Finite Group Databasebeta

← #7124584

Subgroups — #7124584

Order 512.

1723 conjugacy classes of subgroups.

The subgroup lattice has 1299 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3336C211yesmaximal, characteristic, complemented
2C2×#3243C211yesmaximal, characteristic, complemented
3#45016C211yesmaximal, characteristic
4#42964C211yesmaximal, characteristic, complemented
5#31235C211yesmaximal, characteristic, complemented
6#31095C211yesmaximal, characteristic, complemented
7#30951C211yesmaximal, characteristic, complemented
8#30948C211yesmaximal, characteristic, complemented
9#30818C211yesmaximal, characteristic, complemented
10#30801C211yesmaximal, characteristic, complemented
11#30670C211yesmaximal, characteristic, complemented
12#30657C211yesmaximal, characteristic, complemented
13#28910C211yesmaximal, characteristic, complemented
14#28820C211yesmaximal, characteristic, complemented
15#27945C211yesmaximal, characteristic, complemented
16#26830C211yesmaximal, characteristic, complemented
17#26800C211yesmaximal, characteristic, complemented
18#26381C211yesmaximal, characteristic, complemented
19#26336C211yesmaximal, characteristic, complemented
20#26065C211yesmaximal, characteristic, complemented
21#26047C211yesmaximal, characteristic, complemented
22#25560C211yesmaximal, characteristic
23#25514C211yesmaximal, characteristic, complemented
24#25232C211yesmaximal, characteristic
25#25206C211yesmaximal, characteristic, complemented
26#24613C211yesmaximal, characteristic, complemented
27#24587C211yesmaximal, characteristic, complemented
28#24110C211yesmaximal, characteristic, complemented
29#23557C211yesmaximal, characteristic, complemented
30#22928C211yesmaximal, characteristic, complemented
31#22901C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#544C2211yescharacteristic
35C2×#542C2211yescharacteristic
36#3336—28no—
37#3243—28no—
38C2×#501C2211yescharacteristic
39C2×#500C2211yescharacteristic
40C2×#499C2211yescharacteristic
41C2×#489C2211yescharacteristic
42C2×#488C2211yescharacteristic
43C2×#484C2211yescharacteristic
44C2×#485C2211yescharacteristic
45C2×#485C2211yescharacteristic
46C2×#482C2211yescharacteristic
47C2×#483C2211yescharacteristic
48C2×#483C2211yescharacteristic
49C2×#480C2211yescharacteristic
50C2×#479C2211yescharacteristic
51C2×#479C2211yescharacteristic
52C2×#479C2211yescharacteristic
53C2×#477C2211yescharacteristic
54C2×#478C2211yescharacteristic
55C2×#474C2211yescharacteristic
56C2×#468C2211yescharacteristic
57C2×#467C2211yescharacteristic
58C2×#467C2211yescharacteristic
59C2×C4×Q16C2211yescharacteristic
60C2×C8×D4C2211yescharacteristic
61C2×#433C2211yescharacteristic
62C2×#428C2211yescharacteristic
63C2×#427C2211yescharacteristic
64C22×#107C2211yescharacteristic
65#2822—21no—
66#2725—21no—
67#2720—21no—
68#2698—21no—
69#2698—21no—
70#2695—21no—
71#2680—21no—
72#2680—21no—
73#2672—21no—
74#2660—21no—
75#2625C2211yescharacteristic
76#2621—21no—
77#2611—21no—
78#2552C2211yescharacteristic
79#2552C2211yescharacteristic
80#2550C2211yescharacteristic
81#2521—21no—
82#2502C2211yescharacteristic
83#2500C2211yescharacteristic
84#2489C2211yescharacteristic
85#2489C2211yescharacteristic
86#2486C2211yescharacteristic
87#2479—21no—
88#2454C2211yescharacteristic
89#2451C2211yescharacteristic
90#2451C2211yescharacteristic
91#2448C2211yescharacteristic
92#2440C2211yescharacteristic
93#2440C2211yescharacteristic
94#2440C2211yescharacteristic
95#2426C2211yescharacteristic
96#2422—21no—
97#2421C2211yescharacteristic
98#2416C2211yescharacteristic
99#2415—21no—
100#2395C2211yescharacteristic
101#2361C2211yescharacteristic
102#2360C2211yescharacteristic
103Q8×C4⋊C4C2211yescharacteristic
104#2346C2211yescharacteristic
105#2316C2211yescharacteristic
106#2097C2211yescharacteristic
107#2095C2211yescharacteristic
108#2094C2211yescharacteristic
109#2093C2211yescharacteristic
110#2088C2211yescharacteristic
111#2086C2211yescharacteristic
112#2086C2211yescharacteristic
113#2085C2211yescharacteristic
114#2083C2211yescharacteristic
115#2083C2211yescharacteristic
116#2075C2211yescharacteristic
117#2072C2211yescharacteristic
118#2068C2211yescharacteristic
119#2068C2211yescharacteristic
120#2068C2211yescharacteristic
121#2067C2211yescharacteristic
122#2067C2211yescharacteristic
123#2065C2211yescharacteristic
124#2059C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2059C2211yescharacteristic
129#2059C2211yescharacteristic
130#2059C2211yescharacteristic
131#2058C2211yescharacteristic
132#2058C2211yescharacteristic
133#2057C2211yescharacteristic
134#2057C2211yescharacteristic
135#2057C2211yescharacteristic
136#2056C2211yescharacteristic
137#2042C2211yescharacteristic
138#2035C2211yescharacteristic
139#2035C2211yescharacteristic
140#2035C2211yescharacteristic
141#2033C2211yescharacteristic
142#2025C2211yescharacteristic
143#2024C2211yescharacteristic
144#2015C2211yescharacteristic
145#2000C2211yescharacteristic
146#1973C2211yescharacteristic
147#1968C2211yescharacteristic
148#1949C2211yescharacteristic
149#1948C2211yescharacteristic
150#1947C2211yescharacteristic
151#1943C2211yescharacteristic
152#1942C2211yescharacteristic
153#1942C2211yescharacteristic
154#1942C2211yescharacteristic
155#1939C2211yescharacteristic
156#1935C2211yescharacteristic
157#1935C2211yescharacteristic
158#1934C2211yescharacteristic
159#1933C2211yescharacteristic
160#1928C2211yescharacteristic
161#1928C2211yescharacteristic
162#1926C2211yescharacteristic
163#1925C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1920C2211yescharacteristic
167#1918C2211yescharacteristic
168#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1894C2211yescharacteristic
171#1893C2211yescharacteristic
172#1893C2211yescharacteristic
173#1880C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1877C2211yescharacteristic
177#1874C2211yescharacteristic
178#1872C2211yescharacteristic
179#1870C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1862C2211yescharacteristic
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic
188#1852C2211yescharacteristic
189#1852C2211yescharacteristic
190#1850C2211yescharacteristic
191#1850C2211yescharacteristic
192#1847C2211yescharacteristic
193#1845C2211yescharacteristic
194#1825C2211yescharacteristic
195#1808C2211yescharacteristic
196#1803C2211yescharacteristic
197#1776C2211yescharacteristic
198#1771C2211yescharacteristic
199C4×#103C2211yescharacteristic
200#1753C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1736C2211yescharacteristic
203C2×#340C2211yescharacteristic
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×#123—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×#121—21no—
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4—21no—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117—21no—
259C2×#117—21no—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267#501—24no—
268#500—24no—
269#499—24no—
270#489—24no—
271#488—24no—
272#485—24no—
273#485D418yescomplemented
274#484—24no—
275#483—24no—
276#483—24no—
277#482—24no—
278#480—24no—
279#479—24no—
280#479—24no—
281#479—24no—
282#478—24no—
283#477—24no—
284#474—24no—
285#468—42no—
286#467—24no—
287#467—24no—
288C4×Q16—24no—
289C8×D4—24no—
290#433—24no—
291#428—42no—
292#427—24no—
293C2×#107—24no—
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×#97C2311yescharacteristic
347C2×#97C2311yescharacteristic
348C2×C4×C8C2311yescharacteristic
349C2×C4×C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351#400—21no—
352#400—21no—
353#400—21no—
354#400—21no—
355#400D411yescharacteristic
356#399—21no—
357#399—21no—
358#399D411yescharacteristic
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#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398D411yescharacteristic
374#397—21no—
375#397—21no—
376#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#397—21no—
381#397D411yescharacteristic
382#397D411yescharacteristic
383#397D411yescharacteristic
384#396—21no—
385#396—21no—
386#396—21no—
387#395—21no—
388#395—21no—
389#395—21no—
390#395—21no—
391#395—21no—
392#395—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#394—21no—
397#394D411yescharacteristic
398#394D411yescharacteristic
399#391—21no—
400#391—21no—
401#391—21no—
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#390—21no—
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
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#388—21no—
441#388—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#386—21no—
447#386—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#384—21no—
457#384—21no—
458#384—21no—
459#384C2311yescharacteristic
460#384C2311yescharacteristic
461#384C2311yescharacteristic
462#382—21no—
463#382—21no—
464#382—21no—
465#382C2311yescharacteristic
466#381—21no—
467#380—21no—
468#380—21no—
469#380—21no—
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
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⋊C4C2311yescharacteristic
482C4×C22⋊C4C2311yescharacteristic
483C4×C22⋊C4C2311yescharacteristic
484#376—21no—
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×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—41no—
534C2×SD16—22no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—41no—
540C22×C8—22no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C4⋊Q8—22no—
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—44no—
561#126—44no—
562#126—44no—
563#126—44no—
564#125—22no—
565#125—22no—
566#125—22no—
567#125—22no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125—41no—
572#125—44no—
573#125—44no—
574#125—44no—
575#124—22no—
576#124—41no—
577#124—44no—
578#123—44no—
579#123—44no—
580#123—44no—
581#123—82no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—82no—
593C22⋊Q8—82no—
594C22⋊Q8—82no—
595C22⋊Q8C2×D414yes—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—82no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—41no—
613C4×D4—82no—
614#117—22no—
615#117—22no—
616#117—22no—
617#117—22no—
618#117—22no—
619#117—44no—
620#117—44no—
621#117C2×D414yes—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
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⋊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—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
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×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⋊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⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—22no—
737#107—22no—
738#107—22no—
739#107—22no—
740#107—22no—
741#107—22no—
742#107—22no—
743#107—22no—
744#107—22no—
745#107—22no—
746#107—41no—
747#107—41no—
748#107—41no—
749#107—41no—
750#107C2×D414yes—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—22no—
755#106—41no—
756#106—41no—
757#106C2×D414yes—
758C4⋊C8—22no—
759C4⋊C8—22no—
760C4⋊C8—22no—
761C4⋊C8—22no—
762C4⋊C8—41no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103C2×D414yes—
775#103C2×D414yes—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—41no—
782#102—41no—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—41no—
787C22⋊C8C2×D414yes—
788#97—22no—
789#97—22no—
790C4×C8—22no—
791C4×C8—22no—
792C4×C8—41no—
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#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834C24—21no—
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—42no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×Q8—81no—
855C2×Q8—81no—
856C2×Q8—81no—
857C2×Q8C22×D412yes—
858C2×D4—22no—
859C2×D4—22no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—41no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
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—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
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×D412yes—
925C22×C4C22×D411yescharacteristic
926C22×C4H(5,𝔽2)12yes—
927C22×C4C2511yescharacteristic
928Q16—44no—
929SD16—82no—
930M16—44no—
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×C8—21no—
951C2×C8—44no—
952C2×C8—44no—
953C2×C8C22×D412yes—
954C2×C8C22×D412yes—
955C2×C82−1+412yes—
956C2×C82−1+412yes—
957C4⋊C4—24no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
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—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
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—42no—
1008C4⋊C4—42no—
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⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4C22×D412yes—
1028C4⋊C4C22×D412yes—
1029C4⋊C4C22×D412yes—
1030C4⋊C42−1+412yes—
1031C22⋊C4—24no—
1032C22⋊C4—24no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C42—24no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—42no—
1078C42—42no—
1079C42—42no—
1080C42—81no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23D4212yes—
1101C23#57612yes—
1102C23C23×D411yescharacteristic
1103Q8—22no—
1104Q8—22no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—162no—
1112Q8—162no—
1113Q8—162no—
1114D4—44no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—84no—
1120D4—162no—
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—22no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—22no—
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—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
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—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
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—84no—
1209C2×C4—84no—
1210C2×C4—162no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4D4212yes—
1214C2×C4#57812yes—
1215C2×C4C23×D411yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4C2×2−1+411yescharacteristic
1218C2×C4C2×2−1+411yescharacteristic
1219C2×C4C2×2−1+411yescharacteristic
1220C2×C4#58511yescharacteristic
1221C8—22no—
1222C8—22no—
1223C8—22no—
1224C8—22no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C22—22no—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×D4211yescharacteristic
1251C22#348911yescharacteristic
1252C22#349911yescharacteristic
1253C22C2×#57611yescharacteristic
1254C22C2×#57811yescharacteristic
1255C22#358411yescharacteristic
1256C22#358611yescharacteristic
1257C4—22no—
1258C4—22no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—42no—
1265C4—42no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—42no—
1270C4—41no—
1271C4—42no—
1272C4—41no—
1273C4—42no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4#348911yescharacteristic
1285C4#349911yescharacteristic
1286C4#353511yescharacteristic
1287C4#354411yescharacteristic
1288C2—42no—
1289C2—42no—
1290C2—161no—
1291C2#4475811yescharacteristic
1292C2#6105611yescharacteristic
1293C2#6109711yescharacteristic
1294C2#6215511yescharacteristic
1295C2#6221411yescharacteristic
1296C2#6248711yescharacteristic
1297C2#6252311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2416C22
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×#3243C2semidirect
4. #42964C2semidirect
5. #31235C2semidirect
6. #31095C2semidirect
7. #30951C2semidirect
8. #30948C2semidirect
9. #30818C2semidirect
10. #30801C2semidirect
11. #30670C2semidirect
12. #30657C2semidirect
13. #28910C2semidirect
14. #28820C2semidirect
15. #27945C2semidirect
16. #26830C2semidirect
17. #26800C2semidirect
18. #26381C2semidirect
19. #26336C2semidirect
20. #26065C2semidirect
21. #26047C2semidirect
23. #25514C2semidirect
25. #25206C2semidirect
26. #24613C2semidirect
27. #24587C2semidirect
28. #24110C2semidirect
29. #23557C2semidirect
30. #22928C2semidirect
31. #22901C2semidirect
273. #485D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33362
C2×#32432
#450162
#429642
#312352
#310952
#309512
#309482
#308182
#308012
#306702
#306572
#289102
#288202
#279452
#268302
#268002
#263812
#263362
#260652
#260472
#255602
#255142
#252322
#252062
#246132
#245872
#241102
#235572
#229282
#229012