Finite Group Databasebeta

← #6461546

Subgroups — #6461546

Order 512.

2212 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2860C211yesmaximal, characteristic, complemented
2C4×#532C211yesmaximal, characteristic, complemented
3#29503C214yesmaximal, complemented
4#29500C212yesmaximal, complemented
5#29499C212yesmaximal, complemented
6#29497C214yesmaximal, complemented
7#29494C212yesmaximal, complemented
8#29493C212yesmaximal, complemented
9#23657C211yesmaximal, characteristic, complemented
10#23628C211yesmaximal, characteristic, complemented
11#23508C211yesmaximal, characteristic, complemented
12#23428C211yesmaximal, characteristic
13#21236C212yesmaximal, complemented
14#21093C212yesmaximal, complemented
15#20928C212yesmaximal, complemented
16#20875C212yesmaximal, complemented
17#20364C211yesmaximal, characteristic, complemented
18C22×AGL(1,ℤ/8)C2212yes—
19C2×#532C2211yescharacteristic
20C22×#126—21no—
21C2×C4×#41C2212yes—
22C2×#428C2212yes—
23C2×#417C2212yes—
24C2×#417C2212yes—
25C2×#417C2212yes—
26C2×#418C2212yes—
27C2×C4×M16C2212yes—
28#2860—21no—
29#2860—21no—
30#2860—21no—
31#2860—21no—
32#2860C2212yes—
33#2860C2212yes—
34#2860C2212yes—
35#2860C2212yes—
36C4×C4⋊Q8C2211yescharacteristic, complemented
37C4×C4⋊Q8C2211yescharacteristic, complemented
38C4×#127C2211yescharacteristic, complemented
39C4×#127C2211yescharacteristic, complemented
40C4×#124C2212yescomplemented
41C4×#124C2212yescomplemented
42C4×#121—21no—
43C4×#121—21no—
44C4×#121—21no—
45C4×#121—21no—
46#2297C2212yes—
47#2293—21no—
48#2293—21no—
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#388—21no—
56C2×#388—21no—
57C2×#388—21no—
58#2285C2211yescharacteristic
59C42×D4—21no—
60C42×D4—21no—
61C2×C43C2211yescharacteristic
62#2085C2214yescomplemented
63#2084C2212yescomplemented
64#2083C2212yescomplemented
65#2073C2214yes—
66#2071C2212yes—
67#2071C2212yes—
68#2043C2212yescomplemented
69#2042C2214yescomplemented
70#2041C2212yescomplemented
71#2013C2212yes—
72#2012C2214yes—
73#2011C2212yes—
74#1973C2214yes—
75#1972C2214yes—
76#1970C2214yes—
77#1968C2214yes—
78#1936C2214yescomplemented
79#1935C2214yescomplemented
80#1934C2214yescomplemented
81#1933C2214yescomplemented
82#1880C2214yes—
83#1880C2214yes—
84#1879C2214yes—
85#1879C2214yes—
86#1865C2214yescomplemented
87#1864C2214yescomplemented
88#1863C2214yescomplemented
89#1862C2214yescomplemented
90#1745C2212yescomplemented
91#1745C2212yescomplemented
92#1744C2212yescomplemented
93#1744C2212yescomplemented
94#1736C2212yes—
95#1736C2212yes—
96#1728C2211yescharacteristic
97#1728C2211yescharacteristic
98#1728C2212yes—
99C22×#41C2312yes—
100C23×D4C2311yescharacteristic
101C2×AGL(1,ℤ/8)—28no—
102C2×AGL(1,ℤ/8)—28no—
103C2×AGL(1,ℤ/8)—44no—
104C22×SD16C2314yes—
105C22×D8C2314yes—
106C22×M16C2312yes—
107C22×M16C2312yes—
108#532—28no—
109C2×C4⋊Q8C2311yescharacteristic
110C2×#127C2311yescharacteristic
111C2×#126—22no—
112C2×#126—22no—
113C2×#126—22no—
114C2×#126—22no—
115C2×#126—48no—
116C2×#124C2312yes—
117C2×#121—21no—
118C2×#121—21no—
119C4×#41—44no—
120C4×#41—44no—
121C2×C4×Q8C2312yes—
122C2×C4×Q8C2312yes—
123C2×C4×D4—22no—
124C2×C4×D4—22no—
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4C2312yes—
132C2×C4×D4C2312yes—
133C2×#117—22no—
134C2×#117C2312yes—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C42—22no—
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#428—44no—
156C2×#107C2314yes—
157C2×#106C2314yes—
158#418—44no—
159#417—28no—
160#417—28no—
161#417—44no—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C4×M16—28no—
171C2×#97C2314yes—
172C2×C4×C8C2314yes—
173#391C2312yes—
174#391C2312yes—
175#390—21no—
176#390—21no—
177#390—21no—
178#390—21no—
179#390—21no—
180#390—21no—
181#390—21no—
182#390—21no—
183#390—21no—
184#390—21no—
185#390C2312yes—
186#390C2312yes—
187#390C2312yes—
188#390C2312yes—
189#390C2312yes—
190#390C2312yes—
191#390C2312yes—
192#390C2312yes—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389C2312yes—
204#389C2312yes—
205#389C2312yes—
206#389C2312yes—
207#389C2312yes—
208#389C2312yes—
209#388—22no—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
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#386—22no—
226#386—22no—
227#384C2311yescharacteristic
228#384C2311yescharacteristic
229#382C2312yes—
230#380—21no—
231#380—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247C43D411yescharacteristic
248C43D411yescharacteristic
249C43D411yescharacteristic
250C43D411yescharacteristic
251C43C2311yescharacteristic
252C43C2311yescharacteristic
253C43C2311yescharacteristic
254C43C2311yescharacteristic
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#336C2312yes—
260#336C2312yes—
261#336C2312yes—
262#336C2312yes—
263#336C2314yes—
264#336C2314yes—
265C25—21no—
266C2×#41—24no—
267C2×#41—24no—
268C2×#41—24no—
269C2×#41—24no—
270C2×#41—24no—
271C2×#41#4118yes—
272C22×Q8C2412yes—
273C22×D4—22no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—24no—
278C22×D4—24no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4C2412yes—
282C22×D4C2412yes—
283C23×C4—22no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—22no—
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—28no—
299C2×SD16—44no—
300C2×D8—28no—
301C2×D8—28no—
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—24no—
312#127—24no—
313#126—48no—
314#126—48no—
315#126—48no—
316#126—48no—
317#124—24no—
318#124—24no—
319#121—28no—
320#121—28no—
321C4×Q8—42no—
322C4×Q8—42no—
323C4×Q8—42no—
324C4×Q8—42no—
325C4×D4—28no—
326C4×D4—28no—
327C4×D4—42no—
328C4×D4—42no—
329C4×D4—42no—
330C4×D4—42no—
331C4×D4—44no—
332C4×D4—44no—
333C4×D4—44no—
334C4×D4—48no—
335C4×D4—48no—
336C4×D4—44no—
337#117—24no—
338#117—24no—
339#117—48no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
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—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—24no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—48no—
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×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436#107—44no—
437#106—44no—
438#103—28no—
439#103—28no—
440#103—44no—
441#102—28no—
442#102—28no—
443#102—44no—
444#102—44no—
445#102—44no—
446#97—28no—
447C4×C8—28no—
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—
458#95—22no—
459#95—22no—
460C24—22no—
461C24—22no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24C22×D411yescharacteristic
470#41—216no—
471#41—216no—
472#41—48no—
473#41—48no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8C2×#4114yes—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—28no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4C2×#4114yes—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—28no—
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—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—44no—
545C22×C4—44no—
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×C4C22×D411yescharacteristic
559C22×C4C2×#4114yes—
560C22×C4C2×#4114yes—
561C22×C4H(5,𝔽2)12yes—
562C22×C4H(5,𝔽2)12yes—
563C22×C4C2511yescharacteristic
564SD16—416no—
565D8—416no—
566M16—216no—
567M16—48no—
568C2×C8—24no—
569C2×C8—24no—
570C2×C8—24no—
571C2×C8—24no—
572C2×C8—24no—
573C2×C8C2×#4118yes—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
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—44no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C22⋊C4—28no—
600C22⋊C4—28no—
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—
618C22⋊C4—44no—
619C22⋊C4—44no—
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—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—44no—
650C42—44no—
651C42—44no—
652C42AGL(1,ℤ/8)14yescomplemented
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—24no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23#52512yes—
679C23#53212yes—
680C23#53512yes—
681C23C23×D411yescharacteristic
682Q8—24no—
683Q8—24no—
684Q8—42no—
685Q8—42no—
686D4—24no—
687D4—24no—
688D4—48no—
689D4—48no—
690D4—416no—
691D4—42no—
692D4—44no—
693D4—42no—
694D4—44no—
695D4—84no—
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—24no—
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—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—416no—
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—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—88no—
752C2×C4—88no—
753C2×C4—84no—
754C2×C4—84no—
755C2×C4—84no—
756C2×C4#52512yes—
757C2×C4#53212yes—
758C2×C4#53512yes—
759C2×C4#55118yes—
760C2×C4#55318yes—
761C2×C4C2×AGL(1,ℤ/8)12yes—
762C2×C4C2×AGL(1,ℤ/8)12yes—
763C2×C4C2×AGL(1,ℤ/8)12yes—
764C2×C4#57512yes—
765C2×C4#57512yes—
766C2×C4#57512yes—
767C2×C4C22×#4112yes—
768C2×C4C22×#4112yes—
769C2×C4C2×H(5,𝔽2)11yescharacteristic
770C2×C4C2×H(5,𝔽2)11yescharacteristic
771C8—28no—
772C8—44no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—168no—
794C22#260314yes—
795C22C2×#52511yescharacteristic
796C22C2×#53211yescharacteristic
797C22C2×#53511yescharacteristic
798C22C22×AGL(1,ℤ/8)11yescharacteristic
799C22C2×#57511yescharacteristic
800C22C2×#57511yescharacteristic
801C22C2×#57511yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—41no—
809C4—41no—
810C4—44no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4#260314yes—
821C4C2×#55112yes—
822C4C2×#55312yes—
823C2—24no—
824C2—84no—
825C2—162no—
826C2C2×#260311yescharacteristic
827C2#6056111yescharacteristic
828C2#6056311yescharacteristic
829C2#6070011yescharacteristic
830C2#6070211yescharacteristic
831C2#6080311yescharacteristic
832C2#6080511yescharacteristic
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. C2×#2860C2semidirect
2. C4×#532C2semidirect
3. #29503C2semidirect
4. #29500C2semidirect
5. #29499C2semidirect
6. #29497C2semidirect
7. #29494C2semidirect
8. #29493C2semidirect
9. #23657C2semidirect
10. #23628C2semidirect
11. #23508C2semidirect
13. #21236C2semidirect
14. #21093C2semidirect
15. #20928C2semidirect
16. #20875C2semidirect
17. #20364C2semidirect
36. C4×C4⋊Q8C22semidirect
37. C4×C4⋊Q8C22semidirect
38. C4×#127C22semidirect
39. C4×#127C22semidirect
40. C4×#124C22semidirect
41. C4×#124C22semidirect
62. #2085C22semidirect
63. #2084C22semidirect
64. #2083C22semidirect
68. #2043C22semidirect
69. #2042C22semidirect
70. #2041C22semidirect
78. #1936C22semidirect
79. #1935C22semidirect
80. #1934C22semidirect
81. #1933C22semidirect
86. #1865C22semidirect
87. #1864C22semidirect
88. #1863C22semidirect
89. #1862C22semidirect
90. #1745C22semidirect
91. #1745C22semidirect
92. #1744C22semidirect
93. #1744C22semidirect
652. 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
C2×#28602
C4×#5322
#295032
#295002
#294992
#294972
#294942
#294932
#236572
#236282
#235082
#234282
#212362
#210932
#209282
#208752
#203642