Finite Group Databasebeta

← #7618145

Subgroups — #7618145

Order 512.

1659 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59843C211yesmaximal, characteristic, complemented
2#59546C211yesmaximal, characteristic, complemented
3#32666C211yesmaximal, characteristic, complemented
4#32661C211yesmaximal, characteristic, complemented
5#32469C211yesmaximal, characteristic, complemented
6#31063C211yesmaximal, characteristic
7#29537C211yesmaximal, characteristic, complemented
8#29533C211yesmaximal, characteristic, complemented
9#28865C211yesmaximal, characteristic, complemented
10#28861C211yesmaximal, characteristic, complemented
11#28850C211yesmaximal, characteristic, complemented
12#28847C211yesmaximal, characteristic, complemented
13#28199C211yesmaximal, characteristic, complemented
14#28194C211yesmaximal, characteristic, complemented
15#28107C211yesmaximal, characteristic, complemented
16#28101C211yesmaximal, characteristic, complemented
17#27115C211yesmaximal, characteristic, complemented
18#27113C211yesmaximal, characteristic, complemented
19#27095C211yesmaximal, characteristic, complemented
20#27094C211yesmaximal, characteristic, complemented
21#24911C211yesmaximal, characteristic, complemented
22#24909C211yesmaximal, characteristic, complemented
23#24901C211yesmaximal, characteristic, complemented
24#24896C211yesmaximal, characteristic, complemented
25#22878C211yesmaximal, characteristic, complemented
26#22870C211yesmaximal, characteristic, complemented
27#22863C211yesmaximal, characteristic, complemented
28#22854C211yesmaximal, characteristic, complemented
29#21632C211yesmaximal, characteristic, complemented
30#21286C211yesmaximal, characteristic, complemented
31#21279C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#449C2211yescharacteristic
34C2×#449C2211yescharacteristic
35C2×#450C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×#446C2211yescharacteristic, complemented
38C2×#442C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C2×C4×D8C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#417C2211yescharacteristic, complemented
44C22×#102C2211yescharacteristic
45#2786—21no—
46#2743—21no—
47#2728—21no—
48#2697—21no—
49#2609—21no—
50#2581C2211yescharacteristic, complemented
51#2538C2211yescharacteristic
52#2538C2211yescharacteristic
53#2538C2211yescharacteristic, complemented
54#2526—21no—
55#2515—21no—
56#2497C2211yescharacteristic, complemented
57#2496C2211yescharacteristic
58#2496C2211yescharacteristic
59#2495C2211yescharacteristic, complemented
60#2486C2211yescharacteristic
61#2486C2211yescharacteristic
62#2480—21no—
63#2480—21no—
64#2471—21no—
65#2461—21no—
66#2457—21no—
67#2457—21no—
68#2438—21no—
69#2423C2211yescharacteristic
70#2422C2211yescharacteristic
71#2422C2211yescharacteristic
72#2420C2211yescharacteristic
73#2408C2211yescharacteristic
74#2407C2211yescharacteristic
75#2361C2211yescharacteristic
76#2361C2211yescharacteristic
77#2361C2211yescharacteristic
78#2360C2211yescharacteristic
79#2353—21no—
80#2341C2211yescharacteristic, complemented
81#2339C2211yescharacteristic, complemented
82D4×C22⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84C4×#124C2211yescharacteristic
85#2295C2211yescharacteristic, complemented
86#2293C2211yescharacteristic
87#2293C2211yescharacteristic
88#2293C2211yescharacteristic, complemented
89#2096C2211yescharacteristic, complemented
90#2094C2211yescharacteristic
91#2094C2211yescharacteristic, complemented
92#2092C2211yescharacteristic
93#2087C2211yescharacteristic, complemented
94#2087C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic, complemented
104#2077C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#1985C2211yescharacteristic, complemented
122#1973C2211yescharacteristic
123#1973C2211yescharacteristic
124#1972C2211yescharacteristic
125#1970C2211yescharacteristic
126#1955C2211yescharacteristic
127#1944C2211yescharacteristic, complemented
128#1944C2211yescharacteristic, complemented
129#1944C2211yescharacteristic, complemented
130#1941C2211yescharacteristic, complemented
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic, complemented
136#1936C2211yescharacteristic, complemented
137#1935C2211yescharacteristic, complemented
138#1935C2211yescharacteristic, complemented
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic, complemented
142#1933C2211yescharacteristic, complemented
143#1928C2211yescharacteristic, complemented
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic, complemented
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic, complemented
149#1923C2211yescharacteristic
150#1923C2211yescharacteristic, complemented
151#1920C2211yescharacteristic, complemented
152#1920C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1893C2211yescharacteristic
158#1892C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1865C2211yescharacteristic, complemented
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic, complemented
170#1863C2211yescharacteristic, complemented
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic, complemented
175#1852C2211yescharacteristic
176#1852C2211yescharacteristic
177#1852C2211yescharacteristic, complemented
178#1852C2211yescharacteristic, complemented
179#1836C2211yescharacteristic, complemented
180#1834C2211yescharacteristic, complemented
181#1831C2211yescharacteristic, complemented
182#1824C2211yescharacteristic, complemented
183#1823C2211yescharacteristic
184#1809C2211yescharacteristic, complemented
185#1807C2211yescharacteristic
186#1804C2211yescharacteristic
187#1803C2211yescharacteristic, complemented
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic, complemented
190#1788C2211yescharacteristic, complemented
191#1786C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193C4×#107C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic, complemented
196C4×#103C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1752C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202C4×#97C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#551—48no—
212C2×#126—21no—
213C2×#126—21no—
214C2×#124D411yescharacteristic
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#120—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117—21no—
242C2×#117—21no—
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247#450—24no—
248#449—24no—
249#449—24no—
250#447—24no—
251#446—42no—
252#442—24no—
253#440—42no—
254C4×SD16—24no—
255C4×D8—42no—
256#435—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#417—42no—
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#399—21no—
319#398—21no—
320#398—21no—
321#398—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#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#395—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#392—21no—
344#392—21no—
345#391D411yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#390—21no—
350#390—21no—
351#390D411yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#389—21no—
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#388—21no—
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#388D411yescharacteristic
387#388D411yescharacteristic
388#388D411yescharacteristic
389#388D411yescharacteristic
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#383—21no—
421#382D411yescharacteristic
422#382C2311yescharacteristic
423#381—21no—
424#381—21no—
425#381—21no—
426#381—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376—21no—
457C2×#95—21no—
458C43C2311yescharacteristic
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C25—21no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C2×D411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16#4114yes—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8#4114yes—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8—22no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552#126—44no—
553#126—44no—
554#124—24no—
555#123—44no—
556#123—44no—
557#123—44no—
558#123—82no—
559C22⋊Q8—22no—
560C22⋊Q8—41no—
561C22⋊Q8—44no—
562C22⋊Q8—44no—
563C22⋊Q8—82no—
564#121—22no—
565#121—22no—
566#121—22no—
567#121—41no—
568#121—41no—
569#121—41no—
570#120—44no—
571C4×Q8—22no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—44no—
592C4×D4—44no—
593C4×D4—44no—
594#117—44no—
595#117—44no—
596#117—82no—
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—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⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
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—44no—
677C2×C22⋊C4—44no—
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×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#106—22no—
710#106—22no—
711#106—41no—
712#106—41no—
713#106—41no—
714#106—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719#103—22no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—41no—
724#103—41no—
725#102—22no—
726#102—22no—
727#102—22no—
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—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749#97—22no—
750#97—22no—
751#97—22no—
752#97—41no—
753#97—41no—
754C4×C8—22no—
755C4×C8—22no—
756C4×C8—41no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24—21no—
799C24—21no—
800C24—42no—
801C24—42no—
802C24—42no—
803C24—81no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809#41—44no—
810#41—82no—
811#41—82no—
812#41—82no—
813C2×Q8—22no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—41no—
820C2×Q8—41no—
821C2×Q8C2×#4112yes—
822C2×D4—22no—
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—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—44no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—81no—
852C2×D4—82no—
853C2×D4—82no—
854C2×D4—82no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4C2×#4112yes—
860C2×D4C2×#4112yes—
861C2×D4C2×#4112yes—
862C22×C4—21no—
863C22×C4—21no—
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—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—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C2511yescharacteristic
927SD16—44no—
928SD16—44no—
929D8—44no—
930D8—44no—
931M16—82no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
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—82no—
954C2×C8C2×#4112yes—
955C2×C8C2×#4112yes—
956C2×C8H(5,𝔽2)12yes—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
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—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
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—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
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⋊C4AGL(1,ℤ/8)14yes—
1054C42—22no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—41no—
1066C42—41no—
1067C42—41no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—42no—
1072C42—81no—
1073C42—81no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—84no—
1109C23—84no—
1110C23—84no—
1111C23—162no—
1112C23—162no—
1113C23—162no—
1114C23—162no—
1115C23C2×AGL(1,ℤ/8)12yes—
1116C23C23×D411yescharacteristic
1117Q8—22no—
1118Q8—22no—
1119Q8—41no—
1120Q8—41no—
1121Q8—82no—
1122D4—22no—
1123D4—22no—
1124D4—22no—
1125D4—22no—
1126D4—22no—
1127D4—22no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—82no—
1135D4—84no—
1136D4—84no—
1137D4—84no—
1138D4—84no—
1139D4—84no—
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—22no—
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—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—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—84no—
1222C2×C4—84no—
1223C2×C4—84no—
1224C2×C4—84no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4C2×AGL(1,ℤ/8)12yes—
1231C2×C4C2×AGL(1,ℤ/8)12yes—
1232C2×C4C22×#4111yescharacteristic
1233C2×C4C22×#4111yescharacteristic
1234C2×C4C2×H(5,𝔽2)11yescharacteristic
1235C2×C4#58511yescharacteristic
1236C2×C4#58511yescharacteristic
1237C2×C4#58511yescharacteristic
1238C8—22no—
1239C8—22no—
1240C8—22no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—42no—
1254C22—41no—
1255C22—42no—
1256C22—41no—
1257C22—42no—
1258C22—41no—
1259C22—42no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—41no—
1268C22—42no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—168no—
1282C22D4×#4111yescharacteristic
1283C22D4×#4111yescharacteristic
1284C22#349611yescharacteristic
1285C22C22×AGL(1,ℤ/8)11yescharacteristic
1286C22#358411yescharacteristic
1287C22#358511yescharacteristic
1288C22#358611yescharacteristic
1289C4—22no—
1290C4—22no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—42no—
1301C4—41no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4#348111yescharacteristic
1315C4#349111yescharacteristic
1316C4#349111yescharacteristic
1317C4#354511yescharacteristic
1318C2—42no—
1319C2—81no—
1320C2—82no—
1321C2—82no—
1322C2—82no—
1323C2#5983611yescharacteristic
1324C2#6143711yescharacteristic
1325C2#6145211yescharacteristic
1326C2#6151011yescharacteristic
1327C2#6153111yescharacteristic
1328C2#6229911yescharacteristic
1329C2#6234811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#31063C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59843C2semidirect
2. #59546C2semidirect
3. #32666C2semidirect
4. #32661C2semidirect
5. #32469C2semidirect
7. #29537C2semidirect
8. #29533C2semidirect
9. #28865C2semidirect
10. #28861C2semidirect
11. #28850C2semidirect
12. #28847C2semidirect
13. #28199C2semidirect
14. #28194C2semidirect
15. #28107C2semidirect
16. #28101C2semidirect
17. #27115C2semidirect
18. #27113C2semidirect
19. #27095C2semidirect
20. #27094C2semidirect
21. #24911C2semidirect
22. #24909C2semidirect
23. #24901C2semidirect
24. #24896C2semidirect
25. #22878C2semidirect
26. #22870C2semidirect
27. #22863C2semidirect
28. #22854C2semidirect
29. #21632C2semidirect
30. #21286C2semidirect
31. #21279C2semidirect
37. C2×#446C22semidirect
43. C2×#417C22semidirect
50. #2581C22semidirect
53. #2538C22semidirect
56. #2497C22semidirect
59. #2495C22semidirect
80. #2341C22semidirect
81. #2339C22semidirect
85. #2295C22semidirect
88. #2293C22semidirect
89. #2096C22semidirect
91. #2094C22semidirect
93. #2087C22semidirect
94. #2087C22semidirect
95. #2087C22semidirect
96. #2086C22semidirect
97. #2085C22semidirect
98. #2084C22semidirect
99. #2084C22semidirect
100. #2083C22semidirect
103. #2077C22semidirect
104. #2077C22semidirect
105. #2068C22semidirect
108. #2065C22semidirect
121. #1985C22semidirect
127. #1944C22semidirect
128. #1944C22semidirect
129. #1944C22semidirect
130. #1941C22semidirect
135. #1936C22semidirect
136. #1936C22semidirect
137. #1935C22semidirect
138. #1935C22semidirect
141. #1934C22semidirect
142. #1933C22semidirect
143. #1928C22semidirect
146. #1925C22semidirect
148. #1924C22semidirect
150. #1923C22semidirect
151. #1920C22semidirect
152. #1920C22semidirect
153. #1919C22semidirect
154. #1918C22semidirect
167. #1865C22semidirect
169. #1864C22semidirect
170. #1863C22semidirect
174. #1862C22semidirect
177. #1852C22semidirect
178. #1852C22semidirect
179. #1836C22semidirect
180. #1834C22semidirect
181. #1831C22semidirect
182. #1824C22semidirect
184. #1809C22semidirect
187. #1803C22semidirect
189. #1802C22semidirect
190. #1788C22semidirect
192. #1776C22semidirect
193. C4×#107C22semidirect
195. #1762C22semidirect
196. C4×#103C22semidirect
198. #1753C22semidirect
199. #1753C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#598432
#595462
#326662
#326612
#324692
#310632
#295372
#295332
#288652
#288612
#288502
#288472
#281992
#281942
#281072
#281012
#271152
#271132
#270952
#270942
#249112
#249092
#249012
#248962
#228782
#228702
#228632
#228542
#216322
#212862
#212792