Finite Group Databasebeta

← #6599333

Subgroups — #6599333

Order 512.

1935 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38116C211yesmaximal, characteristic, complemented
2#34288C211yesmaximal, characteristic, complemented
3#33090C211yesmaximal, characteristic, complemented
4#33016C211yesmaximal, characteristic, complemented
5#32956C211yesmaximal, characteristic, complemented
6#29506C211yesmaximal, characteristic, complemented
7#29488C211yesmaximal, characteristic, complemented
8#29418C211yesmaximal, characteristic, complemented
9#29380C211yesmaximal, characteristic, complemented
10#29166C211yesmaximal, characteristic, complemented
11#28122C211yesmaximal, characteristic, complemented
12#27552C211yesmaximal, characteristic, complemented
13#27248C211yesmaximal, characteristic, complemented
14#27092C211yesmaximal, characteristic, complemented
15#26901C211yesmaximal, characteristic, complemented
16#26786C211yesmaximal, characteristic, complemented
17#26673C211yesmaximal, characteristic, complemented
18#26392C211yesmaximal, characteristic, complemented
19#24955C211yesmaximal, characteristic, complemented
20#24899C211yesmaximal, characteristic, complemented
21#24879C211yesmaximal, characteristic, complemented
22#24050C211yesmaximal, characteristic, complemented
23#23863C211yesmaximal, characteristic
24#22942C211yesmaximal, characteristic, complemented
25#22882C211yesmaximal, characteristic, complemented
26#22792C211yesmaximal, characteristic, complemented
27#22584C211yesmaximal, characteristic, complemented
28#22442C211yesmaximal, characteristic, complemented
29#21464C211yesmaximal, characteristic, complemented
30#21134C211yesmaximal, characteristic, complemented
31#20925C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#483C2211yescharacteristic, complemented
38C2×#476C2211yescharacteristic
39C2×#476C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#449C2211yescharacteristic
43C2×#442C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic, complemented
45C2×C4×D8C2211yescharacteristic
46C2×#417C2211yescharacteristic
47C2×#418C2211yescharacteristic
48#2857C2211yescharacteristic
49#2778—21no—
50#2750—21no—
51#2728—21no—
52#2696—21no—
53#2645C2211yescharacteristic, complemented
54#2625C2211yescharacteristic, complemented
55#2527—21no—
56#2526—21no—
57#2511C2211yescharacteristic, complemented
58#2505—21no—
59#2492C2211yescharacteristic, complemented
60#2488—21no—
61#2485C2211yescharacteristic
62#2452C2211yescharacteristic, complemented
63#2422C2211yescharacteristic, complemented
64#2407C2211yescharacteristic
65#2367C2211yescharacteristic
66#2361—21no—
67#2361C2211yescharacteristic
68#2360C2211yescharacteristic
69#2359—21no—
70#2358—21no—
71D4×C4⋊C4C2211yescharacteristic
72D4×C4⋊C4C2211yescharacteristic
73#2346C2211yescharacteristic
74#2342—21no—
75#2339C2211yescharacteristic
76#2339C2211yescharacteristic
77D4×C22⋊C4C2211yescharacteristic
78#2326C2211yescharacteristic
79#2325—21no—
80#2324C2211yescharacteristic
81#2324C2211yescharacteristic, complemented
82#2322—21no—
83#2319C2211yescharacteristic, complemented
84C4×C22⋊Q8C2211yescharacteristic
85C4×#120—21no—
86#2297C2211yescharacteristic
87#2290C2211yescharacteristic
88C2×#385—21no—
89#2275C2211yescharacteristic
90#2100C2211yescharacteristic, complemented
91#2099C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2094C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2077C2211yescharacteristic, complemented
96#2076C2211yescharacteristic, complemented
97#2072C2211yescharacteristic, complemented
98#2067C2211yescharacteristic, complemented
99#2066C2211yescharacteristic, complemented
100#2058C2211yescharacteristic, complemented
101#2056C2211yescharacteristic, complemented
102#2055C2211yescharacteristic, complemented
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2035C2211yescharacteristic, complemented
106#2034C2211yescharacteristic
107#2033C2211yescharacteristic
108#2033C2211yescharacteristic, complemented
109#2024C2211yescharacteristic, complemented
110#2015C2211yescharacteristic
111#2012C2211yescharacteristic
112#2000C2211yescharacteristic
113#1999C2211yescharacteristic
114#1973C2211yescharacteristic
115#1971C2211yescharacteristic, complemented
116#1968C2211yescharacteristic
117#1943C2211yescharacteristic, complemented
118#1936C2211yescharacteristic
119#1934C2211yescharacteristic
120#1933C2211yescharacteristic, complemented
121#1933C2211yescharacteristic, complemented
122#1928C2211yescharacteristic, complemented
123#1928C2211yescharacteristic, complemented
124#1927C2211yescharacteristic, complemented
125#1927C2211yescharacteristic, complemented
126#1926C2211yescharacteristic
127#1926C2211yescharacteristic, complemented
128#1926C2211yescharacteristic, complemented
129#1925C2211yescharacteristic
130#1924C2211yescharacteristic, complemented
131#1923C2211yescharacteristic, complemented
132#1921C2211yescharacteristic, complemented
133#1920C2211yescharacteristic, complemented
134#1919C2211yescharacteristic, complemented
135#1918C2211yescharacteristic, complemented
136#1918C2211yescharacteristic, complemented
137#1918C2211yescharacteristic, complemented
138#1917C2211yescharacteristic, complemented
139#1916C2211yescharacteristic, complemented
140#1894C2211yescharacteristic
141#1894C2211yescharacteristic
142#1880C2211yescharacteristic, complemented
143#1879C2211yescharacteristic
144#1879C2211yescharacteristic
145#1879C2211yescharacteristic
146#1879C2211yescharacteristic
147#1879C2211yescharacteristic
148#1879C2211yescharacteristic
149#1879C2211yescharacteristic
150#1878C2211yescharacteristic, complemented
151#1878C2211yescharacteristic, complemented
152#1877C2211yescharacteristic
153#1877C2211yescharacteristic
154#1877C2211yescharacteristic
155#1877C2211yescharacteristic
156#1877C2211yescharacteristic
157#1877C2211yescharacteristic
158#1877C2211yescharacteristic
159#1877C2211yescharacteristic, complemented
160#1874C2211yescharacteristic, complemented
161#1870C2211yescharacteristic
162#1870C2211yescharacteristic
163#1865C2211yescharacteristic, complemented
164#1865C2211yescharacteristic, complemented
165#1865C2211yescharacteristic, complemented
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic, complemented
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1853C2211yescharacteristic, complemented
178#1840C2211yescharacteristic, complemented
179#1825C2211yescharacteristic
180#1824C2211yescharacteristic, complemented
181#1818C2211yescharacteristic, complemented
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic
184#1802C2211yescharacteristic
185#1802C2211yescharacteristic
186#1797C2211yescharacteristic
187#1788C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192C4×#106C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199#1750C2211yescharacteristic, complemented
200#1746C2211yescharacteristic, complemented
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C24×C4—21no—
207C2×AGL(1,ℤ/8)—24no—
208C2×AGL(1,ℤ/8)—24no—
209C2×AGL(1,ℤ/8)—42no—
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C22×M16C2311yescharacteristic
218#546—24no—
219#546—24no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232#520—42no—
233#520—42no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—42no—
243C2×C4×D4—42no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117—21no—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4—21no—
258C22×C4⋊C4—21no—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C42C2311yescharacteristic
265#485—24no—
266#483—42no—
267#476—42no—
268#476—42no—
269#452—24no—
270#452—42no—
271#449—24no—
272#442—42no—
273C4×SD16—42no—
274C4×D8—24no—
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287#418—24no—
288#417—42no—
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#401—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#398—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#393—21no—
345#393—21no—
346#392—21no—
347#391—21no—
348#391—21no—
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390—21no—
357#390—21no—
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388D411yescharacteristic
388#388D411yescharacteristic
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387D411yescharacteristic
395#387D411yescharacteristic
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386D411yescharacteristic
409#386D411yescharacteristic
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385D411yescharacteristic
426#385D411yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#382—21no—
430#381—21no—
431#381—21no—
432#381—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460#376—21no—
461#376C2311yescharacteristic
462C2×#95—21no—
463C2×#95—21no—
464C2×#95—21no—
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#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C22×Q8—21no—
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×D411yescharacteristic
526C22×D4#4114yes—
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—44no—
544C23×C4—82no—
545C23×C4—82no—
546C23×C4C2×D411yescharacteristic
547C23×C4C2×D411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550AGL(1,ℤ/8)—416no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—41no—
568C2×D8#4114yes—
569C2×M16—22no—
570C2×M16—22no—
571C2×M16—22no—
572C2×M16—41no—
573C2×M16—41no—
574C2×M16—41no—
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C4⋊Q8—41no—
584C4⋊Q8—41no—
585#124—22no—
586#124—22no—
587#123—28no—
588#123—82no—
589C22⋊Q8—22no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—82no—
593C22⋊Q8—82no—
594C22⋊Q8#4114yes—
595#121—28no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#120—28no—
601C4×Q8—22no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—44no—
626C4×D4—44no—
627C4×D4—44no—
628C4×D4—44no—
629C4×D4—82no—
630C4×D4—82no—
631#117—22no—
632#117—22no—
633#117—41no—
634#117—41no—
635#117—44no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—44no—
660C2×C4⋊C4—82no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C22⋊C4—28no—
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—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—44no—
711C2×C22⋊C4—82no—
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—41no—
729C2×C42—41no—
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737#107—22no—
738#107—22no—
739#107—41no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—41no—
744#106—41no—
745#106—41no—
746#106—41no—
747C4⋊C8—41no—
748C4⋊C8—41no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777C22⋊C8—22no—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783#97—41no—
784#97—41no—
785C4×C8—22no—
786C4×C8—41no—
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#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830C24—21no—
831C24—21no—
832C24—21no—
833C24—24no—
834C24—42no—
835C24—42no—
836C24—42no—
837C24—42no—
838C24—81no—
839C24—81no—
840C24C22×D411yescharacteristic
841C24C22×D411yescharacteristic
842#41—44no—
843#41—44no—
844#41—44no—
845#41—44no—
846#41—44no—
847#41—44no—
848#41—82no—
849#41—82no—
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—42no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8C2×#4112yes—
865C2×D4—28no—
866C2×D4—24no—
867C2×D4—22no—
868C2×D4—24no—
869C2×D4—24no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4C2×#4112yes—
901C2×D4C2×#4112yes—
902C2×D4C2×#4112yes—
903C2×D4C2×#4112yes—
904C2×D4H(5,𝔽2)12yes—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—24no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—22no—
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—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—816no—
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C2×#4112yes—
987C22×C4C2×#4112yes—
988C22×C4C2511yescharacteristic
989Q16—82no—
990SD16—44no—
991SD16—44no—
992SD16—44no—
993D8—28no—
994D8—44no—
995M16—44no—
996M16—82no—
997C2×C8—21no—
998C2×C8—21no—
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×C8C2×#4112yes—
1021C4⋊C4—24no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
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—41no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4C2×#4112yes—
1066C4⋊C4H(5,𝔽2)12yes—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—22no—
1073C22⋊C4—24no—
1074C22⋊C4—22no—
1075C22⋊C4—22no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—41no—
1080C22⋊C4—41no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
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—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—41no—
1118C42—41no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—81no—
1123C42—81no—
1124C42—81no—
1125C42—81no—
1126C42—81no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—22no—
1131C23—22no—
1132C23—21no—
1133C23—22no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—22no—
1140C23—21no—
1141C23—22no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—48no—
1146C23—48no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—84no—
1164C23—84no—
1165C23—84no—
1166C23—84no—
1167C23—84no—
1168C23#52512yes—
1169C23C23×D411yescharacteristic
1170Q8—22no—
1171Q8—22no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—162no—
1179D4—22no—
1180D4—22no—
1181D4—22no—
1182D4—22no—
1183D4—22no—
1184D4—22no—
1185D4—22no—
1186D4—48no—
1187D4—44no—
1188D4—48no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—84no—
1194D4—84no—
1195D4—162no—
1196D4#55114yes—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—22no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—44no—
1239C2×C4—48no—
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—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—84no—
1283C2×C4—84no—
1284C2×C4—84no—
1285C2×C4—82no—
1286C2×C4—84no—
1287C2×C4—84no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4#52512yes—
1294C2×C4#57712yes—
1295C2×C4C22×#4111yescharacteristic
1296C2×C4C22×#4111yescharacteristic
1297C2×C4C22×#4111yescharacteristic
1298C2×C4C2×H(5,𝔽2)11yescharacteristic
1299C2×C4C2×H(5,𝔽2)11yescharacteristic
1300C2×C4#58511yescharacteristic
1301C8—22no—
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C22—22no—
1310C22—24no—
1311C22—22no—
1312C22—22no—
1313C22—42no—
1314C22—41no—
1315C22—41no—
1316C22—42no—
1317C22—42no—
1318C22—41no—
1319C22—42no—
1320C22—42no—
1321C22—41no—
1322C22—42no—
1323C22—42no—
1324C22—41no—
1325C22—41no—
1326C22—42no—
1327C22—41no—
1328C22—42no—
1329C22—42no—
1330C22—41no—
1331C22—42no—
1332C22—41no—
1333C22—41no—
1334C22—42no—
1335C22—41no—
1336C22—816no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22C2×#52511yescharacteristic
1346C22D4×#4111yescharacteristic
1347C22#348411yescharacteristic
1348C22C2×#57711yescharacteristic
1349C22#358511yescharacteristic
1350C22#358511yescharacteristic
1351C22#358611yescharacteristic
1352C4—22no—
1353C4—22no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—42no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—42no—
1362C4—41no—
1363C4—42no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4C2×#55111yescharacteristic
1378C4#348111yescharacteristic
1379C4#350511yescharacteristic
1380C4#351311yescharacteristic
1381C2—42no—
1382C2—44no—
1383C2—81no—
1384C2—82no—
1385C2—82no—
1386C2#3622011yescharacteristic
1387C2#6056511yescharacteristic
1388C2#6059711yescharacteristic
1389C2#6150511yescharacteristic
1390C2#6154111yescharacteristic
1391C2#6161011yescharacteristic
1392C2#6165611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23863C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38116C2semidirect
2. #34288C2semidirect
3. #33090C2semidirect
4. #33016C2semidirect
5. #32956C2semidirect
6. #29506C2semidirect
7. #29488C2semidirect
8. #29418C2semidirect
9. #29380C2semidirect
10. #29166C2semidirect
11. #28122C2semidirect
12. #27552C2semidirect
13. #27248C2semidirect
14. #27092C2semidirect
15. #26901C2semidirect
16. #26786C2semidirect
17. #26673C2semidirect
18. #26392C2semidirect
19. #24955C2semidirect
20. #24899C2semidirect
21. #24879C2semidirect
22. #24050C2semidirect
24. #22942C2semidirect
25. #22882C2semidirect
26. #22792C2semidirect
27. #22584C2semidirect
28. #22442C2semidirect
29. #21464C2semidirect
30. #21134C2semidirect
31. #20925C2semidirect
37. C2×#483C22semidirect
44. C2×C4×SD16C22semidirect
53. #2645C22semidirect
54. #2625C22semidirect
57. #2511C22semidirect
59. #2492C22semidirect
62. #2452C22semidirect
63. #2422C22semidirect
81. #2324C22semidirect
83. #2319C22semidirect
90. #2100C22semidirect
91. #2099C22semidirect
92. #2095C22semidirect
93. #2094C22semidirect
94. #2084C22semidirect
95. #2077C22semidirect
96. #2076C22semidirect
97. #2072C22semidirect
98. #2067C22semidirect
99. #2066C22semidirect
100. #2058C22semidirect
101. #2056C22semidirect
102. #2055C22semidirect
105. #2035C22semidirect
108. #2033C22semidirect
109. #2024C22semidirect
115. #1971C22semidirect
117. #1943C22semidirect
120. #1933C22semidirect
121. #1933C22semidirect
122. #1928C22semidirect
123. #1928C22semidirect
124. #1927C22semidirect
125. #1927C22semidirect
127. #1926C22semidirect
128. #1926C22semidirect
130. #1924C22semidirect
131. #1923C22semidirect
132. #1921C22semidirect
133. #1920C22semidirect
134. #1919C22semidirect
135. #1918C22semidirect
136. #1918C22semidirect
137. #1918C22semidirect
138. #1917C22semidirect
139. #1916C22semidirect
142. #1880C22semidirect
150. #1878C22semidirect
151. #1878C22semidirect
159. #1877C22semidirect
160. #1874C22semidirect
163. #1865C22semidirect
164. #1865C22semidirect
165. #1865C22semidirect
172. #1864C22semidirect
177. #1853C22semidirect
178. #1840C22semidirect
180. #1824C22semidirect
181. #1818C22semidirect
192. C4×#106C22semidirect
193. #1763C22semidirect
195. #1762C22semidirect
199. #1750C22semidirect
200. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#381162
#342882
#330902
#330162
#329562
#295062
#294882
#294182
#293802
#291662
#281222
#275522
#272482
#270922
#269012
#267862
#266732
#263922
#249552
#248992
#248792
#240502
#238632
#229422
#228822
#227922
#225842
#224422
#214642
#211342
#209252