Finite Group Databasebeta

← #6433576

Subgroups — #6433576

Order 512.

2432 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic, complemented
3#30166C212yesmaximal, complemented
4#30105C212yesmaximal, complemented
5#30007C214yesmaximal, complemented
6#29967C211yesmaximal, characteristic, complemented
7#29950C211yesmaximal, characteristic, complemented
8#29891C212yesmaximal, complemented
9#29755C211yesmaximal, characteristic, complemented
10#29712C211yesmaximal, characteristic, complemented
11#29594C212yesmaximal, complemented
12#23761C212yesmaximal, complemented
13#23708C214yesmaximal, complemented
14#23573C212yesmaximal, complemented
15#21580C212yesmaximal, complemented
16#21452C212yesmaximal, complemented
17#20715C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic, complemented
19C2×#525—21no—
20C22×#121C2211yescharacteristic
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C2×#481C2212yes—
25C2×#447C2212yes—
26C2×#442C2214yescomplemented
27C2×#432C2212yescomplemented
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic, complemented
30#2856C2211yescharacteristic
31#2856C2211yescharacteristic, complemented
32#2854—21no—
33#2854C2212yescomplemented
34#2850—21no—
35#2850—21no—
36#2847—21no—
37#2847C2212yes—
38C4×#121—21no—
39C4×#121—21no—
40C4×#121—21no—
41C4×#121—21no—
42C4×#121—21no—
43C4×#121—21no—
44C4×#121C2212yes—
45C4×#121C2212yes—
46C4×#121C2212yes—
47C4×#121C2212yes—
48C4×#121C2212yes—
49C4×#121C2212yescomplemented
50#2297—21no—
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388—21no—
54C2×#386—21no—
55#2285C2211yescharacteristic, complemented
56C2×#380C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2099C2212yescomplemented
60#2093C2212yescomplemented
61#2088C2214yescomplemented
62#2084C2212yescomplemented
63#2077C2214yescomplemented
64#2076C2214yescomplemented
65#2071C2212yescomplemented
66#2067C2214yescomplemented
67#2065C2214yescomplemented
68#2058C2212yescomplemented
69#2054C2214yescomplemented
70#2041C2212yescomplemented
71#2034C2214yes—
72#2034C2214yes—
73#2034C2214yescomplemented
74#2033C2214yescomplemented
75#2023C2212yescomplemented
76#2011C2212yescomplemented
77#1999C2214yes—
78#1999C2214yes—
79#1925C2214yescomplemented
80#1920C2214yescomplemented
81#1879C2214yescomplemented
82#1874C2212yes—
83#1874C2212yes—
84#1864C2214yescomplemented
85#1853C2212yes—
86#1852C2212yes—
87#1824C2212yes—
88#1817C2212yescomplemented
89#1797C2211yescharacteristic
90#1797C2211yescharacteristic
91#1797C2212yescomplemented
92#1786C2212yes—
93#1779C2212yes—
94#1776C2214yescomplemented
95#1762C2214yescomplemented
96#1762C2214yescomplemented
97#1749C2212yes—
98#1749C2212yescomplemented
99C22×#41—21no—
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C24×C4D411yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4C2311yescharacteristic
106C22×D8C2314yes—
107#532—44no—
108C2×C4⋊Q8C2311yescharacteristic
109C2×#127C2311yescharacteristic
110C2×#124—21no—
111#525—48no—
112C2×#123—22no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×#121—24no—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121—21no—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—24no—
124C2×#121C2312yes—
125C2×#121C2312yes—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×#120—22no—
130C2×C4×D4—22no—
131C2×C4×D4—22no—
132C2×C4×D4—22no—
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—44no—
140C2×C4×D4—48no—
141C2×C4×D4C2312yes—
142C2×C4×D4C2312yes—
143C2×C4×D4C2312yes—
144C2×#117—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C42—21no—
155C22×C42—44no—
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#481—28no—
169#447—28no—
170#442—48no—
171#432—44no—
172C2×#107C2314yes—
173C2×#106C2314yes—
174C2×#106C2314yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2314yes—
186C2×C22⋊C8C2314yes—
187C2×#97C2314yes—
188#391—21no—
189#391—21no—
190#390—21no—
191#390—21no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390—21no—
196#390C2312yes—
197#390C2312yes—
198#390C2312yes—
199#390C2312yes—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389C2312yes—
205#389C2312yes—
206#389C2312yes—
207#389C2312yes—
208#388—22no—
209#388—22no—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#386—22no—
217#386—22no—
218#386—22no—
219#386—22no—
220#386—22no—
221#386—22no—
222#386—22no—
223#386—22no—
224#386—22no—
225#386—22no—
226#384C2311yescharacteristic
227#384C2311yescharacteristic
228#382—21no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#380C2312yes—
238#380C2312yes—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4C2312yes—
243C4×C4⋊C4C2312yes—
244C4×C4⋊C4C2312yes—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#336C2312yes—
261#336C2312yes—
262#336C2314yes—
263C25—21no—
264C25C2×D411yescharacteristic
265C2×#41—44no—
266C2×#41—44no—
267C2×#41—44no—
268C22×Q8—21no—
269C22×D4—28no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—22no—
279C22×D4—42no—
280C22×D4—42no—
281C22×D4—44no—
282C22×D4—44no—
283C22×D4#4114yescomplemented
284C22×D4C2412yes—
285C22×D4C2412yes—
286C23×C4—21no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—44no—
303C23×C4—44no—
304C23×C4—44no—
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C2×D8—28no—
324C2×D8—44no—
325C2×D8—44no—
326C22×C8C2414yes—
327C22×C8C2414yes—
328C4⋊Q8—42no—
329#127—42no—
330#124—44no—
331#123—48no—
332C22⋊Q8—44no—
333C22⋊Q8—44no—
334#121—28no—
335#121—28no—
336#121—24no—
337#121—24no—
338#121—24no—
339#121—24no—
340#121—24no—
341#121—24no—
342#121—44no—
343#121—44no—
344#121—44no—
345#121—44no—
346#121—44no—
347#121—44no—
348#121—44no—
349#120—48no—
350C4×D4—28no—
351C4×D4—28no—
352C4×D4—44no—
353C4×D4—44no—
354C4×D4—44no—
355C4×D4—44no—
356C4×D4—48no—
357C4×D4—48no—
358C4×D4—48no—
359C4×D4—48no—
360C4×D4—48no—
361C4×D4—48no—
362#117—44no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4#4114yescomplemented
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C22⋊C4—28no—
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×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—44no—
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444#107—44no—
445#106—28no—
446#106—44no—
447C4⋊C8—42no—
448C4⋊C8—42no—
449#102—28no—
450#102—28no—
451#102—44no—
452#102—44no—
453#102—44no—
454#102—44no—
455C22⋊C8—24no—
456C22⋊C8—24no—
457C22⋊C8—44no—
458C22⋊C8—44no—
459#97—28no—
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—
471#95—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—24no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—41no—
481C24—41no—
482C24—42no—
483C24—42no—
484C24—42no—
485C24—42no—
486C24—42no—
487C24—42no—
488C24C22×D411yescharacteristic
489C24C22×D411yescharacteristic
490C24C22×D411yescharacteristic
491#41—816no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—24no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—24no—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—48no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—48no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—44no—
514C2×D4—432no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4C2×#4114yes—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—416no—
591C22×C4—416no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—816no—
612C22×C4AGL(1,ℤ/8)14yes—
613C22×C4AGL(1,ℤ/8)14yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C22×C4C2511yescharacteristic
628D8—416no—
629C2×C8—24no—
630C2×C8—24no—
631C2×C8—24no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—24no—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—44no—
646C4⋊C4—42no—
647C4⋊C4—44no—
648C4⋊C4—42no—
649C4⋊C4—44no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—44no—
653C4⋊C4—42no—
654C4⋊C4C2×#4114yes—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—41no—
686C42—41no—
687C42—41no—
688C42—41no—
689C42—41no—
690C42—41no—
691C42—44no—
692C42—44no—
693C42—44no—
694C42H(5,𝔽2)14yes—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—28no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—24no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—48no—
719C23—48no—
720C23—44no—
721C23—48no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23#52512yes—
740C23C2×AGL(1,ℤ/8)12yes—
741C23C2×AGL(1,ℤ/8)12yes—
742C23#57512yes—
743C23#57512yes—
744C23C23×D411yescharacteristic
745Q8—84no—
746D4—28no—
747D4—48no—
748D4—416no—
749D4—416no—
750D4—44no—
751D4—44no—
752D4—44no—
753D4—84no—
754D4—84no—
755D4—88no—
756D4—88no—
757D4—88no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—24no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—48no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—88no—
825C2×C4—88no—
826C2×C4—88no—
827C2×C4—84no—
828C2×C4—84no—
829C2×C4#52512yes—
830C2×C4#53412yes—
831C2×C4#53412yes—
832C2×C4C2×AGL(1,ℤ/8)12yes—
833C2×C4C2×AGL(1,ℤ/8)12yes—
834C2×C4C2×AGL(1,ℤ/8)12yes—
835C2×C4C2×AGL(1,ℤ/8)12yes—
836C2×C4C22×#4111yescharacteristic
837C2×C4C22×#4111yescharacteristic
838C2×C4C2×H(5,𝔽2)12yes—
839C2×C4#58512yes—
840C8—44no—
841C8—44no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—416no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—816no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22#311514yes—
879C22C2×#52511yescharacteristic
880C22C2×#53411yescharacteristic
881C22#344911yescharacteristic
882C22C22×AGL(1,ℤ/8)11yescharacteristic
883C22C22×AGL(1,ℤ/8)11yescharacteristic
884C22C2×#57511yescharacteristic
885C22C2×#57511yescharacteristic
886C4—22no—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—22no—
891C4—22no—
892C4—22no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4—44no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4#345912yes—
904C4#346012yes—
905C2—24no—
906C2—42no—
907C2—42no—
908C2—84no—
909C2—162no—
910C2#3456211yescharacteristic
911C2C2×#311511yescharacteristic
912C2#6055811yescharacteristic
913C2#6075011yescharacteristic
914C2#6075011yescharacteristic
915C2#6095911yescharacteristic
916C2#6096811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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
1. #36624C2semidirect
2. C2×C4×#121C2semidirect
3. #30166C2semidirect
4. #30105C2semidirect
5. #30007C2semidirect
6. #29967C2semidirect
7. #29950C2semidirect
8. #29891C2semidirect
9. #29755C2semidirect
10. #29712C2semidirect
11. #29594C2semidirect
12. #23761C2semidirect
13. #23708C2semidirect
14. #23573C2semidirect
15. #21580C2semidirect
16. #21452C2semidirect
17. #20715C2semidirect
18. C2×#532C22semidirect
26. C2×#442C22semidirect
27. C2×#432C22semidirect
29. #2857C22semidirect
31. #2856C22semidirect
33. #2854C22semidirect
49. C4×#121C22semidirect
55. #2285C22semidirect
59. #2099C22semidirect
60. #2093C22semidirect
61. #2088C22semidirect
62. #2084C22semidirect
63. #2077C22semidirect
64. #2076C22semidirect
65. #2071C22semidirect
66. #2067C22semidirect
67. #2065C22semidirect
68. #2058C22semidirect
69. #2054C22semidirect
70. #2041C22semidirect
73. #2034C22semidirect
74. #2033C22semidirect
75. #2023C22semidirect
76. #2011C22semidirect
79. #1925C22semidirect
80. #1920C22semidirect
81. #1879C22semidirect
84. #1864C22semidirect
88. #1817C22semidirect
91. #1797C22semidirect
94. #1776C22semidirect
95. #1762C22semidirect
96. #1762C22semidirect
98. #1749C22semidirect
283. C22×D4#41semidirect
379. 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×#1212
#301662
#301052
#300072
#299672
#299502
#298912
#297552
#297122
#295942
#237612
#237082
#235732
#215802
#214522
#207152