Finite Group Databasebeta

← #6834339

Subgroups — #6834339

Order 512.

1741 conjugacy classes of subgroups.

The subgroup lattice has 1441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42942C211yesmaximal, characteristic, complemented
2#42463C211yesmaximal, characteristic, complemented
3#32933C211yesmaximal, characteristic, complemented
4#31999C211yesmaximal, characteristic, complemented
5#31605C211yesmaximal, characteristic, complemented
6#31569C211yesmaximal, characteristic, complemented
7#31513C211yesmaximal, characteristic, complemented
8#31403C211yesmaximal, characteristic, complemented
9#31271C211yesmaximal, characteristic, complemented
10#30921C211yesmaximal, characteristic, complemented
11#30400C211yesmaximal, characteristic, complemented
12#29899C211yesmaximal, characteristic, complemented
13#29606C211yesmaximal, characteristic, complemented
14#29069C211yesmaximal, characteristic, complemented
15#28992C211yesmaximal, characteristic, complemented
16#28846C211yesmaximal, characteristic, complemented
17#28147C211yesmaximal, characteristic, complemented
18#28110C211yesmaximal, characteristic, complemented
19#27703C211yesmaximal, characteristic, complemented
20#26959C211yesmaximal, characteristic, complemented
21#25959C211yesmaximal, characteristic, complemented
22#25352C211yesmaximal, characteristic, complemented
23#25260C211yesmaximal, characteristic, complemented
24#25214C211yesmaximal, characteristic, complemented
25#25116C211yesmaximal, characteristic, complemented
26#24941C211yesmaximal, characteristic, complemented
27#24428C211yesmaximal, characteristic, complemented
28#22883C211yesmaximal, characteristic, complemented
29#22427C211yesmaximal, characteristic, complemented
30#21445C211yesmaximal, characteristic, complemented
31#20976C211yesmaximal, characteristic, complemented
32C22×#131C2211yescharacteristic, complemented
33C2×#546C2211yescharacteristic
34C2×#537C2211yescharacteristic
35C2×#481C2211yescharacteristic, complemented
36C2×#477C2211yescharacteristic, complemented
37C2×#466C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#466C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic, complemented
43C2×#436C2211yescharacteristic
44C2×#436C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×#417C2211yescharacteristic
47C2×#418C2211yescharacteristic
48C2×#416C2211yescharacteristic
49#2825—21no—
50#2814—21no—
51#2797—21no—
52#2759—21no—
53#2751—21no—
54#2733—21no—
55#2699—21no—
56#2699—21no—
57#2678—21no—
58#2678—21no—
59#2661—21no—
60#2648—21no—
61#2631—21no—
62#2617—21no—
63#2615C2211yescharacteristic
64#2615C2211yescharacteristic, complemented
65#2561—21no—
66#2547C2211yescharacteristic
67#2536C2211yescharacteristic
68#2536C2211yescharacteristic
69#2535C2211yescharacteristic
70#2504C2211yescharacteristic
71#2495C2211yescharacteristic, complemented
72#2494C2211yescharacteristic, complemented
73#2491C2211yescharacteristic, complemented
74#2486C2211yescharacteristic
75#2485C2211yescharacteristic
76#2459—21no—
77#2439C2211yescharacteristic, complemented
78#2426C2211yescharacteristic
79#2426C2211yescharacteristic
80#2420C2211yescharacteristic
81#2420C2211yescharacteristic
82#2420C2211yescharacteristic, complemented
83#2414C2211yescharacteristic
84#2414C2211yescharacteristic
85#2408C2211yescharacteristic
86#2408C2211yescharacteristic
87#2388C2211yescharacteristic
88#2361C2211yescharacteristic, complemented
89#2352C2211yescharacteristic
90#2341C2211yescharacteristic
91#2311C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2101C2211yescharacteristic, complemented
94#2101C2211yescharacteristic, complemented
95#2092C2211yescharacteristic
96#2088C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic, complemented
102#2077C2211yescharacteristic, complemented
103#2077C2211yescharacteristic, complemented
104#2076C2211yescharacteristic
105#2075C2211yescharacteristic, complemented
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic, complemented
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic, complemented
111#2065C2211yescharacteristic
112#2054C2211yescharacteristic
113#2042C2211yescharacteristic
114#2036C2211yescharacteristic
115#2035C2211yescharacteristic, complemented
116#2035C2211yescharacteristic, complemented
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2033C2211yescharacteristic
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic
126#2012C2211yescharacteristic
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic, complemented
129#2000C2211yescharacteristic, complemented
130#1999C2211yescharacteristic
131#1999C2211yescharacteristic
132#1993C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1972C2211yescharacteristic
135#1958C2211yescharacteristic
136#1949C2211yescharacteristic, complemented
137#1941C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic, complemented
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1921C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1895C2211yescharacteristic
147#1895C2211yescharacteristic
148#1895C2211yescharacteristic
149#1895C2211yescharacteristic
150#1895C2211yescharacteristic
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic, complemented
153#1895C2211yescharacteristic, complemented
154#1895C2211yescharacteristic, complemented
155#1894C2211yescharacteristic
156#1894C2211yescharacteristic, complemented
157#1894C2211yescharacteristic, complemented
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic
160#1892C2211yescharacteristic, complemented
161#1892C2211yescharacteristic, complemented
162#1880C2211yescharacteristic, complemented
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1875C2211yescharacteristic
167#1874C2211yescharacteristic
168#1873C2211yescharacteristic
169#1870C2211yescharacteristic
170#1869C2211yescharacteristic
171#1869C2211yescharacteristic
172#1865C2211yescharacteristic, complemented
173#1865C2211yescharacteristic, complemented
174#1863C2211yescharacteristic, complemented
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic, complemented
178#1853C2211yescharacteristic, complemented
179#1851C2211yescharacteristic, complemented
180#1850C2211yescharacteristic, complemented
181#1850C2211yescharacteristic, complemented
182#1835C2211yescharacteristic, complemented
183#1825C2211yescharacteristic
184#1823C2211yescharacteristic, complemented
185#1809C2211yescharacteristic
186#1808C2211yescharacteristic, complemented
187#1808C2211yescharacteristic, complemented
188#1808C2211yescharacteristic, complemented
189#1805C2211yescharacteristic, complemented
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic, complemented
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1780C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C2×#131—42no—
210C2×#131—42no—
211C2×#131—42no—
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#546—24no—
220#546—42no—
221#537—24no—
222#537—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×#124—21no—
225C2×#124—21no—
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247C2×#120—21no—
248C2×#120—21no—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4—21no—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—21no—
262#481—42no—
263#477—42no—
264#466—42no—
265#466—42no—
266#466—42no—
267#449—24no—
268#447—42no—
269C4×SD16—42no—
270#436—42no—
271#436—42no—
272#435—42no—
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#418—42no—
286#417—42no—
287#416—42no—
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326#401—21no—
327#400—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#395D411yescharacteristic
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#394D411yescharacteristic
363#393—21no—
364#393—21no—
365#393—21no—
366#393—21no—
367#393D411yescharacteristic
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#392—21no—
379#392D411yescharacteristic
380#392D411yescharacteristic
381#392D411yescharacteristic
382#391—21no—
383#391—21no—
384#391—21no—
385#390—21no—
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390—21no—
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#385—21no—
434#383—21no—
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#381—21no—
440#381—21no—
441#381—21no—
442#381—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41#4114yes—
512C22×Q8—21no—
513C22×Q8C2×D411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×D411yescharacteristic
533C22×D4C2×D411yescharacteristic
534C22×D4C2×D411yescharacteristic
535C22×D4C2×D411yescharacteristic
536C22×D4C2×D411yescharacteristic
537C22×D4C2×D411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559#131—416no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—41no—
565C2×M16—41no—
566C2×M16—41no—
567C2×M16—41no—
568C2×M16—41no—
569C2×M16—41no—
570C2×M16—41no—
571C2×M16—41no—
572C22×C8—22no—
573C22×C8—22no—
574C22×C8—22no—
575C22×C8—22no—
576C22×C8—22no—
577C22×C8—41no—
578C22×C8—41no—
579C22×C8—41no—
580C22×C8—41no—
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C4⋊Q8—41no—
590C4⋊Q8—41no—
591#124—22no—
592#124—41no—
593#124—82no—
594#124—82no—
595#123—44no—
596#123—82no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—44no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—44no—
611#121—41no—
612#121—41no—
613#121—44no—
614#121—44no—
615#121—44no—
616#121—41no—
617#121—41no—
618#121—41no—
619#121—41no—
620#121—41no—
621#121—41no—
622#121—41no—
623#121—41no—
624#121—41no—
625#121—41no—
626#120—44no—
627#120—82no—
628#120—82no—
629C4×Q8—41no—
630C4×Q8—41no—
631C4×Q8—41no—
632C4×Q8—41no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—82no—
644#117—41no—
645#117—41no—
646#117—41no—
647#117—41no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—41no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—44no—
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747#107—22no—
748#107—41no—
749#107—41no—
750#107—41no—
751#106—41no—
752#106—41no—
753#106—41no—
754#106—41no—
755#106—41no—
756C4⋊C8—22no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—22no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794#97—41no—
795C4×C8—22no—
796C4×C8—41no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833C24—21no—
834C24—21no—
835C24—21no—
836C24—42no—
837C24—42no—
838C24—81no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845C24C22×D411yescharacteristic
846C24C22×D411yescharacteristic
847#41—44no—
848#41—44no—
849#41—44no—
850#41—44no—
851#41—44no—
852#41—44no—
853#41—82no—
854#41—82no—
855C2×Q8—22no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—41no—
862C2×Q8—41no—
863C2×Q8—42no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8C2×#4112yes—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—22no—
870C2×D4—24no—
871C2×D4—22no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—41no—
890C2×D4—41no—
891C2×D4—41no—
892C2×D4—41no—
893C2×D4—41no—
894C2×D4—41no—
895C2×D4—41no—
896C2×D4—41no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—41no—
902C2×D4—41no—
903C2×D4—42no—
904C2×D4—44no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—82no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4C2×#4112yes—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—24no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
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×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C2×#4112yes—
1001C22×C4H(5,𝔽2)12yes—
1002C22×C4C2511yescharacteristic
1003SD16—44no—
1004D8—82no—
1005D8—82no—
1006M16—44no—
1007M16—44no—
1008M16—44no—
1009M16—82no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—44no—
1033C2×C8—44no—
1034C2×C8—44no—
1035C2×C8H(5,𝔽2)12yes—
1036C2×C8H(5,𝔽2)12yes—
1037C4⋊C4—22no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—41no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—41no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—42no—
1141C42—81no—
1142C42—81no—
1143C42—81no—
1144C42—81no—
1145C42—81no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—22no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—84no—
1195C23—84no—
1196C23—162no—
1197C23—162no—
1198C23—162no—
1199C23—162no—
1200C23—162no—
1201C23#54612yes—
1202C23C23×D411yescharacteristic
1203Q8—22no—
1204Q8—22no—
1205Q8—44no—
1206Q8—41no—
1207Q8—41no—
1208Q8—162no—
1209D4—22no—
1210D4—22no—
1211D4—44no—
1212D4—44no—
1213D4—44no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—82no—
1225D4—84no—
1226D4—82no—
1227D4—82no—
1228D4—84no—
1229D4—84no—
1230D4—162no—
1231D4—162no—
1232D4—162no—
1233D4—162no—
1234D4—162no—
1235D4—162no—
1236D4—162no—
1237D4—162no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—84no—
1323C2×C4—162no—
1324C2×C4—162no—
1325C2×C4—162no—
1326C2×C4—162no—
1327C2×C4#54612yes—
1328C2×C4C22×#4111yescharacteristic
1329C2×C4C2×H(5,𝔽2)11yescharacteristic
1330C2×C4C2×H(5,𝔽2)11yescharacteristic
1331C2×C4C2×H(5,𝔽2)11yescharacteristic
1332C2×C4#58511yescharacteristic
1333C2×C4#58511yescharacteristic
1334C8—22no—
1335C8—22no—
1336C8—41no—
1337C8—41no—
1338C8—41no—
1339C8—41no—
1340C8—41no—
1341C8—41no—
1342C22—22no—
1343C22—22no—
1344C22—22no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—42no—
1353C22—41no—
1354C22—41no—
1355C22—41no—
1356C22—42no—
1357C22—42no—
1358C22—41no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—41no—
1369C22—41no—
1370C22—41no—
1371C22—41no—
1372C22—41no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—81no—
1391C22—168no—
1392C22C2×#54611yescharacteristic
1393C22#349611yescharacteristic
1394C22#349611yescharacteristic
1395C22#358411yescharacteristic
1396C22#358411yescharacteristic
1397C22#358511yescharacteristic
1398C22#358511yescharacteristic
1399C4—22no—
1400C4—41no—
1401C4—41no—
1402C4—41no—
1403C4—42no—
1404C4—41no—
1405C4—41no—
1406C4—41no—
1407C4—41no—
1408C4—41no—
1409C4—41no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4—81no—
1416C4—81no—
1417C4—81no—
1418C4—81no—
1419C4—81no—
1420C4—81no—
1421C4—81no—
1422C4#345911yescharacteristic
1423C4#350511yescharacteristic
1424C4#353211yescharacteristic
1425C4#353311yescharacteristic
1426C2—42no—
1427C2—81no—
1428C2—81no—
1429C2—81no—
1430C2—82no—
1431C2—161no—
1432C2—161no—
1433C2#3942811yescharacteristic
1434C2#6119611yescharacteristic
1435C2#6120811yescharacteristic
1436C2#6228311yescharacteristic
1437C2#6231811yescharacteristic
1438C2#6233011yescharacteristic
1439C2#6234711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42942C2semidirect
2. #42463C2semidirect
3. #32933C2semidirect
4. #31999C2semidirect
5. #31605C2semidirect
6. #31569C2semidirect
7. #31513C2semidirect
8. #31403C2semidirect
9. #31271C2semidirect
10. #30921C2semidirect
11. #30400C2semidirect
12. #29899C2semidirect
13. #29606C2semidirect
14. #29069C2semidirect
15. #28992C2semidirect
16. #28846C2semidirect
17. #28147C2semidirect
18. #28110C2semidirect
19. #27703C2semidirect
20. #26959C2semidirect
21. #25959C2semidirect
22. #25352C2semidirect
23. #25260C2semidirect
24. #25214C2semidirect
25. #25116C2semidirect
26. #24941C2semidirect
27. #24428C2semidirect
28. #22883C2semidirect
29. #22427C2semidirect
30. #21445C2semidirect
31. #20976C2semidirect
32. C22×#131C22semidirect
35. C2×#481C22semidirect
36. C2×#477C22semidirect
42. C2×C4×SD16C22semidirect
64. #2615C22semidirect
71. #2495C22semidirect
72. #2494C22semidirect
73. #2491C22semidirect
77. #2439C22semidirect
82. #2420C22semidirect
88. #2361C22semidirect
91. #2311C22semidirect
92. #2101C22semidirect
93. #2101C22semidirect
94. #2101C22semidirect
96. #2088C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
101. #2077C22semidirect
102. #2077C22semidirect
103. #2077C22semidirect
105. #2075C22semidirect
107. #2073C22semidirect
110. #2067C22semidirect
115. #2035C22semidirect
116. #2035C22semidirect
128. #2000C22semidirect
129. #2000C22semidirect
132. #1993C22semidirect
136. #1949C22semidirect
137. #1941C22semidirect
141. #1934C22semidirect
144. #1921C22semidirect
145. #1920C22semidirect
152. #1895C22semidirect
153. #1895C22semidirect
154. #1895C22semidirect
156. #1894C22semidirect
157. #1894C22semidirect
160. #1892C22semidirect
161. #1892C22semidirect
162. #1880C22semidirect
172. #1865C22semidirect
173. #1865C22semidirect
174. #1863C22semidirect
177. #1854C22semidirect
178. #1853C22semidirect
179. #1851C22semidirect
180. #1850C22semidirect
181. #1850C22semidirect
182. #1835C22semidirect
184. #1823C22semidirect
186. #1808C22semidirect
187. #1808C22semidirect
188. #1808C22semidirect
189. #1805C22semidirect
191. #1804C22semidirect
195. #1780C22semidirect
196. #1763C22semidirect
198. #1753C22semidirect
199. #1753C22semidirect
200. C8×C22⋊C4C22semidirect
201. #1736C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#429422
#424632
#329332
#319992
#316052
#315692
#315132
#314032
#312712
#309212
#304002
#298992
#296062
#290692
#289922
#288462
#281472
#281102
#277032
#269592
#259592
#253522
#252602
#252142
#251162
#249412
#244282
#228832
#224272
#214452
#209762