Finite Group Databasebeta

← #6776903

Subgroups — #6776903

Order 512.

1409 conjugacy classes of subgroups.

The subgroup lattice has 1237 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36392C211yesmaximal, characteristic, complemented
2#34943C211yesmaximal, characteristic, complemented
3#33084C211yesmaximal, characteristic, complemented
4#32435C211yesmaximal, characteristic, complemented
5#32387C211yesmaximal, characteristic, complemented
6#32277C211yesmaximal, characteristic, complemented
7#32019C211yesmaximal, characteristic, complemented
8#31527C211yesmaximal, characteristic, complemented
9#31467C211yesmaximal, characteristic, complemented
10#31279C211yesmaximal, characteristic, complemented
11#30418C211yesmaximal, characteristic
12#30171C211yesmaximal, characteristic, complemented
13#30017C211yesmaximal, characteristic, complemented
14#29520C211yesmaximal, characteristic, complemented
15#29389C211yesmaximal, characteristic, complemented
16#29004C211yesmaximal, characteristic, complemented
17#28870C211yesmaximal, characteristic, complemented
18#28093C211yesmaximal, characteristic, complemented
19#27879C211yesmaximal, characteristic, complemented
20#27866C211yesmaximal, characteristic, complemented
21#27632C211yesmaximal, characteristic, complemented
22#27590C211yesmaximal, characteristic, complemented
23#27547C211yesmaximal, characteristic, complemented
24#27483C211yesmaximal, characteristic, complemented
25#27187C211yesmaximal, characteristic, complemented
26#25048C211yesmaximal, characteristic, complemented
27#24915C211yesmaximal, characteristic, complemented
28#22788C211yesmaximal, characteristic, complemented
29#22187C211yesmaximal, characteristic, complemented
30#22045C211yesmaximal, characteristic, complemented
31#21122C211yesmaximal, characteristic, complemented
32C2×#469C2211yescharacteristic
33C2×#449C2211yescharacteristic
34C2×#442C2211yescharacteristic
35#2863C2211yescharacteristic
36#2855C2211yescharacteristic
37#2851C2211yescharacteristic
38#2600—21no—
39#2598—21no—
40#2578—21no—
41#2576—21no—
42#2576—21no—
43#2575—21no—
44#2572—21no—
45#2572—21no—
46#2571C2211yescharacteristic
47#2563C2211yescharacteristic
48#2563C2211yescharacteristic
49#2537C2211yescharacteristic
50#2514C2211yescharacteristic
51#2495—21no—
52#2495C2211yescharacteristic
53#2495C2211yescharacteristic
54#2489C2211yescharacteristic
55#2485C2211yescharacteristic
56#2454C2211yescharacteristic
57#2420—21no—
58#2420C2211yescharacteristic
59#2420C2211yescharacteristic
60#2420C2211yescharacteristic
61#2407C2211yescharacteristic
62#2398—21no—
63#2398—21no—
64#2353—21no—
65#2346C2211yescharacteristic
66#2343—21no—
67#2339C2211yescharacteristic
68C4×C4⋊Q8C2211yescharacteristic
69C4×#121—21no—
70C4×#121C2211yescharacteristic
71C4×#121C2211yescharacteristic
72C4×#121C2211yescharacteristic
73#2297C2211yescharacteristic
74#2293C2211yescharacteristic
75#2283—21no—
76#2283C2211yescharacteristic
77#2283C2211yescharacteristic
78C42×D4C2211yescharacteristic
79C42×D4C2211yescharacteristic
80#2101C2211yescharacteristic
81#2099C2211yescharacteristic
82#2097C2211yescharacteristic
83#2097C2211yescharacteristic
84#2096C2211yescharacteristic
85#2092C2211yescharacteristic
86#2088C2211yescharacteristic
87#2085C2211yescharacteristic
88#2085C2211yescharacteristic
89#2083C2211yescharacteristic
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2076C2211yescharacteristic
95#2076C2211yescharacteristic
96#2075C2211yescharacteristic
97#2075C2211yescharacteristic
98#2075C2211yescharacteristic
99#2074C2211yescharacteristic
100#2074C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2071C2211yescharacteristic
104#2068C2211yescharacteristic
105#2067C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2057C2211yescharacteristic
109#2055C2211yescharacteristic
110#2035C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2025C2211yescharacteristic
117#2024C2211yescharacteristic
118#2023C2211yescharacteristic
119#2000C2211yescharacteristic
120#1991C2211yescharacteristic
121#1991C2211yescharacteristic
122#1970C2211yescharacteristic
123#1968C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1943C2211yescharacteristic
127#1943C2211yescharacteristic
128#1935C2211yescharacteristic
129#1935C2211yescharacteristic
130#1934C2211yescharacteristic
131#1933C2211yescharacteristic
132#1928C2211yescharacteristic
133#1928C2211yescharacteristic
134#1928C2211yescharacteristic
135#1928C2211yescharacteristic
136#1927C2211yescharacteristic
137#1926C2211yescharacteristic
138#1926C2211yescharacteristic
139#1926C2211yescharacteristic
140#1926C2211yescharacteristic
141#1925C2211yescharacteristic
142#1924C2211yescharacteristic
143#1924C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1920C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1918C2211yescharacteristic
156#1916C2211yescharacteristic
157#1916C2211yescharacteristic
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1875C2211yescharacteristic
169#1870C2211yescharacteristic
170#1870C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1846C2211yescharacteristic
183#1839C2211yescharacteristic
184#1835C2211yescharacteristic
185#1817C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1797C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1776C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1745C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×C22⋊Q8C2311yescharacteristic
211C2×#121—21no—
212C2×#121C2311yescharacteristic
213C2×#121C2311yescharacteristic
214C2×#121C2311yescharacteristic
215C2×C4×Q8—21no—
216C2×C4×D4—21no—
217C2×C4×D4—21no—
218C2×C4×D4—21no—
219C2×C4×D4D411yescharacteristic
220C2×C4×D4D411yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228C2×#117C2311yescharacteristic
229C22×C42—21no—
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232#469—24no—
233#449—24no—
234#442—24no—
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281#401—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#399—21no—
289#397—21no—
290#397—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#396—21no—
297#394—21no—
298#394—21no—
299#394—21no—
300#394—21no—
301#394—21no—
302#394—21no—
303#394—21no—
304#393—21no—
305#393—21no—
306#393—21no—
307#393—21no—
308#392—21no—
309#391—21no—
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#390—21no—
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#390C2311yescharacteristic
321#389—21no—
322#389—21no—
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#388—21no—
334#388—21no—
335#388—21no—
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#386—21no—
354#386—21no—
355#386—21no—
356#386—21no—
357#386—21no—
358#386—21no—
359#386—21no—
360#386—21no—
361#386—21no—
362#386—21no—
363#386—21no—
364#385—21no—
365#385—21no—
366#385—21no—
367#385—21no—
368#385—21no—
369#384C2311yescharacteristic
370#383—21no—
371#383—21no—
372#383—21no—
373#383—21no—
374#383—21no—
375#383—21no—
376#382—21no—
377#382—21no—
378#382—21no—
379#382—21no—
380#382C2311yescharacteristic
381#382C2311yescharacteristic
382#382C2311yescharacteristic
383#382C2311yescharacteristic
384#382C2311yescharacteristic
385#381—21no—
386#381—21no—
387#381—21no—
388#381—21no—
389#381—21no—
390#381—21no—
391#381—21no—
392#380—21no—
393#380—21no—
394#380—21no—
395#380—21no—
396#380C2311yescharacteristic
397#380C2311yescharacteristic
398#380C2311yescharacteristic
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406C4×C4⋊C4—21no—
407C4×C4⋊C4D411yescharacteristic
408C4×C4⋊C4D411yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C22⋊C4—21no—
418C4×C22⋊C4—21no—
419C4×C22⋊C4—21no—
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4D411yescharacteristic
429C4×C22⋊C4D411yescharacteristic
430C4×C22⋊C4D411yescharacteristic
431C4×C22⋊C4D411yescharacteristic
432C4×C22⋊C4C2311yescharacteristic
433C4×C22⋊C4C2311yescharacteristic
434#376—21no—
435#376—21no—
436#376—21no—
437C2×#95—21no—
438C43C2311yescharacteristic
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#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C2×#41—22no—
482C2×#41—41no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4C2×D411yescharacteristic
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2×D411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C2×SD16—22no—
509C2×SD16—41no—
510C2×SD16—41no—
511C2×D8—41no—
512C2×D8—41no—
513C2×D8#4114yes—
514C2×M16—22no—
515C2×M16—41no—
516C2×M16—41no—
517C2×M16—41no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530#125—41no—
531#125—41no—
532C22⋊Q8—41no—
533C22⋊Q8—41no—
534#121—22no—
535#121—22no—
536#121—22no—
537#121—41no—
538#121—41no—
539#121—41no—
540#121—44no—
541C4×Q8—82no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—42no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—42no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—44no—
557C4×D4—82no—
558C4×D4—82no—
559#117—44no—
560#117—41no—
561#117—41no—
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⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
595C2×C22⋊C4—21no—
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—41no—
639C2×C42—41no—
640C2×C42—41no—
641C2×C42—41no—
642C2×C42—44no—
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656#107—41no—
657#107—41no—
658#107—41no—
659#107—41no—
660#107—41no—
661#107—41no—
662#107—41no—
663#106—22no—
664#106—22no—
665#106—41no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672#103—22no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—41no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692C22⋊C8—22no—
693C22⋊C8—41no—
694C22⋊C8—41no—
695C22⋊C8—41no—
696C22⋊C8—41no—
697C22⋊C8—41no—
698#97—22no—
699#97—41no—
700C4×C8—41no—
701C4×C8—41no—
702#95—21no—
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#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#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755C24—21no—
756C24—21no—
757C24C22×D411yescharacteristic
758C24C22×D411yescharacteristic
759#41—82no—
760#41—82no—
761#41—82no—
762#41—82no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—42no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—41no—
784C2×D4—41no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—81no—
797C2×D4C2×#4112yes—
798C2×D4C2×#4112yes—
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—22no—
812C22×C4—22no—
813C22×C4—21no—
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—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C2511yescharacteristic
868SD16—82no—
869D8—44no—
870M16—82no—
871M16—82no—
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—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8C2×#4112yes—
896C4⋊C4—22no—
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—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—81no—
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—
941C22⋊C4—41no—
942C22⋊C4—41no—
943C22⋊C4—41no—
944C22⋊C4—41no—
945C22⋊C4—41no—
946C22⋊C4—41no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C42—22no—
978C42—22no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—41no—
990C42—41no—
991C42—41no—
992C42—41no—
993C42—41no—
994C42—41no—
995C42—42no—
996C42—42no—
997C42—42no—
998C42—42no—
999C42—42no—
1000C42—42no—
1001C42—42no—
1002C42—42no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—22no—
1010C23—22no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23C23×D411yescharacteristic
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—41no—
1036Q8—84no—
1037D4—22no—
1038D4—22no—
1039D4—22no—
1040D4—22no—
1041D4—44no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—84no—
1047D4—84no—
1048D4—84no—
1049D4—84no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
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—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
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—82no—
1135C2×C4—82no—
1136C2×C4—84no—
1137C2×C4—84no—
1138C2×C4—82no—
1139C2×C4—82no—
1140C2×C4—84no—
1141C2×C4—84no—
1142C2×C4—84no—
1143C2×C4—162no—
1144C2×C4#57512yes—
1145C2×C4#57512yes—
1146C2×C4C22×#4111yescharacteristic
1147C2×C4#58511yescharacteristic
1148C2×C4#58511yescharacteristic
1149C2×C4#58511yescharacteristic
1150C2×C4#58511yescharacteristic
1151C2×C4#58511yescharacteristic
1152C8—22no—
1153C8—41no—
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C22—42no—
1161C22—41no—
1162C22—42no—
1163C22—41no—
1164C22—41no—
1165C22—41no—
1166C22—42no—
1167C22—41no—
1168C22—41no—
1169C22—42no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—42no—
1179C22—42no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22#344911yescharacteristic
1189C22D4×#4111yescharacteristic
1190C22#348511yescharacteristic
1191C22C2×#57511yescharacteristic
1192C22C2×#57511yescharacteristic
1193C22#358411yescharacteristic
1194C22#358511yescharacteristic
1195C4—22no—
1196C4—22no—
1197C4—41no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—81no—
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#349111yescharacteristic
1222C4#352111yescharacteristic
1223C4#356611yescharacteristic
1224C4#356811yescharacteristic
1225C2—81no—
1226C2—81no—
1227C2—82no—
1228C2—82no—
1229C2#3837611yescharacteristic
1230C2#6097011yescharacteristic
1231C2#6099711yescharacteristic
1232C2#6144211yescharacteristic
1233C2#6146411yescharacteristic
1234C2#6171011yescharacteristic
1235C2#6174311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30418C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36392C2semidirect
2. #34943C2semidirect
3. #33084C2semidirect
4. #32435C2semidirect
5. #32387C2semidirect
6. #32277C2semidirect
7. #32019C2semidirect
8. #31527C2semidirect
9. #31467C2semidirect
10. #31279C2semidirect
12. #30171C2semidirect
13. #30017C2semidirect
14. #29520C2semidirect
15. #29389C2semidirect
16. #29004C2semidirect
17. #28870C2semidirect
18. #28093C2semidirect
19. #27879C2semidirect
20. #27866C2semidirect
21. #27632C2semidirect
22. #27590C2semidirect
23. #27547C2semidirect
24. #27483C2semidirect
25. #27187C2semidirect
26. #25048C2semidirect
27. #24915C2semidirect
28. #22788C2semidirect
29. #22187C2semidirect
30. #22045C2semidirect
31. #21122C2semidirect

Maximal subgroups

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

subgroupindex
#363922
#349432
#330842
#324352
#323872
#322772
#320192
#315272
#314672
#312792
#304182
#301712
#300172
#295202
#293892
#290042
#288702
#280932
#278792
#278662
#276322
#275902
#275472
#274832
#271872
#250482
#249152
#227882
#221872
#220452
#211222