Finite Group Databasebeta

← #6475943

Subgroups — #6475943

Order 512.

2168 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#32935C214yesmaximal, complemented
4#30291C211yesmaximal, characteristic, complemented
5#30240C211yesmaximal, characteristic, complemented
6#30187C211yesmaximal, characteristic, complemented
7#30185C211yesmaximal, characteristic, complemented
8#29165C212yesmaximal, complemented
9#29162C212yesmaximal, complemented
10#28580C212yesmaximal, complemented
11#28577C212yesmaximal, complemented
12#27863C212yesmaximal, complemented
13#27861C212yesmaximal, complemented
14#25503C212yesmaximal, complemented
15#25501C212yesmaximal, complemented
16#22185C214yesmaximal, complemented
17C2×#1728C211yesmaximal, characteristic, complemented
18C23×M16C2212yes—
19C2×#533C2211yescharacteristic
20C2×#532C2211yescharacteristic
21C2×#525—21no—
22C23×C42C2211yescharacteristic
23C2×#468C2214yes—
24C2×#468C2214yes—
25C2×#465C2214yes—
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2856C2211yescharacteristic
33#2856C2211yescharacteristic
34#2855—21no—
35#2855C2212yes—
36#2854—21no—
37#2854C2212yes—
38#2851—21no—
39#2851—21no—
40#2850—21no—
41#2850—21no—
42#2848—21no—
43#2848C2212yes—
44#2847—21no—
45#2847C2212yes—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8—21no—
48C4×C22⋊Q8C2212yes—
49C4×C22⋊Q8C2212yes—
50C4×#121—21no—
51C4×#121—21no—
52C4×#121C2212yes—
53C4×#121C2212yes—
54#2297—21no—
55#2296—21no—
56#2285C2211yescharacteristic
57#2285C2211yescharacteristic
58#2280—21no—
59#2100C2212yescomplemented
60#2099C2212yescomplemented
61#2096C2212yescomplemented
62#2094C2212yescomplemented
63#2083C2212yescomplemented
64#2083C2212yescomplemented
65#2072C2212yescomplemented
66#2071C2212yescomplemented
67#2057C2212yescomplemented
68#2057C2212yescomplemented
69#2043C2212yescomplemented
70#2041C2212yescomplemented
71#2024C2212yescomplemented
72#2023C2212yescomplemented
73#2014C2212yescomplemented
74#2013C2212yescomplemented
75#1928C2214yescomplemented
76#1925C2214yescomplemented
77#1920C2214yescomplemented
78#1919C2214yescomplemented
79#1895C2214yes—
80#1895C2214yes—
81#1894C2214yes—
82#1894C2214yes—
83#1893C2214yes—
84#1892C2214yes—
85#1880C2214yescomplemented
86#1877C2214yescomplemented
87#1863C2214yescomplemented
88#1862C2214yescomplemented
89#1809C2214yes—
90#1809C2214yes—
91#1808C2214yes—
92#1728C2212yes—
93#1728C2212yes—
94#1728C2212yes—
95#1728C2212yes—
96C2×#336C2211yescharacteristic
97C2×#336C2212yes—
98C2×#336C2211yescharacteristic
99C22×#41—21no—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C22×SD16C2314yes—
104C22×M16—28no—
105C22×M16—44no—
106C22×M16—44no—
107C22×M16C2314yes—
108C22×M16C2314yes—
109C23×C8C2312yes—
110C23×C8C2312yes—
111#533—44no—
112#532—44no—
113C2×C4⋊Q8C2311yescharacteristic
114C2×C4⋊Q8C2311yescharacteristic
115C2×C4⋊Q8C2311yescharacteristic
116C2×#127C2311yescharacteristic
117C2×#125—21no—
118C2×#124—21no—
119#525—48no—
120C2×#123—22no—
121C2×C22⋊Q8—21no—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8C2312yes—
127C2×C22⋊Q8C2312yes—
128C2×C22⋊Q8C2312yes—
129C2×#121—21no—
130C2×#121—21no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121C2312yes—
135C2×#121C2312yes—
136C2×#121C2312yes—
137C2×#120—22no—
138C2×C4×Q8—21no—
139C2×C4×Q8C2312yes—
140C2×C4×D4—22no—
141C2×C4×D4—22no—
142C2×C4×D4—21no—
143C2×C4×D4C2312yes—
144C2×#117—21no—
145C2×#117—21no—
146C2×#117—21no—
147C22×C42—44no—
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#468—48no—
161#468—48no—
162#465—216no—
163C2×#107C2314yes—
164C2×#107C2314yes—
165C2×#106C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172#391—21no—
173#391—21no—
174#391—21no—
175#391—21no—
176#391C2312yes—
177#391C2312yes—
178#390—21no—
179#390—21no—
180#390—21no—
181#390—21no—
182#390C2312yes—
183#390C2312yes—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189#389—21no—
190#389—21no—
191#389—21no—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#389C2312yes—
196#388—22no—
197#388—22no—
198#388—22no—
199#388—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#386—22no—
205#386—22no—
206#386—22no—
207#386—22no—
208#386—22no—
209#386—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#384C2311yescharacteristic
217#384C2311yescharacteristic
218#384C2311yescharacteristic
219#384C2311yescharacteristic
220#382—21no—
221#382—21no—
222#381—22no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380—21no—
233#380C2312yes—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#380C2312yes—
238#380C2312yes—
239#379—22no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2312yes—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#336C2312yes—
257#336C2312yes—
258#336C2312yes—
259#336C2312yes—
260#336C2314yes—
261#336C2314yes—
262C25C2×D411yescharacteristic
263C2×#41—44no—
264C2×#41—44no—
265C2×#41—44no—
266C22×Q8—21no—
267C22×Q8—21no—
268C22×Q8C2412yes—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4C2412yes—
275C23×C4—24no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—22no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C2×SD16—28no—
305C2×SD16—44no—
306C2×SD16—44no—
307C2×M16—28no—
308C2×M16—28no—
309C2×M16—28no—
310C2×M16—28no—
311C2×M16—44no—
312C2×M16—44no—
313C2×M16—432no—
314C22×C8—24no—
315C22×C8—42no—
316C22×C8—42no—
317C22×C8—42no—
318C22×C8—42no—
319C22×C8#4118yescomplemented
320C22×C8C2414yes—
321C22×C8C2414yes—
322C4⋊Q8—42no—
323C4⋊Q8—42no—
324C4⋊Q8—42no—
325#127—42no—
326#125—44no—
327#124—44no—
328#123—48no—
329C22⋊Q8—28no—
330C22⋊Q8—28no—
331C22⋊Q8—24no—
332C22⋊Q8—24no—
333C22⋊Q8—44no—
334C22⋊Q8—44no—
335C22⋊Q8—44no—
336C22⋊Q8—44no—
337C22⋊Q8—44no—
338#121—28no—
339#121—28no—
340#121—24no—
341#121—24no—
342#121—44no—
343#121—44no—
344#121—44no—
345#121—44no—
346#121—44no—
347#120—48no—
348C4×Q8—44no—
349C4×Q8—44no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—48no—
353C4×D4—48no—
354#117—44no—
355#117—44no—
356#117—44no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431#107—44no—
432#107—44no—
433#106—28no—
434#103—28no—
435#103—44no—
436#103—44no—
437#102—28no—
438#102—44no—
439#102—44no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—41no—
463C24—41no—
464C24C22×D411yescharacteristic
465C24C22×D411yescharacteristic
466C24C22×D411yescharacteristic
467#41—816no—
468C2×Q8—24no—
469C2×Q8—22no—
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×D4—24no—
479C2×D4—22no—
480C2×D4—24no—
481C2×D4—22no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—42no—
496C2×D4—42no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—416no—
558C22×C4—416no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4AGL(1,ℤ/8)14yes—
563C22×C4#13714yes—
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C2×#4114yes—
576C22×C4H(5,𝔽2)14yes—
577C22×C4H(5,𝔽2)12yes—
578C22×C42−1+412yes—
579C22×C4C2511yescharacteristic
580SD16—88no—
581M16—416no—
582M16—416no—
583C2×C8—24no—
584C2×C8—24no—
585C2×C8—24no—
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—48no—
589C2×C8—48no—
590C2×C8C2×#4118yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—22no—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—44no—
615C4⋊C4—42no—
616C4⋊C4—44no—
617C4⋊C4—42no—
618C4⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—44no—
653C42—44no—
654C42—44no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—28no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23#53212yes—
686C23#53412yes—
687C23#53712yes—
688C23C2×AGL(1,ℤ/8)12yes—
689C23C2×#13712yes—
690C23C23×D411yescharacteristic
691Q8—44no—
692Q8—44no—
693Q8—84no—
694Q8—84no—
695D4—44no—
696D4—44no—
697D4—84no—
698D4—84no—
699D4—88no—
700D4—88no—
701D4—88no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—88no—
769C2×C4#53212yes—
770C2×C4#53412yes—
771C2×C4#53712yes—
772C2×C4C2×AGL(1,ℤ/8)12yes—
773C2×C4C2×AGL(1,ℤ/8)12yes—
774C2×C4C2×#13712yes—
775C2×C4C2×#13712yes—
776C2×C4#57512yes—
777C2×C4#57512yes—
778C2×C4C22×#4112yes—
779C2×C4C2×H(5,𝔽2)11yescharacteristic
780C2×C4C2×H(5,𝔽2)12yes—
781C2×C4C2×2−1+411yescharacteristic
782C8—28no—
783C8—44no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—416no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22#318214yes—
813C22C2×#53211yescharacteristic
814C22C2×#53411yescharacteristic
815C22C2×#53711yescharacteristic
816C22C22×AGL(1,ℤ/8)11yescharacteristic
817C22C22×#13711yescharacteristic
818C22C2×#57511yescharacteristic
819C22C2×#57511yescharacteristic
820C4—22no—
821C4—22no—
822C4—22no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—22no—
827C4—22no—
828C4—22no—
829C4—41no—
830C4—41no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4#349012yes—
839C4#349212yes—
840C2—24no—
841C2—42no—
842C2—42no—
843C2—162no—
844C2#3505111yescharacteristic
845C2#6067611yescharacteristic
846C2C2×#318211yescharacteristic
847C2#6075011yescharacteristic
848C2#6075111yescharacteristic
849C2#6091611yescharacteristic
850C2#6091811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36625C2semidirect
3. #32935C2semidirect
4. #30291C2semidirect
5. #30240C2semidirect
6. #30187C2semidirect
7. #30185C2semidirect
8. #29165C2semidirect
9. #29162C2semidirect
10. #28580C2semidirect
11. #28577C2semidirect
12. #27863C2semidirect
13. #27861C2semidirect
14. #25503C2semidirect
15. #25501C2semidirect
16. #22185C2semidirect
17. C2×#1728C2semidirect
59. #2100C22semidirect
60. #2099C22semidirect
61. #2096C22semidirect
62. #2094C22semidirect
63. #2083C22semidirect
64. #2083C22semidirect
65. #2072C22semidirect
66. #2071C22semidirect
67. #2057C22semidirect
68. #2057C22semidirect
69. #2043C22semidirect
70. #2041C22semidirect
71. #2024C22semidirect
72. #2023C22semidirect
73. #2014C22semidirect
74. #2013C22semidirect
75. #1928C22semidirect
76. #1925C22semidirect
77. #1920C22semidirect
78. #1919C22semidirect
85. #1880C22semidirect
86. #1877C22semidirect
87. #1863C22semidirect
88. #1862C22semidirect
319. C22×C8#41semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#329352
#302912
#302402
#301872
#301852
#291652
#291622
#285802
#285772
#278632
#278612
#255032
#255012
#221852
C2×#17282