Finite Group Databasebeta

← #6847922

Subgroups — #6847922

Order 512.

1501 conjugacy classes of subgroups.

The subgroup lattice has 1293 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39544C211yesmaximal, characteristic, complemented
2#35171C211yesmaximal, characteristic
3#33070C211yesmaximal, characteristic, complemented
4#32155C211yesmaximal, characteristic, complemented
5#32145C211yesmaximal, characteristic, complemented
6#32096C211yesmaximal, characteristic, complemented
7#32078C211yesmaximal, characteristic, complemented
8#32038C211yesmaximal, characteristic, complemented
9#32035C211yesmaximal, characteristic, complemented
10#32019C211yesmaximal, characteristic, complemented
11#31994C211yesmaximal, characteristic, complemented
12#29698C211yesmaximal, characteristic, complemented
13#29698C211yesmaximal, characteristic, complemented
14#29127C211yesmaximal, characteristic, complemented
15#29064C211yesmaximal, characteristic, complemented
16#29047C211yesmaximal, characteristic, complemented
17#28201C211yesmaximal, characteristic, complemented
18#28089C211yesmaximal, characteristic, complemented
19#28085C211yesmaximal, characteristic, complemented
20#27687C211yesmaximal, characteristic, complemented
21#27640C211yesmaximal, characteristic, complemented
22#27418C211yesmaximal, characteristic, complemented
23#27407C211yesmaximal, characteristic, complemented
24#27353C211yesmaximal, characteristic, complemented
25#27348C211yesmaximal, characteristic, complemented
26#24847C211yesmaximal, characteristic, complemented
27#24712C211yesmaximal, characteristic, complemented
28#22757C211yesmaximal, characteristic, complemented
29#21897C211yesmaximal, characteristic, complemented
30#21872C211yesmaximal, characteristic, complemented
31#21614C211yesmaximal, characteristic, complemented
32C2×#540C2211yescharacteristic
33C2×#540C2211yescharacteristic
34C2×#476C2211yescharacteristic
35C2×#474C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×#433C2211yescharacteristic
38C2×#424C2211yescharacteristic
39#2864C2211yescharacteristic
40#2856—21no—
41#2854—21no—
42#2776—21no—
43#2775—21no—
44#2745—21no—
45#2694—21no—
46#2661—21no—
47#2661—21no—
48#2628C2211yescharacteristic
49#2628C2211yescharacteristic
50#2596—21no—
51#2575—21no—
52#2552C2211yescharacteristic
53#2541C2211yescharacteristic
54#2541C2211yescharacteristic
55#2537C2211yescharacteristic
56#2508C2211yescharacteristic
57#2506C2211yescharacteristic
58#2497C2211yescharacteristic
59#2494C2211yescharacteristic
60#2490C2211yescharacteristic
61#2490C2211yescharacteristic
62#2486C2211yescharacteristic
63#2485C2211yescharacteristic
64#2464—21no—
65#2464—21no—
66#2462—21no—
67#2458—21no—
68#2428—21no—
69#2428C2211yescharacteristic
70#2428C2211yescharacteristic
71#2422—21no—
72#2347C2211yescharacteristic
73#2345C2211yescharacteristic
74#2324C2211yescharacteristic
75#2324C2211yescharacteristic
76#2317C2211yescharacteristic
77#2314C2211yescharacteristic
78C4×C4⋊Q8C2211yescharacteristic
79C4×#127C2211yescharacteristic
80#2293C2211yescharacteristic
81C42×D4C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2093C2211yescharacteristic
87#2092C2211yescharacteristic
88#2087C2211yescharacteristic
89#2086C2211yescharacteristic
90#2083C2211yescharacteristic
91#2083C2211yescharacteristic
92#2076C2211yescharacteristic
93#2076C2211yescharacteristic
94#2075C2211yescharacteristic
95#2075C2211yescharacteristic
96#2067C2211yescharacteristic
97#2065C2211yescharacteristic
98#2059C2211yescharacteristic
99#2059C2211yescharacteristic
100#2059C2211yescharacteristic
101#2059C2211yescharacteristic
102#2041C2211yescharacteristic
103#2041C2211yescharacteristic
104#2041C2211yescharacteristic
105#2041C2211yescharacteristic
106#2041C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2041C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#1992C2211yescharacteristic
123#1991C2211yescharacteristic
124#1989C2211yescharacteristic
125#1989C2211yescharacteristic
126#1987C2211yescharacteristic
127#1982C2211yescharacteristic
128#1982C2211yescharacteristic
129#1961C2211yescharacteristic
130#1957C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1947C2211yescharacteristic
134#1944C2211yescharacteristic
135#1942C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1934C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1924C2211yescharacteristic
149#1924C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1920C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1916C2211yescharacteristic
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic
162#1895C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1875C2211yescharacteristic
167#1875C2211yescharacteristic
168#1875C2211yescharacteristic
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1870C2211yescharacteristic
173#1869C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1854C2211yescharacteristic
181#1852C2211yescharacteristic
182#1831C2211yescharacteristic
183#1809C2211yescharacteristic
184#1808C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1798C2211yescharacteristic
195#1798C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198#1767C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201#1753C2211yescharacteristic
202#1752C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205#540—24no—
206#540—24no—
207#540—42no—
208#540—42no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127—21no—
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#125—21no—
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#121—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×C4×Q8—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C42—21no—
251#476—24no—
252#474—42no—
253#474—42no—
254#433—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267#424—42no—
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308#401—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#399—21no—
315#399—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#395—21no—
328#395—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#393—21no—
337#393—21no—
338#392—21no—
339#392—21no—
340#392—21no—
341#392—21no—
342#392—21no—
343#392—21no—
344#391—21no—
345#390—21no—
346#390—21no—
347#390—21no—
348#390—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390D411yescharacteristic
353#390D411yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389D411yescharacteristic
363#389D411yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#388—21no—
377#388—21no—
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#388D411yescharacteristic
388#388D411yescharacteristic
389#388D411yescharacteristic
390#388D411yescharacteristic
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#384—21no—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#383—21no—
417#382—21no—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#381—21no—
422#380—21no—
423#380—21no—
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448C43C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2×D411yescharacteristic
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C2×M16—41no—
513C2×M16—41no—
514C2×M16—41no—
515C22×C8—41no—
516C22×C8—41no—
517C22×C8—41no—
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C4⋊Q8—22no—
527C4⋊Q8—22no—
528#127—22no—
529#127—22no—
530#127—41no—
531#127—41no—
532#127—41no—
533#127—41no—
534#127—82no—
535#125—22no—
536#125—22no—
537#125—41no—
538#125—41no—
539#125—82no—
540#123—44no—
541#123—44no—
542#123—44no—
543#123—44no—
544#123—82no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—22no—
550#121—22no—
551#121—44no—
552#121—44no—
553#121—44no—
554#121—44no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—82no—
562#121—82no—
563#121—82no—
564#121—82no—
565#121—82no—
566C4×Q8—82no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—82no—
579C4×D4—82no—
580C4×D4#4114yes—
581#117—22no—
582#117—22no—
583#117—22no—
584#117—22no—
585#117—41no—
586#117—41no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
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—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—82no—
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689#107—22no—
690#107—41no—
691#107—41no—
692#107—41no—
693#107—41no—
694#107—41no—
695#107—41no—
696#107—41no—
697#106—22no—
698#106—22no—
699#106—22no—
700#106—41no—
701C4⋊C8—22no—
702C4⋊C8—22no—
703C4⋊C8—22no—
704C4⋊C8—22no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707#102—22no—
708#102—22no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737#97—41no—
738#97—41no—
739#97—41no—
740C4×C8—41no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
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#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780C24—21no—
781C24—21no—
782C24—21no—
783C24C22×D411yescharacteristic
784C24C22×D411yescharacteristic
785C2×Q8—42no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×D4—22no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—41no—
807C2×D4—41no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4C2×#4112yes—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
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—24no—
860C22×C4—21no—
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—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C2511yescharacteristic
901M16—82no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
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—82no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
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—41no—
957C4⋊C4—41no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4C2×#4112yes—
983C4⋊C42−1+412yes—
984C22⋊C4—24no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C42—22no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—42no—
1035C42—42no—
1036C42—81no—
1037C42—81no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42C2×#4112yes—
1043C42H(5,𝔽2)12yes—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—22no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23C23×D411yescharacteristic
1080Q8—84no—
1081D4—22no—
1082D4—22no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—82no—
1094D4—84no—
1095D4—84no—
1096D4—162no—
1097D4—162no—
1098D4—162no—
1099D4—162no—
1100D4—162no—
1101D4—162no—
1102D4—162no—
1103D4—162no—
1104D4—162no—
1105D4—162no—
1106C2×C4—21no—
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—22no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
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—84no—
1187C2×C4—84no—
1188C2×C4—84no—
1189C2×C4—162no—
1190C2×C4—162no—
1191C2×C4—162no—
1192C2×C4#54612yes—
1193C2×C4#54612yes—
1194C2×C4#57612yes—
1195C2×C4C22×#4111yescharacteristic
1196C2×C4C2×H(5,𝔽2)11yescharacteristic
1197C2×C4C2×2−1+411yescharacteristic
1198C2×C4#58511yescharacteristic
1199C2×C4#58511yescharacteristic
1200C2×C4#58511yescharacteristic
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C22—41no—
1210C22—41no—
1211C22—42no—
1212C22—41no—
1213C22—41no—
1214C22—42no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—42no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22#344911yescharacteristic
1245C22C2×#54611yescharacteristic
1246C22#348911yescharacteristic
1247C22C2×#57611yescharacteristic
1248C22#358511yescharacteristic
1249C22#358511yescharacteristic
1250C22#358611yescharacteristic
1251C4—22no—
1252C4—22no—
1253C4—22no—
1254C4—41no—
1255C4—42no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—42no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4#350711yescharacteristic
1277C4#351211yescharacteristic
1278C4#354711yescharacteristic
1279C4#355111yescharacteristic
1280C2—81no—
1281C2—81no—
1282C2—82no—
1283C2—161no—
1284C2—161no—
1285C2#3946311yescharacteristic
1286C2#6097311yescharacteristic
1287C2#6097811yescharacteristic
1288C2#6120511yescharacteristic
1289C2#6121911yescharacteristic
1290C2#6218611yescharacteristic
1291C2#6222311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35171C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39544C2semidirect
3. #33070C2semidirect
4. #32155C2semidirect
5. #32145C2semidirect
6. #32096C2semidirect
7. #32078C2semidirect
8. #32038C2semidirect
9. #32035C2semidirect
10. #32019C2semidirect
11. #31994C2semidirect
12. #29698C2semidirect
13. #29698C2semidirect
14. #29127C2semidirect
15. #29064C2semidirect
16. #29047C2semidirect
17. #28201C2semidirect
18. #28089C2semidirect
19. #28085C2semidirect
20. #27687C2semidirect
21. #27640C2semidirect
22. #27418C2semidirect
23. #27407C2semidirect
24. #27353C2semidirect
25. #27348C2semidirect
26. #24847C2semidirect
27. #24712C2semidirect
28. #22757C2semidirect
29. #21897C2semidirect
30. #21872C2semidirect
31. #21614C2semidirect

Maximal subgroups

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

subgroupindex
#395442
#351712
#330702
#321552
#321452
#320962
#320782
#320382
#320352
#320192
#319942
#296982
#291272
#290642
#290472
#282012
#280892
#280852
#276872
#276402
#274182
#274072
#273532
#273482
#248472
#247122
#227572
#218972
#218722
#216142