C2×#123—22no—
209C2×#123—22no—
210C2×C22⋊Q8—22no—
211C2×C22⋊Q8C2×C412yes—
212C2×#121—22no—
213C2×#121—22no—
214C2×#121—21no—
215C2×#121—22no—
216C2×#121C2×C412yes—
217C2×#121C2×C412yes—
218C4×#41—24no—
219C4×#41—22no—
220C4×#41—22no—
221C4×#41—22no—
222C4×#41—22no—
223C4×#41—24no—
224C4×#41—22no—
225C4×#41—22no—
226C4×#41—22no—
227C4×#41—22no—
228C4×#41C2×C414yes—
229C4×#41C2×C414yes—
230C4×#41C2×C411yescharacteristic
231C4×#41C2×C412yes—
232C4×#41C2×C411yescharacteristic
233C4×#41D412yes—
234C4×#41D411yescharacteristic
235C4×#41D411yescharacteristic
236C4×#41D411yescharacteristic
237C4×#41D411yescharacteristic
238C4×#41D412yes—
239C4×#41C2314yes—
240C4×#41C2314yes—
241C4×#41C2311yescharacteristic
242C4×#41C2311yescharacteristic
243C4×#41C2312yes—
244C2×C4×Q8—21no—
245C2×C4×Q8—21no—
246C2×C4×Q8—21no—
247C2×C4×Q8—21no—
248C2×C4×Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8—21no—
251C2×C4×Q8—21no—
252C2×C4×Q8C2×C411yescharacteristic
253C2×C4×Q8C2×C411yescharacteristic
254C2×C4×Q8C2×C412yes—
255C2×C4×Q8C2×C412yes—
256C2×C4×Q8C2×C412yes—
257C2×C4×Q8C2×C411yescharacteristic
258C2×C4×Q8D411yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×D4—22no—
264C2×C4×D4—22no—
265C2×C4×D4—22no—
266C2×C4×D4—21no—
267C2×C4×D4—21no—
268C2×C4×D4—22no—
269C2×C4×D4—22no—
270C2×C4×D4—21no—
271C2×C4×D4C2×C412yes—
272C2×C4×D4C2×C412yes—
273C2×C4×D4C2×C411yescharacteristic
274C2×C4×D4D412yes—
275C2×C4×D4D411yescharacteristic
276C2×C4×D4C2312yes—
277C2×#117—22no—
278C2×#117—22no—
279C2×#117C2×C412yes—
280C2×#117D411yescharacteristic
281C2×#117D412yes—
282C22×C4⋊C4—21no—
283C22×C4⋊C4C2×C411yescharacteristic
284C22×C42—21no—
285C22×C42—22no—
286C22×C42C2311yescharacteristic
287C22×C42C2312yes—
288#446—22no—
289#446—24no—
290C8×Q8—22no—
291#436—24no—
292#436—22no—
293#435—24no—
294#435—24no—
295#435—24no—
296C8×D4—24no—
297C8×D4—22no—
298#433—24no—
299#433—24no—
300#433—24no—
301#432—21no—
302#432—22no—
303#432—22no—
304#432—21no—
305#432—21no—
306#432—22no—
307#432—21no—
308#432—22no—
309#432—21no—
310#432—22no—
311#432C2311yescharacteristic
312#432C2311yescharacteristic
313#432C2312yes—
314#432C2314yes—
315#432C2312yes—
316#431—22no—
317#431—21no—
318#431C2314yes—
319#431C2312yes—
320#431C2312yes—
321#431C2314yes—
322#431C2314yes—
323#431C2312yes—
324#424—22no—
325#424—24no—
326#423—22no—
327#423—21no—
328#423C2312yes—
329#423C2314yes—
330C2×C4⋊C8C2312yes—
331C2×C4⋊C8C2314yes—
332#408—22no—
333#408—24no—
334#407—21no—
335#407—22no—
336#407—21no—
337#407—22no—
338C2×C22⋊C8—21no—
339C2×C22⋊C8—22no—
340#405—22no—
341#405—24no—
342C4×M16—22no—
343C4×M16—21no—
344C4×M16—21no—
345C4×M16—22no—
346C4×M16—21no—
347C4×M16—22no—
348C4×M16C2311yescharacteristic
349C4×M16C2311yescharacteristic
350C4×M16C2312yes—
351C4×M16C2314yes—
352C4×M16C2312yes—
353C2×#97—21no—
354C2×#97—22no—
355C2×#97—21no—
356C2×#97—22no—
357C2×C4×C8C2312yes—
358C2×C4×C8C2314yes—
359Q8⋊C8C2314yes—
360Q8⋊C8C2314yes—
361Q8⋊C8C2314yes—
362Q8⋊C8C2314yes—
363Q8⋊C8C2318yes—
364Q8⋊C8C2318yes—
365D4⋊C8C2318yes—
366D4⋊C8C2318yes—
367D4⋊C8C2318yes—
368D4⋊C8C2318yes—
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—44no—
376C2×#41—48no—
377C2×#41—48no—
378C2×#41C22⋊C412yes—
379C2×#41C22⋊C411yescharacteristic
380C2×#41C22⋊C411yescharacteristic
381C2×#41C22×C414yes—
382C2×#41C22×C414yes—
383C2×#41C2×D411yescharacteristic
384C2×#41C2×D411yescharacteristic
385C2×#41C2×D412yes—
386C22×Q8—21no—
387C22×Q8—21no—
388C22×Q8—21no—
389C22×Q8—21no—
390C22×Q8—44no—
391C22×Q8C22⋊C411yescharacteristic
392C22×Q8C22×C411yescharacteristic
393C22×Q8C22×C412yes—
394C22×Q8C22×C412yes—
395C22×Q8C22×C411yescharacteristic
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—22no—
399C22×D4—21no—
400C22×D4—21no—
401C22×D4C22⋊C412yes—
402C22×D4C22⋊C411yescharacteristic
403C22×D4C22×C412yes—
404C23×C4—21no—
405C23×C4—21no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4C22×C411yescharacteristic
410C23×C4C22×C412yes—
411C23×C4C2×D411yescharacteristic
412C23×C4C2×D411yescharacteristic
413C23×C4C2×D412yes—
414C23×C4C2×D412yes—
415#131—48no—
416C2×M16—21no—
417C2×M16—21no—
418C2×M16—22no—
419C2×M16—22no—
420C2×M16—24no—
421C2×M16—24no—
422C2×M16—22no—
423C2×M16—48no—
424C2×M16—44no—
425C22×C8—22no—
426C22×C8—24no—
427C22×C8—24no—
428C22×C8—22no—
429C4⋊Q8—22no—
430C4⋊Q8—22no—
431C4⋊Q8—24no—
432C4⋊Q8—21no—
433C4⋊Q8—21no—
434C4⋊Q8C22×C412yes—
435C4⋊Q8C22×C412yes—
436#127—22no—
437#127—22no—
438#127—24no—
439#127—21no—
440#127—21no—
441#127C22×C412yes—
442#127C22×C412yes—
443#126—24no—
444#126—24no—
445#126—24no—
446#126—24no—
447#126—24no—
448#126—24no—
449#126—24no—
450#126—24no—
451#126—24no—
452#126—24no—
453#126—24no—
454#126—24no—
455#125—24no—
456#125—24no—
457#125—24no—
458#125—24no—
459#125—22no—
460#125—22no—
461#125C22×C414yes—
462#125C22×C414yes—
463#124—22no—
464#124—22no—
465#124—24no—
466#124—22no—
467#124—22no—
468#124—24no—
469#124—24no—
470#124—24no—
471#124—24no—
472#124—24no—
473#124—22no—
474#124—22no—
475#124—22no—
476#124—22no—
477#124—22no—
478#124—22no—
479#124C22×C414yes—
480#124C22×C414yes—
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—24no—
497C22⋊Q8—24no—
498C22⋊Q8—24no—
499C22⋊Q8C22×C414yes—
500C22⋊Q8C22×C414yes—
501#121—24no—
502#121—24no—
503#121—24no—
504#121—24no—
505#121—24no—
506#121—24no—
507#121—24no—
508#121—24no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—24no—
518#121—24no—
519#121—24no—
520#121—24no—
521#121C22×C414yes—
522#121C22×C414yes—
523#121C22×C414yes—
524#121C22×C414yes—
525C4×Q8—24no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—24no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—21no—
534C4×Q8—21no—
535C4×Q8—21no—
536C4×Q8—21no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—21no—
542C4×Q8—21no—
543C4×Q8—21no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—21no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8C22⋊C411yescharacteristic
550C4×Q8C22⋊C411yescharacteristic
551C4×Q8C22⋊C412yes—
552C4×Q8C22⋊C411yescharacteristic
553C4×Q8C22⋊C411yescharacteristic
554C4×Q8C22⋊C412yes—
555C4×Q8C22×C412yes—
556C4×Q8C22×C412yes—
557C4×Q8C22×C412yes—
558C4×Q8C22×C412yes—
559C4×Q8C22×C412yes—
560C4×Q8C22×C412yes—
561C4×Q8C22×C414yes—
562C4×Q8C22×C414yes—
563C4×Q8C22×C411yescharacteristic
564C4×Q8C22×C411yescharacteristic
565C4×Q8C22×C412yes—
566C4×Q8C2×D411yescharacteristic
567C4×Q8C2×D412yes—
568C4×Q8C2×D411yescharacteristic
569C4×Q8C2412yes—
570C4×Q8C2412yes—
571C4×D4—24no—
572C4×D4—24no—
573C4×D4—24no—
574C4×D4—24no—
575C4×D4—24no—
576C4×D4—24no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—24no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4C22⋊C412yes—
606C4×D4C22⋊C412yes—
607C4×D4C22⋊C412yes—
608C4×D4C22⋊C412yes—
609C4×D4C22⋊C411yescharacteristic
610C4×D4C22⋊C411yescharacteristic
611C4×D4C22⋊C412yes—
612C4×D4C22⋊C412yes—
613C4×D4C22⋊C412yes—
614C4×D4C22⋊C412yes—
615C4×D4C22⋊C412yes—
616C4×D4C22⋊C411yescharacteristic
617C4×D4C22⋊C411yescharacteristic
618C4×D4C22⋊C412yes—
619C4×D4C22×C414yes—
620C4×D4C22×C414yes—
621C4×D4C22×C414yes—
622C4×D4C22×C412yes—
623C4×D4C22×C412yes—
624C4×D4C22×C412yes—
625C4×D4C22×C412yes—
626C4×D4C22×C411yescharacteristic
627C4×D4C22×C411yescharacteristic
628C4×D4C22×C412yes—
629C4×D4C2×D412yes—
630C4×D4C2×D412yes—
631C4×D4C2×D412yes—
632C4×D4C2×D412yes—
633C4×D4C2×D411yescharacteristic
634C4×D4C2×D412yes—
635C4×D4C2×D411yescharacteristic
636C4×D4C2414yes—
637#117—22no—
638#117—22no—
639#117—24no—
640#117—24no—
641#117—24no—
642#117—24no—
643#117—24no—
644#117—24no—
645#117—24no—
646#117—24no—
647#117C22⋊C411yescharacteristic
648#117C22⋊C412yes—
649#117C22⋊C411yescharacteristic
650#117C22⋊C412yes—
651#117C22⋊C412yes—
652#117C22⋊C412yes—
653#117C22⋊C412yes—
654#117C22×C414yes—
655#117C22×C414yes—
656#117C2×D411yescharacteristic
657#117C2×D411yescharacteristic
658#117C2×D412yes—
659#117C2×D412yes—
660#117C2×D412yes—
661#117C2×D412yes—
662#117C2×D412yes—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
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×C411yescharacteristic
685C2×C4⋊C4C22×C412yes—
686C2×C4⋊C4C22×C412yes—
687C2×C4⋊C4C22×C412yes—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4C22⋊C412yes—
697C2×C22⋊C4C22⋊C412yes—
698C2×C22⋊C4C22⋊C412yes—
699C2×C42—22no—
700C2×C42—22no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—24no—
710C2×C42—24no—
711C2×C42—24no—
712C2×C42—24no—
713C2×C42C22×C412yes—
714C2×C42C22×C411yescharacteristic
715C2×C42C22×C411yescharacteristic
716C2×C42C22×C411yescharacteristic
717C2×C42C22×C412yes—
718C2×C42C22×C412yes—
719C2×C42C2×D412yes—
720C2×C42C2×D412yes—
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2×D411yescharacteristic
727C2×C42C2×D412yes—
728C2×C42C2×D412yes—
729C2×C42C2×D412yes—
730C2×C42C2×D412yes—
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2412yes—
735C2×C42C2412yes—
736C4⋊C8—24no—
737C4⋊C8—22no—
738C4⋊C8—24no—
739C4⋊C8—22no—
740C4⋊C8—24no—
741C4⋊C8—22no—
742C4⋊C8—24no—
743C4⋊C8—22no—
744C4⋊C8C2412yes—
745C4⋊C8C2412yes—
746C4⋊C8C2414yes—
747C22⋊C8—21no—
748C22⋊C8—21no—
749C22⋊C8—22no—
750C22⋊C8—22no—
751C22⋊C8—24no—
752C22⋊C8—22no—
753C22⋊C8—24no—
754C22⋊C8—22no—
755C22⋊C8—24no—
756C22⋊C8—22no—
757C22⋊C8—24no—
758#97—21no—
759#97—21no—
760#97—21no—
761#97—22no—
762#97—21no—
763#97—22no—
764#97—24no—
765#97—22no—
766#97—24no—
767#97—22no—
768C4×C8—24no—
769C4×C8—22no—
770C4×C8—24no—
771C4×C8—22no—
772C4×C8C2412yes—
773C4×C8C2414yes—
774C4×C8C2412yes—
775C24—22no—
776C24C2×C22⋊C411yescharacteristic
777C24C2×C22⋊C412yes—
778#41—24no—
779#41—24no—
780#41—28no—
781#41—28no—
782#41—44no—
783#41—44no—
784#41—42no—
785#41—42no—
786#41—44no—
787#41—44no—
788#41—48no—
789#41—48no—
790#41—48no—
791#41—48no—
792#41—48no—
793#41—48no—
794C2×Q8—24no—
795C2×Q8—21no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—21no—
799C2×Q8—22no—
800C2×Q8—22no—
801C2×Q8—24no—
802C2×Q8—24no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—42no—
806C2×Q8—42no—
807C2×Q8—44no—
808C2×Q8—44no—
809C2×Q8—44no—
810C2×Q8—44no—
811C2×Q8C2×C22⋊C411yescharacteristic
812C2×Q8C2×C22⋊C411yescharacteristic
813C2×Q8C2×C22⋊C412yes—
814C2×Q8C23×C412yes—
815C2×Q8C23×C412yes—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—48no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—48no—
833C2×D4—82no—
834C2×D4—84no—
835C2×D4C2×C22⋊C412yes—
836C2×D4C2×C22⋊C412yes—
837C2×D4C2×C22⋊C411yescharacteristic
838C2×D4C2×C22⋊C411yescharacteristic
839C2×D4C2×C22⋊C412yes—
840C2×D4C2×C22⋊C412yes—
841C2×D4C2×C22⋊C412yes—
842C2×D4C23×C414yes—
843C22×C4—21no—
844C22×C4—24no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—42no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—42no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—84no—
868C22×C4—82no—
869C22×C4C2×C22⋊C411yescharacteristic
870C22×C4C2×C22⋊C411yescharacteristic
871C22×C4C2×C22⋊C411yescharacteristic
872C22×C4C2×C22⋊C412yes—
873C22×C4C2×C22⋊C411yescharacteristic
874C22×C4C2×C22⋊C412yes—
875C22×C4C2×C22⋊C412yes—
876C22×C4C2×C22⋊C411yescharacteristic
877C22×C4C2×C22⋊C411yescharacteristic
878C22×C4C2×C22⋊C412yes—
879C22×C4C2×C22⋊C412yes—
880C22×C4C2×C22⋊C412yes—
881C22×C4C2×C22⋊C412yes—
882C22×C4C2×C22⋊C411yescharacteristic
883C22×C4C2×C22⋊C411yescharacteristic
884C22×C4C2×C22⋊C411yescharacteristic
885C22×C4C2×C22⋊C412yes—
886C22×C4C2×C22⋊C412yes—
887C22×C4C23×C411yescharacteristic
888C22×C4C23×C411yescharacteristic
889C22×C4C23×C411yescharacteristic
890C22×C4C23×C412yes—
891C22×C4C23×C412yes—
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D411yescharacteristic
902M16—24no—
903M16—48no—
904M16—44no—
905M16—42no—
906M16—44no—
907M16—48no—
908M16—44no—
909C2×C8—22no—
910C2×C8—24no—
911C2×C8—22no—
912C2×C8—24no—
913C2×C8—22no—
914C2×C8—22no—
915C2×C8—48no—
916C2×C8—44no—
917C2×C8—48no—
918C2×C8—44no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4C2×C22⋊C412yes—
943C4⋊C4C2×C22⋊C411yescharacteristic
944C4⋊C4C2×C22⋊C411yescharacteristic
945C4⋊C4C2×C22⋊C412yes—
946C4⋊C4C2×C22⋊C411yescharacteristic
947C4⋊C4C2×C22⋊C411yescharacteristic
948C4⋊C4C2×C22⋊C412yes—
949C4⋊C4C2×C22⋊C412yes—
950C4⋊C4C2×C22⋊C412yes—
951C4⋊C4C2×C22⋊C412yes—
952C4⋊C4C2×C22⋊C412yes—
953C4⋊C4C2×C22⋊C412yes—
954C4⋊C4C2×C22⋊C412yes—
955C4⋊C4C2×C22⋊C412yes—
956C4⋊C4C23×C412yes—
957C4⋊C4C23×C412yes—
958C4⋊C4C23×C414yes—
959C22⋊C4—24no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—24no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—24no—
974C22⋊C4—24no—
975C22⋊C4C2×C22⋊C412yes—
976C22⋊C4C2×C22⋊C412yes—
977C22⋊C4C2×C22⋊C412yes—
978C22⋊C4C2×C22⋊C412yes—
979C22⋊C4C2×C22⋊C412yes—
980C22⋊C4C2×C22⋊C412yes—
981C22⋊C4C2×C22⋊C412yes—
982C22⋊C4C2×C22⋊C412yes—
983C22⋊C4C2×C22⋊C412yes—
984C22⋊C4C2×C22⋊C412yes—
985C22⋊C4C2×C22⋊C412yes—
986C22⋊C4C2×C22⋊C412yes—
987C42—22no—
988C42—22no—
989C42—24no—
990C42—24no—
991C42—24no—
992C42—24no—
993C42—22no—
994C42—22no—
995C42—22no—
996C42—22no—
997C42—22no—
998C42—22no—
999C42C2×C22⋊C412yes—
1000C42C2×C22⋊C412yes—
1001C42C2×C22⋊C412yes—
1002C42C2×C22⋊C412yes—
1003C42C2×C22⋊C411yescharacteristic
1004C42C2×C22⋊C411yescharacteristic
1005C42C2×C22⋊C412yes—
1006C42C2×C22⋊C412yes—
1007C42C2×C22⋊C411yescharacteristic
1008C42C2×C22⋊C411yescharacteristic
1009C42C2×C22⋊C411yescharacteristic
1010C42C2×C22⋊C411yescharacteristic
1011C42C23×C411yescharacteristic
1012C42C23×C412yes—
1013C42C23×C412yes—
1014C42C23×C411yescharacteristic
1015C42C23×C411yescharacteristic
1016C42C22×D412yes—
1017C42C22×D411yescharacteristic
1018C42C22×D411yescharacteristic
1019C42C22×D412yes—
1020C42C22×D411yescharacteristic
1021C42C22×D412yes—
1022C42C22×D411yescharacteristic
1023C42C22×D411yescharacteristic
1024C42C22×D412yes—
1025C42C22×D411yescharacteristic
1026C42C2511yescharacteristic
1027C23—22no—
1028C23—22no—
1029C23—24no—
1030C23—24no—
1031C23—41no—
1032C23—42no—
1033C23—42no—
1034C23—44no—
1035C23—44no—
1036C23—44no—
1037C23C22×C22⋊C412yes—
1038C23C22×C22⋊C412yes—
1039C23C22×C22⋊C411yescharacteristic
1040C23C22×C22⋊C411yescharacteristic
1041C23C22×C22⋊C411yescharacteristic
1042Q8—24no—
1043Q8—22no—
1044Q8—22no—
1045Q8—22no—
1046Q8—22no—
1047Q8—22no—
1048Q8—42no—
1049Q8—44no—
1050Q8—44no—
1051Q8—42no—
1052Q8—44no—
1053Q8—44no—
1054Q8#56814yes—
1055D4—24no—
1056D4—24no—
1057D4—22no—
1058D4—22no—
1059D4—24no—
1060D4—24no—
1061D4—42no—
1062D4—42no—
1063D4—42no—
1064D4—48no—
1065D4—48no—
1066D4—44no—
1067D4—44no—
1068D4—48no—
1069D4—48no—
1070D4—44no—
1071D4—82no—
1072D4—82no—
1073D4—84no—
1074D4—84no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—42no—
1097C2×C4—41no—
1098C2×C4—42no—
1099C2×C4—41no—
1100C2×C4—42no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—42no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—42no—
1110C2×C4—42no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—48no—
1114C2×C4—48no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—48no—
1118C2×C4—44no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—48no—
1123C2×C4—84no—
1124C2×C4—84no—
1125C2×C4—82no—
1126C2×C4—82no—
1127C2×C4C22×C22⋊C411yescharacteristic
1128C2×C4C22×C22⋊C411yescharacteristic
1129C2×C4C22×C22⋊C412yes—
1130C2×C4C22×C22⋊C412yes—
1131C2×C4C22×C22⋊C412yes—
1132C2×C4C22×C22⋊C412yes—
1133C2×C4C22×C22⋊C411yescharacteristic
1134C2×C4C22×C22⋊C411yescharacteristic
1135C2×C4C22×C22⋊C412yes—
1136C2×C4C22×C22⋊C412yes—
1137C2×C4C22×C22⋊C411yescharacteristic
1138C2×C4C22×C22⋊C411yescharacteristic
1139C2×C4C22×C22⋊C411yescharacteristic
1140C2×C4C22×C22⋊C411yescharacteristic
1141C2×C4C22×C22⋊C411yescharacteristic
1142C2×C4#57514yes—
1143C2×C4C24×C411yescharacteristic
1144C2×C4C23×D411yescharacteristic
1145C2×C4C23×D411yescharacteristic
1146C8—24no—
1147C8—44no—
1148C8—42no—
1149C8—42no—
1150C8—44no—
1151C8—42no—
1152C22—21no—
1153C22—21no—
1154C22—21no—
1155C22—21no—
1156C22—21no—
1157C22—22no—
1158C22—22no—
1159C22—21no—
1160C22—22no—
1161C22—22no—
1162C22—21no—
1163C22—22no—
1164C22—22no—
1165C22—44no—
1166C22—44no—
1167C22—44no—
1168C22—44no—
1169C22—84no—
1170C22—88no—
1171C22#289612yes—
1172C22#290112yes—
1173C22C23×C22⋊C411yescharacteristic
1174C4—24no—
1175C4—22no—
1176C4—22no—
1177C4—21no—
1178C4—21no—
1179C4—21no—
1180C4—21no—
1181C4—21no—
1182C4—22no—
1183C4—22no—
1184C4—21no—
1185C4—21no—
1186C4—22no—
1187C4—22no—
1188C4—21no—
1189C4—21no—
1190C4—42no—
1191C4—44no—
1192C4—42no—
1193C4—42no—
1194C4#289612yes—
1195C4C2×#56812yes—
1196C4C2×#57512yes—
1197C2—22no—
1198C2—22no—
1199C2—41no—
1200C2—42no—
1201C2—42no—
1202C2—84no—
1203C2#6006411yescharacteristic
1204C2C2×#289611yescharacteristic
1205C2C2×#290111yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radicalC2×#3480C2
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. M16×#41C2semidirect
3. #60128C2semidirect
4. #17516C2semidirect
5. #17515C2semidirect
6. #17510C2semidirect
7. #17502C2semidirect
8. #17500C2semidirect
9. #17497C2semidirect
10. #17495C2semidirect
11. #17452C2semidirect
12. #17449C2semidirect
13. #17447C2semidirect
14. C2×#1491C2semidirect
47. #2965C22semidirect
48. #2965C22semidirect
49. C8×#41C22semidirect
53. #2925C22semidirect
54. #2925C22semidirect
65. #2906C22semidirect
70. #1496C22semidirect
71. #1495C22semidirect
72. #1494C22semidirect
73. #1492C22semidirect
80. #1491C22semidirect
85. #1489C22semidirect
86. #1488C22semidirect
87. #1487C22semidirect
88. #1484C22semidirect
89. #1483C22semidirect
90. #1482C22semidirect
91. #1480C22semidirect
92. #1479C22semidirect
93. #1477C22semidirect
94. #1476C22semidirect
95. C2×Q8⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
C2×#34802
M16×#412
#601282
#175162
#175152
#175102
#175022
#175002
#174972
#174952
#174522
#174492
#174472
C2×#14912