Finite Group Databasebeta

← #6438780

Subgroups — #6438780

Order 512.

3530 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#466C211yesmaximal, characteristic, complemented
2C2×#3041C211yesmaximal, characteristic, complemented
3C2×#3006C211yesmaximal, characteristic, complemented
4C22×#416C211yesmaximal, characteristic, complemented
5#35250C211yesmaximal, characteristic, complemented
6#34204C211yesmaximal, characteristic, complemented
7#25090C214yesmaximal, complemented
8#25087C214yesmaximal, complemented
9#25081C214yesmaximal, complemented
10#25076C214yesmaximal, complemented
11#23611C211yesmaximal, characteristic, complemented
12#23544C211yesmaximal, characteristic, complemented
13#23511C211yesmaximal, characteristic, complemented
14#23422C211yesmaximal, characteristic, complemented
15#21263C211yesmaximal, characteristic, complemented
16#21067C211yesmaximal, characteristic, complemented
17#20929C211yesmaximal, characteristic, complemented
18#20912C211yesmaximal, characteristic, complemented
19#20834C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×AGL(1,ℤ/8)C2211yescharacteristic
22C22×AGL(1,ℤ/8)C2211yescharacteristic
23C23×D8C2211yescharacteristic, complemented
24C24×C8C2211yescharacteristic
25C2×#535C2211yescharacteristic
26C2×#535C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C2×#518C2211yescharacteristic, complemented
30C22×#117C2211yescharacteristic
31C2×#466—28no—
32C2×#466C2214yes—
33C2×#466C2214yescomplemented
34#3041—28no—
35C2×#463C2214yescomplemented
36C2×#459C2214yescomplemented
37#3006—28no—
38C2×#449C2212yescomplemented
39C2×#449C2212yescomplemented
40C2×#448C2212yescomplemented
41C2×#447C2212yescomplemented
42C22×#107C2211yescharacteristic, complemented
43C2×#424C2211yescharacteristic, complemented
44C2×#424C2211yescharacteristic, complemented
45C2×#417C2211yescharacteristic
46C2×#417C2211yescharacteristic
47C2×#418C2211yescharacteristic, complemented
48C2×#418C2211yescharacteristic, complemented
49C2×#416—28no—
50C2×#416C2211yescharacteristic
51C2×#416C2211yescharacteristic
52C2×#416C2211yescharacteristic
53C2×#416C2211yescharacteristic
54C2×#416C2212yescomplemented
55C2×#416C2212yescomplemented
56C22×#103C2212yescomplemented
57C22×#102C2211yescharacteristic, complemented
58C22×#102C2211yescharacteristic, complemented
59C22×#102C2212yescomplemented
60C2×#407C2211yescharacteristic
61#2847—22no—
62#2615—22no—
63#2436C2212yescomplemented
64#2433C2212yescomplemented
65#2431C2212yescomplemented
66#2431C2212yescomplemented
67#2404—22no—
68#2403—22no—
69#2363C2214yescomplemented
70#2361C2214yescomplemented
71#2342—22no—
72D4×C22⋊C4—22no—
73#2324—22no—
74#2316C2211yescharacteristic, complemented
75#2311C2211yescharacteristic
76#2311C2211yescharacteristic
77#2309C2211yescharacteristic, complemented
78C4×#121—22no—
79#2280C2211yescharacteristic
80#2274C2211yescharacteristic, complemented
81#2068C2214yescomplemented
82#2067C2214yescomplemented
83#2055C2214yescomplemented
84#2054C2214yescomplemented
85#2042C2214yescomplemented
86#2041C2214yescomplemented
87#2012C2214yescomplemented
88#2011C2214yescomplemented
89#1983C2214yescomplemented
90#1982C2214yescomplemented
91#1928C2214yescomplemented
92#1925C2214yescomplemented
93#1879C2214yescomplemented
94#1877C2214yescomplemented
95#1875C2214yescomplemented
96#1874C2214yescomplemented
97#1850C2214yescomplemented
98#1850C2214yescomplemented
99#1736C2211yescharacteristic, complemented
100#1736C2211yescharacteristic, complemented
101#1729C2211yescharacteristic, complemented
102#1729C2211yescharacteristic, complemented
103C22×#41—21no—
104C22×#41—21no—
105C22×#41—24no—
106C22×#41—24no—
107C22×#41—24no—
108C22×#41—24no—
109C22×#41—42no—
110C22×#41—42no—
111C22×#41C2311yescharacteristic
112C22×#41C2311yescharacteristic
113C22×#41C2311yescharacteristic
114C22×#41C2311yescharacteristic
115C23×Q8C2311yescharacteristic
116C23×D4—21no—
117C23×D4—21no—
118C23×D4—21no—
119C23×D4C2311yescharacteristic
120C23×D4C2311yescharacteristic
121C23×D4C2311yescharacteristic
122C24×C4—21no—
123C24×C4C2311yescharacteristic
124C2×AGL(1,ℤ/8)—24no—
125C2×AGL(1,ℤ/8)—24no—
126C2×AGL(1,ℤ/8)—24no—
127C2×AGL(1,ℤ/8)—24no—
128C2×AGL(1,ℤ/8)—42no—
129C2×AGL(1,ℤ/8)—42no—
130C22×SD16C2312yes—
131C22×SD16C2312yes—
132C22×D8—24no—
133C22×D8—24no—
134C22×D8—42no—
135C22×D8C2312yes—
136C22×D8C2312yes—
137C22×D8C2314yes—
138C22×M16C2311yescharacteristic
139C22×M16C2311yescharacteristic
140C23×C8—24no—
141C23×C8—24no—
142C23×C8—42no—
143C23×C8C2311yescharacteristic
144C23×C8C2312yes—
145C23×C8C2312yes—
146C23×C8C2311yescharacteristic
147#535—24no—
148#535—24no—
149#535—42no—
150#535—42no—
151C2×#127C2312yes—
152C2×#127C2312yes—
153C2×#124C2312yes—
154C2×#124C2312yes—
155C2×#121—21no—
156C2×#121—21no—
157C2×#121—24no—
158C2×#121—21no—
159C2×#121—21no—
160C2×#121—22no—
161C2×#121—22no—
162C2×#121—24no—
163C2×#121—24no—
164C2×#121D418yescomplemented
165C2×#121C2312yes—
166C2×#121C2312yes—
167C2×#121C2312yes—
168C2×#121C2312yes—
169C2×#120—22no—
170C2×#120—22no—
171C2×#120—24no—
172#518—24no—
173#518—42no—
174C2×C4×D4—22no—
175C2×C4×D4—24no—
176C2×C4×D4C2314yes—
177C2×#117—21no—
178C2×#117—21no—
179C2×#117—24no—
180C2×#117—42no—
181C2×#117C2311yescharacteristic
182C2×#117C2312yes—
183C2×#117C2311yescharacteristic
184C2×#117C2311yescharacteristic
185C2×#117C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2311yescharacteristic
189C22×C22⋊C4—21no—
190C22×C22⋊C4—21no—
191C22×C22⋊C4—21no—
192C22×C22⋊C4—22no—
193C22×C42—21no—
194#466—216no—
195#466—216no—
196#463—216no—
197#459—216no—
198#449—28no—
199#449—28no—
200#448—28no—
201#447—28no—
202C2×#107—24no—
203C2×#107C2314yes—
204#424—24no—
205#424—42no—
206C2×C4⋊C8C2314yes—
207C2×C4⋊C8C2314yes—
208#418—24no—
209#418—42no—
210#417—24no—
211#417—24no—
212#416—24no—
213#416—24no—
214#416—24no—
215#416—28no—
216#416—28no—
217#416D418yescomplemented
218C2×#103—28no—
219C2×#103C2312yes—
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2312yes—
223C2×#103C2312yes—
224C2×#103C2312yes—
225C2×#102—24no—
226C2×#102—24no—
227C2×#102—28no—
228C2×#102C2312yes—
229C2×#102C2314yes—
230C2×#102C2312yes—
231C2×#102C2312yes—
232C2×#102C2312yes—
233C2×#102C2314yes—
234C2×#102C2314yes—
235C2×#102C2312yes—
236C2×#102C2314yes—
237C2×#102C2312yes—
238#407—24no—
239C2×C22⋊C8C2312yes—
240C2×C22⋊C8C2312yes—
241#393—24no—
242#392—24no—
243#392—24no—
244#392—24no—
245#391C2312yes—
246#391C2312yes—
247#390—22no—
248#390—24no—
249#390C2314yes—
250#390C2312yes—
251#390C2312yes—
252#389—22no—
253#389C2314yes—
254#388—24no—
255#388—24no—
256#386—22no—
257#386—22no—
258#386—24no—
259#386—24no—
260#386—24no—
261#386—24no—
262#386—24no—
263#385—24no—
264#381D412yes—
265#380—22no—
266#380—22no—
267#380—22no—
268#380D412yes—
269#380D412yes—
270#379—22no—
271#379D412yes—
272C4×C4⋊C4—22no—
273C4×C4⋊C4C2314yes—
274C4×C22⋊C4—22no—
275C4×C22⋊C4—24no—
276C4×C22⋊C4C2312yes—
277C4×C22⋊C4C2312yes—
278#340C2314yes—
279#340C2314yes—
280#336C2314yes—
281#336C2314yes—
282C25—21no—
283C25—21no—
284C25—21no—
285C25C2×D411yescharacteristic
286C2×#41—22no—
287C2×#41—22no—
288C2×#41—232no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—44no—
306C2×#41—44no—
307C2×#41—41no—
308C2×#41—41no—
309C2×#41—41no—
310C2×#41—41no—
311C2×#41—44no—
312C2×#41—44no—
313C2×#41—416no—
314C2×#41—416no—
315C2×#41—416no—
316C2×#41—44no—
317C2×#41—44no—
318C2×#41C2×D414yes—
319C2×#41#4114yes—
320C22×Q8—21no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—41no—
326C22×Q8—41no—
327C22×Q8C2411yescharacteristic
328C22×Q8C2411yescharacteristic
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—28no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—21no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—41no—
359C22×D4—41no—
360C22×D4—44no—
361C22×D4—44no—
362C22×D4—44no—
363C22×D4—44no—
364C22×D4—84no—
365C22×D4—84no—
366C22×D4C2×D414yes—
367C22×D4C2412yes—
368C22×D4C2412yes—
369C22×D4C2411yescharacteristic
370C22×D4C2411yescharacteristic
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—21no—
376C23×C4—21no—
377C23×C4—21no—
378C23×C4—21no—
379C23×C4—22no—
380C23×C4—21no—
381C23×C4—21no—
382C23×C4—21no—
383C23×C4—24no—
384C23×C4—44no—
385C23×C4—44no—
386C23×C4—44no—
387C23×C4C2×D411yescharacteristic
388C23×C4C2×D411yescharacteristic
389C23×C4C2×D411yescharacteristic
390C23×C4C2×D414yes—
391C23×C4#4114yes—
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395AGL(1,ℤ/8)—416no—
396AGL(1,ℤ/8)—416no—
397C2×SD16—24no—
398C2×SD16—24no—
399C2×SD16—24no—
400C2×SD16—24no—
401C2×SD16—42no—
402C2×SD16—42no—
403C2×D8—28no—
404C2×D8—24no—
405C2×D8—24no—
406C2×D8—24no—
407C2×D8—24no—
408C2×D8—28no—
409C2×D8—44no—
410C2×D8—42no—
411C2×D8—42no—
412C2×D8—416no—
413C2×M16—22no—
414C2×M16—22no—
415C2×M16—22no—
416C2×M16—22no—
417C2×M16—22no—
418C2×M16—22no—
419C22×C8—22no—
420C22×C8—22no—
421C22×C8—22no—
422C22×C8—22no—
423C22×C8—24no—
424C22×C8—24no—
425C22×C8—22no—
426C22×C8—24no—
427C22×C8—24no—
428C22×C8—42no—
429C22×C8—42no—
430C22×C8—416no—
431C22×C8C2×D414yes—
432C22×C8C2412yes—
433C22×C8C2412yes—
434C22×C8C2412yes—
435C22×C8C2412yes—
436#127—24no—
437#127—24no—
438#127—42no—
439#127—42no—
440#124—24no—
441#124—24no—
442#124—42no—
443#124—42no—
444#121—28no—
445#121—28no—
446#121—24no—
447#121—24no—
448#121—24no—
449#121—24no—
450#121—24no—
451#121—24no—
452#121—48no—
453#121—48no—
454#121—44no—
455#121—44no—
456#121C2×D418yes—
457#121C2×D418yes—
458#120—48no—
459#120—48no—
460#120—88no—
461C4×D4—28no—
462C4×D4—44no—
463C4×D4—48no—
464C4×D4—88no—
465#117—22no—
466#117—22no—
467#117—22no—
468#117—22no—
469#117—22no—
470#117—22no—
471#117—22no—
472#117—24no—
473#117—44no—
474#117—44no—
475#117—42no—
476#117C2×D414yes—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4C2×D412yes—
487C2×C4⋊C4C2×D412yes—
488C2×C4⋊C4C2×D414yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2412yes—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—28no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—48no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4—44no—
511C2×C22⋊C4C2×D412yes—
512C2×C22⋊C4C2×D412yes—
513C2×C22⋊C4C2×D414yes—
514C2×C22⋊C4C2×D414yes—
515C2×C42—21no—
516C2×C42—22no—
517C2×C42—21no—
518C2×C42—24no—
519C2×C42—44no—
520C2×C42C2412yes—
521C2×C42C2412yes—
522#107—28no—
523C4⋊C8—28no—
524C4⋊C8—44no—
525#103—24no—
526#103—24no—
527#103—24no—
528#103—24no—
529#103—24no—
530#103C2×D418yescomplemented
531#102—24no—
532#102—28no—
533#102—24no—
534#102—24no—
535#102—28no—
536#102—24no—
537#102—24no—
538#102—28no—
539#102—44no—
540#102C2×D418yescomplemented
541C22⋊C8—24no—
542C22⋊C8—24no—
543#95—24no—
544#95—24no—
545#95—24no—
546#95—24no—
547#95C2×D414yes—
548#95C2×D414yes—
549C24—22no—
550C24—22no—
551C24—24no—
552C24—22no—
553C24—21no—
554C24—21no—
555C24—24no—
556C24—22no—
557C24—42no—
558C24—42no—
559C24—42no—
560C24—42no—
561C24—42no—
562C24—42no—
563C24—42no—
564C24—44no—
565C24—42no—
566C24—42no—
567C24—82no—
568C24—82no—
569C24—82no—
570C24—82no—
571C24—82no—
572C24#12114yes—
573C24C22×D411yescharacteristic
574C24C22×D411yescharacteristic
575C24C22×D411yescharacteristic
576#41—28no—
577#41—28no—
578#41—28no—
579#41—28no—
580#41—28no—
581#41—28no—
582#41—44no—
583#41—44no—
584#41—44no—
585#41—44no—
586#41—432no—
587#41—432no—
588#41—44no—
589#41—44no—
590#41—44no—
591#41—44no—
592#41—44no—
593#41—44no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—28no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—42no—
606C2×Q8—42no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8—44no—
610C2×Q8—42no—
611C2×Q8C22×D412yes—
612C2×Q8C2×#4112yes—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—28no—
618C2×D4—24no—
619C2×D4—28no—
620C2×D4—28no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—432no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—48no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—48no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—42no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—44no—
675C2×D4—42no—
676C2×D4—84no—
677C2×D4—84no—
678C2×D4—84no—
679C2×D4—84no—
680C2×D4—84no—
681C2×D4—84no—
682C2×D4—816no—
683C2×D4—816no—
684C2×D4C22×D412yes—
685C2×D4C22×D414yes—
686C2×D4C2×#4112yes—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—28no—
694C22×C4—22no—
695C22×C4—28no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—22no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—22no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—48no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—432no—
722C22×C4—44no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—44no—
732C22×C4—84no—
733C22×C4—84no—
734C22×C4—82no—
735C22×C4—82no—
736C22×C4—82no—
737C22×C4#12114yes—
738C22×C4#12114yes—
739C22×C4#12114yes—
740C22×C4C22×D414yes—
741C22×C4C22×D414yes—
742C22×C4C22×D411yescharacteristic
743C22×C4C22×D411yescharacteristic
744C22×C4C22×D412yes—
745C22×C4C22×D412yes—
746C22×C4C22×D411yescharacteristic
747C22×C4C22×D412yes—
748C22×C4C22×D412yes—
749C22×C4C2×#4112yes—
750C22×C4C2×#4112yes—
751C22×C4C2×#4112yes—
752C22×C4C2×#4112yes—
753C22×C4H(5,𝔽2)12yes—
754C22×C4H(5,𝔽2)12yes—
755C22×C4C2511yescharacteristic
756SD16—48no—
757SD16—48no—
758D8—416no—
759D8—48no—
760D8—48no—
761M16—44no—
762M16—44no—
763C2×C8—28no—
764C2×C8—22no—
765C2×C8—22no—
766C2×C8—22no—
767C2×C8—22no—
768C2×C8—22no—
769C2×C8—22no—
770C2×C8—22no—
771C2×C8—22no—
772C2×C8—22no—
773C2×C8—22no—
774C2×C8—22no—
775C2×C8—48no—
776C2×C8—48no—
777C2×C8—44no—
778C2×C8C22×D414yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—22no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—44no—
789C4⋊C4—42no—
790C4⋊C4—84no—
791C4⋊C4C22×D414yes—
792C4⋊C4C22×D414yes—
793C22⋊C4—24no—
794C22⋊C4—24no—
795C22⋊C4—24no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—44no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—44no—
804C22⋊C4—42no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C22⋊C4—84no—
808C22⋊C4—84no—
809C22⋊C4—84no—
810C22⋊C4—84no—
811C42—24no—
812C42—22no—
813C42—22no—
814C42—22no—
815C42—22no—
816C42—44no—
817C42—42no—
818C42—84no—
819C23—22no—
820C23—22no—
821C23—21no—
822C23—21no—
823C23—22no—
824C23—22no—
825C23—28no—
826C23—21no—
827C23—21no—
828C23—28no—
829C23—22no—
830C23—24no—
831C23—22no—
832C23—22no—
833C23—44no—
834C23—48no—
835C23—48no—
836C23—48no—
837C23—44no—
838C23—42no—
839C23—42no—
840C23—41no—
841C23—41no—
842C23—42no—
843C23—41no—
844C23—41no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—44no—
849C23—48no—
850C23—44no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—44no—
855C23—84no—
856C23—84no—
857C23—88no—
858C23—88no—
859C23—84no—
860C23—84no—
861C23—84no—
862C23—84no—
863C23—84no—
864C23—164no—
865C23—164no—
866C23—164no—
867C23—164no—
868C23C2×#12112yes—
869C23C2×#12112yes—
870C23C2×#12112yes—
871C23D4212yes—
872C23#54612yes—
873C23#57614yes—
874C23C23×D411yescharacteristic
875Q8—22no—
876Q8—22no—
877Q8—22no—
878Q8—22no—
879Q8—48no—
880Q8—41no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884D4—22no—
885D4—22no—
886D4—24no—
887D4—22no—
888D4—22no—
889D4—24no—
890D4—48no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—416no—
896D4—42no—
897D4—42no—
898D4—48no—
899D4—42no—
900D4—41no—
901D4—41no—
902D4—42no—
903D4—41no—
904D4—42no—
905D4—41no—
906D4—42no—
907D4—88no—
908D4—88no—
909D4—88no—
910D4—84no—
911D4—168no—
912D4—168no—
913C2×C4—28no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—28no—
921C2×C4—28no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—48no—
939C2×C4—48no—
940C2×C4—48no—
941C2×C4—42no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—42no—
947C2×C4—44no—
948C2×C4—48no—
949C2×C4—48no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—44no—
955C2×C4—84no—
956C2×C4—88no—
957C2×C4—84no—
958C2×C4—168no—
959C2×C4C2×#12112yes—
960C2×C4C2×#12112yes—
961C2×C4C2×#12112yes—
962C2×C4#52514yes—
963C2×C4#53814yes—
964C2×C4D4212yes—
965C2×C4D4214yes—
966C2×C4#54612yes—
967C2×C4#54614yes—
968C2×C4C23×D411yescharacteristic
969C2×C4C23×D411yescharacteristic
970C2×C4C22×#4111yescharacteristic
971C2×C4C22×#4111yescharacteristic
972C2×C4C2×H(5,𝔽2)11yescharacteristic
973C2×C4C2×H(5,𝔽2)11yescharacteristic
974C8—24no—
975C8—42no—
976C8—42no—
977C8—42no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—416no—
990C22—42no—
991C22—42no—
992C22—44no—
993C22—44no—
994C22—42no—
995C22—42no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—816no—
1000C22—81no—
1001C22—81no—
1002C22—81no—
1003C22—81no—
1004C22—84no—
1005C22—82no—
1006C22—82no—
1007C22—84no—
1008C22—82no—
1009C22—82no—
1010C22—82no—
1011C22—84no—
1012C22—84no—
1013C22—168no—
1014C22—168no—
1015C22#242414yes—
1016C22#304114yescomplemented
1017C22C22×#12111yescharacteristic
1018C22C2×D4211yescharacteristic
1019C22C2×#54611yescharacteristic
1020C22C2×#57612yes—
1021C22#358412yes—
1022C4—22no—
1023C4—22no—
1024C4—44no—
1025C4—42no—
1026C4—42no—
1027C4—44no—
1028C4—44no—
1029C4—44no—
1030C4—82no—
1031C4—82no—
1032C4#242414yes—
1033C4C2×#52511yescharacteristic
1034C4C2×#53811yescharacteristic
1035C4C2×D4211yescharacteristic
1036C4C2×#54611yescharacteristic
1037C2—24no—
1038C2—24no—
1039C2—42no—
1040C2—82no—
1041C2—82no—
1042C2—84no—
1043C2—162no—
1044C2C2×#242411yescharacteristic
1045C2C2×#304111yescharacteristic
1046C2#6042211yescharacteristic
1047C2#6105612yes—
1048C2#6117112yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#466C2semidirect
2. C2×#3041C2semidirect
3. C2×#3006C2semidirect
4. C22×#416C2semidirect
5. #35250C2semidirect
6. #34204C2semidirect
7. #25090C2semidirect
8. #25087C2semidirect
9. #25081C2semidirect
10. #25076C2semidirect
11. #23611C2semidirect
12. #23544C2semidirect
13. #23511C2semidirect
14. #23422C2semidirect
15. #21263C2semidirect
16. #21067C2semidirect
17. #20929C2semidirect
18. #20912C2semidirect
19. #20834C2semidirect
23. C23×D8C22semidirect
29. C2×#518C22semidirect
33. C2×#466C22semidirect
35. C2×#463C22semidirect
36. C2×#459C22semidirect
38. C2×#449C22semidirect
39. C2×#449C22semidirect
40. C2×#448C22semidirect
41. C2×#447C22semidirect
42. C22×#107C22semidirect
43. C2×#424C22semidirect
44. C2×#424C22semidirect
47. C2×#418C22semidirect
48. C2×#418C22semidirect
54. C2×#416C22semidirect
55. C2×#416C22semidirect
56. C22×#103C22semidirect
57. C22×#102C22semidirect
58. C22×#102C22semidirect
59. C22×#102C22semidirect
63. #2436C22semidirect
64. #2433C22semidirect
65. #2431C22semidirect
66. #2431C22semidirect
69. #2363C22semidirect
70. #2361C22semidirect
74. #2316C22semidirect
77. #2309C22semidirect
80. #2274C22semidirect
81. #2068C22semidirect
82. #2067C22semidirect
83. #2055C22semidirect
84. #2054C22semidirect
85. #2042C22semidirect
86. #2041C22semidirect
87. #2012C22semidirect
88. #2011C22semidirect
89. #1983C22semidirect
90. #1982C22semidirect
91. #1928C22semidirect
92. #1925C22semidirect
93. #1879C22semidirect
94. #1877C22semidirect
95. #1875C22semidirect
96. #1874C22semidirect
97. #1850C22semidirect
98. #1850C22semidirect
99. #1736C22semidirect
100. #1736C22semidirect
101. #1729C22semidirect
102. #1729C22semidirect
164. C2×#121D4semidirect
217. #416D4semidirect
530. #103C2×D4semidirect
540. #102C2×D4semidirect
1016. C22#3041semidirect

Maximal subgroups

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

subgroupindex
C22×#4662
C2×#30412
C2×#30062
C22×#4162
#352502
#342042
#250902
#250872
#250812
#250762
#236112
#235442
#235112
#234222
#212632
#210672
#209292
#209122
#208342