Finite Group Databasebeta

← #6763779

Subgroups — #6763779

Order 512.

1780 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#36189C211yesmaximal, characteristic, complemented
2#36122C211yesmaximal, characteristic
3#33049C211yesmaximal, characteristic, complemented
4#32106C214yesmaximal, complemented
5#31304C214yesmaximal, complemented
6#30219C211yesmaximal, characteristic, complemented
7#29843C211yesmaximal, characteristic, complemented
8#29191C211yesmaximal, characteristic, complemented
9#28750C211yesmaximal, characteristic, complemented
10#27905C211yesmaximal, characteristic, complemented
11#27890C211yesmaximal, characteristic, complemented
12#25857C211yesmaximal, characteristic, complemented
13#25856C211yesmaximal, characteristic, complemented
14#24491C214yesmaximal, complemented
15#24052C214yesmaximal, complemented
16#22218C211yesmaximal, characteristic, complemented
17#21804C211yesmaximal, characteristic, complemented
18#21200C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×#548C2212yes—
21C2×#532C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#487C2211yescharacteristic
24C2×#487C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#483C2214yes—
27C2×#431C2211yescharacteristic
28C2×#417C2214yes—
29C2×C4×M16C2211yescharacteristic
30#2859C2211yescharacteristic
31#2858C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2856C2211yescharacteristic
36#2570—21no—
37#2545C2212yes—
38#2511—21no—
39#2507C2212yes—
40#2497C2212yes—
41#2491—21no—
42#2491—21no—
43#2487C2212yes—
44#2452—21no—
45#2452—21no—
46#2442—21no—
47#2441—21no—
48#2436C2212yes—
49#2432C2212yes—
50#2423—21no—
51#2417—21no—
52#2416—21no—
53#2416—21no—
54#2361—21no—
55#2361—21no—
56#2360—21no—
57#2352—21no—
58#2345C2212yes—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61#2285C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2096C2214yes—
65#2066C2214yes—
66#2065C2214yes—
67#2043C2214yes—
68#2042C2214yes—
69#2042C2214yes—
70#2042C2214yes—
71#2042C2214yes—
72#2034C2214yes—
73#2034C2214yes—
74#1990C2211yescharacteristic
75#1983C2214yes—
76#1981C2214yes—
77#1959C2214yes—
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1956C2211yescharacteristic
87#1935C2214yes—
88#1927C2214yes—
89#1926C2214yes—
90#1924C2212yes—
91#1917C2212yes—
92#1894C2214yes—
93#1870C2212yes—
94#1865C2214yes—
95#1865C2214yes—
96#1851C2212yes—
97#1844C2211yescharacteristic
98#1844C2211yescharacteristic
99#1834C2211yescharacteristic
100#1788C2214yes—
101#1787C2214yes—
102#1787C2214yes—
103C4×C4⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C22×#41C2312yes—
108C23×Q8C2312yes—
109C22×M16C2312yes—
110#548—48no—
111#532—24no—
112#532—42no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2312yes—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×#127C2311yescharacteristic
122C2×#125—21no—
123C2×#124—22no—
124C2×#124C2312yes—
125C2×#124C2312yes—
126C2×#124C2312yes—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—22no—
130C2×C22⋊Q8C2312yes—
131C2×#121—22no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121C2312yes—
137C2×C4×Q8—21no—
138C2×C4×Q8C2312yes—
139C2×C4×D4—22no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4D411yescharacteristic
143C2×C4×D4D411yescharacteristic
144C2×C4×D4C2311yescharacteristic
145C2×#117—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#487—24no—
154#487—42no—
155#486—42no—
156#483—48no—
157#431—42no—
158C2×#106C2314yes—
159C2×#106C2314yes—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2312yes—
162#417—48no—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C4×M16—42no—
179C2×#97C2312yes—
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184#400—22no—
185#400—22no—
186#399—22no—
187#398—22no—
188#398—22no—
189#396—22no—
190#396—22no—
191#396—22no—
192#394—22no—
193#394—22no—
194#393—22no—
195#393—22no—
196#391—21no—
197#391—21no—
198#391—21no—
199#391C2312yes—
200#391C2312yes—
201#390—21no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390C2312yes—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—22no—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#389C2312yes—
222#389C2312yes—
223#388—22no—
224#388—22no—
225#388—22no—
226#387—22no—
227#387—22no—
228#387—22no—
229#387—22no—
230#386—22no—
231#386—22no—
232#386—22no—
233#385—22no—
234#385—22no—
235#385—22no—
236#384—21no—
237#384—21no—
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#384C2311yescharacteristic
242#384C2312yes—
243#382—21no—
244#382—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—22no—
251#380C2312yes—
252#380C2312yes—
253#380C2312yes—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4D411yescharacteristic
259C4×C4⋊C4D411yescharacteristic
260C4×C4⋊C4C2312yes—
261C4×C4⋊C4C2312yes—
262C4×C4⋊C4C2311yescharacteristic
263C4×C22⋊C4—22no—
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4C2311yescharacteristic
269C4×C22⋊C4C2311yescharacteristic
270C43C2311yescharacteristic
271#340C2314yes—
272#340C2314yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C2×#41—24no—
279C2×#41—28no—
280C2×#41—42no—
281C2×#41—44no—
282C22×Q8—21no—
283C22×Q8—22no—
284C22×Q8—24no—
285C22×Q8—42no—
286C22×Q8—44no—
287C22×Q8—44no—
288C22×Q8C2412yes—
289C22×Q8C2412yes—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4C2×D411yescharacteristic
295C22×D4C2412yes—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C2×M16—24no—
306C2×M16—42no—
307C2×M16—42no—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C4⋊Q8—24no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—44no—
319C4⋊Q8—44no—
320C4⋊Q8—42no—
321C4⋊Q8#4114yes—
322#127—22no—
323#127—22no—
324#125—82no—
325#124—24no—
326#124—42no—
327#124—44no—
328#124—44no—
329#124—48no—
330C22⋊Q8—28no—
331C22⋊Q8—48no—
332C22⋊Q8—44no—
333C22⋊Q8—82no—
334#121—44no—
335#121—44no—
336#121—44no—
337#121—44no—
338#121—48no—
339#121—44no—
340C4×Q8—44no—
341C4×Q8—82no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—44no—
345C4×D4—44no—
346C4×D4—42no—
347C4×D4—48no—
348#117—82no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—82no—
378C2×C4⋊C4—82no—
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
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×C22⋊C4C2×D411yescharacteristic
401C2×C22⋊C4C2×D411yescharacteristic
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426#106—44no—
427#106—44no—
428C4⋊C8—42no—
429C4⋊C8—42no—
430#103—28no—
431#103—44no—
432#103—44no—
433#103—44no—
434#103—44no—
435#103—44no—
436#103—44no—
437#103—44no—
438#102—44no—
439#102—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
473#41—416no—
474#41—88no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—24no—
478C2×Q8—24no—
479C2×Q8—22no—
480C2×Q8—24no—
481C2×Q8—24no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—82no—
488C2×Q8—88no—
489C2×Q8—88no—
490C2×Q8C2×#4114yes—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—22no—
496C2×D4—24no—
497C2×D4—41no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—82no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
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—21no—
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—22no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4—82no—
544C22×C4#13714yes—
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×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4H(5,𝔽2)14yes—
558C22×C4C2511yescharacteristic
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—
604C4⋊C4—82no—
605C4⋊C4—82no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C22⋊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—82no—
622C22⋊C4—82no—
623C22⋊C4—82no—
624C22⋊C4—82no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—22no—
638C42—22no—
639C42—44no—
640C42—82no—
641C42—82no—
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—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23#53512yes—
664C23C2×#13712yes—
665C23C23×D411yescharacteristic
666Q8—28no—
667Q8—44no—
668Q8—44no—
669Q8—44no—
670Q8—88no—
671Q8—84no—
672D4—44no—
673D4—44no—
674D4—44no—
675D4—88no—
676D4—88no—
677D4—84no—
678D4—84no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—28no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—24no—
694C2×C4—21no—
695C2×C4—21no—
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—21no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
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—164no—
739C2×C4#53512yes—
740C2×C4#54612yes—
741C2×C4#54612yes—
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—22no—
759C22—22no—
760C22—22no—
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—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—44no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4#331614yes—
801C4#332614yes—
802C4#351312yes—
803C4#354212yes—
804C2—42no—
805C2—42no—
806C2—162no—
807C2#3808411yescharacteristic
808C2#6080411yescharacteristic
809C2#6082011yescharacteristic
810C2C2×#331611yescharacteristic
811C2C2×#332611yescharacteristic
812C2#6254211yescharacteristic
813C2#6254311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36122C2
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
1. #36189C2semidirect
3. #33049C2semidirect
4. #32106C2semidirect
5. #31304C2semidirect
6. #30219C2semidirect
7. #29843C2semidirect
8. #29191C2semidirect
9. #28750C2semidirect
10. #27905C2semidirect
11. #27890C2semidirect
12. #25857C2semidirect
13. #25856C2semidirect
14. #24491C2semidirect
15. #24052C2semidirect
16. #22218C2semidirect
17. #21804C2semidirect
18. #21200C2semidirect
19. #21102C2semidirect

Maximal subgroups

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

subgroupindex
#361892
#361222
#330492
#321062
#313042
#302192
#298432
#291912
#287502
#279052
#278902
#258572
#258562
#244912
#240522
#222182
#218042
#212002
#211022