Finite Group Databasebeta

← #6345460

Subgroups — #6345460

Order 512.

1585 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60942C211yesmaximal, characteristic
2#60208C211yesmaximal, characteristic, complemented
3C2×#2969C211yesmaximal, characteristic, complemented
4#18075C214yesmaximal, complemented
5#18074C214yesmaximal, complemented
6#18005C214yesmaximal, complemented
7#18002C214yesmaximal, complemented
8#17936C211yesmaximal, characteristic, complemented
9#17935C211yesmaximal, characteristic, complemented
10#17934C211yesmaximal, characteristic, complemented
11#17933C211yesmaximal, characteristic, complemented
12#17908C211yesmaximal, characteristic, complemented
13#17907C211yesmaximal, characteristic, complemented
14#17906C211yesmaximal, characteristic, complemented
15#17905C211yesmaximal, characteristic, complemented
16#17803C211yesmaximal, characteristic, complemented
17#17487C211yesmaximal, characteristic, complemented
18#17458C211yesmaximal, characteristic, complemented
19#17319C211yesmaximal, characteristic, complemented
20#3444C2211yescharacteristic
21C2×#529C2211yescharacteristic
22#3248C412yes—
23#3247C412yes—
24#3233C412yes—
25#3232C412yes—
26#3212C412yes—
27#3211C412yes—
28#3190C412yes—
29#3188C412yes—
30#3168C2214yes—
31#3104C2211yescharacteristic
32#3103C2211yescharacteristic
33#3102C2214yes—
34#3101C2211yescharacteristic
35#3100C2211yescharacteristic
36#2971—21no—
37#2971C2212yescomplemented
38#2970—21no—
39#2970C2212yescomplemented
40#2969—21no—
41#2969—21no—
42#2969—21no—
43#2969—21no—
44#2969—21no—
45#2969—21no—
46#2969C2212yes—
47#2969C2212yes—
48#2969C2212yes—
49#2969C2212yes—
50#2969C2212yescomplemented
51#2969C2212yescomplemented
52#2960C2211yescharacteristic
53#2960C2211yescharacteristic
54C2×#446C2211yescharacteristic
55C2×C8×Q8C2211yescharacteristic
56#2931C2211yescharacteristic
57#2931C2211yescharacteristic
58#2930—21no—
59#2930—21no—
60C2×#436—21no—
61C2×#436C2211yescharacteristic
62C2×#435—21no—
63C2×C8×D4C2211yescharacteristic
64#2923—21no—
65#2920C2211yescharacteristic
66C2×#433—21no—
67C2×#431C2211yescharacteristic
68C2×#431C2211yescharacteristic
69C2×#431C2211yescharacteristic
70#2875—21no—
71C2×#405—21no—
72C2×C4×M16C2211yescharacteristic
73#1594C2214yescomplemented
74#1593C2214yescomplemented
75#1592C2214yescomplemented
76#1592C2214yescomplemented
77#1588C2214yescomplemented
78#1588C2214yescomplemented
79#1587C2214yescomplemented
80#1587C2214yescomplemented
81#1586C2214yescomplemented
82#1586C2214yescomplemented
83#1585C2214yescomplemented
84#1585C2214yescomplemented
85#1580C2214yescomplemented
86#1579C2214yescomplemented
87SD16⋊C8C2214yescomplemented
88SD16⋊C8C2214yescomplemented
89#1572C2214yescomplemented
90#1571C2211yescharacteristic
91#1571C2211yescharacteristic
92#1570C2211yescharacteristic
93#1570C2211yescharacteristic
94#1564C2214yescomplemented
95#1494C2214yes—
96#1487C2211yescharacteristic
97#1487C2211yescharacteristic
98#1486C2211yescharacteristic
99#1486C2211yescharacteristic
100#1482C2214yes—
101#1482C2214yescomplemented
102#1481C2211yescharacteristic
103#1481C2211yescharacteristic
104#1480C2211yescharacteristic
105#1480C2211yescharacteristic
106#1476C2214yescomplemented
107#1452C2211yescharacteristic
108#1452C2211yescharacteristic
109#1452C2211yescharacteristic
110#1452C2211yescharacteristic
111#1451C2212yescomplemented
112#1451C2212yescomplemented
113#1451C2212yescomplemented
114#1451C2212yescomplemented
115C2×#131—21no—
116C2×#131—21no—
117C22×M16—21no—
118C22×M16D411yescharacteristic
119C22×M16D411yescharacteristic
120C23×C8—21no—
121#533C2×C411yescharacteristic
122#533C2×C411yescharacteristic
123#533C2311yescharacteristic
124#532C2×C411yescharacteristic
125#532C2×C411yescharacteristic
126#532C2311yescharacteristic
127#529—21no—
128#529—21no—
129#529—21no—
130#529—21no—
131#529—21no—
132#529—21no—
133#529—21no—
134#529—21no—
135#529C2×C412yes—
136#529C2×C412yes—
137#529C2×C412yes—
138#529C2312yes—
139#529C2312yes—
140#529C2312yes—
141C2×#126—21no—
142C2×#125C2×C411yescharacteristic
143C2×#124C2×C411yescharacteristic
144#525—21no—
145#525—21no—
146#525C2×C412yes—
147C2×#123—21no—
148C2×C22⋊Q8C2×C411yescharacteristic
149C2×#121C2×C411yescharacteristic
150C4×#41—21no—
151C4×#41—21no—
152C4×#41C2312yes—
153C2×C4×Q8C2311yescharacteristic
154C2×C4×D4—21no—
155C2×C4×D4C2311yescharacteristic
156C2×#117—21no—
157C22×C42C2311yescharacteristic
158#499C2×C414yes—
159#495C2×C414yes—
160#488C2×C414yes—
161#488C2×C414yes—
162#485C2×C414yes—
163#484C2×C412yes—
164#483C2×C412yes—
165#482C2×C414yes—
166#481C2×C412yes—
167#480C2×C412yes—
168#479C2×C414yes—
169#478C2×C414yes—
170#477C2×C412yes—
171#476C2×C412yes—
172#475C2×C412yes—
173#474C2×C412yes—
174#467C2×C414yes—
175#466C2×C414yes—
176#465C2×C414yes—
177#465C2×C414yes—
178#464C2×C414yes—
179#463C2×C414yes—
180#462C2×C412yes—
181#461C2×C412yes—
182#460C2×C412yes—
183#459C2×C412yes—
184#452C2×C414yes—
185#451C2×C412yes—
186#450C2×C412yes—
187#449C2×C414yes—
188#448C2×C412yes—
189#447C2×C412yes—
190#446—21no—
191#446—21no—
192#446—21no—
193#446—21no—
194#446C2312yes—
195#446C2312yes—
196#446C2312yes—
197#446C2312yes—
198C8×Q8—21no—
199C8×Q8—21no—
200C8×Q8—21no—
201C8×Q8—21no—
202C8×Q8C2312yes—
203C8×Q8C2312yes—
204C8×Q8C2312yes—
205C8×Q8C2312yes—
206C4×Q16C2314yes—
207C4×SD16C2314yes—
208C4×SD16C2314yes—
209C4×D8C2314yes—
210#436—22no—
211#436—22no—
212#436—22no—
213#436—22no—
214#436—22no—
215#436—22no—
216#436—22no—
217#436—22no—
218#436—21no—
219#436—21no—
220#436—21no—
221#436—21no—
222#436C2312yes—
223#436C2312yes—
224#436C2312yes—
225#436C2312yes—
226#435—22no—
227#435—22no—
228#435—22no—
229#435—22no—
230#435—22no—
231#435—22no—
232#435—22no—
233#435—22no—
234C8×D4—21no—
235C8×D4—21no—
236C8×D4—21no—
237C8×D4—21no—
238C8×D4C2312yes—
239C8×D4C2312yes—
240C8×D4C2312yes—
241C8×D4C2312yes—
242#433—22no—
243#433—22no—
244#433—22no—
245#433—22no—
246#433—22no—
247#433—22no—
248#432—21no—
249#432—22no—
250#432—22no—
251#432C2312yes—
252#431—21no—
253#431—21no—
254#431—21no—
255#431—21no—
256#431—21no—
257#431C2×C412yes—
258#431C2×C412yes—
259#431C2312yes—
260#431C2312yes—
261#431C2312yes—
262#431C2312yes—
263#431C2311yescharacteristic
264#431C2311yescharacteristic
265#431C2311yescharacteristic
266#431C2311yescharacteristic
267#431C2312yes—
268#424—21no—
269#424—21no—
270#423C2311yescharacteristic
271#423C2311yescharacteristic
272C2×C4⋊C8—21no—
273C2×C4⋊C8—21no—
274C2×C4⋊C8—21no—
275C2×C4⋊C8C2×C412yes—
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278#408—21no—
279#408—21no—
280#407—21no—
281C2×C22⋊C8—21no—
282C2×C22⋊C8—21no—
283C2×C22⋊C8—21no—
284C2×C22⋊C8—21no—
285C2×C22⋊C8C2×C412yes—
286#405—21no—
287#405—21no—
288#405—22no—
289#405—22no—
290#405—22no—
291#405—22no—
292#405—22no—
293#405—22no—
294C4×M16—21no—
295C4×M16—22no—
296C4×M16D411yescharacteristic
297C4×M16D411yescharacteristic
298C4×M16D411yescharacteristic
299C4×M16D411yescharacteristic
300C4×M16C2311yescharacteristic
301C4×M16C2311yescharacteristic
302C4×M16C2311yescharacteristic
303C4×M16C2311yescharacteristic
304C2×#97—21no—
305C2×#97—22no—
306C2×#97D411yescharacteristic
307C2×#97D411yescharacteristic
308C2×C4×C8—21no—
309C2×C4×C8—21no—
310C2×C4×C8C2312yes—
311C2×C4×C8C2312yes—
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#335C2314yes—
315#335C2314yes—
316#334C2314yes—
317#334C2314yes—
318Q8⋊C8C2314yes—
319Q8⋊C8C2314yes—
320Q8⋊C8C2314yes—
321Q8⋊C8C2314yes—
322D4⋊C8C2314yes—
323D4⋊C8C2314yes—
324D4⋊C8C2314yes—
325D4⋊C8C2314yes—
326#322C2312yes—
327#322C2312yes—
328#322C2312yes—
329#322C2312yes—
330#322C2312yes—
331#322C2312yes—
332#322C2312yes—
333#322C2312yes—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41C22×C412yes—
337C22×Q8C22×C411yescharacteristic
338C22×D4—21no—
339C22×D4C22×C411yescharacteristic
340C23×C4—21no—
341C23×C4C22×C411yescharacteristic
342C23×C4C2×D411yescharacteristic
343C23×C4#4111yescharacteristic
344C2×Q16C22×C414yes—
345C2×SD16C22×C414yes—
346C2×SD16C22×C414yes—
347C2×D8C22×C414yes—
348#131—44no—
349#131—44no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—42no—
357C2×M16—42no—
358C2×M16—44no—
359C2×M16C2×D411yescharacteristic
360C2×M16C2×D411yescharacteristic
361C2×M16C2×D411yescharacteristic
362C2×M16C2×D411yescharacteristic
363C2×M16C2×D411yescharacteristic
364C2×M16C2×D411yescharacteristic
365C2×M16C2×D411yescharacteristic
366C2×M16C2×D411yescharacteristic
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—22no—
374C22×C8—44no—
375C22×C8C22×C414yes—
376C22×C8C2×D411yescharacteristic
377C22×C8C2×D411yescharacteristic
378C22×C8C2×D411yescharacteristic
379C22×C8C2×D411yescharacteristic
380C4⋊Q8C22×C411yescharacteristic
381C4⋊Q8C22×C411yescharacteristic
382C4⋊Q8C22×C411yescharacteristic
383#127C22×C411yescharacteristic
384#126—22no—
385#126—22no—
386#126—22no—
387#126—22no—
388#126—22no—
389#126—22no—
390#125—21no—
391#125—21no—
392#125—21no—
393#125—21no—
394#125C22×C412yes—
395#125C22×C412yes—
396#125C22×C412yes—
397#124—21no—
398#124—21no—
399#124—21no—
400#124—21no—
401#124C22×C412yes—
402#124C22×C412yes—
403#124C22×C412yes—
404#123—22no—
405#123—22no—
406#123—22no—
407#123—22no—
408#123—22no—
409#123—22no—
410#123—22no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8C22×C412yes—
418C22⋊Q8C22×C412yes—
419C22⋊Q8C22×C412yes—
420C22⋊Q8C22×C412yes—
421#121—21no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121—21no—
426#121—21no—
427#121C22×C412yes—
428#121C22×C412yes—
429#121C22×C412yes—
430#121C22×C412yes—
431#120—22no—
432C4×Q8—21no—
433C4×Q8—21no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×Q8C22×C412yes—
439C4×Q8C22×C412yes—
440C4×Q8C2412yes—
441C4×Q8C2412yes—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4—21no—
458C4×D4C22×C412yes—
459C4×D4C22×C412yes—
460C4×D4C2412yes—
461C4×D4C2412yes—
462#117—21no—
463#117—21no—
464#117—22no—
465#117—22no—
466#117—22no—
467#117—22no—
468#117—22no—
469#117—22no—
470#117—22no—
471#117C22×C412yes—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4C22×C411yescharacteristic
477C2×C4⋊C4C22×C411yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C42—21no—
484C2×C42—22no—
485C2×C42C22×C411yescharacteristic
486C2×C42C22×C411yescharacteristic
487C2×C42C22×C411yescharacteristic
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42#4111yescharacteristic
492C2×C42#4111yescharacteristic
493C2×C42#4111yescharacteristic
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496C2×C42C2411yescharacteristic
497#107C22×C414yes—
498#107C22×C414yes—
499#106C22×C414yes—
500#106C22×C414yes—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—22no—
506C4⋊C8—22no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8—22no—
516C4⋊C8C22×C412yes—
517C4⋊C8C22×C412yes—
518C4⋊C8C22×C414yes—
519C4⋊C8C2412yes—
520C4⋊C8C2412yes—
521C4⋊C8C2412yes—
522C4⋊C8C2412yes—
523#103C22×C414yes—
524#103C22×C414yes—
525#103C22×C414yes—
526#103C22×C414yes—
527#102C22×C414yes—
528#102C22×C414yes—
529#102C22×C414yes—
530#102C22×C414yes—
531C22⋊C8—22no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—22no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—22no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8C22×C412yes—
547C22⋊C8C22×C412yes—
548C22⋊C8C22×C414yes—
549#97—22no—
550#97—22no—
551#97—22no—
552#97—22no—
553#97—22no—
554#97C2×D411yescharacteristic
555#97C2×D411yescharacteristic
556#97C2×D411yescharacteristic
557#97C2×D411yescharacteristic
558#97C2×D411yescharacteristic
559#97C2×D411yescharacteristic
560#97C2×D411yescharacteristic
561#97C2×D411yescharacteristic
562C4×C8—22no—
563C4×C8—22no—
564C4×C8—22no—
565C4×C8—22no—
566C4×C8—22no—
567C4×C8—22no—
568C4×C8—22no—
569C4×C8—22no—
570C4×C8C22×C414yes—
571C4×C8C2×D411yescharacteristic
572C4×C8C2×D411yescharacteristic
573C4×C8C2×D411yescharacteristic
574C4×C8C2×D411yescharacteristic
575C4×C8C2412yes—
576C4×C8C2412yes—
577C4×C8C2412yes—
578C4×C8C2412yes—
579C4×C8C2411yescharacteristic
580C4×C8C2411yescharacteristic
581C4×C8C2411yescharacteristic
582C4×C8C2411yescharacteristic
583C24—21no—
584C24C4×D411yescharacteristic
585#41—44no—
586#41—42no—
587#41—42no—
588#41—82no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—42no—
593C2×Q8C23×C412yes—
594C2×Q8C23×C412yes—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—42no—
604C2×D4—82no—
605C2×D4C23×C412yes—
606C2×D4C23×C412yes—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4C4×D411yescharacteristic
622C22×C4C4×D411yescharacteristic
623C22×C4C4×D411yescharacteristic
624C22×C4C4×D411yescharacteristic
625C22×C4C4×D411yescharacteristic
626C22×C4C4×D411yescharacteristic
627C22×C4C4×D411yescharacteristic
628C22×C4C4×D411yescharacteristic
629C22×C4C4×D411yescharacteristic
630C22×C4C23×C411yescharacteristic
631C22×C4C23×C411yescharacteristic
632C22×C4C23×C411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C2×#4111yescharacteristic
637C22×C4C2×#4111yescharacteristic
638C22×C4C2×#4111yescharacteristic
639Q16—44no—
640SD16—44no—
641SD16—44no—
642D8—44no—
643M16—41no—
644M16—41no—
645M16—41no—
646M16—41no—
647M16—41no—
648M16—41no—
649M16—41no—
650M16—41no—
651M16—44no—
652M16—44no—
653M16—44no—
654M16—44no—
655M16—42no—
656M16—42no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—44no—
668C2×C8—44no—
669C2×C8—44no—
670C2×C8—44no—
671C2×C8—44no—
672C2×C8—42no—
673C2×C8—42no—
674C2×C8—82no—
675C2×C8C23×C414yes—
676C2×C8C23×C414yes—
677C2×C8C22×D411yescharacteristic
678C2×C8C22×D411yescharacteristic
679C2×C8C22×D411yescharacteristic
680C2×C8C22×D411yescharacteristic
681C2×C8C22×D411yescharacteristic
682C2×C8C22×D411yescharacteristic
683C2×C8C22×D411yescharacteristic
684C2×C8C22×D411yescharacteristic
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4C23×C412yes—
706C4⋊C4C23×C412yes—
707C4⋊C4C23×C412yes—
708C4⋊C4C23×C412yes—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C42—22no—
729C42—22no—
730C42—22no—
731C42—22no—
732C42—22no—
733C42C4×D411yescharacteristic
734C42C4×D411yescharacteristic
735C42C4×D411yescharacteristic
736C42C4×D411yescharacteristic
737C42C4×D411yescharacteristic
738C42C4×D411yescharacteristic
739C42C23×C411yescharacteristic
740C42C23×C411yescharacteristic
741C42C23×C411yescharacteristic
742C42C22×D411yescharacteristic
743C42C22×D411yescharacteristic
744C42C22×D411yescharacteristic
745C42C2×#4111yescharacteristic
746C42C2×#4111yescharacteristic
747C42C2×#4111yescharacteristic
748C42C2511yescharacteristic
749C23—22no—
750C23—22no—
751C23—22no—
752C23—41no—
753C23—41no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23C2×C4×D411yescharacteristic
758C23C2×C4×D411yescharacteristic
759C23C2×C4×D411yescharacteristic
760Q8—22no—
761Q8—24no—
762Q8—22no—
763Q8—42no—
764Q8—42no—
765Q8—42no—
766D4—22no—
767D4—24no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—44no—
772D4—42no—
773D4—82no—
774D4—82no—
775D4—82no—
776D4—82no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4C2×C4×D411yescharacteristic
813C2×C4C2×C4×D411yescharacteristic
814C2×C4C2×C4×D411yescharacteristic
815C2×C4C2×C4×D411yescharacteristic
816C2×C4C2×C4×D411yescharacteristic
817C2×C4C2×C4×D411yescharacteristic
818C2×C4C2×C4×D411yescharacteristic
819C2×C4C2×C4×D411yescharacteristic
820C2×C4C2×C4×D411yescharacteristic
821C2×C4#57512yes—
822C2×C4#57512yes—
823C2×C4C24×C411yescharacteristic
824C2×C4C23×D411yescharacteristic
825C2×C4C22×#4111yescharacteristic
826C8—24no—
827C8—24no—
828C8—21no—
829C8—21no—
830C8—21no—
831C8—21no—
832C8—21no—
833C8—21no—
834C8—21no—
835C8—21no—
836C8—42no—
837C8—42no—
838C8—42no—
839C8—42no—
840C8—42no—
841C8—42no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—82no—
857C22—84no—
858C22#294312yes—
859C22C22×C4×D411yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4#294312yes—
876C4#357312yes—
877C4C2×#57511yescharacteristic
878C4C2×#57511yescharacteristic
879C2—22no—
880C2—41no—
881C2—41no—
882C2—82no—
883C2—82no—
884C2#6014211yescharacteristic
885C2C2×#294311yescharacteristic
886C2#6018211yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60942C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×M16 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60208C2semidirect
3. C2×#2969C2semidirect
4. #18075C2semidirect
5. #18074C2semidirect
6. #18005C2semidirect
7. #18002C2semidirect
8. #17936C2semidirect
9. #17935C2semidirect
10. #17934C2semidirect
11. #17933C2semidirect
12. #17908C2semidirect
13. #17907C2semidirect
14. #17906C2semidirect
15. #17905C2semidirect
16. #17803C2semidirect
17. #17487C2semidirect
18. #17458C2semidirect
19. #17319C2semidirect
37. #2971C22semidirect
39. #2970C22semidirect
50. #2969C22semidirect
51. #2969C22semidirect
73. #1594C22semidirect
74. #1593C22semidirect
75. #1592C22semidirect
76. #1592C22semidirect
77. #1588C22semidirect
78. #1588C22semidirect
79. #1587C22semidirect
80. #1587C22semidirect
81. #1586C22semidirect
82. #1586C22semidirect
83. #1585C22semidirect
84. #1585C22semidirect
85. #1580C22semidirect
86. #1579C22semidirect
87. SD16⋊C8C22semidirect
88. SD16⋊C8C22semidirect
89. #1572C22semidirect
94. #1564C22semidirect
101. #1482C22semidirect
106. #1476C22semidirect
111. #1451C22semidirect
112. #1451C22semidirect
113. #1451C22semidirect
114. #1451C22semidirect

Maximal subgroups

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

subgroupindex
#609422
#602082
C2×#29692
#180752
#180742
#180052
#180022
#179362
#179352
#179342
#179332
#179082
#179072
#179062
#179052
#178032
#174872
#174582
#173192