Finite Group Databasebeta

← #6797992

Subgroups — #6797992

Order 512.

1859 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#36181C211yesmaximal, characteristic, complemented
2#36127C211yesmaximal, characteristic
3#33294C211yesmaximal, characteristic, complemented
4#31953C214yesmaximal, complemented
5#31950C214yesmaximal, complemented
6#29845C211yesmaximal, characteristic, complemented
7#29844C211yesmaximal, characteristic, complemented
8#28717C211yesmaximal, characteristic, complemented
9#28514C211yesmaximal, characteristic, complemented
10#27950C211yesmaximal, characteristic, complemented
11#27949C211yesmaximal, characteristic, complemented
12#25597C211yesmaximal, characteristic, complemented
13#25597C211yesmaximal, characteristic, complemented
14#24825C214yesmaximal, complemented
15#24137C214yesmaximal, complemented
16#21863C211yesmaximal, characteristic, complemented
17#21859C211yesmaximal, characteristic, complemented
18#21692C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic, complemented
20C2×#552C2212yes—
21C2×#547—21no—
22C2×#532C2211yescharacteristic
23C2×#532C2211yescharacteristic
24C2×#492C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#478C2214yes—
28C2×#440C2214yes—
29C2×#431C2211yescharacteristic
30C2×#431C2211yescharacteristic
31#2868C2211yescharacteristic
32#2859C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2565C2212yes—
38#2547—21no—
39#2537—21no—
40#2537C2212yes—
41#2506—21no—
42#2506—21no—
43#2503C2212yes—
44#2499C2212yes—
45#2496—21no—
46#2496—21no—
47#2486—21no—
48#2486—21no—
49#2432—21no—
50#2432—21no—
51#2422—21no—
52#2422—21no—
53#2422C2212yes—
54#2422C2212yes—
55D4×C4⋊C4—21no—
56D4×C4⋊C4C2212yes—
57#2344—21no—
58#2344—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#127C2211yescharacteristic
61#2285C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2092C2214yes—
65#2085C2214yes—
66#2083C2214yes—
67#2072C2214yes—
68#2068C2214yes—
69#2066C2214yes—
70#2036C2214yes—
71#2035C2214yes—
72#2000C2214yes—
73#2000C2214yes—
74#1992C2214yes—
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1990C2211yescharacteristic
79#1990C2211yescharacteristic
80#1990C2211yescharacteristic
81#1973C2214yes—
82#1957C2211yescharacteristic
83#1957C2211yescharacteristic
84#1957C2211yescharacteristic
85#1956C2211yescharacteristic
86#1955C2212yes—
87#1940C2212yes—
88#1924C2212yes—
89#1924C2212yes—
90#1877C2214yes—
91#1877C2214yes—
92#1875C2214yes—
93#1874C2214yes—
94#1854C2214yes—
95#1852C2214yes—
96#1845C2211yescharacteristic
97#1845C2211yescharacteristic
98#1844C2211yescharacteristic
99#1836C2214yes—
100#1804C2214yes—
101#1803C2214yes—
102#1802C2214yes—
103C4×C4⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×#41—21no—
108C22×#41—21no—
109C22×SD16C2314yes—
110#552—48no—
111#547—48no—
112#532—24no—
113#532—24no—
114#532—42no—
115#532—42no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×#127C2311yescharacteristic
122C2×#126—22no—
123C2×#125—22no—
124C2×#125C2312yes—
125C2×#124—21no—
126C2×#124—21no—
127C2×#123—22no—
128C2×#123—22no—
129C2×#123—22no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×#121—22no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121C2312yes—
138C2×#121C2312yes—
139C2×C4×Q8C2312yes—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4—21no—
144C2×C4×D4D411yescharacteristic
145C2×C4×D4D411yescharacteristic
146C2×C4×D4C2312yes—
147C2×C4×D4C2312yes—
148C2×C4×D4C2312yes—
149C2×C4×D4C2311yescharacteristic
150C2×#117—22no—
151C2×#117C2312yes—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—22no—
155C22×C4⋊C4C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#492—24no—
159#487—42no—
160#487—42no—
161#478—48no—
162#440—48no—
163#431—42no—
164#431—42no—
165C2×#107C2314yes—
166C2×#107C2314yes—
167C2×#106C2314yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×#97C2312yes—
182C2×#97C2312yes—
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187#400—22no—
188#400—22no—
189#398—22no—
190#398—22no—
191#397—22no—
192#397—22no—
193#397—22no—
194#397—22no—
195#394—22no—
196#394—22no—
197#394—22no—
198#394—22no—
199#391—21no—
200#391—21no—
201#391C2312yes—
202#391C2312yes—
203#391C2312yes—
204#390—21no—
205#390—21no—
206#390C2312yes—
207#389—21no—
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—21no—
218#389—21no—
219#389C2312yes—
220#389C2312yes—
221#387—22no—
222#387—22no—
223#387—22no—
224#387—22no—
225#385—22no—
226#385—22no—
227#385—22no—
228#385—22no—
229#384—21no—
230#384—21no—
231#384—21no—
232#384—21no—
233#384C2311yescharacteristic
234#384C2311yescharacteristic
235#384C2312yes—
236#384C2312yes—
237#384C2312yes—
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#382C2312yes—
241#382C2312yes—
242#381—22no—
243#381—22no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—22no—
253#380—22no—
254#380C2312yes—
255#380C2312yes—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4D411yescharacteristic
261C4×C4⋊C4D411yescharacteristic
262C4×C4⋊C4C2311yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4C2311yescharacteristic
268C4×C22⋊C4C2311yescharacteristic
269C43C2311yescharacteristic
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279C2×#41—44no—
280C2×#41—44no—
281C2×#41—44no—
282C2×#41—44no—
283C2×#41—82no—
284C2×#41—82no—
285C22×Q8—21no—
286C22×Q8—21no—
287C22×Q8C2412yes—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4C2×D411yescharacteristic
293C22×D4C2412yes—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C2×SD16—28no—
305C2×SD16—28no—
306C2×SD16—44no—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—44no—
318C4⋊Q8—82no—
319#127—22no—
320#127#4114yes—
321#126—48no—
322#125—28no—
323#125—48no—
324#124—44no—
325#124—44no—
326#123—48no—
327#123—48no—
328#123—48no—
329C22⋊Q8—44no—
330C22⋊Q8—44no—
331C22⋊Q8—44no—
332C22⋊Q8—44no—
333#121—24no—
334#121—24no—
335#121—42no—
336#121—42no—
337#121—44no—
338#121—44no—
339#121—48no—
340C4×Q8—28no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—24no—
345C4×D4—28no—
346C4×D4—42no—
347C4×D4—42no—
348C4×D4—42no—
349C4×D4—44no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—44no—
353#117—48no—
354#117—44no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
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—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—48no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2×D411yescharacteristic
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
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⋊C4—22no—
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
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×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431#107—44no—
432#107—44no—
433#106—44no—
434C4⋊C8—24no—
435C4⋊C8—42no—
436C4⋊C8—42no—
437#103—44no—
438#103—44no—
439#103—44no—
440#102—44no—
441#102—44no—
442#102—44no—
443C22⋊C8—24no—
444C22⋊C8—24no—
445C22⋊C8—42no—
446C22⋊C8—42no—
447#97—24no—
448#97—24no—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—22no—
452C4×C8—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#95—22no—
465#95—22no—
466#95—22no—
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472#95C2×D411yescharacteristic
473C24—22no—
474C24C22×D411yescharacteristic
475C24C22×D411yescharacteristic
476#41—816no—
477#41—816no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—24no—
481C2×Q8—24no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—41no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—82no—
505C2×D4—82no—
506C2×D4C2×#4114yes—
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—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—82no—
544C22×C4—82no—
545C22×C4AGL(1,ℤ/8)14yes—
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×C4C22×D411yescharacteristic
558C22×C4C2511yescharacteristic
559SD16—416no—
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×C82−1+414yes—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—22no—
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—44no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—44no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—82no—
608C4⋊C4—82no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—41no—
614C22⋊C4—41no—
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—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—22no—
640C42—44no—
641C42—44no—
642C42C2×#4112yes—
643C42H(5,𝔽2)14yes—
644C42H(5,𝔽2)12yes—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—24no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23C2×AGL(1,ℤ/8)12yes—
666C23C23×D411yescharacteristic
667Q8—44no—
668Q8—44no—
669Q8—84no—
670Q8—84no—
671D4—28no—
672D4—44no—
673D4—44no—
674D4—48no—
675D4—48no—
676D4—88no—
677D4—88no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—28no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
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—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
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—88no—
735C2×C4—88no—
736C2×C4—88no—
737C2×C4—88no—
738C2×C4#53512yes—
739C2×C4#53512yes—
740C2×C4#54612yes—
741C2×C4#54612yes—
742C2×C4C2×AGL(1,ℤ/8)12yes—
743C2×C4C2×AGL(1,ℤ/8)12yes—
744C2×C4#57512yes—
745C2×C4#57712yes—
746C2×C4#57812yes—
747C2×C4C22×#4111yescharacteristic
748C2×C4C2×H(5,𝔽2)12yes—
749C2×C4C2×H(5,𝔽2)11yescharacteristic
750C2×C4C2×2−1+412yes—
751C8—24no—
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—44no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—44no—
770C22—41no—
771C22—44no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22C2×#53511yescharacteristic
777C22C2×#54611yescharacteristic
778C22#349911yescharacteristic
779C22C22×AGL(1,ℤ/8)11yescharacteristic
780C22C2×#57511yescharacteristic
781C22C2×#57711yescharacteristic
782C22C2×#57811yescharacteristic
783C4—22no—
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4#331014yes—
801C4#331514yes—
802C4#352012yes—
803C4#354812yes—
804C2—42no—
805C2—81no—
806C2—84no—
807C2#3895111yescharacteristic
808C2#6080311yescharacteristic
809C2#6082411yescharacteristic
810C2C2×#331011yescharacteristic
811C2C2×#331511yescharacteristic
812C2#6247911yescharacteristic
813C2#6248311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36127C2
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. #36181C2semidirect
3. #33294C2semidirect
4. #31953C2semidirect
5. #31950C2semidirect
6. #29845C2semidirect
7. #29844C2semidirect
8. #28717C2semidirect
9. #28514C2semidirect
10. #27950C2semidirect
11. #27949C2semidirect
12. #25597C2semidirect
13. #25597C2semidirect
14. #24825C2semidirect
15. #24137C2semidirect
16. #21863C2semidirect
17. #21859C2semidirect
18. #21692C2semidirect
19. #21265C2semidirect

Maximal subgroups

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

subgroupindex
#361812
#361272
#332942
#319532
#319502
#298452
#298442
#287172
#285142
#279502
#279492
#255972
#248252
#241372
#218632
#218592
#216922
#212652