Finite Group Databasebeta

← #6998863

Subgroups — #6998863

Order 512.

1658 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44874C211yesmaximal, characteristic, complemented
2#42757C211yesmaximal, characteristic, complemented
3#31795C211yesmaximal, characteristic, complemented
4#31479C211yesmaximal, characteristic, complemented
5#31401C211yesmaximal, characteristic, complemented
6#31298C211yesmaximal, characteristic, complemented
7#31008C211yesmaximal, characteristic, complemented
8#30992C211yesmaximal, characteristic, complemented
9#30898C211yesmaximal, characteristic, complemented
10#30780C211yesmaximal, characteristic, complemented
11#29116C211yesmaximal, characteristic, complemented
12#29057C211yesmaximal, characteristic, complemented
13#29015C211yesmaximal, characteristic, complemented
14#28992C211yesmaximal, characteristic, complemented
15#27759C211yesmaximal, characteristic, complemented
16#27539C211yesmaximal, characteristic, complemented
17#27281C211yesmaximal, characteristic, complemented
18#27057C211yesmaximal, characteristic, complemented
19#26766C211yesmaximal, characteristic, complemented
20#26669C211yesmaximal, characteristic, complemented
21#26643C211yesmaximal, characteristic, complemented
22#26490C211yesmaximal, characteristic, complemented
23#26162C211yesmaximal, characteristic, complemented
24#25680C211yesmaximal, characteristic, complemented
25#24248C211yesmaximal, characteristic
26#24044C211yesmaximal, characteristic, complemented
27#23579C211yesmaximal, characteristic, complemented
28#23301C211yesmaximal, characteristic, complemented
29#23005C211yesmaximal, characteristic, complemented
30#22880C211yesmaximal, characteristic, complemented
31#22056C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#498C2211yescharacteristic, complemented
35C2×#489C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#459C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×D8C2211yescharacteristic, complemented
44C2×#418C2211yescharacteristic
45#2824—21no—
46#2796—21no—
47#2745—21no—
48#2723—21no—
49#2705—21no—
50#2697—21no—
51#2685—21no—
52#2684—21no—
53#2681—21no—
54#2652—21no—
55#2643—21no—
56#2628C2211yescharacteristic, complemented
57#2571C2211yescharacteristic, complemented
58#2559—21no—
59#2544C2211yescharacteristic
60#2535C2211yescharacteristic
61#2509C2211yescharacteristic, complemented
62#2496C2211yescharacteristic, complemented
63#2494C2211yescharacteristic, complemented
64#2491C2211yescharacteristic
65#2488—21no—
66#2485C2211yescharacteristic
67#2472—21no—
68#2452C2211yescharacteristic
69#2452C2211yescharacteristic, complemented
70#2445C2211yescharacteristic
71#2439C2211yescharacteristic, complemented
72#2435—21no—
73#2435C2211yescharacteristic
74#2435C2211yescharacteristic
75#2426C2211yescharacteristic
76#2422C2211yescharacteristic, complemented
77#2420C2211yescharacteristic, complemented
78#2415C2211yescharacteristic
79#2405—21no—
80#2395C2211yescharacteristic
81#2367C2211yescharacteristic
82#2363C2211yescharacteristic
83#2363C2211yescharacteristic, complemented
84#2349C2211yescharacteristic, complemented
85D4×C22⋊C4C2211yescharacteristic
86#2324C2211yescharacteristic, complemented
87#2309C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2092C2211yescharacteristic, complemented
91#2087C2211yescharacteristic, complemented
92#2077C2211yescharacteristic, complemented
93#2077C2211yescharacteristic, complemented
94#2074C2211yescharacteristic, complemented
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic, complemented
97#2073C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2067C2211yescharacteristic, complemented
100#2066C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic, complemented
103#2065C2211yescharacteristic, complemented
104#2057C2211yescharacteristic, complemented
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic, complemented
108#2042C2211yescharacteristic, complemented
109#2041C2211yescharacteristic
110#2041C2211yescharacteristic
111#2036C2211yescharacteristic, complemented
112#2036C2211yescharacteristic, complemented
113#2035C2211yescharacteristic, complemented
114#2035C2211yescharacteristic, complemented
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic, complemented
121#2023C2211yescharacteristic, complemented
122#2012C2211yescharacteristic, complemented
123#2012C2211yescharacteristic, complemented
124#2000C2211yescharacteristic, complemented
125#2000C2211yescharacteristic, complemented
126#1999C2211yescharacteristic
127#1999C2211yescharacteristic
128#1993C2211yescharacteristic, complemented
129#1983C2211yescharacteristic, complemented
130#1972C2211yescharacteristic
131#1972C2211yescharacteristic, complemented
132#1970C2211yescharacteristic
133#1961C2211yescharacteristic
134#1959C2211yescharacteristic, complemented
135#1958C2211yescharacteristic
136#1958C2211yescharacteristic, complemented
137#1955C2211yescharacteristic
138#1949C2211yescharacteristic, complemented
139#1944C2211yescharacteristic, complemented
140#1943C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic, complemented
147#1934C2211yescharacteristic, complemented
148#1934C2211yescharacteristic, complemented
149#1934C2211yescharacteristic, complemented
150#1926C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic, complemented
153#1924C2211yescharacteristic, complemented
154#1924C2211yescharacteristic, complemented
155#1923C2211yescharacteristic, complemented
156#1923C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic, complemented
164#1894C2211yescharacteristic, complemented
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic, complemented
167#1879C2211yescharacteristic, complemented
168#1879C2211yescharacteristic, complemented
169#1879C2211yescharacteristic, complemented
170#1877C2211yescharacteristic, complemented
171#1875C2211yescharacteristic, complemented
172#1873C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic, complemented
178#1864C2211yescharacteristic, complemented
179#1864C2211yescharacteristic, complemented
180#1864C2211yescharacteristic, complemented
181#1862C2211yescharacteristic
182#1854C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1825C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1804C2211yescharacteristic
187#1802C2211yescharacteristic, complemented
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1771C2211yescharacteristic, complemented
194#1770C2211yescharacteristic, complemented
195#1762C2211yescharacteristic, complemented
196#1762C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1750C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211D42—42no—
212D42—42no—
213#542—42no—
214#542—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121—21no—
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C22⋊C4—21no—
252#498—42no—
253#489—42no—
254#482—42no—
255#463—24no—
256#459—42no—
257#447—24no—
258#447—24no—
259#442—42no—
260#440—42no—
261C4×D8—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#418—42no—
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320#401—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400D411yescharacteristic
328#399—21no—
329#399D411yescharacteristic
330#398D411yescharacteristic
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397D411yescharacteristic
339#397D411yescharacteristic
340#397D411yescharacteristic
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#395—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394D411yescharacteristic
361#394D411yescharacteristic
362#393—21no—
363#393—21no—
364#393—21no—
365#393—21no—
366#393—21no—
367#392—21no—
368#391—21no—
369#391C2311yescharacteristic
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#389—21no—
386#389—21no—
387#389—21no—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#384C2311yescharacteristic
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#381—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446#379—21no—
447#379—21no—
448#379—21no—
449#379—21no—
450#379—21no—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C2×#95—21no—
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C25—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—44no—
519C22×D4—82no—
520C22×D4—82no—
521C22×D4C2×D411yescharacteristic
522C22×D4C2411yescharacteristic
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×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C2×SD16—22no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8#4114yes—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C4⋊Q8—22no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561#127—22no—
562#127—41no—
563#126—44no—
564#126—82no—
565#124—22no—
566#124—22no—
567#124—41no—
568#124—41no—
569#124—41no—
570#124—41no—
571#124—44no—
572#124—82no—
573#123—44no—
574#123—82no—
575#123—82no—
576C22⋊Q8—44no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—82no—
582C22⋊Q8—82no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—44no—
589#121—41no—
590#121—41no—
591#121—41no—
592#120—44no—
593#120—44no—
594C4×Q8—22no—
595C4×Q8—41no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610#117—41no—
611#117—41no—
612#117—41no—
613#117—41no—
614#117—41no—
615#117—41no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
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—82no—
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—22no—
718#107—41no—
719#107—41no—
720#106—22no—
721#106—22no—
722#106—41no—
723#106—41no—
724#106—41no—
725C4⋊C8—22no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728#103—22no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767#97—41no—
768#97—41no—
769#97—41no—
770#97—41no—
771C4×C8—41no—
772C4×C8—41no—
773C4×C8—41no—
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#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—42no—
816C24—42no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—42no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×D4—24no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
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—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—44no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—82no—
886C2×D4—82no—
887C2×D4—82no—
888C2×D4—82no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—82no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—816no—
900C2×D4C2×#4112yes—
901C2×D4C2×#4112yes—
902C2×D4H(5,𝔽2)12yes—
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—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
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×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
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×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C2511yescharacteristic
958SD16—44no—
959D8—44no—
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×C8C2×#4112yes—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
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—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4H(5,𝔽2)12yes—
1033C22⋊C4—24no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
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—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
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—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—42no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C42—81no—
1102C42—81no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—22no—
1112C23—22no—
1113C23—21no—
1114C23—21no—
1115C23—22no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
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—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—84no—
1146C23—84no—
1147C23—84no—
1148C23—84no—
1149C23—84no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23—162no—
1154C23—162no—
1155C23—162no—
1156C23—162no—
1157C23—162no—
1158C23—162no—
1159C23C23×D411yescharacteristic
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—162no—
1165Q8—162no—
1166D4—22no—
1167D4—22no—
1168D4—22no—
1169D4—22no—
1170D4—22no—
1171D4—22no—
1172D4—44no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—84no—
1184D4—84no—
1185D4—84no—
1186D4—84no—
1187D4—84no—
1188D4—162no—
1189D4—162no—
1190D4—162no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
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—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
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—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—84no—
1272C2×C4—162no—
1273C2×C4—162no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4C22×#4111yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4C2×H(5,𝔽2)11yescharacteristic
1280C2×C4#58511yescharacteristic
1281C2×C4#58511yescharacteristic
1282C2×C4#58511yescharacteristic
1283C8—22no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C22—41no—
1292C22—41no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—41no—
1298C22—41no—
1299C22—42no—
1300C22—41no—
1301C22—42no—
1302C22—41no—
1303C22—42no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—42no—
1309C22—41no—
1310C22—41no—
1311C22—42no—
1312C22—41no—
1313C22—41no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—168no—
1334C22—168no—
1335C22D4×#4111yescharacteristic
1336C22#348411yescharacteristic
1337C22#350011yescharacteristic
1338C22#358411yescharacteristic
1339C22#358511yescharacteristic
1340C22#358511yescharacteristic
1341C22#358511yescharacteristic
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—42no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4#350511yescharacteristic
1367C4#351311yescharacteristic
1368C4#356011yescharacteristic
1369C4#356211yescharacteristic
1370C2—81no—
1371C2—81no—
1372C2—82no—
1373C2—82no—
1374C2—82no—
1375C2—161no—
1376C2#4300811yescharacteristic
1377C2#6150511yescharacteristic
1378C2#6152911yescharacteristic
1379C2#6164411yescharacteristic
1380C2#6169011yescharacteristic
1381C2#6257311yescharacteristic
1382C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24248C2
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. #44874C2semidirect
2. #42757C2semidirect
3. #31795C2semidirect
4. #31479C2semidirect
5. #31401C2semidirect
6. #31298C2semidirect
7. #31008C2semidirect
8. #30992C2semidirect
9. #30898C2semidirect
10. #30780C2semidirect
11. #29116C2semidirect
12. #29057C2semidirect
13. #29015C2semidirect
14. #28992C2semidirect
15. #27759C2semidirect
16. #27539C2semidirect
17. #27281C2semidirect
18. #27057C2semidirect
19. #26766C2semidirect
20. #26669C2semidirect
21. #26643C2semidirect
22. #26490C2semidirect
23. #26162C2semidirect
24. #25680C2semidirect
26. #24044C2semidirect
27. #23579C2semidirect
28. #23301C2semidirect
29. #23005C2semidirect
30. #22880C2semidirect
31. #22056C2semidirect
34. C2×#498C22semidirect
35. C2×#489C22semidirect
42. C2×#440C22semidirect
43. C2×C4×D8C22semidirect
56. #2628C22semidirect
57. #2571C22semidirect
61. #2509C22semidirect
62. #2496C22semidirect
63. #2494C22semidirect
69. #2452C22semidirect
71. #2439C22semidirect
76. #2422C22semidirect
77. #2420C22semidirect
83. #2363C22semidirect
84. #2349C22semidirect
86. #2324C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2092C22semidirect
91. #2087C22semidirect
92. #2077C22semidirect
93. #2077C22semidirect
94. #2074C22semidirect
96. #2073C22semidirect
97. #2073C22semidirect
99. #2067C22semidirect
100. #2066C22semidirect
102. #2065C22semidirect
103. #2065C22semidirect
104. #2057C22semidirect
107. #2042C22semidirect
108. #2042C22semidirect
111. #2036C22semidirect
112. #2036C22semidirect
113. #2035C22semidirect
114. #2035C22semidirect
120. #2023C22semidirect
121. #2023C22semidirect
122. #2012C22semidirect
123. #2012C22semidirect
124. #2000C22semidirect
125. #2000C22semidirect
128. #1993C22semidirect
129. #1983C22semidirect
131. #1972C22semidirect
134. #1959C22semidirect
136. #1958C22semidirect
138. #1949C22semidirect
139. #1944C22semidirect
140. #1943C22semidirect
143. #1936C22semidirect
144. #1935C22semidirect
146. #1934C22semidirect
147. #1934C22semidirect
148. #1934C22semidirect
149. #1934C22semidirect
152. #1925C22semidirect
153. #1924C22semidirect
154. #1924C22semidirect
155. #1923C22semidirect
156. #1923C22semidirect
157. #1920C22semidirect
158. #1919C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
163. #1895C22semidirect
164. #1894C22semidirect
166. #1879C22semidirect
167. #1879C22semidirect
168. #1879C22semidirect
169. #1879C22semidirect
170. #1877C22semidirect
171. #1875C22semidirect
172. #1873C22semidirect
174. #1865C22semidirect
175. #1865C22semidirect
177. #1864C22semidirect
178. #1864C22semidirect
179. #1864C22semidirect
180. #1864C22semidirect
182. #1854C22semidirect
183. #1854C22semidirect
184. #1825C22semidirect
185. #1825C22semidirect
187. #1802C22semidirect
193. #1771C22semidirect
194. #1770C22semidirect
195. #1762C22semidirect
196. #1762C22semidirect
197. C4×#103C22semidirect
198. C4×#102C22semidirect
199. #1753C22semidirect
200. #1753C22semidirect
201. #1750C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#448742
#427572
#317952
#314792
#314012
#312982
#310082
#309922
#308982
#307802
#291162
#290572
#290152
#289922
#277592
#275392
#272812
#270572
#267662
#266692
#266432
#264902
#261622
#256802
#242482
#240442
#235792
#233012
#230052
#228802
#220562