Finite Group Databasebeta

← #6446700

Subgroups — #6446700

Order 512.

4894 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3484C211yesmaximal, characteristic
2C2×#3136C211yesmaximal, characteristic, complemented
3C2×#3081C211yesmaximal, characteristic, complemented
4#35542C211yesmaximal, characteristic, complemented
5#25898C212yesmaximal, complemented
6#25897C212yesmaximal, complemented
7#25891C212yesmaximal, complemented
8#25891C212yesmaximal, complemented
9#25890C212yesmaximal, complemented
10#25890C212yesmaximal, complemented
11#25885C212yesmaximal, complemented
12#25881C212yesmaximal, complemented
13#23486C211yesmaximal, characteristic, complemented
14#23483C211yesmaximal, characteristic, complemented
15#23482C211yesmaximal, characteristic, complemented
16#23479C211yesmaximal, characteristic, complemented
17#21263C211yesmaximal, characteristic, complemented
18#21191C211yesmaximal, characteristic, complemented
19#20602C211yesmaximal, characteristic, complemented
20#20602C211yesmaximal, characteristic, complemented
21#20598C211yesmaximal, characteristic, complemented
22C2×#1786C211yesmaximal, characteristic, complemented
23#20416C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic
25C24×D4C2211yescharacteristic
26#3484—28no—
27#3484—28no—
28C2×#546—21no—
29C2×#546—21no—
30C2×#546C2212yes—
31C2×#546C2212yes—
32C2×D42—21no—
33C2×D42—21no—
34C2×D42C2212yes—
35C2×D42C2212yes—
36C2×#544C2211yescharacteristic, complemented
37C2×#535C2211yescharacteristic
38C2×#535C2211yescharacteristic
39C2×#534—22no—
40C2×#525C2211yescharacteristic
41C2×#525C2211yescharacteristic
42C22×#120—22no—
43C2×#518C2211yescharacteristic
44#3136—28no—
45C2×#490C2212yescomplemented
46C2×#489C2212yescomplemented
47C2×#488C2212yescomplemented
48C2×#486C2212yescomplemented
49#3081—28no—
50C2×#478C2212yescomplemented
51C2×#478C2212yescomplemented
52C2×#476C2212yescomplemented
53C2×#474C2212yescomplemented
54C2×#428C2211yescharacteristic, complemented
55C2×#427C2211yescharacteristic, complemented
56C2×#424C2211yescharacteristic, complemented
57C2×#417C2211yescharacteristic, complemented
58C2×#417C2211yescharacteristic, complemented
59C2×#418C2211yescharacteristic
60C2×#418C2211yescharacteristic
61C2×#418C2211yescharacteristic, complemented
62C2×#418C2211yescharacteristic, complemented
63C2×#416C2211yescharacteristic, complemented
64C2×#416C2211yescharacteristic, complemented
65C22×#102C2211yescharacteristic
66C22×#102C2211yescharacteristic
67C22×#102C2211yescharacteristic, complemented
68C22×#102C2211yescharacteristic, complemented
69C2×#408C2211yescharacteristic, complemented
70C2×#408C2211yescharacteristic, complemented
71C2×#407C2211yescharacteristic, complemented
72C22×C22⋊C8C2211yescharacteristic, complemented
73C2×#405C2211yescharacteristic, complemented
74#2563C2212yescomplemented
75#2562C2212yescomplemented
76#2562C2212yescomplemented
77#2547C2212yescomplemented
78#2492—21no—
79#2491—21no—
80#2490—21no—
81#2489—21no—
82#2488—22no—
83#2472—22no—
84#2311C2211yescharacteristic, complemented
85#2311C2211yescharacteristic, complemented
86#2280C2211yescharacteristic, complemented
87C2×#380C2211yescharacteristic, complemented
88#2274C2211yescharacteristic, complemented
89#2036C2211yescharacteristic, complemented
90#2036C2212yescomplemented
91#2036C2211yescharacteristic, complemented
92#2035C2211yescharacteristic, complemented
93#2035C2212yescomplemented
94#2035C2211yescharacteristic, complemented
95#2034C2211yescharacteristic, complemented
96#2034C2212yescomplemented
97#2034C2211yescharacteristic, complemented
98#2034C2212yescomplemented
99#2034C2212yescomplemented
100#2034C2212yescomplemented
101#2034C2212yescomplemented
102#2033C2211yescharacteristic, complemented
103#2033C2212yescomplemented
104#2033C2211yescharacteristic, complemented
105#2033C2212yescomplemented
106#2033C2212yescomplemented
107#2033C2212yescomplemented
108#2033C2212yescomplemented
109#1983C2212yescomplemented
110#1983C2212yescomplemented
111#1982C2212yescomplemented
112#1982C2212yescomplemented
113#1955C2212yescomplemented
114#1955C2212yescomplemented
115#1954C2212yescomplemented
116#1954C2212yescomplemented
117#1788C2212yescomplemented
118#1788C2212yescomplemented
119#1788C2212yescomplemented
120#1788C2212yescomplemented
121#1786C2212yescomplemented
122#1786C2212yescomplemented
123#1786C2212yescomplemented
124#1786C2212yescomplemented
125#1786C2212yescomplemented
126#1786C2212yescomplemented
127#1786C2212yescomplemented
128#1786C2212yescomplemented
129#1786C2212yescomplemented
130#1786C2212yescomplemented
131#1786C2212yescomplemented
132#1786C2212yescomplemented
133#1762C2212yescomplemented
134#1762C2212yescomplemented
135C4×#102C2212yescomplemented
136C4×#102C2212yescomplemented
137#1736C2211yescharacteristic, complemented
138#1735C2211yescharacteristic, complemented
139C26—21no—
140C2×H(5,𝔽2)—24no—
141C2×H(5,𝔽2)—24no—
142C2×H(5,𝔽2)—24no—
143C2×H(5,𝔽2)—24no—
144C2×H(5,𝔽2)—42no—
145C2×H(5,𝔽2)—42no—
146C22×#41—21no—
147C22×#41C2311yescharacteristic
148C22×#41C2312yes—
149C22×#41C2311yescharacteristic
150C23×D4—24no—
151C23×D4—24no—
152C23×D4—22no—
153C23×D4—21no—
154C23×D4—22no—
155C23×D4—22no—
156C23×D4—24no—
157C23×D4—24no—
158C23×D4—21no—
159C23×D4—21no—
160C23×D4—21no—
161C23×D4—42no—
162C23×D4—42no—
163C23×D4C2311yescharacteristic
164C23×D4C2312yes—
165C23×D4C2312yes—
166C23×D4C2312yes—
167C23×D4C2311yescharacteristic
168C24×C4C2311yescharacteristic
169C22×M16C2311yescharacteristic
170C22×M16C2311yescharacteristic
171C23×C8C2311yescharacteristic
172C23×C8C2311yescharacteristic
173#546—216no—
174#546—216no—
175#546—28no—
176#546—28no—
177#546—28no—
178#546—28no—
179D42—216no—
180D42—216no—
181D42—28no—
182D42—28no—
183D42—28no—
184D42—28no—
185#544—24no—
186#544—24no—
187#535—24no—
188#535—24no—
189#535—24no—
190#535D418yes—
191#534—232no—
192C2×C4⋊Q8—21no—
193C2×C4⋊Q8C2312yescomplemented
194C2×#127—21no—
195C2×#127C2312yes—
196C2×#125—21no—
197C2×#125C2312yescomplemented
198C2×#124—21no—
199C2×#124—22no—
200C2×#124C2312yes—
201#525—24no—
202#525—24no—
203#525—24no—
204#525—24no—
205C2×#123—21no—
206C2×#123—22no—
207C2×#123—22no—
208C2×#123D412yes—
209C2×C22⋊Q8—22no—
210C2×C22⋊Q8D411yescharacteristic
211C2×C22⋊Q8D411yescharacteristic
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×#121—22no—
215C2×#121—22no—
216C2×#121—21no—
217C2×#121—21no—
218C2×#121—22no—
219C2×#121—22no—
220C2×#121D411yescharacteristic
221C2×#121D411yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#120—232no—
227C2×#120—21no—
228C2×#120—22no—
229C2×#120—22no—
230C2×#120—22no—
231C2×#120—22no—
232C2×#120—22no—
233C2×#120—22no—
234C2×#120—22no—
235C2×#120—22no—
236C2×#120D412yes—
237#518—24no—
238#518D418yes—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—22no—
254C22×C22⋊C4—22no—
255C22×C22⋊C4—22no—
256C22×C22⋊C4—21no—
257#490—28no—
258#489—28no—
259#488—28no—
260#486—28no—
261#478—28no—
262#478—28no—
263#476—28no—
264#474—28no—
265#428—24no—
266#427—24no—
267C2×#107C2311yescharacteristic, complemented
268C2×#107C2312yescomplemented
269C2×#107C2311yescharacteristic, complemented
270C2×#106C2311yescharacteristic, complemented
271C2×#106C2312yescomplemented
272C2×#106C2311yescharacteristic, complemented
273#424—24no—
274C2×C4⋊C8C2312yescomplemented
275C2×C4⋊C8C2312yescomplemented
276#418—24no—
277#418—24no—
278#418—24no—
279#418—42no—
280#417—24no—
281#417—42no—
282#416—24no—
283#416—42no—
284C2×#103C2311yescharacteristic, complemented
285C2×#103C2312yescomplemented
286C2×#103C2311yescharacteristic, complemented
287C2×#103C2311yescharacteristic, complemented
288C2×#103C2311yescharacteristic, complemented
289C2×#103C2312yescomplemented
290C2×#102—24no—
291C2×#102—24no—
292C2×#102—24no—
293C2×#102—42no—
294C2×#102C2312yes—
295C2×#102C2312yes—
296C2×#102C2312yes—
297C2×#102C2312yes—
298C2×#102C2312yes—
299C2×#102C2312yes—
300C2×#102C2312yes—
301C2×#102C2312yes—
302C2×#102C2312yes—
303C2×#102C2312yes—
304C2×#102C2312yes—
305C2×#102C2312yes—
306C2×#102C2312yes—
307C2×#102C2312yes—
308C2×#102C2312yes—
309C2×#102C2312yes—
310C2×#102C2311yescharacteristic, complemented
311C2×#102C2312yescomplemented
312C2×#102C2311yescharacteristic, complemented
313C2×#102C2311yescharacteristic, complemented
314C2×#102C2311yescharacteristic, complemented
315C2×#102C2312yescomplemented
316#408—42no—
317#408—42no—
318#407—42no—
319C2×C22⋊C8—42no—
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2312yes—
325C2×C22⋊C8C2312yes—
326C2×C22⋊C8C2312yescomplemented
327C2×C22⋊C8C2312yescomplemented
328C2×C22⋊C8C2312yescomplemented
329C2×C22⋊C8C2312yescomplemented
330#405—24no—
331C2×#97C2312yescomplemented
332C2×C4×C8C2312yescomplemented
333#400—22no—
334#400—22no—
335#397—22no—
336#397—22no—
337#394—22no—
338#394—22no—
339#393—22no—
340#393—22no—
341#391—21no—
342#391—21no—
343#391—22no—
344#390—22no—
345#390—21no—
346#390—21no—
347#388—22no—
348#388—22no—
349#388—22no—
350#388—22no—
351#386—22no—
352#386—22no—
353#382—22no—
354#381—21no—
355#380—21no—
356#380—21no—
357#380C2311yescharacteristic
358#380C2311yescharacteristic
359#380C2312yes—
360#380C2312yes—
361#380C2311yescharacteristic
362#380C2311yescharacteristic
363#380C2312yescomplemented
364#380C2312yescomplemented
365#380C2312yescomplemented
366#380C2312yescomplemented
367#379—21no—
368C4×C4⋊C4—21no—
369C4×C4⋊C4—21no—
370C4×C4⋊C4C2312yescomplemented
371C4×C4⋊C4C2312yescomplemented
372C4×C22⋊C4—21no—
373C4×C22⋊C4—21no—
374C4×C22⋊C4—22no—
375C2×#95—21no—
376#340C2311yescharacteristic, complemented
377#340C2311yescharacteristic, complemented
378#340C2311yescharacteristic, complemented
379#340C2311yescharacteristic, complemented
380#340C2312yescomplemented
381#340C2312yescomplemented
382C25—21no—
383C25—28no—
384C25—22no—
385C25—22no—
386C25—21no—
387C25—22no—
388C25—44no—
389C25—44no—
390C25—82no—
391C25—82no—
392C25—82no—
393C25—82no—
394C25C2×D411yescharacteristic
395H(5,𝔽2)—416no—
396H(5,𝔽2)—416no—
397H(5,𝔽2)—416no—
398H(5,𝔽2)—416no—
399C2×#41—28no—
400C2×#41—24no—
401C2×#41—24no—
402C2×#41—22no—
403C2×#41—22no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—22no—
407C2×#41—22no—
408C2×#41—22no—
409C2×#41—24no—
410C2×#41—24no—
411C2×#41—22no—
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—42no—
416C2×#41—42no—
417C2×#41—44no—
418C2×#41—44no—
419C2×#41C2×D414yes—
420C22×Q8—22no—
421C22×Q8C2×D411yescharacteristic
422C22×Q8C2411yescharacteristic
423C22×D4—216no—
424C22×D4—28no—
425C22×D4—28no—
426C22×D4—28no—
427C22×D4—28no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—22no—
432C22×D4—216no—
433C22×D4—216no—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—24no—
437C22×D4—24no—
438C22×D4—24no—
439C22×D4—24no—
440C22×D4—24no—
441C22×D4—24no—
442C22×D4—24no—
443C22×D4—24no—
444C22×D4—24no—
445C22×D4—24no—
446C22×D4—24no—
447C22×D4—24no—
448C22×D4—21no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—21no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—42no—
464C22×D4—42no—
465C22×D4—42no—
466C22×D4—42no—
467C22×D4—42no—
468C22×D4—42no—
469C22×D4—44no—
470C22×D4—44no—
471C22×D4—44no—
472C22×D4—44no—
473C22×D4—44no—
474C22×D4—44no—
475C22×D4—416no—
476C22×D4—416no—
477C22×D4—44no—
478C22×D4—44no—
479C22×D4—48no—
480C22×D4—48no—
481C22×D4—416no—
482C22×D4—416no—
483C22×D4—84no—
484C22×D4—84no—
485C22×D4—84no—
486C22×D4—84no—
487C22×D4C2×D412yes—
488C22×D4C2×D411yescharacteristic
489C22×D4C2×D414yes—
490C22×D4C2×D412yes—
491C22×D4C2×D412yes—
492C22×D4C2×D414yes—
493C22×D4#4114yes—
494C22×D4#4114yes—
495C22×D4C2412yes—
496C22×D4C2411yescharacteristic
497C22×D4C2412yes—
498C23×C4—22no—
499C23×C4—21no—
500C23×C4—22no—
501C23×C4—22no—
502C23×C4—22no—
503C23×C4—22no—
504C23×C4—22no—
505C23×C4—22no—
506C23×C4—22no—
507C23×C4—22no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2412yes—
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C2×M16—22no—
518C2×M16—22no—
519C2×M16—22no—
520C2×M16—22no—
521C2×M16—22no—
522C2×M16—22no—
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2412yes—
534C22×C8C2412yes—
535C4⋊Q8—24no—
536C4⋊Q8—24no—
537C4⋊Q8—44no—
538#127—28no—
539#127—24no—
540#127C2×D418yes—
541#125—24no—
542#125—24no—
543#125—44no—
544#124—28no—
545#124—24no—
546#124—84no—
547#124C2×D418yes—
548#123—28no—
549#123—216no—
550#123—216no—
551#123—28no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—24no—
555C22⋊Q8—24no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—48no—
559#121—216no—
560#121—216no—
561#121—216no—
562#121—216no—
563#121—22no—
564#121—22no—
565#121—24no—
566#121—24no—
567#121—28no—
568#121—28no—
569#121—24no—
570#121—24no—
571#121—22no—
572#121—22no—
573#121—24no—
574#121—24no—
575#120—28no—
576#120—216no—
577#120—216no—
578#120—216no—
579#120—216no—
580#120—216no—
581#120—216no—
582#120—216no—
583#120—28no—
584#120—216no—
585C4×D4—28no—
586C4×D4—28no—
587C4×D4—28no—
588C4×D4—28no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4C2×D418yes—
596C4×D4C2×D418yes—
597#117—22no—
598#117—22no—
599#117—22no—
600#117—22no—
601#117—22no—
602#117C2×D414yes—
603#117C2×D414yes—
604#117C2×D414yes—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4C2×D412yes—
617C2×C4⋊C4C2×D412yes—
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C22⋊C4—216no—
629C2×C22⋊C4—216no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—216no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—82no—
655C2×C22⋊C4C2×D412yes—
656C2×C22⋊C4C2×D412yes—
657C2×C22⋊C4C2×D412yes—
658C2×C22⋊C4C2×D412yes—
659C2×C22⋊C4C2×D412yes—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—22no—
664C2×C42—22no—
665C2×C42C2412yes—
666#107—22no—
667#107—22no—
668#107—24no—
669#106—22no—
670#106—22no—
671#106—24no—
672C4⋊C8—24no—
673C4⋊C8—24no—
674#103—22no—
675#103—22no—
676#103—24no—
677#103—41no—
678#103—41no—
679#103—42no—
680#102—24no—
681#102—24no—
682#102—24no—
683#102—24no—
684#102—24no—
685#102—24no—
686#102—24no—
687#102—24no—
688#102—22no—
689#102—22no—
690#102—24no—
691#102—24no—
692#102—24no—
693#102—24no—
694#102—24no—
695#102—42no—
696#102—42no—
697#102—42no—
698#102—42no—
699#102—41no—
700#102—41no—
701#102—42no—
702C22⋊C8—41no—
703C22⋊C8—41no—
704C22⋊C8—41no—
705C22⋊C8—41no—
706C22⋊C8—42no—
707C22⋊C8—42no—
708C22⋊C8—42no—
709C22⋊C8—42no—
710C22⋊C8—42no—
711C22⋊C8—42no—
712#97—24no—
713C4×C8—24no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726C24—22no—
727C24—22no—
728C24—22no—
729C24—22no—
730C24—24no—
731C24—24no—
732C24—24no—
733C24—28no—
734C24—28no—
735C24—28no—
736C24—22no—
737C24—22no—
738C24—22no—
739C24—21no—
740C24—24no—
741C24—41no—
742C24—41no—
743C24—44no—
744C24—44no—
745C24—44no—
746C24—44no—
747C24—44no—
748C24—44no—
749C24—432no—
750C24—44no—
751C24—44no—
752C24—42no—
753C24—42no—
754C24—44no—
755C24—44no—
756C24—81no—
757C24—81no—
758C24—81no—
759C24—81no—
760C24—81no—
761C24—81no—
762C24—81no—
763C24—81no—
764C24—82no—
765C24—82no—
766C24—82no—
767C24—82no—
768C24—82no—
769C24—82no—
770C24—82no—
771C24—82no—
772C24—816no—
773C24—816no—
774C24—816no—
775C24—816no—
776C24—816no—
777C24—816no—
778C24C22×D412yes—
779C24C22×D411yescharacteristic
780C24C22×D411yescharacteristic
781C24C22×D411yescharacteristic
782#41—28no—
783#41—28no—
784#41—48no—
785#41—48no—
786#41—48no—
787#41—432no—
788#41—48no—
789#41—44no—
790#41—44no—
791#41—44no—
792#41—44no—
793#41—44no—
794#41—44no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—44no—
804C2×Q8—82no—
805C2×Q8—82no—
806C2×Q8C22×D412yes—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—22no—
826C2×D4—28no—
827C2×D4—28no—
828C2×D4—28no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—28no—
832C2×D4—28no—
833C2×D4—28no—
834C2×D4—28no—
835C2×D4—22no—
836C2×D4—22no—
837C2×D4—22no—
838C2×D4—22no—
839C2×D4—21no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—22no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—48no—
859C2×D4—48no—
860C2×D4—48no—
861C2×D4—48no—
862C2×D4—48no—
863C2×D4—48no—
864C2×D4—48no—
865C2×D4—48no—
866C2×D4—432no—
867C2×D4—432no—
868C2×D4—48no—
869C2×D4—432no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—432no—
873C2×D4—464no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—48no—
881C2×D4—48no—
882C2×D4—48no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—82no—
888C2×D4—82no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—82no—
892C2×D4—82no—
893C2×D4—82no—
894C2×D4—82no—
895C2×D4—832no—
896C2×D4—832no—
897C2×D4#124116yescomplemented
898C2×D4C22×D414yes—
899C2×D4C22×D412yes—
900C2×D4C22×D414yes—
901C2×D4C2×#4114yes—
902C2×D4C2×#4114yes—
903C22×C4—28no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—24no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—28no—
936C22×C4—28no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—22no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—22no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—82no—
954C22×C4—82no—
955C22×C4—82no—
956C22×C4—82no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4C22×D412yes—
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D412yes—
965C22×C4C22×D412yes—
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D412yes—
968C22×C4C22×D412yes—
969C22×C4C2×#4112yes—
970C22×C4C2×#4112yes—
971C22×C4H(5,𝔽2)12yes—
972C22×C4H(5,𝔽2)12yes—
973C22×C4C2511yescharacteristic
974M16—44no—
975M16—44no—
976C2×C8—21no—
977C2×C8—22no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—22no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—22no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—22no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—22no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—22no—
994C2×C8—44no—
995C2×C8—44no—
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—22no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—22no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—22no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—22no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—42no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—42no—
1019C4⋊C4#12014yes—
1020C4⋊C4#12014yes—
1021C4⋊C4C22×D412yes—
1022C4⋊C4C22×D412yes—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—24no—
1031C22⋊C4—24no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—44no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—81no—
1044C22⋊C4—82no—
1045C22⋊C4—82no—
1046C22⋊C4—81no—
1047C22⋊C4—82no—
1048C22⋊C4—82no—
1049C22⋊C4—82no—
1050C22⋊C4#12018yes—
1051C42—24no—
1052C42—42no—
1053C42—42no—
1054C42—82no—
1055C42—82no—
1056C42C22×D414yes—
1057C42C22×D414yes—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—28no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—24no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—24no—
1075C23—24no—
1076C23—21no—
1077C23—21no—
1078C23—216no—
1079C23—22no—
1080C23—22no—
1081C23—24no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—44no—
1089C23—44no—
1090C23—44no—
1091C23—44no—
1092C23—44no—
1093C23—416no—
1094C23—416no—
1095C23—416no—
1096C23—416no—
1097C23—416no—
1098C23—42no—
1099C23—42no—
1100C23—44no—
1101C23—42no—
1102C23—42no—
1103C23—41no—
1104C23—41no—
1105C23—42no—
1106C23—42no—
1107C23—48no—
1108C23—41no—
1109C23—41no—
1110C23—42no—
1111C23—42no—
1112C23—41no—
1113C23—42no—
1114C23—41no—
1115C23—42no—
1116C23—84no—
1117C23—84no—
1118C23—84no—
1119C23—84no—
1120C23—84no—
1121C23—84no—
1122C23—84no—
1123C23—84no—
1124C23—88no—
1125C23—88no—
1126C23—88no—
1127C23—88no—
1128C23—84no—
1129C23—84no—
1130C23—84no—
1131C23—84no—
1132C23—88no—
1133C23—88no—
1134C23—88no—
1135C23—88no—
1136C23—88no—
1137C23—88no—
1138C23—88no—
1139C23—88no—
1140C23—8128no—
1141C23—164no—
1142C23—164no—
1143C23—164no—
1144C23—164no—
1145C23C2×#12012yes—
1146C23#54612yes—
1147C23#54612yes—
1148C23#57612yes—
1149C23#57712yes—
1150C23C23×D411yescharacteristic
1151Q8—22no—
1152Q8—22no—
1153Q8—41no—
1154Q8—41no—
1155Q8—44no—
1156Q8—164no—
1157D4—24no—
1158D4—216no—
1159D4—24no—
1160D4—24no—
1161D4—24no—
1162D4—24no—
1163D4—22no—
1164D4—22no—
1165D4—48no—
1166D4—48no—
1167D4—416no—
1168D4—416no—
1169D4—416no—
1170D4—416no—
1171D4—48no—
1172D4—48no—
1173D4—48no—
1174D4—48no—
1175D4—42no—
1176D4—41no—
1177D4—42no—
1178D4—41no—
1179D4—48no—
1180D4—44no—
1181D4—88no—
1182D4—88no—
1183D4—88no—
1184D4—88no—
1185D4C2×#12418yes—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—416no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—44no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—42no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—42no—
1216C2×C4—44no—
1217C2×C4—44no—
1218C2×C4—48no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—41no—
1226C2×C4—42no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—42no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—42no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—42no—
1237C2×C4—41no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—88no—
1244C2×C4—88no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4C2×#12014yes—
1248C2×C4C2×#12014yes—
1249C2×C4C2×#12012yes—
1250C2×C4C2×#12414yes—
1251C2×C4#53514yes—
1252C2×C4#54612yes—
1253C2×C4#54612yes—
1254C2×C4#54614yes—
1255C2×C4#54614yes—
1256C2×C4C23×D411yescharacteristic
1257C2×C4C23×D411yescharacteristic
1258C2×C4C22×#4111yescharacteristic
1259C2×C4C22×#4111yescharacteristic
1260C2×C4C2×H(5,𝔽2)11yescharacteristic
1261C2×C4C2×H(5,𝔽2)11yescharacteristic
1262C8—41no—
1263C8—41no—
1264C8—42no—
1265C8—41no—
1266C8—41no—
1267C8—42no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—28no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—416no—
1282C22—41no—
1283C22—44no—
1284C22—41no—
1285C22—41no—
1286C22—44no—
1287C22—41no—
1288C22—44no—
1289C22—41no—
1290C22—44no—
1291C22—41no—
1292C22—41no—
1293C22—44no—
1294C22—41no—
1295C22—44no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—44no—
1300C22—42no—
1301C22—42no—
1302C22—44no—
1303C22—42no—
1304C22—42no—
1305C22—44no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—816no—
1310C22—816no—
1311C22—832no—
1312C22—832no—
1313C22—82no—
1314C22—81no—
1315C22—82no—
1316C22—81no—
1317C22—82no—
1318C22—81no—
1319C22—82no—
1320C22—81no—
1321C22—1616no—
1322C22#243514yes—
1323C22C22×#12011yescharacteristic
1324C22C2×#54611yescharacteristic
1325C22C2×#54611yescharacteristic
1326C22C2×#57611yescharacteristic
1327C22C2×#57711yescharacteristic
1328C22#358511yescharacteristic
1329C22#358511yescharacteristic
1330C4—24no—
1331C4—24no—
1332C4—41no—
1333C4—41no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—82no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—82no—
1344C4#243514yes—
1345C4C22×#12411yescharacteristic
1346C4C2×#53511yescharacteristic
1347C4C2×#54611yescharacteristic
1348C4C2×#54611yescharacteristic
1349C2—24no—
1350C2—42no—
1351C2—42no—
1352C2—48no—
1353C2—82no—
1354C2—84no—
1355C2—82no—
1356C2C2×#243511yescharacteristic
1357C2#6037211yescharacteristic
1358C2#6037311yescharacteristic
1359C2#6116711yescharacteristic
1360C2#6117511yescharacteristic
1361C2#6118311yescharacteristic
1362C2#6118411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3484C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#525 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3136C2semidirect
3. C2×#3081C2semidirect
4. #35542C2semidirect
5. #25898C2semidirect
6. #25897C2semidirect
7. #25891C2semidirect
8. #25891C2semidirect
9. #25890C2semidirect
10. #25890C2semidirect
11. #25885C2semidirect
12. #25881C2semidirect
13. #23486C2semidirect
14. #23483C2semidirect
15. #23482C2semidirect
16. #23479C2semidirect
17. #21263C2semidirect
18. #21191C2semidirect
19. #20602C2semidirect
20. #20602C2semidirect
21. #20598C2semidirect
22. C2×#1786C2semidirect
23. #20416C2semidirect
36. C2×#544C22semidirect
45. C2×#490C22semidirect
46. C2×#489C22semidirect
47. C2×#488C22semidirect
48. C2×#486C22semidirect
50. C2×#478C22semidirect
51. C2×#478C22semidirect
52. C2×#476C22semidirect
53. C2×#474C22semidirect
54. C2×#428C22semidirect
55. C2×#427C22semidirect
56. C2×#424C22semidirect
57. C2×#417C22semidirect
58. C2×#417C22semidirect
61. C2×#418C22semidirect
62. C2×#418C22semidirect
63. C2×#416C22semidirect
64. C2×#416C22semidirect
67. C22×#102C22semidirect
68. C22×#102C22semidirect
69. C2×#408C22semidirect
70. C2×#408C22semidirect
71. C2×#407C22semidirect
72. C22×C22⋊C8C22semidirect
73. C2×#405C22semidirect
74. #2563C22semidirect
75. #2562C22semidirect
76. #2562C22semidirect
77. #2547C22semidirect
84. #2311C22semidirect
85. #2311C22semidirect
86. #2280C22semidirect
87. C2×#380C22semidirect
88. #2274C22semidirect
89. #2036C22semidirect
90. #2036C22semidirect
91. #2036C22semidirect
92. #2035C22semidirect
93. #2035C22semidirect
94. #2035C22semidirect
95. #2034C22semidirect
96. #2034C22semidirect
97. #2034C22semidirect
98. #2034C22semidirect
99. #2034C22semidirect
100. #2034C22semidirect
101. #2034C22semidirect
102. #2033C22semidirect
103. #2033C22semidirect
104. #2033C22semidirect
105. #2033C22semidirect
106. #2033C22semidirect
107. #2033C22semidirect
108. #2033C22semidirect
109. #1983C22semidirect
110. #1983C22semidirect
111. #1982C22semidirect
112. #1982C22semidirect
113. #1955C22semidirect
114. #1955C22semidirect
115. #1954C22semidirect
116. #1954C22semidirect
117. #1788C22semidirect
118. #1788C22semidirect
119. #1788C22semidirect
120. #1788C22semidirect
121. #1786C22semidirect
122. #1786C22semidirect
123. #1786C22semidirect
124. #1786C22semidirect
125. #1786C22semidirect
126. #1786C22semidirect
127. #1786C22semidirect
128. #1786C22semidirect
129. #1786C22semidirect
130. #1786C22semidirect
131. #1786C22semidirect
132. #1786C22semidirect
133. #1762C22semidirect
134. #1762C22semidirect
135. C4×#102C22semidirect
136. C4×#102C22semidirect
137. #1736C22semidirect
138. #1735C22semidirect
193. C2×C4⋊Q8C23semidirect
197. C2×#125C23semidirect
267. C2×#107C23semidirect
268. C2×#107C23semidirect
269. C2×#107C23semidirect
270. C2×#106C23semidirect
271. C2×#106C23semidirect
272. C2×#106C23semidirect
274. C2×C4⋊C8C23semidirect
275. C2×C4⋊C8C23semidirect
284. C2×#103C23semidirect
285. C2×#103C23semidirect
286. C2×#103C23semidirect
287. C2×#103C23semidirect
288. C2×#103C23semidirect
289. C2×#103C23semidirect
310. C2×#102C23semidirect
311. C2×#102C23semidirect
312. C2×#102C23semidirect
313. C2×#102C23semidirect
314. C2×#102C23semidirect
315. C2×#102C23semidirect
326. C2×C22⋊C8C23semidirect
327. C2×C22⋊C8C23semidirect
328. C2×C22⋊C8C23semidirect
329. C2×C22⋊C8C23semidirect
331. C2×#97C23semidirect
332. C2×C4×C8C23semidirect
363. #380C23semidirect
364. #380C23semidirect
365. #380C23semidirect
366. #380C23semidirect
370. C4×C4⋊C4C23semidirect
371. C4×C4⋊C4C23semidirect
376. #340C23semidirect
377. #340C23semidirect
378. #340C23semidirect
379. #340C23semidirect
380. #340C23semidirect
381. #340C23semidirect
897. C2×D4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#34842
C2×#31362
C2×#30812
#355422
#258982
#258972
#258912
#258902
#258852
#258812
#234862
#234832
#234822
#234792
#212632
#211912
#206022
#205982
C2×#17862
#204162