Finite Group Databasebeta

← #7584554

Subgroups — #7584554

Order 512.

1367 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59497C211yesmaximal, characteristic, complemented
2#36413C211yesmaximal, characteristic, complemented
3#31480C211yesmaximal, characteristic, complemented
4#31252C211yesmaximal, characteristic, complemented
5#31129C211yesmaximal, characteristic, complemented
6#30603C211yesmaximal, characteristic
7#29521C211yesmaximal, characteristic, complemented
8#29444C211yesmaximal, characteristic, complemented
9#29037C211yesmaximal, characteristic, complemented
10#28079C211yesmaximal, characteristic, complemented
11#28007C211yesmaximal, characteristic, complemented
12#27443C211yesmaximal, characteristic, complemented
13#27386C211yesmaximal, characteristic, complemented
14#27184C211yesmaximal, characteristic, complemented
15#27171C211yesmaximal, characteristic, complemented
16#27061C211yesmaximal, characteristic, complemented
17#26876C211yesmaximal, characteristic, complemented
18#26812C211yesmaximal, characteristic
19#26783C211yesmaximal, characteristic, complemented
20#26685C211yesmaximal, characteristic
21#26184C211yesmaximal, characteristic, complemented
22#26099C211yesmaximal, characteristic, complemented
23#25995C211yesmaximal, characteristic, complemented
24#25040C211yesmaximal, characteristic, complemented
25#23292C211yesmaximal, characteristic, complemented
26#23135C211yesmaximal, characteristic, complemented
27#23104C211yesmaximal, characteristic, complemented
28#22979C211yesmaximal, characteristic, complemented
29#22935C211yesmaximal, characteristic, complemented
30#21616C211yesmaximal, characteristic, complemented
31#21124C211yesmaximal, characteristic, complemented
32C2×#482C2211yescharacteristic
33C2×#477C2211yescharacteristic
34C2×#474C2211yescharacteristic
35C2×#465C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#440C2211yescharacteristic
38#2861—21no—
39#2860C2211yescharacteristic
40#2779—21no—
41#2765—21no—
42#2601—21no—
43#2593—21no—
44#2574—21no—
45#2570C2211yescharacteristic
46#2532—21no—
47#2527—21no—
48#2521—21no—
49#2519—21no—
50#2509C2211yescharacteristic
51#2508C2211yescharacteristic
52#2506C2211yescharacteristic
53#2494C2211yescharacteristic
54#2491C2211yescharacteristic
55#2488—21no—
56#2479—21no—
57#2458—21no—
58#2452C2211yescharacteristic
59#2451C2211yescharacteristic
60#2448C2211yescharacteristic
61#2439C2211yescharacteristic
62#2426C2211yescharacteristic
63#2423C2211yescharacteristic
64#2422C2211yescharacteristic
65#2421—21no—
66#2420C2211yescharacteristic
67#2369C2211yescharacteristic
68#2367C2211yescharacteristic
69#2363C2211yescharacteristic
70#2363C2211yescharacteristic
71#2362C2211yescharacteristic
72#2357C2211yescharacteristic
73#2354C2211yescharacteristic
74#2349C2211yescharacteristic
75#2346C2211yescharacteristic
76#2346C2211yescharacteristic
77#2343—21no—
78C4×C4⋊Q8C2211yescharacteristic
79C4×#126C2211yescharacteristic
80#2298—21no—
81#2293C2211yescharacteristic
82C42×Q8C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2094C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2086C2211yescharacteristic
92#2085C2211yescharacteristic
93#2077C2211yescharacteristic
94#2074C2211yescharacteristic
95#2074C2211yescharacteristic
96#2071C2211yescharacteristic
97#2068C2211yescharacteristic
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2066C2211yescharacteristic
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2058C2211yescharacteristic
104#2057C2211yescharacteristic
105#2057C2211yescharacteristic
106#2054C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2036C2211yescharacteristic
110#2035C2211yescharacteristic
111#2034C2211yescharacteristic
112#2033C2211yescharacteristic
113#2023C2211yescharacteristic
114#1999C2211yescharacteristic
115#1993C2211yescharacteristic
116#1987C2211yescharacteristic
117#1973C2211yescharacteristic
118#1972C2211yescharacteristic
119#1958C2211yescharacteristic
120#1949C2211yescharacteristic
121#1949C2211yescharacteristic
122#1948C2211yescharacteristic
123#1948C2211yescharacteristic
124#1943C2211yescharacteristic
125#1943C2211yescharacteristic
126#1943C2211yescharacteristic
127#1943C2211yescharacteristic
128#1942C2211yescharacteristic
129#1941C2211yescharacteristic
130#1940C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1935C2211yescharacteristic
137#1927C2211yescharacteristic
138#1926C2211yescharacteristic
139#1926C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1924C2211yescharacteristic
144#1924C2211yescharacteristic
145#1923C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1917C2211yescharacteristic
161#1893C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1877C2211yescharacteristic
168#1875C2211yescharacteristic
169#1873C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1850C2211yescharacteristic
181#1847C2211yescharacteristic
182#1825C2211yescharacteristic
183#1808C2211yescharacteristic
184#1804C2211yescharacteristic
185#1803C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1771C2211yescharacteristic
190#1770C2211yescharacteristic
191#1767C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic
201#1745C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#126D411yescharacteristic
210C2×#125—21no—
211C2×#124—21no—
212C2×#124C2311yescharacteristic
213C2×#123—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×C4×Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117—21no—
227C2×#117—21no—
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230#482—24no—
231#477—24no—
232#474—24no—
233#465—24no—
234#463—24no—
235#440—24no—
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285#401—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#399—21no—
292#399—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#395—21no—
306#394—21no—
307#394—21no—
308#394—21no—
309#394—21no—
310#393—21no—
311#393—21no—
312#393—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#390—21no—
321#390—21no—
322#390—21no—
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#389—21no—
331#389—21no—
332#389—21no—
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#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
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#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388D411yescharacteristic
374#388D411yescharacteristic
375#388D411yescharacteristic
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387D411yescharacteristic
387#387D411yescharacteristic
388#387D411yescharacteristic
389#386—21no—
390#386—21no—
391#386—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#383D411yescharacteristic
400#382—21no—
401#382—21no—
402#382—21no—
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#381—21no—
407#381—21no—
408#380—21no—
409#380—21no—
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439#376—21no—
440#376—21no—
441C2×#95—21no—
442C43—21no—
443C43C2311yescharacteristic
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#340C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8C2411yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4C2411yescharacteristic
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4C2411yescharacteristic
496C2×SD16—41no—
497C2×SD16—41no—
498C2×SD16#4114yes—
499C2×D8—22no—
500C2×D8—41no—
501C2×D8—41no—
502C22×C8—22no—
503C22×C8—41no—
504C22×C8—41no—
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517#126—42no—
518#126—82no—
519#125—82no—
520#124—22no—
521#124—41no—
522#124—82no—
523#123—82no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526C22⋊Q8—82no—
527#121—22no—
528#121—22no—
529#121—41no—
530#121—41no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8—82no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—41no—
546#117—22no—
547#117—22no—
548#117—44no—
549#117—41no—
550#117—41no—
551#117—44no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654#107—22no—
655#107—22no—
656#107—22no—
657#107—22no—
658#107—41no—
659#107—41no—
660#107#4114yes—
661#106—22no—
662#106—22no—
663#106—41no—
664#106—41no—
665#106—41no—
666#106—41no—
667#106—41no—
668C4⋊C8—22no—
669C4⋊C8—22no—
670C4⋊C8—22no—
671C4⋊C8—41no—
672C4⋊C8—41no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—41no—
679#103—41no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693C22⋊C8—22no—
694C22⋊C8—41no—
695C22⋊C8—41no—
696#97—22no—
697#97—41no—
698#97—41no—
699#97—41no—
700#97—41no—
701#97—41no—
702C4×C8—41no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
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#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24—21no—
753C24—21no—
754C24C22×D411yescharacteristic
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—42no—
761C2×Q8—42no—
762C2×Q8—42no—
763C2×Q8—81no—
764C2×Q8—81no—
765C2×Q8—81no—
766C2×Q8C2×#4112yes—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—81no—
781C2×D4—81no—
782C2×D4—81no—
783C2×D4—81no—
784C2×D4C2×#4112yes—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
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—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C2511yescharacteristic
831SD16—44no—
832D8—82no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—82no—
856C2×C8C2×#4112yes—
857C2×C8C2×#4112yes—
858C4⋊C4—22no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—41no—
883C4⋊C4—41no—
884C4⋊C4—41no—
885C4⋊C4—41no—
886C4⋊C4—41no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4C2×#4112yes—
913C4⋊C4C2×#4112yes—
914C4⋊C42−1+412yes—
915C22⋊C4—22no—
916C22⋊C4—41no—
917C22⋊C4—41no—
918C22⋊C4—41no—
919C22⋊C4—41no—
920C22⋊C4—41no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C42—22no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—41no—
963C42—41no—
964C42—41no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—42no—
970C42—42no—
971C42—42no—
972C42—42no—
973C42—42no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42—81no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23C23×D411yescharacteristic
1001Q8—22no—
1002Q8—22no—
1003Q8—41no—
1004Q8—41no—
1005Q8—84no—
1006Q8—162no—
1007D4—22no—
1008D4—22no—
1009D4—41no—
1010D4—41no—
1011D4—41no—
1012D4—41no—
1013D4—41no—
1014D4—41no—
1015D4—162no—
1016D4—162no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
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—84no—
1102C2×C4—84no—
1103C2×C4—162no—
1104C2×C4—162no—
1105C2×C4#57512yes—
1106C2×C4C22×#4111yescharacteristic
1107C2×C4C22×#4111yescharacteristic
1108C2×C4C2×2−1+411yescharacteristic
1109C2×C4#58511yescharacteristic
1110C2×C4#58511yescharacteristic
1111C2×C4#58511yescharacteristic
1112C8—22no—
1113C8—22no—
1114C8—41no—
1115C8—41no—
1116C8—41no—
1117C8—41no—
1118C8—41no—
1119C8—41no—
1120C22—41no—
1121C22—41no—
1122C22—42no—
1123C22—41no—
1124C22—41no—
1125C22—42no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—41no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22D4×#4111yescharacteristic
1142C22D4×#4111yescharacteristic
1143C22#348911yescharacteristic
1144C22C2×#57511yescharacteristic
1145C22#358511yescharacteristic
1146C22#358511yescharacteristic
1147C22#358611yescharacteristic
1148C4—22no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—42no—
1156C4—41no—
1157C4—41no—
1158C4—42no—
1159C4—42no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—42no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4#348211yescharacteristic
1176C4#349111yescharacteristic
1177C4#351211yescharacteristic
1178C4#356511yescharacteristic
1179C2—81no—
1180C2—82no—
1181C2—161no—
1182C2#5917811yescharacteristic
1183C2#6145811yescharacteristic
1184C2#6145911yescharacteristic
1185C2#6150511yescharacteristic
1186C2#6151311yescharacteristic
1187C2#6211511yescharacteristic
1188C2#6222611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#1999C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59497C2semidirect
2. #36413C2semidirect
3. #31480C2semidirect
4. #31252C2semidirect
5. #31129C2semidirect
7. #29521C2semidirect
8. #29444C2semidirect
9. #29037C2semidirect
10. #28079C2semidirect
11. #28007C2semidirect
12. #27443C2semidirect
13. #27386C2semidirect
14. #27184C2semidirect
15. #27171C2semidirect
16. #27061C2semidirect
17. #26876C2semidirect
19. #26783C2semidirect
21. #26184C2semidirect
22. #26099C2semidirect
23. #25995C2semidirect
24. #25040C2semidirect
25. #23292C2semidirect
26. #23135C2semidirect
27. #23104C2semidirect
28. #22979C2semidirect
29. #22935C2semidirect
30. #21616C2semidirect
31. #21124C2semidirect

Maximal subgroups

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

subgroupindex
#594972
#364132
#314802
#312522
#311292
#306032
#295212
#294442
#290372
#280792
#280072
#274432
#273862
#271842
#271712
#270612
#268762
#268122
#267832
#266852
#261842
#260992
#259952
#250402
#232922
#231352
#231042
#229792
#229352
#216162
#211242