Finite Group Databasebeta

← #6432862

Subgroups — #6432862

Order 512.

4514 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3488C211yesmaximal, characteristic
2C2×#3097C211yesmaximal, characteristic, complemented
3C2×#3009C211yesmaximal, characteristic, complemented
4#35305C211yesmaximal, characteristic, complemented
5#29609C212yesmaximal, complemented
6#29608C212yesmaximal, complemented
7#29604C212yesmaximal, complemented
8#29604C212yesmaximal, complemented
9#29601C212yesmaximal, complemented
10#29601C212yesmaximal, complemented
11#29598C212yesmaximal, complemented
12#29596C212yesmaximal, complemented
13#23486C211yesmaximal, characteristic, complemented
14#23485C211yesmaximal, characteristic, complemented
15#23480C211yesmaximal, characteristic, complemented
16#23479C211yesmaximal, characteristic, complemented
17#23394C211yesmaximal, characteristic, complemented
18#23392C211yesmaximal, characteristic, complemented
19#23388C211yesmaximal, characteristic, complemented
20C2×#2000C211yesmaximal, characteristic, complemented
21#20703C211yesmaximal, characteristic, complemented
22#20602C211yesmaximal, characteristic, complemented
23#20581C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic
25C23×#41C2211yescharacteristic
26C22×#137C2211yescharacteristic, complemented
27C23×SD16C2211yescharacteristic, complemented
28#3488—28no—
29#3488—28no—
30C2×#550—21no—
31C2×#548—21no—
32C2×#546—22no—
33C2×#546—21no—
34C2×D42—22no—
35C2×D42—21no—
36C2×#537C2211yescharacteristic
37C2×#537C2212yes—
38C2×#536C2211yescharacteristic
39C2×#536C2211yescharacteristic, complemented
40C2×#535C2211yescharacteristic
41C2×#535C2212yes—
42C2×#525C2211yescharacteristic
43C2×#525C2212yes—
44C22×C22⋊Q8C2211yescharacteristic, complemented
45C22×#121C2211yescharacteristic
46C22×#121C2212yes—
47C2×#520C2211yescharacteristic
48#3097—28no—
49C2×#484C2212yescomplemented
50C2×#485C2212yescomplemented
51C2×#485C2212yescomplemented
52C2×#483C2212yescomplemented
53#3009—28no—
54C2×#452C2212yescomplemented
55C2×#452C2212yescomplemented
56C2×#450C2212yescomplemented
57C2×#450C2212yescomplemented
58C2×#428C2211yescharacteristic, complemented
59C2×#427C2211yescharacteristic, complemented
60C2×#417C2211yescharacteristic, complemented
61C2×#419C2211yescharacteristic, complemented
62C2×#418C2211yescharacteristic, complemented
63C2×#418C2211yescharacteristic, complemented
64C2×#416C2211yescharacteristic, complemented
65C2×#416C2211yescharacteristic, complemented
66C22×#103C2211yescharacteristic, complemented
67C22×#102C2211yescharacteristic, complemented
68C2×#408C2211yescharacteristic
69C2×#408C2211yescharacteristic
70C2×#408C2211yescharacteristic, complemented
71C2×#408C2211yescharacteristic, complemented
72C2×#407C2211yescharacteristic, complemented
73C22×C22⋊C8C2211yescharacteristic, complemented
74#2848C2212yescomplemented
75#2848C2212yescomplemented
76#2616C2212yescomplemented
77#2616C2212yescomplemented
78#2435—21no—
79#2434—21no—
80#2432—21no—
81#2432—21no—
82#2406—22no—
83#2405—22no—
84#2311C2211yescharacteristic
85#2311C2211yescharacteristic, complemented
86#2280C2211yescharacteristic, complemented
87#2036C2211yescharacteristic, complemented
88#2036C2212yescomplemented
89#2036C2211yescharacteristic, complemented
90#2035C2211yescharacteristic, complemented
91#2035C2212yescomplemented
92#2035C2211yescharacteristic, complemented
93#2034C2211yescharacteristic, complemented
94#2034C2212yescomplemented
95#2034C2212yescomplemented
96#2034C2212yescomplemented
97#2034C2212yescomplemented
98#2034C2211yescharacteristic, complemented
99#2034C2212yescomplemented
100#2033C2211yescharacteristic, complemented
101#2033C2212yescomplemented
102#2033C2212yescomplemented
103#2033C2212yescomplemented
104#2033C2212yescomplemented
105#2033C2211yescharacteristic, complemented
106#2033C2212yescomplemented
107#2001C2212yescomplemented
108#2001C2212yescomplemented
109#2001C2212yescomplemented
110#2001C2212yescomplemented
111#2000C2212yescomplemented
112#2000C2212yescomplemented
113#2000C2212yescomplemented
114#2000C2212yescomplemented
115#2000C2212yescomplemented
116#2000C2212yescomplemented
117#2000C2212yescomplemented
118#2000C2212yescomplemented
119#2000C2212yescomplemented
120#2000C2212yescomplemented
121#2000C2212yescomplemented
122#2000C2212yescomplemented
123#1825C2212yescomplemented
124#1825C2212yescomplemented
125#1824C2212yescomplemented
126#1823C2212yescomplemented
127#1788C2212yescomplemented
128#1788C2212yescomplemented
129#1786C2212yescomplemented
130#1786C2212yescomplemented
131#1780C2212yescomplemented
132#1780C2212yescomplemented
133#1779C2212yescomplemented
134#1779C2212yescomplemented
135#1736C2211yescharacteristic, complemented
136#1736C2211yescharacteristic, complemented
137#1735C2211yescharacteristic, complemented
138C2×#340C2211yescharacteristic, complemented
139C2×H(5,𝔽2)—24no—
140C2×H(5,𝔽2)—42no—
141C2×H(5,𝔽2)—42no—
142C2×H(5,𝔽2)—42no—
143C2×H(5,𝔽2)—42no—
144C2×H(5,𝔽2)D418yes—
145C22×#41—24no—
146C22×#41—24no—
147C22×#41—21no—
148C22×#41—42no—
149C22×#41—42no—
150C22×#41—42no—
151C22×#41—42no—
152C22×#41D412yes—
153C22×#41D411yescharacteristic
154C22×#41D411yescharacteristic
155C22×#41C2311yescharacteristic
156C22×#41C2312yes—
157C22×#41C2311yescharacteristic
158C22×#41C2311yescharacteristic
159C22×#41C2312yes—
160C23×Q8D411yescharacteristic
161C23×Q8C2311yescharacteristic
162C23×D4—21no—
163C23×D4—22no—
164C23×D4—22no—
165C23×D4—21no—
166C23×D4D412yes—
167C23×D4D411yescharacteristic
168C23×D4C2311yescharacteristic
169C23×D4C2312yes—
170C24×C4C2311yescharacteristic
171C24×C4C2312yes—
172C2×#137—24no—
173C2×#137—42no—
174C2×#137—42no—
175C22×Q16C2312yes—
176C22×SD16—24no—
177C22×SD16—42no—
178C22×SD16—42no—
179C22×SD16C2312yes—
180C22×SD16C2312yes—
181C22×SD16C2312yes—
182C22×M16C2311yescharacteristic
183C22×M16C2311yescharacteristic
184C23×C8C2311yescharacteristic
185C23×C8C2311yescharacteristic
186#550—216no—
187#548—216no—
188#546—232no—
189#546—216no—
190D42—232no—
191D42—216no—
192#537—24no—
193#537—28no—
194#537—24no—
195#537—28no—
196#536—24no—
197#536—24no—
198#536—42no—
199#536—42no—
200#535—24no—
201#535—28no—
202#535—24no—
203#535—28no—
204C2×C4⋊Q8—21no—
205C2×C4⋊Q8—21no—
206C2×#127—21no—
207C2×#127—22no—
208C2×#124—21no—
209C2×#124—22no—
210C2×#124—21no—
211C2×#124—21no—
212#525—24no—
213#525—28no—
214#525—24no—
215#525—28no—
216C2×#123—21no—
217C2×#123—22no—
218C2×#123—22no—
219C2×#123—22no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—22no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—42no—
225C2×C22⋊Q8—42no—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×#121—24no—
236C2×#121—28no—
237C2×#121—22no—
238C2×#121—22no—
239C2×#121—22no—
240C2×#121—21no—
241C2×#121—22no—
242C2×#121—21no—
243C2×#121—22no—
244C2×#121—21no—
245C2×#121—22no—
246C2×#121—24no—
247C2×#121—28no—
248C2×#121C2312yes—
249C2×#121C2311yescharacteristic
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2311yescharacteristic
254C2×#121C2312yes—
255C2×#120—21no—
256C2×#120—22no—
257C2×#120—22no—
258C2×#120—22no—
259C2×#120—22no—
260#520—24no—
261#520D418yes—
262C2×C4×Q8—21no—
263C2×C4×D4—22no—
264C2×C4×D4—21no—
265C2×C4×D4—21no—
266C2×C4×D4—22no—
267C2×C4×D4—21no—
268C2×C4×D4—22no—
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C2×#117C2312yes—
272C2×#117C2311yescharacteristic
273C22×C4⋊C4—21no—
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2311yescharacteristic
277C22×C22⋊C4—21no—
278C22×C22⋊C4—22no—
279C22×C22⋊C4—21no—
280#485—28no—
281#485—28no—
282#484—28no—
283#483—28no—
284#452—28no—
285#452—28no—
286#450—28no—
287#450—28no—
288#428—24no—
289#427—24no—
290C2×#107C2311yescharacteristic
291C2×#107C2312yes—
292C2×#107C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2312yes—
295C2×#106C2311yescharacteristic
296#419—24no—
297#418—24no—
298#418—42no—
299#417—42no—
300#416—24no—
301#416—42no—
302C2×#103—24no—
303C2×#103C2312yes—
304C2×#103C2312yes—
305C2×#103C2312yes—
306C2×#103C2312yes—
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2312yes—
312C2×#102—42no—
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2312yes—
316C2×#102C2312yes—
317C2×#102C2312yes—
318C2×#102C2312yes—
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2312yes—
322C2×#102C2312yes—
323C2×#102C2312yes—
324#408—24no—
325#408—24no—
326#408—42no—
327#408—42no—
328#407—42no—
329C2×C22⋊C8—42no—
330C2×C22⋊C8C2312yes—
331C2×C22⋊C8C2312yes—
332C2×C22⋊C8C2312yes—
333C2×C22⋊C8C2312yes—
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2312yes—
339C2×C22⋊C8C2312yes—
340C2×C22⋊C8C2312yes—
341C2×C22⋊C8C2312yes—
342C2×C22⋊C8C2312yes—
343C2×C22⋊C8C2312yes—
344#395—22no—
345#395—22no—
346#394—22no—
347#394—22no—
348#394—22no—
349#394—22no—
350#394—22no—
351#394—22no—
352#391—21no—
353#391—21no—
354#390—21no—
355#390—21no—
356#386—22no—
357#386—22no—
358#385—22no—
359#385—22no—
360#385—22no—
361#385—22no—
362#385—22no—
363#385—22no—
364#381—21no—
365#380C2312yes—
366#380C2312yes—
367#380C2312yes—
368#380C2312yes—
369#380C2311yescharacteristic
370#380C2311yescharacteristic
371#380C2311yescharacteristic
372#380C2311yescharacteristic
373#379—22no—
374#379—22no—
375#379—21no—
376C4×C22⋊C4—21no—
377C4×C22⋊C4—21no—
378#340C2311yescharacteristic
379#340C2312yes—
380#340C2312yes—
381#340C2312yes—
382#340C2311yescharacteristic
383#340C2312yes—
384#340C2312yes—
385#340C2311yescharacteristic
386#340C2311yescharacteristic
387#340C2312yes—
388C25—22no—
389C25—21no—
390C25C2×D411yescharacteristic
391C25C2×D412yes—
392H(5,𝔽2)—416no—
393H(5,𝔽2)—416no—
394H(5,𝔽2)—416no—
395H(5,𝔽2)—416no—
396C2×#41—28no—
397C2×#41—24no—
398C2×#41—28no—
399C2×#41—24no—
400C2×#41—24no—
401C2×#41—22no—
402C2×#41—24no—
403C2×#41—24no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—22no—
407C2×#41—22no—
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—22no—
411C2×#41—22no—
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—22no—
416C2×#41—22no—
417C2×#41—22no—
418C2×#41—42no—
419C2×#41—42no—
420C2×#41—42no—
421C2×#41—42no—
422C2×#41—44no—
423C2×#41—44no—
424C2×#41—42no—
425C2×#41—42no—
426C2×#41—42no—
427C2×#41—42no—
428C2×#41—42no—
429C2×#41—42no—
430C2×#41—42no—
431C2×#41—42no—
432C2×#41—44no—
433C2×#41—44no—
434C2×#41—416no—
435C2×#41—416no—
436C2×#41—416no—
437C2×#41—416no—
438C2×#41C2×D414yes—
439C2×#41C2×D418yes—
440C2×#41C2×D414yes—
441C2×#41C2×D414yes—
442C22×Q8—24no—
443C22×Q8—21no—
444C22×Q8—22no—
445C22×Q8—22no—
446C22×Q8—22no—
447C22×Q8—22no—
448C22×Q8—22no—
449C22×Q8—22no—
450C22×Q8—42no—
451C22×Q8—42no—
452C22×Q8C2×D411yescharacteristic
453C22×Q8C2×D411yescharacteristic
454C22×Q8C2×D412yes—
455C22×Q8C2412yes—
456C22×Q8C2411yescharacteristic
457C22×D4—21no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—21no—
461C22×D4—216no—
462C22×D4—28no—
463C22×D4—21no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—28no—
469C22×D4—24no—
470C22×D4—216no—
471C22×D4—28no—
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—24no—
475C22×D4—22no—
476C22×D4—22no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—42no—
481C22×D4—42no—
482C22×D4—42no—
483C22×D4—42no—
484C22×D4—42no—
485C22×D4—42no—
486C22×D4—44no—
487C22×D4—44no—
488C22×D4—48no—
489C22×D4—48no—
490C22×D4—44no—
491C22×D4—44no—
492C22×D4—82no—
493C22×D4—84no—
494C22×D4—82no—
495C22×D4—84no—
496C22×D4C2×D412yes—
497C22×D4C2×D411yescharacteristic
498C22×D4C2×D414yes—
499C22×D4C2×D412yes—
500C22×D4C2×D411yescharacteristic
501C22×D4C2×D412yes—
502C22×D4C2×D412yes—
503C22×D4C2×D412yes—
504C22×D4C2×D418yes—
505C22×D4C2412yes—
506C22×D4C2411yescharacteristic
507C23×C4—22no—
508C23×C4—21no—
509C23×C4—22no—
510C23×C4—21no—
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—22no—
514C23×C4—22no—
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—42no—
522C23×C4—42no—
523C23×C4—42no—
524C23×C4—42no—
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D412yes—
529C23×C4C2×D412yes—
530C23×C4C2×D412yes—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2411yescharacteristic
536#137—416no—
537C2×Q16—24no—
538C2×Q16—42no—
539C2×Q16—42no—
540C2×SD16—24no—
541C2×SD16—24no—
542C2×SD16—24no—
543C2×SD16—42no—
544C2×SD16—42no—
545C2×SD16—42no—
546C2×SD16—42no—
547C2×SD16—42no—
548C2×SD16—42no—
549C2×SD16—416no—
550C2×M16—22no—
551C2×M16—22no—
552C2×M16—22no—
553C2×M16—22no—
554C2×M16—22no—
555C2×M16—22no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8—22no—
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2412yes—
567C22×C8C2412yes—
568C4⋊Q8—44no—
569C4⋊Q8—44no—
570#127—216no—
571#127—28no—
572#124—216no—
573#124—28no—
574#124—44no—
575#124—44no—
576#123—216no—
577#123—28no—
578#123—48no—
579#123—48no—
580C22⋊Q8—216no—
581C22⋊Q8—28no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—24no—
585C22⋊Q8—22no—
586C22⋊Q8—24no—
587C22⋊Q8—22no—
588C22⋊Q8—24no—
589C22⋊Q8—24no—
590C22⋊Q8—24no—
591C22⋊Q8—24no—
592C22⋊Q8—42no—
593C22⋊Q8—42no—
594C22⋊Q8—42no—
595C22⋊Q8—42no—
596C22⋊Q8—42no—
597C22⋊Q8—42no—
598C22⋊Q8—42no—
599C22⋊Q8—42no—
600C22⋊Q8—44no—
601C22⋊Q8—44no—
602#121—216no—
603#121—28no—
604#121—216no—
605#121—28no—
606#121—216no—
607#121—216no—
608#121—216no—
609#121—216no—
610#121—28no—
611#121—24no—
612#121—22no—
613#121—24no—
614#121—24no—
615#121—24no—
616#121—24no—
617#121—22no—
618#121—24no—
619#121—22no—
620#121—24no—
621#121—24no—
622#121—24no—
623#121—22no—
624#121—24no—
625#120—216no—
626#120—28no—
627#120—216no—
628#120—216no—
629#120—216no—
630C4×Q8—28no—
631C4×D4—216no—
632C4×D4—28no—
633C4×D4—216no—
634C4×D4—28no—
635C4×D4—216no—
636C4×D4—28no—
637#117—24no—
638#117—22no—
639#117—22no—
640#117—22no—
641#117—22no—
642#117—22no—
643#117C2×D414yes—
644#117C2×D418yes—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—24no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—44no—
662C2×C4⋊C4C2×D414yes—
663C2×C4⋊C4C2×D418yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C22⋊C4—216no—
673C2×C22⋊C4—28no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—44no—
703C2×C42—22no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707#107—22no—
708#107—22no—
709#107—24no—
710#106—22no—
711#106—22no—
712#106—24no—
713#103—22no—
714#103—22no—
715#103—24no—
716#103—24no—
717#103—24no—
718#103—24no—
719#103—41no—
720#103—41no—
721#103—42no—
722#102—22no—
723#102—22no—
724#102—24no—
725#102—24no—
726#102—42no—
727#102—42no—
728#102—41no—
729#102—41no—
730#102—42no—
731#102—42no—
732#102—42no—
733C22⋊C8—24no—
734C22⋊C8—24no—
735C22⋊C8—24no—
736C22⋊C8—24no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—42no—
742C22⋊C8—42no—
743C22⋊C8—42no—
744C22⋊C8—42no—
745C22⋊C8—42no—
746C22⋊C8—42no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—22no—
752#95—22no—
753#95—22no—
754#95—22no—
755C24—22no—
756C24—22no—
757C24—21no—
758C24—24no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—28no—
763C24—24no—
764C24—24no—
765C24—42no—
766C24—42no—
767C24—41no—
768C24—42no—
769C24—41no—
770C24—41no—
771C24—42no—
772C24—42no—
773C24—44no—
774C24—44no—
775C24—42no—
776C24—42no—
777C24—81no—
778C24—81no—
779C24—82no—
780C24—82no—
781C24—81no—
782C24—81no—
783C24—82no—
784C24—82no—
785C24C22×D411yescharacteristic
786C24C22×D412yes—
787C24C22×D412yes—
788C24C22×D411yescharacteristic
789C24C22×D411yescharacteristic
790#41—28no—
791#41—28no—
792#41—28no—
793#41—28no—
794#41—28no—
795#41—28no—
796#41—48no—
797#41—48no—
798#41—48no—
799#41—48no—
800#41—48no—
801#41—48no—
802#41—48no—
803#41—48no—
804#41—432no—
805#41—416no—
806#41—416no—
807#41—432no—
808#41—44no—
809#41—44no—
810#41—44no—
811#41—44no—
812#41—44no—
813#41—44no—
814C2×Q8—24no—
815C2×Q8—22no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—22no—
819C2×Q8—22no—
820C2×Q8—21no—
821C2×Q8—22no—
822C2×Q8—22no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—22no—
828C2×Q8—22no—
829C2×Q8—22no—
830C2×Q8—22no—
831C2×Q8—42no—
832C2×Q8—42no—
833C2×Q8—416no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—44no—
838C2×Q8—44no—
839C2×Q8—44no—
840C2×Q8—44no—
841C2×Q8#12014yes—
842C2×Q8C22×D412yes—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—28no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—28no—
851C2×D4—24no—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—28no—
855C2×D4—24no—
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—28no—
859C2×D4—28no—
860C2×D4—24no—
861C2×D4—24no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—28no—
866C2×D4—28no—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—22no—
870C2×D4—21no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—22no—
876C2×D4—22no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—48no—
880C2×D4—48no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—48no—
890C2×D4—48no—
891C2×D4—432no—
892C2×D4—416no—
893C2×D4—464no—
894C2×D4—432no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—44no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—81no—
908C2×D4—82no—
909C2×D4—81no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—82no—
914C2×D4—82no—
915C2×D4—82no—
916C2×D4—82no—
917C2×D4—816no—
918C2×D4—832no—
919C2×D4#12018yes—
920C2×D4#12014yes—
921C2×D4C22×D414yes—
922C2×D4C22×D412yes—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—24no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—21no—
932C22×C4—22no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—28no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—22no—
939C22×C4—24no—
940C22×C4—22no—
941C22×C4—28no—
942C22×C4—24no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—22no—
951C22×C4—21no—
952C22×C4—22no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—22no—
970C22×C4—22no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—48no—
978C22×C4—48no—
979C22×C4—48no—
980C22×C4—48no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4—81no—
996C22×C4—82no—
997C22×C4—81no—
998C22×C4—82no—
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D412yes—
1002C22×C4C22×D412yes—
1003C22×C4C22×D414yes—
1004C22×C4C22×D414yes—
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D412yes—
1007C22×C4C22×D412yes—
1008C22×C4H(5,𝔽2)12yes—
1009C22×C4H(5,𝔽2)12yes—
1010C22×C4H(5,𝔽2)12yes—
1011C22×C4H(5,𝔽2)12yes—
1012C22×C4C2511yescharacteristic
1013Q16—48no—
1014SD16—48no—
1015SD16—48no—
1016SD16—48no—
1017M16—44no—
1018M16—44no—
1019C2×C8—22no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—22no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—22no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—22no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—22no—
1036C2×C8—22no—
1037C2×C8—44no—
1038C2×C8—44no—
1039C4⋊C4—24no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—21no—
1045C4⋊C4—22no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—22no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—22no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4C22×D414yes—
1065C4⋊C4C22×D412yes—
1066C4⋊C4C22×D412yes—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—24no—
1073C22⋊C4—24no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—24no—
1077C22⋊C4—28no—
1078C22⋊C4—24no—
1079C22⋊C4—42no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—42no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—81no—
1090C22⋊C4—82no—
1091C22⋊C4—82no—
1092C22⋊C4—81no—
1093C22⋊C4—82no—
1094C22⋊C4—82no—
1095C42—28no—
1096C42—24no—
1097C42—42no—
1098C42—42no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—22no—
1104C23—21no—
1105C23—22no—
1106C23—21no—
1107C23—21no—
1108C23—22no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—21no—
1116C23—22no—
1117C23—21no—
1118C23—22no—
1119C23—21no—
1120C23—22no—
1121C23—24no—
1122C23—22no—
1123C23—22no—
1124C23—21no—
1125C23—21no—
1126C23—22no—
1127C23—21no—
1128C23—22no—
1129C23—21no—
1130C23—22no—
1131C23—44no—
1132C23—48no—
1133C23—44no—
1134C23—44no—
1135C23—48no—
1136C23—416no—
1137C23—42no—
1138C23—41no—
1139C23—42no—
1140C23—41no—
1141C23—42no—
1142C23—41no—
1143C23—44no—
1144C23—42no—
1145C23—41no—
1146C23—42no—
1147C23—41no—
1148C23—42no—
1149C23—41no—
1150C23—48no—
1151C23—82no—
1152C23—82no—
1153C23—82no—
1154C23—84no—
1155C23—84no—
1156C23—84no—
1157C23—84no—
1158C23—88no—
1159C23—84no—
1160C23—88no—
1161C23—84no—
1162C23—84no—
1163C23—162no—
1164C23—162no—
1165C23—162no—
1166C23—162no—
1167C23—164no—
1168C23—164no—
1169C23—164no—
1170C23—164no—
1171C23C2×#12014yes—
1172C23C2×#12012yes—
1173C23#53412yes—
1174C23#53412yes—
1175C23#57712yes—
1176C23C23×D411yescharacteristic
1177Q8—28no—
1178Q8—22no—
1179Q8—22no—
1180Q8—48no—
1181Q8—44no—
1182Q8—41no—
1183Q8—41no—
1184Q8—42no—
1185Q8—42no—
1186Q8—42no—
1187Q8—42no—
1188Q8—84no—
1189D4—216no—
1190D4—28no—
1191D4—24no—
1192D4—22no—
1193D4—24no—
1194D4—22no—
1195D4—416no—
1196D4—48no—
1197D4—416no—
1198D4—48no—
1199D4—48no—
1200D4—416no—
1201D4—48no—
1202D4—48no—
1203D4—48no—
1204D4—48no—
1205D4—44no—
1206D4—42no—
1207D4—42no—
1208D4—41no—
1209D4—41no—
1210D4—84no—
1211D4—88no—
1212D4—88no—
1213D4—88no—
1214D4—88no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—48no—
1235C2×C4—48no—
1236C2×C4—416no—
1237C2×C4—48no—
1238C2×C4—41no—
1239C2×C4—42no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—44no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—42no—
1246C2×C4—41no—
1247C2×C4—44no—
1248C2×C4—44no—
1249C2×C4—48no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—42no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—42no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—42no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—42no—
1276C2×C4—42no—
1277C2×C4—42no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—84no—
1281C2×C4—88no—
1282C2×C4—84no—
1283C2×C4—84no—
1284C2×C4C2×#12014yes—
1285C2×C4C2×#12012yes—
1286C2×C4#53412yes—
1287C2×C4#53412yes—
1288C2×C4#53414yes—
1289C2×C4#53414yes—
1290C2×C4#53514yes—
1291C2×C4#53514yes—
1292C2×C4C23×D411yescharacteristic
1293C2×C4C23×D411yescharacteristic
1294C2×C4C2×H(5,𝔽2)11yescharacteristic
1295C2×C4C2×H(5,𝔽2)11yescharacteristic
1296C2×C4C2×H(5,𝔽2)11yescharacteristic
1297C2×C4C2×H(5,𝔽2)11yescharacteristic
1298C8—41no—
1299C8—41no—
1300C8—42no—
1301C8—41no—
1302C8—41no—
1303C8—42no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—22no—
1312C22—24no—
1313C22—22no—
1314C22—24no—
1315C22—24no—
1316C22—42no—
1317C22—41no—
1318C22—42no—
1319C22—42no—
1320C22—41no—
1321C22—42no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—42no—
1326C22—41no—
1327C22—42no—
1328C22—41no—
1329C22—42no—
1330C22—42no—
1331C22—41no—
1332C22—44no—
1333C22—42no—
1334C22—41no—
1335C22—42no—
1336C22—41no—
1337C22—42no—
1338C22—44no—
1339C22—42no—
1340C22—42no—
1341C22—41no—
1342C22—44no—
1343C22—42no—
1344C22—88no—
1345C22—816no—
1346C22—82no—
1347C22—81no—
1348C22—82no—
1349C22—81no—
1350C22—82no—
1351C22—81no—
1352C22—82no—
1353C22—81no—
1354C22—168no—
1355C22—1616no—
1356C22#261314yes—
1357C22C22×#12011yescharacteristic
1358C22C2×#53411yescharacteristic
1359C22C2×#53411yescharacteristic
1360C22C2×#57711yescharacteristic
1361C22#358411yescharacteristic
1362C22#358511yescharacteristic
1363C22#358611yescharacteristic
1364C4—24no—
1365C4—44no—
1366C4—42no—
1367C4—42no—
1368C4—41no—
1369C4—41no—
1370C4—42no—
1371C4—42no—
1372C4—82no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—82no—
1378C4#261314yes—
1379C4C2×#53411yescharacteristic
1380C4C2×#53411yescharacteristic
1381C4C2×#53511yescharacteristic
1382C4C2×#53511yescharacteristic
1383C2—24no—
1384C2—42no—
1385C2—44no—
1386C2—81no—
1387C2—82no—
1388C2—84no—
1389C2—82no—
1390C2C2×#261311yescharacteristic
1391C2#6037311yescharacteristic
1392C2#6037711yescharacteristic
1393C2#6075811yescharacteristic
1394C2#6076011yescharacteristic
1395C2#6076911yescharacteristic
1396C2#6077211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3097C2semidirect
3. C2×#3009C2semidirect
4. #35305C2semidirect
5. #29609C2semidirect
6. #29608C2semidirect
7. #29604C2semidirect
8. #29604C2semidirect
9. #29601C2semidirect
10. #29601C2semidirect
11. #29598C2semidirect
12. #29596C2semidirect
13. #23486C2semidirect
14. #23485C2semidirect
15. #23480C2semidirect
16. #23479C2semidirect
17. #23394C2semidirect
18. #23392C2semidirect
19. #23388C2semidirect
20. C2×#2000C2semidirect
21. #20703C2semidirect
22. #20602C2semidirect
23. #20581C2semidirect
26. C22×#137C22semidirect
27. C23×SD16C22semidirect
39. C2×#536C22semidirect
44. C22×C22⋊Q8C22semidirect
49. C2×#484C22semidirect
50. C2×#485C22semidirect
51. C2×#485C22semidirect
52. C2×#483C22semidirect
54. C2×#452C22semidirect
55. C2×#452C22semidirect
56. C2×#450C22semidirect
57. C2×#450C22semidirect
58. C2×#428C22semidirect
59. C2×#427C22semidirect
60. C2×#417C22semidirect
61. C2×#419C22semidirect
62. C2×#418C22semidirect
63. C2×#418C22semidirect
64. C2×#416C22semidirect
65. C2×#416C22semidirect
66. C22×#103C22semidirect
67. C22×#102C22semidirect
70. C2×#408C22semidirect
71. C2×#408C22semidirect
72. C2×#407C22semidirect
73. C22×C22⋊C8C22semidirect
74. #2848C22semidirect
75. #2848C22semidirect
76. #2616C22semidirect
77. #2616C22semidirect
85. #2311C22semidirect
86. #2280C22semidirect
87. #2036C22semidirect
88. #2036C22semidirect
89. #2036C22semidirect
90. #2035C22semidirect
91. #2035C22semidirect
92. #2035C22semidirect
93. #2034C22semidirect
94. #2034C22semidirect
95. #2034C22semidirect
96. #2034C22semidirect
97. #2034C22semidirect
98. #2034C22semidirect
99. #2034C22semidirect
100. #2033C22semidirect
101. #2033C22semidirect
102. #2033C22semidirect
103. #2033C22semidirect
104. #2033C22semidirect
105. #2033C22semidirect
106. #2033C22semidirect
107. #2001C22semidirect
108. #2001C22semidirect
109. #2001C22semidirect
110. #2001C22semidirect
111. #2000C22semidirect
112. #2000C22semidirect
113. #2000C22semidirect
114. #2000C22semidirect
115. #2000C22semidirect
116. #2000C22semidirect
117. #2000C22semidirect
118. #2000C22semidirect
119. #2000C22semidirect
120. #2000C22semidirect
121. #2000C22semidirect
122. #2000C22semidirect
123. #1825C22semidirect
124. #1825C22semidirect
125. #1824C22semidirect
126. #1823C22semidirect
127. #1788C22semidirect
128. #1788C22semidirect
129. #1786C22semidirect
130. #1786C22semidirect
131. #1780C22semidirect
132. #1780C22semidirect
133. #1779C22semidirect
134. #1779C22semidirect
135. #1736C22semidirect
136. #1736C22semidirect
137. #1735C22semidirect
138. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
C2×#34882
C2×#30972
C2×#30092
#353052
#296092
#296082
#296042
#296012
#295982
#295962
#234862
#234852
#234802
#234792
#233942
#233922
#233882
C2×#20002
#207032
#206022
#205812