Finite Group Databasebeta

← #7079772

Subgroups — #7079772

Order 512.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1337 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59272C211yesmaximal, characteristic, complemented
2#59047C211yesmaximal, characteristic, complemented
3#32237C211yesmaximal, characteristic, complemented
4#31948C211yesmaximal, characteristic, complemented
5#31915C211yesmaximal, characteristic, complemented
6#31830C211yesmaximal, characteristic, complemented
7#31755C211yesmaximal, characteristic, complemented
8#31552C211yesmaximal, characteristic, complemented
9#31530C211yesmaximal, characteristic, complemented
10#30908C211yesmaximal, characteristic, complemented
11#27717C211yesmaximal, characteristic, complemented
12#27610C211yesmaximal, characteristic, complemented
13#27554C211yesmaximal, characteristic, complemented
14#27204C211yesmaximal, characteristic, complemented
15#26684C211yesmaximal, characteristic, complemented
16#26643C211yesmaximal, characteristic, complemented
17#26421C211yesmaximal, characteristic, complemented
18#26346C211yesmaximal, characteristic, complemented
19#26136C211yesmaximal, characteristic, complemented
20#26037C211yesmaximal, characteristic, complemented
21#25207C211yesmaximal, characteristic, complemented
22#25108C211yesmaximal, characteristic
23#24824C211yesmaximal, characteristic, complemented
24#24526C211yesmaximal, characteristic, complemented
25#23966C211yesmaximal, characteristic, complemented
26#23936C211yesmaximal, characteristic, complemented
27C2×#2065C211yesmaximal, characteristic, complemented
28#22854C211yesmaximal, characteristic, complemented
29#22486C211yesmaximal, characteristic, complemented
30#22065C211yesmaximal, characteristic, complemented
31#21887C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#482C2211yescharacteristic, complemented
35C2×#479C2211yescharacteristic, complemented
36C2×#466C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×C8×D4C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×C4⋊C8C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2761—21no—
46#2753—21no—
47#2727—21no—
48#2721—21no—
49#2597—21no—
50#2566C2211yescharacteristic
51#2554—21no—
52#2552C2211yescharacteristic, complemented
53#2513C2211yescharacteristic
54#2512C2211yescharacteristic
55#2501—21no—
56#2501C2211yescharacteristic
57#2500C2211yescharacteristic
58#2490C2211yescharacteristic
59#2480—21no—
60#2479—21no—
61#2454C2211yescharacteristic, complemented
62#2448C2211yescharacteristic, complemented
63#2442C2211yescharacteristic
64#2441—21no—
65#2441C2211yescharacteristic, complemented
66#2426C2211yescharacteristic, complemented
67#2425—21no—
68#2423C2211yescharacteristic, complemented
69#2422C2211yescharacteristic
70#2416C2211yescharacteristic
71#2413—21no—
72#2412—21no—
73#2411—21no—
74#2408C2211yescharacteristic
75#2363C2211yescharacteristic
76#2363C2211yescharacteristic, complemented
77#2360C2211yescharacteristic
78#2359—21no—
79#2357C2211yescharacteristic
80#2352C2211yescharacteristic
81Q8×C4⋊C4C2211yescharacteristic, complemented
82#2342—21no—
83D4×C22⋊C4C2211yescharacteristic
84C4×#123C2211yescharacteristic
85C2×#390C2211yescharacteristic
86C2×#389C2211yescharacteristic
87#2285C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2099C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2092C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2073C2211yescharacteristic, complemented
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2067C2211yescharacteristic
103#2066C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic, complemented
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2034C2211yescharacteristic, complemented
117#2033C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic, complemented
123#2012C2211yescharacteristic
124#2012C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#1999C2211yescharacteristic
128#1992C2211yescharacteristic, complemented
129#1991C2211yescharacteristic, complemented
130#1989C2211yescharacteristic, complemented
131#1989C2211yescharacteristic, complemented
132#1989C2211yescharacteristic, complemented
133#1983C2211yescharacteristic, complemented
134#1983C2211yescharacteristic, complemented
135#1973C2211yescharacteristic
136#1970C2211yescharacteristic
137#1949C2211yescharacteristic, complemented
138#1940C2211yescharacteristic, complemented
139#1940C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic, complemented
142#1936C2211yescharacteristic, complemented
143#1934C2211yescharacteristic
144#1926C2211yescharacteristic, complemented
145#1925C2211yescharacteristic
146#1924C2211yescharacteristic, complemented
147#1924C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1918C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1916C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1893C2211yescharacteristic
157#1893C2211yescharacteristic
158#1893C2211yescharacteristic
159#1892C2211yescharacteristic
160#1892C2211yescharacteristic
161#1892C2211yescharacteristic, complemented
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1877C2211yescharacteristic
172#1875C2211yescharacteristic
173#1875C2211yescharacteristic
174#1874C2211yescharacteristic
175#1873C2211yescharacteristic, complemented
176#1872C2211yescharacteristic
177#1869C2211yescharacteristic
178#1865C2211yescharacteristic, complemented
179#1862C2211yescharacteristic
180#1854C2211yescharacteristic, complemented
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1850C2211yescharacteristic
184#1850C2211yescharacteristic, complemented
185#1850C2211yescharacteristic, complemented
186#1836C2211yescharacteristic, complemented
187#1825C2211yescharacteristic, complemented
188#1823C2211yescharacteristic
189#1823C2211yescharacteristic
190#1817C2211yescharacteristic
191#1805C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1803C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1802C2211yescharacteristic, complemented
197#1802C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic, complemented
200#1752C2211yescharacteristic
201#1735C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#552—24no—
212#552—42no—
213#529—24no—
214#529—42no—
215C2×#126—21no—
216C2×#126—21no—
217C2×#126—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×#123D411yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117—21no—
247C2×#117—21no—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4—21no—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C42C2311yescharacteristic
258#482—42no—
259#479—42no—
260#466—42no—
261#450—24no—
262#447—42no—
263#440—42no—
264C8×D4—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106—42no—
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8—42no—
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102—42no—
289C2×#102—42no—
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×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#399—21no—
321#399—21no—
322#399—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#392—21no—
348#391C2311yescharacteristic
349#390—21no—
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390—21no—
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
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#388D411yescharacteristic
397#388D411yescharacteristic
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387D411yescharacteristic
403#387D411yescharacteristic
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386D411yescharacteristic
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385D411yescharacteristic
418#384—21no—
419#384—21no—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#382—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#381—21no—
428#381D411yescharacteristic
429#380—21no—
430#380—21no—
431#380—21no—
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#379—21no—
437#379—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C2×#95—21no—
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8C2411yescharacteristic
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4C2×D411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×D8—22no—
527C2×D8—41no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C22×C8—22no—
533C22×C8—22no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
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—44no—
550#126—44no—
551#126—82no—
552#125—22no—
553#125—22no—
554#125—41no—
555#125—41no—
556#125—41no—
557#125—41no—
558#125—44no—
559#124—22no—
560#124—41no—
561#123—42no—
562#123—44no—
563#123—44no—
564#123—44no—
565#123—82no—
566#123—82no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—41no—
570C22⋊Q8#4114yes—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121—41no—
576#121—41no—
577#121—41no—
578#121—41no—
579#121—82no—
580#120—82no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—22no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—44no—
596#117—22no—
597#117—44no—
598#117—44no—
599#117—41no—
600#117—41no—
601#117—41no—
602#117—82no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
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—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—82no—
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
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—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—44no—
697C2×C22⋊C4—82no—
698C2×C22⋊C4—82no—
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725#107—22no—
726#107—22no—
727#107—41no—
728#107—41no—
729#106—22no—
730#106—22no—
731#106—41no—
732#106—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764C22⋊C8—22no—
765C22⋊C8—22no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769#97—41no—
770#97—41no—
771C4×C8—41no—
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
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8C2×#4112yes—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
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—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—44no—
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—82no—
852C2×D4—82no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D42−1+412yes—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—22no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—41no—
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×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C2×#4112yes—
922C22×C4H(5,𝔽2)12yes—
923C22×C4C2511yescharacteristic
924SD16—44no—
925SD16—82no—
926D8—82no—
927D8—82no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
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—44no—
953C2×C8—82no—
954C2×C8—82no—
955C4⋊C4—24no—
956C4⋊C4—22no—
957C4⋊C4—22no—
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—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—42no—
984C4⋊C4—42no—
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—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4C2×#4112yes—
1013C4⋊C4H(5,𝔽2)12yes—
1014C22⋊C4—24no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
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—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C42—22no—
1062C42—22no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—22no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
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—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—84no—
1115C23—84no—
1116C23—84no—
1117C23—84no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23#54612yes—
1122C23#57512yes—
1123C23#57612yes—
1124C23C23×D411yescharacteristic
1125Q8—22no—
1126Q8—22no—
1127Q8—41no—
1128Q8—41no—
1129D4—22no—
1130D4—22no—
1131D4—44no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—84no—
1143D4—84no—
1144D4—162no—
1145D4—162no—
1146D4—162no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
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—22no—
1165C2×C4—21no—
1166C2×C4—22no—
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—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—44no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—44no—
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—84no—
1231C2×C4—84no—
1232C2×C4—84no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4#54612yes—
1237C2×C4#57712yes—
1238C2×C4C22×#4111yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4C2×H(5,𝔽2)11yescharacteristic
1241C2×C4C2×2−1+411yescharacteristic
1242C2×C4#58511yescharacteristic
1243C2×C4#58511yescharacteristic
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—42no—
1262C22—41no—
1263C22—42no—
1264C22—41no—
1265C22—41no—
1266C22—42no—
1267C22—41no—
1268C22—81no—
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—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—168no—
1287C22#330914yes—
1288C22C2×#54611yescharacteristic
1289C22#348811yescharacteristic
1290C22#348911yescharacteristic
1291C22C2×#57511yescharacteristic
1292C22C2×#57611yescharacteristic
1293C22C2×#57711yescharacteristic
1294C22#358411yescharacteristic
1295C4—22no—
1296C4—22no—
1297C4—41no—
1298C4—41no—
1299C4—42no—
1300C4—41no—
1301C4—41no—
1302C4—42no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—42no—
1309C4—41no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4#352011yescharacteristic
1321C4#352111yescharacteristic
1322C4#353511yescharacteristic
1323C4#354211yescharacteristic
1324C2—24no—
1325C2—81no—
1326C2—82no—
1327C2—161no—
1328C2—161no—
1329C2#4397911yescharacteristic
1330C2C2×#330911yescharacteristic
1331C2#6117411yescharacteristic
1332C2#6198111yescharacteristic
1333C2#6206411yescharacteristic
1334C2#6213811yescharacteristic
1335C2#6220011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25108C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59272C2semidirect
2. #59047C2semidirect
3. #32237C2semidirect
4. #31948C2semidirect
5. #31915C2semidirect
6. #31830C2semidirect
7. #31755C2semidirect
8. #31552C2semidirect
9. #31530C2semidirect
10. #30908C2semidirect
11. #27717C2semidirect
12. #27610C2semidirect
13. #27554C2semidirect
14. #27204C2semidirect
15. #26684C2semidirect
16. #26643C2semidirect
17. #26421C2semidirect
18. #26346C2semidirect
19. #26136C2semidirect
20. #26037C2semidirect
21. #25207C2semidirect
23. #24824C2semidirect
24. #24526C2semidirect
25. #23966C2semidirect
26. #23936C2semidirect
27. C2×#2065C2semidirect
28. #22854C2semidirect
29. #22486C2semidirect
30. #22065C2semidirect
31. #21887C2semidirect
34. C2×#482C22semidirect
35. C2×#479C22semidirect
52. #2552C22semidirect
61. #2454C22semidirect
62. #2448C22semidirect
65. #2441C22semidirect
66. #2426C22semidirect
68. #2423C22semidirect
76. #2363C22semidirect
81. Q8×C4⋊C4C22semidirect
88. #2100C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2099C22semidirect
92. #2097C22semidirect
93. #2092C22semidirect
94. #2088C22semidirect
95. #2085C22semidirect
96. #2083C22semidirect
97. #2083C22semidirect
98. #2077C22semidirect
99. #2073C22semidirect
103. #2066C22semidirect
112. #2059C22semidirect
116. #2034C22semidirect
122. #2025C22semidirect
128. #1992C22semidirect
129. #1991C22semidirect
130. #1989C22semidirect
131. #1989C22semidirect
132. #1989C22semidirect
133. #1983C22semidirect
134. #1983C22semidirect
137. #1949C22semidirect
138. #1940C22semidirect
139. #1940C22semidirect
141. #1936C22semidirect
142. #1936C22semidirect
144. #1926C22semidirect
146. #1924C22semidirect
147. #1924C22semidirect
148. #1920C22semidirect
149. #1920C22semidirect
150. #1918C22semidirect
151. #1918C22semidirect
152. #1918C22semidirect
153. #1918C22semidirect
154. #1916C22semidirect
155. #1916C22semidirect
161. #1892C22semidirect
175. #1873C22semidirect
178. #1865C22semidirect
180. #1854C22semidirect
184. #1850C22semidirect
185. #1850C22semidirect
186. #1836C22semidirect
187. #1825C22semidirect
191. #1805C22semidirect
192. #1803C22semidirect
193. #1803C22semidirect
196. #1802C22semidirect
197. #1802C22semidirect
199. C4×#103C22semidirect
201. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#592722
#590472
#322372
#319482
#319152
#318302
#317552
#315522
#315302
#309082
#277172
#276102
#275542
#272042
#266842
#266432
#264212
#263462
#261362
#260372
#252072
#251082
#248242
#245262
#239662
#239362
C2×#20652
#228542
#224862
#220652
#218872