Finite Group Databasebeta

← #6866589

Subgroups — #6866589

Order 512.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36493C211yesmaximal, characteristic
2#34947C211yesmaximal, characteristic, complemented
3#33111C211yesmaximal, characteristic, complemented
4#31398C211yesmaximal, characteristic, complemented
5#31394C211yesmaximal, characteristic, complemented
6#30717C211yesmaximal, characteristic, complemented
7#30717C211yesmaximal, characteristic, complemented
8#30713C211yesmaximal, characteristic, complemented
9#30709C211yesmaximal, characteristic, complemented
10#30577C211yesmaximal, characteristic, complemented
11#30565C211yesmaximal, characteristic, complemented
12#30110C211yesmaximal, characteristic, complemented
13#30108C211yesmaximal, characteristic, complemented
14#29415C211yesmaximal, characteristic, complemented
15#29413C211yesmaximal, characteristic, complemented
16#28612C211yesmaximal, characteristic, complemented
17#28582C211yesmaximal, characteristic, complemented
18#28574C211yesmaximal, characteristic, complemented
19#28492C211yesmaximal, characteristic, complemented
20#26335C211yesmaximal, characteristic, complemented
21#26295C211yesmaximal, characteristic, complemented
22#25660C211yesmaximal, characteristic, complemented
23#25641C211yesmaximal, characteristic, complemented
24#25603C211yesmaximal, characteristic, complemented
25#25400C211yesmaximal, characteristic, complemented
26#25350C211yesmaximal, characteristic, complemented
27#24153C211yesmaximal, characteristic, complemented
28#22471C211yesmaximal, characteristic, complemented
29#22191C211yesmaximal, characteristic, complemented
30#22182C211yesmaximal, characteristic, complemented
31#21578C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#489C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#480C2211yescharacteristic
39C2×#480C2211yescharacteristic
40C2×#474C2211yescharacteristic
41C2×#470C2211yescharacteristic
42C2×#468C2211yescharacteristic
43C2×#468C2211yescharacteristic
44C2×#467C2211yescharacteristic
45C2×#465C2211yescharacteristic
46C2×#465C2211yescharacteristic
47C2×#461C2211yescharacteristic
48C2×#435C2211yescharacteristic
49C2×#435C2211yescharacteristic
50#2856C2211yescharacteristic
51#2850C2211yescharacteristic
52#2850C2211yescharacteristic
53#2568C2211yescharacteristic
54#2567C2211yescharacteristic
55#2566—21no—
56#2565—21no—
57#2564—21no—
58#2564—21no—
59#2563C2211yescharacteristic
60#2542C2211yescharacteristic
61#2541C2211yescharacteristic
62#2540C2211yescharacteristic
63#2540C2211yescharacteristic
64#2538C2211yescharacteristic
65#2535C2211yescharacteristic
66#2535C2211yescharacteristic
67#2471—21no—
68#2471—21no—
69#2456—21no—
70#2456—21no—
71#2448—21no—
72#2431—21no—
73#2417C2211yescharacteristic
74#2417C2211yescharacteristic
75#2417C2211yescharacteristic
76#2417C2211yescharacteristic
77#2396—21no—
78#2396—21no—
79#2366—21no—
80#2363—21no—
81#2355C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×C22⋊Q8C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×C22⋊Q8C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87C4×#121C2211yescharacteristic
88C4×#121C2211yescharacteristic
89#2297—21no—
90#2285—21no—
91C2×C4×C4⋊C4C2211yescharacteristic
92#2101C2211yescharacteristic
93#2099C2211yescharacteristic
94#2097C2211yescharacteristic
95#2096C2211yescharacteristic
96#2085C2211yescharacteristic
97#2084C2211yescharacteristic
98#2076C2211yescharacteristic
99#2075C2211yescharacteristic
100#2074C2211yescharacteristic
101#2072C2211yescharacteristic
102#2042C2211yescharacteristic
103#2042C2211yescharacteristic
104#2041C2211yescharacteristic
105#2041C2211yescharacteristic
106#2036C2211yescharacteristic
107#2036C2211yescharacteristic
108#2036C2211yescharacteristic
109#2036C2211yescharacteristic
110#2035C2211yescharacteristic
111#2035C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2015C2211yescharacteristic
117#2015C2211yescharacteristic
118#2014C2211yescharacteristic
119#2014C2211yescharacteristic
120#2001C2211yescharacteristic
121#2001C2211yescharacteristic
122#2001C2211yescharacteristic
123#2001C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1993C2211yescharacteristic
133#1988C2211yescharacteristic
134#1985C2211yescharacteristic
135#1985C2211yescharacteristic
136#1983C2211yescharacteristic
137#1983C2211yescharacteristic
138#1981C2211yescharacteristic
139#1960C2211yescharacteristic
140#1949C2211yescharacteristic
141#1949C2211yescharacteristic
142#1928C2211yescharacteristic
143#1928C2211yescharacteristic
144#1928C2211yescharacteristic
145#1928C2211yescharacteristic
146#1928C2211yescharacteristic
147#1927C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1919C2211yescharacteristic
157#1918C2211yescharacteristic
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1874C2211yescharacteristic
177#1874C2211yescharacteristic
178#1872C2211yescharacteristic
179#1870C2211yescharacteristic
180#1870C2211yescharacteristic
181#1869C2211yescharacteristic
182#1869C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1853C2211yescharacteristic
190#1823C2211yescharacteristic
191#1817C2211yescharacteristic
192#1817C2211yescharacteristic
193#1809C2211yescharacteristic
194#1808C2211yescharacteristic
195#1797C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1749C2211yescharacteristic
201#1728C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41D411yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#559—42no—
215#559—42no—
216#533—42no—
217#533—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127—21no—
221C2×#127C2311yescharacteristic
222C2×#125—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C4×#41—42no—
247C4×#41—42no—
248C2×C4×Q8—21no—
249C2×C4×Q8D411yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4D411yescharacteristic
258C2×C4×D4D411yescharacteristic
259C2×C4×D4D411yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×#117—21no—
266C2×#117D411yescharacteristic
267C2×#117D411yescharacteristic
268C2×#117D411yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C42—21no—
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275#497—42no—
276#489—42no—
277#483—42no—
278#480—24no—
279#480—42no—
280#474—42no—
281#470—42no—
282#468—24no—
283#468—42no—
284#467—24no—
285#465—42no—
286#465—42no—
287#461—42no—
288#435—42no—
289#435—42no—
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×C4⋊C8C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×#97C2311yescharacteristic
340#400—21no—
341#400—21no—
342#399—21no—
343#399—21no—
344#399—21no—
345#399—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#397—21no—
351#397—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#395—21no—
359#395—21no—
360#393—21no—
361#393—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#391—21no—
369#391—21no—
370#391—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389—21no—
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#384—21no—
427#384—21no—
428#384C2311yescharacteristic
429#382—21no—
430#382—21no—
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C2×#95—21no—
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#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C2×#41—24no—
500C2×#41—42no—
501C2×#41—42no—
502C22×Q8—21no—
503C22×Q8C2×D411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2×D411yescharacteristic
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2×D411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—22no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×SD16—22no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×M16—22no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16—41no—
557C22×C8—22no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C4⋊Q8—22no—
572C4⋊Q8—22no—
573C4⋊Q8—22no—
574C4⋊Q8—22no—
575#127—41no—
576#127—41no—
577#127—44no—
578#125—44no—
579#124—22no—
580#124—22no—
581#124—41no—
582#124—41no—
583#124—44no—
584#123—44no—
585#123—44no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—44no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605#121—22no—
606#121—22no—
607#121—41no—
608#121—41no—
609#121—44no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#121—41no—
616#121—41no—
617#121—41no—
618#121—82no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8—42no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8—44no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—42no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—42no—
641C4×D4—42no—
642C4×D4—44no—
643C4×D4—82no—
644C4×D4—82no—
645#117—42no—
646#117—42no—
647#117—42no—
648#117—44no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
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—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
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—21no—
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×C42—22no—
733C2×C42—22no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—41no—
745C2×C42—41no—
746C2×C42—41no—
747C2×C42—41no—
748C2×C42—44no—
749C2×C42C2×D411yescharacteristic
750C2×C42C2×D411yescharacteristic
751C2×C42C2×D411yescharacteristic
752C2×C42C2×D411yescharacteristic
753C2×C42C2×D411yescharacteristic
754C2×C42C2×D411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759#107—22no—
760#107—22no—
761#107—41no—
762#107—41no—
763#107—41no—
764#107#4114yescomplemented
765#106—22no—
766#106—22no—
767#106—41no—
768#106—41no—
769C4⋊C8—22no—
770C4⋊C8—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#103—41no—
785#103—41no—
786#103—41no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798#102—41no—
799C22⋊C8—22no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804C22⋊C8—41no—
805C22⋊C8—41no—
806C22⋊C8—41no—
807#97—22no—
808#97—22no—
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#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842C24—21no—
843C24—21no—
844C24C22×D411yescharacteristic
845C24C22×D411yescharacteristic
846C24C22×D411yescharacteristic
847#41—416no—
848C2×Q8—22no—
849C2×Q8—22no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—41no—
869C2×Q8—42no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—22no—
877C2×D4—22no—
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—21no—
890C2×D4—41no—
891C2×D4—41no—
892C2×D4—41no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—22no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—22no—
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—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—41no—
960C22×C4—41no—
961C22×C4—41no—
962C22×C4—41no—
963C22×C4—41no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4#13714yes—
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C2511yescharacteristic
991Q16—82no—
992Q16—82no—
993SD16—82no—
994SD16—82no—
995SD16—82no—
996SD16—82no—
997M16—82no—
998M16—82no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
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—82no—
1023C2×C8—82no—
1024C2×C8C2×#4112yes—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
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—41no—
1049C4⋊C4—41no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4C2×#4112yes—
1075C4⋊C4C2×#4112yes—
1076C4⋊C4H(5,𝔽2)12yes—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—41no—
1080C22⋊C4—41no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
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—81no—
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—
1115C42—22no—
1116C42—22no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—41no—
1124C42—41no—
1125C42—41no—
1126C42—41no—
1127C42—42no—
1128C42—42no—
1129C42—42no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42—81no—
1136C42—81no—
1137C42H(5,𝔽2)12yes—
1138C42H(5,𝔽2)12yes—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
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—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23C2×#13712yes—
1173C23#57512yes—
1174C23C23×D411yescharacteristic
1175Q8—44no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—84no—
1189D4—44no—
1190D4—44no—
1191D4—44no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—84no—
1201D4—84no—
1202D4—84no—
1203D4—162no—
1204D4—162no—
1205D4—162no—
1206D4—162no—
1207D4—162no—
1208C2×C4—28no—
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—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—44no—
1242C2×C4—44no—
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—41no—
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—82no—
1295C2×C4—82no—
1296C2×C4—82no—
1297C2×C4—84no—
1298C2×C4—84no—
1299C2×C4—162no—
1300C2×C4—162no—
1301C2×C4#53412yes—
1302C2×C4#53412yes—
1303C2×C4C2×#13712yes—
1304C2×C4C2×#13712yes—
1305C2×C4C22×#4111yescharacteristic
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4#58511yescharacteristic
1310C2×C4#58511yescharacteristic
1311C8—22no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—22no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22C2×#53411yescharacteristic
1355C22D4×#4111yescharacteristic
1356C22#348811yescharacteristic
1357C22C22×#13711yescharacteristic
1358C22C2×#57511yescharacteristic
1359C22#358411yescharacteristic
1360C22#358511yescharacteristic
1361C4—22no—
1362C4—22no—
1363C4—22no—
1364C4—22no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4#350811yescharacteristic
1387C4#351711yescharacteristic
1388C4#354611yescharacteristic
1389C4#356211yescharacteristic
1390C2—42no—
1391C2—42no—
1392C2—81no—
1393C2—161no—
1394C2—161no—
1395C2#3986511yescharacteristic
1396C2#6075111yescharacteristic
1397C2#6076011yescharacteristic
1398C2#6144011yescharacteristic
1399C2#6145411yescharacteristic
1400C2#6196511yescharacteristic
1401C2#6199011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36493C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34947C2semidirect
3. #33111C2semidirect
4. #31398C2semidirect
5. #31394C2semidirect
6. #30717C2semidirect
7. #30717C2semidirect
8. #30713C2semidirect
9. #30709C2semidirect
10. #30577C2semidirect
11. #30565C2semidirect
12. #30110C2semidirect
13. #30108C2semidirect
14. #29415C2semidirect
15. #29413C2semidirect
16. #28612C2semidirect
17. #28582C2semidirect
18. #28574C2semidirect
19. #28492C2semidirect
20. #26335C2semidirect
21. #26295C2semidirect
22. #25660C2semidirect
23. #25641C2semidirect
24. #25603C2semidirect
25. #25400C2semidirect
26. #25350C2semidirect
27. #24153C2semidirect
28. #22471C2semidirect
29. #22191C2semidirect
30. #22182C2semidirect
31. #21578C2semidirect
764. #107#41semidirect

Maximal subgroups

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

subgroupindex
#364932
#349472
#331112
#313982
#313942
#307172
#307132
#307092
#305772
#305652
#301102
#301082
#294152
#294132
#286122
#285822
#285742
#284922
#263352
#262952
#256602
#256412
#256032
#254002
#253502
#241532
#224712
#221912
#221822
#215782