Finite Group Databasebeta

← #6552524

Subgroups — #6552524

Order 512.

1898 conjugacy classes of subgroups.

The subgroup lattice has 1395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3339C211yesmaximal, characteristic, complemented
2C2×#3307C211yesmaximal, characteristic, complemented
3#38092C211yesmaximal, characteristic, complemented
4#34466C211yesmaximal, characteristic, complemented
5#29836C211yesmaximal, characteristic, complemented
6#29768C211yesmaximal, characteristic, complemented
7#29762C211yesmaximal, characteristic, complemented
8#28664C211yesmaximal, characteristic, complemented
9#28292C211yesmaximal, characteristic, complemented
10#28127C211yesmaximal, characteristic, complemented
11#28119C211yesmaximal, characteristic, complemented
12#25457C211yesmaximal, characteristic, complemented
13#25289C211yesmaximal, characteristic, complemented
14#25225C211yesmaximal, characteristic, complemented
15#25205C211yesmaximal, characteristic, complemented
16#25087C211yesmaximal, characteristic, complemented
17#25087C211yesmaximal, characteristic, complemented
18#24823C211yesmaximal, characteristic, complemented
19#24763C211yesmaximal, characteristic, complemented
20#24754C211yesmaximal, characteristic, complemented
21#24727C211yesmaximal, characteristic, complemented
22#24586C211yesmaximal, characteristic, complemented
23#24577C211yesmaximal, characteristic, complemented
24#24488C211yesmaximal, characteristic, complemented
25#24486C211yesmaximal, characteristic, complemented
26#23688C211yesmaximal, characteristic, complemented
27#23611C211yesmaximal, characteristic, complemented
28#23609C211yesmaximal, characteristic, complemented
29#22647C211yesmaximal, characteristic, complemented
30#22498C211yesmaximal, characteristic, complemented
31#22417C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#547C2211yescharacteristic
35#3339—28no—
36#3307—28no—
37C2×#499C2211yescharacteristic
38C2×#491C2211yescharacteristic
39C2×#481C2211yescharacteristic
40C2×#481C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#482C2211yescharacteristic
43C2×#482C2211yescharacteristic
44C2×#483C2211yescharacteristic
45C2×#478C2211yescharacteristic
46C2×#478C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#468C2211yescharacteristic
49C2×#466C2211yescharacteristic
50C2×#466C2211yescharacteristic
51C2×#465C2211yescharacteristic
52C2×#463C2211yescharacteristic
53C2×#463C2211yescharacteristic
54C2×#461C2211yescharacteristic
55C2×#449C2211yescharacteristic
56C2×#449C2211yescharacteristic
57C2×#442C2211yescharacteristic
58C2×C4×D8C2211yescharacteristic
59C2×#435C2211yescharacteristic
60C2×C8×D4C2211yescharacteristic
61C2×#427C2211yescharacteristic
62C22×#107C2211yescharacteristic
63C2×#424C2211yescharacteristic
64C22×C4⋊C8C2211yescharacteristic
65C2×#417C2211yescharacteristic
66C2×#416C2211yescharacteristic
67C2×#416C2211yescharacteristic
68C2×#416C2211yescharacteristic
69#2850C2211yescharacteristic
70#2693—21no—
71#2693—21no—
72#2688—21no—
73#2688—21no—
74#2642C2211yescharacteristic
75#2620C2211yescharacteristic
76#2566C2211yescharacteristic
77#2547C2211yescharacteristic
78#2503C2211yescharacteristic
79#2499C2211yescharacteristic
80#2481—21no—
81#2481—21no—
82#2457—21no—
83#2457—21no—
84#2431C2211yescharacteristic
85#2431C2211yescharacteristic
86#2377—21no—
87#2376—21no—
88#2373—21no—
89#2370C2211yescharacteristic
90#2363C2211yescharacteristic
91#2363C2211yescharacteristic
92#2354C2211yescharacteristic
93#2352—21no—
94D4×C4⋊C4C2211yescharacteristic
95#2346C2211yescharacteristic
96#2344C2211yescharacteristic
97#2334—21no—
98#2330C2211yescharacteristic
99#2328C2211yescharacteristic
100#2324—21no—
101#2324C2211yescharacteristic
102#2322—21no—
103#2319—21no—
104#2319C2211yescharacteristic
105#2316C2211yescharacteristic
106#2311C2211yescharacteristic
107C4×#121C2211yescharacteristic
108#2297C2211yescharacteristic
109#2296C2211yescharacteristic
110#2290C2211yescharacteristic
111#2085C2211yescharacteristic
112#2085C2211yescharacteristic
113#2085C2211yescharacteristic
114#2084C2211yescharacteristic
115#2084C2211yescharacteristic
116#2073C2211yescharacteristic
117#2068C2211yescharacteristic
118#2068C2211yescharacteristic
119#2068C2211yescharacteristic
120#2068C2211yescharacteristic
121#2068C2211yescharacteristic
122#2068C2211yescharacteristic
123#2068C2211yescharacteristic
124#2067C2211yescharacteristic
125#2067C2211yescharacteristic
126#2067C2211yescharacteristic
127#2067C2211yescharacteristic
128#2067C2211yescharacteristic
129#2067C2211yescharacteristic
130#2066C2211yescharacteristic
131#2066C2211yescharacteristic
132#2066C2211yescharacteristic
133#2066C2211yescharacteristic
134#2066C2211yescharacteristic
135#2065C2211yescharacteristic
136#2065C2211yescharacteristic
137#2065C2211yescharacteristic
138#2065C2211yescharacteristic
139#2055C2211yescharacteristic
140#2055C2211yescharacteristic
141#2055C2211yescharacteristic
142#2055C2211yescharacteristic
143#2054C2211yescharacteristic
144#2054C2211yescharacteristic
145#2042C2211yescharacteristic
146#2042C2211yescharacteristic
147#2042C2211yescharacteristic
148#2042C2211yescharacteristic
149#2041C2211yescharacteristic
150#2011C2211yescharacteristic
151#1992C2211yescharacteristic
152#1989C2211yescharacteristic
153#1983C2211yescharacteristic
154#1983C2211yescharacteristic
155#1982C2211yescharacteristic
156#1982C2211yescharacteristic
157#1981C2211yescharacteristic
158#1956C2211yescharacteristic
159#1949C2211yescharacteristic
160#1949C2211yescharacteristic
161#1949C2211yescharacteristic
162#1947C2211yescharacteristic
163#1940C2211yescharacteristic
164#1939C2211yescharacteristic
165#1928C2211yescharacteristic
166#1928C2211yescharacteristic
167#1928C2211yescharacteristic
168#1927C2211yescharacteristic
169#1927C2211yescharacteristic
170#1927C2211yescharacteristic
171#1926C2211yescharacteristic
172#1926C2211yescharacteristic
173#1895C2211yescharacteristic
174#1893C2211yescharacteristic
175#1892C2211yescharacteristic
176#1892C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1875C2211yescharacteristic
182#1875C2211yescharacteristic
183#1873C2211yescharacteristic
184#1873C2211yescharacteristic
185#1851C2211yescharacteristic
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic
189#1843C2211yescharacteristic
190#1825C2211yescharacteristic
191#1823C2211yescharacteristic
192#1804C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1798C2211yescharacteristic
197#1797C2211yescharacteristic
198#1788C2211yescharacteristic
199#1788C2211yescharacteristic
200#1768C2211yescharacteristic
201#1762C2211yescharacteristic
202C4×#102C2211yescharacteristic
203#1736C2211yescharacteristic
204#1735C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C22×#41C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#553—24no—
216#553—24no—
217#553—24no—
218#553D418yescomplemented
219#547—24no—
220#547—24no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#126—21no—
224C2×#126—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4—21no—
258C22×C4⋊C4—21no—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C42C2311yescharacteristic
262#499—24no—
263#491—24no—
264#485—24no—
265#483—24no—
266#482—24no—
267#482—24no—
268#481—24no—
269#481—24no—
270#478—24no—
271#478—24no—
272#478—24no—
273#468—24no—
274#466—24no—
275#466—24no—
276#465—24no—
277#463—42no—
278#463—42no—
279#461—24no—
280#449—24no—
281#449—24no—
282#442—24no—
283C4×D8—24no—
284#435—24no—
285C8×D4—24no—
286#427—24no—
287C2×#107—24no—
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300#424—42no—
301C2×C4⋊C8—42no—
302C2×C4⋊C8C2311yescharacteristic
303C2×C4⋊C8C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314#417—24no—
315#416—24no—
316#416—42no—
317#416—42no—
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353C2×C22⋊C8C2311yescharacteristic
354C2×#97C2311yescharacteristic
355C2×C4×C8C2311yescharacteristic
356#400—21no—
357#400—21no—
358#400—21no—
359#400—21no—
360#400—21no—
361#400—21no—
362#397—21no—
363#397—21no—
364#397—21no—
365#397—21no—
366#396—21no—
367#396—21no—
368#396—21no—
369#396—21no—
370#394—21no—
371#394—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388D411yescharacteristic
418#388D411yescharacteristic
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387D411yescharacteristic
428#387D411yescharacteristic
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386D411yescharacteristic
448#386D411yescharacteristic
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385D411yescharacteristic
457#385D411yescharacteristic
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#382—21no—
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#381—21no—
464#381—21no—
465#381—21no—
466#381—21no—
467#380—21no—
468#380—21no—
469#380—21no—
470#380—21no—
471#380—21no—
472#380—21no—
473#380—21no—
474#380—21no—
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477C4×C4⋊C4—21no—
478C4×C4⋊C4—21no—
479C4×C4⋊C4—21no—
480C4×C4⋊C4—21no—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C22⋊C4—21no—
488C4×C22⋊C4—21no—
489C4×C22⋊C4—21no—
490C4×C22⋊C4—21no—
491C4×C22⋊C4—21no—
492C4×C22⋊C4C2311yescharacteristic
493C4×C22⋊C4C2311yescharacteristic
494#376—21no—
495#376C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41—41no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41—41no—
530C22×Q8C2411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4C2×D411yescharacteristic
541C22×D4C2411yescharacteristic
542C22×D4C2411yescharacteristic
543C22×D4C2411yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C2×D411yescharacteristic
554C23×C4C2×D411yescharacteristic
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—41no—
568C2×D8—41no—
569C2×M16—22no—
570C2×M16—41no—
571C2×M16—41no—
572C22×C8—22no—
573C22×C8—22no—
574C22×C8—22no—
575C22×C8—22no—
576C22×C8—22no—
577C22×C8—41no—
578C22×C8—41no—
579C22×C8—41no—
580C22×C8—41no—
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C4⋊Q8—22no—
590C4⋊Q8—22no—
591#127—22no—
592#127—41no—
593#126—28no—
594#126—44no—
595#125—22no—
596#125—22no—
597#125—22no—
598#125C2×D414yes—
599#124—41no—
600#124—41no—
601#124—41no—
602#124—41no—
603#123—28no—
604#123—44no—
605#123—44no—
606#123—44no—
607C22⋊Q8—22no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611#121—28no—
612#121—22no—
613#121—22no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121—22no—
618#121—44no—
619#121—44no—
620#121C2×D414yes—
621#121C2×D414yes—
622C4×D4—28no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—44no—
633C4×D4—82no—
634C4×D4C2×D414yes—
635C4×D4C2×D414yes—
636C4×D4#4114yes—
637#117—22no—
638#117—22no—
639#117—22no—
640#117—41no—
641#117—41no—
642#117—41no—
643#117—41no—
644#117—41no—
645#117—41no—
646#117—82no—
647#117C2×D414yes—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—44no—
674C2×C4⋊C4—82no—
675C2×C4⋊C4C2×D414yes—
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—41no—
743C2×C42—41no—
744C2×C42C2×D411yescharacteristic
745C2×C42C2×D411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751#107—22no—
752#107—22no—
753#107—22no—
754#107—22no—
755#107—22no—
756#107—22no—
757#106—22no—
758#106—22no—
759#106—22no—
760#106—22no—
761#106—22no—
762#106—22no—
763C4⋊C8—22no—
764C4⋊C8—22no—
765C4⋊C8—22no—
766C4⋊C8—22no—
767C4⋊C8—22no—
768C4⋊C8—41no—
769C4⋊C8—41no—
770C4⋊C8—41no—
771C4⋊C8—41no—
772C4⋊C8—41no—
773C4⋊C8—41no—
774C4⋊C8—41no—
775#103—22no—
776#103—22no—
777#103—22no—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—41no—
784#103—41no—
785#103—41no—
786#103—41no—
787#103—41no—
788#103—41no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—41no—
802#102—41no—
803#102—41no—
804#102—41no—
805#102—41no—
806#102—41no—
807C22⋊C8—22no—
808C22⋊C8—22no—
809C22⋊C8—22no—
810C22⋊C8—22no—
811#97—22no—
812C4×C8—22no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854C24—21no—
855C24—21no—
856C24—21no—
857C24C22×D411yescharacteristic
858C24C22×D411yescharacteristic
859#41—44no—
860#41—44no—
861#41—44no—
862#41—44no—
863#41—82no—
864#41—82no—
865#41—82no—
866#41—82no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×D4—24no—
880C2×D4—24no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4#12114yes—
922C2×D4C22×D412yes—
923C2×D42−1+412yes—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D412yes—
991C22×C4C22×D412yes—
992C22×C4C2×#4112yes—
993C22×C4C2×#4112yes—
994C22×C4C2511yescharacteristic
995SD16—82no—
996SD16—82no—
997D8—44no—
998D8—44no—
999M16—82no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—44no—
1024C2×C8—44no—
1025C2×C8—82no—
1026C2×C8H(5,𝔽2)12yes—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4#12114yes—
1073C4⋊C4C22×D412yes—
1074C4⋊C4C22×D412yes—
1075C4⋊C4C22×D412yes—
1076C22⋊C4—24no—
1077C22⋊C4—24no—
1078C22⋊C4—24no—
1079C22⋊C4—24no—
1080C22⋊C4—41no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—41no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4#12114yes—
1116C22⋊C4#12114yes—
1117C42—24no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—41no—
1127C42—41no—
1128C42—42no—
1129C42—42no—
1130C42—81no—
1131C42—81no—
1132C42—81no—
1133C42—81no—
1134C42—81no—
1135C42—81no—
1136C42C22×D412yes—
1137C42C2×#4112yes—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—22no—
1151C23—22no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23C2×#12112yes—
1172C23C2×#12112yes—
1173C23C23×D411yescharacteristic
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182D4—22no—
1183D4—22no—
1184D4—22no—
1185D4—22no—
1186D4—44no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—84no—
1196D4—84no—
1197D4—84no—
1198D4—84no—
1199D4—84no—
1200D4—162no—
1201D4—162no—
1202D4—162no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—44no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—84no—
1284C2×C4—84no—
1285C2×C4—84no—
1286C2×C4—84no—
1287C2×C4—84no—
1288C2×C4—82no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4C2×#12112yes—
1294C2×C4C2×#12112yes—
1295C2×C4C2×#12112yes—
1296C2×C4C2×#12112yes—
1297C2×C4C23×D411yescharacteristic
1298C2×C4C22×#4111yescharacteristic
1299C2×C4C2×H(5,𝔽2)11yescharacteristic
1300C2×C4C2×2−1+411yescharacteristic
1301C2×C4#58511yescharacteristic
1302C2×C4#58511yescharacteristic
1303C8—22no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C22—22no—
1312C22—22no—
1313C22—22no—
1314C22—22no—
1315C22—22no—
1316C22—22no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22C22×#12111yescharacteristic
1347C22#348911yescharacteristic
1348C22#349611yescharacteristic
1349C22#358411yescharacteristic
1350C22#358411yescharacteristic
1351C22#358411yescharacteristic
1352C22#358511yescharacteristic
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4#348811yescharacteristic
1379C4#348911yescharacteristic
1380C4#352011yescharacteristic
1381C4#352111yescharacteristic
1382C2—42no—
1383C2—42no—
1384C2—82no—
1385C2—82no—
1386C2—161no—
1387C2#3582111yescharacteristic
1388C2#6042211yescharacteristic
1389C2#6043011yescharacteristic
1390C2#6217111yescharacteristic
1391C2#6220711yescharacteristic
1392C2#6227611yescharacteristic
1393C2#6231311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3339C2semidirect
2. C2×#3307C2semidirect
3. #38092C2semidirect
4. #34466C2semidirect
5. #29836C2semidirect
6. #29768C2semidirect
7. #29762C2semidirect
8. #28664C2semidirect
9. #28292C2semidirect
10. #28127C2semidirect
11. #28119C2semidirect
12. #25457C2semidirect
13. #25289C2semidirect
14. #25225C2semidirect
15. #25205C2semidirect
16. #25087C2semidirect
17. #25087C2semidirect
18. #24823C2semidirect
19. #24763C2semidirect
20. #24754C2semidirect
21. #24727C2semidirect
22. #24586C2semidirect
23. #24577C2semidirect
24. #24488C2semidirect
25. #24486C2semidirect
26. #23688C2semidirect
27. #23611C2semidirect
28. #23609C2semidirect
29. #22647C2semidirect
30. #22498C2semidirect
31. #22417C2semidirect
218. #553D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33392
C2×#33072
#380922
#344662
#298362
#297682
#297622
#286642
#282922
#281272
#281192
#254572
#252892
#252252
#252052
#250872
#248232
#247632
#247542
#247272
#245862
#245772
#244882
#244862
#236882
#236112
#236092
#226472
#224982
#224172