Finite Group Databasebeta

← #7037468

Subgroups — #7037468

Order 512.

1456 conjugacy classes of subgroups.

The subgroup lattice has 1279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59224C211yesmaximal, characteristic, complemented
2#40077C211yesmaximal, characteristic, complemented
3#32394C211yesmaximal, characteristic, complemented
4#31946C211yesmaximal, characteristic, complemented
5#31706C211yesmaximal, characteristic, complemented
6#31676C211yesmaximal, characteristic, complemented
7#31547C211yesmaximal, characteristic, complemented
8#31381C211yesmaximal, characteristic, complemented
9#31350C211yesmaximal, characteristic, complemented
10#30396C211yesmaximal, characteristic
11#29103C211yesmaximal, characteristic, complemented
12#29079C211yesmaximal, characteristic, complemented
13#28062C211yesmaximal, characteristic, complemented
14#28041C211yesmaximal, characteristic, complemented
15#27883C211yesmaximal, characteristic, complemented
16#27735C211yesmaximal, characteristic, complemented
17#27712C211yesmaximal, characteristic, complemented
18#27560C211yesmaximal, characteristic, complemented
19#27525C211yesmaximal, characteristic, complemented
20#27360C211yesmaximal, characteristic, complemented
21#27109C211yesmaximal, characteristic, complemented
22#26729C211yesmaximal, characteristic, complemented
23#25042C211yesmaximal, characteristic, complemented
24#24982C211yesmaximal, characteristic, complemented
25#24938C211yesmaximal, characteristic, complemented
26#24913C211yesmaximal, characteristic, complemented
27#23758C211yesmaximal, characteristic, complemented
28#23300C211yesmaximal, characteristic, complemented
29#23130C211yesmaximal, characteristic, complemented
30#22780C211yesmaximal, characteristic, complemented
31#22046C211yesmaximal, characteristic, complemented
32C2×#466C2211yescharacteristic
33C2×#447C2211yescharacteristic
34C2×#442C2211yescharacteristic
35#2857C2211yescharacteristic
36#2787—21no—
37#2756—21no—
38#2737—21no—
39#2707—21no—
40#2687—21no—
41#2681—21no—
42#2653—21no—
43#2610—21no—
44#2563C2211yescharacteristic
45#2561—21no—
46#2552C2211yescharacteristic, complemented
47#2537C2211yescharacteristic
48#2531—21no—
49#2513C2211yescharacteristic
50#2513C2211yescharacteristic
51#2507C2211yescharacteristic, complemented
52#2500C2211yescharacteristic
53#2497C2211yescharacteristic, complemented
54#2494C2211yescharacteristic
55#2491C2211yescharacteristic
56#2485C2211yescharacteristic
57#2472—21no—
58#2460—21no—
59#2452C2211yescharacteristic, complemented
60#2440C2211yescharacteristic
61#2439C2211yescharacteristic, complemented
62#2425—21no—
63#2422C2211yescharacteristic
64#2422C2211yescharacteristic, complemented
65#2420C2211yescharacteristic
66#2412—21no—
67#2408C2211yescharacteristic
68#2363C2211yescharacteristic
69#2363C2211yescharacteristic, complemented
70#2354C2211yescharacteristic
71#2352C2211yescharacteristic
72#2349C2211yescharacteristic, complemented
73#2342—21no—
74D4×C22⋊C4C2211yescharacteristic
75#2329—21no—
76C4×#123C2211yescharacteristic
77C4×#121C2211yescharacteristic
78C2×#390C2211yescharacteristic
79#2283C2211yescharacteristic
80#2101C2211yescharacteristic, complemented
81#2101C2211yescharacteristic, complemented
82#2101C2211yescharacteristic, complemented
83#2099C2211yescharacteristic, complemented
84#2094C2211yescharacteristic
85#2093C2211yescharacteristic
86#2092C2211yescharacteristic, complemented
87#2088C2211yescharacteristic, complemented
88#2086C2211yescharacteristic, complemented
89#2085C2211yescharacteristic, complemented
90#2085C2211yescharacteristic, complemented
91#2084C2211yescharacteristic, complemented
92#2083C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic, complemented
97#2076C2211yescharacteristic
98#2075C2211yescharacteristic
99#2075C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic, complemented
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2065C2211yescharacteristic
108#2058C2211yescharacteristic, complemented
109#2054C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic, complemented
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2023C2211yescharacteristic
117#2023C2211yescharacteristic
118#2023C2211yescharacteristic, complemented
119#1999C2211yescharacteristic
120#1993C2211yescharacteristic, complemented
121#1993C2211yescharacteristic, complemented
122#1990C2211yescharacteristic, complemented
123#1987C2211yescharacteristic, complemented
124#1972C2211yescharacteristic
125#1972C2211yescharacteristic
126#1955C2211yescharacteristic
127#1948C2211yescharacteristic, complemented
128#1944C2211yescharacteristic, complemented
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic, complemented
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1924C2211yescharacteristic
144#1924C2211yescharacteristic, complemented
145#1923C2211yescharacteristic
146#1923C2211yescharacteristic, complemented
147#1921C2211yescharacteristic, complemented
148#1921C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1920C2211yescharacteristic, complemented
152#1920C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1917C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1893C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic, complemented
166#1874C2211yescharacteristic
167#1869C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic, complemented
172#1854C2211yescharacteristic, complemented
173#1853C2211yescharacteristic
174#1847C2211yescharacteristic, complemented
175#1836C2211yescharacteristic, complemented
176#1836C2211yescharacteristic, complemented
177#1836C2211yescharacteristic, complemented
178#1825C2211yescharacteristic, complemented
179#1825C2211yescharacteristic, complemented
180#1823C2211yescharacteristic
181#1823C2211yescharacteristic
182#1807C2211yescharacteristic, complemented
183#1804C2211yescharacteristic
184#1804C2211yescharacteristic, complemented
185#1802C2211yescharacteristic
186#1802C2211yescharacteristic, complemented
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190C4×#107C2211yescharacteristic, complemented
191C4×#106C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1770C2211yescharacteristic, complemented
194#1762C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic, complemented
198#1752C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic, complemented
200#1749C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202#1735C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125—21no—
210C2×#124—21no—
211C2×#123—21no—
212C2×#123—21no—
213C2×#123D411yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×#121—21no—
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×C4×D4—21no—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C22⋊C4—21no—
235C22×C22⋊C4—21no—
236C22×C22⋊C4—21no—
237C22×C42C2311yescharacteristic
238#466—24no—
239#447—24no—
240#442—24no—
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288#401—21no—
289#400—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#396—21no—
305#396—21no—
306#396—21no—
307#395—21no—
308#394—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#393—21no—
319#393—21no—
320#393—21no—
321#393—21no—
322#393—21no—
323#392—21no—
324#391—21no—
325#391—21no—
326#390—21no—
327#390—21no—
328#390—21no—
329#390—21no—
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#389—21no—
341#389—21no—
342#389—21no—
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
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#388D411yescharacteristic
370#388D411yescharacteristic
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387D411yescharacteristic
378#387D411yescharacteristic
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386D411yescharacteristic
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385D411yescharacteristic
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#383—21no—
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#381—21no—
404#381—21no—
405#381D411yescharacteristic
406#380—21no—
407#380—21no—
408#380—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#379—21no—
421#379—21no—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436C4×C22⋊C4C2311yescharacteristic
437#376—21no—
438C2×#95—21no—
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C25—21no—
482C22×Q8—21no—
483C22×Q8—21no—
484C22×D4—22no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—41no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4—41no—
494C22×D4—41no—
495C22×D4C2×D411yescharacteristic
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2×D411yescharacteristic
506C23×C4C2×D411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C2×D8—22no—
510C2×D8—41no—
511C2×D8—41no—
512C2×D8—41no—
513C2×D8—41no—
514C2×D8#4114yes—
515C22×C8—22no—
516C22×C8—41no—
517C22×C8—41no—
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530#125—82no—
531#124—82no—
532#123—42no—
533#123—82no—
534#123—82no—
535C22⋊Q8—44no—
536C22⋊Q8—82no—
537C22⋊Q8—82no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—41no—
542#121—41no—
543#121—41no—
544#121—41no—
545#121—41no—
546#121—82no—
547#120—82no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—41no—
551C4×D4—41no—
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—
561#117—41no—
562#117—41no—
563#117—41no—
564#117—41no—
565#117—82no—
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—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
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⋊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—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—44no—
647C2×C22⋊C4—82no—
648C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—41no—
665C2×C42—41no—
666C2×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673#107—22no—
674#107—41no—
675#107—41no—
676#107—41no—
677#106—22no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706C22⋊C8—22no—
707C22⋊C8—41no—
708C22⋊C8—41no—
709C22⋊C8—41no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712C22⋊C8—41no—
713#97—22no—
714#97—41no—
715#97—41no—
716#97—41no—
717C4×C8—41no—
718C4×C8—41no—
719C4×C8—41no—
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#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761C24—21no—
762C24—21no—
763C24—21no—
764C24—42no—
765C24—42no—
766C24—42no—
767C24—42no—
768C24—81no—
769C24—81no—
770C24—81no—
771C24C22×D411yescharacteristic
772C24C22×D411yescharacteristic
773C2×Q8—42no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×Q8—81no—
777C2×Q8—81no—
778C2×Q8—81no—
779C2×D4—22no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
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—41no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—81no—
805C2×D4—82no—
806C2×D4—82no—
807C2×D4—82no—
808C2×D4—82no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4—81no—
817C2×D4C2×#4112yes—
818C2×D4C2×#4112yes—
819C22×C4—22no—
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—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C2511yescharacteristic
881D8—44no—
882D8—82no—
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—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—82no—
907C2×C8C2×#4112yes—
908C4⋊C4—22no—
909C4⋊C4—22no—
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—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
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⋊C4—81no—
959C4⋊C4—81no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—42no—
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—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
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—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—41no—
1018C42—41no—
1019C42—42no—
1020C42—81no—
1021C42—81no—
1022C42—81no—
1023C42—81no—
1024C42—81no—
1025C42—81no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—22no—
1034C23—22no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—84no—
1061C23—84no—
1062C23—84no—
1063C23—84no—
1064C23—162no—
1065C23—162no—
1066C23—162no—
1067C23#57612yes—
1068C23C23×D411yescharacteristic
1069Q8—162no—
1070Q8—162no—
1071D4—22no—
1072D4—22no—
1073D4—22no—
1074D4—22no—
1075D4—41no—
1076D4—41no—
1077D4—41no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—82no—
1084D4—84no—
1085D4—84no—
1086D4—162no—
1087D4—162no—
1088D4—162no—
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—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
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—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—82no—
1171C2×C4—82no—
1172C2×C4—84no—
1173C2×C4—162no—
1174C2×C4—162no—
1175C2×C4—162no—
1176C2×C4—162no—
1177C2×C4—162no—
1178C2×C4#57512yes—
1179C2×C4#57712yes—
1180C2×C4C22×#4111yescharacteristic
1181C2×C4#58511yescharacteristic
1182C2×C4#58511yescharacteristic
1183C2×C4#58511yescharacteristic
1184C2×C4#58511yescharacteristic
1185C2×C4#58511yescharacteristic
1186C8—22no—
1187C8—41no—
1188C8—41no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C22—22no—
1195C22—22no—
1196C22—22no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—42no—
1202C22—41no—
1203C22—42no—
1204C22—41no—
1205C22—41no—
1206C22—42no—
1207C22—41no—
1208C22—42no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—42no—
1213C22—42no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—168no—
1230C22D4×#4111yescharacteristic
1231C22#348511yescharacteristic
1232C22#350011yescharacteristic
1233C22C2×#57511yescharacteristic
1234C22C2×#57611yescharacteristic
1235C22C2×#57711yescharacteristic
1236C22#358511yescharacteristic
1237C4—22no—
1238C4—22no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4#349111yescharacteristic
1263C4#352111yescharacteristic
1264C4#356611yescharacteristic
1265C4#356611yescharacteristic
1266C2—42no—
1267C2—81no—
1268C2—82no—
1269C2—82no—
1270C2—161no—
1271C2#4350011yescharacteristic
1272C2#6144811yescharacteristic
1273C2#6151911yescharacteristic
1274C2#6174011yescharacteristic
1275C2#6175811yescharacteristic
1276C2#6255211yescharacteristic
1277C2#6258411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30396C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59224C2semidirect
2. #40077C2semidirect
3. #32394C2semidirect
4. #31946C2semidirect
5. #31706C2semidirect
6. #31676C2semidirect
7. #31547C2semidirect
8. #31381C2semidirect
9. #31350C2semidirect
11. #29103C2semidirect
12. #29079C2semidirect
13. #28062C2semidirect
14. #28041C2semidirect
15. #27883C2semidirect
16. #27735C2semidirect
17. #27712C2semidirect
18. #27560C2semidirect
19. #27525C2semidirect
20. #27360C2semidirect
21. #27109C2semidirect
22. #26729C2semidirect
23. #25042C2semidirect
24. #24982C2semidirect
25. #24938C2semidirect
26. #24913C2semidirect
27. #23758C2semidirect
28. #23300C2semidirect
29. #23130C2semidirect
30. #22780C2semidirect
31. #22046C2semidirect
46. #2552C22semidirect
51. #2507C22semidirect
53. #2497C22semidirect
59. #2452C22semidirect
61. #2439C22semidirect
64. #2422C22semidirect
69. #2363C22semidirect
72. #2349C22semidirect
80. #2101C22semidirect
81. #2101C22semidirect
82. #2101C22semidirect
83. #2099C22semidirect
86. #2092C22semidirect
87. #2088C22semidirect
88. #2086C22semidirect
89. #2085C22semidirect
90. #2085C22semidirect
91. #2084C22semidirect
92. #2083C22semidirect
96. #2077C22semidirect
101. #2073C22semidirect
108. #2058C22semidirect
112. #2034C22semidirect
118. #2023C22semidirect
120. #1993C22semidirect
121. #1993C22semidirect
122. #1990C22semidirect
123. #1987C22semidirect
127. #1948C22semidirect
128. #1944C22semidirect
139. #1934C22semidirect
144. #1924C22semidirect
146. #1923C22semidirect
147. #1921C22semidirect
148. #1921C22semidirect
149. #1921C22semidirect
150. #1920C22semidirect
151. #1920C22semidirect
152. #1920C22semidirect
153. #1919C22semidirect
154. #1917C22semidirect
155. #1916C22semidirect
165. #1875C22semidirect
171. #1862C22semidirect
172. #1854C22semidirect
174. #1847C22semidirect
175. #1836C22semidirect
176. #1836C22semidirect
177. #1836C22semidirect
178. #1825C22semidirect
179. #1825C22semidirect
182. #1807C22semidirect
184. #1804C22semidirect
186. #1802C22semidirect
190. C4×#107C22semidirect
191. C4×#106C22semidirect
192. #1771C22semidirect
193. #1770C22semidirect
194. #1762C22semidirect
196. C4×#102C22semidirect
197. C4×#102C22semidirect
198. #1752C22semidirect
199. C8×C22⋊C4C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#592242
#400772
#323942
#319462
#317062
#316762
#315472
#313812
#313502
#303962
#291032
#290792
#280622
#280412
#278832
#277352
#277122
#275602
#275252
#273602
#271092
#267292
#250422
#249822
#249382
#249132
#237582
#233002
#231302
#227802
#220462