Finite Group Databasebeta

← #6772573

Subgroups — #6772573

Order 512.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38072C211yesmaximal, characteristic, complemented
2#35237C211yesmaximal, characteristic
3#33007C211yesmaximal, characteristic, complemented
4#32455C211yesmaximal, characteristic, complemented
5#32373C211yesmaximal, characteristic, complemented
6#32351C211yesmaximal, characteristic, complemented
7#32164C211yesmaximal, characteristic, complemented
8#32094C211yesmaximal, characteristic, complemented
9#32080C211yesmaximal, characteristic, complemented
10#31529C211yesmaximal, characteristic, complemented
11#30892C211yesmaximal, characteristic, complemented
12#30138C211yesmaximal, characteristic, complemented
13#30085C211yesmaximal, characteristic, complemented
14#29504C211yesmaximal, characteristic, complemented
15#29377C211yesmaximal, characteristic, complemented
16#29265C211yesmaximal, characteristic, complemented
17#29201C211yesmaximal, characteristic, complemented
18#28365C211yesmaximal, characteristic, complemented
19#27947C211yesmaximal, characteristic, complemented
20#27725C211yesmaximal, characteristic, complemented
21#27279C211yesmaximal, characteristic, complemented
22#25501C211yesmaximal, characteristic, complemented
23#25231C211yesmaximal, characteristic, complemented
24#25093C211yesmaximal, characteristic, complemented
25#24599C211yesmaximal, characteristic, complemented
26#24494C211yesmaximal, characteristic, complemented
27#24062C211yesmaximal, characteristic, complemented
28#22596C211yesmaximal, characteristic, complemented
29#22232C211yesmaximal, characteristic, complemented
30#22160C211yesmaximal, characteristic, complemented
31#20873C211yesmaximal, characteristic, complemented
32C2×#532C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C2×#418C2211yescharacteristic
45#2855C2211yescharacteristic
46#2847—21no—
47#2847—21no—
48#2771—21no—
49#2765—21no—
50#2739—21no—
51#2738—21no—
52#2647C2211yescharacteristic, complemented
53#2645C2211yescharacteristic, complemented
54#2631—21no—
55#2631—21no—
56#2563C2211yescharacteristic
57#2563C2211yescharacteristic
58#2541C2211yescharacteristic
59#2541C2211yescharacteristic
60#2535—21no—
61#2535—21no—
62#2533—21no—
63#2528—21no—
64#2524—21no—
65#2511C2211yescharacteristic, complemented
66#2509C2211yescharacteristic, complemented
67#2508—21no—
68#2507C2211yescharacteristic, complemented
69#2504C2211yescharacteristic
70#2504C2211yescharacteristic
71#2499C2211yescharacteristic
72#2453C2211yescharacteristic, complemented
73#2441C2211yescharacteristic
74#2433C2211yescharacteristic
75#2433C2211yescharacteristic
76#2404—21no—
77#2404—21no—
78#2362C2211yescharacteristic
79#2346C2211yescharacteristic
80#2330C2211yescharacteristic, complemented
81#2328C2211yescharacteristic
82#2328C2211yescharacteristic
83#2328C2211yescharacteristic
84#2328C2211yescharacteristic
85#2320C2211yescharacteristic, complemented
86#2296C2211yescharacteristic
87#2283C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2094C2211yescharacteristic, complemented
93#2093C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2074C2211yescharacteristic, complemented
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic, complemented
108#2058C2211yescharacteristic, complemented
109#2057C2211yescharacteristic, complemented
110#2057C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic, complemented
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic, complemented
119#2041C2211yescharacteristic, complemented
120#2041C2211yescharacteristic, complemented
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2014C2211yescharacteristic
125#2014C2211yescharacteristic
126#2014C2211yescharacteristic
127#2014C2211yescharacteristic, complemented
128#1991C2211yescharacteristic, complemented
129#1982C2211yescharacteristic
130#1982C2211yescharacteristic
131#1982C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic, complemented
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic, complemented
136#1961C2211yescharacteristic
137#1957C2211yescharacteristic
138#1957C2211yescharacteristic
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic, complemented
146#1926C2211yescharacteristic, complemented
147#1926C2211yescharacteristic, complemented
148#1926C2211yescharacteristic, complemented
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1917C2211yescharacteristic, complemented
153#1917C2211yescharacteristic, complemented
154#1916C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic, complemented
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic, complemented
165#1877C2211yescharacteristic, complemented
166#1875C2211yescharacteristic
167#1875C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic, complemented
177#1864C2211yescharacteristic, complemented
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic, complemented
183#1862C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1862C2211yescharacteristic, complemented
186#1851C2211yescharacteristic
187#1851C2211yescharacteristic
188#1847C2211yescharacteristic, complemented
189#1846C2211yescharacteristic, complemented
190#1840C2211yescharacteristic, complemented
191#1836C2211yescharacteristic, complemented
192#1832C2211yescharacteristic, complemented
193#1823C2211yescharacteristic
194#1817C2211yescharacteristic
195#1805C2211yescharacteristic, complemented
196#1786C2211yescharacteristic
197#1768C2211yescharacteristic, complemented
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1746C2211yescharacteristic, complemented
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×#41—21no—
204C23×D4C2311yescharacteristic
205C24×C4—21no—
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212#532—42no—
213#532—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120—21no—
232C2×#120—21no—
233C2×#120—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—42no—
239C2×C4×D4—42no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250C22×C42C2311yescharacteristic
251#490—24no—
252#483—42no—
253#482—42no—
254#482—42no—
255#468—42no—
256#468—42no—
257#460—24no—
258#450—42no—
259#428—42no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#418—24no—
277#418—42no—
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#401—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#399—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#396—21no—
340#393—21no—
341#393—21no—
342#393—21no—
343#393—21no—
344#392—21no—
345#392—21no—
346#392—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#392—21no—
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#388—21no—
383#388—21no—
384#388—21no—
385#388—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#387—21no—
399#387—21no—
400#387—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#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#383—21no—
427#383D411yescharacteristic
428#383D411yescharacteristic
429#382—21no—
430#382—21no—
431#382D411yescharacteristic
432#382D411yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#381—21no—
439#381D411yescharacteristic
440#381D411yescharacteristic
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380D411yescharacteristic
446#380D411yescharacteristic
447#380C2311yescharacteristic
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458#376—21no—
459#376C2311yescharacteristic
460#376C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
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—
494C2×#41—44no—
495C2×#41—82no—
496C2×#41—82no—
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—44no—
530C23×C4—82no—
531C23×C4—82no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563#127—22no—
564#127—22no—
565#127—22no—
566#127—22no—
567#127—41no—
568#127—41no—
569#127—41no—
570#127—41no—
571#127—41no—
572#127—41no—
573#125—22no—
574#125—41no—
575#124—44no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—44no—
583#121—82no—
584#121—82no—
585#121—82no—
586#121—82no—
587#120—82no—
588#120—82no—
589#120—82no—
590#120—82no—
591C4×Q8—22no—
592C4×Q8—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—44no—
606C4×D4—44no—
607C4×D4—44no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—41no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
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—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
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—44no—
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C42—22no—
684C2×C42—22no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699#107—41no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711C4⋊C8—22no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102#4114yescomplemented
747C22⋊C8—22no—
748C22⋊C8—22no—
749#97—22no—
750#97—41no—
751C4×C8—41no—
752C4×C8—41no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
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#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—42no—
812C24—42no—
813C24—81no—
814C24—81no—
815C24C22×D411yescharacteristic
816#41—816no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—42no—
824C2×Q8—81no—
825C2×Q8—81no—
826C2×D4—28no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—44no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4C2×#4112yes—
892C2×D42−1+412yes—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—22no—
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—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—42no—
916C22×C4—42no—
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—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—816no—
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
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×C4H(5,𝔽2)12yes—
951C22×C4H(5,𝔽2)12yes—
952C22×C4C2511yescharacteristic
953SD16—82no—
954SD16—82no—
955SD16—82no—
956SD16—82no—
957M16—44no—
958M16—82no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
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×C8C2×#4112yes—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
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—41no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4C2×#4112yes—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
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—42no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C42—22no—
1063C42—22no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—42no—
1077C42—42no—
1078C42—42no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—22no—
1090C23—48no—
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—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—84no—
1118C23—84no—
1119C23—84no—
1120C23—84no—
1121C23—84no—
1122C23—84no—
1123C23#53512yes—
1124C23C23×D411yescharacteristic
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—84no—
1130D4—22no—
1131D4—22no—
1132D4—22no—
1133D4—22no—
1134D4—48no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—84no—
1148D4—84no—
1149D4—84no—
1150D4—84no—
1151D4—162no—
1152D4—162no—
1153D4—162no—
1154D4—162no—
1155D4—162no—
1156D4—162no—
1157D4—162no—
1158D4—162no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—22no—
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—44no—
1202C2×C4—44no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—84no—
1239C2×C4—84no—
1240C2×C4—84no—
1241C2×C4—84no—
1242C2×C4—84no—
1243C2×C4—84no—
1244C2×C4—84no—
1245C2×C4#53512yes—
1246C2×C4#57712yes—
1247C2×C4C22×#4111yescharacteristic
1248C2×C4C2×H(5,𝔽2)11yescharacteristic
1249C2×C4C2×H(5,𝔽2)11yescharacteristic
1250C2×C4C2×2−1+411yescharacteristic
1251C2×C4#58511yescharacteristic
1252C2×C4#58511yescharacteristic
1253C8—22no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—816no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22C2×#53511yescharacteristic
1298C22D4×#4111yescharacteristic
1299C22#348911yescharacteristic
1300C22C2×#57711yescharacteristic
1301C22#358511yescharacteristic
1302C22#358511yescharacteristic
1303C22#358511yescharacteristic
1304C4—22no—
1305C4—22no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—42no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4#349211yescharacteristic
1330C4#351311yescharacteristic
1331C4#353311yescharacteristic
1332C4#353511yescharacteristic
1333C2—42no—
1334C2—82no—
1335C2—82no—
1336C2—161no—
1337C2—161no—
1338C2#3836711yescharacteristic
1339C2#6080611yescharacteristic
1340C2#6081211yescharacteristic
1341C2#6150411yescharacteristic
1342C2#6155111yescharacteristic
1343C2#6218811yescharacteristic
1344C2#6222311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35237C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38072C2semidirect
3. #33007C2semidirect
4. #32455C2semidirect
5. #32373C2semidirect
6. #32351C2semidirect
7. #32164C2semidirect
8. #32094C2semidirect
9. #32080C2semidirect
10. #31529C2semidirect
11. #30892C2semidirect
12. #30138C2semidirect
13. #30085C2semidirect
14. #29504C2semidirect
15. #29377C2semidirect
16. #29265C2semidirect
17. #29201C2semidirect
18. #28365C2semidirect
19. #27947C2semidirect
20. #27725C2semidirect
21. #27279C2semidirect
22. #25501C2semidirect
23. #25231C2semidirect
24. #25093C2semidirect
25. #24599C2semidirect
26. #24494C2semidirect
27. #24062C2semidirect
28. #22596C2semidirect
29. #22232C2semidirect
30. #22160C2semidirect
31. #20873C2semidirect
52. #2647C22semidirect
53. #2645C22semidirect
65. #2511C22semidirect
66. #2509C22semidirect
68. #2507C22semidirect
72. #2453C22semidirect
80. #2330C22semidirect
85. #2320C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2097C22semidirect
91. #2097C22semidirect
92. #2094C22semidirect
95. #2092C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2074C22semidirect
101. #2071C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
107. #2065C22semidirect
108. #2058C22semidirect
109. #2057C22semidirect
110. #2057C22semidirect
112. #2055C22semidirect
118. #2041C22semidirect
119. #2041C22semidirect
120. #2041C22semidirect
122. #2025C22semidirect
123. #2024C22semidirect
127. #2014C22semidirect
128. #1991C22semidirect
133. #1973C22semidirect
135. #1968C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1949C22semidirect
143. #1936C22semidirect
145. #1934C22semidirect
146. #1926C22semidirect
147. #1926C22semidirect
148. #1926C22semidirect
152. #1917C22semidirect
153. #1917C22semidirect
154. #1916C22semidirect
155. #1916C22semidirect
159. #1880C22semidirect
164. #1877C22semidirect
165. #1877C22semidirect
176. #1864C22semidirect
177. #1864C22semidirect
182. #1862C22semidirect
183. #1862C22semidirect
184. #1862C22semidirect
185. #1862C22semidirect
188. #1847C22semidirect
189. #1846C22semidirect
190. #1840C22semidirect
191. #1836C22semidirect
192. #1832C22semidirect
195. #1805C22semidirect
197. #1768C22semidirect
200. #1746C22semidirect
746. #102#41semidirect

Maximal subgroups

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

subgroupindex
#380722
#352372
#330072
#324552
#323732
#323512
#321642
#320942
#320802
#315292
#308922
#301382
#300852
#295042
#293772
#292652
#292012
#283652
#279472
#277252
#272792
#255012
#252312
#250932
#245992
#244942
#240622
#225962
#222322
#221602
#208732