Finite Group Databasebeta

← #6475155

Subgroups — #6475155

Order 512.

1552 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35037C211yesmaximal, characteristic, complemented
2#35025C211yesmaximal, characteristic, complemented
3#33279C211yesmaximal, characteristic, complemented
4#33266C211yesmaximal, characteristic, complemented
5#33143C211yesmaximal, characteristic, complemented
6#33057C211yesmaximal, characteristic, complemented
7#30381C211yesmaximal, characteristic, complemented
8#30356C211yesmaximal, characteristic, complemented
9#30340C211yesmaximal, characteristic, complemented
10#30320C211yesmaximal, characteristic, complemented
11#29079C211yesmaximal, characteristic, complemented
12#29065C211yesmaximal, characteristic, complemented
13#29018C211yesmaximal, characteristic, complemented
14#29000C211yesmaximal, characteristic, complemented
15#28787C211yesmaximal, characteristic, complemented
16#28570C211yesmaximal, characteristic, complemented
17#28357C211yesmaximal, characteristic, complemented
18#28110C211yesmaximal, characteristic, complemented
19#28089C211yesmaximal, characteristic, complemented
20#28061C211yesmaximal, characteristic, complemented
21#27726C211yesmaximal, characteristic, complemented
22#27281C211yesmaximal, characteristic, complemented
23#26982C211yesmaximal, characteristic, complemented
24#26844C211yesmaximal, characteristic, complemented
25#25261C211yesmaximal, characteristic, complemented
26#25132C211yesmaximal, characteristic
27#22077C211yesmaximal, characteristic, complemented
28#22040C211yesmaximal, characteristic, complemented
29#21540C211yesmaximal, characteristic, complemented
30#21095C211yesmaximal, characteristic, complemented
31C4×#436C211yesmaximal, characteristic, complemented
32C2×#489C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#469C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×#440C2211yescharacteristic, complemented
38C2×#436C2211yescharacteristic
39C2×#436C2211yescharacteristic
40C2×#418C2211yescharacteristic
41C2×#418C2211yescharacteristic
42C2×C4×M16C2211yescharacteristic
43C2×C4×M16C2211yescharacteristic, complemented
44#2864C2211yescharacteristic, complemented
45#2861C2211yescharacteristic
46#2860C2211yescharacteristic
47#2860C2211yescharacteristic, complemented
48#2857C2211yescharacteristic, complemented
49#2854C2211yescharacteristic
50#2854C2211yescharacteristic, complemented
51#2850C2211yescharacteristic
52#2653—21no—
53#2651—21no—
54#2648—21no—
55#2630—21no—
56#2594—21no—
57#2593—21no—
58#2560—21no—
59#2554—21no—
60#2513C2211yescharacteristic
61#2507C2211yescharacteristic, complemented
62#2500C2211yescharacteristic
63#2494C2211yescharacteristic, complemented
64#2490C2211yescharacteristic
65#2485C2211yescharacteristic
66#2480—21no—
67#2466—21no—
68#2463—21no—
69#2452C2211yescharacteristic, complemented
70#2448C2211yescharacteristic
71#2442C2211yescharacteristic
72#2439C2211yescharacteristic
73#2435C2211yescharacteristic
74#2426C2211yescharacteristic
75#2420C2211yescharacteristic, complemented
76#2418—21no—
77#2417C2211yescharacteristic
78#2414C2211yescharacteristic
79#2408C2211yescharacteristic
80#2335—21no—
81#2332—21no—
82#2321—21no—
83#2312—21no—
84C4×C22⋊Q8C2211yescharacteristic
85C4×#121C2211yescharacteristic
86#2296C2211yescharacteristic
87C2×#390C2211yescharacteristic
88C42×D4C2211yescharacteristic
89#2101C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2093C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic, complemented
94#2087C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2075C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2059C2211yescharacteristic, complemented
106#2057C2211yescharacteristic, complemented
107#2055C2211yescharacteristic, complemented
108#2054C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2036C2211yescharacteristic, complemented
112#2034C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2025C2211yescharacteristic, complemented
116#2023C2211yescharacteristic
117#2012C2211yescharacteristic
118#2012C2211yescharacteristic
119#2000C2211yescharacteristic, complemented
120#1999C2211yescharacteristic
121#1993C2211yescharacteristic, complemented
122#1991C2211yescharacteristic, complemented
123#1991C2211yescharacteristic, complemented
124#1972C2211yescharacteristic
125#1970C2211yescharacteristic
126#1970C2211yescharacteristic
127#1970C2211yescharacteristic
128#1970C2211yescharacteristic
129#1968C2211yescharacteristic, complemented
130#1959C2211yescharacteristic
131#1958C2211yescharacteristic
132#1958C2211yescharacteristic
133#1943C2211yescharacteristic, complemented
134#1942C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1942C2211yescharacteristic, complemented
137#1942C2211yescharacteristic, complemented
138#1941C2211yescharacteristic, complemented
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic, complemented
156#1934C2211yescharacteristic, complemented
157#1934C2211yescharacteristic, complemented
158#1933C2211yescharacteristic, complemented
159#1933C2211yescharacteristic, complemented
160#1933C2211yescharacteristic, complemented
161#1933C2211yescharacteristic, complemented
162#1933C2211yescharacteristic, complemented
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
165#1920C2211yescharacteristic, complemented
166#1918C2211yescharacteristic, complemented
167#1895C2211yescharacteristic
168#1895C2211yescharacteristic
169#1895C2211yescharacteristic
170#1895C2211yescharacteristic
171#1895C2211yescharacteristic, complemented
172#1894C2211yescharacteristic
173#1894C2211yescharacteristic, complemented
174#1894C2211yescharacteristic, complemented
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1874C2211yescharacteristic
178#1873C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1854C2211yescharacteristic
182#1852C2211yescharacteristic
183#1836C2211yescharacteristic, complemented
184#1825C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic, complemented
187#1786C2211yescharacteristic
188#1776C2211yescharacteristic, complemented
189#1770C2211yescharacteristic, complemented
190#1770C2211yescharacteristic, complemented
191C4×C4⋊C8C2211yescharacteristic, complemented
192#1763C2211yescharacteristic, complemented
193#1762C2211yescharacteristic, complemented
194#1753C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic, complemented
197#1753C2211yescharacteristic, complemented
198C4×C22⋊C8C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic, complemented
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202C42×C8C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4D411yescharacteristic
231C2×C4×D4D411yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C22⋊C4—21no—
238C22×C22⋊C4—21no—
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241#489—42no—
242#485—24no—
243#469—42no—
244#468—24no—
245#447—24no—
246#440—42no—
247#436—24no—
248#436—24no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260#418—24no—
261#418—42no—
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C4×M16—42no—
293C4×M16—42no—
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#401—21no—
307#400—21no—
308#399—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#393—21no—
335#393—21no—
336#392—21no—
337#392—21no—
338#391—21no—
339#391—21no—
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#390—21no—
343#390—21no—
344#390—21no—
345#390—21no—
346#390—21no—
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#389—21no—
360#389—21no—
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
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#388—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#384C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#381—21no—
429#380—21no—
430#380—21no—
431#380—21no—
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#379—21no—
439#379—21no—
440#379—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4D411yescharacteristic
445C4×C4⋊C4D411yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4D411yescharacteristic
452C4×C22⋊C4D411yescharacteristic
453C4×C22⋊C4D411yescharacteristic
454C4×C22⋊C4D411yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C43C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
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#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
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—22no—
499C22×D4—22no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4C2×D411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C2×SD16—22no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×D8—22no—
520C2×D8—22no—
521C2×D8—41no—
522C2×D8—41no—
523C2×D8—41no—
524C2×D8—41no—
525C2×M16—22no—
526C2×M16—22no—
527C2×M16—22no—
528C2×M16—22no—
529C2×M16—22no—
530C2×M16—41no—
531C2×M16—41no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16#4114yes—
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547#126—82no—
548#126—82no—
549#125—41no—
550#125—41no—
551#124—41no—
552#124—41no—
553#124—41no—
554#124—41no—
555#123—44no—
556#123—82no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—44no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—82no—
563#121—22no—
564#121—22no—
565#121—41no—
566#121—41no—
567#121—41no—
568#121—41no—
569#121—41no—
570#121—41no—
571#120—44no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—42no—
577C4×D4—42no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—82no—
581#117—22no—
582#117—22no—
583#117—41no—
584#117—41no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
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—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
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—44no—
669C2×C22⋊C4—82no—
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—41no—
682C2×C42—41no—
683C2×C42—41no—
684C2×C42—41no—
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698#107—22no—
699#107—22no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#106—22no—
705#106—41no—
706#106—41no—
707C4⋊C8—22no—
708C4⋊C8—22no—
709#103—22no—
710#103—22no—
711#103—22no—
712#103—22no—
713#103—41no—
714#103—41no—
715#103—41no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735C22⋊C8—22no—
736C22⋊C8—22no—
737C22⋊C8—22no—
738C22⋊C8#4114yes—
739#97—22no—
740#97—22no—
741#97—41no—
742#97—41no—
743C4×C8—22no—
744C4×C8—22no—
745C4×C8—22no—
746C4×C8—41no—
747C4×C8—41no—
748C4×C8—41no—
749C4×C8—41no—
750C4×C8—41no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789C24—21no—
790C24—21no—
791C24—21no—
792C24—42no—
793C24—42no—
794C24—42no—
795C24—81no—
796C24—81no—
797C24—81no—
798C24—81no—
799C24C22×D411yescharacteristic
800C24C22×D411yescharacteristic
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—42no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
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—41no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—82no—
839C2×D4—82no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C2×#4112yes—
904C22×C4C2×#4112yes—
905C22×C4C2511yescharacteristic
906SD16—44no—
907D8—82no—
908D8—82no—
909M16—44no—
910M16—44no—
911M16—44no—
912M16—44no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8C2×#4112yes—
933C2×C8C2×#4112yes—
934C2×C8C2×#4112yes—
935C2×C8C2×#4112yes—
936C2×C8H(5,𝔽2)12yes—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—41no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
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—
1036C42—22no—
1037C42—22no—
1038C42—22no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—41no—
1050C42—41no—
1051C42—41no—
1052C42—41no—
1053C42—41no—
1054C42—42no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—84no—
1094C23—84no—
1095C23—84no—
1096C23—162no—
1097C23—162no—
1098C23—162no—
1099C23—162no—
1100C23#53212yes—
1101C23C23×D411yescharacteristic
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—162no—
1107D4—44no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—84no—
1121D4—84no—
1122D4—162no—
1123D4—162no—
1124D4—162no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—82no—
1205C2×C4—82no—
1206C2×C4—82no—
1207C2×C4—82no—
1208C2×C4—162no—
1209C2×C4—162no—
1210C2×C4#53212yes—
1211C2×C4#57512yes—
1212C2×C4#57512yes—
1213C2×C4#57612yes—
1214C2×C4C22×#4111yescharacteristic
1215C2×C4C22×#4111yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4#58511yescharacteristic
1218C2×C4#58511yescharacteristic
1219C2×C4#58511yescharacteristic
1220C8—22no—
1221C8—22no—
1222C8—22no—
1223C8—22no—
1224C8—22no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—168no—
1264C22C2×#53211yescharacteristic
1265C22#349611yescharacteristic
1266C22#350011yescharacteristic
1267C22C2×#57511yescharacteristic
1268C22C2×#57511yescharacteristic
1269C22C2×#57611yescharacteristic
1270C22#358411yescharacteristic
1271C4—22no—
1272C4—22no—
1273C4—22no—
1274C4—22no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4#345511yescharacteristic
1297C4#345911yescharacteristic
1298C4#351311yescharacteristic
1299C4#352111yescharacteristic
1300C2—42no—
1301C2—81no—
1302C2—161no—
1303C2—161no—
1304C2—161no—
1305C2#3500911yescharacteristic
1306C2#6069511yescharacteristic
1307C2#6070211yescharacteristic
1308C2#6226111yescharacteristic
1309C2#6226311yescharacteristic
1310C2#6254611yescharacteristic
1311C2#6254811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25132C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35037C2semidirect
2. #35025C2semidirect
3. #33279C2semidirect
4. #33266C2semidirect
5. #33143C2semidirect
6. #33057C2semidirect
7. #30381C2semidirect
8. #30356C2semidirect
9. #30340C2semidirect
10. #30320C2semidirect
11. #29079C2semidirect
12. #29065C2semidirect
13. #29018C2semidirect
14. #29000C2semidirect
15. #28787C2semidirect
16. #28570C2semidirect
17. #28357C2semidirect
18. #28110C2semidirect
19. #28089C2semidirect
20. #28061C2semidirect
21. #27726C2semidirect
22. #27281C2semidirect
23. #26982C2semidirect
24. #26844C2semidirect
25. #25261C2semidirect
27. #22077C2semidirect
28. #22040C2semidirect
29. #21540C2semidirect
30. #21095C2semidirect
31. C4×#436C2semidirect
37. C2×#440C22semidirect
43. C2×C4×M16C22semidirect
44. #2864C22semidirect
47. #2860C22semidirect
48. #2857C22semidirect
50. #2854C22semidirect
61. #2507C22semidirect
63. #2494C22semidirect
69. #2452C22semidirect
75. #2420C22semidirect
89. #2101C22semidirect
90. #2099C22semidirect
93. #2088C22semidirect
94. #2087C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2075C22semidirect
98. #2075C22semidirect
100. #2073C22semidirect
101. #2068C22semidirect
105. #2059C22semidirect
106. #2057C22semidirect
107. #2055C22semidirect
111. #2036C22semidirect
115. #2025C22semidirect
119. #2000C22semidirect
121. #1993C22semidirect
122. #1991C22semidirect
123. #1991C22semidirect
129. #1968C22semidirect
133. #1943C22semidirect
134. #1942C22semidirect
135. #1942C22semidirect
136. #1942C22semidirect
137. #1942C22semidirect
138. #1941C22semidirect
144. #1936C22semidirect
155. #1934C22semidirect
156. #1934C22semidirect
157. #1934C22semidirect
158. #1933C22semidirect
159. #1933C22semidirect
160. #1933C22semidirect
161. #1933C22semidirect
162. #1933C22semidirect
165. #1920C22semidirect
166. #1918C22semidirect
171. #1895C22semidirect
173. #1894C22semidirect
174. #1894C22semidirect
179. #1865C22semidirect
180. #1863C22semidirect
183. #1836C22semidirect
186. #1809C22semidirect
188. #1776C22semidirect
189. #1770C22semidirect
190. #1770C22semidirect
191. C4×C4⋊C8C22semidirect
192. #1763C22semidirect
193. #1762C22semidirect
196. #1753C22semidirect
197. #1753C22semidirect
199. C4×C22⋊C8C22semidirect
202. C42×C8C22semidirect

Maximal subgroups

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

subgroupindex
#350372
#350252
#332792
#332662
#331432
#330572
#303812
#303562
#303402
#303202
#290792
#290652
#290182
#290002
#287872
#285702
#283572
#281102
#280892
#280612
#277262
#272812
#269822
#268442
#252612
#251322
#220772
#220402
#215402
#210952
C4×#4362