Finite Group Databasebeta

← #7039054

Subgroups — #7039054

Order 512.

1445 conjugacy classes of subgroups.

The subgroup lattice has 1289 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59215C211yesmaximal, characteristic, complemented
2#39537C211yesmaximal, characteristic, complemented
3#32386C211yesmaximal, characteristic, complemented
4#32265C211yesmaximal, characteristic, complemented
5#32011C211yesmaximal, characteristic, complemented
6#31995C211yesmaximal, characteristic, complemented
7#31475C211yesmaximal, characteristic, complemented
8#31387C211yesmaximal, characteristic, complemented
9#30402C211yesmaximal, characteristic, complemented
10#30398C211yesmaximal, characteristic, complemented
11#29481C211yesmaximal, characteristic, complemented
12#28225C211yesmaximal, characteristic, complemented
13#28103C211yesmaximal, characteristic, complemented
14#28081C211yesmaximal, characteristic, complemented
15#27860C211yesmaximal, characteristic, complemented
16#27854C211yesmaximal, characteristic, complemented
17#27579C211yesmaximal, characteristic, complemented
18#27549C211yesmaximal, characteristic, complemented
19#27110C211yesmaximal, characteristic, complemented
20#27054C211yesmaximal, characteristic, complemented
21#26813C211yesmaximal, characteristic, complemented
22#26370C211yesmaximal, characteristic, complemented
23#25355C211yesmaximal, characteristic, complemented
24#25239C211yesmaximal, characteristic, complemented
25#24940C211yesmaximal, characteristic, complemented
26#24891C211yesmaximal, characteristic, complemented
27#23764C211yesmaximal, characteristic, complemented
28#23137C211yesmaximal, characteristic, complemented
29#23117C211yesmaximal, characteristic, complemented
30#22878C211yesmaximal, characteristic, complemented
31#22184C211yesmaximal, characteristic, complemented
32C2×#485C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#466C2211yescharacteristic
35C2×#466C2211yescharacteristic
36C2×#449C2211yescharacteristic
37C2×C4×D8C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×C8×D4C2211yescharacteristic
40C2×#417C2211yescharacteristic
41#2855C2211yescharacteristic
42#2797—21no—
43#2778—21no—
44#2771—21no—
45#2749—21no—
46#2746—21no—
47#2688—21no—
48#2635—21no—
49#2603—21no—
50#2578—21no—
51#2570C2211yescharacteristic
52#2562C2211yescharacteristic
53#2537C2211yescharacteristic
54#2535C2211yescharacteristic
55#2535C2211yescharacteristic
56#2535C2211yescharacteristic
57#2530—21no—
58#2518—21no—
59#2514C2211yescharacteristic
60#2510—21no—
61#2510—21no—
62#2496C2211yescharacteristic
63#2495C2211yescharacteristic
64#2494C2211yescharacteristic
65#2489C2211yescharacteristic
66#2487C2211yescharacteristic
67#2485C2211yescharacteristic
68#2485C2211yescharacteristic
69#2467—21no—
70#2454C2211yescharacteristic
71#2415C2211yescharacteristic
72#2407C2211yescharacteristic
73#2407C2211yescharacteristic
74#2364—21no—
75#2363C2211yescharacteristic
76#2363C2211yescharacteristic
77#2361C2211yescharacteristic
78#2352C2211yescharacteristic
79#2349C2211yescharacteristic
80#2339C2211yescharacteristic
81#2318—21no—
82C4×#121C2211yescharacteristic
83C4×#121C2211yescharacteristic
84C4×#121C2211yescharacteristic
85#2283C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2097C2211yescharacteristic
91#2095C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic
104#2075C2211yescharacteristic
105#2074C2211yescharacteristic
106#2074C2211yescharacteristic
107#2073C2211yescharacteristic
108#2071C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2036C2211yescharacteristic
115#2035C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1992C2211yescharacteristic
127#1973C2211yescharacteristic
128#1948C2211yescharacteristic
129#1944C2211yescharacteristic
130#1942C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1933C2211yescharacteristic
136#1928C2211yescharacteristic
137#1927C2211yescharacteristic
138#1927C2211yescharacteristic
139#1926C2211yescharacteristic
140#1926C2211yescharacteristic
141#1924C2211yescharacteristic
142#1924C2211yescharacteristic
143#1921C2211yescharacteristic
144#1921C2211yescharacteristic
145#1919C2211yescharacteristic
146#1919C2211yescharacteristic
147#1918C2211yescharacteristic
148#1918C2211yescharacteristic
149#1918C2211yescharacteristic
150#1917C2211yescharacteristic
151#1916C2211yescharacteristic
152#1895C2211yescharacteristic
153#1893C2211yescharacteristic
154#1893C2211yescharacteristic
155#1892C2211yescharacteristic
156#1892C2211yescharacteristic
157#1892C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic
166#1870C2211yescharacteristic
167#1869C2211yescharacteristic
168#1869C2211yescharacteristic
169#1869C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1853C2211yescharacteristic
179#1852C2211yescharacteristic
180#1846C2211yescharacteristic
181#1825C2211yescharacteristic
182#1823C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1808C2211yescharacteristic
186#1808C2211yescharacteristic
187#1807C2211yescharacteristic
188#1807C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1749C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×#126—21no—
211C2×#125C2311yescharacteristic
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×#121—21no—
215C2×#121D411yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×C4×D4—21no—
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C42C2311yescharacteristic
236#485—42no—
237#478—42no—
238#466—24no—
239#466—24no—
240#449—24no—
241C4×D8—42no—
242#435—42no—
243C8×D4—42no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260#417—42no—
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293#401—21no—
294#401—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#399—21no—
303#399—21no—
304#398—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#392—21no—
325#392—21no—
326#392—21no—
327#392—21no—
328#392—21no—
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#390—21no—
334#390—21no—
335#390D411yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#389—21no—
340#389D411yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388D411yescharacteristic
365#388D411yescharacteristic
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386D411yescharacteristic
394#386D411yescharacteristic
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#384C2311yescharacteristic
404#383—21no—
405#383—21no—
406#383—21no—
407#382—21no—
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#381—21no—
413#381—21no—
414#381—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380D411yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446#376—21no—
447C2×#95—21no—
448C2×#95—21no—
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
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2×D411yescharacteristic
501C22×D4C2×D411yescharacteristic
502C22×D4C2×D411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C2×SD16—22no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×D8—41no—
521C2×D8—41no—
522C2×D8#4114yes—
523C2×M16—22no—
524C2×M16—41no—
525C2×M16—41no—
526C22×C8—22no—
527C22×C8—22no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543#126—82no—
544#125—41no—
545#125—41no—
546C22⋊Q8—41no—
547C22⋊Q8—41no—
548C22⋊Q8—41no—
549C22⋊Q8—41no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—22no—
554#121—22no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—41no—
559#121—41no—
560#121—42no—
561#121—44no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—44no—
579C4×D4—82no—
580C4×D4—82no—
581#117—41no—
582#117—41no—
583#117—41no—
584#117—41no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
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—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—41no—
672C2×C42—41no—
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679#107—22no—
680#107—22no—
681#107—22no—
682#107—41no—
683#107—41no—
684#107—41no—
685#107—41no—
686#106—41no—
687#106—41no—
688#106—41no—
689#106—41no—
690#106—41no—
691#106—41no—
692#106—41no—
693C4⋊C8—22no—
694C4⋊C8—41no—
695#103—22no—
696#103—22no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715C22⋊C8—22no—
716C22⋊C8—22no—
717C22⋊C8—22no—
718C22⋊C8—41no—
719C22⋊C8—41no—
720C22⋊C8—41no—
721C22⋊C8—41no—
722C22⋊C8—41no—
723#97—41no—
724#97—41no—
725#97—41no—
726C4×C8—22no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
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#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776C24—21no—
777C24—21no—
778C24C22×D411yescharacteristic
779C24C22×D411yescharacteristic
780C24C22×D411yescharacteristic
781#41—44no—
782#41—82no—
783#41—82no—
784#41—82no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×D4—22no—
792C2×D4—22no—
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—41no—
804C2×D4—41no—
805C2×D4—41no—
806C2×D4—41no—
807C2×D4—41no—
808C2×D4—41no—
809C2×D4—41no—
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—81no—
820C2×D4—81no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4C2×#4112yes—
829C2×D4C2×#4112yes—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
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—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
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×C4—81no—
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
901SD16—82no—
902D8—44no—
903M16—82no—
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—
927C2×C8—82no—
928C2×C8—82no—
929C2×C8C2×#4112yes—
930C2×C8H(5,𝔽2)12yes—
931C4⋊C4—21no—
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—21no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
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—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
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—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—41no—
1030C42—41no—
1031C42—42no—
1032C42—42no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—22no—
1051C23—22no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
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#57512yes—
1073C23C23×D411yescharacteristic
1074Q8—41no—
1075Q8—41no—
1076Q8—41no—
1077Q8—41no—
1078D4—22no—
1079D4—22no—
1080D4—22no—
1081D4—22no—
1082D4—44no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—82no—
1088D4—82no—
1089D4—84no—
1090D4—84no—
1091D4—84no—
1092D4—84no—
1093D4—162no—
1094D4—162no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
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—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
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—82no—
1183C2×C4—82no—
1184C2×C4—84no—
1185C2×C4—162no—
1186C2×C4—162no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4—162no—
1190C2×C4—162no—
1191C2×C4C22×#4111yescharacteristic
1192C2×C4C2×H(5,𝔽2)11yescharacteristic
1193C2×C4#58511yescharacteristic
1194C2×C4#58511yescharacteristic
1195C2×C4#58511yescharacteristic
1196C2×C4#58511yescharacteristic
1197C8—22no—
1198C8—22no—
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C22—22no—
1206C22—22no—
1207C22—22no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—42no—
1214C22—42no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—42no—
1220C22—42no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—42no—
1231C22—42no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22D4×#4111yescharacteristic
1241C22#348511yescharacteristic
1242C22#349611yescharacteristic
1243C22C2×#57511yescharacteristic
1244C22#358411yescharacteristic
1245C22#358411yescharacteristic
1246C22#358511yescharacteristic
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4#350511yescharacteristic
1273C4#352111yescharacteristic
1274C4#356011yescharacteristic
1275C4#356611yescharacteristic
1276C2—42no—
1277C2—81no—
1278C2—81no—
1279C2—82no—
1280C2—82no—
1281C2#4350311yescharacteristic
1282C2#6145411yescharacteristic
1283C2#6148711yescharacteristic
1284C2#6174111yescharacteristic
1285C2#6176111yescharacteristic
1286C2#6225511yescharacteristic
1287C2#6235111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59215C2semidirect
2. #39537C2semidirect
3. #32386C2semidirect
4. #32265C2semidirect
5. #32011C2semidirect
6. #31995C2semidirect
7. #31475C2semidirect
8. #31387C2semidirect
9. #30402C2semidirect
10. #30398C2semidirect
11. #29481C2semidirect
12. #28225C2semidirect
13. #28103C2semidirect
14. #28081C2semidirect
15. #27860C2semidirect
16. #27854C2semidirect
17. #27579C2semidirect
18. #27549C2semidirect
19. #27110C2semidirect
20. #27054C2semidirect
21. #26813C2semidirect
22. #26370C2semidirect
23. #25355C2semidirect
24. #25239C2semidirect
25. #24940C2semidirect
26. #24891C2semidirect
27. #23764C2semidirect
28. #23137C2semidirect
29. #23117C2semidirect
30. #22878C2semidirect
31. #22184C2semidirect

Maximal subgroups

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

subgroupindex
#592152
#395372
#323862
#322652
#320112
#319952
#314752
#313872
#304022
#303982
#294812
#282252
#281032
#280812
#278602
#278542
#275792
#275492
#271102
#270542
#268132
#263702
#253552
#252392
#249402
#248912
#237642
#231372
#231172
#228782
#221842