Finite Group Databasebeta

← #6795610

Subgroups — #6795610

Order 512.

1640 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36184C211yesmaximal, characteristic, complemented
2#34932C211yesmaximal, characteristic, complemented
3#33199C211yesmaximal, characteristic, complemented
4#32301C211yesmaximal, characteristic, complemented
5#32299C211yesmaximal, characteristic, complemented
6#32280C211yesmaximal, characteristic, complemented
7#32278C211yesmaximal, characteristic, complemented
8#31950C211yesmaximal, characteristic, complemented
9#31946C211yesmaximal, characteristic, complemented
10#31934C211yesmaximal, characteristic, complemented
11#31930C211yesmaximal, characteristic, complemented
12#29928C211yesmaximal, characteristic, complemented
13#29927C211yesmaximal, characteristic, complemented
14#28692C211yesmaximal, characteristic, complemented
15#28548C211yesmaximal, characteristic, complemented
16#28545C211yesmaximal, characteristic, complemented
17#28282C211yesmaximal, characteristic, complemented
18#27741C211yesmaximal, characteristic, complemented
19#27739C211yesmaximal, characteristic, complemented
20#27684C211yesmaximal, characteristic, complemented
21#27683C211yesmaximal, characteristic, complemented
22#25716C211yesmaximal, characteristic, complemented
23#25714C211yesmaximal, characteristic, complemented
24#24656C211yesmaximal, characteristic, complemented
25#24654C211yesmaximal, characteristic, complemented
26#24137C211yesmaximal, characteristic, complemented
27#24136C211yesmaximal, characteristic
28#22797C211yesmaximal, characteristic, complemented
29#21986C211yesmaximal, characteristic, complemented
30#21984C211yesmaximal, characteristic, complemented
31#21507C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#529—21no—
35C2×#501C2211yescharacteristic
36C2×#501C2211yescharacteristic
37C2×#477C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#476C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#442C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×#432C2211yescharacteristic
45C2×#431C2211yescharacteristic
46#2859C2211yescharacteristic
47#2850C2211yescharacteristic
48#2850C2211yescharacteristic
49#2566C2211yescharacteristic
50#2565C2211yescharacteristic
51#2553—21no—
52#2553—21no—
53#2553—21no—
54#2553—21no—
55#2552C2211yescharacteristic
56#2547C2211yescharacteristic
57#2542C2211yescharacteristic
58#2537C2211yescharacteristic
59#2519—21no—
60#2519—21no—
61#2502C2211yescharacteristic
62#2501C2211yescharacteristic
63#2500C2211yescharacteristic
64#2499C2211yescharacteristic
65#2496C2211yescharacteristic
66#2496C2211yescharacteristic
67#2489—21no—
68#2427—21no—
69#2425—21no—
70#2425—21no—
71#2422C2211yescharacteristic
72#2422C2211yescharacteristic
73#2395—21no—
74#2395—21no—
75#2359—21no—
76#2359—21no—
77C4×C4⋊Q8C2211yescharacteristic
78C4×#124C2211yescharacteristic
79C4×C22⋊Q8—21no—
80C4×#121C2211yescharacteristic
81C4×#121C2211yescharacteristic
82#2285C2211yescharacteristic
83#2285C2211yescharacteristic
84#2285C2211yescharacteristic
85C2×#382C2211yescharacteristic
86C42×D4C2211yescharacteristic
87C42×D4C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2100C2211yescharacteristic
91#2099C2211yescharacteristic
92#2096C2211yescharacteristic
93#2095C2211yescharacteristic
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic
96#2093C2211yescharacteristic
97#2093C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2084C2211yescharacteristic
101#2084C2211yescharacteristic
102#2083C2211yescharacteristic
103#2083C2211yescharacteristic
104#2072C2211yescharacteristic
105#2072C2211yescharacteristic
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1999C2211yescharacteristic
127#1999C2211yescharacteristic
128#1992C2211yescharacteristic
129#1992C2211yescharacteristic
130#1989C2211yescharacteristic
131#1989C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1973C2211yescharacteristic
136#1972C2211yescharacteristic
137#1970C2211yescharacteristic
138#1968C2211yescharacteristic
139#1955C2211yescharacteristic
140#1955C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1949C2211yescharacteristic
146#1949C2211yescharacteristic
147#1949C2211yescharacteristic
148#1949C2211yescharacteristic
149#1949C2211yescharacteristic
150#1948C2211yescharacteristic
151#1947C2211yescharacteristic
152#1936C2211yescharacteristic
153#1935C2211yescharacteristic
154#1934C2211yescharacteristic
155#1933C2211yescharacteristic
156#1927C2211yescharacteristic
157#1925C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic
162#1879C2211yescharacteristic
163#1877C2211yescharacteristic
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1853C2211yescharacteristic
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic
180#1847C2211yescharacteristic
181#1847C2211yescharacteristic
182#1845C2211yescharacteristic
183#1844C2211yescharacteristic
184#1842C2211yescharacteristic
185#1836C2211yescharacteristic
186#1836C2211yescharacteristic
187#1834C2211yescharacteristic
188#1834C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1803C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1797C2211yescharacteristic
197#1797C2211yescharacteristic
198#1771C2211yescharacteristic
199#1771C2211yescharacteristic
200#1767C2211yescharacteristic
201#1763C2211yescharacteristic
202#1762C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×D8C2311yescharacteristic
205#553—42no—
206#553—42no—
207#552—42no—
208#552—42no—
209C2×C4⋊Q8C2311yescharacteristic
210#529—48no—
211C2×#126—21no—
212C2×#126—21no—
213C2×#126—21no—
214C2×#126—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×C4×Q8—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4D411yescharacteristic
243C2×C4×D4D411yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C2×#117—21no—
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C42—21no—
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259#501—42no—
260#501—42no—
261#478—42no—
262#478—42no—
263#477—42no—
264#476—42no—
265#463—24no—
266#442—42no—
267#440—42no—
268#432—24no—
269#431—24no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#400—21no—
331#400—21no—
332#399—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#396—21no—
351#396—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#391—21no—
359#391—21no—
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#382—21no—
416#382—21no—
417#382—21no—
418#382—21no—
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4D411yescharacteristic
441C4×C4⋊C4D411yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4D411yescharacteristic
456C4×C22⋊C4D411yescharacteristic
457C4×C22⋊C4D411yescharacteristic
458C4×C22⋊C4D411yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C2×#95—21no—
462C2×#95—21no—
463C43C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2×D411yescharacteristic
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—41no—
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—41no—
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C4⋊Q8—22no—
530C4⋊Q8—22no—
531#126—44no—
532#126—44no—
533#126—44no—
534#126—44no—
535#125—22no—
536#125—22no—
537#125—22no—
538#125—22no—
539#125—44no—
540#125—44no—
541#124—22no—
542#124—22no—
543#124—44no—
544#123—44no—
545#123—44no—
546#123—44no—
547#123—44no—
548#123—44no—
549#123—44no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—41no—
554C22⋊Q8—44no—
555C22⋊Q8—44no—
556#121—22no—
557#121—22no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—44no—
565#121—44no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×Q8—44no—
569C4×D4—24no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—41no—
580C4×D4—42no—
581C4×D4—44no—
582C4×D4—44no—
583C4×D4—44no—
584#117—44no—
585#117—41no—
586#117—41no—
587#117—41no—
588#117—41no—
589#117—44no—
590#117—44no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C42—22no—
680C2×C42—22no—
681C2×C42—22no—
682C2×C42—22no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—44no—
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#107—41no—
712#107—41no—
713#107—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723C4⋊C8—22no—
724C4⋊C8—22no—
725C4⋊C8—22no—
726C4⋊C8—22no—
727C4⋊C8—22no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8#4114yes—
731#103—22no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#102—22no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751C22⋊C8—22no—
752C22⋊C8—22no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759#97—22no—
760#97—22no—
761#97—22no—
762#97—22no—
763C4×C8—22no—
764C4×C8—22no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802C24—21no—
803C24—21no—
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—42no—
813C2×Q8—42no—
814C2×Q8—42no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—41no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D42−1+412yes—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C2511yescharacteristic
911SD16—44no—
912D8—44no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8C2×#4112yes—
936C2×C8C2×#4112yes—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—41no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4AGL(1,ℤ/8)14yes—
1034C42—22no—
1035C42—22no—
1036C42—22no—
1037C42—22no—
1038C42—22no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—41no—
1046C42—41no—
1047C42—41no—
1048C42—42no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—42no—
1056C42C2×#4112yes—
1057C42H(5,𝔽2)12yes—
1058C42H(5,𝔽2)12yes—
1059C422−1+412yes—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—22no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23C2×AGL(1,ℤ/8)12yes—
1088C23C23×D411yescharacteristic
1089Q8—41no—
1090Q8—41no—
1091Q8—41no—
1092Q8—41no—
1093Q8—84no—
1094D4—22no—
1095D4—22no—
1096D4—44no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—41no—
1102D4—41no—
1103D4—84no—
1104D4—84no—
1105D4—84no—
1106D4—162no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—44no—
1137C2×C4—44no—
1138C2×C4—44no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—82no—
1190C2×C4—84no—
1191C2×C4—84no—
1192C2×C4—84no—
1193C2×C4—84no—
1194C2×C4—162no—
1195C2×C4—162no—
1196C2×C4#53512yes—
1197C2×C4#53512yes—
1198C2×C4#54712yes—
1199C2×C4#54712yes—
1200C2×C4C2×AGL(1,ℤ/8)12yes—
1201C2×C4C2×AGL(1,ℤ/8)12yes—
1202C2×C4#57512yes—
1203C2×C4C22×#4111yescharacteristic
1204C2×C4C2×H(5,𝔽2)11yescharacteristic
1205C2×C4C2×H(5,𝔽2)11yescharacteristic
1206C2×C4C2×2−1+411yescharacteristic
1207C2×C4C2×2−1+411yescharacteristic
1208C2×C4#58511yescharacteristic
1209C8—22no—
1210C8—22no—
1211C8—41no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C22—22no—
1218C22—22no—
1219C22—22no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—42no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—42no—
1232C22—42no—
1233C22—41no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22C2×#53511yescharacteristic
1246C22C2×#54711yescharacteristic
1247C22#348911yescharacteristic
1248C22C22×AGL(1,ℤ/8)11yescharacteristic
1249C22C2×#57511yescharacteristic
1250C22#358411yescharacteristic
1251C22#358611yescharacteristic
1252C4—22no—
1253C4—22no—
1254C4—22no—
1255C4—22no—
1256C4—22no—
1257C4—22no—
1258C4—22no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4#351711yescharacteristic
1279C4#352011yescharacteristic
1280C4#354711yescharacteristic
1281C4#355211yescharacteristic
1282C2—42no—
1283C2—81no—
1284C2—82no—
1285C2—161no—
1286C2#3892011yescharacteristic
1287C2#6080311yescharacteristic
1288C2#6083511yescharacteristic
1289C2#6124311yescharacteristic
1290C2#6125211yescharacteristic
1291C2#6212111yescharacteristic
1292C2#6213711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24136C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36184C2semidirect
2. #34932C2semidirect
3. #33199C2semidirect
4. #32301C2semidirect
5. #32299C2semidirect
6. #32280C2semidirect
7. #32278C2semidirect
8. #31950C2semidirect
9. #31946C2semidirect
10. #31934C2semidirect
11. #31930C2semidirect
12. #29928C2semidirect
13. #29927C2semidirect
14. #28692C2semidirect
15. #28548C2semidirect
16. #28545C2semidirect
17. #28282C2semidirect
18. #27741C2semidirect
19. #27739C2semidirect
20. #27684C2semidirect
21. #27683C2semidirect
22. #25716C2semidirect
23. #25714C2semidirect
24. #24656C2semidirect
25. #24654C2semidirect
26. #24137C2semidirect
28. #22797C2semidirect
29. #21986C2semidirect
30. #21984C2semidirect
31. #21507C2semidirect

Maximal subgroups

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

subgroupindex
#361842
#349322
#331992
#323012
#322992
#322802
#322782
#319502
#319462
#319342
#319302
#299282
#299272
#286922
#285482
#285452
#282822
#277412
#277392
#276842
#276832
#257162
#257142
#246562
#246542
#241372
#241362
#227972
#219862
#219842
#215072