Finite Group Databasebeta

← #6345301

Subgroups — #6345301

Order 512.

1771 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60558C211yesmaximal, characteristic
2#60268C211yesmaximal, characteristic, complemented
3C2×#2974C211yesmaximal, characteristic, complemented
4#18052C214yesmaximal, complemented
5#18050C214yesmaximal, complemented
6#18020C214yesmaximal, complemented
7#18014C214yesmaximal, complemented
8#17935C211yesmaximal, characteristic, complemented
9#17933C211yesmaximal, characteristic, complemented
10#17930C211yesmaximal, characteristic, complemented
11#17928C211yesmaximal, characteristic, complemented
12#17907C211yesmaximal, characteristic, complemented
13#17905C211yesmaximal, characteristic, complemented
14#17902C211yesmaximal, characteristic, complemented
15#17900C211yesmaximal, characteristic, complemented
16#17822C211yesmaximal, characteristic, complemented
17#17488C211yesmaximal, characteristic, complemented
18C2×#1486C211yesmaximal, characteristic, complemented
19#17325C211yesmaximal, characteristic, complemented
20#3444C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22#3114C412yes—
23#3114C412yes—
24#3110C412yes—
25#3109C412yes—
26#3105C2214yes—
27#3101C2211yescharacteristic
28#3101C2211yescharacteristic
29#3100C2211yescharacteristic
30#3100C2211yescharacteristic
31#3092C412yes—
32#3077C412yes—
33#3036C412yes—
34#3003C412yes—
35#2994C2212yescomplemented
36#2994C2212yescomplemented
37#2993—21no—
38#2993—21no—
39#2991C2212yescomplemented
40#2990C2212yescomplemented
41#2989—21no—
42#2988—21no—
43#2974—21no—
44#2974—21no—
45#2974—21no—
46#2974—21no—
47#2974C2212yes—
48#2974C2212yes—
49#2974C2212yes—
50#2974C2212yes—
51#2960C2211yescharacteristic, complemented
52#2960C2211yescharacteristic, complemented
53C4×AGL(1,ℤ/8)C2214yes—
54#2933—21no—
55#2933—21no—
56#2931C2211yescharacteristic, complemented
57#2931C2211yescharacteristic, complemented
58C2×#436C2211yescharacteristic
59C2×#436C2211yescharacteristic
60C2×#435—21no—
61C2×#435—21no—
62C2×C8×D4C2211yescharacteristic
63C2×C8×D4C2211yescharacteristic
64#2925—21no—
65#2920C2211yescharacteristic
66C2×#432C2211yescharacteristic
67C2×#431C2211yescharacteristic
68C2×#431C2211yescharacteristic
69#2906—21no—
70C2×#423C2211yescharacteristic
71C2×#407—21no—
72C22×C22⋊C8—21no—
73#1594C2214yescomplemented
74#1592C2214yescomplemented
75#1590C2214yescomplemented
76#1589C2214yescomplemented
77#1588C2214yescomplemented
78#1586C2214yescomplemented
79#1586C2214yescomplemented
80#1585C2214yescomplemented
81#1583C2214yescomplemented
82#1582C2214yescomplemented
83#1581C2214yescomplemented
84#1581C2214yescomplemented
85#1580C2214yescomplemented
86SD16⋊C8C2214yescomplemented
87C8×SD16C2214yescomplemented
88C8×D8C2214yescomplemented
89#1573C2214yescomplemented
90#1571C2211yescharacteristic, complemented
91#1571C2211yescharacteristic, complemented
92#1570C2211yescharacteristic, complemented
93#1570C2211yescharacteristic, complemented
94#1569C2214yescomplemented
95#1494C2214yescomplemented
96#1488C2214yescomplemented
97#1486C2211yescharacteristic
98#1486C2211yescharacteristic
99#1486C2214yes—
100#1486C2211yescharacteristic
101#1486C2211yescharacteristic
102#1481C2211yescharacteristic, complemented
103#1481C2211yescharacteristic, complemented
104#1480C2211yescharacteristic, complemented
105#1480C2211yescharacteristic, complemented
106C2×D4⋊C8C2214yes—
107#1453C2212yescomplemented
108#1453C2212yescomplemented
109#1452C2211yescharacteristic, complemented
110#1452C2211yescharacteristic, complemented
111#1452C2212yescomplemented
112#1450C2211yescharacteristic, complemented
113#1450C2211yescharacteristic, complemented
114#1450C2212yescomplemented
115C23×D4C2×C411yescharacteristic
116C24×C4—21no—
117C2×AGL(1,ℤ/8)C2×C414yes—
118C2×#131—21no—
119C2×#131—21no—
120C22×M16—21no—
121C22×M16—21no—
122C22×M16—21no—
123C23×C8—21no—
124C23×C8—21no—
125#533C2×C411yescharacteristic
126#533C2×C411yescharacteristic
127#533C2311yescharacteristic
128#532C2×C411yescharacteristic
129#532C2×C411yescharacteristic
130#532C2311yescharacteristic
131#529—21no—
132#529—21no—
133#529—21no—
134#529—21no—
135#529C2×C412yes—
136#529C2312yes—
137#525—21no—
138#525—21no—
139#525C2×C412yes—
140C4×#41—21no—
141C4×#41—21no—
142C4×#41C2312yes—
143C2×C4×D4—21no—
144C2×C4×D4—21no—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4C2×C412yes—
150C2×C4×D4C2×C412yes—
151C2×C4×D4C2×C411yescharacteristic
152C2×C4×D4C2×C411yescharacteristic
153C2×C4×D4C2311yescharacteristic
154C2×C4×D4C2311yescharacteristic
155C2×C4×D4C2312yes—
156C2×C4×D4C2312yes—
157C22×C4⋊C4C2×C411yescharacteristic
158C22×C22⋊C4—21no—
159C22×C42C2311yescharacteristic
160#484C2×C414yes—
161#483C2×C412yes—
162#483C2×C412yes—
163#481C2×C414yes—
164#480C2×C412yes—
165#480C2×C412yes—
166#478C2×C414yes—
167#478C2×C414yes—
168#476C2×C412yes—
169#476C2×C412yes—
170#474C2×C412yes—
171#474C2×C412yes—
172#463C2×C414yes—
173#463C2×C414yes—
174#461C2×C412yes—
175#461C2×C412yes—
176#459C2×C412yes—
177#459C2×C412yes—
178#450C2×C412yes—
179#450C2×C412yes—
180#450C2×C414yes—
181#447C2×C412yes—
182#447C2×C412yes—
183#447C2×C414yes—
184#446—21no—
185#446—21no—
186#446C2312yescomplemented
187#446C2312yescomplemented
188C8×Q8—21no—
189C8×Q8—21no—
190C8×Q8C2312yescomplemented
191C8×Q8C2312yescomplemented
192#442C2×C414yes—
193#442C2×C414yes—
194#440C2×C414yes—
195#440C2×C414yes—
196C4×SD16C2314yes—
197C4×SD16C2314yes—
198C4×D8C2314yes—
199C4×D8C2314yes—
200#436—22no—
201#436—22no—
202#436—21no—
203#436—21no—
204#436—21no—
205#436—21no—
206#436—21no—
207#436—21no—
208#436C2312yes—
209#436C2312yes—
210#436C2312yes—
211#436C2312yes—
212#436C2312yescomplemented
213#436C2312yescomplemented
214#435—22no—
215#435—22no—
216#435—22no—
217#435—22no—
218#435—22no—
219#435—22no—
220#435—22no—
221#435—22no—
222#435—22no—
223#435—22no—
224#435—22no—
225#435—22no—
226C8×D4—22no—
227C8×D4—22no—
228C8×D4—21no—
229C8×D4—21no—
230C8×D4—21no—
231C8×D4—21no—
232C8×D4—21no—
233C8×D4—21no—
234C8×D4C2312yes—
235C8×D4C2312yes—
236C8×D4C2312yes—
237C8×D4C2312yes—
238C8×D4C2312yescomplemented
239C8×D4C2312yescomplemented
240#433—22no—
241#433—22no—
242#432—21no—
243#432—21no—
244#432—22no—
245#432C2×C412yes—
246#432C2×C412yes—
247#432C2312yes—
248#432C2312yes—
249#431—21no—
250#431—21no—
251#431—22no—
252#431D411yescharacteristic
253#431D411yescharacteristic
254#431D411yescharacteristic
255#431D411yescharacteristic
256#431C2311yescharacteristic
257#431C2311yescharacteristic
258#431C2312yes—
259#431C2311yescharacteristic
260#431C2311yescharacteristic
261#431C2312yes—
262#431C2311yescharacteristic
263#431C2311yescharacteristic
264#431C2311yescharacteristic
265#431C2311yescharacteristic
266#428C2×C414yes—
267#424—21no—
268#424—21no—
269#424—22no—
270#424—22no—
271#423—21no—
272#423—21no—
273#423—22no—
274#423C2×C412yes—
275#423C2312yes—
276#423C2311yescharacteristic
277#423C2311yescharacteristic
278C2×C4⋊C8—21no—
279C2×C4⋊C8—21no—
280C2×C4⋊C8—22no—
281C2×C4⋊C8D411yescharacteristic
282C2×C4⋊C8D411yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2312yes—
286#418C2×C414yes—
287#417C2×C414yes—
288#408—21no—
289#408—21no—
290#407—22no—
291#407—22no—
292#407—22no—
293#407—22no—
294#407C2×C412yes—
295C2×C22⋊C8—21no—
296C2×C22⋊C8—21no—
297C2×C22⋊C8—21no—
298C2×C22⋊C8—21no—
299C2×C22⋊C8—21no—
300C2×C22⋊C8—21no—
301C2×C22⋊C8—22no—
302C2×C22⋊C8—22no—
303C2×C22⋊C8—22no—
304C2×C22⋊C8—22no—
305C2×C22⋊C8D411yescharacteristic
306C2×C22⋊C8D411yescharacteristic
307#405—21no—
308#405—21no—
309C4×M16C2312yes—
310C2×#97—21no—
311C2×C4×C8C2312yes—
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#335C2314yescomplemented
315#335C2314yescomplemented
316#334C2314yescomplemented
317#334C2314yescomplemented
318Q8⋊C8C2314yescomplemented
319Q8⋊C8C2314yescomplemented
320D4⋊C8C2314yes—
321D4⋊C8C2314yes—
322D4⋊C8C2314yes—
323D4⋊C8C2314yes—
324D4⋊C8C2314yescomplemented
325D4⋊C8C2314yescomplemented
326#322C2312yescomplemented
327#322C2312yescomplemented
328#322C2312yescomplemented
329#322C2312yescomplemented
330#322C2312yescomplemented
331#322C2312yescomplemented
332C82C2312yescomplemented
333C82C2312yescomplemented
334C25—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41C22×C412yes—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—44no—
342C22×D4C22×C411yescharacteristic
343C22×D4C22×C412yes—
344C22×D4C22×C412yes—
345C22×D4C22×C411yescharacteristic
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—82no—
356C23×C4—82no—
357C23×C4C22×C411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4#4111yescharacteristic
360AGL(1,ℤ/8)—48no—
361C2×SD16C22×C414yes—
362C2×SD16C22×C414yes—
363C2×D8C22×C414yes—
364C2×D8C22×C414yes—
365#131—82no—
366#131—82no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—22no—
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—82no—
377C2×M16—82no—
378C2×M16—82no—
379C2×M16C22×C414yes—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—22no—
383C22×C8—22no—
384C22×C8—22no—
385C22×C8—22no—
386C22×C8—22no—
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—82no—
391C22×C8—82no—
392C22×C8C2×D411yescharacteristic
393C22×C8C2×D411yescharacteristic
394C22×C8C2×D411yescharacteristic
395C22×C8C2×D411yescharacteristic
396C4⋊Q8C22×C411yescharacteristic
397C4⋊Q8C22×C411yescharacteristic
398C4⋊Q8C22×C411yescharacteristic
399#127C22×C411yescharacteristic
400#126—22no—
401#126—22no—
402#125—21no—
403#125—21no—
404#125C22×C412yes—
405#124—21no—
406#124—21no—
407#124C22×C412yes—
408#123—22no—
409#123—22no—
410#123—22no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8C22×C412yes—
416C22⋊Q8C22×C412yes—
417#121—21no—
418#121—21no—
419#121—21no—
420#121—21no—
421#121C22×C412yes—
422#121C22×C412yes—
423#120—22no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8C22×C412yes—
429C4×Q8C2412yes—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4C22×C412yes—
457C4×D4C22×C412yes—
458C4×D4C22×C412yes—
459C4×D4C22×C412yes—
460C4×D4C22×C412yes—
461C4×D4C22×C412yes—
462C4×D4C22×C412yes—
463C4×D4C2412yes—
464C4×D4C2412yes—
465C4×D4C2412yes—
466#117—21no—
467#117—21no—
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⋊C4C22×C412yes—
476C2×C4⋊C4C22×C411yescharacteristic
477C2×C4⋊C4C22×C411yescharacteristic
478C2×C4⋊C4C22×C412yes—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C42—22no—
488C2×C42C22×C411yescharacteristic
489C2×C42C22×C411yescharacteristic
490C2×C42C22×C411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D411yescharacteristic
494C2×C42#4111yescharacteristic
495C2×C42#4111yescharacteristic
496C2×C42#4111yescharacteristic
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500#107C22×C414yes—
501#107C22×C414yes—
502#106C22×C414yes—
503#106C22×C414yes—
504C4⋊C8—22no—
505C4⋊C8—22no—
506C4⋊C8—22no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—22no—
512C4⋊C8—21no—
513C4⋊C8—21no—
514C4⋊C8—22no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8C22×C412yes—
518C4⋊C8C22×C412yes—
519C4⋊C8C22×C414yes—
520C4⋊C8C2×D411yescharacteristic
521C4⋊C8C2×D411yescharacteristic
522C4⋊C8C2×D411yescharacteristic
523C4⋊C8C2×D411yescharacteristic
524C4⋊C8C2×D411yescharacteristic
525C4⋊C8C2×D411yescharacteristic
526C4⋊C8C2×D411yescharacteristic
527C4⋊C8C2×D411yescharacteristic
528C4⋊C8C2412yes—
529C4⋊C8C2412yes—
530C4⋊C8C2412yes—
531C4⋊C8C2412yes—
532#103C22×C414yes—
533#103C22×C414yes—
534#102C22×C414yes—
535#102C22×C414yes—
536#102C22×C414yes—
537#102C22×C414yes—
538#102C22×C414yes—
539#102C22×C414yes—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—21no—
544C22⋊C8—21no—
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—22no—
556C22⋊C8—22no—
557C22⋊C8C22×C412yes—
558C22⋊C8C22×C412yes—
559C22⋊C8C22×C414yes—
560C22⋊C8C2×D411yescharacteristic
561C22⋊C8C2×D411yescharacteristic
562C22⋊C8C2×D411yescharacteristic
563C22⋊C8C2×D411yescharacteristic
564C22⋊C8C2×D411yescharacteristic
565C22⋊C8C2×D411yescharacteristic
566C22⋊C8C2×D411yescharacteristic
567C22⋊C8C2×D411yescharacteristic
568#97—22no—
569#97—22no—
570#97—22no—
571#97—22no—
572#97C22×C414yes—
573C4×C8—22no—
574C4×C8—22no—
575C4×C8—22no—
576C4×C8C2×D411yescharacteristic
577C4×C8C2×D411yescharacteristic
578C4×C8C2×D411yescharacteristic
579C4×C8C2×D411yescharacteristic
580C4×C8C2412yes—
581C4×C8C2412yes—
582C4×C8C2412yes—
583C4×C8C2412yes—
584C4×C8C2411yescharacteristic
585C4×C8C2411yescharacteristic
586C4×C8C2411yescharacteristic
587C4×C8C2411yescharacteristic
588C24—21no—
589C24—21no—
590C24—22no—
591C24—22no—
592C24—44no—
593C24—44no—
594C24—82no—
595C24C4×D411yescharacteristic
596#41—44no—
597#41—44no—
598#41—42no—
599#41—42no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8C23×C412yes—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—44no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4C23×C412yes—
622C2×D4C23×C412yes—
623C2×D4C23×C412yes—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—84no—
648C22×C4—84no—
649C22×C4—82no—
650C22×C4—82no—
651C22×C4—82no—
652C22×C4—82no—
653C22×C4—82no—
654C22×C4—82no—
655C22×C4—82no—
656C22×C4C4×D411yescharacteristic
657C22×C4C4×D411yescharacteristic
658C22×C4C4×D411yescharacteristic
659C22×C4C4×D411yescharacteristic
660C22×C4C4×D411yescharacteristic
661C22×C4C4×D411yescharacteristic
662C22×C4C4×D411yescharacteristic
663C22×C4C4×D411yescharacteristic
664C22×C4C4×D411yescharacteristic
665C22×C4C23×C411yescharacteristic
666C22×C4C23×C411yescharacteristic
667C22×C4C23×C411yescharacteristic
668C22×C4C22×D411yescharacteristic
669C22×C4C22×D411yescharacteristic
670C22×C4C22×D411yescharacteristic
671C22×C4C2×#4111yescharacteristic
672C22×C4C2×#4111yescharacteristic
673C22×C4C2×#4111yescharacteristic
674SD16—28no—
675SD16—44no—
676D8—28no—
677D8—44no—
678M16—44no—
679M16—42no—
680M16—42no—
681M16—82no—
682M16—82no—
683M16—82no—
684M16—82no—
685M16—82no—
686M16—82no—
687M16—82no—
688C2×C8—22no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—22no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—22no—
697C2×C8—22no—
698C2×C8—44no—
699C2×C8—42no—
700C2×C8—42no—
701C2×C8—82no—
702C2×C8—82no—
703C2×C8—82no—
704C2×C8—82no—
705C2×C8—82no—
706C2×C8—82no—
707C2×C8—82no—
708C2×C8C23×C414yes—
709C2×C8C23×C414yes—
710C2×C8C22×D411yescharacteristic
711C2×C8C22×D411yescharacteristic
712C2×C8C22×D411yescharacteristic
713C2×C8C22×D411yescharacteristic
714C2×C8C22×D411yescharacteristic
715C2×C8C22×D411yescharacteristic
716C2×C8C22×D411yescharacteristic
717C2×C8C22×D411yescharacteristic
718C4⋊C4—22no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—22no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—22no—
732C4⋊C4C23×C412yes—
733C4⋊C4C23×C412yes—
734C4⋊C4C23×C412yes—
735C4⋊C4C23×C412yes—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42C4×D411yescharacteristic
757C42C4×D411yescharacteristic
758C42C4×D411yescharacteristic
759C42C4×D411yescharacteristic
760C42C4×D411yescharacteristic
761C42C4×D411yescharacteristic
762C42C23×C411yescharacteristic
763C42C23×C411yescharacteristic
764C42C23×C411yescharacteristic
765C42C22×D411yescharacteristic
766C42C22×D411yescharacteristic
767C42C22×D411yescharacteristic
768C42C2×#4111yescharacteristic
769C42C2×#4111yescharacteristic
770C42C2×#4111yescharacteristic
771C42C2511yescharacteristic
772C23—24no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—44no—
780C23—44no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—44no—
785C23—42no—
786C23—42no—
787C23—44no—
788C23—82no—
789C23—82no—
790C23—816no—
791C23C2×C4×D411yescharacteristic
792C23C2×C4×D411yescharacteristic
793C23C2×C4×D411yescharacteristic
794Q8—24no—
795Q8—42no—
796Q8—42no—
797D4—24no—
798D4—22no—
799D4—24no—
800D4—22no—
801D4—22no—
802D4—44no—
803D4—44no—
804D4—42no—
805D4—42no—
806D4—44no—
807D4—44no—
808D4—42no—
809D4—82no—
810D4#56814yes—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—44no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—82no—
847C2×C4—82no—
848C2×C4—82no—
849C2×C4—82no—
850C2×C4—82no—
851C2×C4—82no—
852C2×C4—82no—
853C2×C4C2×C4×D411yescharacteristic
854C2×C4C2×C4×D411yescharacteristic
855C2×C4C2×C4×D411yescharacteristic
856C2×C4C2×C4×D411yescharacteristic
857C2×C4C2×C4×D411yescharacteristic
858C2×C4C2×C4×D411yescharacteristic
859C2×C4C2×C4×D411yescharacteristic
860C2×C4C2×C4×D411yescharacteristic
861C2×C4C2×C4×D411yescharacteristic
862C2×C4#57612yes—
863C2×C4#57712yes—
864C2×C4C24×C411yescharacteristic
865C2×C4C23×D411yescharacteristic
866C2×C4C22×#4111yescharacteristic
867C8—24no—
868C8—24no—
869C8—21no—
870C8—21no—
871C8—21no—
872C8—21no—
873C8—21no—
874C8—21no—
875C8—21no—
876C8—21no—
877C8—42no—
878C8—42no—
879C8—42no—
880C8—42no—
881C8—42no—
882C8—42no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—21no—
889C22—24no—
890C22—21no—
891C22—44no—
892C22—48no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—88no—
902C22—84no—
903C22—88no—
904C22#294612yes—
905C22#295512yes—
906C22C22×C4×D411yescharacteristic
907C4—21no—
908C4—21no—
909C4—21no—
910C4—21no—
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—42no—
917C4—42no—
918C4—42no—
919C4—42no—
920C4—42no—
921C4#294612yes—
922C4C2×#56812yes—
923C4C2×#57611yescharacteristic
924C4C2×#57711yescharacteristic
925C2—22no—
926C2—22no—
927C2—41no—
928C2—44no—
929C2—82no—
930C2—82no—
931C2#6014111yescharacteristic
932C2C2×#294611yescharacteristic
933C2C2×#295511yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60558C2
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×#2974C2semidirect
4. #18052C2semidirect
5. #18050C2semidirect
6. #18020C2semidirect
7. #18014C2semidirect
8. #17935C2semidirect
9. #17933C2semidirect
10. #17930C2semidirect
11. #17928C2semidirect
12. #17907C2semidirect
13. #17905C2semidirect
14. #17902C2semidirect
15. #17900C2semidirect
16. #17822C2semidirect
17. #17488C2semidirect
18. C2×#1486C2semidirect
19. #17325C2semidirect
35. #2994C22semidirect
36. #2994C22semidirect
39. #2991C22semidirect
40. #2990C22semidirect
51. #2960C22semidirect
52. #2960C22semidirect
56. #2931C22semidirect
57. #2931C22semidirect
73. #1594C22semidirect
74. #1592C22semidirect
75. #1590C22semidirect
76. #1589C22semidirect
77. #1588C22semidirect
78. #1586C22semidirect
79. #1586C22semidirect
80. #1585C22semidirect
81. #1583C22semidirect
82. #1582C22semidirect
83. #1581C22semidirect
84. #1581C22semidirect
85. #1580C22semidirect
86. SD16⋊C8C22semidirect
87. C8×SD16C22semidirect
88. C8×D8C22semidirect
89. #1573C22semidirect
90. #1571C22semidirect
91. #1571C22semidirect
92. #1570C22semidirect
93. #1570C22semidirect
94. #1569C22semidirect
95. #1494C22semidirect
96. #1488C22semidirect
102. #1481C22semidirect
103. #1481C22semidirect
104. #1480C22semidirect
105. #1480C22semidirect
107. #1453C22semidirect
108. #1453C22semidirect
109. #1452C22semidirect
110. #1452C22semidirect
111. #1452C22semidirect
112. #1450C22semidirect
113. #1450C22semidirect
114. #1450C22semidirect
186. #446C23semidirect
187. #446C23semidirect
190. C8×Q8C23semidirect
191. C8×Q8C23semidirect
212. #436C23semidirect
213. #436C23semidirect
238. C8×D4C23semidirect
239. C8×D4C23semidirect
314. #335C23semidirect
315. #335C23semidirect
316. #334C23semidirect
317. #334C23semidirect
318. Q8⋊C8C23semidirect
319. Q8⋊C8C23semidirect
324. D4⋊C8C23semidirect
325. D4⋊C8C23semidirect
326. #322C23semidirect
327. #322C23semidirect
328. #322C23semidirect
329. #322C23semidirect
330. #322C23semidirect
331. #322C23semidirect
332. C82C23semidirect
333. C82C23semidirect

Maximal subgroups

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

subgroupindex
#605582
#602682
C2×#29742
#180522
#180502
#180202
#180142
#179352
#179332
#179302
#179282
#179072
#179052
#179022
#179002
#178222
#174882
C2×#14862
#173252