Finite Group Databasebeta

← #6576259

Subgroups — #6576259

Order 512.

2051 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3108C211yesmaximal, characteristic, complemented
2C2×#3084C211yesmaximal, characteristic, complemented
3#37759C211yesmaximal, characteristic, complemented
4#34294C211yesmaximal, characteristic, complemented
5#33037C211yesmaximal, characteristic, complemented
6#32954C211yesmaximal, characteristic, complemented
7#32919C211yesmaximal, characteristic, complemented
8#28395C211yesmaximal, characteristic, complemented
9#28215C211yesmaximal, characteristic, complemented
10#27241C211yesmaximal, characteristic, complemented
11#27225C211yesmaximal, characteristic, complemented
12#26901C211yesmaximal, characteristic, complemented
13#26892C211yesmaximal, characteristic, complemented
14#26802C211yesmaximal, characteristic, complemented
15#26786C211yesmaximal, characteristic, complemented
16#26373C211yesmaximal, characteristic, complemented
17#26371C211yesmaximal, characteristic, complemented
18#26142C211yesmaximal, characteristic, complemented
19#26128C211yesmaximal, characteristic, complemented
20#24769C211yesmaximal, characteristic, complemented
21#24701C211yesmaximal, characteristic, complemented
22#24449C211yesmaximal, characteristic, complemented
23#24425C211yesmaximal, characteristic
24#24310C211yesmaximal, characteristic, complemented
25#24159C211yesmaximal, characteristic, complemented
26#23036C211yesmaximal, characteristic, complemented
27#23022C211yesmaximal, characteristic, complemented
28#22883C211yesmaximal, characteristic, complemented
29#22873C211yesmaximal, characteristic, complemented
30#22752C211yesmaximal, characteristic, complemented
31#21622C211yesmaximal, characteristic, complemented
32C2×#548C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#3108—28no—
38C2×#483C2211yescharacteristic
39C2×#480C2211yescharacteristic
40#3084—28no—
41C2×#479C2211yescharacteristic
42C2×#479C2211yescharacteristic
43C2×#479C2211yescharacteristic
44C2×#475C2211yescharacteristic
45C2×#475C2211yescharacteristic
46C2×#475C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#476C2211yescharacteristic
50C2×#476C2211yescharacteristic
51C2×#470C2211yescharacteristic
52C2×#465C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#464C2211yescharacteristic
55C2×#463C2211yescharacteristic
56C2×#452C2211yescharacteristic
57C2×#449C2211yescharacteristic
58C2×#451C2211yescharacteristic
59C2×#448C2211yescharacteristic
60C2×C4×Q16C2211yescharacteristic
61C2×C4×Q16C2211yescharacteristic
62C2×C4×SD16C2211yescharacteristic
63C2×C4×SD16C2211yescharacteristic
64C2×#431C2211yescharacteristic
65C2×#428C2211yescharacteristic
66C22×#106C2211yescharacteristic
67C2×#424C2211yescharacteristic
68C2×#417C2211yescharacteristic
69C2×#416C2211yescharacteristic
70#2857C2211yescharacteristic
71#2716—21no—
72#2707—21no—
73#2702—21no—
74#2696—21no—
75#2640C2211yescharacteristic
76#2620C2211yescharacteristic
77#2492C2211yescharacteristic
78#2490C2211yescharacteristic
79#2475—21no—
80#2463—21no—
81#2453C2211yescharacteristic
82#2452—21no—
83#2452C2211yescharacteristic
84#2417C2211yescharacteristic
85#2415—21no—
86#2414C2211yescharacteristic
87#2367—21no—
88#2367C2211yescharacteristic
89#2362C2211yescharacteristic
90#2361—21no—
91#2361C2211yescharacteristic
92#2361C2211yescharacteristic
93#2360—21no—
94#2360C2211yescharacteristic
95Q8×C4⋊C4C2211yescharacteristic
96D4×C4⋊C4—21no—
97D4×C4⋊C4C2211yescharacteristic
98#2341C2211yescharacteristic
99Q8×C22⋊C4C2211yescharacteristic
100#2330C2211yescharacteristic
101#2326—21no—
102#2326C2211yescharacteristic
103#2323—21no—
104#2323C2211yescharacteristic
105C4×#121—21no—
106C4×#121C2211yescharacteristic
107#2290—21no—
108#2290C2211yescharacteristic
109#2276C2211yescharacteristic
110#2096C2211yescharacteristic
111#2094C2211yescharacteristic
112#2084C2211yescharacteristic
113#2083C2211yescharacteristic
114#2077C2211yescharacteristic
115#2077C2211yescharacteristic
116#2066C2211yescharacteristic
117#2065C2211yescharacteristic
118#2059C2211yescharacteristic
119#2058C2211yescharacteristic
120#2056C2211yescharacteristic
121#2055C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2035C2211yescharacteristic
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic
127#2033C2211yescharacteristic
128#2026C2211yescharacteristic
129#2024C2211yescharacteristic
130#2015C2211yescharacteristic
131#2012C2211yescharacteristic
132#2000C2211yescharacteristic
133#1999C2211yescharacteristic
134#1989C2211yescharacteristic
135#1987C2211yescharacteristic
136#1983C2211yescharacteristic
137#1972C2211yescharacteristic
138#1971C2211yescharacteristic
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic
141#1948C2211yescharacteristic
142#1941C2211yescharacteristic
143#1941C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1928C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1927C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic
156#1921C2211yescharacteristic
157#1920C2211yescharacteristic
158#1916C2211yescharacteristic
159#1916C2211yescharacteristic
160#1895C2211yescharacteristic
161#1892C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1877C2211yescharacteristic
172#1874C2211yescharacteristic
173#1873C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1870C2211yescharacteristic
177#1869C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1865C2211yescharacteristic
184#1864C2211yescharacteristic
185#1863C2211yescharacteristic
186#1854C2211yescharacteristic
187#1853C2211yescharacteristic
188#1853C2211yescharacteristic
189#1853C2211yescharacteristic
190#1832C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1802C2211yescharacteristic
194#1798C2211yescharacteristic
195#1797C2211yescharacteristic
196#1787C2211yescharacteristic
197#1787C2211yescharacteristic
198#1776C2211yescharacteristic
199C4×#106C2211yescharacteristic
200#1768C2211yescharacteristic
201#1763C2211yescharacteristic
202C4×#103C2211yescharacteristic
203#1753C2211yescharacteristic
204C8×C22⋊C4C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#548—24no—
216#548—24no—
217#544—24no—
218#544—42no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222#529—24no—
223#529—42no—
224C2×#126—21no—
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×#121—21no—
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244#520—24no—
245#520—42no—
246C2×C4×Q8—21no—
247C2×C4×Q8—21no—
248C2×C4×Q8—24no—
249C2×C4×Q8—42no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×D4—21no—
259C2×C4×D4—21no—
260C2×C4×D4—21no—
261C2×C4×D4—21no—
262C2×C4×D4—21no—
263C2×C4×D4—21no—
264C2×C4×D4—21no—
265C2×C4×D4—21no—
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×#117—21no—
271C2×#117—21no—
272C2×#117C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C22×C4⋊C4—21no—
275C22×C4⋊C4—21no—
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C42—21no—
280C22×C42C2311yescharacteristic
281#483—24no—
282#480—24no—
283#479—24no—
284#479—24no—
285#479D418yescomplemented
286#478—24no—
287#478—24no—
288#476—24no—
289#476—24no—
290#475—24no—
291#475—24no—
292#475—42no—
293#470—24no—
294#465—24no—
295#464—24no—
296#464—24no—
297#463—42no—
298#452—24no—
299#451—24no—
300#449—24no—
301#448—24no—
302C4×Q16—24no—
303C4×Q16—24no—
304C4×SD16—24no—
305C4×SD16—24no—
306#431—24no—
307#428—24no—
308C2×#107C2311yescharacteristic
309C2×#107C2311yescharacteristic
310C2×#107C2311yescharacteristic
311C2×#106—24no—
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×#106C2311yescharacteristic
317C2×#106C2311yescharacteristic
318C2×#106C2311yescharacteristic
319C2×#106C2311yescharacteristic
320C2×#106C2311yescharacteristic
321C2×#106C2311yescharacteristic
322C2×#106C2311yescharacteristic
323#424—24no—
324C2×C4⋊C8C2311yescharacteristic
325C2×C4⋊C8C2311yescharacteristic
326C2×C4⋊C8C2311yescharacteristic
327C2×C4⋊C8C2311yescharacteristic
328C2×C4⋊C8C2311yescharacteristic
329C2×C4⋊C8C2311yescharacteristic
330#417—24no—
331#416—24no—
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×#102C2311yescharacteristic
358C2×#102C2311yescharacteristic
359C2×#102C2311yescharacteristic
360C2×C22⋊C8C2311yescharacteristic
361C2×C22⋊C8C2311yescharacteristic
362C2×C22⋊C8C2311yescharacteristic
363C2×C22⋊C8C2311yescharacteristic
364C2×C22⋊C8C2311yescharacteristic
365C2×C22⋊C8C2311yescharacteristic
366C2×#97C2311yescharacteristic
367C2×C4×C8C2311yescharacteristic
368C2×C4×C8C2311yescharacteristic
369C2×C4×C8C2311yescharacteristic
370#400—21no—
371#400—21no—
372#398—21no—
373#398—21no—
374#397—21no—
375#397—21no—
376#397—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#396—21no—
381#394—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#393—21no—
386#393—21no—
387#393—21no—
388#393—21no—
389#392—21no—
390#391—21no—
391#391—21no—
392#391—21no—
393#391—21no—
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#390—21no—
400#390—21no—
401#390—21no—
402#390—21no—
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#389—21no—
409#389—21no—
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#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
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#388D411yescharacteristic
438#388D411yescharacteristic
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387D411yescharacteristic
446#387D411yescharacteristic
447#386—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#386D411yescharacteristic
452#386D411yescharacteristic
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#385D411yescharacteristic
463#385D411yescharacteristic
464#384—21no—
465#384C2311yescharacteristic
466#384C2311yescharacteristic
467#380—21no—
468#380—21no—
469#380—21no—
470#380—21no—
471#380C2311yescharacteristic
472#380C2311yescharacteristic
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475C4×C4⋊C4—21no—
476C4×C4⋊C4—21no—
477C4×C4⋊C4—21no—
478C4×C4⋊C4—21no—
479C4×C4⋊C4—21no—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C22⋊C4—21no—
487C4×C22⋊C4—21no—
488C4×C22⋊C4—21no—
489C4×C22⋊C4—21no—
490C4×C22⋊C4—21no—
491C4×C22⋊C4C2311yescharacteristic
492C4×C22⋊C4C2311yescharacteristic
493#376—21no—
494#376C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518#336C2311yescharacteristic
519#336C2311yescharacteristic
520#336C2311yescharacteristic
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41#4114yes—
527C22×Q8—22no—
528C22×Q8—22no—
529C22×Q8—21no—
530C22×Q8—21no—
531C22×Q8—21no—
532C22×Q8—22no—
533C22×Q8—22no—
534C22×Q8—41no—
535C22×Q8—41no—
536C22×Q8C2411yescharacteristic
537C22×Q8C2411yescharacteristic
538C22×Q8C2411yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4C2×D411yescharacteristic
544C22×D4C2411yescharacteristic
545C22×D4C2411yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—21no—
554C23×C4C2×D411yescharacteristic
555C23×C4C2×D411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C2×Q16—22no—
559C2×Q16—22no—
560C2×Q16—22no—
561C2×Q16—22no—
562C2×Q16—22no—
563C2×Q16—41no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×D8—22no—
574C2×D8—41no—
575C2×D8—41no—
576C2×M16—22no—
577C2×M16—22no—
578C2×M16—41no—
579C22×C8—22no—
580C22×C8—22no—
581C22×C8—41no—
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C4⋊Q8—22no—
591C4⋊Q8—22no—
592C4⋊Q8—22no—
593C4⋊Q8—41no—
594C4⋊Q8—44no—
595#126—44no—
596#125—22no—
597#125—22no—
598#125—41no—
599#125—44no—
600#125C2×D414yes—
601#124—28no—
602#124—22no—
603#124—22no—
604#124—22no—
605#124—22no—
606#123—44no—
607C22⋊Q8—28no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—44no—
613C22⋊Q8—44no—
614C22⋊Q8—41no—
615C22⋊Q8—82no—
616C22⋊Q8—82no—
617C22⋊Q8#4114yes—
618#121—28no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—41no—
625C4×Q8—22no—
626C4×Q8—22no—
627C4×Q8—22no—
628C4×Q8—22no—
629C4×Q8—22no—
630C4×Q8—22no—
631C4×Q8—22no—
632C4×Q8—22no—
633C4×Q8—22no—
634C4×Q8—22no—
635C4×Q8—44no—
636C4×Q8—41no—
637C4×Q8—41no—
638C4×Q8—41no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8—44no—
642C4×Q8C2×D414yes—
643C4×D4—28no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—44no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—44no—
654C4×D4—44no—
655C4×D4—82no—
656C4×D4—82no—
657C4×D4—82no—
658C4×D4—82no—
659#117—22no—
660#117—22no—
661#117—22no—
662#117—44no—
663#117—44no—
664#117—41no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—41no—
699C2×C4⋊C4—41no—
700C2×C4⋊C4—41no—
701C2×C4⋊C4—44no—
702C2×C4⋊C4—44no—
703C2×C4⋊C4C2×D411yescharacteristic
704C2×C4⋊C4C2×D411yescharacteristic
705C2×C4⋊C4C2×D411yescharacteristic
706C2×C4⋊C4C2×D411yescharacteristic
707C2×C4⋊C4C2×D411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
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—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C22⋊C4C2×D411yescharacteristic
752C2×C22⋊C4C2×D411yescharacteristic
753C2×C22⋊C4C2×D411yescharacteristic
754C2×C22⋊C4C2×D411yescharacteristic
755C2×C42—21no—
756C2×C42—21no—
757C2×C42—22no—
758C2×C42—22no—
759C2×C42—21no—
760C2×C42—21no—
761C2×C42—21no—
762C2×C42—21no—
763C2×C42—21no—
764C2×C42—21no—
765C2×C42—21no—
766C2×C42—21no—
767C2×C42—21no—
768C2×C42—21no—
769C2×C42—21no—
770C2×C42—21no—
771C2×C42—44no—
772C2×C42C2×D411yescharacteristic
773C2×C42C2×D411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2411yescharacteristic
776C2×C42C2411yescharacteristic
777C2×C42C2411yescharacteristic
778C2×C42C2411yescharacteristic
779#107—22no—
780#107—22no—
781#107C2×D414yes—
782#106—22no—
783#106—22no—
784#106—22no—
785#106—22no—
786#106—22no—
787#106—22no—
788#106—22no—
789#106—22no—
790#106—41no—
791#106—41no—
792#106C2×D414yes—
793C4⋊C8—22no—
794C4⋊C8—22no—
795C4⋊C8—22no—
796C4⋊C8—22no—
797C4⋊C8—22no—
798C4⋊C8C2×D414yes—
799#103—22no—
800#103—22no—
801#103—22no—
802#103—22no—
803#103—22no—
804#103—22no—
805#103—22no—
806#103—22no—
807#103—22no—
808#103—22no—
809#103—22no—
810#103—41no—
811#103—41no—
812#103—41no—
813#103—41no—
814#103C2×D414yes—
815#103C2×D414yes—
816#102—22no—
817#102—22no—
818#102—22no—
819#102—22no—
820#102—22no—
821#102—22no—
822#102—22no—
823#102—22no—
824#102—22no—
825#102—41no—
826#102—41no—
827C22⋊C8—22no—
828C22⋊C8—22no—
829C22⋊C8—22no—
830C22⋊C8—22no—
831C22⋊C8—41no—
832C22⋊C8—41no—
833#97—41no—
834C4×C8—22no—
835C4×C8—22no—
836C4×C8—41no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95—21no—
859#95—21no—
860#95—21no—
861#95—21no—
862#95C2×D411yescharacteristic
863#95C2×D411yescharacteristic
864#95C2×D411yescharacteristic
865#95C2×D411yescharacteristic
866#95C2×D411yescharacteristic
867#95C2×D411yescharacteristic
868#95C2×D411yescharacteristic
869#95C2×D411yescharacteristic
870#95C2×D411yescharacteristic
871#95C2×D411yescharacteristic
872C24—21no—
873C24—21no—
874C24C22×D411yescharacteristic
875C24C22×D411yescharacteristic
876#41—28no—
877#41—44no—
878#41—44no—
879#41—44no—
880C2×Q8—24no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—42no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—44no—
899C2×Q8—44no—
900C2×Q8—44no—
901C2×Q8—44no—
902C2×Q8—42no—
903C2×Q8—81no—
904C2×Q8—81no—
905C2×Q8—81no—
906C2×Q8—81no—
907C2×Q8C22×D412yes—
908C2×Q8C2×#4112yes—
909C2×Q8C2×#4112yes—
910C2×Q82−1+412yes—
911C2×D4—24no—
912C2×D4—22no—
913C2×D4—24no—
914C2×D4—22no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—41no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4C2×#4112yes—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—24no—
944C22×C4—22no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—24no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—41no—
969C22×C4—41no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C2×#4112yes—
1005C22×C4C2×#4112yes—
1006C22×C4C2511yescharacteristic
1007Q16—44no—
1008Q16—44no—
1009SD16—44no—
1010SD16—44no—
1011SD16—82no—
1012D8—82no—
1013M16—44no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—44no—
1037C2×C8C22×D412yes—
1038C2×C8C22×D412yes—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—22no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—41no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4—81no—
1092C4⋊C4C22×D412yes—
1093C4⋊C4C22×D412yes—
1094C4⋊C4C22×D412yes—
1095C4⋊C4C2×#4112yes—
1096C22⋊C4—24no—
1097C22⋊C4—24no—
1098C22⋊C4—24no—
1099C22⋊C4—24no—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—22no—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—41no—
1107C22⋊C4—41no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C42—24no—
1133C42—22no—
1134C42—22no—
1135C42—24no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—42no—
1148C42—42no—
1149C42—42no—
1150C42—42no—
1151C42—81no—
1152C42—81no—
1153C42—81no—
1154C42—81no—
1155C42—81no—
1156C42C22×D412yes—
1157C42H(5,𝔽2)12yes—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—22no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23#52512yes—
1185C23#57712yes—
1186C23C23×D411yescharacteristic
1187Q8—22no—
1188Q8—22no—
1189Q8—22no—
1190Q8—22no—
1191Q8—22no—
1192Q8—48no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—162no—
1200Q8—162no—
1201Q8#54814yes—
1202D4—22no—
1203D4—22no—
1204D4—48no—
1205D4—44no—
1206D4—48no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—84no—
1214D4—84no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
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—22no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—44no—
1260C2×C4—48no—
1261C2×C4—44no—
1262C2×C4—48no—
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—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—84no—
1302C2×C4—84no—
1303C2×C4—162no—
1304C2×C4—162no—
1305C2×C4—162no—
1306C2×C4—162no—
1307C2×C4#52512yes—
1308C2×C4D4212yes—
1309C2×C4D4212yes—
1310C2×C4#57712yes—
1311C2×C4C23×D411yescharacteristic
1312C2×C4C22×#4111yescharacteristic
1313C2×C4C22×#4111yescharacteristic
1314C2×C4C2×H(5,𝔽2)11yescharacteristic
1315C2×C4C2×2−1+411yescharacteristic
1316C2×C4#58511yescharacteristic
1317C8—22no—
1318C8—22no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C8—41no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22C2×#52511yescharacteristic
1354C22C2×D4211yescharacteristic
1355C22#348911yescharacteristic
1356C22C2×#57711yescharacteristic
1357C22C2×#57711yescharacteristic
1358C22#358411yescharacteristic
1359C22#358611yescharacteristic
1360C4—22no—
1361C4—24no—
1362C4—22no—
1363C4—22no—
1364C4—22no—
1365C4—41no—
1366C4—42no—
1367C4—41no—
1368C4—41no—
1369C4—42no—
1370C4—42no—
1371C4—41no—
1372C4—42no—
1373C4—41no—
1374C4—41no—
1375C4—42no—
1376C4—41no—
1377C4—41no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4C2×#54811yescharacteristic
1387C4D4×#4111yescharacteristic
1388C4#350511yescharacteristic
1389C4#352011yescharacteristic
1390C2—42no—
1391C2—42no—
1392C2—82no—
1393C2—161no—
1394C2#3609711yescharacteristic
1395C2#6057211yescharacteristic
1396C2#6058511yescharacteristic
1397C2#6105511yescharacteristic
1398C2#6107511yescharacteristic
1399C2#6217711yescharacteristic
1400C2#6220511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24425C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3108C2semidirect
2. C2×#3084C2semidirect
3. #37759C2semidirect
4. #34294C2semidirect
5. #33037C2semidirect
6. #32954C2semidirect
7. #32919C2semidirect
8. #28395C2semidirect
9. #28215C2semidirect
10. #27241C2semidirect
11. #27225C2semidirect
12. #26901C2semidirect
13. #26892C2semidirect
14. #26802C2semidirect
15. #26786C2semidirect
16. #26373C2semidirect
17. #26371C2semidirect
18. #26142C2semidirect
19. #26128C2semidirect
20. #24769C2semidirect
21. #24701C2semidirect
22. #24449C2semidirect
24. #24310C2semidirect
25. #24159C2semidirect
26. #23036C2semidirect
27. #23022C2semidirect
28. #22883C2semidirect
29. #22873C2semidirect
30. #22752C2semidirect
31. #21622C2semidirect
285. #479D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31082
C2×#30842
#377592
#342942
#330372
#329542
#329192
#283952
#282152
#272412
#272252
#269012
#268922
#268022
#267862
#263732
#263712
#261422
#261282
#247692
#247012
#244492
#244252
#243102
#241592
#230362
#230222
#228832
#228732
#227522
#216222