Finite Group Databasebeta

← #7574871

Subgroups — #7574871

Order 512.

1473 conjugacy classes of subgroups.

The subgroup lattice has 1255 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45377C211yesmaximal, characteristic
2#35911C211yesmaximal, characteristic, complemented
3#32665C211yesmaximal, characteristic, complemented
4#32546C211yesmaximal, characteristic, complemented
5#32008C211yesmaximal, characteristic, complemented
6#30408C211yesmaximal, characteristic
7#29586C211yesmaximal, characteristic, complemented
8#29584C211yesmaximal, characteristic, complemented
9#28843C211yesmaximal, characteristic, complemented
10#28841C211yesmaximal, characteristic, complemented
11#27845C211yesmaximal, characteristic, complemented
12#27525C211yesmaximal, characteristic, complemented
13#27473C211yesmaximal, characteristic, complemented
14#27158C211yesmaximal, characteristic, complemented
15#27111C211yesmaximal, characteristic, complemented
16#27036C211yesmaximal, characteristic, complemented
17#26659C211yesmaximal, characteristic, complemented
18#26566C211yesmaximal, characteristic, complemented
19#25072C211yesmaximal, characteristic, complemented
20#25041C211yesmaximal, characteristic, complemented
21#24993C211yesmaximal, characteristic, complemented
22#24939C211yesmaximal, characteristic, complemented
23#24921C211yesmaximal, characteristic, complemented
24#24861C211yesmaximal, characteristic
25#23274C211yesmaximal, characteristic, complemented
26#23126C211yesmaximal, characteristic, complemented
27#22938C211yesmaximal, characteristic, complemented
28#22854C211yesmaximal, characteristic, complemented
29#22574C211yesmaximal, characteristic, complemented
30#21128C211yesmaximal, characteristic, complemented
31#21128C211yesmaximal, characteristic, complemented
32C2×#480C2211yescharacteristic
33C2×#465C2211yescharacteristic
34C2×#450C2211yescharacteristic
35C2×#440C2211yescharacteristic
36C2×#440C2211yescharacteristic
37C22×#102C2211yescharacteristic
38#2750—21no—
39#2750—21no—
40#2735—21no—
41#2693—21no—
42#2655—21no—
43#2647C2211yescharacteristic, complemented
44#2589—21no—
45#2585—21no—
46#2582C2211yescharacteristic, complemented
47#2538C2211yescharacteristic
48#2538C2211yescharacteristic
49#2536C2211yescharacteristic
50#2534—21no—
51#2534—21no—
52#2530—21no—
53#2527—21no—
54#2497C2211yescharacteristic
55#2497C2211yescharacteristic
56#2496C2211yescharacteristic, complemented
57#2494C2211yescharacteristic
58#2487C2211yescharacteristic
59#2478—21no—
60#2468—21no—
61#2463—21no—
62#2437—21no—
63#2423C2211yescharacteristic
64#2422C2211yescharacteristic
65#2422C2211yescharacteristic
66#2421C2211yescharacteristic, complemented
67#2408C2211yescharacteristic
68#2398C2211yescharacteristic
69#2395—21no—
70#2361C2211yescharacteristic
71#2361C2211yescharacteristic
72#2360C2211yescharacteristic
73#2360C2211yescharacteristic, complemented
74#2355C2211yescharacteristic, complemented
75D4×C4⋊C4C2211yescharacteristic
76#2345C2211yescharacteristic
77#2344C2211yescharacteristic, complemented
78D4×C22⋊C4C2211yescharacteristic
79D4×C22⋊C4C2211yescharacteristic
80#2319C2211yescharacteristic
81#2319C2211yescharacteristic
82#2276C2211yescharacteristic, complemented
83#2101C2211yescharacteristic, complemented
84#2101C2211yescharacteristic, complemented
85#2100C2211yescharacteristic, complemented
86#2099C2211yescharacteristic, complemented
87#2095C2211yescharacteristic, complemented
88#2093C2211yescharacteristic
89#2093C2211yescharacteristic
90#2092C2211yescharacteristic
91#2088C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2083C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic
100#2075C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2072C2211yescharacteristic, complemented
104#2071C2211yescharacteristic
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2055C2211yescharacteristic
108#2036C2211yescharacteristic
109#2036C2211yescharacteristic
110#2035C2211yescharacteristic, complemented
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2000C2211yescharacteristic
115#1985C2211yescharacteristic, complemented
116#1984C2211yescharacteristic, complemented
117#1973C2211yescharacteristic
118#1947C2211yescharacteristic, complemented
119#1947C2211yescharacteristic, complemented
120#1944C2211yescharacteristic, complemented
121#1943C2211yescharacteristic, complemented
122#1943C2211yescharacteristic, complemented
123#1942C2211yescharacteristic, complemented
124#1942C2211yescharacteristic, complemented
125#1936C2211yescharacteristic
126#1936C2211yescharacteristic
127#1934C2211yescharacteristic
128#1934C2211yescharacteristic
129#1934C2211yescharacteristic
130#1933C2211yescharacteristic, complemented
131#1926C2211yescharacteristic
132#1926C2211yescharacteristic
133#1926C2211yescharacteristic
134#1925C2211yescharacteristic
135#1925C2211yescharacteristic
136#1925C2211yescharacteristic
137#1924C2211yescharacteristic
138#1924C2211yescharacteristic, complemented
139#1923C2211yescharacteristic
140#1923C2211yescharacteristic, complemented
141#1921C2211yescharacteristic, complemented
142#1921C2211yescharacteristic, complemented
143#1921C2211yescharacteristic, complemented
144#1921C2211yescharacteristic, complemented
145#1921C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1918C2211yescharacteristic, complemented
150#1918C2211yescharacteristic, complemented
151#1893C2211yescharacteristic
152#1892C2211yescharacteristic
153#1880C2211yescharacteristic
154#1880C2211yescharacteristic
155#1880C2211yescharacteristic
156#1880C2211yescharacteristic
157#1877C2211yescharacteristic
158#1877C2211yescharacteristic
159#1874C2211yescharacteristic
160#1872C2211yescharacteristic, complemented
161#1869C2211yescharacteristic
162#1869C2211yescharacteristic
163#1865C2211yescharacteristic, complemented
164#1865C2211yescharacteristic, complemented
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1863C2211yescharacteristic, complemented
169#1863C2211yescharacteristic, complemented
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1853C2211yescharacteristic, complemented
174#1852C2211yescharacteristic
175#1852C2211yescharacteristic
176#1852C2211yescharacteristic, complemented
177#1847C2211yescharacteristic, complemented
178#1834C2211yescharacteristic, complemented
179#1824C2211yescharacteristic
180#1824C2211yescharacteristic, complemented
181#1808C2211yescharacteristic
182#1808C2211yescharacteristic, complemented
183#1807C2211yescharacteristic
184#1804C2211yescharacteristic
185#1802C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1776C2211yescharacteristic, complemented
189#1776C2211yescharacteristic, complemented
190#1762C2211yescharacteristic
191C4×#103C2211yescharacteristic, complemented
192C4×#103C2211yescharacteristic, complemented
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196#1752C2211yescharacteristic
197#1752C2211yescharacteristic, complemented
198C8×C22⋊C4C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic, complemented
200#1746C2211yescharacteristic, complemented
201#1746C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×#126—21no—
209C2×#123—21no—
210C2×#123—21no—
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#120—21no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C22⋊C4—21no—
235C22×C22⋊C4—21no—
236#480—24no—
237#465—24no—
238#450—24no—
239#440—24no—
240#440—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×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#102—24no—
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290#401—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400D411yescharacteristic
299#400D411yescharacteristic
300#399—21no—
301#399—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397D411yescharacteristic
314#397D411yescharacteristic
315#396—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394D411yescharacteristic
326#394D411yescharacteristic
327#393D411yescharacteristic
328#393D411yescharacteristic
329#392—21no—
330#391—21no—
331#391—21no—
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
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#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#381—21no—
406#381—21no—
407#381—21no—
408#380—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412#380—21no—
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#379—21no—
422#379—21no—
423#379—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376—21no—
443#376C2311yescharacteristic
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
484C25—21no—
485C22×Q8C2×D411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×D4—22no—
488C22×D4—22no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—41no—
493C22×D4—41no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4C2×D411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×SD16#4114yes—
514C22×C8—22no—
515C22×C8—22no—
516C22×C8—41no—
517C22×C8—41no—
518C22×C8—41no—
519C22×C8—41no—
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528#126—82no—
529#123—82no—
530#123—82no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—41no—
534C22⋊Q8—41no—
535C22⋊Q8—82no—
536C22⋊Q8—82no—
537#121—22no—
538#121—22no—
539#121—41no—
540#121—41no—
541#120—82no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×D4—22no—
551C4×D4—22no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—82no—
561C4×D4—82no—
562C4×D4—82no—
563#117—82no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
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—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
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⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—82no—
644C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670#107—22no—
671#107—22no—
672#107—22no—
673#107—22no—
674#107—41no—
675#107—41no—
676#107—41no—
677#107—41no—
678#107—41no—
679#107—41no—
680#106—22no—
681#106—41no—
682#106—41no—
683#106—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—41no—
690#103—41no—
691#103—41no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—22no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102#4114yes—
706C22⋊C8—22no—
707C22⋊C8—22no—
708C22⋊C8—41no—
709C22⋊C8—41no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712#97—22no—
713#97—22no—
714#97—41no—
715C4×C8—41no—
716C4×C8—41no—
717C4×C8—41no—
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#95—21no—
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765C24—21no—
766C24—21no—
767C24—42no—
768C24—42no—
769C24—42no—
770C24—81no—
771C24—81no—
772C24—81no—
773C24—81no—
774C24C22×D411yescharacteristic
775C24C22×D411yescharacteristic
776C2×Q8—22no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—41no—
783C2×Q8—41no—
784C2×Q8C2×#4112yes—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—44no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—81no—
806C2×D4—82no—
807C2×D4—82no—
808C2×D4—82no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4C2×#4112yes—
812C2×D4C2×#4112yes—
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—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C2511yescharacteristic
873SD16—44no—
874SD16—44no—
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×C8—21no—
896C2×C8—21no—
897C2×C8—82no—
898C2×C8—82no—
899C2×C8C2×#4112yes—
900C2×C8C2×#4112yes—
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—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
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⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4C2×#4112yes—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—42no—
1008C42—42no—
1009C42—42no—
1010C42—81no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—22no—
1030C23—22no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—84no—
1044C23—84no—
1045C23—84no—
1046C23—162no—
1047C23—162no—
1048C23—162no—
1049C23—162no—
1050C23#57612yes—
1051C23#57812yes—
1052C23C23×D411yescharacteristic
1053Q8—22no—
1054Q8—22no—
1055Q8—41no—
1056Q8—41no—
1057Q8—82no—
1058D4—22no—
1059D4—22no—
1060D4—22no—
1061D4—22no—
1062D4—44no—
1063D4—41no—
1064D4—41no—
1065D4—41no—
1066D4—41no—
1067D4—84no—
1068D4—84no—
1069D4—84no—
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—22no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—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—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—84no—
1156C2×C4—162no—
1157C2×C4—162no—
1158C2×C4—162no—
1159C2×C4—162no—
1160C2×C4—162no—
1161C2×C4—162no—
1162C2×C4#57712yes—
1163C2×C4C22×#4111yescharacteristic
1164C2×C4C22×#4111yescharacteristic
1165C2×C4#58511yescharacteristic
1166C2×C4#58511yescharacteristic
1167C2×C4#58511yescharacteristic
1168C2×C4#58511yescharacteristic
1169C8—22no—
1170C8—22no—
1171C8—41no—
1172C8—41no—
1173C8—41no—
1174C8—41no—
1175C8—41no—
1176C8—41no—
1177C22—22no—
1178C22—22no—
1179C22—22no—
1180C22—22no—
1181C22—22no—
1182C22—22no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—168no—
1206C22D4×#4111yescharacteristic
1207C22D4×#4111yescharacteristic
1208C22#348511yescharacteristic
1209C22C2×#57611yescharacteristic
1210C22C2×#57711yescharacteristic
1211C22C2×#57811yescharacteristic
1212C22#358511yescharacteristic
1213C4—22no—
1214C4—41no—
1215C4—41no—
1216C4—42no—
1217C4—41no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—41no—
1225C4—42no—
1226C4—41no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4#347511yescharacteristic
1240C4#349111yescharacteristic
1241C4#352111yescharacteristic
1242C4#356611yescharacteristic
1243C2—42no—
1244C2—42no—
1245C2—82no—
1246C2—82no—
1247C2#5915811yescharacteristic
1248C2#6149711yescharacteristic
1249C2#6149811yescharacteristic
1250C2#6151911yescharacteristic
1251C2#6152411yescharacteristic
1252C2#6175611yescharacteristic
1253C2#6176411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35911C2semidirect
3. #32665C2semidirect
4. #32546C2semidirect
5. #32008C2semidirect
7. #29586C2semidirect
8. #29584C2semidirect
9. #28843C2semidirect
10. #28841C2semidirect
11. #27845C2semidirect
12. #27525C2semidirect
13. #27473C2semidirect
14. #27158C2semidirect
15. #27111C2semidirect
16. #27036C2semidirect
17. #26659C2semidirect
18. #26566C2semidirect
19. #25072C2semidirect
20. #25041C2semidirect
21. #24993C2semidirect
22. #24939C2semidirect
23. #24921C2semidirect
25. #23274C2semidirect
26. #23126C2semidirect
27. #22938C2semidirect
28. #22854C2semidirect
29. #22574C2semidirect
30. #21128C2semidirect
31. #21128C2semidirect
43. #2647C22semidirect
46. #2582C22semidirect
56. #2496C22semidirect
66. #2421C22semidirect
73. #2360C22semidirect
74. #2355C22semidirect
77. #2344C22semidirect
82. #2276C22semidirect
83. #2101C22semidirect
84. #2101C22semidirect
85. #2100C22semidirect
86. #2099C22semidirect
87. #2095C22semidirect
91. #2088C22semidirect
92. #2085C22semidirect
93. #2083C22semidirect
94. #2083C22semidirect
95. #2083C22semidirect
100. #2075C22semidirect
103. #2072C22semidirect
105. #2068C22semidirect
110. #2035C22semidirect
115. #1985C22semidirect
116. #1984C22semidirect
118. #1947C22semidirect
119. #1947C22semidirect
120. #1944C22semidirect
121. #1943C22semidirect
122. #1943C22semidirect
123. #1942C22semidirect
124. #1942C22semidirect
130. #1933C22semidirect
138. #1924C22semidirect
140. #1923C22semidirect
141. #1921C22semidirect
142. #1921C22semidirect
143. #1921C22semidirect
144. #1921C22semidirect
145. #1921C22semidirect
146. #1920C22semidirect
147. #1919C22semidirect
148. #1918C22semidirect
149. #1918C22semidirect
150. #1918C22semidirect
160. #1872C22semidirect
163. #1865C22semidirect
164. #1865C22semidirect
168. #1863C22semidirect
169. #1863C22semidirect
173. #1853C22semidirect
176. #1852C22semidirect
177. #1847C22semidirect
178. #1834C22semidirect
180. #1824C22semidirect
182. #1808C22semidirect
188. #1776C22semidirect
189. #1776C22semidirect
191. C4×#103C22semidirect
192. C4×#103C22semidirect
197. #1752C22semidirect
199. C8×C22⋊C4C22semidirect
200. #1746C22semidirect
201. #1746C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#453772
#359112
#326652
#325462
#320082
#304082
#295862
#295842
#288432
#288412
#278452
#275252
#274732
#271582
#271112
#270362
#266592
#265662
#250722
#250412
#249932
#249392
#249212
#248612
#232742
#231262
#229382
#228542
#225742
#211282