Finite Group Databasebeta

← #6672589

Subgroups — #6672589

Order 512.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3244C211yesmaximal, characteristic, complemented
2C2×#3084C211yesmaximal, characteristic, complemented
3#39365C211yesmaximal, characteristic, complemented
4#35539C211yesmaximal, characteristic
5#32968C211yesmaximal, characteristic, complemented
6#31123C211yesmaximal, characteristic, complemented
7#31118C211yesmaximal, characteristic, complemented
8#31089C211yesmaximal, characteristic, complemented
9#31083C211yesmaximal, characteristic, complemented
10#30974C211yesmaximal, characteristic, complemented
11#30947C211yesmaximal, characteristic, complemented
12#30830C211yesmaximal, characteristic, complemented
13#30812C211yesmaximal, characteristic, complemented
14#29871C211yesmaximal, characteristic, complemented
15#29702C211yesmaximal, characteristic, complemented
16#28514C211yesmaximal, characteristic, complemented
17#28202C211yesmaximal, characteristic, complemented
18#27282C211yesmaximal, characteristic, complemented
19#27259C211yesmaximal, characteristic, complemented
20#26143C211yesmaximal, characteristic, complemented
21#26136C211yesmaximal, characteristic, complemented
22#26077C211yesmaximal, characteristic, complemented
23#26060C211yesmaximal, characteristic, complemented
24#24891C211yesmaximal, characteristic, complemented
25#24868C211yesmaximal, characteristic, complemented
26#24852C211yesmaximal, characteristic, complemented
27#24717C211yesmaximal, characteristic, complemented
28#24309C211yesmaximal, characteristic, complemented
29#24309C211yesmaximal, characteristic, complemented
30#22756C211yesmaximal, characteristic, complemented
31#22112C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#520C2211yescharacteristic
36#3244—28no—
37C2×#501C2211yescharacteristic
38C2×#498C2211yescharacteristic
39C2×#489C2211yescharacteristic
40C2×#488C2211yescharacteristic
41C2×#481C2211yescharacteristic
42C2×#485C2211yescharacteristic
43C2×#482C2211yescharacteristic
44C2×#483C2211yescharacteristic
45#3084—28no—
46C2×#479C2211yescharacteristic
47C2×#479C2211yescharacteristic
48C2×#479C2211yescharacteristic
49C2×#475C2211yescharacteristic
50C2×#475C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#478C2211yescharacteristic
53C2×#478C2211yescharacteristic
54C2×#478C2211yescharacteristic
55C2×#478C2211yescharacteristic
56C2×#476C2211yescharacteristic
57C2×#476C2211yescharacteristic
58C2×#476C2211yescharacteristic
59C2×#433C2211yescharacteristic
60C2×#428C2211yescharacteristic
61C22×#106C2211yescharacteristic
62C2×#424C2211yescharacteristic
63C2×#417C2211yescharacteristic
64C2×#416C2211yescharacteristic
65#2859C2211yescharacteristic
66#2734—21no—
67#2732—21no—
68#2726—21no—
69#2683—21no—
70#2629C2211yescharacteristic
71#2629C2211yescharacteristic
72#2610—21no—
73#2603—21no—
74#2601—21no—
75#2556—21no—
76#2556—21no—
77#2550C2211yescharacteristic
78#2550C2211yescharacteristic
79#2540—21no—
80#2463—21no—
81#2456—21no—
82#2452C2211yescharacteristic
83#2449—21no—
84#2448C2211yescharacteristic
85#2443—21no—
86#2441C2211yescharacteristic
87#2441C2211yescharacteristic
88#2440C2211yescharacteristic
89#2440C2211yescharacteristic
90#2440C2211yescharacteristic
91#2431C2211yescharacteristic
92#2429—21no—
93#2429—21no—
94#2428C2211yescharacteristic
95#2423C2211yescharacteristic
96#2416C2211yescharacteristic
97#2407C2211yescharacteristic
98#2352C2211yescharacteristic
99#2352C2211yescharacteristic
100#2324C2211yescharacteristic
101#2324C2211yescharacteristic
102C4×C4⋊Q8C2211yescharacteristic
103C4×#127C2211yescharacteristic
104#2295C2211yescharacteristic
105#2293C2211yescharacteristic
106#2092C2211yescharacteristic
107#2092C2211yescharacteristic
108#2092C2211yescharacteristic
109#2092C2211yescharacteristic
110#2088C2211yescharacteristic
111#2086C2211yescharacteristic
112#2085C2211yescharacteristic
113#2085C2211yescharacteristic
114#2084C2211yescharacteristic
115#2084C2211yescharacteristic
116#2084C2211yescharacteristic
117#2083C2211yescharacteristic
118#2077C2211yescharacteristic
119#2075C2211yescharacteristic
120#2074C2211yescharacteristic
121#2074C2211yescharacteristic
122#2072C2211yescharacteristic
123#2072C2211yescharacteristic
124#2065C2211yescharacteristic
125#2065C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2058C2211yescharacteristic
129#2058C2211yescharacteristic
130#2058C2211yescharacteristic
131#2057C2211yescharacteristic
132#2042C2211yescharacteristic
133#2042C2211yescharacteristic
134#2041C2211yescharacteristic
135#2041C2211yescharacteristic
136#2036C2211yescharacteristic
137#2035C2211yescharacteristic
138#2034C2211yescharacteristic
139#2034C2211yescharacteristic
140#2034C2211yescharacteristic
141#2033C2211yescharacteristic
142#2025C2211yescharacteristic
143#2025C2211yescharacteristic
144#2023C2211yescharacteristic
145#2023C2211yescharacteristic
146#1989C2211yescharacteristic
147#1989C2211yescharacteristic
148#1988C2211yescharacteristic
149#1957C2211yescharacteristic
150#1957C2211yescharacteristic
151#1948C2211yescharacteristic
152#1944C2211yescharacteristic
153#1941C2211yescharacteristic
154#1941C2211yescharacteristic
155#1941C2211yescharacteristic
156#1936C2211yescharacteristic
157#1934C2211yescharacteristic
158#1933C2211yescharacteristic
159#1933C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1920C2211yescharacteristic
169#1920C2211yescharacteristic
170#1917C2211yescharacteristic
171#1916C2211yescharacteristic
172#1895C2211yescharacteristic
173#1893C2211yescharacteristic
174#1875C2211yescharacteristic
175#1875C2211yescharacteristic
176#1874C2211yescharacteristic
177#1874C2211yescharacteristic
178#1870C2211yescharacteristic
179#1869C2211yescharacteristic
180#1865C2211yescharacteristic
181#1864C2211yescharacteristic
182#1863C2211yescharacteristic
183#1862C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1853C2211yescharacteristic
187#1853C2211yescharacteristic
188#1853C2211yescharacteristic
189#1852C2211yescharacteristic
190#1845C2211yescharacteristic
191#1844C2211yescharacteristic
192#1831C2211yescharacteristic
193#1809C2211yescharacteristic
194#1807C2211yescharacteristic
195#1803C2211yescharacteristic
196#1802C2211yescharacteristic
197#1802C2211yescharacteristic
198#1798C2211yescharacteristic
199#1798C2211yescharacteristic
200#1788C2211yescharacteristic
201#1788C2211yescharacteristic
202C4×C4⋊C8C2211yescharacteristic
203#1753C2211yescharacteristic
204C8×C22⋊C4C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#544—24no—
209#544—24no—
210#544—42no—
211#544—42no—
212#542—24no—
213#542—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#125—21no—
223C2×#125—21no—
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8C2311yescharacteristic
241C2×#121—21no—
242C2×#121—21no—
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246#520—24no—
247#520—42no—
248C2×C4×Q8—21no—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×#117—21no—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C22×C4⋊C4—21no—
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268#501—24no—
269#498—24no—
270#489—24no—
271#488—24no—
272#485—24no—
273#483—24no—
274#482—24no—
275#481—24no—
276#479—24no—
277#479—24no—
278#479—24no—
279#478—24no—
280#478—24no—
281#478—24no—
282#478—42no—
283#478—42no—
284#476—24no—
285#476—24no—
286#476—24no—
287#475—24no—
288#475D418yescomplemented
289#433—24no—
290#428—24no—
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#106—24no—
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312#424—24no—
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319#417—24no—
320#416—24no—
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×#97C2311yescharacteristic
352C2×C4×C8C2311yescharacteristic
353C2×C4×C8C2311yescharacteristic
354C2×C4×C8C2311yescharacteristic
355#399—21no—
356#399—21no—
357#399—21no—
358#399—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#397—21no—
370#396—21no—
371#396—21no—
372#396—21no—
373#396—21no—
374#396—21no—
375#396—21no—
376#396—21no—
377#396—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#395—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#393—21no—
387#392—21no—
388#392—21no—
389#392—21no—
390#392—21no—
391#391—21no—
392#391—21no—
393#391—21no—
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#390—21no—
397#390—21no—
398#390—21no—
399#390—21no—
400#390D411yescharacteristic
401#390D411yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389D411yescharacteristic
416#389D411yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388D411yescharacteristic
435#388D411yescharacteristic
436#388D411yescharacteristic
437#388D411yescharacteristic
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#386—21no—
452#386—21no—
453#386—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#382C2311yescharacteristic
466#382C2311yescharacteristic
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473C4×C4⋊C4—21no—
474C4×C4⋊C4—21no—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C22⋊C4—21no—
480C4×C22⋊C4—21no—
481C4×C22⋊C4C2311yescharacteristic
482C4×C22⋊C4C2311yescharacteristic
483#376—21no—
484C43C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—41no—
520C2×#41—41no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8—21no—
525C22×Q8C2411yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4C2×D411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C2×M16—22no—
545C2×M16—22no—
546C2×M16—41no—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—41no—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—22no—
561C4⋊Q8—22no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—44no—
566C4⋊Q8—44no—
567C4⋊Q8C2×D414yes—
568#127—22no—
569#127—41no—
570#126—44no—
571#125—22no—
572#125—22no—
573#125—22no—
574#125—22no—
575#125—22no—
576#125—22no—
577#125—41no—
578#125—41no—
579#125—44no—
580#125—44no—
581#124—22no—
582#124—44no—
583#124—41no—
584#123—44no—
585C22⋊Q8—22no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—44no—
591C22⋊Q8—41no—
592C22⋊Q8—82no—
593C22⋊Q8—82no—
594C22⋊Q8—82no—
595C22⋊Q8—82no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—41no—
601#121—41no—
602#121—82no—
603#121—82no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—41no—
607C4×Q8—82no—
608C4×Q8C2×D414yes—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—44no—
617C4×D4—41no—
618C4×D4—44no—
619C4×D4—82no—
620C4×D4—82no—
621#117—22no—
622#117—22no—
623#117—22no—
624#117—22no—
625#117—22no—
626#117—22no—
627#117—44no—
628#117—41no—
629#117—41no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
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—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—44no—
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42C2×D411yescharacteristic
736C2×C42C2×D411yescharacteristic
737C2×C42C2×D411yescharacteristic
738C2×C42C2×D411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744#107—22no—
745#107—22no—
746#107—22no—
747#107—22no—
748#107—41no—
749#107—41no—
750#106—22no—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—22no—
755#106—22no—
756#106—22no—
757#106—22no—
758#106—41no—
759#106—41no—
760#106—41no—
761#106—41no—
762#106C2×D414yes—
763#106C2×D414yes—
764C4⋊C8—22no—
765C4⋊C8—22no—
766C4⋊C8—22no—
767C4⋊C8—22no—
768C4⋊C8—22no—
769C4⋊C8C2×D414yes—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—41no—
775#103—41no—
776#103C2×D414yes—
777#103C2×D414yes—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—22no—
787#102—22no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794C22⋊C8—22no—
795C22⋊C8—22no—
796C22⋊C8—22no—
797C22⋊C8—22no—
798C22⋊C8—41no—
799C22⋊C8—41no—
800#97—22no—
801C4×C8—22no—
802C4×C8—41no—
803C4×C8—41no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
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#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837C24—21no—
838C24—21no—
839C24C22×D411yescharacteristic
840C24C22×D411yescharacteristic
841#41—28no—
842#41—44no—
843#41—44no—
844#41—44no—
845C2×Q8—24no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×Q8—42no—
854C2×Q8—81no—
855C2×Q8—81no—
856C2×Q8—81no—
857C2×Q8—81no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8C22×D412yes—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—42no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D42−1+412yes—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C42−1+412yes—
954C22×C42−1+412yes—
955C22×C4C2511yescharacteristic
956M16—44no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—44no—
980C2×C8C22×D412yes—
981C2×C8C22×D412yes—
982C4⋊C4—22no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4C22×D412yes—
1049C4⋊C4C22×D412yes—
1050C4⋊C4C22×D412yes—
1051C22⋊C4—22no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C42—24no—
1087C42—22no—
1088C42—22no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—41no—
1098C42—41no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42C22×D412yes—
1106C42H(5,𝔽2)12yes—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—22no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23#53612yes—
1135C23C23×D411yescharacteristic
1136Q8—22no—
1137Q8—22no—
1138Q8—41no—
1139Q8—41no—
1140Q8—84no—
1141Q8—162no—
1142Q8—162no—
1143Q8—162no—
1144D4—22no—
1145D4—22no—
1146D4—48no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—84no—
1154D4—84no—
1155D4—82no—
1156D4—162no—
1157D4—162no—
1158D4—162no—
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—22no—
1171C2×C4—22no—
1172C2×C4—22no—
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—22no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—22no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—48no—
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—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4#53612yes—
1248C2×C4D4212yes—
1249C2×C4D4212yes—
1250C2×C4#57712yes—
1251C2×C4#57712yes—
1252C2×C4C23×D411yescharacteristic
1253C2×C4C2×H(5,𝔽2)11yescharacteristic
1254C2×C4C2×2−1+411yescharacteristic
1255C2×C4C2×2−1+411yescharacteristic
1256C2×C4C2×2−1+411yescharacteristic
1257C2×C4#58511yescharacteristic
1258C8—22no—
1259C8—22no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—42no—
1274C22—41no—
1275C22—42no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—42no—
1282C22—41no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C2×#53611yescharacteristic
1295C22C2×D4211yescharacteristic
1296C22#348911yescharacteristic
1297C22C2×#57711yescharacteristic
1298C22C2×#57711yescharacteristic
1299C22#358411yescharacteristic
1300C22#358511yescharacteristic
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—22no—
1306C4—41no—
1307C4—42no—
1308C4—41no—
1309C4—41no—
1310C4—42no—
1311C4—42no—
1312C4—41no—
1313C4—41no—
1314C4—42no—
1315C4—41no—
1316C4—41no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4#348611yescharacteristic
1328C4#348911yescharacteristic
1329C4#353811yescharacteristic
1330C4#354111yescharacteristic
1331C2—42no—
1332C2—81no—
1333C2—82no—
1334C2—161no—
1335C2#3765111yescharacteristic
1336C2#6087511yescharacteristic
1337C2#6088111yescharacteristic
1338C2#6108511yescharacteristic
1339C2#6109511yescharacteristic
1340C2#6216611yescharacteristic
1341C2#6221211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35539C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3244C2semidirect
2. C2×#3084C2semidirect
3. #39365C2semidirect
5. #32968C2semidirect
6. #31123C2semidirect
7. #31118C2semidirect
8. #31089C2semidirect
9. #31083C2semidirect
10. #30974C2semidirect
11. #30947C2semidirect
12. #30830C2semidirect
13. #30812C2semidirect
14. #29871C2semidirect
15. #29702C2semidirect
16. #28514C2semidirect
17. #28202C2semidirect
18. #27282C2semidirect
19. #27259C2semidirect
20. #26143C2semidirect
21. #26136C2semidirect
22. #26077C2semidirect
23. #26060C2semidirect
24. #24891C2semidirect
25. #24868C2semidirect
26. #24852C2semidirect
27. #24717C2semidirect
28. #24309C2semidirect
29. #24309C2semidirect
30. #22756C2semidirect
31. #22112C2semidirect
288. #475D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32442
C2×#30842
#393652
#355392
#329682
#311232
#311182
#310892
#310832
#309742
#309472
#308302
#308122
#298712
#297022
#285142
#282022
#272822
#272592
#261432
#261362
#260772
#260602
#248912
#248682
#248522
#247172
#243092
#227562
#221122