Finite Group Databasebeta

← #6343252

Subgroups — #6343252

Order 512.

3015 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62800C211yesmaximal, characteristic
2#60282C211yesmaximal, characteristic, complemented
3#60127C211yesmaximal, characteristic, complemented
4#17526C214yesmaximal, complemented
5#17521C218yesmaximal, complemented
6#17517C214yesmaximal, complemented
7#17499C211yesmaximal, characteristic, complemented
8#17495C212yesmaximal, complemented
9#17494C212yesmaximal, complemented
10#17490C211yesmaximal, characteristic, complemented
11#17482C212yesmaximal, complemented
12#17478C211yesmaximal, characteristic, complemented
13#17477C211yesmaximal, characteristic, complemented
14C2×#1496C212yesmaximal, complemented
15#3522C412yes—
16#3519C412yes—
17#3519C414yes—
18#3517—21no—
19#3514—21no—
20#3514—22no—
21#3511C412yes—
22#3511C411yescharacteristic
23#3508C412yes—
24#3508C411yescharacteristic
25#3503C411yescharacteristic
26#3498C411yescharacteristic
27#3494—22no—
28#3494—21no—
29#3488—21no—
30#3483C2212yes—
31#3481C2212yes—
32#3481C2214yes—
33#3480—21no—
34D4×#41—21no—
35D4×#41—22no—
36#3460—22no—
37#3460—21no—
38#3444C2211yescharacteristic
39#3444C2212yes—
40C2×#532C2212yes—
41C2×#532C2211yescharacteristic
42C4×H(5,𝔽2)—21no—
43C2×C4×#41C2211yescharacteristic
44#2990C2212yescomplemented
45#2990C2214yescomplemented
46#2990C2212yescomplemented
47#2983—21no—
48#2973—22no—
49#2972—21no—
50#2970—21no—
51#2970—22no—
52#2970—21no—
53#2925—22no—
54#2925—21no—
55#2924—22no—
56#2924—21no—
57#2922C2214yescomplemented
58#2922C2212yescomplemented
59#2920C2211yescharacteristic, complemented
60#2920C2211yescharacteristic, complemented
61#2920C2211yescharacteristic, complemented
62#2920C2212yescomplemented
63C2×#432C2212yescomplemented
64C2×#432C2212yescomplemented
65C2×#431C2212yescomplemented
66C2×#431C2211yescharacteristic, complemented
67#2906—21no—
68#2880—21no—
69C4×#131C2212yescomplemented
70#1497C2211yescharacteristic, complemented
71#1497C2211yescharacteristic, complemented
72#1497C2212yescomplemented
73#1496C2211yescharacteristic, complemented
74#1496C2212yescomplemented
75#1496C2212yescomplemented
76#1496C2212yescomplemented
77#1496C2218yescomplemented
78#1496C2211yescharacteristic, complemented
79#1496C2212yescomplemented
80#1496C2212yescomplemented
81#1495C2214yescomplemented
82#1494C2218yescomplemented
83#1492C2214yescomplemented
84#1490C2218yescomplemented
85#1489C2214yescomplemented
86#1488C2218yescomplemented
87#1486C2214yescomplemented
88#1484C2214yescomplemented
89#1483C2218yescomplemented
90#1482C2214yescomplemented
91#1480C2218yescomplemented
92#1478C2214yescomplemented
93#1477C2218yescomplemented
94#1476C2214yescomplemented
95C2×D4⋊C8C2218yescomplemented
96C2×H(5,𝔽2)—21no—
97C22×#41—22no—
98C22×#41—21no—
99C22×#41D411yescharacteristic
100C2×#131—22no—
101#559—21no—
102#559—22no—
103#559C2×C412yes—
104#559C2×C414yes—
105Q82C2×C412yes—
106#557—21no—
107#556—21no—
108#556—22no—
109#555—22no—
110#555—24no—
111#555C2×C414yes—
112#555C2×C412yes—
113#554C2×C412yes—
114#554C2×C414yes—
115#554C2×C412yes—
116#554C2×C414yes—
117#553—22no—
118#553—24no—
119#553—22no—
120#553—24no—
121#553C2×C414yes—
122#553C2×C414yes—
123#553C2×C414yes—
124#551—24no—
125#551—24no—
126#551—24no—
127#550—22no—
128#550—21no—
129#550—21no—
130#550—22no—
131#550C2×C412yes—
132#550C2×C414yes—
133#550C2×C412yes—
134D4×Q8—22no—
135D4×Q8—21no—
136#548—22no—
137#548—22no—
138#548—22no—
139#548—22no—
140#547—21no—
141#547—22no—
142#547—22no—
143#547—24no—
144#546—22no—
145#546—24no—
146#546—22no—
147#546—22no—
148#546—22no—
149#546—24no—
150#546—24no—
151#546—24no—
152#546C2×C414yes—
153#546C2×C414yes—
154#546C2×C414yes—
155D42—22no—
156D42—24no—
157D42—22no—
158D42—21no—
159D42C2×C412yes—
160D42C2×C414yes—
161#544—22no—
162#544—21no—
163#542—22no—
164#542—24no—
165#542—22no—
166#542—22no—
167#542—22no—
168#540—22no—
169#540—24no—
170#540—22no—
171#540—22no—
172#540—22no—
173#538—24no—
174#538—24no—
175#538—24no—
176#537—22no—
177#537—21no—
178#535—22no—
179#535—21no—
180#535—21no—
181#535—22no—
182#533C2×C411yescharacteristic
183#533C2×C412yes—
184#533C2×C411yescharacteristic
185#533C2×C412yes—
186#533C2311yescharacteristic
187#532—22no—
188#532—24no—
189#532—22no—
190#532—21no—
191#532—21no—
192#532—22no—
193#532—22no—
194#532—21no—
195#532—21no—
196#532—22no—
197#532C2×C411yescharacteristic
198#532C2×C412yes—
199#532C2×C412yes—
200#532C2×C412yes—
201#532C2×C412yes—
202#532C2×C414yes—
203#532C2×C412yes—
204#532C2×C411yescharacteristic
205#532C2×C412yes—
206#532C2311yescharacteristic
207#532C2312yes—
208#532C2314yes—
209#532C2312yes—
210C2×C4⋊Q8C2×C412yes—
211C2×C4⋊Q8C2×C411yescharacteristic
212C2×#127C2×C412yes—
213C2×#127C2×C411yescharacteristic
214#529—22no—
215#529—24no—
216#529—22no—
217#529—21no—
218#529—21no—
219#529—22no—
220#529—22no—
221#529—21no—
222#529—21no—
223#529—22no—
224#529C2×C412yes—
225#529C2×C414yes—
226#529C2312yes—
227#529C2314yes—
228C2×#124—22no—
229C2×#124—21no—
230#525—22no—
231#525—21no—
232#525—21no—
233#525—22no—
234#525—24no—
235#525—24no—
236#525—24no—
237#525C2×C412yes—
238#525C2×C414yes—
239C2×#121—22no—
240C2×#121—21no—
241C2×#121C2×C414yes—
242C2×#121C2×C412yes—
243#520—21no—
244#520—22no—
245#520—22no—
246#520—21no—
247#518—24no—
248#518—22no—
249#518—21no—
250#518—22no—
251C4×#41—22no—
252C4×#41—22no—
253C4×#41—21no—
254C4×#41—21no—
255C4×#41—22no—
256C4×#41C2×C411yescharacteristic
257C4×#41C2×C412yes—
258C4×#41C2×C411yescharacteristic
259C4×#41D411yescharacteristic
260C4×#41D412yes—
261C4×#41D411yescharacteristic
262C4×#41D411yescharacteristic
263C4×#41D412yes—
264C4×#41D411yescharacteristic
265C4×#41C2312yes—
266C4×#41C2314yes—
267C4×#41C2311yescharacteristic
268C4×#41C2312yes—
269C4×#41C2311yescharacteristic
270C2×C4×Q8C2×C411yescharacteristic
271C2×C4×Q8D411yescharacteristic
272C2×C4×D4—22no—
273C2×C4×D4—24no—
274C2×C4×D4—22no—
275C2×C4×D4—21no—
276C2×C4×D4C2×C411yescharacteristic
277C2×C4×D4C2×C412yes—
278C2×C4×D4D411yescharacteristic
279C2×C4×D4D412yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2312yes—
282C2×#117D412yes—
283C2×#117D411yescharacteristic
284C22×C42C2312yes—
285C22×C42C2311yescharacteristic
286#446—22no—
287#446—22no—
288#446—24no—
289#435—24no—
290#435—24no—
291#435—24no—
292#435—24no—
293C8×D4—22no—
294C8×D4—24no—
295C8×D4—22no—
296#433—24no—
297#433—24no—
298#433—24no—
299#432—22no—
300#432—22no—
301#432—22no—
302#432—22no—
303#432—21no—
304#432—22no—
305#432—21no—
306#432—22no—
307#432—21no—
308#432—21no—
309#432C2311yescharacteristic
310#432C2312yes—
311#432C2311yescharacteristic
312#432C2314yes—
313#432C2314yes—
314#431—22no—
315#431—21no—
316#431—21no—
317#431—22no—
318#431—21no—
319#431—21no—
320#431C2312yes—
321#431C2312yes—
322#431C2311yescharacteristic
323#431C2312yes—
324#431C2311yescharacteristic
325#431C2314yes—
326#431C2312yes—
327#431C2314yes—
328#431C2312yes—
329#424—24no—
330#424—22no—
331#423—22no—
332#423—21no—
333#423C2312yes—
334#423C2312yes—
335C2×C4⋊C8—22no—
336C2×C4⋊C8—21no—
337C2×C4⋊C8C2314yes—
338C2×C4⋊C8C2314yes—
339#408—24no—
340#408—22no—
341#407—21no—
342#407—22no—
343#407—21no—
344#407—21no—
345C2×C22⋊C8—22no—
346C2×C22⋊C8—21no—
347C2×C22⋊C8—22no—
348C2×C22⋊C8—22no—
349#405—24no—
350#405—22no—
351C4×M16—21no—
352C4×M16—21no—
353C4×M16C2314yes—
354C4×M16C2312yes—
355C2×#97—22no—
356C2×#97—22no—
357C2×C4×C8C2314yes—
358C2×C4×C8C2312yes—
359Q8⋊C8C2314yes—
360Q8⋊C8C2314yes—
361Q8⋊C8C2318yes—
362D4⋊C8C2314yes—
363D4⋊C8C2318yes—
364D4⋊C8C2318yes—
365D4⋊C8C2318yes—
366D4⋊C8C2314yes—
367D4⋊C8C2318yes—
368D4⋊C8C2318yes—
369H(5,𝔽2)—48no—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—21no—
373C2×#41—24no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—22no—
378C2×#41—21no—
379C2×#41—22no—
380C2×#41—24no—
381C2×#41—22no—
382C2×#41—44no—
383C2×#41—88no—
384C2×#41—84no—
385C2×#41C22⋊C411yescharacteristic
386C2×#41C22⋊C412yes—
387C2×#41C22⋊C411yescharacteristic
388C2×#41C22×C412yes—
389C2×#41C22×C414yes—
390C2×#41C2×D411yescharacteristic
391C2×#41C2×D412yes—
392C2×#41C2×D411yescharacteristic
393C22×Q8—21no—
394C22×Q8—22no—
395C22×Q8C22⋊C411yescharacteristic
396C22×D4—24no—
397C22×D4—22no—
398C22×D4—24no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—21no—
402C22×D4—21no—
403C22×D4—22no—
404C22×D4C22⋊C411yescharacteristic
405C22×D4C22⋊C412yes—
406C22×D4C22×C414yes—
407C22×D4C22×C412yes—
408C23×C4—24no—
409C23×C4—22no—
410C23×C4C22×C412yes—
411C23×C4C22×C411yescharacteristic
412C23×C4C2×D411yescharacteristic
413C23×C4C2×D412yes—
414C23×C4C2×D412yes—
415C23×C4C2×D411yescharacteristic
416#131—48no—
417C2×M16—24no—
418C2×M16—22no—
419C2×M16—22no—
420C2×M16—22no—
421C22×C8—24no—
422C22×C8—22no—
423C22×C8—24no—
424C22×C8—24no—
425C4⋊Q8—24no—
426C4⋊Q8—22no—
427C4⋊Q8—22no—
428C4⋊Q8—21no—
429C4⋊Q8—22no—
430C4⋊Q8—21no—
431C4⋊Q8C22×C411yescharacteristic
432C4⋊Q8C22×C411yescharacteristic
433C4⋊Q8C22×C412yes—
434C4⋊Q8C22×C414yes—
435C4⋊Q8C22×C412yes—
436C4⋊Q8C22×C411yescharacteristic
437#127—22no—
438#127—24no—
439#127—22no—
440#127—21no—
441#127—22no—
442#127—21no—
443#127C22×C411yescharacteristic
444#127C22×C412yes—
445#127C22×C414yes—
446#127C22×C412yes—
447#126—24no—
448#126—24no—
449#126—24no—
450#126—24no—
451#126—22no—
452#126—24no—
453#126—22no—
454#125—24no—
455#125—22no—
456#125—22no—
457#125—21no—
458#125—21no—
459#125C22×C412yes—
460#125C22×C414yes—
461#124—22no—
462#124—24no—
463#124—24no—
464#124—24no—
465#124—24no—
466#124—24no—
467#124—22no—
468#124—22no—
469#124—22no—
470#124—22no—
471#124—22no—
472#124—21no—
473#124—21no—
474#124—22no—
475#124—22no—
476#124—24no—
477#124C22×C412yes—
478#124C22×C414yes—
479#123—24no—
480#123—22no—
481#123—24no—
482#123—22no—
483#123—24no—
484#123—22no—
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—
494C22⋊Q8—22no—
495C22⋊Q8—24no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—22no—
500C22⋊Q8—21no—
501C22⋊Q8—22no—
502C22⋊Q8—21no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8C22×C412yes—
510C22⋊Q8C22×C412yes—
511C22⋊Q8C22×C414yes—
512#121—24no—
513#121—24no—
514#121—24no—
515#121—22no—
516#121—24no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—24no—
522#121—24no—
523#121—22no—
524#121—22no—
525#121—24no—
526#121—22no—
527#121—21no—
528#121—21no—
529#121—22no—
530#121—21no—
531#121—22no—
532#121—21no—
533#121—22no—
534#121—22no—
535#121—24no—
536#121—24no—
537#121—22no—
538#121—24no—
539#121—22no—
540#121—24no—
541#121—24no—
542#121—24no—
543#121—24no—
544#121—24no—
545#121—24no—
546#121C22×C412yes—
547#121C22×C414yes—
548#121C22×C414yes—
549#121C22×C414yes—
550#121C22×C414yes—
551#121C22×C412yes—
552#121C22×C414yes—
553#120—24no—
554#120—22no—
555#120—24no—
556#120—24no—
557#120—24no—
558#120—24no—
559#120—24no—
560#120—24no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—21no—
564C4×Q8—21no—
565C4×Q8—22no—
566C4×Q8—22no—
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8C22⋊C411yescharacteristic
570C4×Q8C22⋊C411yescharacteristic
571C4×Q8C22⋊C412yes—
572C4×Q8C22⋊C411yescharacteristic
573C4×Q8C22⋊C411yescharacteristic
574C4×Q8C22⋊C412yes—
575C4×Q8C22×C412yes—
576C4×Q8C22×C414yes—
577C4×Q8C22×C411yescharacteristic
578C4×Q8C22×C411yescharacteristic
579C4×Q8C22×C412yes—
580C4×Q8C2×D411yescharacteristic
581C4×Q8C2×D411yescharacteristic
582C4×Q8C2×D412yes—
583C4×Q8C2412yes—
584C4×D4—24no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—24no—
588C4×D4—22no—
589C4×D4—24no—
590C4×D4—22no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—22no—
594C4×D4—24no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—22no—
600C4×D4—24no—
601C4×D4—22no—
602C4×D4—24no—
603C4×D4—24no—
604C4×D4—24no—
605C4×D4—24no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—21no—
612C4×D4—22no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—21no—
618C4×D4—22no—
619C4×D4—24no—
620C4×D4—22no—
621C4×D4—24no—
622C4×D4—24no—
623C4×D4—22no—
624C4×D4C22⋊C412yes—
625C4×D4C22⋊C411yescharacteristic
626C4×D4C22⋊C412yes—
627C4×D4C22⋊C412yes—
628C4×D4C22⋊C412yes—
629C4×D4C22⋊C411yescharacteristic
630C4×D4C22⋊C412yes—
631C4×D4C22⋊C412yes—
632C4×D4C22⋊C411yescharacteristic
633C4×D4C22⋊C412yes—
634C4×D4C22⋊C412yes—
635C4×D4C22⋊C412yes—
636C4×D4C22⋊C411yescharacteristic
637C4×D4C22⋊C412yes—
638C4×D4C22×C414yes—
639C4×D4C22×C414yes—
640C4×D4C22×C414yes—
641C4×D4C22×C412yes—
642C4×D4C22×C414yes—
643C4×D4C22×C412yes—
644C4×D4C22×C411yescharacteristic
645C4×D4C22×C412yes—
646C4×D4C22×C412yes—
647C4×D4C22×C412yes—
648C4×D4C22×C411yescharacteristic
649C4×D4C22×C412yes—
650C4×D4C2×D411yescharacteristic
651C4×D4C2×D412yes—
652C4×D4C2×D412yes—
653C4×D4C2×D412yes—
654C4×D4C2×D412yes—
655C4×D4C2×D411yescharacteristic
656C4×D4C2×D412yes—
657C4×D4C2412yes—
658C4×D4C2414yes—
659#117—22no—
660#117—21no—
661#117—21no—
662#117—24no—
663#117—22no—
664#117—24no—
665#117—22no—
666#117—22no—
667#117—24no—
668#117—22no—
669#117—24no—
670#117C22⋊C411yescharacteristic
671#117C22⋊C412yes—
672#117C22⋊C411yescharacteristic
673#117C22⋊C412yes—
674#117C22⋊C412yes—
675#117C22⋊C412yes—
676#117C22⋊C412yes—
677#117C22×C412yes—
678#117C22×C414yes—
679#117C2×D412yes—
680#117C2×D412yes—
681#117C2×D412yes—
682#117C2×D411yescharacteristic
683#117C2×D412yes—
684#117C2×D411yescharacteristic
685#117C2×D412yes—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—24no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4C22⋊C411yescharacteristic
691C2×C4⋊C4C22⋊C412yes—
692C2×C4⋊C4C22⋊C411yescharacteristic
693C2×C4⋊C4C22⋊C412yes—
694C2×C4⋊C4C22×C414yes—
695C2×C4⋊C4C22×C412yes—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—24no—
698C2×C22⋊C4—24no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—24no—
701C2×C22⋊C4—24no—
702C2×C22⋊C4—24no—
703C2×C22⋊C4C22⋊C412yes—
704C2×C22⋊C4C22⋊C412yes—
705C2×C22⋊C4C22⋊C412yes—
706C2×C42—22no—
707C2×C42—24no—
708C2×C42C22×C411yescharacteristic
709C2×C42C22×C412yes—
710C2×C42C22×C412yes—
711C2×C42C22×C411yescharacteristic
712C2×C42C22×C412yes—
713C2×C42C22×C411yescharacteristic
714C2×C42C2×D411yescharacteristic
715C2×C42C2×D412yes—
716C2×C42C2×D412yes—
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D412yes—
720C2×C42C2×D412yes—
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D412yes—
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D412yes—
726C2×C42C2412yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2412yes—
730C2×C42C2411yescharacteristic
731C4⋊C8—21no—
732C4⋊C8—22no—
733C4⋊C8—21no—
734C4⋊C8—24no—
735C4⋊C8—22no—
736C4⋊C8—24no—
737C4⋊C8—24no—
738C4⋊C8—24no—
739C4⋊C8—22no—
740C4⋊C8—22no—
741C4⋊C8—22no—
742C4⋊C8C2412yes—
743C4⋊C8C2414yes—
744C4⋊C8C2412yes—
745C22⋊C8—21no—
746C22⋊C8—21no—
747C22⋊C8—22no—
748C22⋊C8—21no—
749C22⋊C8—22no—
750C22⋊C8—21no—
751C22⋊C8—22no—
752C22⋊C8—24no—
753C22⋊C8—24no—
754C22⋊C8—24no—
755C22⋊C8—22no—
756C22⋊C8—24no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759#97—21no—
760#97—22no—
761#97—21no—
762#97—24no—
763#97—24no—
764#97—22no—
765#97—24no—
766C4×C8—22no—
767C4×C8—24no—
768C4×C8—22no—
769C4×C8—22no—
770C4×C8C2412yes—
771C4×C8C2414yes—
772C4×C8C2412yes—
773C24—22no—
774C24—24no—
775C24C2×C22⋊C412yes—
776C24C2×C22⋊C411yescharacteristic
777#41—24no—
778#41—24no—
779#41—44no—
780#41—44no—
781#41—42no—
782#41—42no—
783#41—44no—
784#41—48no—
785#41—48no—
786#41—44no—
787#41—44no—
788#41—48no—
789#41—48no—
790#41—88no—
791#41—84no—
792#41—88no—
793#41—84no—
794#41—84no—
795#41—84no—
796#41—84no—
797C2×Q8—21no—
798C2×Q8—22no—
799C2×Q8—21no—
800C2×Q8—22no—
801C2×Q8—24no—
802C2×Q8—42no—
803C2×Q8—84no—
804C2×Q8—82no—
805C2×Q8C2×C22⋊C411yescharacteristic
806C2×Q8C2×C22⋊C411yescharacteristic
807C2×Q8C2×C22⋊C412yes—
808C2×Q8C23×C412yes—
809C2×D4—24no—
810C2×D4—22no—
811C2×D4—24no—
812C2×D4—22no—
813C2×D4—24no—
814C2×D4—22no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—22no—
821C2×D4—21no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—21no—
825C2×D4—24no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—24no—
829C2×D4—48no—
830C2×D4—44no—
831C2×D4—48no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—416no—
835C2×D4—48no—
836C2×D4—84no—
837C2×D4—82no—
838C2×D4—88no—
839C2×D4—84no—
840C2×D4C2×C22⋊C412yes—
841C2×D4C2×C22⋊C412yes—
842C2×D4C2×C22⋊C412yes—
843C2×D4C2×C22⋊C411yescharacteristic
844C2×D4C2×C22⋊C412yes—
845C2×D4C2×C22⋊C412yes—
846C2×D4C2×C22⋊C411yescharacteristic
847C2×D4C23×C412yes—
848C2×D4C23×C414yes—
849C22×C4—22no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—24no—
855C22×C4—22no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—44no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—44no—
864C22×C4—42no—
865C22×C4—44no—
866C22×C4—88no—
867C22×C4—84no—
868C22×C4C2×C22⋊C412yes—
869C22×C4C2×C22⋊C411yescharacteristic
870C22×C4C2×C22⋊C411yescharacteristic
871C22×C4C2×C22⋊C412yes—
872C22×C4C2×C22⋊C411yescharacteristic
873C22×C4C2×C22⋊C412yes—
874C22×C4C2×C22⋊C412yes—
875C22×C4C2×C22⋊C411yescharacteristic
876C22×C4C2×C22⋊C411yescharacteristic
877C22×C4C2×C22⋊C412yes—
878C22×C4C2×C22⋊C411yescharacteristic
879C22×C4C2×C22⋊C412yes—
880C22×C4C2×C22⋊C411yescharacteristic
881C22×C4C2×C22⋊C412yes—
882C22×C4C2×C22⋊C411yescharacteristic
883C22×C4C2×C22⋊C412yes—
884C22×C4C2×C22⋊C412yes—
885C22×C4C2×C22⋊C411yescharacteristic
886C22×C4C23×C411yescharacteristic
887C22×C4C23×C411yescharacteristic
888C22×C4C23×C412yes—
889C22×C4C23×C411yescharacteristic
890C22×C4C23×C412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D412yes—
895C22×C4C22×D412yes—
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D412yes—
901M16—48no—
902M16—44no—
903M16—82no—
904M16—82no—
905C2×C8—22no—
906C2×C8—22no—
907C2×C8—24no—
908C2×C8—22no—
909C2×C8—22no—
910C2×C8—24no—
911C2×C8—48no—
912C2×C8—44no—
913C2×C8—84no—
914C2×C8—84no—
915C4⋊C4—24no—
916C4⋊C4—22no—
917C4⋊C4—21no—
918C4⋊C4—22no—
919C4⋊C4—24no—
920C4⋊C4—22no—
921C4⋊C4—24no—
922C4⋊C4—22no—
923C4⋊C4—21no—
924C4⋊C4—22no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—22no—
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—24no—
933C4⋊C4—22no—
934C4⋊C4C2×C22⋊C412yes—
935C4⋊C4C2×C22⋊C411yescharacteristic
936C4⋊C4C2×C22⋊C412yes—
937C4⋊C4C2×C22⋊C411yescharacteristic
938C4⋊C4C2×C22⋊C412yes—
939C4⋊C4C2×C22⋊C411yescharacteristic
940C4⋊C4C2×C22⋊C412yes—
941C4⋊C4C2×C22⋊C412yes—
942C4⋊C4C2×C22⋊C412yes—
943C4⋊C4C2×C22⋊C412yes—
944C4⋊C4C2×C22⋊C411yescharacteristic
945C4⋊C4C2×C22⋊C412yes—
946C4⋊C4C2×C22⋊C412yes—
947C4⋊C4C2×C22⋊C412yes—
948C4⋊C4C23×C412yes—
949C4⋊C4C23×C414yes—
950C4⋊C4C23×C412yes—
951C22⋊C4—22no—
952C22⋊C4—24no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—24no—
956C22⋊C4—24no—
957C22⋊C4—22no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—22no—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—24no—
970C22⋊C4—22no—
971C22⋊C4—24no—
972C22⋊C4—22no—
973C22⋊C4—24no—
974C22⋊C4C2×C22⋊C412yes—
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—
986C42—22no—
987C42—24no—
988C42—24no—
989C42—22no—
990C42—22no—
991C42C2×C22⋊C412yes—
992C42C2×C22⋊C411yescharacteristic
993C42C2×C22⋊C412yes—
994C42C2×C22⋊C411yescharacteristic
995C42C2×C22⋊C412yes—
996C42C2×C22⋊C411yescharacteristic
997C42C2×C22⋊C411yescharacteristic
998C42C2×C22⋊C412yes—
999C42C2×C22⋊C412yes—
1000C42C2×C22⋊C411yescharacteristic
1001C42C2×C22⋊C412yes—
1002C42C2×C22⋊C411yescharacteristic
1003C42C23×C411yescharacteristic
1004C42C23×C412yes—
1005C42C23×C411yescharacteristic
1006C42C23×C412yes—
1007C42C23×C411yescharacteristic
1008C42C22×D411yescharacteristic
1009C42C22×D412yes—
1010C42C22×D411yescharacteristic
1011C42C22×D412yes—
1012C42C22×D411yescharacteristic
1013C42C22×D411yescharacteristic
1014C42C22×D411yescharacteristic
1015C42C22×D411yescharacteristic
1016C42C22×D412yes—
1017C42C22×D412yes—
1018C42C2511yescharacteristic
1019C23—24no—
1020C23—24no—
1021C23—22no—
1022C23—41no—
1023C23—42no—
1024C23—41no—
1025C23—42no—
1026C23—41no—
1027C23—44no—
1028C23—48no—
1029C23—84no—
1030C23—82no—
1031C23—84no—
1032C23—82no—
1033C23C22×C22⋊C411yescharacteristic
1034C23C22×C22⋊C411yescharacteristic
1035C23C22×C22⋊C412yes—
1036C23C22×C22⋊C411yescharacteristic
1037C23C22×C22⋊C412yes—
1038Q8—22no—
1039Q8—22no—
1040Q8—24no—
1041Q8—42no—
1042Q8—42no—
1043Q8—44no—
1044Q8—42no—
1045Q8—84no—
1046Q8—82no—
1047D4—24no—
1048D4—24no—
1049D4—24no—
1050D4—22no—
1051D4—24no—
1052D4—28no—
1053D4—42no—
1054D4—42no—
1055D4—44no—
1056D4—42no—
1057D4—48no—
1058D4—42no—
1059D4—44no—
1060D4—44no—
1061D4—44no—
1062D4—48no—
1063D4—48no—
1064D4—44no—
1065D4—84no—
1066D4—82no—
1067D4—84no—
1068D4—82no—
1069D4—84no—
1070D4—84no—
1071D4—84no—
1072D4—82no—
1073D4—84no—
1074D4#42114yes—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
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—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—41no—
1095C2×C4—42no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—42no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—41no—
1108C2×C4—42no—
1109C2×C4—41no—
1110C2×C4—42no—
1111C2×C4—41no—
1112C2×C4—48no—
1113C2×C4—44no—
1114C2×C4—48no—
1115C2×C4—44no—
1116C2×C4—84no—
1117C2×C4—84no—
1118C2×C4—84no—
1119C2×C4—84no—
1120C2×C4—82no—
1121C2×C4—84no—
1122C2×C4—82no—
1123C2×C4C22×C22⋊C412yes—
1124C2×C4C22×C22⋊C411yescharacteristic
1125C2×C4C22×C22⋊C412yes—
1126C2×C4C22×C22⋊C411yescharacteristic
1127C2×C4C22×C22⋊C411yescharacteristic
1128C2×C4C22×C22⋊C411yescharacteristic
1129C2×C4C22×C22⋊C411yescharacteristic
1130C2×C4C22×C22⋊C412yes—
1131C2×C4C22×C22⋊C412yes—
1132C2×C4C22×C22⋊C411yescharacteristic
1133C2×C4C22×C22⋊C411yescharacteristic
1134C2×C4C22×C22⋊C412yes—
1135C2×C4C22×C22⋊C412yes—
1136C2×C4C22×C22⋊C411yescharacteristic
1137C2×C4C22×C22⋊C411yescharacteristic
1138C2×C4C24×C411yescharacteristic
1139C2×C4C23×D411yescharacteristic
1140C2×C4C23×D411yescharacteristic
1141C8—42no—
1142C8—44no—
1143C8—42no—
1144C8—42no—
1145C8—44no—
1146C8—42no—
1147C22—22no—
1148C22—22no—
1149C22—21no—
1150C22—21no—
1151C22—22no—
1152C22—21no—
1153C22—21no—
1154C22—21no—
1155C22—22no—
1156C22—21no—
1157C22—21no—
1158C22—21no—
1159C22—21no—
1160C22—22no—
1161C22—42no—
1162C22—44no—
1163C22—42no—
1164C22—44no—
1165C22—44no—
1166C22—42no—
1167C22—84no—
1168C22—82no—
1169C22—168no—
1170C22—164no—
1171C22C2×#42114yes—
1172C22C23×C22⋊C411yescharacteristic
1173C4—21no—
1174C4—22no—
1175C4—21no—
1176C4—22no—
1177C4—21no—
1178C4—21no—
1179C4—22no—
1180C4—21no—
1181C4—22no—
1182C4—21no—
1183C4—21no—
1184C4—21no—
1185C4—22no—
1186C4—21no—
1187C4—22no—
1188C4—42no—
1189C4—42no—
1190C4—44no—
1191C4—42no—
1192C4C2×#42112yes—
1193C4#357312yes—
1194C4#358512yes—
1195C2—24no—
1196C2—41no—
1197C2—42no—
1198C2—41no—
1199C2—41no—
1200C2—82no—
1201C2—84no—
1202C2#6006511yescharacteristic
1203C2#6008711yescharacteristic
1204C2C22×#42111yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62800C2
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. #60282C2semidirect
3. #60127C2semidirect
4. #17526C2semidirect
5. #17521C2semidirect
6. #17517C2semidirect
7. #17499C2semidirect
8. #17495C2semidirect
9. #17494C2semidirect
10. #17490C2semidirect
11. #17482C2semidirect
12. #17478C2semidirect
13. #17477C2semidirect
14. C2×#1496C2semidirect
44. #2990C22semidirect
45. #2990C22semidirect
46. #2990C22semidirect
57. #2922C22semidirect
58. #2922C22semidirect
59. #2920C22semidirect
60. #2920C22semidirect
61. #2920C22semidirect
62. #2920C22semidirect
63. C2×#432C22semidirect
64. C2×#432C22semidirect
65. C2×#431C22semidirect
66. C2×#431C22semidirect
69. C4×#131C22semidirect
70. #1497C22semidirect
71. #1497C22semidirect
72. #1497C22semidirect
73. #1496C22semidirect
74. #1496C22semidirect
75. #1496C22semidirect
76. #1496C22semidirect
77. #1496C22semidirect
78. #1496C22semidirect
79. #1496C22semidirect
80. #1496C22semidirect
81. #1495C22semidirect
82. #1494C22semidirect
83. #1492C22semidirect
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

Maximal subgroups

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

subgroupindex
#628002
#602822
#601272
#175262
#175212
#175172
#174992
#174952
#174942
#174902
#174822
#174782
#174772
C2×#14962