Finite Group Databasebeta

← #7271631

Subgroups — #7271631

Order 512.

1480 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39929C211yesmaximal, characteristic, complemented
2#39503C211yesmaximal, characteristic, complemented
3#32775C211yesmaximal, characteristic, complemented
4#32391C211yesmaximal, characteristic, complemented
5#32384C211yesmaximal, characteristic, complemented
6#32067C211yesmaximal, characteristic, complemented
7#32064C211yesmaximal, characteristic, complemented
8#31961C211yesmaximal, characteristic, complemented
9#31959C211yesmaximal, characteristic, complemented
10#31032C211yesmaximal, characteristic, complemented
11#31028C211yesmaximal, characteristic, complemented
12#30722C211yesmaximal, characteristic, complemented
13#30704C211yesmaximal, characteristic, complemented
14#30420C211yesmaximal, characteristic, complemented
15#30400C211yesmaximal, characteristic, complemented
16#28992C211yesmaximal, characteristic, complemented
17#28990C211yesmaximal, characteristic, complemented
18#28312C211yesmaximal, characteristic, complemented
19#27946C211yesmaximal, characteristic, complemented
20#27935C211yesmaximal, characteristic, complemented
21#27882C211yesmaximal, characteristic, complemented
22#27588C211yesmaximal, characteristic, complemented
23#27093C211yesmaximal, characteristic, complemented
24#27072C211yesmaximal, characteristic, complemented
25#26152C211yesmaximal, characteristic, complemented
26#26147C211yesmaximal, characteristic, complemented
27#26133C211yesmaximal, characteristic, complemented
28#26127C211yesmaximal, characteristic, complemented
29#25029C211yesmaximal, characteristic, complemented
30#25019C211yesmaximal, characteristic, complemented
31#22335C211yesmaximal, characteristic, complemented
32C2×#481C2211yescharacteristic
33C2×#485C2211yescharacteristic, complemented
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic, complemented
36C2×#483C2211yescharacteristic
37C2×#480C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#466C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#428C2211yescharacteristic, complemented
43C2×#427C2211yescharacteristic, complemented
44#2857C2211yescharacteristic
45#2850C2211yescharacteristic
46#2808—21no—
47#2803—21no—
48#2803—21no—
49#2777—21no—
50#2749—21no—
51#2743—21no—
52#2733—21no—
53#2699—21no—
54#2648—21no—
55#2617—21no—
56#2570C2211yescharacteristic, complemented
57#2540C2211yescharacteristic, complemented
58#2538C2211yescharacteristic
59#2535C2211yescharacteristic
60#2526—21no—
61#2526—21no—
62#2513C2211yescharacteristic
63#2513C2211yescharacteristic
64#2503C2211yescharacteristic, complemented
65#2500C2211yescharacteristic
66#2500C2211yescharacteristic
67#2500C2211yescharacteristic, complemented
68#2491C2211yescharacteristic
69#2491C2211yescharacteristic
70#2472—21no—
71#2472—21no—
72#2421C2211yescharacteristic, complemented
73#2420C2211yescharacteristic, complemented
74#2416C2211yescharacteristic
75#2415C2211yescharacteristic
76#2414C2211yescharacteristic
77#2414C2211yescharacteristic
78#2408C2211yescharacteristic
79#2408C2211yescharacteristic
80#2367C2211yescharacteristic, complemented
81#2352C2211yescharacteristic
82#2352C2211yescharacteristic
83#2352C2211yescharacteristic, complemented
84#2333—21no—
85#2312—21no—
86C4×#121C2211yescharacteristic
87C2×#390C2211yescharacteristic
88#2283C2211yescharacteristic
89#2097C2211yescharacteristic, complemented
90#2096C2211yescharacteristic, complemented
91#2093C2211yescharacteristic
92#2093C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2085C2211yescharacteristic, complemented
101#2085C2211yescharacteristic, complemented
102#2085C2211yescharacteristic, complemented
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic, complemented
106#2076C2211yescharacteristic
107#2076C2211yescharacteristic
108#2075C2211yescharacteristic, complemented
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2073C2211yescharacteristic
112#2071C2211yescharacteristic
113#2067C2211yescharacteristic
114#2065C2211yescharacteristic
115#2055C2211yescharacteristic
116#2054C2211yescharacteristic
117#2042C2211yescharacteristic, complemented
118#2042C2211yescharacteristic, complemented
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2035C2211yescharacteristic, complemented
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic, complemented
126#2033C2211yescharacteristic
127#2024C2211yescharacteristic, complemented
128#2023C2211yescharacteristic, complemented
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1999C2211yescharacteristic
135#1999C2211yescharacteristic
136#1999C2211yescharacteristic
137#1993C2211yescharacteristic, complemented
138#1993C2211yescharacteristic, complemented
139#1973C2211yescharacteristic
140#1973C2211yescharacteristic
141#1972C2211yescharacteristic
142#1972C2211yescharacteristic
143#1972C2211yescharacteristic
144#1968C2211yescharacteristic
145#1955C2211yescharacteristic
146#1954C2211yescharacteristic
147#1949C2211yescharacteristic, complemented
148#1948C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1934C2211yescharacteristic
151#1928C2211yescharacteristic, complemented
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic, complemented
157#1924C2211yescharacteristic, complemented
158#1924C2211yescharacteristic, complemented
159#1921C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1919C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1895C2211yescharacteristic
168#1895C2211yescharacteristic, complemented
169#1893C2211yescharacteristic
170#1892C2211yescharacteristic, complemented
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1875C2211yescharacteristic
176#1875C2211yescharacteristic, complemented
177#1874C2211yescharacteristic
178#1873C2211yescharacteristic, complemented
179#1870C2211yescharacteristic
180#1870C2211yescharacteristic, complemented
181#1869C2211yescharacteristic
182#1869C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1854C2211yescharacteristic, complemented
185#1854C2211yescharacteristic, complemented
186#1853C2211yescharacteristic
187#1852C2211yescharacteristic
188#1852C2211yescharacteristic, complemented
189#1847C2211yescharacteristic, complemented
190#1847C2211yescharacteristic, complemented
191#1846C2211yescharacteristic, complemented
192#1836C2211yescharacteristic, complemented
193#1817C2211yescharacteristic
194#1805C2211yescharacteristic, complemented
195#1804C2211yescharacteristic, complemented
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1763C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1752C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#124—21no—
212C2×#124—21no—
213C2×#124C2311yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121—21no—
219C2×#121D411yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C2×#120—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241C22×C42C2311yescharacteristic
242#485—42no—
243#483—42no—
244#482—42no—
245#482—42no—
246#481—42no—
247#480—42no—
248#468—42no—
249#466—42no—
250#450—42no—
251#447—42no—
252#428—42no—
253#427—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#399—21no—
315#398—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#393—21no—
343#393—21no—
344#392—21no—
345#392—21no—
346#392—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#391—21no—
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#390—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390D411yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#389—21no—
372#389—21no—
373#389—21no—
374#389D411yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#388—21no—
380#388—21no—
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#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388D411yescharacteristic
403#388D411yescharacteristic
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—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#386D411yescharacteristic
420#386D411yescharacteristic
421#385—21no—
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#383—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#381—21no—
432#381—21no—
433#381—21no—
434#381—21no—
435#380—21no—
436#380D411yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446#379—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459#376—21no—
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4C2×D411yescharacteristic
508C22×D4C2×D411yescharacteristic
509C22×D4C2×D411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C2×SD16—22no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×D8—22no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×M16—22no—
534C2×M16—41no—
535C2×M16—41no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549#124—41no—
550#124—41no—
551#124—82no—
552#124—82no—
553C22⋊Q8—41no—
554C22⋊Q8—41no—
555C22⋊Q8—41no—
556C22⋊Q8—41no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8—82no—
560#121—42no—
561#121—44no—
562#121—41no—
563#121—41no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—41no—
568#121—41no—
569#121—41no—
570#121—41no—
571#121—41no—
572#121—41no—
573#121—41no—
574#121—41no—
575#121—41no—
576#120—82no—
577#120—82no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588#117—41no—
589#117—41no—
590#117—41no—
591#117—41no—
592#117—41no—
593#117—41no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
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—44no—
675C2×C22⋊C4—82no—
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—41no—
695C2×C42—41no—
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—22no—
703#107—22no—
704#107—22no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#106—22no—
711#106—22no—
712#106—22no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720#103—22no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#102—22no—
727#102—22no—
728#102—22no—
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—
744C22⋊C8—22no—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—22no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754#97—41no—
755#97—41no—
756#97—41no—
757C4×C8—41no—
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#95—21no—
789#95—21no—
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796C24—21no—
797C24—21no—
798C24—21no—
799C24—42no—
800C24—42no—
801C24—42no—
802C24—81no—
803C24—81no—
804C24—81no—
805C24—81no—
806C24C22×D411yescharacteristic
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—42no—
816C2×Q8—81no—
817C2×Q8—81no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
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—41no—
839C2×D4—41no—
840C2×D4—41no—
841C2×D4—41no—
842C2×D4—41no—
843C2×D4—41no—
844C2×D4—41no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—82no—
851C2×D4—82no—
852C2×D4—82no—
853C2×D4—82no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C22×C4—22no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
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—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C2511yescharacteristic
931SD16—82no—
932SD16—82no—
933D8—82no—
934D8—82no—
935M16—44no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—44no—
959C2×C8H(5,𝔽2)12yes—
960C2×C8H(5,𝔽2)12yes—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—42no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
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—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—41no—
1068C42—41no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
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—41no—
1118C23—84no—
1119C23—84no—
1120C23—84no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23—162no—
1125C23#57512yes—
1126C23C23×D411yescharacteristic
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—162no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—82no—
1145D4—82no—
1146D4—82no—
1147D4—84no—
1148D4—162no—
1149D4—162no—
1150D4—162no—
1151D4—162no—
1152D4—162no—
1153D4—162no—
1154D4—162no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—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—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—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—82no—
1240C2×C4—82no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C2×C4#58511yescharacteristic
1250C8—22no—
1251C8—22no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
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—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—168no—
1301C22#348511yescharacteristic
1302C22#348511yescharacteristic
1303C22#349811yescharacteristic
1304C22C2×#57511yescharacteristic
1305C22#358411yescharacteristic
1306C22#358511yescharacteristic
1307C22#358511yescharacteristic
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4#353311yescharacteristic
1333C4#353311yescharacteristic
1334C4#356211yescharacteristic
1335C4#356211yescharacteristic
1336C2—42no—
1337C2—81no—
1338C2—81no—
1339C2—161no—
1340C2—161no—
1341C2—161no—
1342C2#4721311yescharacteristic
1343C2#6171011yescharacteristic
1344C2#6173211yescharacteristic
1345C2#6177811yescharacteristic
1346C2#6180411yescharacteristic
1347C2#6244911yescharacteristic
1348C2#6246811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39929C2semidirect
2. #39503C2semidirect
3. #32775C2semidirect
4. #32391C2semidirect
5. #32384C2semidirect
6. #32067C2semidirect
7. #32064C2semidirect
8. #31961C2semidirect
9. #31959C2semidirect
10. #31032C2semidirect
11. #31028C2semidirect
12. #30722C2semidirect
13. #30704C2semidirect
14. #30420C2semidirect
15. #30400C2semidirect
16. #28992C2semidirect
17. #28990C2semidirect
18. #28312C2semidirect
19. #27946C2semidirect
20. #27935C2semidirect
21. #27882C2semidirect
22. #27588C2semidirect
23. #27093C2semidirect
24. #27072C2semidirect
25. #26152C2semidirect
26. #26147C2semidirect
27. #26133C2semidirect
28. #26127C2semidirect
29. #25029C2semidirect
30. #25019C2semidirect
31. #22335C2semidirect
33. C2×#485C22semidirect
35. C2×#482C22semidirect
42. C2×#428C22semidirect
43. C2×#427C22semidirect
56. #2570C22semidirect
57. #2540C22semidirect
64. #2503C22semidirect
67. #2500C22semidirect
72. #2421C22semidirect
73. #2420C22semidirect
80. #2367C22semidirect
83. #2352C22semidirect
89. #2097C22semidirect
90. #2096C22semidirect
92. #2093C22semidirect
98. #2092C22semidirect
99. #2085C22semidirect
100. #2085C22semidirect
101. #2085C22semidirect
102. #2085C22semidirect
105. #2077C22semidirect
108. #2075C22semidirect
117. #2042C22semidirect
118. #2042C22semidirect
121. #2035C22semidirect
125. #2034C22semidirect
127. #2024C22semidirect
128. #2023C22semidirect
137. #1993C22semidirect
138. #1993C22semidirect
147. #1949C22semidirect
148. #1948C22semidirect
151. #1928C22semidirect
156. #1925C22semidirect
157. #1924C22semidirect
158. #1924C22semidirect
159. #1921C22semidirect
160. #1920C22semidirect
161. #1919C22semidirect
162. #1919C22semidirect
163. #1918C22semidirect
164. #1918C22semidirect
165. #1917C22semidirect
166. #1916C22semidirect
168. #1895C22semidirect
170. #1892C22semidirect
176. #1875C22semidirect
178. #1873C22semidirect
180. #1870C22semidirect
182. #1869C22semidirect
183. #1854C22semidirect
184. #1854C22semidirect
185. #1854C22semidirect
188. #1852C22semidirect
189. #1847C22semidirect
190. #1847C22semidirect
191. #1846C22semidirect
192. #1836C22semidirect
194. #1805C22semidirect
195. #1804C22semidirect
198. #1763C22semidirect
199. C4×#102C22semidirect
200. #1753C22semidirect
201. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#399292
#395032
#327752
#323912
#323842
#320672
#320642
#319612
#319592
#310322
#310282
#307222
#307042
#304202
#304002
#289922
#289902
#283122
#279462
#279352
#278822
#275882
#270932
#270722
#261522
#261472
#261332
#261272
#250292
#250192
#223352