Finite Group Databasebeta

← #7124583

Subgroups — #7124583

Order 512.

1676 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3336C211yesmaximal, characteristic, complemented
2C2×#3244C211yesmaximal, characteristic, complemented
3#45239C211yesmaximal, characteristic
4#42644C211yesmaximal, characteristic, complemented
5#31243C211yesmaximal, characteristic, complemented
6#31101C211yesmaximal, characteristic, complemented
7#30958C211yesmaximal, characteristic, complemented
8#30956C211yesmaximal, characteristic, complemented
9#30810C211yesmaximal, characteristic, complemented
10#30798C211yesmaximal, characteristic, complemented
11#30668C211yesmaximal, characteristic, complemented
12#30660C211yesmaximal, characteristic, complemented
13#28910C211yesmaximal, characteristic, complemented
14#28820C211yesmaximal, characteristic, complemented
15#27947C211yesmaximal, characteristic, complemented
16#26830C211yesmaximal, characteristic, complemented
17#26814C211yesmaximal, characteristic, complemented
18#26383C211yesmaximal, characteristic, complemented
19#26345C211yesmaximal, characteristic, complemented
20#26061C211yesmaximal, characteristic, complemented
21#26048C211yesmaximal, characteristic, complemented
22#25555C211yesmaximal, characteristic
23#25514C211yesmaximal, characteristic, complemented
24#25237C211yesmaximal, characteristic
25#25215C211yesmaximal, characteristic, complemented
26#24616C211yesmaximal, characteristic, complemented
27#24583C211yesmaximal, characteristic, complemented
28#24106C211yesmaximal, characteristic, complemented
29#23555C211yesmaximal, characteristic, complemented
30#22927C211yesmaximal, characteristic, complemented
31#22901C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#544C2211yescharacteristic
35C2×#542C2211yescharacteristic
36#3336—28no—
37#3244—28no—
38C2×#501C2211yescharacteristic
39C2×#499C2211yescharacteristic
40C2×#498C2211yescharacteristic
41C2×#489C2211yescharacteristic
42C2×#488C2211yescharacteristic
43C2×#481C2211yescharacteristic
44C2×#485C2211yescharacteristic
45C2×#485C2211yescharacteristic
46C2×#485C2211yescharacteristic
47C2×#482C2211yescharacteristic
48C2×#483C2211yescharacteristic
49C2×#483C2211yescharacteristic
50C2×#479C2211yescharacteristic
51C2×#479C2211yescharacteristic
52C2×#479C2211yescharacteristic
53C2×#475C2211yescharacteristic
54C2×#478C2211yescharacteristic
55C2×#476C2211yescharacteristic
56C2×#468C2211yescharacteristic
57C2×#467C2211yescharacteristic
58C2×#467C2211yescharacteristic
59C2×C4×Q16C2211yescharacteristic
60C2×C8×D4C2211yescharacteristic
61C2×#433C2211yescharacteristic
62C2×#428C2211yescharacteristic
63C2×#427C2211yescharacteristic
64C22×#107C2211yescharacteristic
65#2814—21no—
66#2723—21no—
67#2721—21no—
68#2721—21no—
69#2719—21no—
70#2716—21no—
71#2713—21no—
72#2710—21no—
73#2706—21no—
74#2663—21no—
75#2625—21no—
76#2625C2211yescharacteristic
77#2552C2211yescharacteristic
78#2550C2211yescharacteristic
79#2550C2211yescharacteristic
80#2512—21no—
81#2504C2211yescharacteristic
82#2499—21no—
83#2499C2211yescharacteristic
84#2492C2211yescharacteristic
85#2489—21no—
86#2489C2211yescharacteristic
87#2485C2211yescharacteristic
88#2474—21no—
89#2470—21no—
90#2454C2211yescharacteristic
91#2453C2211yescharacteristic
92#2451C2211yescharacteristic
93#2448C2211yescharacteristic
94#2441C2211yescharacteristic
95#2439C2211yescharacteristic
96#2439C2211yescharacteristic
97#2426C2211yescharacteristic
98#2421C2211yescharacteristic
99#2414C2211yescharacteristic
100#2395C2211yescharacteristic
101#2363C2211yescharacteristic
102#2362C2211yescharacteristic
103#2351C2211yescharacteristic
104#2345C2211yescharacteristic
105#2317C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2094C2211yescharacteristic
109#2092C2211yescharacteristic
110#2088C2211yescharacteristic
111#2088C2211yescharacteristic
112#2088C2211yescharacteristic
113#2085C2211yescharacteristic
114#2085C2211yescharacteristic
115#2085C2211yescharacteristic
116#2076C2211yescharacteristic
117#2072C2211yescharacteristic
118#2068C2211yescharacteristic
119#2068C2211yescharacteristic
120#2067C2211yescharacteristic
121#2067C2211yescharacteristic
122#2066C2211yescharacteristic
123#2065C2211yescharacteristic
124#2059C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2059C2211yescharacteristic
129#2059C2211yescharacteristic
130#2059C2211yescharacteristic
131#2057C2211yescharacteristic
132#2057C2211yescharacteristic
133#2057C2211yescharacteristic
134#2057C2211yescharacteristic
135#2057C2211yescharacteristic
136#2056C2211yescharacteristic
137#2042C2211yescharacteristic
138#2036C2211yescharacteristic
139#2035C2211yescharacteristic
140#2035C2211yescharacteristic
141#2033C2211yescharacteristic
142#2025C2211yescharacteristic
143#2024C2211yescharacteristic
144#2015C2211yescharacteristic
145#2000C2211yescharacteristic
146#1973C2211yescharacteristic
147#1968C2211yescharacteristic
148#1949C2211yescharacteristic
149#1949C2211yescharacteristic
150#1947C2211yescharacteristic
151#1943C2211yescharacteristic
152#1942C2211yescharacteristic
153#1941C2211yescharacteristic
154#1941C2211yescharacteristic
155#1939C2211yescharacteristic
156#1935C2211yescharacteristic
157#1935C2211yescharacteristic
158#1934C2211yescharacteristic
159#1933C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1919C2211yescharacteristic
167#1919C2211yescharacteristic
168#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1894C2211yescharacteristic
171#1893C2211yescharacteristic
172#1893C2211yescharacteristic
173#1880C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1877C2211yescharacteristic
177#1875C2211yescharacteristic
178#1873C2211yescharacteristic
179#1870C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1862C2211yescharacteristic
186#1854C2211yescharacteristic
187#1854C2211yescharacteristic
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic
190#1850C2211yescharacteristic
191#1850C2211yescharacteristic
192#1847C2211yescharacteristic
193#1846C2211yescharacteristic
194#1824C2211yescharacteristic
195#1807C2211yescharacteristic
196#1805C2211yescharacteristic
197#1776C2211yescharacteristic
198#1771C2211yescharacteristic
199C4×#103C2211yescharacteristic
200#1753C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1736C2211yescharacteristic
203#1735C2211yescharacteristic
204#1729C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#552—24no—
211#552—24no—
212#552—42no—
213#552—42no—
214#544—24no—
215#544—42no—
216#542—24no—
217#542—42no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#126—21no—
223C2×#126—21no—
224C2×#126—21no—
225C2×#125—21no—
226C2×#125—21no—
227C2×#125—21no—
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#124—21no—
233C2×#124C2311yescharacteristic
234C2×#123—21no—
235C2×#123—21no—
236C2×#123—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117—21no—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261#501—24no—
262#499—24no—
263#498—24no—
264#489—24no—
265#488—24no—
266#485—24no—
267#485—24no—
268#485—24no—
269#483—24no—
270#483D418yescomplemented
271#482—24no—
272#481—24no—
273#479—24no—
274#479—24no—
275#479—24no—
276#478—24no—
277#476—24no—
278#475—24no—
279#468—42no—
280#467—24no—
281#467—24no—
282C4×Q16—24no—
283C8×D4—24no—
284#433—24no—
285#428—42no—
286#427—24no—
287C2×#107—24no—
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×#97C2311yescharacteristic
341C2×#97C2311yescharacteristic
342C2×C4×C8C2311yescharacteristic
343C2×C4×C8C2311yescharacteristic
344C2×C4×C8C2311yescharacteristic
345#400—21no—
346#400—21no—
347#400—21no—
348#400—21no—
349#400—21no—
350#400D411yescharacteristic
351#399—21no—
352#399—21no—
353#399—21no—
354#399D411yescharacteristic
355#398—21no—
356#398—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398D411yescharacteristic
363#397—21no—
364#397—21no—
365#397—21no—
366#397—21no—
367#397—21no—
368#397—21no—
369#397—21no—
370#397—21no—
371#397—21no—
372#397—21no—
373#397D411yescharacteristic
374#397D411yescharacteristic
375#397D411yescharacteristic
376#396—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#396—21no—
381#395—21no—
382#395—21no—
383#395—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394D411yescharacteristic
388#394D411yescharacteristic
389#393—21no—
390#393—21no—
391#393—21no—
392#392—21no—
393#391—21no—
394#391—21no—
395#391—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#390—21no—
405#390—21no—
406#390—21no—
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#387—21no—
451#387—21no—
452#386—21no—
453#386—21no—
454#386—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#384—21no—
459#384—21no—
460#384C2311yescharacteristic
461#382—21no—
462#382—21no—
463#382—21no—
464#382C2311yescharacteristic
465#382C2311yescharacteristic
466#382C2311yescharacteristic
467#380—21no—
468#380—21no—
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×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4—21no—
482C4×C22⋊C4C2311yescharacteristic
483C4×C22⋊C4C2311yescharacteristic
484C4×C22⋊C4C2311yescharacteristic
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
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×D4—21no—
521C22×D4—21no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—41no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8—22no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C4⋊Q8—22no—
553C4⋊Q8—22no—
554C4⋊Q8—22no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—44no—
559#126—44no—
560#126—44no—
561#126—44no—
562#125—22no—
563#125—22no—
564#125—22no—
565#125—22no—
566#125—41no—
567#125—41no—
568#125—41no—
569#125—41no—
570#125—44no—
571#125—44no—
572#125—44no—
573#124—22no—
574#124—41no—
575#124—44no—
576#123—44no—
577#123—44no—
578#123—44no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—44no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8C2×D414yes—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—41no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—41no—
606#117—22no—
607#117—22no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—22no—
612#117—22no—
613#117—44no—
614#117—44no—
615#117—41no—
616#117—41no—
617#117—41no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
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—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D414yes—
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#107—22no—
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#107—41no—
736#107—41no—
737#106—22no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—41no—
744#106—41no—
745#106—41no—
746#106C2×D414yes—
747#106C2×D414yes—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—41no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103C2×D414yes—
765#103C2×D414yes—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—41no—
772#102—41no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—41no—
777C22⋊C8C2×D414yes—
778#97—22no—
779#97—22no—
780C4×C8—22no—
781C4×C8—22no—
782C4×C8—41no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#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#95—21no—
817#95—21no—
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828C24—21no—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—42no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8—81no—
850C2×Q8—81no—
851C2×Q8C22×D412yes—
852C2×D4—22no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—24no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D412yes—
914C22×C4H(5,𝔽2)12yes—
915C22×C4C2511yescharacteristic
916Q16—44no—
917SD16—82no—
918M16—44no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
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—44no—
940C2×C8—44no—
941C2×C8C22×D412yes—
942C2×C8C22×D412yes—
943C2×C82−1+412yes—
944C2×C82−1+412yes—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
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—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4C22×D412yes—
1010C4⋊C4C22×D412yes—
1011C4⋊C4C22×D412yes—
1012C4⋊C42−1+412yes—
1013C22⋊C4—24no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—42no—
1057C42—42no—
1058C42—42no—
1059C42—42no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—42no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23D4212yes—
1088C23C23×D411yescharacteristic
1089Q8—22no—
1090Q8—22no—
1091Q8—41no—
1092Q8—41no—
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—162no—
1098Q8—162no—
1099Q8—162no—
1100D4—44no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—162no—
1106D4—162no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
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—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
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—84no—
1196C2×C4—84no—
1197C2×C4—162no—
1198C2×C4D4212yes—
1199C2×C4C23×D411yescharacteristic
1200C2×C4C2×H(5,𝔽2)11yescharacteristic
1201C2×C4C2×2−1+411yescharacteristic
1202C2×C4C2×2−1+411yescharacteristic
1203C2×C4C2×2−1+411yescharacteristic
1204C2×C4#58511yescharacteristic
1205C8—22no—
1206C8—22no—
1207C8—22no—
1208C8—22no—
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C8—41no—
1213C22—22no—
1214C22—22no—
1215C22—22no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22C2×D4211yescharacteristic
1235C22#348911yescharacteristic
1236C22#349911yescharacteristic
1237C22#358411yescharacteristic
1238C22#358411yescharacteristic
1239C22#358411yescharacteristic
1240C22#358611yescharacteristic
1241C4—22no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—42no—
1248C4—42no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—42no—
1253C4—41no—
1254C4—42no—
1255C4—41no—
1256C4—41no—
1257C4—42no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4#348911yescharacteristic
1269C4#349911yescharacteristic
1270C4#353511yescharacteristic
1271C4#354411yescharacteristic
1272C2—42no—
1273C2—81no—
1274C2—161no—
1275C2#4475811yescharacteristic
1276C2#6105211yescharacteristic
1277C2#6109611yescharacteristic
1278C2#6217411yescharacteristic
1279C2#6220711yescharacteristic
1280C2#6249011yescharacteristic
1281C2#6252311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2414C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3336C2semidirect
2. C2×#3244C2semidirect
4. #42644C2semidirect
5. #31243C2semidirect
6. #31101C2semidirect
7. #30958C2semidirect
8. #30956C2semidirect
9. #30810C2semidirect
10. #30798C2semidirect
11. #30668C2semidirect
12. #30660C2semidirect
13. #28910C2semidirect
14. #28820C2semidirect
15. #27947C2semidirect
16. #26830C2semidirect
17. #26814C2semidirect
18. #26383C2semidirect
19. #26345C2semidirect
20. #26061C2semidirect
21. #26048C2semidirect
23. #25514C2semidirect
25. #25215C2semidirect
26. #24616C2semidirect
27. #24583C2semidirect
28. #24106C2semidirect
29. #23555C2semidirect
30. #22927C2semidirect
31. #22901C2semidirect
270. #483D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33362
C2×#32442
#452392
#426442
#312432
#311012
#309582
#309562
#308102
#307982
#306682
#306602
#289102
#288202
#279472
#268302
#268142
#263832
#263452
#260612
#260482
#255552
#255142
#252372
#252152
#246162
#245832
#241062
#235552
#229272
#229012