Finite Group Databasebeta

← #6809837

Subgroups — #6809837

Order 512.

1747 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3243C211yesmaximal, characteristic, complemented
2C2×#3234C211yesmaximal, characteristic
3#37794C211yesmaximal, characteristic
4#35640C211yesmaximal, characteristic, complemented
5#33120C211yesmaximal, characteristic, complemented
6#30977C211yesmaximal, characteristic, complemented
7#30975C211yesmaximal, characteristic, complemented
8#30968C211yesmaximal, characteristic, complemented
9#30955C211yesmaximal, characteristic, complemented
10#30835C211yesmaximal, characteristic, complemented
11#30831C211yesmaximal, characteristic, complemented
12#30825C211yesmaximal, characteristic, complemented
13#30819C211yesmaximal, characteristic, complemented
14#29646C211yesmaximal, characteristic, complemented
15#29643C211yesmaximal, characteristic, complemented
16#28821C211yesmaximal, characteristic, complemented
17#28817C211yesmaximal, characteristic, complemented
18#27920C211yesmaximal, characteristic, complemented
19#27779C211yesmaximal, characteristic, complemented
20#27773C211yesmaximal, characteristic, complemented
21#27654C211yesmaximal, characteristic, complemented
22#26479C211yesmaximal, characteristic, complemented
23#26468C211yesmaximal, characteristic, complemented
24#26052C211yesmaximal, characteristic, complemented
25#26045C211yesmaximal, characteristic, complemented
26#24618C211yesmaximal, characteristic, complemented
27#24611C211yesmaximal, characteristic, complemented
28#24074C211yesmaximal, characteristic, complemented
29#24062C211yesmaximal, characteristic
30#22605C211yesmaximal, characteristic, complemented
31#21586C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C22×#125C2211yescharacteristic
36#3243—28no—
37#3234—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#501C2211yescharacteristic
41C2×#500C2211yescharacteristic
42C2×#490C2211yescharacteristic
43C2×#490C2211yescharacteristic
44C2×#489C2211yescharacteristic
45C2×#488C2211yescharacteristic
46C2×#484C2211yescharacteristic
47C2×#481C2211yescharacteristic
48C2×#481C2211yescharacteristic
49C2×#485C2211yescharacteristic
50C2×#482C2211yescharacteristic
51C2×#482C2211yescharacteristic
52C2×#483C2211yescharacteristic
53C2×#480C2211yescharacteristic
54C2×#480C2211yescharacteristic
55C2×#479C2211yescharacteristic
56C2×#477C2211yescharacteristic
57C2×#478C2211yescharacteristic
58C2×#478C2211yescharacteristic
59C2×#478C2211yescharacteristic
60C2×#478C2211yescharacteristic
61C2×#478C2211yescharacteristic
62C2×#474C2211yescharacteristic
63C2×#433C2211yescharacteristic
64C2×#432C2211yescharacteristic
65#2855C2211yescharacteristic
66#2715—21no—
67#2701—21no—
68#2686—21no—
69#2674—21no—
70#2624C2211yescharacteristic
71#2620C2211yescharacteristic
72#2583—21no—
73#2583—21no—
74#2552—21no—
75#2552—21no—
76#2552C2211yescharacteristic
77#2552C2211yescharacteristic
78#2552C2211yescharacteristic
79#2552C2211yescharacteristic
80#2551C2211yescharacteristic
81#2550—21no—
82#2550—21no—
83#2550C2211yescharacteristic
84#2550C2211yescharacteristic
85#2550C2211yescharacteristic
86#2550C2211yescharacteristic
87#2544C2211yescharacteristic
88#2502—21no—
89#2502—21no—
90#2466—21no—
91#2452C2211yescharacteristic
92#2451C2211yescharacteristic
93#2449—21no—
94#2447C2211yescharacteristic
95#2445C2211yescharacteristic
96#2432—21no—
97#2406—21no—
98#2367C2211yescharacteristic
99D4×C4⋊C4C2211yescharacteristic
100#2324C2211yescharacteristic
101#2317C2211yescharacteristic
102#2317C2211yescharacteristic
103#2296C2211yescharacteristic
104#2296C2211yescharacteristic
105#2274C2211yescharacteristic
106#2097C2211yescharacteristic
107#2096C2211yescharacteristic
108#2094C2211yescharacteristic
109#2092C2211yescharacteristic
110#2088C2211yescharacteristic
111#2088C2211yescharacteristic
112#2088C2211yescharacteristic
113#2087C2211yescharacteristic
114#2085C2211yescharacteristic
115#2084C2211yescharacteristic
116#2073C2211yescharacteristic
117#2071C2211yescharacteristic
118#2068C2211yescharacteristic
119#2067C2211yescharacteristic
120#2066C2211yescharacteristic
121#2065C2211yescharacteristic
122#2059C2211yescharacteristic
123#2059C2211yescharacteristic
124#2059C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2058C2211yescharacteristic
129#2058C2211yescharacteristic
130#2058C2211yescharacteristic
131#2057C2211yescharacteristic
132#2057C2211yescharacteristic
133#2057C2211yescharacteristic
134#2042C2211yescharacteristic
135#2042C2211yescharacteristic
136#2041C2211yescharacteristic
137#2041C2211yescharacteristic
138#2026C2211yescharacteristic
139#2026C2211yescharacteristic
140#2026C2211yescharacteristic
141#2026C2211yescharacteristic
142#2025C2211yescharacteristic
143#2025C2211yescharacteristic
144#2023C2211yescharacteristic
145#2023C2211yescharacteristic
146#1983C2211yescharacteristic
147#1983C2211yescharacteristic
148#1959C2211yescharacteristic
149#1958C2211yescharacteristic
150#1949C2211yescharacteristic
151#1948C2211yescharacteristic
152#1947C2211yescharacteristic
153#1947C2211yescharacteristic
154#1944C2211yescharacteristic
155#1943C2211yescharacteristic
156#1943C2211yescharacteristic
157#1941C2211yescharacteristic
158#1940C2211yescharacteristic
159#1939C2211yescharacteristic
160#1936C2211yescharacteristic
161#1935C2211yescharacteristic
162#1935C2211yescharacteristic
163#1934C2211yescharacteristic
164#1928C2211yescharacteristic
165#1928C2211yescharacteristic
166#1926C2211yescharacteristic
167#1925C2211yescharacteristic
168#1925C2211yescharacteristic
169#1925C2211yescharacteristic
170#1921C2211yescharacteristic
171#1918C2211yescharacteristic
172#1917C2211yescharacteristic
173#1917C2211yescharacteristic
174#1917C2211yescharacteristic
175#1916C2211yescharacteristic
176#1875C2211yescharacteristic
177#1875C2211yescharacteristic
178#1873C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1864C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1854C2211yescharacteristic
188#1847C2211yescharacteristic
189#1844C2211yescharacteristic
190#1825C2211yescharacteristic
191#1824C2211yescharacteristic
192#1823C2211yescharacteristic
193#1818C2211yescharacteristic
194#1817C2211yescharacteristic
195#1804C2211yescharacteristic
196#1802C2211yescharacteristic
197#1798C2211yescharacteristic
198#1776C2211yescharacteristic
199C4×#107C2211yescharacteristic
200#1771C2211yescharacteristic
201#1770C2211yescharacteristic
202#1762C2211yescharacteristic
203C4×#102C2211yescharacteristic
204#1750C2211yescharacteristic
205C22×#41—21no—
206#544—24no—
207#544—42no—
208#542—24no—
209#542—42no—
210#532—24no—
211#532—42no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#126—21no—
220C2×#125—21no—
221C2×#125—24no—
222C2×#125—21no—
223C2×#125—21no—
224C2×#125—42no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#124—21no—
232C2×#124—21no—
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#123—21no—
236C2×#123—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8C2311yescharacteristic
242C2×#121—21no—
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C22×C4⋊C4—21no—
256C22×C4⋊C4—21no—
257C22×C4⋊C4—21no—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C42C2311yescharacteristic
261#501—24no—
262#501—24no—
263#501—24no—
264#500—24no—
265#490—24no—
266#490—24no—
267#489—24no—
268#488—24no—
269#485—24no—
270#484—24no—
271#483—42no—
272#482—24no—
273#482—42no—
274#481—24no—
275#481—24no—
276#480—24no—
277#480D418yes—
278#479—24no—
279#478—24no—
280#478—24no—
281#478—24no—
282#478—24no—
283#478—24no—
284#477—24no—
285#474—24no—
286#433—24no—
287#432—24no—
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×#97C2311yescharacteristic
343C2×#97C2311yescharacteristic
344C2×#97C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347C2×C4×C8C2311yescharacteristic
348#399—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398—21no—
356#398—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#397—21no—
363#397—21no—
364#397—21no—
365#396—21no—
366#396—21no—
367#396—21no—
368#395—21no—
369#395—21no—
370#395—21no—
371#395—21no—
372#395—21no—
373#395—21no—
374#395—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394—21no—
382#394—21no—
383#393—21no—
384#391—21no—
385#391—21no—
386#391—21no—
387#391—21no—
388#391—21no—
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#390—21no—
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389D411yescharacteristic
409#389D411yescharacteristic
410#389D411yescharacteristic
411#389D411yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#388—21no—
426#388—21no—
427#388—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385D411yescharacteristic
449#385D411yescharacteristic
450#385D411yescharacteristic
451#385D411yescharacteristic
452#384—21no—
453#384—21no—
454#384—21no—
455#384—21no—
456#384—21no—
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#382—21no—
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#381—21no—
464#381—21no—
465#380—21no—
466#380C2311yescharacteristic
467C4×C4⋊C4—21no—
468C4×C4⋊C4—21no—
469C4×C4⋊C4—21no—
470C4×C4⋊C4—21no—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483#340C2311yescharacteristic
484#340C2311yescharacteristic
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#336C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C2×#41—44no—
516C2×#41—82no—
517C2×#41—82no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8C2411yescharacteristic
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—22no—
547C4⋊Q8—22no—
548C4⋊Q8—22no—
549C4⋊Q8—22no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—44no—
555C4⋊Q8—82no—
556#127—22no—
557#127—41no—
558#126—44no—
559#125—22no—
560#125—22no—
561#125—22no—
562#125—22no—
563#125—22no—
564#125—22no—
565#125—41no—
566#125—41no—
567#125—41no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125—44no—
572#125—44no—
573#125—44no—
574#124—22no—
575#124—22no—
576#124—22no—
577#124—44no—
578#124—41no—
579#124—44no—
580#123—44no—
581#123—82no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—44no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—82no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—44no—
592#121C2×D414yes—
593C4×Q8—22no—
594C4×Q8—41no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—44no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604#117—22no—
605#117—22no—
606#117—22no—
607#117—22no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—22no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—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—44no—
655C2×C4⋊C4—44no—
656C2×C4⋊C4—82no—
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D414yes—
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—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⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#107—22no—
728#107—22no—
729#107—22no—
730#107—22no—
731#107—22no—
732#107—22no—
733#107—22no—
734#107—41no—
735#107C2×D414yes—
736#107C2×D414yes—
737#106—22no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—41no—
745#106—41no—
746#106—41no—
747C4⋊C8—22no—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—41no—
760#103—41no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—41no—
774#102—41no—
775#102C2×D414yes—
776#102C2×D414yes—
777C22⋊C8—22no—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8C2×D414yes—
781#97—22no—
782#97—22no—
783#97—22no—
784#97—22no—
785C4×C8—22no—
786C4×C8—22no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
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#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824C24—21no—
825C24—21no—
826C24C22×D411yescharacteristic
827#41—816no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—42no—
838C2×Q8—42no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×D4—24no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4C22×D412yes—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—22no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D412yes—
926C22×C4H(5,𝔽2)12yes—
927C22×C4C2511yescharacteristic
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8C22×D412yes—
951C2×C8C22×D412yes—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—24no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4C22×D412yes—
1025C4⋊C4C22×D412yes—
1026C4⋊C4C22×D412yes—
1027C4⋊C42−1+412yes—
1028C4⋊C42−1+412yes—
1029C22⋊C4—24no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—24no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C42—24no—
1056C42—22no—
1057C42—22no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—42no—
1069C42—42no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C422−1+412yes—
1076C422−1+412yes—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—22no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23D4212yes—
1098C23C23×D411yescharacteristic
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—84no—
1104Q8—162no—
1105Q8—162no—
1106Q8—162no—
1107D4—22no—
1108D4—22no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—84no—
1116D4—84no—
1117D4—84no—
1118D4—84no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—44no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—84no—
1203C2×C4—82no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4—84no—
1207C2×C4—84no—
1208C2×C4—162no—
1209C2×C4#53612yes—
1210C2×C4#53612yes—
1211C2×C4D4212yes—
1212C2×C4C23×D411yescharacteristic
1213C2×C4C2×H(5,𝔽2)11yescharacteristic
1214C2×C4C2×2−1+411yescharacteristic
1215C2×C4C2×2−1+411yescharacteristic
1216C2×C4C2×2−1+411yescharacteristic
1217C2×C4C2×2−1+411yescharacteristic
1218C8—22no—
1219C8—22no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22C2×#53611yescharacteristic
1248C22C2×D4211yescharacteristic
1249C22#348611yescharacteristic
1250C22#358411yescharacteristic
1251C22#358511yescharacteristic
1252C22#358511yescharacteristic
1253C22#358611yescharacteristic
1254C4—22no—
1255C4—22no—
1256C4—22no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—42no—
1269C4—42no—
1270C4—41no—
1271C4—41no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4#349911yescharacteristic
1282C4#349911yescharacteristic
1283C4#354411yescharacteristic
1284C4#354411yescharacteristic
1285C2—42no—
1286C2—82no—
1287C2—161no—
1288C2#3933711yescharacteristic
1289C2#6088611yescharacteristic
1290C2#6089011yescharacteristic
1291C2#6105811yescharacteristic
1292C2#6107811yescharacteristic
1293C2#6186111yescharacteristic
1294C2#6187811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3243C2semidirect
4. #35640C2semidirect
5. #33120C2semidirect
6. #30977C2semidirect
7. #30975C2semidirect
8. #30968C2semidirect
9. #30955C2semidirect
10. #30835C2semidirect
11. #30831C2semidirect
12. #30825C2semidirect
13. #30819C2semidirect
14. #29646C2semidirect
15. #29643C2semidirect
16. #28821C2semidirect
17. #28817C2semidirect
18. #27920C2semidirect
19. #27779C2semidirect
20. #27773C2semidirect
21. #27654C2semidirect
22. #26479C2semidirect
23. #26468C2semidirect
24. #26052C2semidirect
25. #26045C2semidirect
26. #24618C2semidirect
27. #24611C2semidirect
28. #24074C2semidirect
30. #22605C2semidirect
31. #21586C2semidirect

Maximal subgroups

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

subgroupindex
C2×#32432
C2×#32342
#377942
#356402
#331202
#309772
#309752
#309682
#309552
#308352
#308312
#308252
#308192
#296462
#296432
#288212
#288172
#279202
#277792
#277732
#276542
#264792
#264682
#260522
#260452
#246182
#246112
#240742
#240622
#226052
#215862