Finite Group Databasebeta

← #6516142

Subgroups — #6516142

Order 512.

1731 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35570C211yesmaximal, characteristic, complemented
2#34474C211yesmaximal, characteristic, complemented
3#29423C211yesmaximal, characteristic, complemented
4#29411C211yesmaximal, characteristic, complemented
5#28132C211yesmaximal, characteristic, complemented
6#28116C211yesmaximal, characteristic, complemented
7#27251C211yesmaximal, characteristic, complemented
8#27225C211yesmaximal, characteristic, complemented
9#26747C211yesmaximal, characteristic, complemented
10#26732C211yesmaximal, characteristic, complemented
11#26647C211yesmaximal, characteristic, complemented
12#26618C211yesmaximal, characteristic, complemented
13#26479C211yesmaximal, characteristic, complemented
14#26243C211yesmaximal, characteristic, complemented
15#26023C211yesmaximal, characteristic, complemented
16#25761C211yesmaximal, characteristic, complemented
17#25373C211yesmaximal, characteristic, complemented
18#25177C211yesmaximal, characteristic, complemented
19#25162C211yesmaximal, characteristic, complemented
20#24966C211yesmaximal, characteristic, complemented
21#24639C211yesmaximal, characteristic, complemented
22#24256C211yesmaximal, characteristic, complemented
23#24162C211yesmaximal, characteristic, complemented
24#24161C211yesmaximal, characteristic, complemented
25#23940C211yesmaximal, characteristic, complemented
26#23938C211yesmaximal, characteristic, complemented
27#22274C211yesmaximal, characteristic, complemented
28#22159C211yesmaximal, characteristic, complemented
29#22017C211yesmaximal, characteristic, complemented
30#21509C211yesmaximal, characteristic, complemented
31#21125C211yesmaximal, characteristic, complemented
32C2×#548C2211yescharacteristic
33C2×#540C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#495C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#479C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#464C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#459C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#449C2211yescharacteristic
46C2×#449C2211yescharacteristic
47C2×#451C2211yescharacteristic
48C2×#448C2211yescharacteristic
49C2×#448C2211yescharacteristic
50C2×#440C2211yescharacteristic
51C2×#440C2211yescharacteristic
52C2×C4×D8C2211yescharacteristic
53#2602—21no—
54#2559—21no—
55#2553—21no—
56#2552C2211yescharacteristic
57#2544C2211yescharacteristic
58#2543—21no—
59#2540C2211yescharacteristic
60#2537C2211yescharacteristic
61#2500—21no—
62#2498—21no—
63#2490C2211yescharacteristic
64#2489C2211yescharacteristic
65#2464—21no—
66#2428C2211yescharacteristic
67#2427C2211yescharacteristic
68#2422—21no—
69#2379—21no—
70#2377—21no—
71#2368—21no—
72#2367C2211yescharacteristic
73#2363C2211yescharacteristic
74#2362C2211yescharacteristic
75#2357—21no—
76#2355C2211yescharacteristic
77#2354C2211yescharacteristic
78Q8×C22⋊C4C2211yescharacteristic
79#2339C2211yescharacteristic
80#2337—21no—
81#2333—21no—
82#2332—21no—
83#2326C2211yescharacteristic
84#2326C2211yescharacteristic
85#2324C2211yescharacteristic
86#2323C2211yescharacteristic
87#2320C2211yescharacteristic
88#2318—21no—
89#2310C2211yescharacteristic
90C4×C22⋊Q8C2211yescharacteristic
91C4×#121C2211yescharacteristic
92#2297C2211yescharacteristic
93#2290C2211yescharacteristic
94#2275C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2066C2211yescharacteristic
100#2065C2211yescharacteristic
101#2056C2211yescharacteristic
102#2056C2211yescharacteristic
103#2055C2211yescharacteristic
104#2054C2211yescharacteristic
105#2036C2211yescharacteristic
106#2036C2211yescharacteristic
107#2036C2211yescharacteristic
108#2034C2211yescharacteristic
109#2034C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2026C2211yescharacteristic
114#2026C2211yescharacteristic
115#2026C2211yescharacteristic
116#2025C2211yescharacteristic
117#2015C2211yescharacteristic
118#2014C2211yescharacteristic
119#2014C2211yescharacteristic
120#2012C2211yescharacteristic
121#2001C2211yescharacteristic
122#2000C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#1999C2211yescharacteristic
126#1999C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1982C2211yescharacteristic
133#1971C2211yescharacteristic
134#1968C2211yescharacteristic
135#1959C2211yescharacteristic
136#1959C2211yescharacteristic
137#1955C2211yescharacteristic
138#1954C2211yescharacteristic
139#1948C2211yescharacteristic
140#1947C2211yescharacteristic
141#1940C2211yescharacteristic
142#1939C2211yescharacteristic
143#1936C2211yescharacteristic
144#1933C2211yescharacteristic
145#1928C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1927C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic
153#1923C2211yescharacteristic
154#1923C2211yescharacteristic
155#1921C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1918C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1875C2211yescharacteristic
176#1875C2211yescharacteristic
177#1875C2211yescharacteristic
178#1873C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1862C2211yescharacteristic
185#1834C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1818C2211yescharacteristic
189#1817C2211yescharacteristic
190#1803C2211yescharacteristic
191#1802C2211yescharacteristic
192#1798C2211yescharacteristic
193#1797C2211yescharacteristic
194#1788C2211yescharacteristic
195#1787C2211yescharacteristic
196#1776C2211yescharacteristic
197#1768C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214#548—24no—
215#548—24no—
216#540—42no—
217#540—42no—
218C2×#127C2311yescharacteristic
219#529—42no—
220#529—42no—
221C2×#126—21no—
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#124—21no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×#117—21no—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C22×C42C2311yescharacteristic
264#495—24no—
265#485—42no—
266#482—42no—
267#479—42no—
268#478—42no—
269#464—24no—
270#464—42no—
271#463—24no—
272#459—42no—
273#452—42no—
274#451—42no—
275#449—42no—
276#449—42no—
277#448—42no—
278#448—42no—
279#440—24no—
280#440—42no—
281C4×D8—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337#400—21no—
338#399—21no—
339#398—21no—
340#398—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#392—21no—
352#392—21no—
353#391—21no—
354#391—21no—
355#391—21no—
356#391—21no—
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#389—21no—
376#389—21no—
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
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#388D411yescharacteristic
399#388D411yescharacteristic
400#387—21no—
401#387—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#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386D411yescharacteristic
421#386D411yescharacteristic
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385D411yescharacteristic
430#385D411yescharacteristic
431#384—21no—
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#383—21no—
435#382—21no—
436#382—21no—
437#382—21no—
438#381—21no—
439#381—21no—
440#381—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471#376C2311yescharacteristic
472C2×#95—21no—
473C2×#95—21no—
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C22×Q8—22no—
509C22×Q8—22no—
510C22×Q8—21no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C2×D411yescharacteristic
539C23×C4C2×D411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—41no—
567C2×D8—41no—
568C2×D8—41no—
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577#127—22no—
578#127—41no—
579#126—44no—
580#125—22no—
581#125—22no—
582#125—41no—
583#125—41no—
584#124—28no—
585#124—22no—
586#124—22no—
587#124—22no—
588#124—22no—
589#124—41no—
590#124#4114yes—
591#123—44no—
592#123—44no—
593#123—44no—
594C22⋊Q8—28no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601#121—28no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—44no—
609#121—41no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—44no—
614#121—82no—
615#121—82no—
616C4×Q8—22no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8#4114yes—
624C4×D4—28no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—44no—
640C4×D4—82no—
641#117—41no—
642#117—41no—
643#117—44no—
644#117—41no—
645#117—41no—
646#117—41no—
647#117—41no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—41no—
737C2×C42—41no—
738C2×C42C2×D411yescharacteristic
739C2×C42C2×D411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745#107—22no—
746#107—22no—
747#107—22no—
748#107—22no—
749#106—22no—
750#106—41no—
751#106—41no—
752C4⋊C8—22no—
753C4⋊C8—22no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756C4⋊C8—41no—
757C4⋊C8—41no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796#97—22no—
797#97—41no—
798C4×C8—22no—
799C4×C8—41no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840C24—21no—
841C24—21no—
842C24—21no—
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845#41—82no—
846#41—82no—
847#41—82no—
848#41—82no—
849C2×Q8—24no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8—82no—
869C2×Q8—82no—
870C2×Q8—82no—
871C2×Q8—82no—
872C2×Q8C2×#4112yes—
873C2×Q8C2×#4112yes—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—22no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—41no—
894C2×D4—41no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4C2×#4112yes—
918C2×D4H(5,𝔽2)12yes—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C2511yescharacteristic
987Q16—82no—
988Q16—82no—
989SD16—44no—
990SD16—44no—
991SD16—82no—
992SD16—82no—
993SD16—82no—
994D8—44no—
995D8—82no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—22no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4C2×#4112yes—
1062C4⋊C4H(5,𝔽2)12yes—
1063C4⋊C4H(5,𝔽2)12yes—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C42—24no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—41no—
1116C42—41no—
1117C42—42no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C42—81no—
1122C42—81no—
1123C42—81no—
1124C42—81no—
1125C42—81no—
1126C42—81no—
1127C42—81no—
1128C42C2×#4112yes—
1129C42C2×#4112yes—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—22no—
1140C23—21no—
1141C23—22no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23C23×D411yescharacteristic
1166Q8—22no—
1167Q8—22no—
1168Q8—22no—
1169Q8—22no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—84no—
1179D4—22no—
1180D4—22no—
1181D4—22no—
1182D4—22no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—82no—
1192D4—84no—
1193D4—84no—
1194D4—84no—
1195D4—84no—
1196D4—162no—
1197D4—162no—
1198D4—162no—
1199D4—162no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—22no—
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—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—84no—
1282C2×C4—84no—
1283C2×C4—84no—
1284C2×C4—82no—
1285C2×C4—82no—
1286C2×C4—162no—
1287C2×C4—162no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4#52512yes—
1292C2×C4#52512yes—
1293C2×C4C22×#4111yescharacteristic
1294C2×C4C22×#4111yescharacteristic
1295C2×C4C2×H(5,𝔽2)11yescharacteristic
1296C2×C4C2×H(5,𝔽2)11yescharacteristic
1297C2×C4C2×H(5,𝔽2)11yescharacteristic
1298C2×C4#58511yescharacteristic
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—42no—
1314C22—41no—
1315C22—41no—
1316C22—42no—
1317C22—41no—
1318C22—41no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—42no—
1326C22—41no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22C2×#52511yescharacteristic
1343C22#348411yescharacteristic
1344C22#348811yescharacteristic
1345C22#358411yescharacteristic
1346C22#358411yescharacteristic
1347C22#358511yescharacteristic
1348C22#358611yescharacteristic
1349C4—22no—
1350C4—22no—
1351C4—41no—
1352C4—41no—
1353C4—42no—
1354C4—42no—
1355C4—41no—
1356C4—41no—
1357C4—42no—
1358C4—42no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—42no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4#349411yescharacteristic
1375C4#350811yescharacteristic
1376C4#351411yescharacteristic
1377C4#351911yescharacteristic
1378C2—81no—
1379C2—81no—
1380C2—82no—
1381C2—82no—
1382C2—161no—
1383C2#3552411yescharacteristic
1384C2#6058711yescharacteristic
1385C2#6059811yescharacteristic
1386C2#6163611yescharacteristic
1387C2#6165411yescharacteristic
1388C2#6202511yescharacteristic
1389C2#6202811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35570C2semidirect
2. #34474C2semidirect
3. #29423C2semidirect
4. #29411C2semidirect
5. #28132C2semidirect
6. #28116C2semidirect
7. #27251C2semidirect
8. #27225C2semidirect
9. #26747C2semidirect
10. #26732C2semidirect
11. #26647C2semidirect
12. #26618C2semidirect
13. #26479C2semidirect
14. #26243C2semidirect
15. #26023C2semidirect
16. #25761C2semidirect
17. #25373C2semidirect
18. #25177C2semidirect
19. #25162C2semidirect
20. #24966C2semidirect
21. #24639C2semidirect
22. #24256C2semidirect
23. #24162C2semidirect
24. #24161C2semidirect
25. #23940C2semidirect
26. #23938C2semidirect
27. #22274C2semidirect
28. #22159C2semidirect
29. #22017C2semidirect
30. #21509C2semidirect
31. #21125C2semidirect

Maximal subgroups

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

subgroupindex
#355702
#344742
#294232
#294112
#281322
#281162
#272512
#272252
#267472
#267322
#266472
#266182
#264792
#262432
#260232
#257612
#253732
#251772
#251622
#249662
#246392
#242562
#241622
#241612
#239402
#239382
#222742
#221592
#220172
#215092
#211252