Finite Group Databasebeta

← #6830717

Subgroups — #6830717

Order 512.

1563 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42982C211yesmaximal, characteristic
2#42675C211yesmaximal, characteristic, complemented
3#33046C211yesmaximal, characteristic, complemented
4#31853C211yesmaximal, characteristic, complemented
5#31853C211yesmaximal, characteristic, complemented
6#31817C211yesmaximal, characteristic, complemented
7#31805C211yesmaximal, characteristic, complemented
8#31768C211yesmaximal, characteristic, complemented
9#31767C211yesmaximal, characteristic, complemented
10#31726C211yesmaximal, characteristic, complemented
11#31720C211yesmaximal, characteristic, complemented
12#29975C211yesmaximal, characteristic, complemented
13#29723C211yesmaximal, characteristic, complemented
14#29102C211yesmaximal, characteristic, complemented
15#29093C211yesmaximal, characteristic, complemented
16#28927C211yesmaximal, characteristic, complemented
17#28909C211yesmaximal, characteristic, complemented
18#28565C211yesmaximal, characteristic, complemented
19#28559C211yesmaximal, characteristic, complemented
20#27703C211yesmaximal, characteristic, complemented
21#27701C211yesmaximal, characteristic, complemented
22#26205C211yesmaximal, characteristic, complemented
23#26201C211yesmaximal, characteristic, complemented
24#25136C211yesmaximal, characteristic, complemented
25#25120C211yesmaximal, characteristic, complemented
26#23969C211yesmaximal, characteristic, complemented
27#23966C211yesmaximal, characteristic, complemented
28#22499C211yesmaximal, characteristic, complemented
29#22497C211yesmaximal, characteristic, complemented
30#21496C211yesmaximal, characteristic, complemented
31#21089C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#487C2211yescharacteristic, complemented
35C2×#468C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#436C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#435C2211yescharacteristic, complemented
42C2×#418C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C2×#405C2211yescharacteristic
45#2830—21no—
46#2814—21no—
47#2735—21no—
48#2726—21no—
49#2725—21no—
50#2704—21no—
51#2702—21no—
52#2684—21no—
53#2684—21no—
54#2668—21no—
55#2648—21no—
56#2648—21no—
57#2630—21no—
58#2628C2211yescharacteristic
59#2625—21no—
60#2621C2211yescharacteristic
61#2555—21no—
62#2513C2211yescharacteristic
63#2513C2211yescharacteristic
64#2504C2211yescharacteristic
65#2504C2211yescharacteristic
66#2491C2211yescharacteristic
67#2491C2211yescharacteristic
68#2485—21no—
69#2453C2211yescharacteristic, complemented
70#2451C2211yescharacteristic, complemented
71#2442C2211yescharacteristic, complemented
72#2439C2211yescharacteristic, complemented
73#2429C2211yescharacteristic, complemented
74#2429C2211yescharacteristic, complemented
75#2417C2211yescharacteristic, complemented
76#2416C2211yescharacteristic
77#2416C2211yescharacteristic
78#2415C2211yescharacteristic
79#2415C2211yescharacteristic
80#2415C2211yescharacteristic, complemented
81#2408C2211yescharacteristic
82#2408C2211yescharacteristic
83#2392C2211yescharacteristic
84#2352C2211yescharacteristic
85#2352C2211yescharacteristic
86#2316C2211yescharacteristic
87#2309C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2087C2211yescharacteristic, complemented
95#2086C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2075C2211yescharacteristic, complemented
98#2074C2211yescharacteristic, complemented
99#2074C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2067C2211yescharacteristic
103#2065C2211yescharacteristic
104#2058C2211yescharacteristic, complemented
105#2057C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2036C2211yescharacteristic, complemented
113#2035C2211yescharacteristic, complemented
114#2034C2211yescharacteristic
115#2033C2211yescharacteristic
116#2025C2211yescharacteristic
117#2025C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#2013C2211yescharacteristic
121#2013C2211yescharacteristic
122#2000C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1993C2211yescharacteristic, complemented
129#1993C2211yescharacteristic, complemented
130#1991C2211yescharacteristic, complemented
131#1989C2211yescharacteristic, complemented
132#1988C2211yescharacteristic, complemented
133#1973C2211yescharacteristic
134#1968C2211yescharacteristic
135#1960C2211yescharacteristic, complemented
136#1954C2211yescharacteristic, complemented
137#1939C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1924C2211yescharacteristic, complemented
155#1924C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic
174#1873C2211yescharacteristic
175#1873C2211yescharacteristic
176#1872C2211yescharacteristic, complemented
177#1872C2211yescharacteristic, complemented
178#1872C2211yescharacteristic, complemented
179#1872C2211yescharacteristic, complemented
180#1869C2211yescharacteristic
181#1869C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1835C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1824C2211yescharacteristic
187#1824C2211yescharacteristic, complemented
188#1824C2211yescharacteristic, complemented
189#1823C2211yescharacteristic
190#1823C2211yescharacteristic, complemented
191#1805C2211yescharacteristic, complemented
192#1805C2211yescharacteristic, complemented
193#1798C2211yescharacteristic
194#1771C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196C4×#103C2211yescharacteristic, complemented
197#1753C2211yescharacteristic, complemented
198C8×C22⋊C4C2211yescharacteristic, complemented
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#554—24no—
213#554—42no—
214#552—24no—
215#552—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#125—21no—
221C2×#125—21no—
222C2×#125C2311yescharacteristic
223C2×#124—21no—
224C2×#124—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117—21no—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257#487—42no—
258#468—42no—
259#465—42no—
260#450—42no—
261#450—42no—
262#436—42no—
263#435—42no—
264#435—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#418—42no—
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102—24no—
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307#405—42no—
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#400—21no—
315#400—21no—
316#400—21no—
317#399—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398D411yescharacteristic
327#397—21no—
328#397—21no—
329#397—21no—
330#397—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#397D411yescharacteristic
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396D411yescharacteristic
348#396D411yescharacteristic
349#395—21no—
350#395—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#392—21no—
368#392—21no—
369#392D411yescharacteristic
370#391—21no—
371#391—21no—
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#390—21no—
377#390—21no—
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
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#388—21no—
413#388—21no—
414#388—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—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#385—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446#379—21no—
447#379—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#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
493C25—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C2×D411yescharacteristic
510C22×D4C2×D411yescharacteristic
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—22no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559#126—44no—
560#125—22no—
561#125—41no—
562#125—44no—
563#125—44no—
564#124—82no—
565#124—82no—
566#123—44no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—82no—
590#121—82no—
591#120—82no—
592#120—82no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—44no—
604#117—22no—
605#117—41no—
606#117—41no—
607#117—44no—
608#117—41no—
609#117—41no—
610#117—41no—
611#117—41no—
612#117—41no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊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—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4#4114yes—
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⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724#107—41no—
725#107—41no—
726#106—41no—
727#106—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732#103—22no—
733#103—22no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764#97—22no—
765#97—41no—
766#97—41no—
767C4×C8—22no—
768C4×C8—41no—
769C4×C8—41no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—21no—
809C24—21no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—42no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—41no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—82no—
867C2×D4—82no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—24no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—42no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C2×#4112yes—
932C22×C4H(5,𝔽2)12yes—
933C22×C4C2511yescharacteristic
934SD16—82no—
935SD16—82no—
936SD16—82no—
937SD16—82no—
938M16—44no—
939M16—82no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—44no—
964C2×C8—82no—
965C2×C8H(5,𝔽2)12yes—
966C4⋊C4—24no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4C2×#4112yes—
1022C4⋊C4C2×#4112yes—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—84no—
1119C23—162no—
1120C23—162no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23—162no—
1125C23#54612yes—
1126C23#57712yes—
1127C23C23×D411yescharacteristic
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—162no—
1137Q8—162no—
1138D4—44no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—84no—
1148D4—82no—
1149D4—82no—
1150D4—162no—
1151D4—162no—
1152D4—162no—
1153D4—162no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
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—84no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4#54612yes—
1245C2×C4C22×#4111yescharacteristic
1246C2×C4C2×H(5,𝔽2)11yescharacteristic
1247C2×C4C2×H(5,𝔽2)11yescharacteristic
1248C2×C4#58511yescharacteristic
1249C2×C4#58511yescharacteristic
1250C2×C4#58511yescharacteristic
1251C8—22no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C22—22no—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—168no—
1295C22C2×#54611yescharacteristic
1296C22#349611yescharacteristic
1297C22#350011yescharacteristic
1298C22C2×#57711yescharacteristic
1299C22#358411yescharacteristic
1300C22#358511yescharacteristic
1301C22#358611yescharacteristic
1302C4—22no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—42no—
1308C4—42no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4#346011yescharacteristic
1328C4#349311yescharacteristic
1329C4#353411yescharacteristic
1330C4#356011yescharacteristic
1331C2—42no—
1332C2—42no—
1333C2—81no—
1334C2—161no—
1335C2—161no—
1336C2#3941511yescharacteristic
1337C2#6118511yescharacteristic
1338C2#6118711yescharacteristic
1339C2#6230811yescharacteristic
1340C2#6235211yescharacteristic
1341C2#6255611yescharacteristic
1342C2#6256811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42982C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42675C2semidirect
3. #33046C2semidirect
4. #31853C2semidirect
5. #31853C2semidirect
6. #31817C2semidirect
7. #31805C2semidirect
8. #31768C2semidirect
9. #31767C2semidirect
10. #31726C2semidirect
11. #31720C2semidirect
12. #29975C2semidirect
13. #29723C2semidirect
14. #29102C2semidirect
15. #29093C2semidirect
16. #28927C2semidirect
17. #28909C2semidirect
18. #28565C2semidirect
19. #28559C2semidirect
20. #27703C2semidirect
21. #27701C2semidirect
22. #26205C2semidirect
23. #26201C2semidirect
24. #25136C2semidirect
25. #25120C2semidirect
26. #23969C2semidirect
27. #23966C2semidirect
28. #22499C2semidirect
29. #22497C2semidirect
30. #21496C2semidirect
31. #21089C2semidirect
34. C2×#487C22semidirect
41. C2×#435C22semidirect
69. #2453C22semidirect
70. #2451C22semidirect
71. #2442C22semidirect
72. #2439C22semidirect
73. #2429C22semidirect
74. #2429C22semidirect
75. #2417C22semidirect
80. #2415C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2101C22semidirect
92. #2088C22semidirect
93. #2088C22semidirect
94. #2087C22semidirect
95. #2086C22semidirect
96. #2077C22semidirect
97. #2075C22semidirect
98. #2074C22semidirect
99. #2074C22semidirect
104. #2058C22semidirect
105. #2057C22semidirect
112. #2036C22semidirect
113. #2035C22semidirect
128. #1993C22semidirect
129. #1993C22semidirect
130. #1991C22semidirect
131. #1989C22semidirect
132. #1988C22semidirect
135. #1960C22semidirect
136. #1954C22semidirect
137. #1939C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
153. #1927C22semidirect
154. #1924C22semidirect
155. #1924C22semidirect
156. #1921C22semidirect
157. #1920C22semidirect
161. #1894C22semidirect
165. #1892C22semidirect
176. #1872C22semidirect
177. #1872C22semidirect
178. #1872C22semidirect
179. #1872C22semidirect
184. #1835C22semidirect
185. #1825C22semidirect
187. #1824C22semidirect
188. #1824C22semidirect
190. #1823C22semidirect
191. #1805C22semidirect
192. #1805C22semidirect
194. #1771C22semidirect
195. #1763C22semidirect
196. C4×#103C22semidirect
197. #1753C22semidirect
198. C8×C22⋊C4C22semidirect
200. #1736C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#429822
#426752
#330462
#318532
#318172
#318052
#317682
#317672
#317262
#317202
#299752
#297232
#291022
#290932
#289272
#289092
#285652
#285592
#277032
#277012
#262052
#262012
#251362
#251202
#239692
#239662
#224992
#224972
#214962
#210892