Finite Group Databasebeta

← #6469277

Subgroups — #6469277

Order 512.

2086 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36631C211yesmaximal, characteristic, complemented
2C4×#532C211yesmaximal, characteristic, complemented
3#29503C214yesmaximal, complemented
4#29192C211yesmaximal, characteristic, complemented
5#29191C211yesmaximal, characteristic, complemented
6#28615C211yesmaximal, characteristic, complemented
7#28614C211yesmaximal, characteristic, complemented
8#27974C211yesmaximal, characteristic, complemented
9#27949C211yesmaximal, characteristic, complemented
10#25857C211yesmaximal, characteristic, complemented
11#25720C211yesmaximal, characteristic
12#24510C214yesmaximal, complemented
13#23686C214yesmaximal, complemented
14#21692C211yesmaximal, characteristic, complemented
15#21690C211yesmaximal, characteristic, complemented
16#21647C211yesmaximal, characteristic, complemented
17#21646C211yesmaximal, characteristic, complemented
18#21456C214yesmaximal, complemented
19C4×#432C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C2×#529—21no—
22C2×C4×#41C2212yes—
23C2×#493C2211yescharacteristic
24C2×#492C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#449C2214yes—
28C2×#442C2214yes—
29C2×#440C2214yes—
30C2×#432C2212yes—
31#2861—21no—
32#2860—21no—
33#2860C2212yes—
34#2859C2211yescharacteristic
35#2858C2211yescharacteristic
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2854—21no—
39#2854C2212yes—
40#2850—21no—
41C4×C4⋊Q8C2211yescharacteristic
42C4×C4⋊Q8C2211yescharacteristic
43C4×C4⋊Q8C2211yescharacteristic
44C4×#127C2211yescharacteristic
45C4×#127C2211yescharacteristic
46C4×#127C2211yescharacteristic
47C4×#124—21no—
48C4×#124C2212yes—
49C4×#124C2212yes—
50C4×#121—21no—
51C4×#121—21no—
52C4×#121—21no—
53C4×#121—21no—
54C4×#121—21no—
55C4×#121C2212yes—
56#2297C2212yes—
57#2293—21no—
58#2293—21no—
59#2293—21no—
60#2293C2212yes—
61#2285C2211yescharacteristic
62C42×D4—21no—
63C42×D4—21no—
64C2×C43C2211yescharacteristic
65#2085C2214yes—
66#2073C2214yes—
67#2067C2214yes—
68#2066C2214yes—
69#2055C2214yes—
70#2054C2214yes—
71#2042C2214yes—
72#2012C2214yes—
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1973C2214yes—
76#1972C2214yes—
77#1957C2211yescharacteristic
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1936C2214yes—
84#1935C2214yes—
85#1880C2214yes—
86#1879C2214yes—
87#1875C2214yes—
88#1865C2214yes—
89#1862C2214yes—
90#1854C2214yes—
91#1845C2211yescharacteristic
92#1844C2211yescharacteristic
93#1834C2211yescharacteristic
94#1834C2211yescharacteristic
95#1788C2214yes—
96#1767C2212yes—
97C4×C4⋊C8C2211yescharacteristic
98C4×C4⋊C8C2211yescharacteristic
99#1763C2214yes—
100#1762C2214yes—
101#1749C2212yes—
102C4×C22⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104#1745C2212yes—
105C4×#97C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×#41C2312yes—
108C22×SD16C2314yes—
109C22×D8C2314yes—
110#532—24no—
111#532—24no—
112C2×C4⋊Q8C2311yescharacteristic
113C2×C4⋊Q8C2311yescharacteristic
114C2×#127C2311yescharacteristic
115C2×#127C2311yescharacteristic
116#529—48no—
117C2×#126—22no—
118C2×#125—21no—
119C2×#124—21no—
120C2×#124—21no—
121C2×#124C2312yes—
122C2×#123—22no—
123C2×C22⋊Q8—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121—21no—
128C2×#121C2312yes—
129C4×#41—48no—
130C2×C4×Q8—21no—
131C2×C4×Q8C2312yes—
132C2×C4×Q8C2312yes—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—22no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4—21no—
144C2×C4×D4C2312yes—
145C2×C4×D4C2312yes—
146C2×C4×D4C2312yes—
147C2×#117—22no—
148C2×#117—22no—
149C2×#117C2312yes—
150C22×C42—22no—
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#493—24no—
159#492—24no—
160#487—24no—
161#486—24no—
162#449—216no—
163#442—48no—
164#440—48no—
165#432—28no—
166C2×#107C2314yes—
167C2×#106C2314yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×#97C2312yes—
181C2×#97C2312yes—
182C2×#97C2312yes—
183C2×#97C2312yes—
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187C2×C4×C8C2311yescharacteristic
188#391—21no—
189#391—21no—
190#391C2312yes—
191#391C2312yes—
192#390—21no—
193#390—21no—
194#390—21no—
195#390—21no—
196#390—21no—
197#390—21no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390C2312yes—
203#390C2312yes—
204#390C2312yes—
205#390C2312yes—
206#390C2312yes—
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#389C2312yes—
217#389C2312yes—
218#389C2312yes—
219#389C2312yes—
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#386—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#384C2311yescharacteristic
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#382—21no—
241#382C2312yes—
242#380—21no—
243#380—21no—
244#380—21no—
245#380C2312yes—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4C2312yes—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—22no—
256C4×C22⋊C4—22no—
257C4×C22⋊C4—22no—
258C4×C22⋊C4—22no—
259C4×C22⋊C4—22no—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C43D411yescharacteristic
263C43D411yescharacteristic
264C43D411yescharacteristic
265C43D411yescharacteristic
266C43C2311yescharacteristic
267C43C2311yescharacteristic
268C43C2311yescharacteristic
269C43C2311yescharacteristic
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C2×#41—24no—
279C2×#41—24no—
280C2×#41—28no—
281C2×#41—44no—
282C22×Q8—21no—
283C22×Q8C2412yes—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4C2412yes—
291C22×D4C2412yes—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C2×SD16—28no—
304C2×SD16—28no—
305C2×SD16—44no—
306C2×D8—28no—
307C2×D8—28no—
308C2×D8—44no—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8#4114yes—
317#127—22no—
318#127—22no—
319#127—22no—
320#127#4114yes—
321#126—48no—
322#125—44no—
323#124—24no—
324#124—24no—
325#124—44no—
326#124—44no—
327#123—48no—
328C22⋊Q8—44no—
329#121—28no—
330#121—28no—
331#121—28no—
332#121—44no—
333#121—44no—
334C4×Q8—28no—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×D4—28no—
338C4×D4—28no—
339C4×D4—28no—
340C4×D4—28no—
341C4×D4—44no—
342C4×D4—44no—
343C4×D4—44no—
344C4×D4—44no—
345C4×D4—44no—
346C4×D4—44no—
347C4×D4—48no—
348C4×D4—48no—
349C4×D4—48no—
350C4×D4—44no—
351#117—48no—
352#117—48no—
353#117—44no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
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—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
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—22no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—48no—
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×C42C2×D411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437#107—44no—
438#106—44no—
439C4⋊C8—24no—
440C4⋊C8—24no—
441#103—28no—
442#103—28no—
443#103—44no—
444#102—28no—
445#102—28no—
446#102—44no—
447#102—44no—
448#102—44no—
449C22⋊C8—24no—
450C22⋊C8#4118yes—
451#97—24no—
452#97—24no—
453#97—24no—
454#97—24no—
455C4×C8—22no—
456C4×C8—22no—
457C4×C8—22no—
458C4×C8—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#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471C24—22no—
472C24—22no—
473C24C22×D411yescharacteristic
474#41—416no—
475#41—416no—
476C2×Q8—22no—
477C2×Q8—24no—
478C2×Q8—24no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8C2×#4114yes—
483C2×D4—28no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—22no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4C2×#4114yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—28no—
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—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
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×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C2×#4114yes—
562C22×C4C2511yescharacteristic
563SD16—416no—
564D8—416no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8C2×#4114yes—
576C2×C8C2×#4114yes—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—24no—
581C4⋊C4—22no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—42no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—44no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C22⋊C4—28no—
601C22⋊C4—28no—
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—21no—
638C42—21no—
639C42—22no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—44no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42AGL(1,ℤ/8)14yes—
651C42C2×#4112yes—
652C42C2×#4112yes—
653C42H(5,𝔽2)14yes—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—24no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23#53212yes—
675C23C23×D411yescharacteristic
676Q8—28no—
677Q8—44no—
678Q8—84no—
679D4—28no—
680D4—416no—
681D4—48no—
682D4—48no—
683D4—44no—
684D4—44no—
685D4—44no—
686D4—88no—
687D4—84no—
688D4—84no—
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—24no—
700C2×C4—24no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—24no—
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—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—416no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—42no—
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—88no—
745C2×C4—88no—
746C2×C4—88no—
747C2×C4#52512yes—
748C2×C4#52512yes—
749C2×C4#53212yes—
750C2×C4#53512yes—
751C2×C4#53512yes—
752C2×C4C2×AGL(1,ℤ/8)12yes—
753C2×C4C2×AGL(1,ℤ/8)12yes—
754C2×C4C2×AGL(1,ℤ/8)12yes—
755C2×C4#57512yes—
756C2×C4#57512yes—
757C2×C4#57512yes—
758C2×C4C22×#4111yescharacteristic
759C2×C4C22×#4111yescharacteristic
760C2×C4C22×#4112yes—
761C2×C4C2×H(5,𝔽2)12yes—
762C8—24no—
763C8—24no—
764C8—42no—
765C8—42no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22C2×#52511yescharacteristic
788C22C2×#53211yescharacteristic
789C22C2×#53511yescharacteristic
790C22C22×AGL(1,ℤ/8)11yescharacteristic
791C22C2×#57511yescharacteristic
792C22C2×#57511yescharacteristic
793C22C2×#57511yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—22no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—44no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4#311114yes—
812C4#311514yes—
813C4#348112yes—
814C4#348112yes—
815C2—42no—
816C2—84no—
817C2—162no—
818C2#3496511yescharacteristic
819C2C2×#311511yescharacteristic
820C2C2×#311111yescharacteristic
821C2#6069311yescharacteristic
822C2#6070011yescharacteristic
823C2#6080111yescharacteristic
824C2#6080311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25720C2
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. #36631C2semidirect
2. C4×#532C2semidirect
3. #29503C2semidirect
4. #29192C2semidirect
5. #29191C2semidirect
6. #28615C2semidirect
7. #28614C2semidirect
8. #27974C2semidirect
9. #27949C2semidirect
10. #25857C2semidirect
12. #24510C2semidirect
13. #23686C2semidirect
14. #21692C2semidirect
15. #21690C2semidirect
16. #21647C2semidirect
17. #21646C2semidirect
18. #21456C2semidirect
19. C4×#432C2semidirect

Maximal subgroups

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

subgroupindex
#366312
C4×#5322
#295032
#291922
#291912
#286152
#286142
#279742
#279492
#258572
#257202
#245102
#236862
#216922
#216902
#216472
#216462
#214562
C4×#4322