Finite Group Databasebeta

← #6763430

Subgroups — #6763430

Order 512.

1765 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36187C211yesmaximal, characteristic
2#36129C211yesmaximal, characteristic, complemented
3#33048C211yesmaximal, characteristic, complemented
4#31852C214yesmaximal, complemented
5#31663C214yesmaximal, complemented
6#30205C211yesmaximal, characteristic, complemented
7#29807C211yesmaximal, characteristic, complemented
8#29141C211yesmaximal, characteristic, complemented
9#28613C211yesmaximal, characteristic, complemented
10#27975C211yesmaximal, characteristic, complemented
11#27962C211yesmaximal, characteristic, complemented
12#25718C211yesmaximal, characteristic, complemented
13#25598C211yesmaximal, characteristic, complemented
14#24541C214yesmaximal, complemented
15#23977C214yesmaximal, complemented
16#22268C211yesmaximal, characteristic, complemented
17#21864C211yesmaximal, characteristic, complemented
18#21202C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×#555C2212yes—
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#492C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#448C2214yes—
27C2×#431C2211yescharacteristic
28C2×#419C2214yes—
29C2×C4×M16C2211yescharacteristic
30#2868C2211yescharacteristic
31#2862C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2856C2211yescharacteristic
35#2856C2211yescharacteristic
36#2563C2212yes—
37#2550—21no—
38#2537—21no—
39#2537—21no—
40#2500C2212yes—
41#2500C2212yes—
42#2492—21no—
43#2491—21no—
44#2491—21no—
45#2491—21no—
46#2491—21no—
47#2451—21no—
48#2446C2212yes—
49#2442—21no—
50#2439—21no—
51#2429C2212yes—
52#2417—21no—
53#2409C2212yes—
54#2360—21no—
55#2354—21no—
56#2354—21no—
57#2352—21no—
58Q8×C22⋊C4C2212yes—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#127C2211yescharacteristic
61#2285C2211yescharacteristic
62#2285C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2101C2214yes—
65#2074C2214yes—
66#2072C2214yes—
67#2055C2214yes—
68#2055C2214yes—
69#2024C2214yes—
70#2024C2214yes—
71#2013C2214yes—
72#2000C2214yes—
73#2000C2214yes—
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1960C2214yes—
78#1957C2211yescharacteristic
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1936C2214yes—
86#1924C2212yes—
87#1917C2212yes—
88#1895C2214yes—
89#1880C2214yes—
90#1880C2214yes—
91#1877C2214yes—
92#1877C2214yes—
93#1873C2214yes—
94#1873C2214yes—
95#1870C2212yes—
96#1851C2212yes—
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1834C2211yescharacteristic
100#1825C2214yes—
101#1805C2214yes—
102#1803C2214yes—
103C4×C4⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C23×Q8C2312yes—
108C22×SD16C2314yes—
109C22×SD16C2314yes—
110C22×M16C2312yes—
111#555—48no—
112#533—24no—
113#533—42no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—42no—
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2312yes—
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2312yes—
125C2×#127C2311yescharacteristic
126C2×#125—21no—
127C2×#124—22no—
128C2×#124—22no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8C2312yes—
132C2×C22⋊Q8C2312yes—
133C2×#121—22no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121C2312yes—
139C2×#121C2312yes—
140C2×C4×Q8—21no—
141C2×C4×Q8C2312yes—
142C2×C4×Q8C2312yes—
143C2×C4×D4—21no—
144C2×C4×D4—21no—
145C2×C4×D4D411yescharacteristic
146C2×C4×D4D411yescharacteristic
147C2×C4×D4C2312yes—
148C2×C4×D4C2311yescharacteristic
149C2×#117—21no—
150C2×#117—22no—
151C2×#117C2312yes—
152C2×#117C2312yes—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#492—24no—
158#492—42no—
159#486—42no—
160#448—48no—
161#431—42no—
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2312yes—
164#419—48no—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C4×M16—42no—
177C2×#97C2312yes—
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182#400—22no—
183#398—22no—
184#398—22no—
185#396—22no—
186#395—22no—
187#394—22no—
188#394—22no—
189#394—22no—
190#394—22no—
191#393—22no—
192#393—22no—
193#393—22no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391—22no—
198#391—22no—
199#391C2312yes—
200#391C2312yes—
201#391C2312yes—
202#391C2312yes—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390C2312yes—
210#390C2312yes—
211#390C2312yes—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—22no—
218#389C2312yes—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#387—22no—
225#387—22no—
226#386—22no—
227#385—22no—
228#384—21no—
229#384—21no—
230#384C2311yescharacteristic
231#384C2311yescharacteristic
232#384C2312yes—
233#384C2311yescharacteristic
234#384C2311yescharacteristic
235#382—21no—
236#382—21no—
237#382C2312yes—
238#382C2312yes—
239#380—21no—
240#380—21no—
241#380—21no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—22no—
247#380—22no—
248#380—22no—
249#380C2312yes—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4D411yescharacteristic
257C4×C4⋊C4D411yescharacteristic
258C4×C4⋊C4C2311yescharacteristic
259C4×C22⋊C4—22no—
260C4×C22⋊C4D411yescharacteristic
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4C2311yescharacteristic
265C4×C22⋊C4C2311yescharacteristic
266C43C2311yescharacteristic
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C22×Q8—21no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—24no—
282C22×Q8—28no—
283C22×Q8—42no—
284C22×Q8—44no—
285C22×Q8C2412yes—
286C22×Q8C2412yes—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C2×D411yescharacteristic
292C22×D4C2412yes—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C2×SD16—28no—
302C2×SD16—44no—
303C2×SD16—44no—
304C2×SD16—44no—
305C2×SD16—44no—
306C2×SD16—44no—
307C2×M16—24no—
308C2×M16—42no—
309C2×M16—42no—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C4⋊Q8—24no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—44no—
321C4⋊Q8—44no—
322C4⋊Q8—44no—
323C4⋊Q8—42no—
324C4⋊Q8—82no—
325C4⋊Q8—82no—
326C4⋊Q8#4114yes—
327#127—22no—
328#127—22no—
329#125—44no—
330#124—48no—
331#124—48no—
332C22⋊Q8—24no—
333C22⋊Q8—42no—
334C22⋊Q8—44no—
335C22⋊Q8—44no—
336C22⋊Q8—44no—
337#121—28no—
338#121—44no—
339#121—48no—
340#121—82no—
341#121—82no—
342#121—82no—
343#121—82no—
344C4×Q8—24no—
345C4×Q8—42no—
346C4×Q8—44no—
347C4×Q8—44no—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—44no—
351C4×D4—42no—
352C4×D4—44no—
353C4×D4—44no—
354#117—28no—
355#117—44no—
356#117—44no—
357#117—48no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4C2×D411yescharacteristic
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
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×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
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
431C2×C42C2411yescharacteristic
432C4⋊C8—42no—
433C4⋊C8—42no—
434#103—44no—
435#103—44no—
436#103—44no—
437#103—44no—
438#103—44no—
439#103—44no—
440#102—44no—
441#102—44no—
442C22⋊C8—24no—
443C22⋊C8—42no—
444C22⋊C8—42no—
445#97—42no—
446C4×C8—22no—
447C4×C8—22no—
448C4×C8—22no—
449C4×C8—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470C24—22no—
471C24C22×D411yescharacteristic
472C24C22×D411yescharacteristic
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—22no—
478C2×Q8—24no—
479C2×Q8—24no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—416no—
483C2×Q8—44no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—82no—
488C2×Q8—82no—
489C2×Q8—82no—
490C2×Q8—88no—
491C2×Q8C2×#4114yes—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—41no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—82no—
508C2×D4—82no—
509C2×D4—82no—
510C2×D4—82no—
511C22×C4—21no—
512C22×C4—21no—
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—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
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—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—82no—
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4H(5,𝔽2)14yes—
556C22×C4C2511yescharacteristic
557SD16—88no—
558SD16—88no—
559M16—48no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C4⋊C4—22no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—41no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C4⋊C4—82no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—82no—
620C22⋊C4—82no—
621C22⋊C4—82no—
622C22⋊C4—82no—
623C22⋊C4—82no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—22no—
636C42—22no—
637C42—44no—
638C42—44no—
639C42—44no—
640C42—82no—
641C42#13714yes—
642C42C2×#4112yes—
643C42H(5,𝔽2)12yes—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23#53512yes—
665C23C23×D411yescharacteristic
666Q8—28no—
667Q8—44no—
668Q8—44no—
669Q8—44no—
670Q8—88no—
671Q8—84no—
672Q8—164no—
673D4—44no—
674D4—44no—
675D4—44no—
676D4—84no—
677D4—84no—
678D4—164no—
679D4—164no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—24no—
696C2×C4—21no—
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—21no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—88no—
737C2×C4—88no—
738C2×C4#53512yes—
739C2×C4#54612yes—
740C2×C4#54612yes—
741C2×C4C2×#13712yes—
742C2×C4C2×#13712yes—
743C2×C4C2×#13712yes—
744C2×C4#57512yes—
745C2×C4#57712yes—
746C2×C4#57712yes—
747C2×C4C22×#4111yescharacteristic
748C2×C4C2×H(5,𝔽2)12yes—
749C2×C4C2×H(5,𝔽2)11yescharacteristic
750C2×C4#58512yes—
751C8—42no—
752C8—42no—
753C8—42no—
754C8—42no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22C2×#53511yescharacteristic
777C22C2×#54611yescharacteristic
778C22#350011yescharacteristic
779C22C22×#13711yescharacteristic
780C22C2×#57511yescharacteristic
781C22C2×#57711yescharacteristic
782C22C2×#57711yescharacteristic
783C4—22no—
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—44no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4#332114yes—
801C4#332914yes—
802C4#351312yes—
803C4#354212yes—
804C2—42no—
805C2—81no—
806C2—162no—
807C2#3808211yescharacteristic
808C2#6080411yescharacteristic
809C2#6081811yescharacteristic
810C2C2×#332111yescharacteristic
811C2C2×#332911yescharacteristic
812C2#6254011yescharacteristic
813C2#6254311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36187C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36129C2semidirect
3. #33048C2semidirect
4. #31852C2semidirect
5. #31663C2semidirect
6. #30205C2semidirect
7. #29807C2semidirect
8. #29141C2semidirect
9. #28613C2semidirect
10. #27975C2semidirect
11. #27962C2semidirect
12. #25718C2semidirect
13. #25598C2semidirect
14. #24541C2semidirect
15. #23977C2semidirect
16. #22268C2semidirect
17. #21864C2semidirect
18. #21202C2semidirect
19. #21102C2semidirect

Maximal subgroups

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

subgroupindex
#361872
#361292
#330482
#318522
#316632
#302052
#298072
#291412
#286132
#279752
#279622
#257182
#255982
#245412
#239772
#222682
#218642
#212022
#211022