Finite Group Databasebeta

← #7038285

Subgroups — #7038285

Order 512.

1576 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59282C211yesmaximal, characteristic, complemented
2#40053C211yesmaximal, characteristic, complemented
3#32443C211yesmaximal, characteristic, complemented
4#32294C211yesmaximal, characteristic, complemented
5#31661C211yesmaximal, characteristic, complemented
6#31147C211yesmaximal, characteristic, complemented
7#31057C211yesmaximal, characteristic, complemented
8#31004C211yesmaximal, characteristic, complemented
9#30804C211yesmaximal, characteristic, complemented
10#30398C211yesmaximal, characteristic, complemented
11#28890C211yesmaximal, characteristic, complemented
12#28852C211yesmaximal, characteristic, complemented
13#28547C211yesmaximal, characteristic, complemented
14#28341C211yesmaximal, characteristic, complemented
15#28316C211yesmaximal, characteristic, complemented
16#28022C211yesmaximal, characteristic, complemented
17#27897C211yesmaximal, characteristic, complemented
18#27798C211yesmaximal, characteristic, complemented
19#27517C211yesmaximal, characteristic, complemented
20#27249C211yesmaximal, characteristic, complemented
21#27243C211yesmaximal, characteristic, complemented
22#27080C211yesmaximal, characteristic, complemented
23#26806C211yesmaximal, characteristic, complemented
24#25179C211yesmaximal, characteristic, complemented
25#25018C211yesmaximal, characteristic, complemented
26#24873C211yesmaximal, characteristic, complemented
27#23764C211yesmaximal, characteristic, complemented
28#23302C211yesmaximal, characteristic, complemented
29#23106C211yesmaximal, characteristic, complemented
30#22854C211yesmaximal, characteristic, complemented
31#22051C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic, complemented
33C2×#481C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic, complemented
36C2×#479C2211yescharacteristic, complemented
37C2×#476C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#449C2211yescharacteristic
42C2×#449C2211yescharacteristic, complemented
43C2×#450C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2856C2211yescharacteristic
48#2797—21no—
49#2751—21no—
50#2749—21no—
51#2697—21no—
52#2688—21no—
53#2678—21no—
54#2648—21no—
55#2578—21no—
56#2568C2211yescharacteristic, complemented
57#2566C2211yescharacteristic
58#2557—21no—
59#2535C2211yescharacteristic
60#2530—21no—
61#2526—21no—
62#2523—21no—
63#2513C2211yescharacteristic
64#2513C2211yescharacteristic, complemented
65#2513C2211yescharacteristic, complemented
66#2504C2211yescharacteristic
67#2497C2211yescharacteristic
68#2491C2211yescharacteristic
69#2490C2211yescharacteristic
70#2490C2211yescharacteristic
71#2456—21no—
72#2445C2211yescharacteristic
73#2439C2211yescharacteristic, complemented
74#2433C2211yescharacteristic
75#2428C2211yescharacteristic
76#2424—21no—
77#2421C2211yescharacteristic
78#2408C2211yescharacteristic
79#2407C2211yescharacteristic
80#2372—21no—
81#2366C2211yescharacteristic
82#2360C2211yescharacteristic
83#2356C2211yescharacteristic, complemented
84#2352C2211yescharacteristic
85#2341C2211yescharacteristic, complemented
86D4×C22⋊C4C2211yescharacteristic
87#2321—21no—
88C4×#123C2211yescharacteristic
89C4×#121C2211yescharacteristic
90#2297C2211yescharacteristic, complemented
91#2283C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2096C2211yescharacteristic, complemented
95#2093C2211yescharacteristic, complemented
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2085C2211yescharacteristic, complemented
100#2085C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic, complemented
103#2075C2211yescharacteristic, complemented
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic, complemented
109#2067C2211yescharacteristic, complemented
110#2059C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2041C2211yescharacteristic
115#2036C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic, complemented
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic, complemented
125#2025C2211yescharacteristic, complemented
126#2023C2211yescharacteristic
127#2023C2211yescharacteristic, complemented
128#2014C2211yescharacteristic
129#2011C2211yescharacteristic
130#2011C2211yescharacteristic
131#2000C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic, complemented
135#1972C2211yescharacteristic
136#1972C2211yescharacteristic
137#1972C2211yescharacteristic
138#1972C2211yescharacteristic, complemented
139#1972C2211yescharacteristic, complemented
140#1970C2211yescharacteristic
141#1968C2211yescharacteristic
142#1961C2211yescharacteristic
143#1961C2211yescharacteristic
144#1961C2211yescharacteristic
145#1954C2211yescharacteristic
146#1949C2211yescharacteristic, complemented
147#1949C2211yescharacteristic, complemented
148#1944C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic, complemented
151#1935C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic, complemented
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic, complemented
159#1925C2211yescharacteristic, complemented
160#1925C2211yescharacteristic, complemented
161#1924C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic, complemented
164#1924C2211yescharacteristic, complemented
165#1920C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1892C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic, complemented
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic, complemented
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic, complemented
177#1875C2211yescharacteristic
178#1869C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic, complemented
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1847C2211yescharacteristic, complemented
185#1846C2211yescharacteristic, complemented
186#1836C2211yescharacteristic, complemented
187#1807C2211yescharacteristic
188#1804C2211yescharacteristic, complemented
189#1788C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1776C2211yescharacteristic, complemented
192#1776C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#102C2211yescharacteristic, complemented
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic
201#1749C2211yescharacteristic, complemented
202#1749C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#123—21no—
218C2×#123D411yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121—21no—
221C2×#121—21no—
222C2×#121—21no—
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#120—21no—
229C2×#120—21no—
230C2×#120—21no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C22⋊C4—21no—
242C22×C42C2311yescharacteristic
243#501—42no—
244#482—42no—
245#482—42no—
246#481—42no—
247#479—42no—
248#476—42no—
249#466—42no—
250#460—24no—
251#450—24no—
252#449—24no—
253#449—42no—
254#449—42no—
255#447—42no—
256#440—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#102—42no—
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#393—21no—
346#393—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#392—21no—
352#392—21no—
353#391—21no—
354#391—21no—
355#391—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
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#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
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#388D411yescharacteristic
398#388D411yescharacteristic
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387D411yescharacteristic
407#387D411yescharacteristic
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#386—21no—
422#386—21no—
423#386D411yescharacteristic
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385D411yescharacteristic
429#384C2311yescharacteristic
430#383—21no—
431#383—21no—
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#381—21no—
438#381D411yescharacteristic
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447#379—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465#376—21no—
466#376—21no—
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×D4—22no—
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—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16#4114yes—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C22×C8—22no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564#127—22no—
565#127—41no—
566#127—41no—
567#127—41no—
568#125—41no—
569#125—41no—
570#124—44no—
571#123—42no—
572#123—82no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575#121—22no—
576#121—41no—
577#121—41no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—41no—
585#121—82no—
586#121—82no—
587#121—82no—
588#120—44no—
589#120—82no—
590#120—82no—
591C4×Q8—22no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—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—82no—
604C4×D4—82no—
605#117—41no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
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—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
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—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—82no—
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—41no—
698C2×C42—41no—
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#107—22no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#107—41no—
712#107—41no—
713#106—22no—
714#106—22no—
715#106—22no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720C4⋊C8—22no—
721C4⋊C8—22no—
722C4⋊C8—41no—
723#103—22no—
724#103—22no—
725#103—22no—
726#103—41no—
727#103—41no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
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—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751C22⋊C8—22no—
752C22⋊C8—22no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—22no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758#97—22no—
759#97—41no—
760#97—41no—
761#97—41no—
762#97—41no—
763#97—41no—
764C4×C8—41no—
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#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—42no—
811C24—42no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819#41—82no—
820#41—82no—
821#41—82no—
822#41—82no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—42no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8C2×#4112yes—
832C2×D4—22no—
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—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—44no—
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—82no—
883C2×D4—82no—
884C2×D4—82no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4C2×#4112yes—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
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×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C2511yescharacteristic
954SD16—44no—
955SD16—82no—
956SD16—82no—
957D8—82no—
958D8—82no—
959D8—82no—
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—82no—
982C2×C8C2×#4112yes—
983C2×C8H(5,𝔽2)12yes—
984C2×C8H(5,𝔽2)12yes—
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—21no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
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—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
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—81no—
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—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—41no—
1086C42—41no—
1087C42—42no—
1088C42—42no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—22no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—84no—
1137C23—84no—
1138C23—162no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23—162no—
1143C23#57512yes—
1144C23C23×D411yescharacteristic
1145Q8—22no—
1146Q8—22no—
1147Q8—41no—
1148Q8—41no—
1149Q8—162no—
1150D4—22no—
1151D4—22no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—82no—
1167D4—84no—
1168D4—84no—
1169D4—84no—
1170D4—84no—
1171D4—162no—
1172D4—162no—
1173D4—162no—
1174D4—162no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
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—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—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—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—82no—
1259C2×C4—82no—
1260C2×C4—84no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4C22×#4111yescharacteristic
1266C2×C4C2×H(5,𝔽2)11yescharacteristic
1267C2×C4C2×H(5,𝔽2)11yescharacteristic
1268C2×C4#58511yescharacteristic
1269C2×C4#58511yescharacteristic
1270C2×C4#58511yescharacteristic
1271C8—22no—
1272C8—22no—
1273C8—22no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—42no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—42no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—42no—
1295C22—41no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—168no—
1322C22D4×#4111yescharacteristic
1323C22#348511yescharacteristic
1324C22#349811yescharacteristic
1325C22C2×#57511yescharacteristic
1326C22#358511yescharacteristic
1327C22#358511yescharacteristic
1328C22#358511yescharacteristic
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—42no—
1341C4—41no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4#350511yescharacteristic
1354C4#351411yescharacteristic
1355C4#354511yescharacteristic
1356C4#356011yescharacteristic
1357C2—42no—
1358C2—81no—
1359C2—82no—
1360C2—161no—
1361C2—161no—
1362C2—161no—
1363C2#4350211yescharacteristic
1364C2#6145611yescharacteristic
1365C2#6150411yescharacteristic
1366C2#6171411yescharacteristic
1367C2#6177811yescharacteristic
1368C2#6244111yescharacteristic
1369C2#6244911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59282C2semidirect
2. #40053C2semidirect
3. #32443C2semidirect
4. #32294C2semidirect
5. #31661C2semidirect
6. #31147C2semidirect
7. #31057C2semidirect
8. #31004C2semidirect
9. #30804C2semidirect
10. #30398C2semidirect
11. #28890C2semidirect
12. #28852C2semidirect
13. #28547C2semidirect
14. #28341C2semidirect
15. #28316C2semidirect
16. #28022C2semidirect
17. #27897C2semidirect
18. #27798C2semidirect
19. #27517C2semidirect
20. #27249C2semidirect
21. #27243C2semidirect
22. #27080C2semidirect
23. #26806C2semidirect
24. #25179C2semidirect
25. #25018C2semidirect
26. #24873C2semidirect
27. #23764C2semidirect
28. #23302C2semidirect
29. #23106C2semidirect
30. #22854C2semidirect
31. #22051C2semidirect
32. C2×#501C22semidirect
35. C2×#482C22semidirect
36. C2×#479C22semidirect
42. C2×#449C22semidirect
56. #2568C22semidirect
64. #2513C22semidirect
65. #2513C22semidirect
73. #2439C22semidirect
83. #2356C22semidirect
85. #2341C22semidirect
90. #2297C22semidirect
91. #2283C22semidirect
92. #2101C22semidirect
93. #2097C22semidirect
94. #2096C22semidirect
95. #2093C22semidirect
99. #2085C22semidirect
100. #2085C22semidirect
102. #2077C22semidirect
103. #2075C22semidirect
106. #2073C22semidirect
108. #2067C22semidirect
109. #2067C22semidirect
110. #2059C22semidirect
120. #2034C22semidirect
124. #2033C22semidirect
125. #2025C22semidirect
127. #2023C22semidirect
134. #1973C22semidirect
138. #1972C22semidirect
139. #1972C22semidirect
146. #1949C22semidirect
147. #1949C22semidirect
148. #1944C22semidirect
150. #1936C22semidirect
151. #1935C22semidirect
152. #1927C22semidirect
155. #1926C22semidirect
158. #1925C22semidirect
159. #1925C22semidirect
160. #1925C22semidirect
163. #1924C22semidirect
164. #1924C22semidirect
165. #1920C22semidirect
166. #1917C22semidirect
167. #1917C22semidirect
171. #1880C22semidirect
174. #1879C22semidirect
176. #1877C22semidirect
179. #1865C22semidirect
181. #1854C22semidirect
184. #1847C22semidirect
185. #1846C22semidirect
186. #1836C22semidirect
188. #1804C22semidirect
189. #1788C22semidirect
191. #1776C22semidirect
192. #1776C22semidirect
193. #1771C22semidirect
194. #1771C22semidirect
195. #1763C22semidirect
198. C4×#102C22semidirect
201. #1749C22semidirect
202. #1749C22semidirect

Maximal subgroups

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

subgroupindex
#592822
#400532
#324432
#322942
#316612
#311472
#310572
#310042
#308042
#303982
#288902
#288522
#285472
#283412
#283162
#280222
#278972
#277982
#275172
#272492
#272432
#270802
#268062
#251792
#250182
#248732
#237642
#233022
#231062
#228542
#220512