Finite Group Databasebeta

← #6345241

Subgroups — #6345241

Order 512.

1644 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60946C211yesmaximal, characteristic
2#60268C211yesmaximal, characteristic, complemented
3#60236C211yesmaximal, characteristic, complemented
4#17981C211yesmaximal, characteristic, complemented
5#17979C211yesmaximal, characteristic, complemented
6#17976C211yesmaximal, characteristic, complemented
7#17975C211yesmaximal, characteristic, complemented
8#17962C211yesmaximal, characteristic, complemented
9#17960C211yesmaximal, characteristic, complemented
10#17957C211yesmaximal, characteristic, complemented
11#17956C211yesmaximal, characteristic, complemented
12#17948C214yesmaximal, complemented
13#17946C214yesmaximal, complemented
14#17920C214yesmaximal, complemented
15#17918C214yesmaximal, complemented
16#17817C211yesmaximal, characteristic, complemented
17#17489C211yesmaximal, characteristic, complemented
18#17485C211yesmaximal, characteristic, complemented
19C2×#1454C211yesmaximal, characteristic, complemented
20#3444C2211yescharacteristic
21C2×#532C2211yescharacteristic
22#3247C414yes—
23#3230C411yescharacteristic
24#3228C411yescharacteristic
25#3228C411yescharacteristic
26#3227C411yescharacteristic
27#3208C411yescharacteristic
28#3207C411yescharacteristic
29#3207C411yescharacteristic
30#3205C411yescharacteristic
31#3188C414yes—
32#3169C2211yescharacteristic
33#3169C2211yescharacteristic
34#3167C2211yescharacteristic
35#3167C2211yescharacteristic
36#3106C2214yes—
37#3105C2214yes—
38#2994—21no—
39#2994—21no—
40#2993C2212yes—
41#2993C2212yes—
42#2991—21no—
43#2990—21no—
44#2989C2212yescomplemented
45#2988C2212yescomplemented
46#2981C2212yes—
47#2981C2212yes—
48#2979—21no—
49#2979—21no—
50#2975C2212yes—
51#2974—21no—
52#2974—21no—
53#2972C2212yes—
54#2960C2211yescharacteristic, complemented
55#2960C2211yescharacteristic, complemented
56#2935—21no—
57#2935—21no—
58#2933—21no—
59#2933—21no—
60#2931C2211yescharacteristic
61#2931C2211yescharacteristic
62#2931C2211yescharacteristic
63#2931C2211yescharacteristic
64#2931C2211yescharacteristic, complemented
65#2931C2211yescharacteristic, complemented
66#2925—21no—
67#2920C2211yescharacteristic
68C2×#431C2211yescharacteristic
69C2×#431C2211yescharacteristic
70C2×#431C2211yescharacteristic
71#2906—21no—
72C2×#423C2211yescharacteristic
73#2880—21no—
74#2880—21no—
75#1594C2214yescomplemented
76#1592C2214yescomplemented
77#1590C2214yescomplemented
78#1589C2214yescomplemented
79#1588C2214yescomplemented
80#1586C2214yescomplemented
81#1586C2214yescomplemented
82#1585C2214yescomplemented
83#1583C2214yescomplemented
84#1582C2214yescomplemented
85#1581C2214yescomplemented
86#1581C2214yescomplemented
87#1580C2214yescomplemented
88SD16⋊C8C2214yescomplemented
89C8×SD16C2214yescomplemented
90C8×D8C2214yescomplemented
91#1574C2214yes—
92#1573C2214yescomplemented
93#1567C2211yescharacteristic, complemented
94#1567C2211yescharacteristic, complemented
95#1566C2211yescharacteristic, complemented
96#1566C2211yescharacteristic, complemented
97#1493C2211yescharacteristic, complemented
98#1493C2211yescharacteristic, complemented
99#1492C2211yescharacteristic
100#1492C2211yescharacteristic
101#1492C2211yescharacteristic
102#1492C2211yescharacteristic
103#1492C2211yescharacteristic, complemented
104#1492C2211yescharacteristic, complemented
105#1488C2214yescomplemented
106#1486C2214yes—
107#1482C2214yes—
108#1480C2214yes—
109#1454C2212yes—
110#1454C2212yes—
111#1454C2212yescomplemented
112#1454C2212yescomplemented
113C2×#322C2211yescharacteristic, complemented
114C2×#322C2211yescharacteristic, complemented
115C2×#322C2211yescharacteristic, complemented
116C2×C82C2211yescharacteristic, complemented
117C22×#41—21no—
118C2×#131—21no—
119C2×#131—21no—
120C2×#131—21no—
121C2×#131—21no—
122C2×#131—21no—
123C2×#131—21no—
124C22×M16—21no—
125#533C2×C411yescharacteristic
126#533C2×C411yescharacteristic
127#533C2311yescharacteristic
128#532—21no—
129#532—21no—
130#532—21no—
131#532—21no—
132#532C2×C411yescharacteristic
133#532C2×C411yescharacteristic
134#532C2×C411yescharacteristic
135#532C2×C412yes—
136#532C2×C411yescharacteristic
137#532C2312yes—
138#532C2311yescharacteristic
139#532C2311yescharacteristic
140#532C2311yescharacteristic
141C2×C4⋊Q8C2×C411yescharacteristic
142C2×#127C2×C411yescharacteristic
143#529—21no—
144#529—21no—
145#529—21no—
146#529—21no—
147#529C2×C412yes—
148#529C2312yes—
149C2×#124—21no—
150#525—21no—
151#525—21no—
152#525C2×C412yes—
153C2×#121—21no—
154C2×#121C2×C412yes—
155C4×#41—21no—
156C4×#41—21no—
157C4×#41C2312yes—
158C2×C4×D4—21no—
159C2×C4×D4C2312yes—
160C22×C42C2311yescharacteristic
161#500C2×C411yescharacteristic
162#500C2×C411yescharacteristic
163#498C2×C411yescharacteristic
164#498C2×C411yescharacteristic
165#493C2×C411yescharacteristic
166#493C2×C411yescharacteristic
167#492C2×C411yescharacteristic
168#492C2×C411yescharacteristic
169#487C2×C411yescharacteristic
170#487C2×C411yescharacteristic
171#486C2×C411yescharacteristic
172#486C2×C411yescharacteristic
173#486C2×C411yescharacteristic
174#486C2×C411yescharacteristic
175#486C2×C411yescharacteristic
176#486C2×C411yescharacteristic
177#484C2×C414yes—
178#482C2×C414yes—
179#482C2×C414yes—
180#481C2×C414yes—
181#478C2×C414yes—
182#478C2×C414yes—
183#477C2×C414yes—
184#476C2×C414yes—
185#466C2×C414yes—
186#466C2×C414yes—
187#465C2×C414yes—
188#465C2×C414yes—
189#463C2×C414yes—
190#463C2×C414yes—
191#460C2×C414yes—
192#459C2×C414yes—
193#450C2×C414yes—
194#449C2×C414yes—
195#449C2×C414yes—
196#447C2×C414yes—
197#446—21no—
198#446—21no—
199#446C2312yes—
200#446C2312yes—
201C8×Q8—21no—
202C8×Q8—21no—
203C8×Q8C2312yes—
204C8×Q8C2312yes—
205C4×SD16C2314yes—
206C4×SD16C2314yes—
207C4×D8C2314yes—
208C4×D8C2314yes—
209#436—22no—
210#436—22no—
211#436—22no—
212#436—22no—
213#436—21no—
214#436—21no—
215#436—21no—
216#436—21no—
217#436—21no—
218#436—21no—
219#436C2312yes—
220#436C2312yes—
221#436C2312yes—
222#436C2312yes—
223#436C2312yes—
224#436C2312yes—
225#435—22no—
226#435—22no—
227#435—22no—
228#435—22no—
229#435—22no—
230#435—22no—
231#435—22no—
232#435—22no—
233C8×D4—22no—
234C8×D4—22no—
235C8×D4—22no—
236C8×D4—22no—
237C8×D4—21no—
238C8×D4—21no—
239C8×D4—21no—
240C8×D4—21no—
241C8×D4—21no—
242C8×D4—21no—
243C8×D4C2312yes—
244C8×D4C2312yes—
245C8×D4C2312yes—
246C8×D4C2312yes—
247C8×D4C2312yes—
248C8×D4C2312yes—
249#433—22no—
250#433—22no—
251#432—21no—
252#432—22no—
253#432C2312yes—
254#431—21no—
255#431—21no—
256#431—21no—
257#431—22no—
258#431C2×C411yescharacteristic
259#431C2×C411yescharacteristic
260#431C2×C411yescharacteristic
261#431C2×C411yescharacteristic
262#431D411yescharacteristic
263#431D411yescharacteristic
264#431D411yescharacteristic
265#431D411yescharacteristic
266#431C2312yes—
267#431C2312yes—
268#431C2312yes—
269#431C2312yes—
270#431C2312yes—
271#431C2311yescharacteristic
272#431C2311yescharacteristic
273#431C2311yescharacteristic
274#431C2311yescharacteristic
275#424—21no—
276#424—21no—
277#424—22no—
278#424—22no—
279#423—21no—
280#423—21no—
281#423—22no—
282#423C2311yescharacteristic
283#423C2311yescharacteristic
284#423C2311yescharacteristic
285#423C2311yescharacteristic
286#423C2312yes—
287C2×C4⋊C8—21no—
288C2×C4⋊C8—21no—
289C2×C4⋊C8—22no—
290C2×C4⋊C8C2×C412yes—
291C2×C4⋊C8D411yescharacteristic
292C2×C4⋊C8D411yescharacteristic
293C2×C4⋊C8C2312yes—
294#408—21no—
295#408—21no—
296#408—21no—
297#408—21no—
298#408—21no—
299#408—21no—
300#408—22no—
301#408—22no—
302#408—22no—
303#408—22no—
304#407—21no—
305#407—22no—
306#407—22no—
307C2×C22⋊C8—21no—
308C2×C22⋊C8—22no—
309C2×C22⋊C8—22no—
310C2×C22⋊C8C2×C412yes—
311C2×C22⋊C8D411yescharacteristic
312C2×C22⋊C8D411yescharacteristic
313#405—21no—
314#405—21no—
315C4×M16—21no—
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#335C2314yes—
323#335C2314yes—
324#334C2314yes—
325#334C2314yes—
326Q8⋊C8C2314yes—
327Q8⋊C8C2314yes—
328D4⋊C8C2314yes—
329D4⋊C8C2314yes—
330D4⋊C8C2314yes—
331D4⋊C8C2314yes—
332D4⋊C8C2314yes—
333D4⋊C8C2314yes—
334#322C2312yes—
335#322C2312yes—
336#322C2312yes—
337#322C2312yes—
338#322C2312yes—
339#322C2312yes—
340C82C2312yes—
341C82C2312yes—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—22no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—22no—
350C2×#41—82no—
351C2×#41—82no—
352C2×#41C22×C412yes—
353C22×Q8—21no—
354C22×D4—22no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4C22×C412yes—
358C23×C4—22no—
359C23×C4C22×C411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4#4111yescharacteristic
362C2×SD16C22×C414yes—
363C2×SD16C22×C414yes—
364C2×D8C22×C414yes—
365C2×D8C22×C414yes—
366#131—82no—
367#131—82no—
368#131—82no—
369#131—82no—
370#131—82no—
371#131—82no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—22no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16—22no—
383C2×M16—82no—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—22no—
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—22no—
393C22×C8C22×C412yes—
394C22×C8C22×C412yes—
395C22×C8C2×D411yescharacteristic
396C22×C8C2×D411yescharacteristic
397C22×C8C2×D411yescharacteristic
398C22×C8C2×D411yescharacteristic
399C4⋊Q8—21no—
400C4⋊Q8—21no—
401C4⋊Q8C22×C411yescharacteristic
402C4⋊Q8C22×C412yes—
403C4⋊Q8C22×C411yescharacteristic
404C4⋊Q8C22×C411yescharacteristic
405C4⋊Q8C22×C411yescharacteristic
406C4⋊Q8C22×C411yescharacteristic
407#127—21no—
408#127—21no—
409#127C22×C412yes—
410#127C22×C411yescharacteristic
411#127C22×C411yescharacteristic
412#127C22×C411yescharacteristic
413#126—22no—
414#126—22no—
415#125—21no—
416#125—21no—
417#125C22×C412yes—
418#124—21no—
419#124—21no—
420#124—22no—
421#124—21no—
422#124—21no—
423#124—21no—
424#124—22no—
425#124—21no—
426#124C22×C412yes—
427#123—22no—
428#123—22no—
429#123—22no—
430C22⋊Q8—21no—
431C22⋊Q8—21no—
432C22⋊Q8—21no—
433C22⋊Q8—21no—
434C22⋊Q8C22×C412yes—
435C22⋊Q8C22×C412yes—
436#121—21no—
437#121—21no—
438#121—22no—
439#121—22no—
440#121—22no—
441#121—21no—
442#121—21no—
443#121—21no—
444#121—21no—
445#121—21no—
446#121—22no—
447#121—21no—
448#121C22×C412yes—
449#121C22×C412yes—
450#121C22×C412yes—
451#121C22×C412yes—
452#121C22×C412yes—
453#121C22×C412yes—
454#120—22no—
455C4×Q8—21no—
456C4×Q8—21no—
457C4×Q8—21no—
458C4×Q8—21no—
459C4×Q8C22×C412yes—
460C4×Q8C2412yes—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—22no—
466C4×D4—22no—
467C4×D4—22no—
468C4×D4—21no—
469C4×D4—21no—
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—22no—
476C4×D4—22no—
477C4×D4—21no—
478C4×D4—22no—
479C4×D4C22×C412yes—
480C4×D4C22×C412yes—
481C4×D4C22×C412yes—
482C4×D4C2412yes—
483C4×D4C2412yes—
484C4×D4C2412yes—
485#117—21no—
486#117—21no—
487#117—22no—
488#117—22no—
489#117—22no—
490#117C22×C412yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4C22×C412yes—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C42—22no—
496C2×C42C22×C411yescharacteristic
497C2×C42C22×C411yescharacteristic
498C2×C42C22×C411yescharacteristic
499C2×C42C2×D411yescharacteristic
500C2×C42C2×D411yescharacteristic
501C2×C42C2×D411yescharacteristic
502C2×C42#4111yescharacteristic
503C2×C42#4111yescharacteristic
504C2×C42#4111yescharacteristic
505C2×C42C2411yescharacteristic
506C2×C42C2411yescharacteristic
507C2×C42C2411yescharacteristic
508#107C22×C414yes—
509#107C22×C414yes—
510#106C22×C414yes—
511#106C22×C414yes—
512C4⋊C8—22no—
513C4⋊C8—22no—
514C4⋊C8—22no—
515C4⋊C8—22no—
516C4⋊C8—22no—
517C4⋊C8—22no—
518C4⋊C8—21no—
519C4⋊C8—21no—
520C4⋊C8—21no—
521C4⋊C8—21no—
522C4⋊C8—22no—
523C4⋊C8—22no—
524C4⋊C8C22×C412yes—
525C4⋊C8C22×C412yes—
526C4⋊C8C22×C412yes—
527C4⋊C8C22×C412yes—
528C4⋊C8C2×D411yescharacteristic
529C4⋊C8C2×D411yescharacteristic
530C4⋊C8C2×D411yescharacteristic
531C4⋊C8C2×D411yescharacteristic
532C4⋊C8C2×D411yescharacteristic
533C4⋊C8C2×D411yescharacteristic
534C4⋊C8C2×D411yescharacteristic
535C4⋊C8C2×D411yescharacteristic
536C4⋊C8C2412yes—
537C4⋊C8C2412yes—
538C4⋊C8C2412yes—
539C4⋊C8C2412yes—
540#103C22×C414yes—
541#103C22×C414yes—
542#102C22×C414yes—
543#102C22×C414yes—
544#102C22×C414yes—
545#102C22×C414yes—
546#102C22×C414yes—
547#102C22×C414yes—
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⋊C8—22no—
558C22⋊C8—22no—
559C22⋊C8—22no—
560C22⋊C8—22no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564C22⋊C8C22×C412yes—
565C22⋊C8C22×C412yes—
566C22⋊C8C22×C412yes—
567C22⋊C8C22×C412yes—
568C22⋊C8C2×D411yescharacteristic
569C22⋊C8C2×D411yescharacteristic
570C22⋊C8C2×D411yescharacteristic
571C22⋊C8C2×D411yescharacteristic
572C22⋊C8C2×D411yescharacteristic
573C22⋊C8C2×D411yescharacteristic
574C22⋊C8C2×D411yescharacteristic
575C22⋊C8C2×D411yescharacteristic
576#97—22no—
577#97—22no—
578#97—22no—
579C4×C8—22no—
580C4×C8—22no—
581C4×C8—22no—
582C4×C8—21no—
583C4×C8—21no—
584C4×C8C22×C411yescharacteristic
585C4×C8C22×C411yescharacteristic
586C4×C8C22×C411yescharacteristic
587C4×C8C22×C411yescharacteristic
588C4×C8C2×D411yescharacteristic
589C4×C8C2×D411yescharacteristic
590C4×C8C2×D411yescharacteristic
591C4×C8C2×D411yescharacteristic
592C4×C8C2412yes—
593C4×C8C2412yes—
594C4×C8C2412yes—
595C4×C8C2412yes—
596C4×C8C2411yescharacteristic
597C4×C8C2411yescharacteristic
598C4×C8C2411yescharacteristic
599C4×C8C2411yescharacteristic
600C24—22no—
601C24C4×D411yescharacteristic
602#41—44no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—82no—
610#41—82no—
611#41—84no—
612#41—82no—
613#41—82no—
614#41—82no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—22no—
620C2×Q8—82no—
621C2×Q8C23×C412yes—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—44no—
639C2×D4—82no—
640C2×D4—82no—
641C2×D4—84no—
642C2×D4C23×C412yes—
643C2×D4C23×C412yes—
644C2×D4C23×C412yes—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—82no—
658C22×C4—82no—
659C22×C4C4×D411yescharacteristic
660C22×C4C4×D411yescharacteristic
661C22×C4C4×D411yescharacteristic
662C22×C4C4×D411yescharacteristic
663C22×C4C4×D411yescharacteristic
664C22×C4C4×D411yescharacteristic
665C22×C4C4×D411yescharacteristic
666C22×C4C4×D411yescharacteristic
667C22×C4C4×D411yescharacteristic
668C22×C4C23×C411yescharacteristic
669C22×C4C23×C411yescharacteristic
670C22×C4C23×C411yescharacteristic
671C22×C4C22×D411yescharacteristic
672C22×C4C22×D411yescharacteristic
673C22×C4C22×D411yescharacteristic
674C22×C4C2×#4111yescharacteristic
675C22×C4C2×#4111yescharacteristic
676C22×C4C2×#4111yescharacteristic
677SD16—44no—
678SD16—44no—
679D8—44no—
680D8—44no—
681M16—42no—
682M16—42no—
683M16—42no—
684M16—42no—
685M16—82no—
686M16—82no—
687M16—82no—
688M16—82no—
689M16—82no—
690M16—82no—
691M16—82no—
692C2×C8—22no—
693C2×C8—22no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—22no—
697C2×C8—22no—
698C2×C8—22no—
699C2×C8—22no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8—42no—
705C2×C8—42no—
706C2×C8—82no—
707C2×C8—82no—
708C2×C8—82no—
709C2×C8—82no—
710C2×C8—82no—
711C2×C8—82no—
712C2×C8—82no—
713C2×C8C23×C412yes—
714C2×C8C23×C412yes—
715C2×C8C23×C412yes—
716C2×C8C23×C412yes—
717C2×C8C22×D411yescharacteristic
718C2×C8C22×D411yescharacteristic
719C2×C8C22×D411yescharacteristic
720C2×C8C22×D411yescharacteristic
721C2×C8C22×D411yescharacteristic
722C2×C8C22×D411yescharacteristic
723C2×C8C22×D411yescharacteristic
724C2×C8C22×D411yescharacteristic
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—22no—
738C4⋊C4—22no—
739C4⋊C4C23×C412yes—
740C4⋊C4C23×C412yes—
741C4⋊C4C23×C412yes—
742C4⋊C4C23×C412yes—
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—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C42—22no—
761C42—22no—
762C42—22no—
763C42C4×D411yescharacteristic
764C42C4×D411yescharacteristic
765C42C4×D411yescharacteristic
766C42C4×D411yescharacteristic
767C42C4×D411yescharacteristic
768C42C4×D411yescharacteristic
769C42C23×C411yescharacteristic
770C42C23×C411yescharacteristic
771C42C23×C411yescharacteristic
772C42C22×D411yescharacteristic
773C42C22×D411yescharacteristic
774C42C22×D411yescharacteristic
775C42C2×#4111yescharacteristic
776C42C2×#4111yescharacteristic
777C42C2×#4111yescharacteristic
778C42C2511yescharacteristic
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—82no—
787C23—82no—
788C23C2×C4×D411yescharacteristic
789C23C2×C4×D411yescharacteristic
790C23C2×C4×D411yescharacteristic
791Q8—24no—
792Q8—42no—
793Q8—42no—
794Q8—42no—
795Q8—42no—
796Q8—82no—
797D4—24no—
798D4—24no—
799D4—24no—
800D4—44no—
801D4—44no—
802D4—44no—
803D4—44no—
804D4—44no—
805D4—42no—
806D4—42no—
807D4—42no—
808D4—42no—
809D4—42no—
810D4—42no—
811D4—82no—
812D4—82no—
813D4—82no—
814D4—82no—
815D4—82no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—44no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—82no—
848C2×C4—82no—
849C2×C4—82no—
850C2×C4—82no—
851C2×C4C2×C4×D411yescharacteristic
852C2×C4C2×C4×D411yescharacteristic
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×C4#57612yes—
861C2×C4#57712yes—
862C2×C4C24×C411yescharacteristic
863C2×C4C23×D411yescharacteristic
864C2×C4C22×#4111yescharacteristic
865C8—22no—
866C8—22no—
867C8—22no—
868C8—22no—
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—21no—
890C22—21no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—82no—
901C22—164no—
902C22#294612yes—
903C22C22×C4×D411yescharacteristic
904C4—21no—
905C4—21no—
906C4—21no—
907C4—21no—
908C4—21no—
909C4—21no—
910C4—21no—
911C4—21no—
912C4—42no—
913C4—42no—
914C4—42no—
915C4—42no—
916C4—42no—
917C4#294612yes—
918C4#295712yes—
919C4#357312yes—
920C4C2×#57611yescharacteristic
921C4C2×#57711yescharacteristic
922C2—22no—
923C2—41no—
924C2—41no—
925C2—82no—
926C2—82no—
927C2—82no—
928C2#6014011yescharacteristic
929C2C2×#294611yescharacteristic
930C2C2×#295711yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60946C2
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. #60236C2semidirect
4. #17981C2semidirect
5. #17979C2semidirect
6. #17976C2semidirect
7. #17975C2semidirect
8. #17962C2semidirect
9. #17960C2semidirect
10. #17957C2semidirect
11. #17956C2semidirect
12. #17948C2semidirect
13. #17946C2semidirect
14. #17920C2semidirect
15. #17918C2semidirect
16. #17817C2semidirect
17. #17489C2semidirect
18. #17485C2semidirect
19. C2×#1454C2semidirect
44. #2989C22semidirect
45. #2988C22semidirect
54. #2960C22semidirect
55. #2960C22semidirect
64. #2931C22semidirect
65. #2931C22semidirect
75. #1594C22semidirect
76. #1592C22semidirect
77. #1590C22semidirect
78. #1589C22semidirect
79. #1588C22semidirect
80. #1586C22semidirect
81. #1586C22semidirect
82. #1585C22semidirect
83. #1583C22semidirect
84. #1582C22semidirect
85. #1581C22semidirect
86. #1581C22semidirect
87. #1580C22semidirect
88. SD16⋊C8C22semidirect
89. C8×SD16C22semidirect
90. C8×D8C22semidirect
92. #1573C22semidirect
93. #1567C22semidirect
94. #1567C22semidirect
95. #1566C22semidirect
96. #1566C22semidirect
97. #1493C22semidirect
98. #1493C22semidirect
103. #1492C22semidirect
104. #1492C22semidirect
105. #1488C22semidirect
111. #1454C22semidirect
112. #1454C22semidirect
113. C2×#322C22semidirect
114. C2×#322C22semidirect
115. C2×#322C22semidirect
116. C2×C82C22semidirect

Maximal subgroups

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

subgroupindex
#609462
#602682
#602362
#179812
#179792
#179762
#179752
#179622
#179602
#179572
#179562
#179482
#179462
#179202
#179182
#178172
#174892
#174852
C2×#14542