Finite Group Databasebeta

← #7032860

Subgroups — #7032860

Order 512.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59424C211yesmaximal, characteristic, complemented
2#59079C211yesmaximal, characteristic, complemented
3#32676C211yesmaximal, characteristic, complemented
4#32598C211yesmaximal, characteristic, complemented
5#32189C211yesmaximal, characteristic, complemented
6#32074C211yesmaximal, characteristic, complemented
7#31858C211yesmaximal, characteristic, complemented
8#30739C211yesmaximal, characteristic, complemented
9#30531C211yesmaximal, characteristic, complemented
10#30452C211yesmaximal, characteristic
11#29413C211yesmaximal, characteristic, complemented
12#29086C211yesmaximal, characteristic, complemented
13#27440C211yesmaximal, characteristic, complemented
14#27391C211yesmaximal, characteristic, complemented
15#27327C211yesmaximal, characteristic, complemented
16#27238C211yesmaximal, characteristic, complemented
17#27130C211yesmaximal, characteristic, complemented
18#27090C211yesmaximal, characteristic, complemented
19#26909C211yesmaximal, characteristic, complemented
20#26839C211yesmaximal, characteristic, complemented
21#26708C211yesmaximal, characteristic, complemented
22#26615C211yesmaximal, characteristic, complemented
23#25938C211yesmaximal, characteristic, complemented
24#25172C211yesmaximal, characteristic
25#24347C211yesmaximal, characteristic, complemented
26#23933C211yesmaximal, characteristic, complemented
27#23577C211yesmaximal, characteristic, complemented
28#23189C211yesmaximal, characteristic, complemented
29#23109C211yesmaximal, characteristic, complemented
30#22323C211yesmaximal, characteristic, complemented
31#22046C211yesmaximal, characteristic
32C2×#554C2211yescharacteristic, complemented
33C2×#533C2211yescharacteristic
34C2×#495C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#442C2211yescharacteristic
43C2×#441C2211yescharacteristic, complemented
44C2×#441C2211yescharacteristic, complemented
45#2786—21no—
46#2740—21no—
47#2728—21no—
48#2728—21no—
49#2601—21no—
50#2592C2211yescharacteristic
51#2568C2211yescharacteristic, complemented
52#2560—21no—
53#2547C2211yescharacteristic, complemented
54#2538C2211yescharacteristic
55#2512C2211yescharacteristic
56#2512C2211yescharacteristic
57#2502C2211yescharacteristic
58#2489—21no—
59#2489C2211yescharacteristic
60#2489C2211yescharacteristic
61#2480—21no—
62#2480—21no—
63#2453C2211yescharacteristic, complemented
64#2453C2211yescharacteristic, complemented
65#2448C2211yescharacteristic
66#2447C2211yescharacteristic
67#2442—21no—
68#2437—21no—
69#2435C2211yescharacteristic
70#2427C2211yescharacteristic
71#2427C2211yescharacteristic
72#2421—21no—
73#2421—21no—
74#2415—21no—
75#2369C2211yescharacteristic, complemented
76#2367C2211yescharacteristic
77#2367C2211yescharacteristic, complemented
78#2367C2211yescharacteristic, complemented
79#2354C2211yescharacteristic
80#2352—21no—
81#2345C2211yescharacteristic
82#2342—21no—
83D4×C22⋊C4C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×C22⋊Q8C2211yescharacteristic
86C4×#121C2211yescharacteristic
87C2×#390C2211yescharacteristic
88#2099C2211yescharacteristic, complemented
89#2096C2211yescharacteristic, complemented
90#2086C2211yescharacteristic, complemented
91#2075C2211yescharacteristic
92#2072C2211yescharacteristic, complemented
93#2072C2211yescharacteristic, complemented
94#2066C2211yescharacteristic, complemented
95#2065C2211yescharacteristic
96#2059C2211yescharacteristic, complemented
97#2058C2211yescharacteristic, complemented
98#2056C2211yescharacteristic, complemented
99#2056C2211yescharacteristic, complemented
100#2055C2211yescharacteristic
101#2055C2211yescharacteristic
102#2055C2211yescharacteristic
103#2043C2211yescharacteristic, complemented
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic, complemented
106#2035C2211yescharacteristic
107#2035C2211yescharacteristic
108#2035C2211yescharacteristic
109#2033C2211yescharacteristic
110#2026C2211yescharacteristic, complemented
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic
113#2024C2211yescharacteristic, complemented
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2016C2211yescharacteristic, complemented
117#2015C2211yescharacteristic
118#2015C2211yescharacteristic
119#2015C2211yescharacteristic
120#2015C2211yescharacteristic, complemented
121#2013C2211yescharacteristic
122#2013C2211yescharacteristic
123#2012C2211yescharacteristic
124#2012C2211yescharacteristic
125#2001C2211yescharacteristic
126#2001C2211yescharacteristic
127#2000C2211yescharacteristic
128#1992C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1985C2211yescharacteristic, complemented
131#1984C2211yescharacteristic, complemented
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic, complemented
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1972C2211yescharacteristic
137#1972C2211yescharacteristic
138#1971C2211yescharacteristic, complemented
139#1968C2211yescharacteristic
140#1959C2211yescharacteristic, complemented
141#1948C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1933C2211yescharacteristic, complemented
147#1933C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic, complemented
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic
162#1921C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1920C2211yescharacteristic, complemented
165#1919C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic, complemented
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1877C2211yescharacteristic, complemented
183#1877C2211yescharacteristic, complemented
184#1874C2211yescharacteristic
185#1872C2211yescharacteristic
186#1872C2211yescharacteristic
187#1864C2211yescharacteristic, complemented
188#1863C2211yescharacteristic, complemented
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic, complemented
191#1853C2211yescharacteristic
192#1817C2211yescharacteristic
193#1802C2211yescharacteristic, complemented
194#1786C2211yescharacteristic
195C4×#106C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1770C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213#554—42no—
214#554—42no—
215#533—42no—
216#533—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#126—21no—
221C2×#125—21no—
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8D411yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×C4×Q8—21no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C2×#117—21no—
251C22×C4⋊C4—21no—
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C42C2311yescharacteristic
257#495—24no—
258#488—42no—
259#478—42no—
260#463—24no—
261#463—42no—
262#450—42no—
263#450—42no—
264#447—24no—
265#442—42no—
266#441—42no—
267#441—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#399—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—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#397—21no—
341#397—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#393—21no—
351#391—21no—
352#391—21no—
353#391—21no—
354#391D411yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#390—21no—
365#390—21no—
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#389—21no—
376#389—21no—
377#389—21no—
378#389D411yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387D411yescharacteristic
408#387D411yescharacteristic
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385D411yescharacteristic
422#385D411yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#382—21no—
426#382—21no—
427#382—21no—
428#381—21no—
429#380—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380D411yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8C2×D411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2411yescharacteristic
519C2×Q16—22no—
520C2×Q16—41no—
521C2×Q16—41no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×D8—22no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8#4114yes—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C4⋊Q8—22no—
555C4⋊Q8—22no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558#126—82no—
559#126—82no—
560#125—22no—
561#125—22no—
562#125—41no—
563#125—41no—
564#125—44no—
565#124—22no—
566#124—22no—
567#124—22no—
568#124—41no—
569#124—41no—
570#124—41no—
571#124—41no—
572#124—41no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—42no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—44no—
581C22⋊Q8—44no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584C22⋊Q8—82no—
585#121—22no—
586#121—41no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—44no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—44no—
607#117—44no—
608#117—82no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
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—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—44no—
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
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×C22⋊C4—21no—
656C2×C22⋊C4—21no—
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—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—44no—
693C2×C22⋊C4—82no—
694C2×C22⋊C4—82no—
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—41no—
709C2×C42—41no—
710C2×C42C2×D411yescharacteristic
711C2×C42C2×D411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#107—41no—
719#107—41no—
720#106—22no—
721#106—22no—
722#106—41no—
723#106—41no—
724#106—41no—
725C4⋊C8—22no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—41no—
733#103—41no—
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—22no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759C22⋊C8—22no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763#97—41no—
764#97—41no—
765#97—41no—
766#97—41no—
767C4×C8—22no—
768C4×C8—41no—
769#95—21no—
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#95C2×D411yescharacteristic
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
811C24—21no—
812C24—21no—
813C24—21no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—42no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24C22×D411yescharacteristic
822C2×Q8—24no—
823C2×Q8—22no—
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—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—41no—
844C2×Q8—81no—
845C2×Q8—81no—
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—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—81no—
867C2×D4—82no—
868C2×D4—82no—
869C2×D4—82no—
870C2×D4—82no—
871C2×D4—81no—
872C2×D4C2×#4112yes—
873C2×D4C2×#4112yes—
874C22×C4—22no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—22no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
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—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
931Q16—44no—
932Q16—44no—
933SD16—82no—
934SD16—82no—
935SD16—82no—
936SD16—82no—
937SD16—82no—
938D8—44no—
939D8—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×C8C2×#4112yes—
964C4⋊C4—24no—
965C4⋊C4—22no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
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—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
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—81no—
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⋊C4H(5,𝔽2)12yes—
1016C4⋊C4H(5,𝔽2)12yes—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
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—42no—
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—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—41no—
1071C42—41no—
1072C42—42no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—22no—
1088C23—22no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—84no—
1109C23—84no—
1110C23—84no—
1111C23—84no—
1112C23—162no—
1113C23—162no—
1114C23—162no—
1115C23#57512yes—
1116C23C23×D411yescharacteristic
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—82no—
1130Q8—84no—
1131D4—22no—
1132D4—22no—
1133D4—22no—
1134D4—22no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—84no—
1144D4—84no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
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—22no—
1173C2×C4—22no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—44no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
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—84no—
1228C2×C4—82no—
1229C2×C4—84no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4#57712yes—
1235C2×C4C22×#4111yescharacteristic
1236C2×C4C2×H(5,𝔽2)11yescharacteristic
1237C2×C4C2×H(5,𝔽2)11yescharacteristic
1238C2×C4#58511yescharacteristic
1239C2×C4#58511yescharacteristic
1240C2×C4#58511yescharacteristic
1241C8—22no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—168no—
1278C22D4×#4111yescharacteristic
1279C22#348411yescharacteristic
1280C22#348711yescharacteristic
1281C22C2×#57511yescharacteristic
1282C22C2×#57711yescharacteristic
1283C22#358511yescharacteristic
1284C22#358611yescharacteristic
1285C4—22no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—42no—
1299C4—42no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4#350511yescharacteristic
1312C4#351411yescharacteristic
1313C4#354011yescharacteristic
1314C4#356211yescharacteristic
1315C2—42no—
1316C2—82no—
1317C2—82no—
1318C2—161no—
1319C2#4312011yescharacteristic
1320C2#6145411yescharacteristic
1321C2#6154111yescharacteristic
1322C2#6159411yescharacteristic
1323C2#6164711yescharacteristic
1324C2#6189411yescharacteristic
1325C2#6192111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59424C2semidirect
2. #59079C2semidirect
3. #32676C2semidirect
4. #32598C2semidirect
5. #32189C2semidirect
6. #32074C2semidirect
7. #31858C2semidirect
8. #30739C2semidirect
9. #30531C2semidirect
11. #29413C2semidirect
12. #29086C2semidirect
13. #27440C2semidirect
14. #27391C2semidirect
15. #27327C2semidirect
16. #27238C2semidirect
17. #27130C2semidirect
18. #27090C2semidirect
19. #26909C2semidirect
20. #26839C2semidirect
21. #26708C2semidirect
22. #26615C2semidirect
23. #25938C2semidirect
25. #24347C2semidirect
26. #23933C2semidirect
27. #23577C2semidirect
28. #23189C2semidirect
29. #23109C2semidirect
30. #22323C2semidirect
32. C2×#554C22semidirect
43. C2×#441C22semidirect
44. C2×#441C22semidirect
51. #2568C22semidirect
53. #2547C22semidirect
63. #2453C22semidirect
64. #2453C22semidirect
75. #2369C22semidirect
77. #2367C22semidirect
78. #2367C22semidirect
88. #2099C22semidirect
89. #2096C22semidirect
90. #2086C22semidirect
92. #2072C22semidirect
93. #2072C22semidirect
94. #2066C22semidirect
96. #2059C22semidirect
97. #2058C22semidirect
98. #2056C22semidirect
99. #2056C22semidirect
103. #2043C22semidirect
105. #2042C22semidirect
110. #2026C22semidirect
113. #2024C22semidirect
116. #2016C22semidirect
120. #2015C22semidirect
128. #1992C22semidirect
129. #1989C22semidirect
130. #1985C22semidirect
131. #1984C22semidirect
133. #1983C22semidirect
138. #1971C22semidirect
140. #1959C22semidirect
141. #1948C22semidirect
144. #1935C22semidirect
146. #1933C22semidirect
147. #1933C22semidirect
148. #1928C22semidirect
149. #1928C22semidirect
150. #1928C22semidirect
151. #1927C22semidirect
152. #1927C22semidirect
157. #1926C22semidirect
162. #1921C22semidirect
163. #1920C22semidirect
164. #1920C22semidirect
165. #1919C22semidirect
166. #1917C22semidirect
167. #1917C22semidirect
168. #1917C22semidirect
169. #1916C22semidirect
174. #1880C22semidirect
182. #1877C22semidirect
183. #1877C22semidirect
187. #1864C22semidirect
188. #1863C22semidirect
190. #1862C22semidirect
193. #1802C22semidirect
195. C4×#106C22semidirect
196. #1771C22semidirect
197. #1770C22semidirect
198. #1763C22semidirect
199. #1763C22semidirect
201. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#594242
#590792
#326762
#325982
#321892
#320742
#318582
#307392
#305312
#304522
#294132
#290862
#274402
#273912
#273272
#272382
#271302
#270902
#269092
#268392
#267082
#266152
#259382
#251722
#243472
#239332
#235772
#231892
#231092
#223232
#220462