Finite Group Databasebeta

← #6345217

Subgroups — #6345217

Order 512.

1565 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60942C211yesmaximal, characteristic
2#60268C211yesmaximal, characteristic, complemented
3C2×#2993C211yesmaximal, characteristic, complemented
4#17992C214yesmaximal, complemented
5#17973C214yesmaximal, complemented
6#17954C214yesmaximal, complemented
7#17936C211yesmaximal, characteristic, complemented
8#17933C211yesmaximal, characteristic, complemented
9#17931C211yesmaximal, characteristic, complemented
10#17928C211yesmaximal, characteristic, complemented
11#17926C214yesmaximal, complemented
12#17908C211yesmaximal, characteristic, complemented
13#17905C211yesmaximal, characteristic, complemented
14#17903C211yesmaximal, characteristic, complemented
15#17900C211yesmaximal, characteristic, complemented
16#17814C211yesmaximal, characteristic, complemented
17#17498C211yesmaximal, characteristic, complemented
18#17492C211yesmaximal, characteristic, complemented
19#17325C211yesmaximal, 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#2994—21no—
37#2994—21no—
38#2993—21no—
39#2993—21no—
40#2993—21no—
41#2993—21no—
42#2993C2212yes—
43#2993C2212yes—
44#2993C2212yes—
45#2993C2212yes—
46#2993C2212yescomplemented
47#2993C2212yescomplemented
48#2991—21no—
49#2990—21no—
50#2989C2212yescomplemented
51#2988C2212yescomplemented
52#2960C2211yescharacteristic
53#2960C2211yescharacteristic
54C2×#446C2211yescharacteristic
55C2×C8×Q8C2211yescharacteristic
56#2933—21no—
57#2933—21no—
58#2931C2211yescharacteristic
59#2931C2211yescharacteristic
60C2×#436—21no—
61C2×#436C2211yescharacteristic
62C2×#435—21no—
63C2×C8×D4C2211yescharacteristic
64#2925—21no—
65#2920C2211yescharacteristic
66C2×#433—21no—
67C2×#431C2211yescharacteristic
68C2×#431C2211yescharacteristic
69#2906—21no—
70C2×#424—21no—
71C2×#423C2211yescharacteristic
72C2×#423C2211yescharacteristic
73#1592C2214yescomplemented
74#1592C2214yescomplemented
75#1591C2214yescomplemented
76#1589C2214yescomplemented
77#1588C2214yescomplemented
78#1588C2214yescomplemented
79#1585C2214yescomplemented
80#1585C2214yescomplemented
81#1584C2214yescomplemented
82#1584C2214yescomplemented
83#1581C2214yescomplemented
84#1581C2214yescomplemented
85SD16⋊C8C2214yescomplemented
86SD16⋊C8C2214yescomplemented
87C8×Q16C2214yescomplemented
88C8×D8C2214yescomplemented
89#1571C2211yescharacteristic
90#1571C2211yescharacteristic
91#1571C2211yescharacteristic
92#1571C2211yescharacteristic
93#1571C2214yescomplemented
94#1567C2214yescomplemented
95#1495C2214yes—
96#1495C2214yescomplemented
97#1489C2214yescomplemented
98#1487C2211yescharacteristic
99#1487C2211yescharacteristic
100#1486C2211yescharacteristic
101#1486C2211yescharacteristic
102#1483C2214yes—
103#1481C2211yescharacteristic
104#1481C2211yescharacteristic
105#1480C2211yescharacteristic
106#1480C2211yescharacteristic
107#1453C2212yescomplemented
108#1453C2212yescomplemented
109#1452C2211yescharacteristic
110#1452C2211yescharacteristic
111#1452C2212yescomplemented
112#1450C2211yescharacteristic
113#1450C2211yescharacteristic
114#1450C2212yescomplemented
115C2×#131—21no—
116C2×#131—21no—
117C22×M16—21no—
118C22×M16—21no—
119C22×M16—21no—
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—21no—
217#436—21no—
218#436—21no—
219#436—21no—
220#436C2312yes—
221#436C2312yes—
222#436C2312yes—
223#436C2312yes—
224#435—22no—
225#435—22no—
226#435—22no—
227#435—22no—
228#435—22no—
229#435—22no—
230#435—22no—
231#435—22no—
232C8×D4—22no—
233C8×D4—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—21no—
250#432—22no—
251#431—22no—
252#431C2×C412yes—
253#431C2×C412yes—
254#431D411yescharacteristic
255#431D411yescharacteristic
256#431D411yescharacteristic
257#431D411yescharacteristic
258#431C2311yescharacteristic
259#431C2311yescharacteristic
260#431C2312yes—
261#431C2311yescharacteristic
262#431C2311yescharacteristic
263#431C2312yes—
264#431C2311yescharacteristic
265#431C2311yescharacteristic
266#431C2311yescharacteristic
267#431C2311yescharacteristic
268#424—21no—
269#424—21no—
270#424—22no—
271#424—22no—
272#424—22no—
273#424—22no—
274#424—22no—
275#424—22no—
276#423—21no—
277#423—21no—
278#423—21no—
279#423—21no—
280#423—21no—
281#423—22no—
282#423C2312yes—
283#423C2312yes—
284#423C2311yescharacteristic
285#423C2311yescharacteristic
286#423C2312yes—
287C2×C4⋊C8—21no—
288C2×C4⋊C8—21no—
289C2×C4⋊C8—21no—
290C2×C4⋊C8—21no—
291C2×C4⋊C8—22no—
292C2×C4⋊C8C2×C412yes—
293C2×C4⋊C8D411yescharacteristic
294C2×C4⋊C8D411yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×C4⋊C8C2311yescharacteristic
297C2×C4⋊C8C2312yes—
298#408—21no—
299#408—21no—
300#407—21no—
301C2×C22⋊C8—21no—
302C2×C22⋊C8—21no—
303C2×C22⋊C8C2×C412yes—
304C2×C22⋊C8D411yescharacteristic
305C2×C22⋊C8D411yescharacteristic
306#405—21no—
307#405—21no—
308C4×M16C2312yes—
309C2×#97—21no—
310C2×C4×C8—21no—
311C2×C4×C8C2312yes—
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#335C2314yes—
315#335C2314yes—
316#335C2314yes—
317#335C2314yes—
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—
332C82C2312yes—
333C82C2312yes—
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—82no—
349#131—82no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—22no—
360C2×M16—82no—
361C2×M16—82no—
362C2×M16—82no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—82no—
371C22×C8C22×C414yes—
372C22×C8C2×D411yescharacteristic
373C22×C8C2×D411yescharacteristic
374C22×C8C2×D411yescharacteristic
375C22×C8C2×D411yescharacteristic
376C4⋊Q8C22×C411yescharacteristic
377C4⋊Q8C22×C411yescharacteristic
378C4⋊Q8C22×C411yescharacteristic
379#127C22×C411yescharacteristic
380#126—22no—
381#126—22no—
382#126—22no—
383#126—22no—
384#126—22no—
385#126—22no—
386#125—21no—
387#125—21no—
388#125—21no—
389#125—21no—
390#125C22×C412yes—
391#125C22×C412yes—
392#125C22×C412yes—
393#124—21no—
394#124—21no—
395#124—21no—
396#124—21no—
397#124C22×C412yes—
398#124C22×C412yes—
399#124C22×C412yes—
400#123—22no—
401#123—22no—
402#123—22no—
403#123—22no—
404#123—22no—
405#123—22no—
406#123—22no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8C22×C412yes—
414C22⋊Q8C22×C412yes—
415C22⋊Q8C22×C412yes—
416C22⋊Q8C22×C412yes—
417#121—21no—
418#121—21no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121—21no—
423#121C22×C412yes—
424#121C22×C412yes—
425#121C22×C412yes—
426#121C22×C412yes—
427#120—22no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×Q8—21no—
434C4×Q8C22×C412yes—
435C4×Q8C22×C412yes—
436C4×Q8C2412yes—
437C4×Q8C2412yes—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4C22×C412yes—
455C4×D4C22×C412yes—
456C4×D4C2412yes—
457C4×D4C2412yes—
458#117—21no—
459#117—21no—
460#117—22no—
461#117—22no—
462#117—22no—
463#117—22no—
464#117—22no—
465#117—22no—
466#117—22no—
467#117C22×C412yes—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4C22×C411yescharacteristic
473C2×C4⋊C4C22×C411yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C42—21no—
480C2×C42—22no—
481C2×C42C22×C411yescharacteristic
482C2×C42C22×C411yescharacteristic
483C2×C42C22×C411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
487C2×C42#4111yescharacteristic
488C2×C42#4111yescharacteristic
489C2×C42#4111yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493#107C22×C414yes—
494#107C22×C414yes—
495#106C22×C414yes—
496#106C22×C414yes—
497C4⋊C8—22no—
498C4⋊C8—22no—
499C4⋊C8—22no—
500C4⋊C8—22no—
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⋊C8C2×D411yescharacteristic
520C4⋊C8C2×D411yescharacteristic
521C4⋊C8C2×D411yescharacteristic
522C4⋊C8C2×D411yescharacteristic
523C4⋊C8C2×D411yescharacteristic
524C4⋊C8C2×D411yescharacteristic
525C4⋊C8C2×D411yescharacteristic
526C4⋊C8C2×D411yescharacteristic
527C4⋊C8C2412yes—
528C4⋊C8C2412yes—
529C4⋊C8C2412yes—
530C4⋊C8C2412yes—
531#103C22×C414yes—
532#103C22×C414yes—
533#103C22×C414yes—
534#103C22×C414yes—
535#102C22×C414yes—
536#102C22×C414yes—
537#102C22×C414yes—
538#102C22×C414yes—
539C22⋊C8—21no—
540C22⋊C8—21no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—22no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8C22×C412yes—
551C22⋊C8C22×C412yes—
552C22⋊C8C22×C414yes—
553C22⋊C8C2×D411yescharacteristic
554C22⋊C8C2×D411yescharacteristic
555C22⋊C8C2×D411yescharacteristic
556C22⋊C8C2×D411yescharacteristic
557C22⋊C8C2×D411yescharacteristic
558C22⋊C8C2×D411yescharacteristic
559C22⋊C8C2×D411yescharacteristic
560C22⋊C8C2×D411yescharacteristic
561#97—22no—
562#97—22no—
563#97—22no—
564#97—22no—
565#97—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—42no—
644M16—42no—
645M16—82no—
646M16—82no—
647M16—82no—
648M16—82no—
649M16—82no—
650M16—82no—
651M16—82no—
652M16—82no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8—42no—
665C2×C8—42no—
666C2×C8—82no—
667C2×C8—82no—
668C2×C8—82no—
669C2×C8—82no—
670C2×C8—82no—
671C2×C8C23×C414yes—
672C2×C8C23×C414yes—
673C2×C8C22×D411yescharacteristic
674C2×C8C22×D411yescharacteristic
675C2×C8C22×D411yescharacteristic
676C2×C8C22×D411yescharacteristic
677C2×C8C22×D411yescharacteristic
678C2×C8C22×D411yescharacteristic
679C2×C8C22×D411yescharacteristic
680C2×C8C22×D411yescharacteristic
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4C23×C412yes—
702C4⋊C4C23×C412yes—
703C4⋊C4C23×C412yes—
704C4⋊C4C23×C412yes—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
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—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—22no—
728C42—22no—
729C42C4×D411yescharacteristic
730C42C4×D411yescharacteristic
731C42C4×D411yescharacteristic
732C42C4×D411yescharacteristic
733C42C4×D411yescharacteristic
734C42C4×D411yescharacteristic
735C42C23×C411yescharacteristic
736C42C23×C411yescharacteristic
737C42C23×C411yescharacteristic
738C42C22×D411yescharacteristic
739C42C22×D411yescharacteristic
740C42C22×D411yescharacteristic
741C42C2×#4111yescharacteristic
742C42C2×#4111yescharacteristic
743C42C2×#4111yescharacteristic
744C42C2511yescharacteristic
745C23—22no—
746C23—22no—
747C23—22no—
748C23—41no—
749C23—41no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23C2×C4×D411yescharacteristic
754C23C2×C4×D411yescharacteristic
755C23C2×C4×D411yescharacteristic
756Q8—22no—
757Q8—24no—
758Q8—22no—
759Q8—42no—
760Q8—42no—
761Q8—42no—
762D4—22no—
763D4—24no—
764D4—22no—
765D4—42no—
766D4—42no—
767D4—44no—
768D4—44no—
769D4—42no—
770D4—82no—
771D4—82no—
772D4—82no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—82no—
808C2×C4C2×C4×D411yescharacteristic
809C2×C4C2×C4×D411yescharacteristic
810C2×C4C2×C4×D411yescharacteristic
811C2×C4C2×C4×D411yescharacteristic
812C2×C4C2×C4×D411yescharacteristic
813C2×C4C2×C4×D411yescharacteristic
814C2×C4C2×C4×D411yescharacteristic
815C2×C4C2×C4×D411yescharacteristic
816C2×C4C2×C4×D411yescharacteristic
817C2×C4#57612yes—
818C2×C4#57812yes—
819C2×C4C24×C411yescharacteristic
820C2×C4C23×D411yescharacteristic
821C2×C4C22×#4111yescharacteristic
822C8—24no—
823C8—24no—
824C8—21no—
825C8—21no—
826C8—21no—
827C8—21no—
828C8—21no—
829C8—21no—
830C8—21no—
831C8—21no—
832C8—42no—
833C8—42no—
834C8—42no—
835C8—42no—
836C8—42no—
837C8—42no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—82no—
853C22—84no—
854C22#295112yes—
855C22C22×C4×D411yescharacteristic
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4#295112yes—
872C4#357312yes—
873C4C2×#57611yescharacteristic
874C4C2×#57811yescharacteristic
875C2—22no—
876C2—41no—
877C2—41no—
878C2—82no—
879C2—82no—
880C2#6014011yescharacteristic
881C2C2×#295111yescharacteristic
882C2#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×#431 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60268C2semidirect
3. C2×#2993C2semidirect
4. #17992C2semidirect
5. #17973C2semidirect
6. #17954C2semidirect
7. #17936C2semidirect
8. #17933C2semidirect
9. #17931C2semidirect
10. #17928C2semidirect
11. #17926C2semidirect
12. #17908C2semidirect
13. #17905C2semidirect
14. #17903C2semidirect
15. #17900C2semidirect
16. #17814C2semidirect
17. #17498C2semidirect
18. #17492C2semidirect
19. #17325C2semidirect
46. #2993C22semidirect
47. #2993C22semidirect
50. #2989C22semidirect
51. #2988C22semidirect
73. #1592C22semidirect
74. #1592C22semidirect
75. #1591C22semidirect
76. #1589C22semidirect
77. #1588C22semidirect
78. #1588C22semidirect
79. #1585C22semidirect
80. #1585C22semidirect
81. #1584C22semidirect
82. #1584C22semidirect
83. #1581C22semidirect
84. #1581C22semidirect
85. SD16⋊C8C22semidirect
86. SD16⋊C8C22semidirect
87. C8×Q16C22semidirect
88. C8×D8C22semidirect
93. #1571C22semidirect
94. #1567C22semidirect
96. #1495C22semidirect
97. #1489C22semidirect
107. #1453C22semidirect
108. #1453C22semidirect
111. #1452C22semidirect
114. #1450C22semidirect

Maximal subgroups

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

subgroupindex
#609422
#602682
C2×#29932
#179922
#179732
#179542
#179362
#179332
#179312
#179282
#179262
#179082
#179052
#179032
#179002
#178142
#174982
#174922
#173252