Finite Group Databasebeta

← #6495404

Subgroups — #6495404

Order 512.

1678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36645C211yesmaximal, characteristic, complemented
2C4×#529C211yesmaximal, characteristic
3#33196C211yesmaximal, characteristic, complemented
4#33196C211yesmaximal, characteristic, complemented
5#33195C211yesmaximal, characteristic, complemented
6#33195C211yesmaximal, characteristic, complemented
7#29941C212yesmaximal, complemented
8#29689C212yesmaximal
9#29321C212yesmaximal, complemented
10#29274C212yesmaximal, complemented
11#29131C212yesmaximal, complemented
12#28203C212yesmaximal, complemented
13#27629C212yesmaximal, complemented
14#27625C212yesmaximal
15#24710C212yesmaximal, complemented
16#24709C212yesmaximal
17#22118C212yesmaximal, complemented
18#22116C212yesmaximal, complemented
19#20810C211yesmaximal, characteristic, complemented
20C2×#533—21no—
21C2×#529C2211yescharacteristic
22C2×#475C2212yes—
23C2×#475C2212yes—
24C2×#474C2212yes—
25C2×#474C2212yes—
26C2×#432C2212yes—
27#2868C2211yescharacteristic
28#2868C2211yescharacteristic
29#2862—21no—
30#2859—21no—
31#2859C2212yes—
32#2857—21no—
33#2857—21no—
34#2857C2212yes—
35#2857C2212yes—
36C4×C4⋊Q8—21no—
37C4×C4⋊Q8—21no—
38C4×C4⋊Q8C2212yes—
39C4×C4⋊Q8C2212yes—
40C4×#125C2211yescharacteristic
41C4×#125C2211yescharacteristic
42C4×#126—21no—
43C4×#126—21no—
44C4×#124C2211yescharacteristic
45C4×#124C2211yescharacteristic
46C4×C22⋊Q8C2211yescharacteristic
47C4×C22⋊Q8C2211yescharacteristic
48C4×#123—21no—
49C4×#123—21no—
50C4×#121C2211yescharacteristic
51C4×#121C2211yescharacteristic
52#2298—21no—
53#2295C2211yescharacteristic
54#2293C2211yescharacteristic
55#2290—21no—
56#2285—21no—
57#2285C2212yes—
58#2283C2211yescharacteristic
59C42×Q8C2211yescharacteristic
60C42×D4—21no—
61C42×D4C2211yescharacteristic
62C4×#117—21no—
63C2×C43C2211yescharacteristic
64#2101C2214yes—
65#2085C2214yes—
66#2077C2214yes—
67#2076C2214yes—
68#2059C2214yes—
69#2042C2214yes—
70#2036C2214yes—
71#2034C2214yes—
72#1988C2212yes—
73#1988C2212yes—
74#1988C2212yes—
75#1988C2212yes—
76#1948C2212yes—
77#1948C2212yes—
78#1948C2212yes—
79#1948C2212yes—
80#1947C2212yes—
81#1947C2212yes—
82#1947C2212yes—
83#1947C2212yes—
84#1944C2214yes—
85#1943C2214yes—
86#1936C2214yes—
87#1935C2214yes—
88#1928C2214yes—
89#1926C2214yes—
90#1921C2214yes—
91#1919C2214yes—
92#1842C2211yescharacteristic
93#1842C2211yescharacteristic
94#1831C2212yes—
95#1803C2212yes—
96#1803C2212yes—
97#1803C2212yes—
98#1803C2212yes—
99#1802C2212yes—
100#1802C2212yes—
101#1802C2212yes—
102#1802C2212yes—
103#1797C2212yes—
104#1797C2212yes—
105#1767C2212yes—
106#1767C2212yes—
107#533—48no—
108C2×C4⋊Q8—21no—
109C2×C4⋊Q8—21no—
110C2×C4⋊Q8—21no—
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8C2312yes—
113C2×C4⋊Q8C2312yes—
114#529—24no—
115#529—24no—
116C2×#126—21no—
117C2×#125—22no—
118C2×#125C2311yescharacteristic
119C2×#124C2311yescharacteristic
120C2×#123—21no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8C2311yescharacteristic
124C2×#121C2311yescharacteristic
125C2×C4×Q8—22no—
126C2×C4×Q8—22no—
127C2×C4×Q8C2311yescharacteristic
128C2×C4×Q8C2311yescharacteristic
129C2×C4×Q8C2311yescharacteristic
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4C2311yescharacteristic
134C2×C4×D4C2311yescharacteristic
135C2×C4×D4C2311yescharacteristic
136C2×#117—22no—
137C2×#117—21no—
138C2×#117—21no—
139C22×C42—21no—
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#475—28no—
148#475—44no—
149#474—28no—
150#474—44no—
151#432—44no—
152C2×#107C2314yes—
153C2×#107C2314yes—
154C2×#106C2314yes—
155C2×#106C2314yes—
156C2×C4⋊C8C2312yes—
157C2×C4⋊C8C2312yes—
158C2×C4⋊C8C2312yes—
159C2×C4⋊C8C2312yes—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2312yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×C22⋊C8C2314yes—
167C2×#97C2314yes—
168#391—22no—
169#391—22no—
170#391—22no—
171#391—22no—
172#391C2311yescharacteristic
173#391C2311yescharacteristic
174#390C2311yescharacteristic
175#390C2311yescharacteristic
176#389—22no—
177#389—22no—
178#389—22no—
179#389—22no—
180#389—22no—
181#389—22no—
182#389C2311yescharacteristic
183#389C2311yescharacteristic
184#389C2311yescharacteristic
185#389C2311yescharacteristic
186#389C2314yes—
187#389C2314yes—
188#388—21no—
189#388—21no—
190#388—21no—
191#388—21no—
192#388—21no—
193#388—21no—
194#388—21no—
195#388—21no—
196#387—21no—
197#387—21no—
198#387—21no—
199#387—21no—
200#387—21no—
201#387—21no—
202#387—21no—
203#387—21no—
204#386—21no—
205#386—21no—
206#385—21no—
207#385—21no—
208#384—21no—
209#384—21no—
210#384—21no—
211#384—21no—
212#384C2312yes—
213#384C2312yes—
214#384C2312yes—
215#384C2312yes—
216#383—21no—
217#382—22no—
218#382—22no—
219#382C2311yescharacteristic
220#382C2311yescharacteristic
221#381—21no—
222#380—22no—
223#380—22no—
224#380—22no—
225#380C2311yescharacteristic
226#380C2314yes—
227#380C2311yescharacteristic
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4—22no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4C2311yescharacteristic
242C4×C4⋊C4C2311yescharacteristic
243C4×C4⋊C4C2311yescharacteristic
244C4×C4⋊C4C2311yescharacteristic
245C4×C4⋊C4C2314yes—
246C4×C4⋊C4C2311yescharacteristic
247C4×C4⋊C4C2311yescharacteristic
248C4×C22⋊C4—21no—
249C4×C22⋊C4—21no—
250C4×C22⋊C4—21no—
251C4×C22⋊C4—21no—
252C4×C22⋊C4—21no—
253C4×C22⋊C4—21no—
254C4×C22⋊C4—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261#376—21no—
262#376—21no—
263C43—21no—
264C43D411yescharacteristic
265C43D411yescharacteristic
266C43D411yescharacteristic
267C43D411yescharacteristic
268C43C2311yescharacteristic
269C43C2311yescharacteristic
270C43C2311yescharacteristic
271C43C2311yescharacteristic
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#336C2314yes—
281#336C2314yes—
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8C2411yescharacteristic
285C22×D4—21no—
286C22×D4C2411yescharacteristic
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2411yescharacteristic
297C22×C8C2414yes—
298C22×C8C2414yes—
299C4⋊Q8—24no—
300C4⋊Q8—24no—
301C4⋊Q8—24no—
302C4⋊Q8—24no—
303C4⋊Q8—44no—
304C4⋊Q8—44no—
305C4⋊Q8—44no—
306C4⋊Q8—44no—
307#126—28no—
308#125—22no—
309#125—22no—
310#125—48no—
311#124—22no—
312#124—22no—
313#123—28no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—48no—
317C22⋊Q8—48no—
318#121—22no—
319#121—22no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—48no—
326C4×Q8—48no—
327C4×Q8#4114yes—
328C4×D4—28no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—44no—
335C4×D4—44no—
336C4×D4#4114yes—
337#117—28no—
338#117—44no—
339#117—48no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
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—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4C2411yescharacteristic
363C2×C4⋊C4C2411yescharacteristic
364C2×C4⋊C4C2411yescharacteristic
365C2×C4⋊C4C2411yescharacteristic
366C2×C4⋊C4C2414yes—
367C2×C4⋊C4C2414yes—
368C2×C4⋊C4C2411yescharacteristic
369C2×C4⋊C4C2411yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C42—24no—
385C2×C42—21no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—44no—
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×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433#107—28no—
434#107—44no—
435#106—28no—
436#106—44no—
437C4⋊C8—24no—
438C4⋊C8—24no—
439C4⋊C8—24no—
440C4⋊C8—24no—
441C4⋊C8—24no—
442C4⋊C8—24no—
443#103—28no—
444#103—44no—
445#102—28no—
446#102—44no—
447C22⋊C8—44no—
448#97—44no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—24no—
470#95—24no—
471#95—24no—
472#95—24no—
473C24—21no—
474C24C22×D411yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8C2×#4112yes—
487C2×D4—24no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4C2×#4112yes—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4#13714yes—
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C2511yescharacteristic
552C2×C8—24no—
553C2×C8—24no—
554C2×C8—24no—
555C2×C8—24no—
556C2×C8—24no—
557C2×C8—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—24no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—48no—
580C4⋊C4—48no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—42no—
594C4⋊C4C2×#4112yes—
595C4⋊C4C2×#4112yes—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—48no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C42—22no—
611C42—22no—
612C42—24no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—48no—
639C42—42no—
640C42—42no—
641C42—42no—
642C42—42no—
643C42—42no—
644C42—42no—
645C42—42no—
646C42—42no—
647C42AGL(1,ℤ/8)14yes—
648C42C2×#4112yes—
649C42C2×#4112yes—
650C42H(5,𝔽2)12yes—
651C422−1+412yes—
652C422−1+412yes—
653C422−1+412yes—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—22no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C2×#13712yes—
668C23C23×D411yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673Q8—88no—
674Q8—88no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—41no—
679D4—41no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—28no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
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—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—44no—
720C2×C4—48no—
721C2×C4—44no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—44no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—44no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4#52512yes—
747C2×C4#52512yes—
748C2×C4#53612yes—
749C2×C4#53612yes—
750C2×C4#53712yes—
751C2×C4#53712yes—
752C2×C4C2×AGL(1,ℤ/8)12yes—
753C2×C4C2×AGL(1,ℤ/8)12yes—
754C2×C4C2×AGL(1,ℤ/8)12yes—
755C2×C4C2×#13712yes—
756C2×C4C2×#13712yes—
757C2×C4#57512yes—
758C2×C4#57512yes—
759C2×C4C22×#4111yescharacteristic
760C2×C4C22×#4111yescharacteristic
761C2×C4C2×H(5,𝔽2)11yescharacteristic
762C2×C4C2×2−1+411yescharacteristic
763C2×C4C2×2−1+411yescharacteristic
764C2×C4C2×2−1+411yescharacteristic
765C8—44no—
766C8—44no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22C2×#52511yescharacteristic
782C22C2×#53611yescharacteristic
783C22C2×#53711yescharacteristic
784C22C22×AGL(1,ℤ/8)11yescharacteristic
785C22C22×#13711yescharacteristic
786C22C2×#57511yescharacteristic
787C22C2×#57511yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—41no—
793C4—42no—
794C4—41no—
795C4—42no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—41no—
800C4—41no—
801C4—84no—
802C4—81no—
803C4—81no—
804C4—81no—
805C4—84no—
806C4—81no—
807C4#311514yes—
808C4#323914yes—
809C4#325114yes—
810C4#350911yescharacteristic
811C4#350911yescharacteristic
812C4#351111yescharacteristic
813C4#351111yescharacteristic
814C2—42no—
815C2—82no—
816C2#3529711yescharacteristic
817C2C2×#311511yescharacteristic
818C2#6056211yescharacteristic
819C2C2×#323911yescharacteristic
820C2#6086311yescharacteristic
821C2C2×#325111yescharacteristic
822C2#6091811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
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. #36645C2semidirect
3. #33196C2semidirect
4. #33196C2semidirect
5. #33195C2semidirect
6. #33195C2semidirect
7. #29941C2semidirect
9. #29321C2semidirect
10. #29274C2semidirect
11. #29131C2semidirect
12. #28203C2semidirect
13. #27629C2semidirect
15. #24710C2semidirect
17. #22118C2semidirect
18. #22116C2semidirect
19. #20810C2semidirect

Maximal subgroups

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

subgroupindex
#366452
C4×#5292
#331962
#331952
#299412
#296892
#293212
#292742
#291312
#282032
#276292
#276252
#247102
#247092
#221182
#221162
#208102