Finite Group Databasebeta

← #6580480

Subgroups — #6580480

Order 512.

1905 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36310C211yesmaximal, characteristic, complemented
2D4×#123C211yesmaximal, characteristic
3#33145C211yesmaximal, characteristic, complemented
4#33097C211yesmaximal, characteristic, complemented
5#33009C211yesmaximal, characteristic, complemented
6#29032C211yesmaximal, characteristic, complemented
7#29003C211yesmaximal, characteristic, complemented
8#28877C211yesmaximal, characteristic, complemented
9#28857C211yesmaximal, characteristic, complemented
10#27719C211yesmaximal, characteristic, complemented
11#27552C211yesmaximal, characteristic, complemented
12#27525C211yesmaximal, characteristic, complemented
13#27317C211yesmaximal, characteristic, complemented
14#27245C211yesmaximal, characteristic, complemented
15#27214C211yesmaximal, characteristic, complemented
16#27182C211yesmaximal, characteristic, complemented
17#26688C211yesmaximal, characteristic, complemented
18#26665C211yesmaximal, characteristic, complemented
19#25966C211yesmaximal, characteristic, complemented
20#25256C211yesmaximal, characteristic, complemented
21#25217C211yesmaximal, characteristic, complemented
22#24958C211yesmaximal, characteristic, complemented
23#24448C211yesmaximal, characteristic
24#22962C211yesmaximal, characteristic, complemented
25#22864C211yesmaximal, characteristic, complemented
26#22864C211yesmaximal, characteristic, complemented
27#22778C211yesmaximal, characteristic, complemented
28#22584C211yesmaximal, characteristic, complemented
29#22428C211yesmaximal, characteristic
30#21565C211yesmaximal, characteristic, complemented
31C4×#418C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C22×#123—21no—
34C22×C4×D4C2211yescharacteristic
35C2×#484C2211yescharacteristic, complemented
36C2×#474C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×#436C2211yescharacteristic
42C2×#418C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C2×#418C2211yescharacteristic
45C2×C4×M16C2211yescharacteristic, complemented
46#2866—21no—
47#2855C2211yescharacteristic, complemented
48#2854C2211yescharacteristic
49#2849—21no—
50#2532—21no—
51#2528—21no—
52#2527—21no—
53#2526—21no—
54#2515—21no—
55#2511C2211yescharacteristic, complemented
56#2507C2211yescharacteristic, complemented
57#2501C2211yescharacteristic
58#2494C2211yescharacteristic, complemented
59#2492C2211yescharacteristic, complemented
60#2486C2211yescharacteristic
61#2458—21no—
62#2445C2211yescharacteristic
63#2445C2211yescharacteristic
64#2443—21no—
65#2443—21no—
66#2439C2211yescharacteristic, complemented
67#2422C2211yescharacteristic
68#2422C2211yescharacteristic
69#2418—21no—
70#2418—21no—
71#2415C2211yescharacteristic
72#2412—21no—
73#2405—21no—
74#2365C2211yescharacteristic, complemented
75#2362C2211yescharacteristic, complemented
76#2362C2211yescharacteristic, complemented
77#2356C2211yescharacteristic, complemented
78#2354C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic
81#2346C2211yescharacteristic, complemented
82D4×C22⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85C4×#123C2211yescharacteristic
86#2295—21no—
87C4×#117C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2092C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2077C2211yescharacteristic, complemented
96#2076C2211yescharacteristic, complemented
97#2076C2211yescharacteristic, complemented
98#2073C2211yescharacteristic, complemented
99#2072C2211yescharacteristic, complemented
100#2067C2211yescharacteristic, complemented
101#2067C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2065C2211yescharacteristic, complemented
104#2055C2211yescharacteristic, complemented
105#2041C2211yescharacteristic
106#2036C2211yescharacteristic, complemented
107#2033C2211yescharacteristic
108#2023C2211yescharacteristic, complemented
109#2023C2211yescharacteristic, complemented
110#2014C2211yescharacteristic
111#2000C2211yescharacteristic
112#1990C2211yescharacteristic, complemented
113#1982C2211yescharacteristic
114#1973C2211yescharacteristic, complemented
115#1968C2211yescharacteristic, complemented
116#1968C2211yescharacteristic, complemented
117#1957C2211yescharacteristic
118#1947C2211yescharacteristic, complemented
119#1944C2211yescharacteristic, complemented
120#1942C2211yescharacteristic, complemented
121#1942C2211yescharacteristic, complemented
122#1936C2211yescharacteristic, complemented
123#1936C2211yescharacteristic, complemented
124#1936C2211yescharacteristic, complemented
125#1935C2211yescharacteristic, complemented
126#1934C2211yescharacteristic, complemented
127#1934C2211yescharacteristic, complemented
128#1933C2211yescharacteristic, complemented
129#1933C2211yescharacteristic, complemented
130#1926C2211yescharacteristic, complemented
131#1926C2211yescharacteristic, complemented
132#1925C2211yescharacteristic, complemented
133#1925C2211yescharacteristic, complemented
134#1925C2211yescharacteristic, complemented
135#1925C2211yescharacteristic, complemented
136#1924C2211yescharacteristic, complemented
137#1923C2211yescharacteristic, complemented
138#1921C2211yescharacteristic, complemented
139#1920C2211yescharacteristic, complemented
140#1919C2211yescharacteristic, complemented
141#1918C2211yescharacteristic, complemented
142#1918C2211yescharacteristic, complemented
143#1918C2211yescharacteristic, complemented
144#1917C2211yescharacteristic, complemented
145#1916C2211yescharacteristic, complemented
146#1895C2211yescharacteristic
147#1895C2211yescharacteristic
148#1894C2211yescharacteristic, complemented
149#1894C2211yescharacteristic, complemented
150#1880C2211yescharacteristic, complemented
151#1880C2211yescharacteristic, complemented
152#1877C2211yescharacteristic
153#1877C2211yescharacteristic
154#1877C2211yescharacteristic
155#1877C2211yescharacteristic
156#1877C2211yescharacteristic, complemented
157#1877C2211yescharacteristic, complemented
158#1875C2211yescharacteristic
159#1875C2211yescharacteristic
160#1875C2211yescharacteristic
161#1870C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1862C2211yescharacteristic
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic, complemented
169#1862C2211yescharacteristic, complemented
170#1854C2211yescharacteristic, complemented
171#1854C2211yescharacteristic, complemented
172#1854C2211yescharacteristic, complemented
173#1851C2211yescharacteristic, complemented
174#1836C2211yescharacteristic, complemented
175#1825C2211yescharacteristic, complemented
176#1824C2211yescharacteristic, complemented
177#1817C2211yescharacteristic, complemented
178#1809C2211yescharacteristic, complemented
179#1809C2211yescharacteristic, complemented
180#1804C2211yescharacteristic
181#1803C2211yescharacteristic, complemented
182#1802C2211yescharacteristic
183#1786C2211yescharacteristic
184#1786C2211yescharacteristic
185#1786C2211yescharacteristic
186#1771C2211yescharacteristic, complemented
187C8×C4⋊C4C2211yescharacteristic, complemented
188#1762C2211yescharacteristic
189#1762C2211yescharacteristic
190#1762C2211yescharacteristic, complemented
191#1762C2211yescharacteristic, complemented
192C4×#102C2211yescharacteristic
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic, complemented
198#1753C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C24×C4—21no—
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213D42—24no—
214D42—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—48no—
226C2×#123D411yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233C2×#120—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—24no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—42no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4—21no—
252C22×C4⋊C4—21no—
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258C22×C42C2311yescharacteristic
259#484—42no—
260#474—24no—
261#468—42no—
262#450—24no—
263#450—24no—
264#440—24no—
265#436—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278#418—24no—
279#418—24no—
280#418—24no—
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C4×M16—42no—
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320#401—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#399—21no—
325#399—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#393—21no—
343#393—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390—21no—
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389—21no—
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
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#388D411yescharacteristic
384#388D411yescharacteristic
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387D411yescharacteristic
399#387D411yescharacteristic
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#386—21no—
409#386D411yescharacteristic
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385D411yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#383—21no—
422#382—21no—
423#382C2311yescharacteristic
424#381—21no—
425#381—21no—
426#381D411yescharacteristic
427#380—21no—
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#379—21no—
436#379—21no—
437#379—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454#376—21no—
455#376—21no—
456#376—21no—
457C43—21no—
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#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C25—21no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—44no—
516C22×D4—44no—
517C22×D4—82no—
518C22×D4C2×D411yescharacteristic
519C22×D4#4114yes—
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—44no—
532C23×C4—44no—
533C23×C4—82no—
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—22no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C4⋊Q8—22no—
565C4⋊Q8—41no—
566#127—22no—
567#127—41no—
568#123—24no—
569#123—44no—
570#123—44no—
571#123—44no—
572#123—44no—
573#123—44no—
574#123—44no—
575#123—44no—
576#123—82no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—41no—
585#121—44no—
586#120—44no—
587#120—44no—
588C4×Q8—22no—
589C4×Q8—41no—
590C4×Q8—44no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—44no—
608C4×D4—44no—
609#117—22no—
610#117—22no—
611#117—22no—
612#117—41no—
613#117—41no—
614#117—41no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
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—44no—
639C2×C4⋊C4—44no—
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
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—44no—
690C2×C22⋊C4—44no—
691C2×C22⋊C4—44no—
692C2×C22⋊C4—44no—
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C42—22no—
702C2×C42—22no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42C2×D411yescharacteristic
714C2×C42C2×D411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720#107—22no—
721#107—22no—
722#107—22no—
723#107—41no—
724#107—41no—
725#107—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729C4⋊C8—22no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732#103—22no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
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—
756#102#4114yes—
757#102#4114yes—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763#97—22no—
764#97—41no—
765#97—41no—
766C4×C8—41no—
767C4×C8—41no—
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
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812C24—21no—
813C24—21no—
814C24—24no—
815C24—21no—
816C24—42no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—42no—
821C24—42no—
822C24—42no—
823C24—42no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—42no—
838C2×Q8—42no—
839C2×Q8—81no—
840C2×D4—28no—
841C2×D4—22no—
842C2×D4—24no—
843C2×D4—22no—
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—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—41no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—44no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—82no—
880C2×D4—82no—
881C2×D4—82no—
882C2×D4—81no—
883C2×D4—816no—
884C2×D4C2×#4112yes—
885C2×D4C2×#4112yes—
886C2×D4C2×#4112yes—
887C2×D4C2×#4112yes—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—22no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—22no—
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—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—816no—
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C2×#4112yes—
955C22×C4H(5,𝔽2)12yes—
956C22×C4C2511yescharacteristic
957SD16—44no—
958SD16—82no—
959SD16—82no—
960M16—44no—
961M16—44no—
962M16—82no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
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×C8C2×#4112yes—
986C2×C8C2×#4112yes—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
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—41no—
1012C4⋊C4—41no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4AGL(1,ℤ/8)14yes—
1035C4⋊C4C2×#4112yes—
1036C4⋊C4C2×#4112yes—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C42—22no—
1078C42—22no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—42no—
1094C42—42no—
1095C42—42no—
1096C42—42no—
1097C42—81no—
1098C42—81no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—22no—
1103C23—21no—
1104C23—21no—
1105C23—22no—
1106C23—22no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—22no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—48no—
1117C23—48no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—84no—
1136C23—84no—
1137C23—84no—
1138C23—84no—
1139C23—84no—
1140C23—84no—
1141C23—84no—
1142C23—84no—
1143C23—84no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23#54612yes—
1148C23C23×D411yescharacteristic
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—84no—
1154D4—22no—
1155D4—22no—
1156D4—22no—
1157D4—22no—
1158D4—22no—
1159D4—48no—
1160D4—44no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—84no—
1168D4—84no—
1169D4—84no—
1170D4—84no—
1171D4—162no—
1172D4#52914yes—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
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—22no—
1206C2×C4—21no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—44no—
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—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—84no—
1254C2×C4—84no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4—82no—
1258C2×C4—84no—
1259C2×C4—84no—
1260C2×C4—84no—
1261C2×C4—84no—
1262C2×C4#54612yes—
1263C2×C4C2×AGL(1,ℤ/8)12yes—
1264C2×C4C2×AGL(1,ℤ/8)12yes—
1265C2×C4C2×AGL(1,ℤ/8)12yes—
1266C2×C4C22×#4111yescharacteristic
1267C2×C4C22×#4111yescharacteristic
1268C2×C4C22×#4111yescharacteristic
1269C2×C4C2×H(5,𝔽2)11yescharacteristic
1270C2×C4#58511yescharacteristic
1271C2×C4#58511yescharacteristic
1272C8—22no—
1273C8—22no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C22—22no—
1281C22—22no—
1282C22—24no—
1283C22—22no—
1284C22—42no—
1285C22—42no—
1286C22—41no—
1287C22—41no—
1288C22—42no—
1289C22—41no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—41no—
1294C22—42no—
1295C22—41no—
1296C22—41no—
1297C22—42no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—42no—
1302C22—41no—
1303C22—41no—
1304C22—816no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—168no—
1317C22C2×#54611yescharacteristic
1318C22D4×#4111yescharacteristic
1319C22D4×#4111yescharacteristic
1320C22C22×AGL(1,ℤ/8)11yescharacteristic
1321C22#358411yescharacteristic
1322C22#358511yescharacteristic
1323C22#358611yescharacteristic
1324C4—22no—
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—42no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—42no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4C2×#52911yescharacteristic
1350C4#349111yescharacteristic
1351C4#351311yescharacteristic
1352C4#351311yescharacteristic
1353C2—42no—
1354C2—44no—
1355C2—81no—
1356C2—82no—
1357C2—161no—
1358C2#3610911yescharacteristic
1359C2#6115511yescharacteristic
1360C2#6118811yescharacteristic
1361C2#6143711yescharacteristic
1362C2#6146611yescharacteristic
1363C2#6150311yescharacteristic
1364C2#6154711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36310C2semidirect
3. #33145C2semidirect
4. #33097C2semidirect
5. #33009C2semidirect
6. #29032C2semidirect
7. #29003C2semidirect
8. #28877C2semidirect
9. #28857C2semidirect
10. #27719C2semidirect
11. #27552C2semidirect
12. #27525C2semidirect
13. #27317C2semidirect
14. #27245C2semidirect
15. #27214C2semidirect
16. #27182C2semidirect
17. #26688C2semidirect
18. #26665C2semidirect
19. #25966C2semidirect
20. #25256C2semidirect
21. #25217C2semidirect
22. #24958C2semidirect
24. #22962C2semidirect
25. #22864C2semidirect
26. #22864C2semidirect
27. #22778C2semidirect
28. #22584C2semidirect
30. #21565C2semidirect
31. C4×#418C2semidirect
35. C2×#484C22semidirect
45. C2×C4×M16C22semidirect
47. #2855C22semidirect
55. #2511C22semidirect
56. #2507C22semidirect
58. #2494C22semidirect
59. #2492C22semidirect
66. #2439C22semidirect
74. #2365C22semidirect
75. #2362C22semidirect
76. #2362C22semidirect
77. #2356C22semidirect
81. #2346C22semidirect
87. C4×#117C22semidirect
88. #2100C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2092C22semidirect
92. #2086C22semidirect
93. #2084C22semidirect
94. #2083C22semidirect
95. #2077C22semidirect
96. #2076C22semidirect
97. #2076C22semidirect
98. #2073C22semidirect
99. #2072C22semidirect
100. #2067C22semidirect
101. #2067C22semidirect
102. #2066C22semidirect
103. #2065C22semidirect
104. #2055C22semidirect
106. #2036C22semidirect
108. #2023C22semidirect
109. #2023C22semidirect
112. #1990C22semidirect
114. #1973C22semidirect
115. #1968C22semidirect
116. #1968C22semidirect
118. #1947C22semidirect
119. #1944C22semidirect
120. #1942C22semidirect
121. #1942C22semidirect
122. #1936C22semidirect
123. #1936C22semidirect
124. #1936C22semidirect
125. #1935C22semidirect
126. #1934C22semidirect
127. #1934C22semidirect
128. #1933C22semidirect
129. #1933C22semidirect
130. #1926C22semidirect
131. #1926C22semidirect
132. #1925C22semidirect
133. #1925C22semidirect
134. #1925C22semidirect
135. #1925C22semidirect
136. #1924C22semidirect
137. #1923C22semidirect
138. #1921C22semidirect
139. #1920C22semidirect
140. #1919C22semidirect
141. #1918C22semidirect
142. #1918C22semidirect
143. #1918C22semidirect
144. #1917C22semidirect
145. #1916C22semidirect
148. #1894C22semidirect
149. #1894C22semidirect
150. #1880C22semidirect
151. #1880C22semidirect
156. #1877C22semidirect
157. #1877C22semidirect
168. #1862C22semidirect
169. #1862C22semidirect
170. #1854C22semidirect
171. #1854C22semidirect
172. #1854C22semidirect
173. #1851C22semidirect
174. #1836C22semidirect
175. #1825C22semidirect
176. #1824C22semidirect
177. #1817C22semidirect
178. #1809C22semidirect
179. #1809C22semidirect
181. #1803C22semidirect
186. #1771C22semidirect
187. C8×C4⋊C4C22semidirect
190. #1762C22semidirect
191. #1762C22semidirect
196. C4×#102C22semidirect
197. C4×#102C22semidirect
198. #1753C22semidirect
199. #1753C22semidirect
200. #1753C22semidirect
201. #1736C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#363102
D4×#1232
#331452
#330972
#330092
#290322
#290032
#288772
#288572
#277192
#275522
#275252
#273172
#272452
#272142
#271822
#266882
#266652
#259662
#252562
#252172
#249582
#244482
#229622
#228642
#227782
#225842
#224282
#215652
C4×#4182