Finite Group Databasebeta

← #6995894

Subgroups — #6995894

Order 512.

1643 conjugacy classes of subgroups.

The subgroup lattice has 1389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44887C211yesmaximal, characteristic
2#42919C211yesmaximal, characteristic, complemented
3#32305C211yesmaximal, characteristic, complemented
4#32057C211yesmaximal, characteristic, complemented
5#31796C211yesmaximal, characteristic, complemented
6#31621C211yesmaximal, characteristic, complemented
7#31321C211yesmaximal, characteristic, complemented
8#30680C211yesmaximal, characteristic, complemented
9#30585C211yesmaximal, characteristic, complemented
10#30565C211yesmaximal, characteristic, complemented
11#28787C211yesmaximal, characteristic, complemented
12#28079C211yesmaximal, characteristic, complemented
13#27033C211yesmaximal, characteristic, complemented
14#26800C211yesmaximal, characteristic, complemented
15#26337C211yesmaximal, characteristic, complemented
16#26227C211yesmaximal, characteristic, complemented
17#25960C211yesmaximal, characteristic, complemented
18#25344C211yesmaximal, characteristic, complemented
19#25128C211yesmaximal, characteristic, complemented
20#25041C211yesmaximal, characteristic, complemented
21#24882C211yesmaximal, characteristic, complemented
22#24795C211yesmaximal, characteristic, complemented
23#24566C211yesmaximal, characteristic, complemented
24#24394C211yesmaximal, characteristic, complemented
25#24133C211yesmaximal, characteristic, complemented
26#24105C211yesmaximal, characteristic, complemented
27#23486C211yesmaximal, characteristic, complemented
28#22864C211yesmaximal, characteristic, complemented
29#22849C211yesmaximal, characteristic, complemented
30#22662C211yesmaximal, characteristic, complemented
31#21947C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#483C2211yescharacteristic, complemented
35C2×#480C2211yescharacteristic
36C2×#475C2211yescharacteristic, complemented
37C2×#478C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C2×#436C2211yescharacteristic, complemented
44C2×#435C2211yescharacteristic
45C2×#428C2211yescharacteristic, complemented
46C2×#427C2211yescharacteristic
47C2×#418C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C2×#408C2211yescharacteristic
50C2×#408C2211yescharacteristic
51#2833—21no—
52#2781—21no—
53#2778—21no—
54#2778—21no—
55#2741—21no—
56#2712—21no—
57#2684—21no—
58#2673—21no—
59#2670—21no—
60#2651—21no—
61#2648—21no—
62#2616C2211yescharacteristic
63#2574—21no—
64#2562C2211yescharacteristic, complemented
65#2544—21no—
66#2536C2211yescharacteristic, complemented
67#2535C2211yescharacteristic
68#2500C2211yescharacteristic
69#2494C2211yescharacteristic, complemented
70#2494C2211yescharacteristic, complemented
71#2491C2211yescharacteristic
72#2489C2211yescharacteristic, complemented
73#2487C2211yescharacteristic, complemented
74#2474—21no—
75#2442C2211yescharacteristic
76#2439C2211yescharacteristic
77#2424—21no—
78#2422C2211yescharacteristic
79#2421C2211yescharacteristic, complemented
80#2417C2211yescharacteristic
81#2417C2211yescharacteristic, complemented
82#2416C2211yescharacteristic
83#2414C2211yescharacteristic
84#2411—21no—
85#2408C2211yescharacteristic
86#2388C2211yescharacteristic
87#2362C2211yescharacteristic
88#2361C2211yescharacteristic
89#2354C2211yescharacteristic
90#2352C2211yescharacteristic
91D4×C22⋊C4C2211yescharacteristic
92#2311C2211yescharacteristic
93#2311C2211yescharacteristic
94#2099C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2088C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2085C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2077C2211yescharacteristic, complemented
103#2075C2211yescharacteristic, complemented
104#2073C2211yescharacteristic
105#2072C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic, complemented
111#2057C2211yescharacteristic, complemented
112#2057C2211yescharacteristic, complemented
113#2055C2211yescharacteristic
114#2036C2211yescharacteristic, complemented
115#2036C2211yescharacteristic, complemented
116#2035C2211yescharacteristic, complemented
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2033C2211yescharacteristic
130#2025C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1993C2211yescharacteristic, complemented
135#1991C2211yescharacteristic, complemented
136#1973C2211yescharacteristic
137#1968C2211yescharacteristic
138#1955C2211yescharacteristic, complemented
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1948C2211yescharacteristic, complemented
142#1943C2211yescharacteristic, complemented
143#1942C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1928C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1924C2211yescharacteristic, complemented
151#1923C2211yescharacteristic, complemented
152#1921C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1894C2211yescharacteristic
157#1893C2211yescharacteristic
158#1892C2211yescharacteristic
159#1880C2211yescharacteristic
160#1877C2211yescharacteristic
161#1874C2211yescharacteristic
162#1873C2211yescharacteristic
163#1873C2211yescharacteristic, complemented
164#1873C2211yescharacteristic, complemented
165#1870C2211yescharacteristic
166#1870C2211yescharacteristic, complemented
167#1869C2211yescharacteristic, complemented
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1863C2211yescharacteristic, complemented
171#1862C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1854C2211yescharacteristic, complemented
178#1854C2211yescharacteristic, complemented
179#1853C2211yescharacteristic, complemented
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic, complemented
183#1852C2211yescharacteristic, complemented
184#1851C2211yescharacteristic, complemented
185#1850C2211yescharacteristic
186#1847C2211yescharacteristic, complemented
187#1825C2211yescharacteristic, complemented
188#1824C2211yescharacteristic, complemented
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic, complemented
191#1809C2211yescharacteristic, complemented
192#1809C2211yescharacteristic, complemented
193#1808C2211yescharacteristic, complemented
194#1808C2211yescharacteristic, complemented
195#1807C2211yescharacteristic
196#1804C2211yescharacteristic
197#1786C2211yescharacteristic
198#1776C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1752C2211yescharacteristic, complemented
202#1736C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#555—42no—
213#555—42no—
214#535—42no—
215#535—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127—21no—
218C2×#125C2311yescharacteristic
219C2×#124—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#123—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117—21no—
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255#483—42no—
256#480—42no—
257#478—42no—
258#475—42no—
259#468—42no—
260#468—42no—
261#465—42no—
262#450—24no—
263#440—42no—
264#436—42no—
265#435—24no—
266#428—42no—
267#427—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289#418—42no—
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#102—42no—
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
311#408—24no—
312#408—42no—
313C2×C22⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#401—21no—
328#401—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#399—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#395—21no—
350#395D411yescharacteristic
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#394—21no—
361#394—21no—
362#394—21no—
363#394D411yescharacteristic
364#394D411yescharacteristic
365#394D411yescharacteristic
366#393—21no—
367#393—21no—
368#393D411yescharacteristic
369#392—21no—
370#392—21no—
371#392—21no—
372#392D411yescharacteristic
373#392D411yescharacteristic
374#392D411yescharacteristic
375#391—21no—
376#391—21no—
377#391—21no—
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389C2311yescharacteristic
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#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
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#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—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#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#384C2311yescharacteristic
437#382—21no—
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#380—21no—
442#380—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⋊C4—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C22⋊C4—21no—
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
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—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2×D411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2×D411yescharacteristic
524C22×D4C2×D411yescharacteristic
525C22×D4C2×D411yescharacteristic
526C22×D4C2×D411yescharacteristic
527C22×D4C2×D411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×M16—22no—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C22×C8—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—22no—
569C4⋊Q8—41no—
570#127—44no—
571#125—41no—
572#125—41no—
573#124—44no—
574#124—44no—
575#124—44no—
576#124—82no—
577#123—82no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—44no—
597#121—41no—
598#121—41no—
599#121—82no—
600#120—44no—
601#120—44no—
602#120—82no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—82no—
616#117—22no—
617#117—22no—
618#117—44no—
619#117—41no—
620#117—41no—
621#117—41no—
622#117—41no—
623#117—41no—
624#117—41no—
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⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
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—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—82no—
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#107—22no—
729#107—22no—
730#107—41no—
731#107—41no—
732#107—41no—
733#107—41no—
734#107—41no—
735#107—41no—
736#107—41no—
737#107—41no—
738#106—22no—
739#106—22no—
740#106—41no—
741#106—41no—
742#106—41no—
743#106—41no—
744#106—41no—
745#106—41no—
746C4⋊C8—22no—
747C4⋊C8—22no—
748C4⋊C8—41no—
749#103—22no—
750#103—22no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8#4114yes—
780#97—22no—
781#97—41no—
782C4×C8—41no—
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#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#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822C24—21no—
823C24—21no—
824C24—42no—
825C24—42no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24C22×D411yescharacteristic
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835#41—82no—
836#41—82no—
837#41—82no—
838#41—82no—
839C2×Q8—22no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—41no—
847C2×Q8—41no—
848C2×Q8—42no—
849C2×Q8—81no—
850C2×Q8—81no—
851C2×D4—24no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—22no—
855C2×D4—22no—
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—21no—
866C2×D4—21no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—41no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4H(5,𝔽2)12yes—
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—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—42no—
943C22×C4—42no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C2×#4112yes—
968C22×C42−1+412yes—
969C22×C4C2511yescharacteristic
970SD16—44no—
971SD16—82no—
972M16—44no—
973M16—82no—
974M16—82no—
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×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—44no—
997C2×C8—82no—
998C2×C8C2×#4112yes—
999C2×C8C2×#4112yes—
1000C2×C8H(5,𝔽2)12yes—
1001C4⋊C4—22no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4H(5,𝔽2)12yes—
1049C22⋊C4—24no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
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—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—22no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—84no—
1155C23—84no—
1156C23—162no—
1157C23—162no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23#54712yes—
1162C23C23×D411yescharacteristic
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—82no—
1168Q8—162no—
1169D4—22no—
1170D4—22no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—82no—
1178D4—84no—
1179D4—82no—
1180D4—82no—
1181D4—82no—
1182D4—84no—
1183D4—82no—
1184D4—82no—
1185D4—162no—
1186D4—162no—
1187D4—162no—
1188D4—162no—
1189D4—162no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
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—22no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
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—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—84no—
1278C2×C4—162no—
1279C2×C4—162no—
1280C2×C4—162no—
1281C2×C4—162no—
1282C2×C4#54712yes—
1283C2×C4C22×#4111yescharacteristic
1284C2×C4C2×H(5,𝔽2)11yescharacteristic
1285C2×C4C2×H(5,𝔽2)11yescharacteristic
1286C2×C4C2×H(5,𝔽2)11yescharacteristic
1287C2×C4C2×2−1+411yescharacteristic
1288C2×C4#58511yescharacteristic
1289C8—22no—
1290C8—22no—
1291C8—22no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C8—41no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—42no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—42no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—42no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—168no—
1340C22C2×#54711yescharacteristic
1341C22#348411yescharacteristic
1342C22#349611yescharacteristic
1343C22#358411yescharacteristic
1344C22#358511yescharacteristic
1345C22#358511yescharacteristic
1346C22#358611yescharacteristic
1347C4—22no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—42no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4#351311yescharacteristic
1372C4#351911yescharacteristic
1373C4#353611yescharacteristic
1374C4#356111yescharacteristic
1375C2—42no—
1376C2—81no—
1377C2—81no—
1378C2—81no—
1379C2—82no—
1380C2—161no—
1381C2#4299911yescharacteristic
1382C2#6126811yescharacteristic
1383C2#6128311yescharacteristic
1384C2#6165411yescharacteristic
1385C2#6167811yescharacteristic
1386C2#6230911yescharacteristic
1387C2#6233611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#44887C2
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
2. #42919C2semidirect
3. #32305C2semidirect
4. #32057C2semidirect
5. #31796C2semidirect
6. #31621C2semidirect
7. #31321C2semidirect
8. #30680C2semidirect
9. #30585C2semidirect
10. #30565C2semidirect
11. #28787C2semidirect
12. #28079C2semidirect
13. #27033C2semidirect
14. #26800C2semidirect
15. #26337C2semidirect
16. #26227C2semidirect
17. #25960C2semidirect
18. #25344C2semidirect
19. #25128C2semidirect
20. #25041C2semidirect
21. #24882C2semidirect
22. #24795C2semidirect
23. #24566C2semidirect
24. #24394C2semidirect
25. #24133C2semidirect
26. #24105C2semidirect
27. #23486C2semidirect
28. #22864C2semidirect
29. #22849C2semidirect
30. #22662C2semidirect
31. #21947C2semidirect
34. C2×#483C22semidirect
36. C2×#475C22semidirect
43. C2×#436C22semidirect
45. C2×#428C22semidirect
64. #2562C22semidirect
66. #2536C22semidirect
69. #2494C22semidirect
70. #2494C22semidirect
72. #2489C22semidirect
73. #2487C22semidirect
79. #2421C22semidirect
81. #2417C22semidirect
94. #2099C22semidirect
95. #2097C22semidirect
98. #2088C22semidirect
99. #2085C22semidirect
100. #2085C22semidirect
101. #2077C22semidirect
102. #2077C22semidirect
103. #2075C22semidirect
105. #2072C22semidirect
106. #2068C22semidirect
110. #2059C22semidirect
111. #2057C22semidirect
112. #2057C22semidirect
114. #2036C22semidirect
115. #2036C22semidirect
116. #2035C22semidirect
134. #1993C22semidirect
135. #1991C22semidirect
138. #1955C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1948C22semidirect
142. #1943C22semidirect
143. #1942C22semidirect
146. #1928C22semidirect
150. #1924C22semidirect
151. #1923C22semidirect
152. #1921C22semidirect
153. #1919C22semidirect
163. #1873C22semidirect
164. #1873C22semidirect
166. #1870C22semidirect
167. #1869C22semidirect
170. #1863C22semidirect
175. #1854C22semidirect
176. #1854C22semidirect
177. #1854C22semidirect
178. #1854C22semidirect
179. #1853C22semidirect
182. #1852C22semidirect
183. #1852C22semidirect
184. #1851C22semidirect
186. #1847C22semidirect
187. #1825C22semidirect
188. #1824C22semidirect
190. #1809C22semidirect
191. #1809C22semidirect
192. #1809C22semidirect
193. #1808C22semidirect
194. #1808C22semidirect
198. #1776C22semidirect
201. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#448872
#429192
#323052
#320572
#317962
#316212
#313212
#306802
#305852
#305652
#287872
#280792
#270332
#268002
#263372
#262272
#259602
#253442
#251282
#250412
#248822
#247952
#245662
#243942
#241332
#241052
#234862
#228642
#228492
#226622
#219472