Finite Group Databasebeta

← #6487444

Subgroups — #6487444

Order 512.

4877 conjugacy classes of subgroups.

The subgroup lattice has 1013 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#535C211yesmaximal, characteristic, complemented
2C2×#3217C211yesmaximal, characteristic, complemented
3C2×#3211C211yesmaximal, characteristic, complemented
4#35302C211yesmaximal, characteristic, complemented
5#32883C211yesmaximal, characteristic, complemented
6#32881C211yesmaximal, characteristic, complemented
7#32880C211yesmaximal, characteristic, complemented
8#32878C211yesmaximal, characteristic, complemented
9#29626C211yesmaximal, characteristic, complemented
10#29625C211yesmaximal, characteristic, complemented
11#29623C211yesmaximal, characteristic, complemented
12#29622C211yesmaximal, characteristic, complemented
13#25867C214yesmaximal, complemented
14#25736C214yesmaximal, complemented
15#24220C214yesmaximal, complemented
16#24218C214yesmaximal, complemented
17#21808C211yesmaximal, characteristic, complemented
18#21803C211yesmaximal, characteristic, complemented
19#20717C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C24×D4C2211yescharacteristic
22C2×#535—28no—
23C2×#535—28no—
24C2×#535—22no—
25C2×#535—22no—
26C2×#535C2214yes—
27C2×#535C2214yes—
28C22×#127C2211yescharacteristic
29C22×#127C2211yescharacteristic
30C2×#529C2211yescharacteristic, complemented
31C22×#124C2211yescharacteristic
32C22×#124C2211yescharacteristic
33C22×#121—21no—
34C22×#121—21no—
35C22×#120—21no—
36C22×#120—21no—
37C22×#117C2211yescharacteristic
38#3217—28no—
39#3211—28no—
40C2×#496C2212yescomplemented
41C2×#495C2212yescomplemented
42C2×#490C2212yescomplemented
43C2×#488C2212yescomplemented
44C2×#464C2212yescomplemented
45C2×#460C2212yescomplemented
46C2×#463C2212yescomplemented
47C2×#459C2212yescomplemented
48C2×#452C2214yescomplemented
49C2×#449C2214yescomplemented
50C2×#451C2211yescharacteristic, complemented
51C2×#448C2211yescharacteristic, complemented
52C2×#450C2211yescharacteristic
53C2×#450C2211yescharacteristic
54C2×#450C2214yescomplemented
55C2×#450C2211yescharacteristic, complemented
56C2×#447C2211yescharacteristic
57C2×#447C2211yescharacteristic
58C2×#447C2214yescomplemented
59C2×#447C2211yescharacteristic, complemented
60C2×#432C2211yescharacteristic, complemented
61C2×#431C2211yescharacteristic, complemented
62#2855C2211yescharacteristic, complemented
63#2854C2211yescharacteristic, complemented
64#2848C2211yescharacteristic
65#2847C2211yescharacteristic
66#2629C2212yescomplemented
67#2620C2212yescomplemented
68#2609—22no—
69#2601—22no—
70#2579—21no—
71#2534—21no—
72#2413—21no—
73#2411—21no—
74#2324C2212yescomplemented
75#2323C2212yescomplemented
76#2285C2211yescharacteristic, complemented
77#2042C2214yescomplemented
78#2042C2214yescomplemented
79#2041C2214yescomplemented
80#2041C2214yescomplemented
81#2015C2214yescomplemented
82#2014C2214yescomplemented
83#2012C2214yescomplemented
84#2011C2214yescomplemented
85#1983C2214yescomplemented
86#1982C2214yescomplemented
87#1959C2214yescomplemented
88#1957C2214yescomplemented
89#1817C2211yescharacteristic, complemented
90#1817C2211yescharacteristic, complemented
91#1798C2214yescomplemented
92#1788C2214yescomplemented
93#1788C2214yescomplemented
94#1787C2211yescharacteristic, complemented
95#1787C2211yescharacteristic, complemented
96#1786C2211yescharacteristic
97#1786C2211yescharacteristic
98#1786C2211yescharacteristic
99#1786C2211yescharacteristic
100#1786C2214yescomplemented
101#1786C2214yescomplemented
102#1786C2211yescharacteristic, complemented
103#1786C2211yescharacteristic, complemented
104#1779C2211yescharacteristic
105#1779C2211yescharacteristic
106#1750C2214yescomplemented
107C26—21no—
108C22×#41—24no—
109C22×#41—24no—
110C22×#41—22no—
111C22×#41—48no—
112C22×#41C2314yes—
113C23×Q8C2311yescharacteristic
114C23×D4—21no—
115C23×D4—24no—
116C23×D4—24no—
117C23×D4—21no—
118C23×D4—22no—
119C23×D4—21no—
120C23×D4—21no—
121C23×D4—21no—
122C23×D4—21no—
123C23×D4—48no—
124C23×D4C2314yes—
125C23×D4C2311yescharacteristic
126C23×D4C2311yescharacteristic
127C23×D4C2311yescharacteristic
128C24×C4—21no—
129C24×C4C2311yescharacteristic
130C22×Q16C2312yescomplemented
131C22×SD16C2312yes—
132C22×SD16C2312yes—
133C22×SD16C2312yescomplemented
134C22×SD16C2312yescomplemented
135C22×D8C2312yes—
136C22×D8C2312yes—
137C22×D8C2312yescomplemented
138#535—232no—
139#535—232no—
140#535—216no—
141#535—216no—
142#535—216no—
143#535—216no—
144C2×#127—24no—
145C2×#127—24no—
146C2×#127—22no—
147C2×#127—21no—
148C2×#127—21no—
149C2×#127—24no—
150C2×#127D418yescomplemented
151C2×#127C2314yes—
152C2×#127C2312yes—
153C2×#127C2312yes—
154#529—24no—
155#529—24no—
156C2×#126—21no—
157C2×#125C2311yescharacteristic, complemented
158C2×#124—24no—
159C2×#124—24no—
160C2×#124—22no—
161C2×#124—21no—
162C2×#124—21no—
163C2×#124—24no—
164C2×#124D418yescomplemented
165C2×#124C2314yes—
166C2×#124C2312yes—
167C2×#124C2312yes—
168C2×#124C2311yescharacteristic, complemented
169C2×#123—21no—
170C2×#123—21no—
171C2×C22⋊Q8C2312yes—
172C2×C22⋊Q8C2311yescharacteristic
173C2×#121—216no—
174C2×#121—216no—
175C2×#121—24no—
176C2×#121—24no—
177C2×#121—24no—
178C2×#121—24no—
179C2×#121C2312yes—
180C2×#121C2311yescharacteristic
181C2×#120—216no—
182C2×#120—216no—
183C2×#120—21no—
184C2×#120—24no—
185C2×#120—24no—
186C2×#120—24no—
187C2×#120—24no—
188C2×C4×Q8C2311yescharacteristic, complemented
189C2×C4×D4—21no—
190C2×C4×D4C2311yescharacteristic, complemented
191C2×#117—21no—
192C2×#117—24no—
193C2×#117—24no—
194C2×#117—21no—
195C2×#117D412yes—
196C2×#117D412yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C22×C4⋊C4D411yescharacteristic
200C22×C4⋊C4D411yescharacteristic
201C22×C22⋊C4—21no—
202C22×C22⋊C4—21no—
203C22×C22⋊C4—21no—
204C22×C22⋊C4—21no—
205C22×C22⋊C4D411yescharacteristic
206C22×C22⋊C4D411yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209#496—28no—
210#495—28no—
211#490—28no—
212#488—28no—
213#464—28no—
214#463—28no—
215#460—28no—
216#459—28no—
217#452—48no—
218#451—24no—
219#450—24no—
220#450—24no—
221#450—24no—
222#450—48no—
223#449—48no—
224#448—24no—
225#447—24no—
226#447—24no—
227#447—24no—
228#447—48no—
229#432—24no—
230#431—24no—
231C2×C4⋊C8C2312yescomplemented
232C2×C4⋊C8C2312yescomplemented
233C2×#103C2312yescomplemented
234C2×#103C2312yescomplemented
235C2×#103C2314yescomplemented
236C2×#103C2314yescomplemented
237C2×#102C2312yes—
238C2×#102C2312yes—
239C2×#102C2312yes—
240C2×#102C2312yes—
241C2×#102C2314yes—
242C2×#102C2314yes—
243C2×#102C2314yes—
244C2×#102C2314yes—
245C2×#102C2312yescomplemented
246C2×#102C2312yescomplemented
247C2×#102C2314yescomplemented
248C2×#102C2314yescomplemented
249C2×C22⋊C8C2314yes—
250C2×C22⋊C8C2314yes—
251C2×C22⋊C8C2311yescharacteristic
252C2×C22⋊C8C2311yescharacteristic
253C2×C22⋊C8C2311yescharacteristic
254C2×C22⋊C8C2311yescharacteristic
255C2×#97C2312yescomplemented
256C2×C4×C8C2312yescomplemented
257#398—22no—
258#398—22no—
259#396—22no—
260#396—22no—
261#396—22no—
262#396—22no—
263#394—22no—
264#394—22no—
265#391C2312yescomplemented
266#390—22no—
267#390C2312yescomplemented
268#389—22no—
269#389C2312yescomplemented
270#389C2312yescomplemented
271#388—22no—
272#388—22no—
273#388—22no—
274#388—22no—
275#387—22no—
276#387—22no—
277#386—21no—
278#386—21no—
279#386—22no—
280#386—22no—
281#385—21no—
282#385—21no—
283#385—22no—
284#385—22no—
285#384C2312yescomplemented
286#382—21no—
287#381—21no—
288#380—21no—
289#380C2312yes—
290#380C2312yes—
291#380C2311yescharacteristic
292#380C2311yescharacteristic
293#379—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4C2312yescomplemented
296#336C2314yescomplemented
297#336C2314yescomplemented
298C25—28no—
299C25—21no—
300C25—21no—
301C25—21no—
302C25—24no—
303C25—48no—
304C25—82no—
305C25—82no—
306C25—84no—
307C25C2×D411yescharacteristic
308C2×#41—216no—
309C2×#41—28no—
310C2×#41—28no—
311C2×#41—28no—
312C2×#41—28no—
313C2×#41—44no—
314C2×#41—44no—
315C2×#41—432no—
316C2×#41—432no—
317C2×#41—48no—
318C2×#41—48no—
319C22×Q8—22no—
320C22×Q8—21no—
321C22×Q8—44no—
322C22×Q8C2×D414yes—
323C22×Q8C2411yescharacteristic
324C22×Q8C2412yes—
325C22×D4—28no—
326C22×D4—28no—
327C22×D4—216no—
328C22×D4—24no—
329C22×D4—28no—
330C22×D4—28no—
331C22×D4—28no—
332C22×D4—28no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—28no—
336C22×D4—28no—
337C22×D4—24no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—21no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—28no—
351C22×D4—28no—
352C22×D4—44no—
353C22×D4—44no—
354C22×D4—44no—
355C22×D4—44no—
356C22×D4—44no—
357C22×D4—432no—
358C22×D4—432no—
359C22×D4—48no—
360C22×D4—48no—
361C22×D4—48no—
362C22×D4—48no—
363C22×D4—82no—
364C22×D4—82no—
365C22×D4—82no—
366C22×D4—82no—
367C22×D4—84no—
368C22×D4—84no—
369C22×D4C2×D414yes—
370C22×D4C2×D414yes—
371C22×D4C2×D414yes—
372C22×D4C2411yescharacteristic
373C22×D4C2412yes—
374C22×D4C2412yes—
375C22×D4C2412yes—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—28no—
379C23×C4—28no—
380C23×C4—21no—
381C23×C4—24no—
382C23×C4—21no—
383C23×C4—48no—
384C23×C4C2×D411yescharacteristic
385C23×C4C2×D411yescharacteristic
386C23×C4C2×D412yes—
387C23×C4C2×D411yescharacteristic
388C23×C4C2×D411yescharacteristic
389C23×C4C2×D411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C2×Q16—24no—
393C2×Q16—44no—
394C2×SD16—24no—
395C2×SD16—24no—
396C2×SD16—24no—
397C2×SD16—24no—
398C2×SD16—44no—
399C2×SD16—44no—
400C2×SD16—44no—
401C2×SD16—44no—
402C2×D8—24no—
403C2×D8—24no—
404C2×D8—24no—
405C2×D8—44no—
406C2×D8—44no—
407C2×D8—44no—
408C22×C8C2412yes—
409C22×C8C2412yes—
410C22×C8C2412yes—
411C22×C8C2412yes—
412#127—216no—
413#127—28no—
414#127—28no—
415#127—28no—
416#127—28no—
417#127—24no—
418#127—24no—
419#127C2×D418yes—
420#127C2×D418yes—
421#126—44no—
422#125—22no—
423#125—22no—
424#124—216no—
425#124—28no—
426#124—28no—
427#124—28no—
428#124—28no—
429#124—24no—
430#124—24no—
431#124—22no—
432#124—22no—
433#124C2×D418yes—
434#124C2×D418yes—
435#123—44no—
436#123—82no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8—28no—
440#121—232no—
441#121—232no—
442#121—232no—
443#121—232no—
444#121—22no—
445#121—22no—
446#121—28no—
447#120—232no—
448#120—232no—
449#120—232no—
450#120—232no—
451#120—82no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—44no—
457#117—28no—
458#117—28no—
459#117—24no—
460#117—24no—
461#117—24no—
462#117—24no—
463#117—44no—
464#117—82no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4C2×D412yes—
477C2×C4⋊C4C2×D412yes—
478C2×C4⋊C4C2×D412yes—
479C2×C4⋊C4C2×D412yes—
480C2×C4⋊C4C2411yescharacteristic
481C2×C4⋊C4C2411yescharacteristic
482C2×C4⋊C4C2412yes—
483C2×C4⋊C4C2412yes—
484C2×C22⋊C4—28no—
485C2×C22⋊C4—28no—
486C2×C22⋊C4—28no—
487C2×C22⋊C4—28no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4C2×D412yes—
510C2×C22⋊C4C2×D412yes—
511C2×C22⋊C4C2×D412yes—
512C2×C22⋊C4C2×D412yes—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—21no—
516C2×C42—22no—
517C2×C42C2×D412yes—
518C2×C42C2×D411yescharacteristic
519C2×C42C2×D411yescharacteristic
520C2×C42C2×D414yes—
521C2×C42C2×D414yes—
522C2×C42C2412yes—
523C2×C42C2411yescharacteristic
524C2×C42C2411yescharacteristic
525C4⋊C8—24no—
526C4⋊C8—24no—
527#103—24no—
528#103—24no—
529#103—44no—
530#103—44no—
531#102—24no—
532#102—24no—
533#102—24no—
534#102—24no—
535#102—24no—
536#102—24no—
537#102—44no—
538#102—44no—
539#102—44no—
540#102—44no—
541#102—44no—
542#102—44no—
543C22⋊C8—22no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—28no—
548C22⋊C8—28no—
549#97—24no—
550C4×C8—24no—
551#95—21no—
552#95—21no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560C24—22no—
561C24—24no—
562C24—216no—
563C24—24no—
564C24—24no—
565C24—24no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—21no—
572C24—42no—
573C24—44no—
574C24—44no—
575C24—44no—
576C24—432no—
577C24—48no—
578C24—44no—
579C24—44no—
580C24—44no—
581C24—48no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—84no—
589C24—84no—
590C24—84no—
591C24—84no—
592C24—816no—
593C24—816no—
594C24—832no—
595C24—832no—
596C24C22×D412yes—
597C24C22×D411yescharacteristic
598#41—416no—
599#41—416no—
600#41—416no—
601#41—416no—
602#41—464no—
603C2×Q8—24no—
604C2×Q8—22no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—24no—
609C2×Q8—24no—
610C2×Q8—48no—
611C2×Q8—44no—
612C2×Q8—48no—
613C2×Q8C22×D414yes—
614C2×D4—216no—
615C2×D4—216no—
616C2×D4—216no—
617C2×D4—216no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—28no—
624C2×D4—28no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—24no—
631C2×D4—24no—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—24no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—48no—
638C2×D4—48no—
639C2×D4—48no—
640C2×D4—416no—
641C2×D4—416no—
642C2×D4—416no—
643C2×D4—416no—
644C2×D4—432no—
645C2×D4—464no—
646C2×D4—48no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—44no—
652C2×D4—48no—
653C2×D4—432no—
654C2×D4—48no—
655C2×D4—48no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—44no—
660C2×D4—48no—
661C2×D4—84no—
662C2×D4—84no—
663C2×D4—816no—
664C2×D4—82no—
665C2×D4—82no—
666C2×D4—82no—
667C2×D4—82no—
668C2×D4—84no—
669C2×D4—84no—
670C2×D4—84no—
671C2×D4—84no—
672C2×D4—816no—
673C2×D4—816no—
674C2×D4—816no—
675C2×D4—82no—
676C2×D4—82no—
677C2×D4C22×D414yes—
678C2×D4C22×D414yes—
679C2×D4C22×D414yes—
680C22×C4—216no—
681C22×C4—216no—
682C22×C4—22no—
683C22×C4—24no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—216no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—24no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—432no—
708C22×C4—48no—
709C22×C4—44no—
710C22×C4—48no—
711C22×C4—42no—
712C22×C4—82no—
713C22×C4#12014yes—
714C22×C4#12014yes—
715C22×C4C22×D412yes—
716C22×C4C22×D412yes—
717C22×C4C22×D411yescharacteristic
718C22×C4C22×D411yescharacteristic
719C22×C4C22×D411yescharacteristic
720C22×C4C22×D411yescharacteristic
721C22×C4C22×D411yescharacteristic
722C22×C4C22×D412yes—
723C22×C4C22×D412yes—
724C22×C4C22×D412yes—
725C22×C4H(5,𝔽2)18yes—
726C22×C4C2511yescharacteristic
727Q16—84no—
728SD16—84no—
729SD16—84no—
730SD16—84no—
731SD16—84no—
732D8—84no—
733D8—84no—
734D8—84no—
735C2×C8—22no—
736C2×C8—22no—
737C2×C8—22no—
738C2×C8—22no—
739C2×C8—24no—
740C2×C8—24no—
741C2×C8—24no—
742C2×C8—24no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—42no—
754C4⋊C4—42no—
755C4⋊C4—42no—
756C4⋊C4—42no—
757C4⋊C4—44no—
758C4⋊C4—82no—
759C4⋊C4—82no—
760C4⋊C4—82no—
761C4⋊C4—82no—
762C22⋊C4—216no—
763C22⋊C4—216no—
764C22⋊C4—28no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—42no—
773C22⋊C4—44no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—44no—
781C22⋊C4—82no—
782C22⋊C4—82no—
783C22⋊C4—82no—
784C22⋊C4—82no—
785C42—24no—
786C42—22no—
787C42—22no—
788C42—42no—
789C42—82no—
790C42#12014yes—
791C42#12014yes—
792C42C22×D412yes—
793C42C22×D412yes—
794C42C22×D412yes—
795C42C22×D412yes—
796C23—22no—
797C23—22no—
798C23—28no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—48no—
809C23—48no—
810C23—44no—
811C23—48no—
812C23—48no—
813C23—48no—
814C23—432no—
815C23—48no—
816C23—48no—
817C23—48no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—48no—
826C23—48no—
827C23—48no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—41no—
836C23—42no—
837C23—41no—
838C23—41no—
839C23—88no—
840C23—88no—
841C23—88no—
842C23—88no—
843C23—88no—
844C23—88no—
845C23—816no—
846C23—816no—
847C23—816no—
848C23—816no—
849C23—8128no—
850C23—816no—
851C23—816no—
852C23C2×#12012yes—
853C23#53514yes—
854C23#57612yes—
855C23#57712yes—
856C23C23×D411yescharacteristic
857Q8—24no—
858Q8—24no—
859Q8—48no—
860Q8—44no—
861Q8—42no—
862Q8—42no—
863D4—24no—
864D4—24no—
865D4—24no—
866D4—24no—
867D4—24no—
868D4—24no—
869D4—432no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—432no—
874D4—44no—
875D4—44no—
876D4—44no—
877D4—42no—
878D4—42no—
879D4—88no—
880D4—88no—
881D4—88no—
882D4—88no—
883D4—816no—
884D4—816no—
885D4—84no—
886D4—164no—
887C2×C4—28no—
888C2×C4—216no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—28no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—28no—
902C2×C4—28no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—44no—
911C2×C4—432no—
912C2×C4—48no—
913C2×C4—44no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—84no—
930C2×C4C2×#12012yes—
931C2×C4C2×#12012yes—
932C2×C4C2×#12012yes—
933C2×C4C2×#12012yes—
934C2×C4C2×#12012yes—
935C2×C4#53514yes—
936C2×C4C23×D411yescharacteristic
937C2×C4C23×D411yescharacteristic
938C2×C4C2×H(5,𝔽2)14yes—
939C8—42no—
940C8—42no—
941C8—42no—
942C8—42no—
943C22—24no—
944C22—24no—
945C22—22no—
946C22—22no—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—416no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—44no—
956C22—44no—
957C22—44no—
958C22—44no—
959C22—44no—
960C22—44no—
961C22—44no—
962C22—44no—
963C22—44no—
964C22—816no—
965C22—816no—
966C22—816no—
967C22—864no—
968C22—84no—
969C22—84no—
970C22—84no—
971C22—84no—
972C22—84no—
973C22—84no—
974C22—82no—
975C22—82no—
976C22—81no—
977C22—81no—
978C22—81no—
979C22#301214yes—
980C22C22×#12011yescharacteristic
981C22C2×#53512yes—
982C22C2×#57611yescharacteristic
983C22C2×#57711yescharacteristic
984C22#358512yes—
985C4—24no—
986C4—22no—
987C4—22no—
988C4—22no—
989C4—22no—
990C4—22no—
991C4—44no—
992C4—42no—
993C4—42no—
994C4—82no—
995C4—82no—
996C4—81no—
997C4—81no—
998C4—81no—
999C4#348412yes—
1000C4#348412yes—
1001C2—24no—
1002C2—44no—
1003C2—84no—
1004C2—84no—
1005C2—84no—
1006C2—161no—
1007C2#3522211yescharacteristic
1008C2C2×#301211yescharacteristic
1009C2#6036711yescharacteristic
1010C2#6081112yes—
1011C2#6081212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#535C2semidirect
2. C2×#3217C2semidirect
3. C2×#3211C2semidirect
4. #35302C2semidirect
5. #32883C2semidirect
6. #32881C2semidirect
7. #32880C2semidirect
8. #32878C2semidirect
9. #29626C2semidirect
10. #29625C2semidirect
11. #29623C2semidirect
12. #29622C2semidirect
13. #25867C2semidirect
14. #25736C2semidirect
15. #24220C2semidirect
16. #24218C2semidirect
17. #21808C2semidirect
18. #21803C2semidirect
19. #20717C2semidirect
30. C2×#529C22semidirect
40. C2×#496C22semidirect
41. C2×#495C22semidirect
42. C2×#490C22semidirect
43. C2×#488C22semidirect
44. C2×#464C22semidirect
45. C2×#460C22semidirect
46. C2×#463C22semidirect
47. C2×#459C22semidirect
48. C2×#452C22semidirect
49. C2×#449C22semidirect
50. C2×#451C22semidirect
51. C2×#448C22semidirect
54. C2×#450C22semidirect
55. C2×#450C22semidirect
58. C2×#447C22semidirect
59. C2×#447C22semidirect
60. C2×#432C22semidirect
61. C2×#431C22semidirect
62. #2855C22semidirect
63. #2854C22semidirect
66. #2629C22semidirect
67. #2620C22semidirect
74. #2324C22semidirect
75. #2323C22semidirect
76. #2285C22semidirect
77. #2042C22semidirect
78. #2042C22semidirect
79. #2041C22semidirect
80. #2041C22semidirect
81. #2015C22semidirect
82. #2014C22semidirect
83. #2012C22semidirect
84. #2011C22semidirect
85. #1983C22semidirect
86. #1982C22semidirect
87. #1959C22semidirect
88. #1957C22semidirect
89. #1817C22semidirect
90. #1817C22semidirect
91. #1798C22semidirect
92. #1788C22semidirect
93. #1788C22semidirect
94. #1787C22semidirect
95. #1787C22semidirect
100. #1786C22semidirect
101. #1786C22semidirect
102. #1786C22semidirect
103. #1786C22semidirect
106. #1750C22semidirect
130. C22×Q16C23semidirect
133. C22×SD16C23semidirect
134. C22×SD16C23semidirect
137. C22×D8C23semidirect
150. C2×#127D4semidirect
157. C2×#125C23semidirect
164. C2×#124D4semidirect
168. C2×#124C23semidirect
188. C2×C4×Q8C23semidirect
190. C2×C4×D4C23semidirect
231. C2×C4⋊C8C23semidirect
232. C2×C4⋊C8C23semidirect
233. C2×#103C23semidirect
234. C2×#103C23semidirect
235. C2×#103C23semidirect
236. C2×#103C23semidirect
245. C2×#102C23semidirect
246. C2×#102C23semidirect
247. C2×#102C23semidirect
248. C2×#102C23semidirect
255. C2×#97C23semidirect
256. C2×C4×C8C23semidirect
265. #391C23semidirect
267. #390C23semidirect
269. #389C23semidirect
270. #389C23semidirect
285. #384C23semidirect
295. C4×C4⋊C4C23semidirect
296. #336C23semidirect
297. #336C23semidirect

Maximal subgroups

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

subgroupindex
C22×#5352
C2×#32172
C2×#32112
#353022
#328832
#328812
#328802
#328782
#296262
#296252
#296232
#296222
#258672
#257362
#242202
#242182
#218082
#218032
#207172