Finite Group Databasebeta

← #6695082

Subgroups — #6695082

Order 512.

1641 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42615C211yesmaximal, characteristic, complemented
2#35987C211yesmaximal, characteristic, complemented
3#32968C211yesmaximal, characteristic, complemented
4#32467C211yesmaximal, characteristic, complemented
5#32308C211yesmaximal, characteristic, complemented
6#31996C211yesmaximal, characteristic, complemented
7#31930C211yesmaximal, characteristic, complemented
8#31588C211yesmaximal, characteristic, complemented
9#31552C211yesmaximal, characteristic, complemented
10#31153C211yesmaximal, characteristic, complemented
11#31105C211yesmaximal, characteristic, complemented
12#30373C211yesmaximal, characteristic, complemented
13#30022C211yesmaximal, characteristic, complemented
14#29029C211yesmaximal, characteristic, complemented
15#28847C211yesmaximal, characteristic, complemented
16#27539C211yesmaximal, characteristic, complemented
17#27526C211yesmaximal, characteristic, complemented
18#27317C211yesmaximal, characteristic, complemented
19#26571C211yesmaximal, characteristic, complemented
20#26390C211yesmaximal, characteristic, complemented
21#26184C211yesmaximal, characteristic, complemented
22#26106C211yesmaximal, characteristic, complemented
23#25960C211yesmaximal, characteristic, complemented
24#24913C211yesmaximal, characteristic, complemented
25#24911C211yesmaximal, characteristic, complemented
26#24257C211yesmaximal, characteristic
27#24039C211yesmaximal, characteristic, complemented
28#22870C211yesmaximal, characteristic, complemented
29#22676C211yesmaximal, characteristic, complemented
30#22362C211yesmaximal, characteristic, complemented
31#21460C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#479C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#449C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#442C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×D8C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2827—21no—
46#2770—21no—
47#2695—21no—
48#2694—21no—
49#2691—21no—
50#2646—21no—
51#2633—21no—
52#2629C2211yescharacteristic, complemented
53#2624C2211yescharacteristic
54#2623—21no—
55#2552C2211yescharacteristic, complemented
56#2537C2211yescharacteristic
57#2507C2211yescharacteristic, complemented
58#2501C2211yescharacteristic
59#2498—21no—
60#2496C2211yescharacteristic
61#2495C2211yescharacteristic, complemented
62#2487C2211yescharacteristic
63#2487C2211yescharacteristic
64#2482—21no—
65#2454C2211yescharacteristic, complemented
66#2448C2211yescharacteristic
67#2448C2211yescharacteristic
68#2443—21no—
69#2443—21no—
70#2442C2211yescharacteristic
71#2425—21no—
72#2423C2211yescharacteristic
73#2423C2211yescharacteristic
74#2422C2211yescharacteristic
75#2422C2211yescharacteristic, complemented
76#2418—21no—
77#2418—21no—
78#2395C2211yescharacteristic
79C2×#399—21no—
80#2361C2211yescharacteristic
81#2349C2211yescharacteristic, complemented
82D4×C4⋊C4C2211yescharacteristic
83D4×C4⋊C4C2211yescharacteristic
84#2339C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87#2324C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2096C2211yescharacteristic, complemented
92#2094C2211yescharacteristic
93#2093C2211yescharacteristic, complemented
94#2092C2211yescharacteristic
95#2086C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2086C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic, complemented
105#2077C2211yescharacteristic, complemented
106#2077C2211yescharacteristic, complemented
107#2074C2211yescharacteristic, complemented
108#2071C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic, complemented
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic, complemented
114#2059C2211yescharacteristic, complemented
115#2055C2211yescharacteristic, complemented
116#2054C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2035C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic, complemented
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2025C2211yescharacteristic
126#2000C2211yescharacteristic
127#1999C2211yescharacteristic
128#1970C2211yescharacteristic
129#1959C2211yescharacteristic
130#1955C2211yescharacteristic
131#1947C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1944C2211yescharacteristic, complemented
134#1944C2211yescharacteristic, complemented
135#1941C2211yescharacteristic, complemented
136#1939C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1935C2211yescharacteristic, complemented
140#1934C2211yescharacteristic
141#1933C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1926C2211yescharacteristic
144#1925C2211yescharacteristic
145#1924C2211yescharacteristic
146#1924C2211yescharacteristic
147#1924C2211yescharacteristic, complemented
148#1923C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1917C2211yescharacteristic, complemented
151#1917C2211yescharacteristic, complemented
152#1893C2211yescharacteristic
153#1892C2211yescharacteristic
154#1880C2211yescharacteristic, complemented
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1877C2211yescharacteristic, complemented
160#1874C2211yescharacteristic, complemented
161#1869C2211yescharacteristic
162#1865C2211yescharacteristic, complemented
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic, complemented
168#1864C2211yescharacteristic, complemented
169#1863C2211yescharacteristic, complemented
170#1863C2211yescharacteristic, complemented
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic, complemented
176#1853C2211yescharacteristic, complemented
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic, complemented
180#1852C2211yescharacteristic, complemented
181#1850C2211yescharacteristic
182#1847C2211yescharacteristic, complemented
183#1834C2211yescharacteristic, complemented
184#1807C2211yescharacteristic
185#1804C2211yescharacteristic
186#1803C2211yescharacteristic, complemented
187#1802C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic, complemented
191#1798C2211yescharacteristic, complemented
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1771C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1750C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#546—42no—
210#546—42no—
211C2×#126—21no—
212C2×#125—21no—
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×#121—21no—
222C2×#121—21no—
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#120—21no—
227#520—42no—
228#520—42no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117—21no—
244C2×#117C2311yescharacteristic
245C22×C4⋊C4—21no—
246C22×C4⋊C4—21no—
247C22×C4⋊C4—21no—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253#484—42no—
254#479—42no—
255#478—42no—
256#463—42no—
257#449—24no—
258#447—24no—
259#442—24no—
260#442—42no—
261#440—42no—
262C4×D8—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102—42no—
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400D411yescharacteristic
326#399—21no—
327#399—21no—
328#399—21no—
329#399—21no—
330#399—21no—
331#399—21no—
332#399—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#399D411yescharacteristic
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398D411yescharacteristic
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397D411yescharacteristic
355#397D411yescharacteristic
356#397D411yescharacteristic
357#396—21no—
358#396—21no—
359#396—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394D411yescharacteristic
367#394D411yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389—21no—
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
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#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#383—21no—
434#382C2311yescharacteristic
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#379—21no—
451#379—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C2×#95—21no—
460C2×#95—21no—
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
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8C2411yescharacteristic
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
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×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—41no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8#4114yes—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549#126—82no—
550#125—41no—
551#125—41no—
552#125—82no—
553#124—22no—
554#124—41no—
555#123—44no—
556#123—82no—
557#123—82no—
558#123—82no—
559#123—82no—
560C22⋊Q8—22no—
561C22⋊Q8—41no—
562#121—22no—
563#121—22no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—41no—
568#121—44no—
569#121—82no—
570#120—44no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
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—41no—
592C4×D4—41no—
593C4×D4—44no—
594C4×D4—44no—
595C4×D4—82no—
596#117—41no—
597#117—41no—
598#117—44no—
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—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—44no—
633C2×C4⋊C4—82no—
634C2×C4⋊C4—82no—
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—44no—
689C2×C22⋊C4—82no—
690C2×C22⋊C4—82no—
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710#107—41no—
711#107—41no—
712#107—41no—
713#107—41no—
714#107—41no—
715#107—41no—
716#106—22no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—41no—
733#103—41no—
734#103—41no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754C22⋊C8—22no—
755C22⋊C8—22no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761#97—22no—
762#97—41no—
763#97—41no—
764C4×C8—41no—
765C4×C8—41no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—21no—
806C24—21no—
807C24—42no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816#41—44no—
817#41—44no—
818#41—44no—
819#41—44no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8H(5,𝔽2)12yes—
826C2×D4—24no—
827C2×D4—22no—
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—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—41no—
843C2×D4—41no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—44no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—82no—
855C2×D4—82no—
856C2×D4—82no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4C2×#4112yes—
863C2×D4C2×#4112yes—
864C2×D4H(5,𝔽2)12yes—
865C2×D42−1+412yes—
866C22×C4—24no—
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—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
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—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
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×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C2511yescharacteristic
937SD16—44no—
938D8—28no—
939D8—82no—
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—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—82no—
964C2×C8C2×#4112yes—
965C4⋊C4—22no—
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—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—42no—
1080C42—42no—
1081C42—42no—
1082C42—81no—
1083C23—21no—
1084C23—21no—
1085C23—22no—
1086C23—21no—
1087C23—22no—
1088C23—21no—
1089C23—22no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—22no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
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—84no—
1118C23—84no—
1119C23—84no—
1120C23—84no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23#57712yes—
1125C23C23×D411yescharacteristic
1126Q8—22no—
1127Q8—22no—
1128Q8—41no—
1129Q8—41no—
1130D4—22no—
1131D4—22no—
1132D4—22no—
1133D4—22no—
1134D4—22no—
1135D4—48no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—82no—
1143D4—84no—
1144D4—84no—
1145D4—162no—
1146D4—162no—
1147D4#53914yes—
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—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—22no—
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—48no—
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—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—84no—
1232C2×C4—84no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4#57612yes—
1242C2×C4C22×#4111yescharacteristic
1243C2×C4C2×H(5,𝔽2)11yescharacteristic
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4C2×2−1+411yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C8—22no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C22—22no—
1257C22—24no—
1258C22—22no—
1259C22—22no—
1260C22—42no—
1261C22—42no—
1262C22—41no—
1263C22—41no—
1264C22—42no—
1265C22—42no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—41no—
1270C22—42no—
1271C22—41no—
1272C22—41no—
1273C22—42no—
1274C22—41no—
1275C22—42no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—168no—
1292C22D4×#4111yescharacteristic
1293C22#348411yescharacteristic
1294C22#348911yescharacteristic
1295C22C2×#57611yescharacteristic
1296C22C2×#57711yescharacteristic
1297C22#358511yescharacteristic
1298C22#358611yescharacteristic
1299C4—22no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—42no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4C2×#53911yescharacteristic
1325C4#351311yescharacteristic
1326C4#353311yescharacteristic
1327C4#353511yescharacteristic
1328C2—42no—
1329C2—44no—
1330C2—81no—
1331C2—82no—
1332C2—161no—
1333C2#3771211yescharacteristic
1334C2#6149611yescharacteristic
1335C2#6150911yescharacteristic
1336C2#6162011yescharacteristic
1337C2#6168811yescharacteristic
1338C2#6215511yescharacteristic
1339C2#6216611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24257C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42615C2semidirect
2. #35987C2semidirect
3. #32968C2semidirect
4. #32467C2semidirect
5. #32308C2semidirect
6. #31996C2semidirect
7. #31930C2semidirect
8. #31588C2semidirect
9. #31552C2semidirect
10. #31153C2semidirect
11. #31105C2semidirect
12. #30373C2semidirect
13. #30022C2semidirect
14. #29029C2semidirect
15. #28847C2semidirect
16. #27539C2semidirect
17. #27526C2semidirect
18. #27317C2semidirect
19. #26571C2semidirect
20. #26390C2semidirect
21. #26184C2semidirect
22. #26106C2semidirect
23. #25960C2semidirect
24. #24913C2semidirect
25. #24911C2semidirect
27. #24039C2semidirect
28. #22870C2semidirect
29. #22676C2semidirect
30. #22362C2semidirect
31. #21460C2semidirect
35. C2×#479C22semidirect
42. C2×#440C22semidirect
52. #2629C22semidirect
55. #2552C22semidirect
57. #2507C22semidirect
61. #2495C22semidirect
65. #2454C22semidirect
75. #2422C22semidirect
81. #2349C22semidirect
87. #2324C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2099C22semidirect
91. #2096C22semidirect
93. #2093C22semidirect
95. #2086C22semidirect
96. #2086C22semidirect
97. #2086C22semidirect
98. #2084C22semidirect
99. #2084C22semidirect
100. #2083C22semidirect
104. #2077C22semidirect
105. #2077C22semidirect
106. #2077C22semidirect
107. #2074C22semidirect
110. #2066C22semidirect
113. #2065C22semidirect
114. #2059C22semidirect
115. #2055C22semidirect
122. #2034C22semidirect
131. #1947C22semidirect
132. #1944C22semidirect
133. #1944C22semidirect
134. #1944C22semidirect
135. #1941C22semidirect
136. #1939C22semidirect
139. #1935C22semidirect
141. #1933C22semidirect
142. #1927C22semidirect
147. #1924C22semidirect
148. #1923C22semidirect
149. #1920C22semidirect
150. #1917C22semidirect
151. #1917C22semidirect
154. #1880C22semidirect
159. #1877C22semidirect
160. #1874C22semidirect
162. #1865C22semidirect
167. #1864C22semidirect
168. #1864C22semidirect
169. #1863C22semidirect
170. #1863C22semidirect
175. #1862C22semidirect
176. #1853C22semidirect
179. #1852C22semidirect
180. #1852C22semidirect
182. #1847C22semidirect
183. #1834C22semidirect
186. #1803C22semidirect
190. #1802C22semidirect
191. #1798C22semidirect
197. #1771C22semidirect
199. C4×#103C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#426152
#359872
#329682
#324672
#323082
#319962
#319302
#315882
#315522
#311532
#311052
#303732
#300222
#290292
#288472
#275392
#275262
#273172
#265712
#263902
#261842
#261062
#259602
#249132
#249112
#242572
#240392
#228702
#226762
#223622
#214602