Finite Group Databasebeta

← #6433579

Subgroups — #6433579

Order 512.

2140 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
3#30169C212yesmaximal, complemented
4#30108C212yesmaximal, complemented
5#30011C214yesmaximal, complemented
6#29966C211yesmaximal, characteristic, complemented
7#29951C211yesmaximal, characteristic, complemented
8#29891C212yesmaximal, complemented
9#29754C211yesmaximal, characteristic, complemented
10#29713C211yesmaximal, characteristic, complemented
11#29595C212yesmaximal, complemented
12#23763C212yesmaximal, complemented
13#23711C214yesmaximal, complemented
14#23576C212yesmaximal, complemented
15#21578C212yesmaximal, complemented
16#21454C212yesmaximal, complemented
17#20715C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525—21no—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#480C2212yes—
24C2×#448C2212yes—
25C2×#440C2214yescomplemented
26C2×#432C2212yes—
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2856C2211yescharacteristic
30#2856C2211yescharacteristic
31#2854—21no—
32#2854C2212yes—
33#2850—21no—
34#2850—21no—
35#2847—21no—
36#2847C2212yes—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8—21no—
41C4×C22⋊Q8C2212yes—
42C4×C22⋊Q8C2212yes—
43C4×C22⋊Q8C2212yes—
44C4×C22⋊Q8C2212yes—
45C4×#121—21no—
46C4×#121—21no—
47C4×#121C2212yes—
48C4×#121C2212yes—
49#2297—21no—
50C2×#391C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#387—21no—
53C2×#385—21no—
54#2285C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4—21no—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2099C2212yescomplemented
60#2096C2212yescomplemented
61#2086C2214yescomplemented
62#2083C2212yescomplemented
63#2077C2214yes—
64#2076C2214yes—
65#2072C2212yescomplemented
66#2067C2214yescomplemented
67#2066C2214yescomplemented
68#2057C2212yescomplemented
69#2055C2214yescomplemented
70#2041C2212yescomplemented
71#2036C2214yes—
72#2036C2214yes—
73#2034C2214yes—
74#2033C2214yes—
75#2024C2212yescomplemented
76#2014C2212yescomplemented
77#2000C2214yes—
78#2000C2214yes—
79#1926C2214yescomplemented
80#1921C2214yescomplemented
81#1880C2214yescomplemented
82#1874C2212yes—
83#1874C2212yes—
84#1863C2214yescomplemented
85#1853C2212yes—
86#1852C2212yes—
87#1823C2212yes—
88#1817C2212yes—
89#1797C2211yescharacteristic
90#1797C2211yescharacteristic
91#1797C2212yes—
92#1787C2212yes—
93#1779C2212yes—
94#1776C2214yescomplemented
95#1763C2214yescomplemented
96#1762C2214yescomplemented
97#1749C2212yes—
98#1749C2212yes—
99C22×#41—21no—
100C23×Q8C2311yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4C2311yescharacteristic
104C22×SD16C2314yes—
105#532—44no—
106C2×C4⋊Q8C2311yescharacteristic
107C2×#127C2311yescharacteristic
108C2×#124—21no—
109#525—48no—
110C2×#123—22no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121C2312yes—
125C2×#121C2312yes—
126C2×#121C2312yes—
127C2×#120—22no—
128C2×C4×Q8—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8—44no—
131C2×C4×Q8C2312yes—
132C2×C4×Q8C2312yes—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—21no—
136C2×C4×D4C2312yes—
137C2×#117—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C42—21no—
147C22×C42—21no—
148C22×C42—44no—
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#480—28no—
162#448—28no—
163#440—48no—
164#432—44no—
165C2×#107C2314yes—
166C2×#107C2314yes—
167C2×#106C2314yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2314yes—
179C2×C22⋊C8C2314yes—
180C2×#97C2314yes—
181#391—21no—
182#391—21no—
183#391—21no—
184#391—21no—
185#391C2312yes—
186#391C2312yes—
187#390—21no—
188#390—21no—
189#390—21no—
190#390—21no—
191#390C2312yes—
192#390C2312yes—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389C2312yes—
198#389C2312yes—
199#389C2312yes—
200#389C2312yes—
201#388—22no—
202#388—22no—
203#388—22no—
204#388—22no—
205#387—22no—
206#387—22no—
207#387—22no—
208#387—22no—
209#386—22no—
210#386—22no—
211#386—22no—
212#386—22no—
213#386—22no—
214#386—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#384C2311yescharacteristic
220#384C2311yescharacteristic
221#382—21no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380C2312yes—
228#380C2312yes—
229#380C2312yes—
230#380C2312yes—
231#380C2312yes—
232C4×C4⋊C4—22no—
233C4×C4⋊C4—22no—
234C4×C4⋊C4—22no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4C2312yes—
240C4×C4⋊C4C2312yes—
241C4×C4⋊C4C2312yes—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C2×#95—21no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95—21no—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#336C2312yes—
260#336C2312yes—
261#336C2314yes—
262C25C2×D411yescharacteristic
263C2×#41—44no—
264C2×#41—44no—
265C2×#41—44no—
266C22×Q8—21no—
267C22×Q8—21no—
268C22×Q8—22no—
269C22×Q8—42no—
270C22×Q8—42no—
271C22×Q8#4114yescomplemented
272C22×Q8C2412yes—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4C2412yes—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—22no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C2×SD16—28no—
313C2×SD16—44no—
314C2×SD16—44no—
315C22×C8C2414yes—
316C22×C8C2414yes—
317C4⋊Q8—42no—
318#127—42no—
319#124—44no—
320#123—48no—
321C22⋊Q8—28no—
322C22⋊Q8—28no—
323C22⋊Q8—24no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329#121—24no—
330#121—24no—
331#121—44no—
332#121—44no—
333#121—44no—
334#121—44no—
335#121—44no—
336#121—44no—
337#121—44no—
338#120—48no—
339C4×Q8—28no—
340C4×Q8—44no—
341C4×Q8—44no—
342C4×Q8—44no—
343C4×D4—28no—
344C4×D4—44no—
345C4×D4—48no—
346C4×D4—48no—
347#117—44no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
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—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4#4114yescomplemented
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C22⋊C4—28no—
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—44no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—44no—
412C2×C42—44no—
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×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429#107—28no—
430#107—44no—
431#106—44no—
432C4⋊C8—42no—
433C4⋊C8—42no—
434#103—28no—
435#103—44no—
436#103—44no—
437#102—28no—
438#102—44no—
439#102—44no—
440C22⋊C8—24no—
441C22⋊C8—24no—
442C22⋊C8—44no—
443C22⋊C8—44no—
444#97—28no—
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—
458#95—22no—
459#95—22no—
460#95—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—41no—
468C24—41no—
469C24C22×D411yescharacteristic
470C24C22×D411yescharacteristic
471C24C22×D411yescharacteristic
472#41—816no—
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—48no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—48no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8C2×#4114yes—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—42no—
503C2×D4—42no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
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—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—416no—
567C22×C4—416no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4AGL(1,ℤ/8)14yes—
584C22×C4#13714yes—
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4C2511yescharacteristic
599SD16—416no—
600C2×C8—24no—
601C2×C8—24no—
602C2×C8—24no—
603C2×C8—24no—
604C2×C8—24no—
605C2×C8—24no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—44no—
619C4⋊C4—42no—
620C4⋊C4—44no—
621C4⋊C4—42no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—44no—
628C4⋊C4—42no—
629C4⋊C4C2×#4114yes—
630C22⋊C4—28no—
631C22⋊C4—28no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—44no—
661C42—44no—
662C42—44no—
663C42—44no—
664C42—44no—
665C42H(5,𝔽2)14yes—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—28no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23#52512yes—
697C23C2×AGL(1,ℤ/8)12yes—
698C23C2×#13712yes—
699C23#57512yes—
700C23#57512yes—
701C23C23×D411yescharacteristic
702Q8—28no—
703Q8—48no—
704Q8—44no—
705Q8—84no—
706D4—44no—
707D4—44no—
708D4—84no—
709D4—84no—
710D4—88no—
711D4—88no—
712D4—88no—
713C2×C4—28no—
714C2×C4—28no—
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—21no—
728C2×C4—21no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—88no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4#52512yes—
787C2×C4#53412yes—
788C2×C4#53412yes—
789C2×C4C2×AGL(1,ℤ/8)12yes—
790C2×C4C2×AGL(1,ℤ/8)12yes—
791C2×C4C2×#13712yes—
792C2×C4C2×#13712yes—
793C2×C4C22×#4111yescharacteristic
794C2×C4C22×#4111yescharacteristic
795C2×C4C2×H(5,𝔽2)12yes—
796C2×C4#58512yes—
797C8—44no—
798C8—44no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—416no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22#311514yes—
828C22C2×#52511yescharacteristic
829C22C2×#53411yescharacteristic
830C22#344911yescharacteristic
831C22C22×AGL(1,ℤ/8)11yescharacteristic
832C22C22×#13711yescharacteristic
833C22C2×#57511yescharacteristic
834C22C2×#57511yescharacteristic
835C4—22no—
836C4—22no—
837C4—22no—
838C4—22no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—41no—
843C4—41no—
844C4—44no—
845C4—41no—
846C4—41no—
847C4—44no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4#345912yes—
854C4#346012yes—
855C2—24no—
856C2—42no—
857C2—42no—
858C2—162no—
859C2#3456211yescharacteristic
860C2C2×#311511yescharacteristic
861C2#6056011yescharacteristic
862C2#6075011yescharacteristic
863C2#6075111yescharacteristic
864C2#6095911yescharacteristic
865C2#6096911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Q8C2semidirect
3. #30169C2semidirect
4. #30108C2semidirect
5. #30011C2semidirect
6. #29966C2semidirect
7. #29951C2semidirect
8. #29891C2semidirect
9. #29754C2semidirect
10. #29713C2semidirect
11. #29595C2semidirect
12. #23763C2semidirect
13. #23711C2semidirect
14. #23576C2semidirect
15. #21578C2semidirect
16. #21454C2semidirect
17. #20715C2semidirect
25. C2×#440C22semidirect
59. #2099C22semidirect
60. #2096C22semidirect
61. #2086C22semidirect
62. #2083C22semidirect
65. #2072C22semidirect
66. #2067C22semidirect
67. #2066C22semidirect
68. #2057C22semidirect
69. #2055C22semidirect
70. #2041C22semidirect
75. #2024C22semidirect
76. #2014C22semidirect
79. #1926C22semidirect
80. #1921C22semidirect
81. #1880C22semidirect
84. #1863C22semidirect
94. #1776C22semidirect
95. #1763C22semidirect
96. #1762C22semidirect
271. C22×Q8#41semidirect
370. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
#366242
C2×C4×C22⋊Q82
#301692
#301082
#300112
#299662
#299512
#298912
#297542
#297132
#295952
#237632
#237112
#235762
#215782
#214542
#207152