Finite Group Databasebeta

← #6434293

Subgroups — #6434293

Order 512.

2026 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36639C211yesmaximal, characteristic, complemented
2C2×#2860C211yesmaximal, characteristic, complemented
3#30346C214yesmaximal, complemented
4#30345C212yesmaximal, complemented
5#30342C212yesmaximal, complemented
6#30340C214yesmaximal, complemented
7#30339C212yesmaximal, complemented
8#30336C212yesmaximal, complemented
9#23617C212yesmaximal, complemented
10#23554C211yesmaximal, characteristic, complemented
11#23546C212yesmaximal, complemented
12#23508C211yesmaximal, characteristic, complemented
13#23454C211yesmaximal, characteristic, complemented
14#23428C211yesmaximal, characteristic
15#21236C212yesmaximal, complemented
16#21093C212yesmaximal, complemented
17C4×#423C211yesmaximal, characteristic, complemented
18C22×AGL(1,ℤ/8)C2212yes—
19C2×#533C2211yescharacteristic
20C2×#532C2211yescharacteristic
21C22×#126—21no—
22C2×#428C2212yes—
23C2×#423C2212yes—
24C2×#417C2212yes—
25C2×#417C2212yes—
26C2×#417C2212yes—
27C2×#418C2212yes—
28C2×C4×M16C2212yes—
29#2862C2211yescharacteristic, complemented
30#2862C2211yescharacteristic, complemented
31#2861C2212yescomplemented
32#2861C2212yescomplemented
33#2860—21no—
34#2860—21no—
35#2860—21no—
36#2860—21no—
37#2860C2212yes—
38#2860C2212yes—
39#2860C2212yes—
40#2860C2212yes—
41#2858C2211yescharacteristic, complemented
42#2858C2211yescharacteristic, complemented
43#2850—21no—
44#2850—21no—
45#2850—21no—
46#2850—21no—
47C4×#124—21no—
48C4×#124—21no—
49C4×#124—21no—
50C4×#124—21no—
51#2297C2212yes—
52#2297C2212yes—
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#388—21no—
60C2×#388—21no—
61C2×#388—21no—
62C2×C43C2211yescharacteristic
63#2068C2214yescomplemented
64#2067C2214yescomplemented
65#2066C2214yescomplemented
66#2065C2214yescomplemented
67#2059C2214yescomplemented
68#2058C2212yescomplemented
69#2057C2212yescomplemented
70#2055C2214yes—
71#2055C2214yes—
72#2054C2214yes—
73#2054C2214yes—
74#2043C2212yescomplemented
75#2042C2214yescomplemented
76#2041C2212yescomplemented
77#2025C2214yes—
78#2023C2212yes—
79#2023C2212yes—
80#2013C2212yes—
81#2012C2214yes—
82#2011C2212yes—
83#1973C2214yes—
84#1972C2214yes—
85#1970C2214yes—
86#1968C2214yes—
87#1936C2214yescomplemented
88#1935C2214yescomplemented
89#1934C2214yescomplemented
90#1933C2214yescomplemented
91#1767C2212yescomplemented
92#1767C2212yescomplemented
93C4×C4⋊C8C2212yescomplemented
94C4×C4⋊C8C2212yescomplemented
95#1736C2212yes—
96#1736C2212yes—
97#1728C2211yescharacteristic
98#1728C2211yescharacteristic
99C22×#41C2312yes—
100C23×D4C2311yescharacteristic
101C2×AGL(1,ℤ/8)—28no—
102C2×AGL(1,ℤ/8)—44no—
103C2×AGL(1,ℤ/8)—44no—
104C22×SD16C2314yes—
105C22×D8C2314yes—
106C22×M16C2312yes—
107C22×M16C2312yes—
108#533—44no—
109#532—44no—
110C2×C4⋊Q8C2311yescharacteristic
111C2×C4⋊Q8C2311yescharacteristic
112C2×C4⋊Q8C2311yescharacteristic
113C2×#127C2311yescharacteristic
114C2×#126—22no—
115C2×#126—22no—
116C2×#126—22no—
117C2×#126—22no—
118C2×#126—48no—
119C2×#125C2312yes—
120C2×#124—21no—
121C2×#124—21no—
122C2×#124—21no—
123C2×#124—21no—
124C2×#124C2312yes—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×#121—21no—
128C2×#121—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8—21no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×#117C2312yes—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#428—44no—
154C2×#107C2314yes—
155C2×#106C2314yes—
156#423—28no—
157C2×C4⋊C8C2314yes—
158C2×C4⋊C8C2314yes—
159#418—44no—
160#417—28no—
161#417—44no—
162#417—44no—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C4×M16—44no—
172C2×#97C2314yes—
173C2×C4×C8C2314yes—
174#391—21no—
175#391—21no—
176#391—21no—
177#391—21no—
178#391C2312yes—
179#391C2312yes—
180#391C2312yes—
181#391C2312yes—
182#390—21no—
183#390—21no—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390C2312yes—
193#390C2312yes—
194#390C2312yes—
195#390C2312yes—
196#390C2312yes—
197#390C2312yes—
198#390C2312yes—
199#390C2312yes—
200#390C2312yes—
201#390C2312yes—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389C2312yes—
209#389C2312yes—
210#389C2312yes—
211#389C2312yes—
212#389C2312yes—
213#389C2312yes—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#388—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#386—22no—
238#382—21no—
239#382—21no—
240#382—21no—
241#382—21no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C43D411yescharacteristic
250C43D411yescharacteristic
251C43D411yescharacteristic
252C43D411yescharacteristic
253C43C2311yescharacteristic
254C43C2311yescharacteristic
255C43C2311yescharacteristic
256C43C2311yescharacteristic
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#336C2312yes—
262#336C2312yes—
263#336C2312yes—
264#336C2312yes—
265C25—21no—
266C2×#41—24no—
267C2×#41—24no—
268C2×#41—24no—
269C2×#41—24no—
270C2×#41—24no—
271C2×#41—24no—
272C22×Q8—21no—
273C22×Q8—21no—
274C22×Q8C2412yes—
275C22×D4—22no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—24no—
280C22×D4—22no—
281C22×D4—24no—
282C22×D4—22no—
283C22×D4C2412yes—
284C22×D4C2412yes—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—22no—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2411yescharacteristic
296AGL(1,ℤ/8)—432no—
297C2×SD16—28no—
298C2×SD16—44no—
299C2×SD16—44no—
300C2×D8—28no—
301C2×D8—44no—
302C2×D8—44no—
303C2×M16—24no—
304C2×M16—24no—
305C2×M16—24no—
306C2×M16—24no—
307C2×M16—24no—
308C2×M16#4118yes—
309C22×C8C2414yes—
310C22×C8C2414yes—
311C4⋊Q8—42no—
312C4⋊Q8—42no—
313C4⋊Q8—42no—
314#127—42no—
315#126—48no—
316#126—48no—
317#126—48no—
318#126—48no—
319#125—42no—
320#125—42no—
321#124—42no—
322#124—42no—
323#124—44no—
324#124—44no—
325#124—44no—
326#124—44no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329#121—44no—
330#121—44no—
331C4×Q8—44no—
332C4×Q8—44no—
333C4×D4—44no—
334C4×D4—44no—
335#117—24no—
336#117—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
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—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
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×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430#107—44no—
431#106—44no—
432C4⋊C8—28no—
433C4⋊C8—28no—
434#103—28no—
435#103—44no—
436#103—44no—
437#102—28no—
438#102—44no—
439#102—44no—
440#102—44no—
441#102—44no—
442#97—44no—
443C4×C8—44no—
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—
456#95—22no—
457#95—22no—
458C24—22no—
459C24—22no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24C22×D411yescharacteristic
468#41—48no—
469#41—48no—
470#41—48no—
471#41—48no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—24no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—42no—
507C2×D4—42no—
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—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
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×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C2×#4114yes—
558C22×C4H(5,𝔽2)14yes—
559C22×C4H(5,𝔽2)12yes—
560C22×C42−1+412yes—
561C22×C4C2511yescharacteristic
562SD16—416no—
563D8—416no—
564M16—216no—
565M16—48no—
566C2×C8—24no—
567C2×C8—24no—
568C2×C8—24no—
569C2×C8—24no—
570C2×C8—24no—
571C2×C8C2×#4118yes—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—21no—
636C42—21no—
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—44no—
648C42AGL(1,ℤ/8)14yescomplemented
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23#53212yes—
675C23#53512yes—
676C23#53712yes—
677C23C23×D411yescharacteristic
678Q8—42no—
679Q8—42no—
680Q8—42no—
681Q8—42no—
682Q8—84no—
683Q8—84no—
684D4—42no—
685D4—44no—
686D4—42no—
687D4—44no—
688D4—42no—
689D4—42no—
690D4—84no—
691D4—84no—
692D4—88no—
693D4—84no—
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—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—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
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—84no—
749C2×C4—84no—
750C2×C4—84no—
751C2×C4—88no—
752C2×C4#53212yes—
753C2×C4#53512yes—
754C2×C4#53712yes—
755C2×C4#53818yes—
756C2×C4#54218yes—
757C2×C4C2×AGL(1,ℤ/8)12yes—
758C2×C4C2×AGL(1,ℤ/8)12yes—
759C2×C4C2×AGL(1,ℤ/8)12yes—
760C2×C4#57512yes—
761C2×C4#57512yes—
762C2×C4#57512yes—
763C2×C4C22×#4112yes—
764C2×C4C2×H(5,𝔽2)11yescharacteristic
765C2×C4C2×H(5,𝔽2)12yes—
766C2×C4C2×2−1+411yescharacteristic
767C8—28no—
768C8—44no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—168no—
790C22#266214yes—
791C22C2×#53211yescharacteristic
792C22C2×#53511yescharacteristic
793C22C2×#53711yescharacteristic
794C22C22×AGL(1,ℤ/8)11yescharacteristic
795C22C2×#57511yescharacteristic
796C22C2×#57511yescharacteristic
797C22C2×#57511yescharacteristic
798C4—22no—
799C4—22no—
800C4—22no—
801C4—22no—
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4#266214yes—
817C4C2×#53812yes—
818C4C2×#54212yes—
819C2—24no—
820C2—162no—
821C2—162no—
822C2C2×#266211yescharacteristic
823C2#6070011yescharacteristic
824C2#6070211yescharacteristic
825C2#6080311yescharacteristic
826C2#6080511yescharacteristic
827C2#6091611yescharacteristic
828C2#6091711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36639C2semidirect
2. C2×#2860C2semidirect
3. #30346C2semidirect
4. #30345C2semidirect
5. #30342C2semidirect
6. #30340C2semidirect
7. #30339C2semidirect
8. #30336C2semidirect
9. #23617C2semidirect
10. #23554C2semidirect
11. #23546C2semidirect
12. #23508C2semidirect
13. #23454C2semidirect
15. #21236C2semidirect
16. #21093C2semidirect
17. C4×#423C2semidirect
29. #2862C22semidirect
30. #2862C22semidirect
31. #2861C22semidirect
32. #2861C22semidirect
41. #2858C22semidirect
42. #2858C22semidirect
63. #2068C22semidirect
64. #2067C22semidirect
65. #2066C22semidirect
66. #2065C22semidirect
67. #2059C22semidirect
68. #2058C22semidirect
69. #2057C22semidirect
74. #2043C22semidirect
75. #2042C22semidirect
76. #2041C22semidirect
87. #1936C22semidirect
88. #1935C22semidirect
89. #1934C22semidirect
90. #1933C22semidirect
91. #1767C22semidirect
92. #1767C22semidirect
93. C4×C4⋊C8C22semidirect
94. C4×C4⋊C8C22semidirect
648. C42AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
#366392
C2×#28602
#303462
#303452
#303422
#303402
#303392
#303362
#236172
#235542
#235462
#235082
#234542
#234282
#212362
#210932
C4×#4232