Finite Group Databasebeta

← #6684536

Subgroups — #6684536

Order 512.

1861 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3241C211yesmaximal, characteristic, complemented
2C2×#3136C211yesmaximal, characteristic, complemented
3#39416C211yesmaximal, characteristic
4#39365C211yesmaximal, characteristic, complemented
5#33214C211yesmaximal, characteristic, complemented
6#30825C211yesmaximal, characteristic, complemented
7#30823C211yesmaximal, characteristic, complemented
8#30817C211yesmaximal, characteristic, complemented
9#30815C211yesmaximal, characteristic, complemented
10#30653C211yesmaximal, characteristic, complemented
11#30648C211yesmaximal, characteristic, complemented
12#30638C211yesmaximal, characteristic, complemented
13#30631C211yesmaximal, characteristic, complemented
14#30282C211yesmaximal, characteristic, complemented
15#29850C211yesmaximal, characteristic, complemented
16#28724C211yesmaximal, characteristic, complemented
17#28659C211yesmaximal, characteristic, complemented
18#25970C211yesmaximal, characteristic, complemented
19#25968C211yesmaximal, characteristic, complemented
20#25964C211yesmaximal, characteristic, complemented
21#25958C211yesmaximal, characteristic, complemented
22#25916C211yesmaximal, characteristic, complemented
23#25867C211yesmaximal, characteristic, complemented
24#25822C211yesmaximal, characteristic, complemented
25#25682C211yesmaximal, characteristic, complemented
26#24885C211yesmaximal, characteristic, complemented
27#24882C211yesmaximal, characteristic, complemented
28#24873C211yesmaximal, characteristic, complemented
29#24862C211yesmaximal, characteristic, complemented
30#22219C211yesmaximal, characteristic, complemented
31#21110C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#544C2211yescharacteristic, complemented
34C2×#540C2211yescharacteristic
35C2×#535C2211yescharacteristic
36#3241—28no—
37C2×#501C2211yescharacteristic, complemented
38C2×#499C2211yescharacteristic, complemented
39C2×#499C2211yescharacteristic, complemented
40#3136—28no—
41C2×#490C2211yescharacteristic
42C2×#490C2211yescharacteristic
43C2×#490C2211yescharacteristic
44C2×#489C2211yescharacteristic
45C2×#489C2211yescharacteristic
46C2×#488C2211yescharacteristic
47C2×#488C2211yescharacteristic
48C2×#488C2211yescharacteristic
49C2×#486C2211yescharacteristic
50C2×#486C2211yescharacteristic
51C2×#481C2211yescharacteristic, complemented
52C2×#482C2211yescharacteristic
53C2×#482C2211yescharacteristic, complemented
54C2×#480C2211yescharacteristic
55C2×#478C2211yescharacteristic
56C2×#478C2211yescharacteristic, complemented
57C2×#476C2211yescharacteristic
58C2×#474C2211yescharacteristic, complemented
59C2×#433C2211yescharacteristic, complemented
60C2×#417C2211yescharacteristic
61C2×#418C2211yescharacteristic
62C2×#416C2211yescharacteristic
63C22×#102C2211yescharacteristic
64C2×#405C2211yescharacteristic
65#2861C2211yescharacteristic
66#2859C2211yescharacteristic, complemented
67#2734—21no—
68#2732—21no—
69#2726—21no—
70#2701—21no—
71#2699—21no—
72#2697—21no—
73#2683—21no—
74#2678—21no—
75#2629C2211yescharacteristic
76#2629C2211yescharacteristic
77#2629C2211yescharacteristic, complemented
78#2620C2211yescharacteristic
79#2556—21no—
80#2556—21no—
81#2550C2211yescharacteristic, complemented
82#2550C2211yescharacteristic, complemented
83#2543—21no—
84#2534—21no—
85#2447C2211yescharacteristic
86#2445C2211yescharacteristic
87#2441C2211yescharacteristic
88#2441C2211yescharacteristic, complemented
89#2440C2211yescharacteristic
90#2440C2211yescharacteristic, complemented
91#2429—21no—
92#2429—21no—
93#2428C2211yescharacteristic
94#2427C2211yescharacteristic
95#2425—21no—
96#2424—21no—
97#2408C2211yescharacteristic
98#2407C2211yescharacteristic
99#2352C2211yescharacteristic
100#2352C2211yescharacteristic
101#2339C2211yescharacteristic
102D4×C22⋊C4C2211yescharacteristic
103C4×C4⋊Q8C2211yescharacteristic, complemented
104C4×#127C2211yescharacteristic
105#2293C2211yescharacteristic
106#2097C2211yescharacteristic, complemented
107#2097C2211yescharacteristic, complemented
108#2096C2211yescharacteristic, complemented
109#2095C2211yescharacteristic, complemented
110#2094C2211yescharacteristic
111#2093C2211yescharacteristic
112#2092C2211yescharacteristic
113#2092C2211yescharacteristic
114#2073C2211yescharacteristic
115#2073C2211yescharacteristic
116#2073C2211yescharacteristic, complemented
117#2073C2211yescharacteristic, complemented
118#2068C2211yescharacteristic, complemented
119#2068C2211yescharacteristic, complemented
120#2066C2211yescharacteristic, complemented
121#2066C2211yescharacteristic, complemented
122#2065C2211yescharacteristic
123#2065C2211yescharacteristic
124#2065C2211yescharacteristic
125#2065C2211yescharacteristic
126#2059C2211yescharacteristic, complemented
127#2059C2211yescharacteristic, complemented
128#2058C2211yescharacteristic, complemented
129#2057C2211yescharacteristic, complemented
130#2042C2211yescharacteristic
131#2042C2211yescharacteristic
132#2041C2211yescharacteristic
133#2041C2211yescharacteristic
134#2035C2211yescharacteristic, complemented
135#2035C2211yescharacteristic, complemented
136#2034C2211yescharacteristic
137#2034C2211yescharacteristic
138#2034C2211yescharacteristic
139#2034C2211yescharacteristic, complemented
140#2033C2211yescharacteristic
141#2033C2211yescharacteristic, complemented
142#2026C2211yescharacteristic, complemented
143#2025C2211yescharacteristic
144#2024C2211yescharacteristic, complemented
145#2023C2211yescharacteristic
146#1992C2211yescharacteristic, complemented
147#1992C2211yescharacteristic, complemented
148#1992C2211yescharacteristic, complemented
149#1990C2211yescharacteristic, complemented
150#1959C2211yescharacteristic
151#1957C2211yescharacteristic
152#1944C2211yescharacteristic, complemented
153#1944C2211yescharacteristic, complemented
154#1941C2211yescharacteristic, complemented
155#1941C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic, complemented
161#1926C2211yescharacteristic, complemented
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1924C2211yescharacteristic, complemented
165#1923C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1875C2211yescharacteristic
169#1874C2211yescharacteristic
170#1873C2211yescharacteristic, complemented
171#1872C2211yescharacteristic, complemented
172#1870C2211yescharacteristic
173#1869C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic, complemented
178#1864C2211yescharacteristic, complemented
179#1864C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic, complemented
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1853C2211yescharacteristic
185#1852C2211yescharacteristic
186#1851C2211yescharacteristic
187#1850C2211yescharacteristic
188#1844C2211yescharacteristic, complemented
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1807C2211yescharacteristic
192#1807C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic, complemented
196#1802C2211yescharacteristic, complemented
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1786C2211yescharacteristic
200#1786C2211yescharacteristic
201#1767C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203#1750C2211yescharacteristic, complemented
204#1744C2211yescharacteristic, complemented
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#544—24no—
210#544—24no—
211#544—42no—
212#544—42no—
213#540—24no—
214#540—42no—
215#535—24no—
216#535—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#125—21no—
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×#123—21no—
235C2×#123—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8C2311yescharacteristic
243C2×#121—21no—
244C2×#121—21no—
245C2×#121—21no—
246C2×#121—21no—
247C2×#121—21no—
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×#120—21no—
252C2×#120—21no—
253C2×#120—21no—
254C2×C4×Q8—21no—
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C22⋊C4—21no—
269#501—24no—
270#499—24no—
271#499—42no—
272#490—24no—
273#490—24no—
274#490—24no—
275#489—24no—
276#489—24no—
277#488—24no—
278#488—24no—
279#488—42no—
280#486—24no—
281#486D418yescomplemented
282#482—24no—
283#482—24no—
284#481—24no—
285#480—24no—
286#478—24no—
287#478—24no—
288#476—24no—
289#474—24no—
290#433—24no—
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311#418—24no—
312#417—24no—
313#416—24no—
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#102—24no—
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353#405—24no—
354C2×#97C2311yescharacteristic
355C2×#97C2311yescharacteristic
356C2×#97C2311yescharacteristic
357C2×C4×C8C2311yescharacteristic
358C2×C4×C8C2311yescharacteristic
359C2×C4×C8C2311yescharacteristic
360#399—21no—
361#399—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#397—21no—
373#397—21no—
374#397—21no—
375#396—21no—
376#396—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#396—21no—
381#396—21no—
382#396—21no—
383#396—21no—
384#396—21no—
385#395—21no—
386#395—21no—
387#395—21no—
388#395—21no—
389#394—21no—
390#394—21no—
391#394—21no—
392#394—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#394—21no—
397#392—21no—
398#392—21no—
399#392—21no—
400#391—21no—
401#391—21no—
402#391—21no—
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#390—21no—
407#390—21no—
408#390D411yescharacteristic
409#390D411yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#390C2311yescharacteristic
413#390C2311yescharacteristic
414#390C2311yescharacteristic
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389—21no—
420#389—21no—
421#389—21no—
422#389—21no—
423#389—21no—
424#389D411yescharacteristic
425#389D411yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388D411yescharacteristic
441#388D411yescharacteristic
442#388D411yescharacteristic
443#388D411yescharacteristic
444#387—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#386—21no—
452#386—21no—
453#386—21no—
454#386—21no—
455#386—21no—
456#386—21no—
457#386—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#384C2311yescharacteristic
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#381—21no—
469#381—21no—
470#380—21no—
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477#379—21no—
478#379—21no—
479C4×C4⋊C4—21no—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C22⋊C4—21no—
484C4×C22⋊C4—21no—
485C4×C22⋊C4C2311yescharacteristic
486C4×C22⋊C4C2311yescharacteristic
487C2×#95—21no—
488C43C2311yescharacteristic
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
515C25—21no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41—41no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8—21no—
525C22×Q8C2411yescharacteristic
526C22×D4—22no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—41no—
539C22×D4—41no—
540C22×D4—41no—
541C22×D4C2×D411yescharacteristic
542C22×D4C2411yescharacteristic
543C22×D4C2411yescharacteristic
544C22×D4C2411yescharacteristic
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C2×M16—22no—
555C2×M16—22no—
556C2×M16—41no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—22no—
569C4⋊Q8—22no—
570C4⋊Q8—22no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573C4⋊Q8—44no—
574C4⋊Q8—44no—
575C4⋊Q8C2×D414yes—
576#127—22no—
577#127—22no—
578#127—41no—
579#127C2×D414yes—
580#125—22no—
581#125—22no—
582#125—22no—
583#125—22no—
584#125—22no—
585#125—22no—
586#125—22no—
587#125—22no—
588#125—41no—
589#125—41no—
590#125—44no—
591#125—44no—
592#124—22no—
593#124—22no—
594#124—22no—
595#124—41no—
596#123—44no—
597#123—44no—
598#123—82no—
599C22⋊Q8—44no—
600C22⋊Q8—44no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—82no—
606C22⋊Q8—82no—
607#121—22no—
608#121—22no—
609#121—44no—
610#121—44no—
611#121—41no—
612#121—41no—
613#121—44no—
614#121—44no—
615#121—41no—
616#121—41no—
617#121—82no—
618#120—44no—
619#120—44no—
620#120—82no—
621C4×Q8—82no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—82no—
633C4×D4—82no—
634#117—22no—
635#117—22no—
636#117—22no—
637#117—22no—
638#117—22no—
639#117—22no—
640#117—41no—
641#117—41no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
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—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—82no—
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D411yescharacteristic
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—41no—
756#107—41no—
757#106—22no—
758#106—22no—
759#106—22no—
760#106—22no—
761#106—41no—
762#106—41no—
763#106—41no—
764#106—41no—
765#106—41no—
766#106—41no—
767C4⋊C8—22no—
768C4⋊C8—22no—
769C4⋊C8—41no—
770C4⋊C8—41no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
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—22no—
789#102—22no—
790#102—22no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798#102—41no—
799#102C2×D414yes—
800#102C2×D414yes—
801#102C2×D414yes—
802#102C2×D414yes—
803C22⋊C8—22no—
804C22⋊C8—22no—
805C22⋊C8—22no—
806C22⋊C8—22no—
807C22⋊C8—41no—
808C22⋊C8—41no—
809#97—22no—
810#97—22no—
811#97—22no—
812C4×C8—22no—
813C4×C8—22no—
814C4×C8C2×D414yes—
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#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847C24—21no—
848C24—21no—
849C24—21no—
850C24—42no—
851C24—42no—
852C24—81no—
853C24—81no—
854C24—81no—
855C24—81no—
856C24—81no—
857C24C22×D411yescharacteristic
858C24C22×D411yescharacteristic
859#41—44no—
860#41—44no—
861#41—82no—
862#41—82no—
863C2×Q8—24no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×D4—22no—
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—44no—
898C2×D4—44no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—82no—
910C2×D4—82no—
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—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4C22×D412yes—
929C2×D4C22×D412yes—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
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—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
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×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
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×C42−1+412yes—
987C22×C42−1+412yes—
988C22×C4C2511yescharacteristic
989M16—44no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
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—44no—
1013C2×C8C22×D412yes—
1014C2×C8C22×D412yes—
1015C4⋊C4—22no—
1016C4⋊C4—24no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—22no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
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—41no—
1044C4⋊C4—41no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
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—42no—
1062C4⋊C4—42no—
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—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4C22×D412yes—
1077C4⋊C4C22×D412yes—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—22no—
1084C22⋊C4—22no—
1085C22⋊C4—22no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
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—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C42—22no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—41no—
1128C42—41no—
1129C42—41no—
1130C42—42no—
1131C42—42no—
1132C42—81no—
1133C42—81no—
1134C42C22×D412yes—
1135C42H(5,𝔽2)12yes—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—22no—
1148C23—22no—
1149C23—21no—
1150C23—21no—
1151C23—41no—
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—84no—
1171C23—84no—
1172C23—162no—
1173C23—162no—
1174C23—162no—
1175C23—162no—
1176C23—162no—
1177C23#53612yes—
1178C23C23×D411yescharacteristic
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—84no—
1184Q8—162no—
1185Q8—162no—
1186D4—22no—
1187D4—22no—
1188D4—22no—
1189D4—22no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—84no—
1199D4—84no—
1200D4—84no—
1201D4—82no—
1202D4—84no—
1203D4—162no—
1204D4—162no—
1205D4—162no—
1206D4—162no—
1207D4—162no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
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—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—41no—
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—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—84no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4—162no—
1294C2×C4#53612yes—
1295C2×C4D4212yes—
1296C2×C4D4212yes—
1297C2×C4#57712yes—
1298C2×C4C23×D411yescharacteristic
1299C2×C4C2×H(5,𝔽2)11yescharacteristic
1300C2×C4C2×2−1+411yescharacteristic
1301C2×C4C2×2−1+411yescharacteristic
1302C2×C4#58511yescharacteristic
1303C2×C4#58511yescharacteristic
1304C8—22no—
1305C8—22no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C22—22no—
1313C22—22no—
1314C22—22no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—42no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
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—
1346C22—81no—
1347C22—168no—
1348C22C2×#53611yescharacteristic
1349C22C2×D4211yescharacteristic
1350C22#350011yescharacteristic
1351C22C2×#57711yescharacteristic
1352C22#358411yescharacteristic
1353C22#358511yescharacteristic
1354C22#358511yescharacteristic
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—42no—
1364C4—42no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4#348911yescharacteristic
1381C4#348911yescharacteristic
1382C4#356111yescharacteristic
1383C4#356111yescharacteristic
1384C2—42no—
1385C2—81no—
1386C2—82no—
1387C2—82no—
1388C2—161no—
1389C2#3767611yescharacteristic
1390C2#6087511yescharacteristic
1391C2#6089211yescharacteristic
1392C2#6107911yescharacteristic
1393C2#6108511yescharacteristic
1394C2#6259611yescharacteristic
1395C2#6261311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39416C2
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×#3241C2semidirect
2. C2×#3136C2semidirect
4. #39365C2semidirect
5. #33214C2semidirect
6. #30825C2semidirect
7. #30823C2semidirect
8. #30817C2semidirect
9. #30815C2semidirect
10. #30653C2semidirect
11. #30648C2semidirect
12. #30638C2semidirect
13. #30631C2semidirect
14. #30282C2semidirect
15. #29850C2semidirect
16. #28724C2semidirect
17. #28659C2semidirect
18. #25970C2semidirect
19. #25968C2semidirect
20. #25964C2semidirect
21. #25958C2semidirect
22. #25916C2semidirect
23. #25867C2semidirect
24. #25822C2semidirect
25. #25682C2semidirect
26. #24885C2semidirect
27. #24882C2semidirect
28. #24873C2semidirect
29. #24862C2semidirect
30. #22219C2semidirect
31. #21110C2semidirect
33. C2×#544C22semidirect
37. C2×#501C22semidirect
38. C2×#499C22semidirect
39. C2×#499C22semidirect
51. C2×#481C22semidirect
53. C2×#482C22semidirect
56. C2×#478C22semidirect
58. C2×#474C22semidirect
59. C2×#433C22semidirect
66. #2859C22semidirect
77. #2629C22semidirect
81. #2550C22semidirect
82. #2550C22semidirect
88. #2441C22semidirect
90. #2440C22semidirect
103. C4×C4⋊Q8C22semidirect
106. #2097C22semidirect
107. #2097C22semidirect
108. #2096C22semidirect
109. #2095C22semidirect
116. #2073C22semidirect
117. #2073C22semidirect
118. #2068C22semidirect
119. #2068C22semidirect
120. #2066C22semidirect
121. #2066C22semidirect
126. #2059C22semidirect
127. #2059C22semidirect
128. #2058C22semidirect
129. #2057C22semidirect
134. #2035C22semidirect
135. #2035C22semidirect
139. #2034C22semidirect
141. #2033C22semidirect
142. #2026C22semidirect
144. #2024C22semidirect
146. #1992C22semidirect
147. #1992C22semidirect
148. #1992C22semidirect
149. #1990C22semidirect
152. #1944C22semidirect
153. #1944C22semidirect
154. #1941C22semidirect
155. #1941C22semidirect
156. #1927C22semidirect
157. #1927C22semidirect
160. #1926C22semidirect
161. #1926C22semidirect
164. #1924C22semidirect
165. #1923C22semidirect
166. #1917C22semidirect
167. #1916C22semidirect
170. #1873C22semidirect
171. #1872C22semidirect
177. #1864C22semidirect
178. #1864C22semidirect
179. #1864C22semidirect
181. #1862C22semidirect
188. #1844C22semidirect
195. #1802C22semidirect
196. #1802C22semidirect
201. #1767C22semidirect
203. #1750C22semidirect
204. #1744C22semidirect
281. #486D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32412
C2×#31362
#394162
#393652
#332142
#308252
#308232
#308172
#308152
#306532
#306482
#306382
#306312
#302822
#298502
#287242
#286592
#259702
#259682
#259642
#259582
#259162
#258672
#258222
#256822
#248852
#248822
#248732
#248622
#222192
#211102