Finite Group Databasebeta

← #7525774

Subgroups — #7525774

Order 512.

1726 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44918C211yesmaximal, characteristic, complemented
2#35976C211yesmaximal, characteristic, complemented
3#31943C211yesmaximal, characteristic, complemented
4#31912C211yesmaximal, characteristic, complemented
5#31655C211yesmaximal, characteristic, complemented
6#31558C211yesmaximal, characteristic, complemented
7#28982C211yesmaximal, characteristic, complemented
8#28888C211yesmaximal, characteristic, complemented
9#28101C211yesmaximal, characteristic, complemented
10#27871C211yesmaximal, characteristic, complemented
11#27701C211yesmaximal, characteristic, complemented
12#27574C211yesmaximal, characteristic, complemented
13#27563C211yesmaximal, characteristic, complemented
14#27240C211yesmaximal, characteristic, complemented
15#27200C211yesmaximal, characteristic, complemented
16#26678C211yesmaximal, characteristic, complemented
17#25972C211yesmaximal, characteristic, complemented
18#24937C211yesmaximal, characteristic, complemented
19#24901C211yesmaximal, characteristic, complemented
20#24822C211yesmaximal, characteristic, complemented
21#24547C211yesmaximal, characteristic, complemented
22#24531C211yesmaximal, characteristic, complemented
23#24519C211yesmaximal, characteristic, complemented
24#23850C211yesmaximal, characteristic
25#22905C211yesmaximal, characteristic, complemented
26#22874C211yesmaximal, characteristic, complemented
27#22760C211yesmaximal, characteristic, complemented
28#22449C211yesmaximal, characteristic, complemented
29#22419C211yesmaximal, characteristic, complemented
30#20937C211yesmaximal, characteristic, complemented
31#20746C211yesmaximal, characteristic, complemented
32C22×#135C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#449C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×#433C2211yescharacteristic, complemented
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic, complemented
45C22×#102C2211yescharacteristic
46#2786—21no—
47#2757—21no—
48#2748—21no—
49#2722—21no—
50#2624C2211yescharacteristic
51#2623—21no—
52#2603—21no—
53#2578—21no—
54#2565C2211yescharacteristic, complemented
55#2530—21no—
56#2512C2211yescharacteristic, complemented
57#2512C2211yescharacteristic, complemented
58#2504C2211yescharacteristic
59#2504C2211yescharacteristic
60#2498—21no—
61#2490C2211yescharacteristic
62#2486C2211yescharacteristic
63#2482—21no—
64#2467—21no—
65#2448C2211yescharacteristic
66#2448C2211yescharacteristic
67#2444—21no—
68#2444—21no—
69#2442C2211yescharacteristic, complemented
70#2423C2211yescharacteristic
71#2421C2211yescharacteristic
72#2421C2211yescharacteristic
73#2418—21no—
74#2418—21no—
75#2407C2211yescharacteristic
76#2395C2211yescharacteristic
77C2×#397—21no—
78#2360C2211yescharacteristic
79#2356C2211yescharacteristic, complemented
80#2349C2211yescharacteristic
81#2349C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83#2341C2211yescharacteristic, complemented
84#2339C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87#2314C2211yescharacteristic, complemented
88#2311C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2100C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2094C2211yescharacteristic
95#2085C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic, complemented
102#2073C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2066C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic, complemented
108#2065C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2035C2211yescharacteristic
114#2033C2211yescharacteristic
115#2026C2211yescharacteristic, complemented
116#2025C2211yescharacteristic
117#2015C2211yescharacteristic
118#2012C2211yescharacteristic
119#2001C2211yescharacteristic
120#2000C2211yescharacteristic
121#1991C2211yescharacteristic, complemented
122#1983C2211yescharacteristic
123#1972C2211yescharacteristic
124#1968C2211yescharacteristic
125#1968C2211yescharacteristic, complemented
126#1968C2211yescharacteristic, complemented
127#1959C2211yescharacteristic
128#1939C2211yescharacteristic, complemented
129#1936C2211yescharacteristic, complemented
130#1935C2211yescharacteristic, complemented
131#1935C2211yescharacteristic, complemented
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic, complemented
135#1926C2211yescharacteristic
136#1925C2211yescharacteristic
137#1924C2211yescharacteristic
138#1923C2211yescharacteristic
139#1920C2211yescharacteristic, complemented
140#1919C2211yescharacteristic, complemented
141#1919C2211yescharacteristic, complemented
142#1919C2211yescharacteristic, complemented
143#1917C2211yescharacteristic, complemented
144#1916C2211yescharacteristic, complemented
145#1895C2211yescharacteristic
146#1893C2211yescharacteristic
147#1893C2211yescharacteristic
148#1892C2211yescharacteristic
149#1892C2211yescharacteristic
150#1880C2211yescharacteristic
151#1880C2211yescharacteristic
152#1880C2211yescharacteristic, complemented
153#1880C2211yescharacteristic, complemented
154#1879C2211yescharacteristic
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1878C2211yescharacteristic, complemented
160#1878C2211yescharacteristic, complemented
161#1878C2211yescharacteristic, complemented
162#1878C2211yescharacteristic, complemented
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1874C2211yescharacteristic
167#1872C2211yescharacteristic
168#1869C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1853C2211yescharacteristic
172#1853C2211yescharacteristic, complemented
173#1851C2211yescharacteristic, complemented
174#1850C2211yescharacteristic
175#1835C2211yescharacteristic, complemented
176#1824C2211yescharacteristic
177#1824C2211yescharacteristic, complemented
178#1823C2211yescharacteristic, complemented
179#1809C2211yescharacteristic, complemented
180#1807C2211yescharacteristic, complemented
181#1805C2211yescharacteristic, complemented
182#1805C2211yescharacteristic, complemented
183#1805C2211yescharacteristic, complemented
184#1804C2211yescharacteristic
185#1804C2211yescharacteristic
186#1803C2211yescharacteristic, complemented
187#1802C2211yescharacteristic
188#1802C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193#1770C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×#135—24no—
207C2×#135—24no—
208C2×#135—42no—
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218#546—24no—
219#546—42no—
220C2×#126—21no—
221C2×#126—21no—
222C2×#125C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232#520—24no—
233#520—42no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117—21no—
248C2×#117C2311yescharacteristic
249C22×C4⋊C4—21no—
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256#478—42no—
257#450—24no—
258#449—42no—
259#447—42no—
260C4×SD16—24no—
261C4×SD16—42no—
262#435—42no—
263#433—42no—
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275#417—42no—
276#417—42no—
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102—42no—
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#400—21no—
318#400—21no—
319#400D411yescharacteristic
320#399—21no—
321#399—21no—
322#399—21no—
323#399—21no—
324#399D411yescharacteristic
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398D411yescharacteristic
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397D411yescharacteristic
345#397D411yescharacteristic
346#397D411yescharacteristic
347#396—21no—
348#396—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394D411yescharacteristic
354#394D411yescharacteristic
355#392—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390—21no—
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#389—21no—
374#389—21no—
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#383—21no—
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#381—21no—
433#381—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447#379—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458#376—21no—
459C2×#95—21no—
460C2×#95—21no—
461C2×#95—21no—
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41#4114yes—
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—22no—
513C22×D4—22no—
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538#135—416no—
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—41no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16#4114yes—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×M16—22no—
558C2×M16—41no—
559C2×M16—41no—
560C22×C8—22no—
561C22×C8—22no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8—41no—
565C22×C8—41no—
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574#126—82no—
575#126—82no—
576#125—41no—
577#125—41no—
578#124—22no—
579#124—41no—
580#123—44no—
581#123—82no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586#121—22no—
587#121—22no—
588#121—44no—
589#121—41no—
590#121—41no—
591#120—44no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—44no—
613C4×D4—44no—
614C4×D4—82no—
615#117—22no—
616#117—22no—
617#117—44no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—44no—
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—44no—
700C2×C22⋊C4—82no—
701C2×C22⋊C4—82no—
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724#107—41no—
725#106—22no—
726#106—41no—
727#106—41no—
728#106—41no—
729#106—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735#103—22no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8—22no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768#97—41no—
769#97—41no—
770C4×C8—22no—
771C4×C8—41no—
772C4×C8—41no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816C24—21no—
817C24—21no—
818C24—21no—
819C24—42no—
820C24—42no—
821C24—42no—
822C24—42no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24C22×D411yescharacteristic
827C24C22×D411yescharacteristic
828#41—28no—
829#41—44no—
830#41—44no—
831#41—44no—
832#41—44no—
833#41—44no—
834#41—82no—
835#41—82no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8C2×#4112yes—
847C2×Q8C2×#4112yes—
848C2×D4—22no—
849C2×D4—24no—
850C2×D4—22no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—41no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—44no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—82no—
878C2×D4—82no—
879C2×D4—82no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4C2×#4112yes—
886C2×D4C2×#4112yes—
887C2×D4H(5,𝔽2)12yes—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—24no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C2×#4112yes—
954C22×C4H(5,𝔽2)12yes—
955C22×C4C2511yescharacteristic
956Q16—44no—
957SD16—28no—
958SD16—44no—
959SD16—82no—
960D8—44no—
961D8—82no—
962M16—82no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—44no—
987C2×C8—82no—
988C2×C8C2×#4112yes—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—42no—
1095C42—42no—
1096C42—42no—
1097C42—42no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—22no—
1109C23—21no—
1110C23—22no—
1111C23—21no—
1112C23—22no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—84no—
1135C23—84no—
1136C23—84no—
1137C23—84no—
1138C23—162no—
1139C23—162no—
1140C23—162no—
1141C23#54612yes—
1142C23#57712yes—
1143C23C23×D411yescharacteristic
1144Q8—22no—
1145Q8—22no—
1146Q8—22no—
1147Q8—22no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152D4—22no—
1153D4—22no—
1154D4—22no—
1155D4—44no—
1156D4—48no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—84no—
1166D4—84no—
1167D4—162no—
1168D4—162no—
1169D4#55114yes—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—48no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—84no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4—162no—
1260C2×C4—162no—
1261C2×C4—162no—
1262C2×C4#54612yes—
1263C2×C4C22×#4111yescharacteristic
1264C2×C4C22×#4111yescharacteristic
1265C2×C4C2×H(5,𝔽2)11yescharacteristic
1266C2×C4C2×H(5,𝔽2)11yescharacteristic
1267C2×C4#58511yescharacteristic
1268C2×C4#58511yescharacteristic
1269C8—22no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—24no—
1284C22—42no—
1285C22—42no—
1286C22—41no—
1287C22—42no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—42no—
1292C22—41no—
1293C22—41no—
1294C22—42no—
1295C22—42no—
1296C22—41no—
1297C22—41no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—168no—
1313C22C2×#54611yescharacteristic
1314C22D4×#4111yescharacteristic
1315C22#348811yescharacteristic
1316C22C2×#57711yescharacteristic
1317C22#358411yescharacteristic
1318C22#358411yescharacteristic
1319C22#358511yescharacteristic
1320C4—22no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—42no—
1333C4—42no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4C2×#55111yescharacteristic
1346C4#349111yescharacteristic
1347C4#351311yescharacteristic
1348C4#353411yescharacteristic
1349C2—42no—
1350C2—42no—
1351C2—44no—
1352C2—161no—
1353C2—161no—
1354C2#5901111yescharacteristic
1355C2#6119211yescharacteristic
1356C2#6121611yescharacteristic
1357C2#6147211yescharacteristic
1358C2#6153111yescharacteristic
1359C2#6202411yescharacteristic
1360C2#6206311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23850C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44918C2semidirect
2. #35976C2semidirect
3. #31943C2semidirect
4. #31912C2semidirect
5. #31655C2semidirect
6. #31558C2semidirect
7. #28982C2semidirect
8. #28888C2semidirect
9. #28101C2semidirect
10. #27871C2semidirect
11. #27701C2semidirect
12. #27574C2semidirect
13. #27563C2semidirect
14. #27240C2semidirect
15. #27200C2semidirect
16. #26678C2semidirect
17. #25972C2semidirect
18. #24937C2semidirect
19. #24901C2semidirect
20. #24822C2semidirect
21. #24547C2semidirect
22. #24531C2semidirect
23. #24519C2semidirect
25. #22905C2semidirect
26. #22874C2semidirect
27. #22760C2semidirect
28. #22449C2semidirect
29. #22419C2semidirect
30. #20937C2semidirect
31. #20746C2semidirect
42. C2×#433C22semidirect
44. C2×#417C22semidirect
54. #2565C22semidirect
56. #2512C22semidirect
57. #2512C22semidirect
69. #2442C22semidirect
79. #2356C22semidirect
83. #2341C22semidirect
87. #2314C22semidirect
88. #2311C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2100C22semidirect
92. #2099C22semidirect
93. #2097C22semidirect
95. #2085C22semidirect
96. #2084C22semidirect
101. #2073C22semidirect
102. #2073C22semidirect
103. #2068C22semidirect
104. #2066C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
107. #2065C22semidirect
108. #2065C22semidirect
115. #2026C22semidirect
121. #1991C22semidirect
125. #1968C22semidirect
126. #1968C22semidirect
128. #1939C22semidirect
129. #1936C22semidirect
130. #1935C22semidirect
131. #1935C22semidirect
134. #1934C22semidirect
139. #1920C22semidirect
140. #1919C22semidirect
141. #1919C22semidirect
142. #1919C22semidirect
143. #1917C22semidirect
144. #1916C22semidirect
152. #1880C22semidirect
153. #1880C22semidirect
159. #1878C22semidirect
160. #1878C22semidirect
161. #1878C22semidirect
162. #1878C22semidirect
172. #1853C22semidirect
173. #1851C22semidirect
175. #1835C22semidirect
177. #1824C22semidirect
178. #1823C22semidirect
179. #1809C22semidirect
180. #1807C22semidirect
181. #1805C22semidirect
182. #1805C22semidirect
183. #1805C22semidirect
186. #1803C22semidirect
191. #1788C22semidirect
193. #1770C22semidirect
194. #1763C22semidirect
197. C4×#103C22semidirect
200. C8×C22⋊C4C22semidirect
201. C2×#340C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#449182
#359762
#319432
#319122
#316552
#315582
#289822
#288882
#281012
#278712
#277012
#275742
#275632
#272402
#272002
#266782
#259722
#249372
#249012
#248222
#245472
#245312
#245192
#238502
#229052
#228742
#227602
#224492
#224192
#209372
#207462