Finite Group Databasebeta

← #7050072

Subgroups — #7050072

Order 512.

1387 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59441C211yesmaximal, characteristic, complemented
2#59217C211yesmaximal, characteristic
3#32392C211yesmaximal, characteristic, complemented
4#32310C211yesmaximal, characteristic, complemented
5#31994C211yesmaximal, characteristic, complemented
6#31792C211yesmaximal, characteristic, complemented
7#31782C211yesmaximal, characteristic, complemented
8#31384C211yesmaximal, characteristic, complemented
9#30582C211yesmaximal, characteristic, complemented
10#30573C211yesmaximal, characteristic, complemented
11#29414C211yesmaximal, characteristic, complemented
12#28843C211yesmaximal, characteristic, complemented
13#27841C211yesmaximal, characteristic, complemented
14#27614C211yesmaximal, characteristic, complemented
15#27555C211yesmaximal, characteristic, complemented
16#27469C211yesmaximal, characteristic, complemented
17#27315C211yesmaximal, characteristic, complemented
18#27106C211yesmaximal, characteristic, complemented
19#27036C211yesmaximal, characteristic, complemented
20#26671C211yesmaximal, characteristic, complemented
21#26211C211yesmaximal, characteristic, complemented
22#25027C211yesmaximal, characteristic, complemented
23#24967C211yesmaximal, characteristic, complemented
24#24958C211yesmaximal, characteristic, complemented
25#24953C211yesmaximal, characteristic, complemented
26#24940C211yesmaximal, characteristic, complemented
27#23756C211yesmaximal, characteristic, complemented
28#23142C211yesmaximal, characteristic, complemented
29#22921C211yesmaximal, characteristic, complemented
30#22333C211yesmaximal, characteristic, complemented
31#22075C211yesmaximal, characteristic, complemented
32C2×#482C2211yescharacteristic
33C2×#480C2211yescharacteristic
34C2×#468C2211yescharacteristic
35#2781—21no—
36#2781—21no—
37#2777—21no—
38#2765—21no—
39#2606—21no—
40#2562—21no—
41#2558—21no—
42#2552C2211yescharacteristic
43#2537C2211yescharacteristic
44#2537C2211yescharacteristic
45#2537C2211yescharacteristic
46#2514C2211yescharacteristic
47#2510—21no—
48#2506C2211yescharacteristic
49#2497C2211yescharacteristic
50#2497C2211yescharacteristic
51#2495C2211yescharacteristic
52#2490—21no—
53#2486C2211yescharacteristic
54#2485C2211yescharacteristic
55#2485C2211yescharacteristic
56#2476—21no—
57#2476—21no—
58#2443—21no—
59#2442—21no—
60#2423C2211yescharacteristic
61#2417C2211yescharacteristic
62#2417C2211yescharacteristic
63#2416—21no—
64#2415C2211yescharacteristic
65#2363C2211yescharacteristic
66#2363C2211yescharacteristic
67#2360C2211yescharacteristic
68#2354C2211yescharacteristic
69#2353—21no—
70#2352C2211yescharacteristic
71D4×C4⋊C4C2211yescharacteristic
72D4×C4⋊C4C2211yescharacteristic
73#2346C2211yescharacteristic
74#2345—21no—
75C4×C22⋊Q8C2211yescharacteristic
76C4×#121C2211yescharacteristic
77C4×#121C2211yescharacteristic
78C2×#389C2211yescharacteristic
79#2285C2211yescharacteristic
80#2101C2211yescharacteristic
81#2100C2211yescharacteristic
82#2100C2211yescharacteristic
83#2099C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2096C2211yescharacteristic
87#2095C2211yescharacteristic
88#2088C2211yescharacteristic
89#2086C2211yescharacteristic
90#2085C2211yescharacteristic
91#2084C2211yescharacteristic
92#2083C2211yescharacteristic
93#2083C2211yescharacteristic
94#2083C2211yescharacteristic
95#2083C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic
104#2072C2211yescharacteristic
105#2072C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2036C2211yescharacteristic
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2000C2211yescharacteristic
119#2000C2211yescharacteristic
120#1955C2211yescharacteristic
121#1954C2211yescharacteristic
122#1948C2211yescharacteristic
123#1947C2211yescharacteristic
124#1943C2211yescharacteristic
125#1942C2211yescharacteristic
126#1942C2211yescharacteristic
127#1942C2211yescharacteristic
128#1935C2211yescharacteristic
129#1934C2211yescharacteristic
130#1934C2211yescharacteristic
131#1933C2211yescharacteristic
132#1927C2211yescharacteristic
133#1925C2211yescharacteristic
134#1923C2211yescharacteristic
135#1923C2211yescharacteristic
136#1921C2211yescharacteristic
137#1921C2211yescharacteristic
138#1921C2211yescharacteristic
139#1921C2211yescharacteristic
140#1921C2211yescharacteristic
141#1920C2211yescharacteristic
142#1920C2211yescharacteristic
143#1918C2211yescharacteristic
144#1918C2211yescharacteristic
145#1918C2211yescharacteristic
146#1918C2211yescharacteristic
147#1918C2211yescharacteristic
148#1917C2211yescharacteristic
149#1916C2211yescharacteristic
150#1893C2211yescharacteristic
151#1892C2211yescharacteristic
152#1880C2211yescharacteristic
153#1877C2211yescharacteristic
154#1877C2211yescharacteristic
155#1877C2211yescharacteristic
156#1874C2211yescharacteristic
157#1874C2211yescharacteristic
158#1873C2211yescharacteristic
159#1873C2211yescharacteristic
160#1870C2211yescharacteristic
161#1870C2211yescharacteristic
162#1869C2211yescharacteristic
163#1869C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1863C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1852C2211yescharacteristic
175#1852C2211yescharacteristic
176#1852C2211yescharacteristic
177#1852C2211yescharacteristic
178#1847C2211yescharacteristic
179#1834C2211yescharacteristic
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1824C2211yescharacteristic
183#1824C2211yescharacteristic
184#1824C2211yescharacteristic
185#1823C2211yescharacteristic
186#1817C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1808C2211yescharacteristic
190#1804C2211yescharacteristic
191#1802C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C4×#106C2211yescharacteristic
194#1762C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1736C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×#125—21no—
207C2×#125—21no—
208C2×#123—21no—
209C2×C22⋊Q8C2311yescharacteristic
210C2×C22⋊Q8C2311yescharacteristic
211C2×C22⋊Q8C2311yescharacteristic
212C2×#121—21no—
213C2×#121—21no—
214C2×#121—21no—
215C2×#121D411yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4—21no—
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×#117—21no—
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C22×C4⋊C4—21no—
233C22×C4⋊C4—21no—
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C42C2311yescharacteristic
238#482—24no—
239#480—24no—
240#468—24no—
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
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×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286#401—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#399—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#390—21no—
322#390—21no—
323#390—21no—
324#390D411yescharacteristic
325#390C2311yescharacteristic
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389D411yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
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#388D411yescharacteristic
361#388D411yescharacteristic
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#386—21no—
373#386—21no—
374#386—21no—
375#386—21no—
376#386—21no—
377#386—21no—
378#386D411yescharacteristic
379#386D411yescharacteristic
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#384C2311yescharacteristic
387#384C2311yescharacteristic
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#383—21no—
392#383—21no—
393#382—21no—
394#382—21no—
395#382C2311yescharacteristic
396#381—21no—
397#380—21no—
398#380—21no—
399#380—21no—
400#380—21no—
401#380—21no—
402#380—21no—
403#380—21no—
404#380D411yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4C2311yescharacteristic
434C4×C22⋊C4C2311yescharacteristic
435#376—21no—
436C2×#95—21no—
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
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#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8C2411yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4C2×D411yescharacteristic
486C22×D4C2×D411yescharacteristic
487C22×D4C2×D411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4C2×D411yescharacteristic
496C23×C4C2×D411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C2×SD16—22no—
501C2×SD16—41no—
502C2×SD16—41no—
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C22×C8—41no—
507C22×C8—41no—
508C22×C8—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517#125—82no—
518#125—82no—
519#123—82no—
520C22⋊Q8—22no—
521C22⋊Q8—41no—
522C22⋊Q8—41no—
523C22⋊Q8—41no—
524C22⋊Q8—41no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121—42no—
530#121—41no—
531#121—41no—
532#121—41no—
533#121—82no—
534#121—82no—
535#121—82no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×D4—41no—
539C4×D4—41no—
540C4×D4—41no—
541C4×D4—41no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—44no—
551C4×D4—82no—
552#117—22no—
553#117—41no—
554#117—41no—
555#117—41no—
556#117—41no—
557#117—41no—
558#117—82no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—44no—
595C2×C4⋊C4—82no—
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—41no—
662C2×C42—41no—
663C2×C42C2×D411yescharacteristic
664C2×C42C2×D411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669#107—22no—
670#107—22no—
671#107—22no—
672#107—22no—
673#107—41no—
674#107—41no—
675#107—41no—
676#107—41no—
677#107—41no—
678#107—41no—
679#106—22no—
680#106—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686#103—22no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#102—22no—
694#102—22no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102#4114yes—
700C22⋊C8—22no—
701C22⋊C8—22no—
702C22⋊C8—41no—
703C22⋊C8—41no—
704C22⋊C8—41no—
705C22⋊C8—41no—
706C22⋊C8—41no—
707C22⋊C8—41no—
708C22⋊C8—41no—
709C22⋊C8—41no—
710#97—41no—
711C4×C8—41no—
712C4×C8—41no—
713C4×C8—41no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
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#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758C24—21no—
759C24C22×D411yescharacteristic
760C24C22×D411yescharacteristic
761C24C22×D411yescharacteristic
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—41no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—81no—
787C2×D4—81no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4C2×#4112yes—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C2511yescharacteristic
861SD16—82no—
862M16—82no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—82no—
887C2×C8C2×#4112yes—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4C2×#4112yes—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—22no—
953C22⋊C4—41no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—41no—
995C42—41no—
996C42—42no—
997C42—42no—
998C42—42no—
999C42—42no—
1000C42—81no—
1001C42—81no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—22no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23#57712yes—
1034C23C23×D411yescharacteristic
1035Q8—41no—
1036Q8—41no—
1037Q8—41no—
1038Q8—41no—
1039D4—22no—
1040D4—22no—
1041D4—44no—
1042D4—41no—
1043D4—41no—
1044D4—82no—
1045D4—82no—
1046D4—84no—
1047D4—162no—
1048D4—162no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—44no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
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—82no—
1138C2×C4—84no—
1139C2×C4—84no—
1140C2×C4—162no—
1141C2×C4—162no—
1142C2×C4—162no—
1143C2×C4—162no—
1144C2×C4#57512yes—
1145C2×C4#57612yes—
1146C2×C4#57812yes—
1147C2×C4C22×#4111yescharacteristic
1148C2×C4#58511yescharacteristic
1149C2×C4#58511yescharacteristic
1150C2×C4#58511yescharacteristic
1151C2×C4#58511yescharacteristic
1152C2×C4#58511yescharacteristic
1153C8—22no—
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C22—22no—
1162C22—22no—
1163C22—22no—
1164C22—41no—
1165C22—41no—
1166C22—41no—
1167C22—41no—
1168C22—41no—
1169C22—41no—
1170C22—42no—
1171C22—41no—
1172C22—41no—
1173C22—42no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—42no—
1179C22—41no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22D4×#4111yescharacteristic
1190C22#348511yescharacteristic
1191C22#348511yescharacteristic
1192C22C2×#57511yescharacteristic
1193C22C2×#57611yescharacteristic
1194C22C2×#57711yescharacteristic
1195C22C2×#57811yescharacteristic
1196C4—22no—
1197C4—22no—
1198C4—22no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—42no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4#351211yescharacteristic
1223C4#352111yescharacteristic
1224C4#356611yescharacteristic
1225C4#356711yescharacteristic
1226C2—42no—
1227C2—81no—
1228C2—81no—
1229C2—82no—
1230C2#4354211yescharacteristic
1231C2#6144711yescharacteristic
1232C2#6149611yescharacteristic
1233C2#6172911yescharacteristic
1234C2#6174011yescharacteristic
1235C2#6176711yescharacteristic
1236C2#6179111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59217C2
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. #59441C2semidirect
3. #32392C2semidirect
4. #32310C2semidirect
5. #31994C2semidirect
6. #31792C2semidirect
7. #31782C2semidirect
8. #31384C2semidirect
9. #30582C2semidirect
10. #30573C2semidirect
11. #29414C2semidirect
12. #28843C2semidirect
13. #27841C2semidirect
14. #27614C2semidirect
15. #27555C2semidirect
16. #27469C2semidirect
17. #27315C2semidirect
18. #27106C2semidirect
19. #27036C2semidirect
20. #26671C2semidirect
21. #26211C2semidirect
22. #25027C2semidirect
23. #24967C2semidirect
24. #24958C2semidirect
25. #24953C2semidirect
26. #24940C2semidirect
27. #23756C2semidirect
28. #23142C2semidirect
29. #22921C2semidirect
30. #22333C2semidirect
31. #22075C2semidirect

Maximal subgroups

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

subgroupindex
#594412
#592172
#323922
#323102
#319942
#317922
#317822
#313842
#305822
#305732
#294142
#288432
#278412
#276142
#275552
#274692
#273152
#271062
#270362
#266712
#262112
#250272
#249672
#249582
#249532
#249402
#237562
#231422
#229212
#223332
#220752