Finite Group Databasebeta

← #6661066

Subgroups — #6661066

Order 512.

1934 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#32747C214yesmaximal, complemented
4#30295C212yesmaximal, complemented
5#30201C212yesmaximal, complemented
6#29971C212yesmaximal, complemented
7#29938C211yesmaximal, characteristic, complemented
8#29936C211yesmaximal, characteristic, complemented
9#29758C212yesmaximal, complemented
10#29690C211yesmaximal, characteristic, complemented
11#29687C211yesmaximal, characteristic, complemented
12#27646C212yesmaximal, complemented
13#24844C212yesmaximal, complemented
14#24843C212yesmaximal, complemented
15#24560C214yesmaximal, complemented
16#24300C212yesmaximal, complemented
17#20626C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×#525—21no—
21C23×C42C2211yescharacteristic
22C2×#482C2214yes—
23C2×#476C2212yescomplemented
24C2×#474C2212yescomplemented
25C2×#423C2212yes—
26C2×#407C2212yes—
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2856C2211yescharacteristic
34#2856C2211yescharacteristic
35#2855—21no—
36#2855—21no—
37#2854—21no—
38#2854C2212yes—
39#2851C2212yes—
40#2851C2212yes—
41#2850—21no—
42#2850—21no—
43#2848—21no—
44#2848—21no—
45#2847—21no—
46#2847C2212yes—
47C4×C22⋊Q8—21no—
48C4×C22⋊Q8—21no—
49C4×C22⋊Q8—21no—
50C4×C22⋊Q8—21no—
51C4×#121—21no—
52C4×#121—21no—
53C4×#121C2212yes—
54C4×#121C2212yes—
55#2297—21no—
56#2296C2212yes—
57#2285C2211yescharacteristic
58#2285C2211yescharacteristic
59#2280C2212yes—
60#2099C2212yescomplemented
61#2099C2212yescomplemented
62#2088C2214yescomplemented
63#2087C2214yescomplemented
64#2085C2214yescomplemented
65#2084C2212yescomplemented
66#2083C2212yescomplemented
67#2077C2214yes—
68#2075C2214yes—
69#2073C2214yescomplemented
70#2067C2214yescomplemented
71#2065C2214yescomplemented
72#2059C2214yescomplemented
73#2058C2212yescomplemented
74#2057C2212yescomplemented
75#2041C2212yescomplemented
76#2041C2212yescomplemented
77#2034C2214yes—
78#2033C2214yes—
79#2025C2214yescomplemented
80#1988C2212yescomplemented
81#1987C2212yescomplemented
82#1948C2212yescomplemented
83#1947C2212yescomplemented
84#1895C2214yes—
85#1895C2214yes—
86#1875C2214yes—
87#1854C2214yes—
88#1825C2214yes—
89#1809C2214yes—
90#1809C2214yes—
91#1802C2212yescomplemented
92#1802C2212yescomplemented
93#1797C2212yes—
94#1797C2212yes—
95#1797C2212yes—
96#1797C2211yescharacteristic
97#1797C2211yescharacteristic
98#1728C2212yes—
99C22×#41—21no—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C22×M16C2314yes—
104#533—44no—
105#532—44no—
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×#127C2311yescharacteristic
110C2×#125C2312yes—
111C2×#124—21no—
112#525—48no—
113C2×#123—22no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—21no—
121C2×C22⋊Q8—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×#121C2312yes—
130C2×#120—22no—
131C2×C4×Q8—21no—
132C2×C4×Q8—21no—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—21no—
136C2×C4×D4C2312yes—
137C2×#117—21no—
138C2×#117C2312yes—
139C2×#117C2312yes—
140C22×C42—44no—
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#482—48no—
154#476—44no—
155#474—44no—
156C2×#107C2314yes—
157C2×#107C2314yes—
158C2×#106C2314yes—
159C2×#106C2314yes—
160#423—44no—
161C2×C4⋊C8C2312yes—
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168#407—44no—
169C2×C22⋊C8C2314yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172#391—21no—
173#391—21no—
174#391—21no—
175#391—21no—
176#391—21no—
177#391—21no—
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#389C2312yes—
191#389C2312yes—
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#382C2312yes—
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#380C2312yes—
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—21no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—22no—
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#340C2314yes—
257#340C2314yes—
258#336C2312yes—
259#336C2312yes—
260#336C2314yes—
261C25C2×D411yescharacteristic
262C2×#41—44no—
263C2×#41—44no—
264C2×#41—44no—
265C22×Q8—21no—
266C22×Q8—21no—
267C22×Q8—21no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4C2412yes—
274C23×C4—24no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C2×M16—28no—
304C2×M16—44no—
305C2×M16—44no—
306C22×C8C2414yes—
307C22×C8C2414yes—
308C4⋊Q8—24no—
309C4⋊Q8—24no—
310C4⋊Q8—42no—
311#127—42no—
312#125—44no—
313#124—44no—
314#123—48no—
315C22⋊Q8—44no—
316C22⋊Q8—44no—
317C22⋊Q8—44no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320C22⋊Q8—44no—
321C22⋊Q8—44no—
322C22⋊Q8—44no—
323#121—24no—
324#121—24no—
325#121—24no—
326#121—24no—
327#121—42no—
328#121—42no—
329#121—44no—
330#121—44no—
331#121—44no—
332#121—44no—
333#121—44no—
334#120—48no—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×D4—24no—
338C4×D4—24no—
339C4×D4—44no—
340C4×D4—48no—
341C4×D4—48no—
342#117—24no—
343#117—24no—
344#117—44no—
345#117—44no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
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×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420#107—44no—
421#107—44no—
422#106—44no—
423#106—44no—
424C4⋊C8—24no—
425C4⋊C8—24no—
426C4⋊C8—44no—
427#102—44no—
428#102—44no—
429#102—44no—
430#102—44no—
431C22⋊C8—28no—
432C22⋊C8—42no—
433C22⋊C8—42no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
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—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—41no—
455C24—41no—
456C24—41no—
457C24—41no—
458C24C22×D411yescharacteristic
459C24C22×D411yescharacteristic
460C24C22×D411yescharacteristic
461#41—816no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—42no—
491C2×D4—42no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
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—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
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—48no—
553C22×C4—48no—
554C22×C4—416no—
555C22×C4—416no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4AGL(1,ℤ/8)14yes—
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4H(5,𝔽2)12yes—
572C22×C42−1+414yes—
573C22×C42−1+412yes—
574C22×C4C2511yescharacteristic
575M16—88no—
576C2×C8—24no—
577C2×C8—24no—
578C2×C8—24no—
579C2×C8—24no—
580C2×C8—24no—
581C2×C8—24no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—42no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—44no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—44no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊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—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—44no—
646C42—44no—
647C42—44no—
648C42H(5,𝔽2)14yes—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23#53612yes—
682C23#53712yes—
683C23C2×AGL(1,ℤ/8)12yes—
684C23C23×D411yescharacteristic
685Q8—84no—
686Q8—84no—
687Q8—84no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—84no—
693D4—84no—
694D4—88no—
695D4—88no—
696D4—88no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—28no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
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—21no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
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—88no—
764C2×C4#53412yes—
765C2×C4#53412yes—
766C2×C4#53612yes—
767C2×C4#53712yes—
768C2×C4C2×AGL(1,ℤ/8)12yes—
769C2×C4C2×AGL(1,ℤ/8)12yes—
770C2×C4#57512yes—
771C2×C4#57512yes—
772C2×C4#57512yes—
773C2×C4C2×H(5,𝔽2)11yescharacteristic
774C2×C4C2×H(5,𝔽2)12yes—
775C2×C4C2×2−1+412yes—
776C2×C4C2×2−1+411yescharacteristic
777C8—44no—
778C8—44no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—416no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22C2×#53411yescharacteristic
809C22C2×#53611yescharacteristic
810C22C2×#53711yescharacteristic
811C22C22×AGL(1,ℤ/8)11yescharacteristic
812C22C2×#57511yescharacteristic
813C22C2×#57511yescharacteristic
814C22C2×#57511yescharacteristic
815C4—22no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—22no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4#319414yes—
833C4#353612yes—
834C4#353812yes—
835C2—42no—
836C2—42no—
837C2—42no—
838C2—162no—
839C2#3744211yescharacteristic
840C2C2×#319411yescharacteristic
841C2#6075211yescharacteristic
842C2#6086311yescharacteristic
843C2#6086411yescharacteristic
844C2#6090711yescharacteristic
845C2#6091611yescharacteristic
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. #32747C2semidirect
4. #30295C2semidirect
5. #30201C2semidirect
6. #29971C2semidirect
7. #29938C2semidirect
8. #29936C2semidirect
9. #29758C2semidirect
10. #29690C2semidirect
11. #29687C2semidirect
12. #27646C2semidirect
13. #24844C2semidirect
14. #24843C2semidirect
15. #24560C2semidirect
16. #24300C2semidirect
17. #20626C2semidirect
23. C2×#476C22semidirect
24. C2×#474C22semidirect
60. #2099C22semidirect
61. #2099C22semidirect
62. #2088C22semidirect
63. #2087C22semidirect
64. #2085C22semidirect
65. #2084C22semidirect
66. #2083C22semidirect
69. #2073C22semidirect
70. #2067C22semidirect
71. #2065C22semidirect
72. #2059C22semidirect
73. #2058C22semidirect
74. #2057C22semidirect
75. #2041C22semidirect
76. #2041C22semidirect
79. #2025C22semidirect
80. #1988C22semidirect
81. #1987C22semidirect
82. #1948C22semidirect
83. #1947C22semidirect
91. #1802C22semidirect
92. #1802C22semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#327472
#302952
#302012
#299712
#299382
#299362
#297582
#296902
#296872
#276462
#248442
#248432
#245602
#243002
#206262