Finite Group Databasebeta

← #6461473

Subgroups — #6461473

Order 512.

2394 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#532C211yesmaximal, characteristic, complemented
2C2×#2293C211yesmaximal, characteristic, complemented
3#29373C214yesmaximal, complemented
4#29372C214yesmaximal, complemented
5#29369C212yesmaximal, complemented
6#29368C212yesmaximal, complemented
7#29365C212yesmaximal, complemented
8#29364C212yesmaximal, complemented
9#23747C211yesmaximal, characteristic, complemented
10#23731C211yesmaximal, characteristic, complemented
11#23508C211yesmaximal, characteristic, complemented
12#23428C211yesmaximal, characteristic
13#21059C212yesmaximal, complemented
14#20928C212yesmaximal, complemented
15#20925C212yesmaximal, complemented
16#20875C212yesmaximal, complemented
17#20772C211yesmaximal, characteristic, complemented
18C22×AGL(1,ℤ/8)C2212yes—
19C2×#532C2211yescharacteristic
20C2×C4×#41C2212yes—
21C22×C4×D4C2211yescharacteristic
22C22×#117—21no—
23C2×#428C2212yes—
24C2×#417C2212yes—
25C2×#417C2212yes—
26C2×#417C2212yes—
27C2×#418C2212yes—
28C4×C4⋊Q8C2211yescharacteristic, complemented
29C4×C4⋊Q8C2211yescharacteristic, complemented
30C4×#127C2211yescharacteristic, complemented
31C4×#127C2211yescharacteristic, complemented
32C4×#124C2212yescomplemented
33C4×#124C2212yescomplemented
34C4×#121—21no—
35C4×#121—21no—
36C4×#121—21no—
37C4×#121—21no—
38#2297C2212yes—
39#2293—21no—
40#2293—21no—
41#2293—21no—
42#2293—21no—
43#2293—21no—
44#2293—21no—
45#2293C2212yes—
46#2293C2212yes—
47#2293C2212yes—
48#2293C2212yes—
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388—21no—
54C2×#388—21no—
55#2285C2211yescharacteristic
56C42×D4—21no—
57C42×D4—21no—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4—21no—
60C2×C43C2211yescharacteristic
61#2101C2214yescomplemented
62#2100C2212yescomplemented
63#2099C2212yescomplemented
64#2094C2212yes—
65#2093C2212yes—
66#2092C2214yes—
67#2043C2212yescomplemented
68#2042C2214yescomplemented
69#2041C2212yescomplemented
70#2013C2212yes—
71#2012C2214yes—
72#2011C2212yes—
73#1928C2214yescomplemented
74#1927C2214yescomplemented
75#1926C2214yescomplemented
76#1925C2214yescomplemented
77#1880C2214yes—
78#1880C2214yes—
79#1879C2214yes—
80#1879C2214yes—
81#1879C2214yes—
82#1879C2214yes—
83#1877C2214yes—
84#1877C2214yes—
85#1865C2214yescomplemented
86#1864C2214yescomplemented
87#1863C2214yescomplemented
88#1862C2214yescomplemented
89#1839C2212yescomplemented
90#1839C2212yescomplemented
91#1839C2212yescomplemented
92#1839C2212yescomplemented
93#1736C2212yes—
94#1736C2212yes—
95#1728C2212yes—
96#1728C2211yescharacteristic
97#1728C2212yes—
98#1728C2211yescharacteristic
99C22×#41C2312yes—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C2×AGL(1,ℤ/8)—28no—
103C2×AGL(1,ℤ/8)—28no—
104C2×AGL(1,ℤ/8)—44no—
105C22×SD16C2314yes—
106C22×D8C2314yes—
107C22×M16C2312yes—
108C22×M16C2312yes—
109#532—28no—
110C2×C4⋊Q8C2311yescharacteristic
111C2×#127C2311yescharacteristic
112C2×#124C2312yes—
113C2×#121—21no—
114C2×#121—21no—
115C4×#41—44no—
116C4×#41—44no—
117C2×C4×Q8C2312yes—
118C2×C4×Q8C2312yes—
119C2×C4×D4—24no—
120C2×C4×D4—22no—
121C2×C4×D4—22no—
122C2×C4×D4—24no—
123C2×C4×D4—21no—
124C2×C4×D4—21no—
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×C4×D4C2312yes—
134C2×C4×D4C2312yes—
135C2×#117—22no—
136C2×#117—22no—
137C2×#117—22no—
138C2×#117—22no—
139C2×#117—22no—
140C2×#117—48no—
141C2×#117C2312yes—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C42—21no—
153C22×C42—22no—
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#428—44no—
162C2×#107C2314yes—
163C2×#106C2314yes—
164#418—44no—
165#417—28no—
166#417—28no—
167#417—44no—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176#391C2312yes—
177#391C2312yes—
178#390—21no—
179#390—21no—
180#390—21no—
181#390—21no—
182#390—21no—
183#390—21no—
184#390—21no—
185#390—21no—
186#390C2312yes—
187#390C2312yes—
188#390C2312yes—
189#390C2312yes—
190#390C2312yes—
191#390C2312yes—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389C2312yes—
201#389C2312yes—
202#389C2312yes—
203#389C2312yes—
204#388—22no—
205#388—22no—
206#388—22no—
207#388—22no—
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#384C2311yescharacteristic
219#384C2311yescharacteristic
220#382C2312yes—
221#380—21no—
222#380—21no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4C2312yes—
232C4×C4⋊C4C2312yes—
233C4×C22⋊C4—22no—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C2×#95—21no—
244C2×#95—21no—
245C2×#95—21no—
246C43D411yescharacteristic
247C43D411yescharacteristic
248C43D411yescharacteristic
249C43D411yescharacteristic
250C43C2311yescharacteristic
251C43C2311yescharacteristic
252C43C2311yescharacteristic
253C43C2311yescharacteristic
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2312yes—
259#336C2312yes—
260#336C2312yes—
261#336C2312yes—
262#336C2314yes—
263#336C2314yes—
264#336C2314yes—
265#336C2314yes—
266C25—21no—
267C2×#41—24no—
268C2×#41—24no—
269C2×#41—24no—
270C2×#41—24no—
271C2×#41—24no—
272C2×#41#4118yes—
273C22×Q8C2412yes—
274C22×D4—22no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—24no—
279C22×D4—22no—
280C22×D4—24no—
281C22×D4#4114yes—
282C22×D4C2412yes—
283C22×D4C2412yes—
284C23×C4—28no—
285C23×C4—21no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2411yescharacteristic
302AGL(1,ℤ/8)—432no—
303C2×SD16—28no—
304C2×SD16—28no—
305C2×SD16—44no—
306C2×D8—28no—
307C2×D8—28no—
308C2×D8—44no—
309C2×M16—24no—
310C2×M16—24no—
311C2×M16—24no—
312C2×M16—24no—
313C2×M16—24no—
314C2×M16—24no—
315C22×C8C2414yes—
316C22×C8C2414yes—
317C4⋊Q8—24no—
318#127—24no—
319#124—24no—
320#124—24no—
321#121—28no—
322#121—28no—
323C4×Q8—42no—
324C4×Q8—42no—
325C4×Q8—42no—
326C4×Q8—42no—
327C4×D4—28no—
328C4×D4—28no—
329C4×D4—28no—
330C4×D4—28no—
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—42no—
336C4×D4—42no—
337C4×D4—42no—
338C4×D4—42no—
339C4×D4—44no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—48no—
343C4×D4—48no—
344C4×D4—44no—
345#117—24no—
346#117—24no—
347#117—48no—
348#117—48no—
349#117—48no—
350#117—48no—
351#117—48no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4#4114yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C22⋊C4—28no—
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×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42—48no—
416C2×C42—44no—
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×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445#107—44no—
446#106—44no—
447#103—28no—
448#103—28no—
449#103—44no—
450#102—28no—
451#102—28no—
452#102—44no—
453#102—44no—
454#102—44no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—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—
467C24—24no—
468C24—22no—
469C24—22no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24—42no—
476C24C22×D411yescharacteristic
477#41—216no—
478#41—216no—
479#41—48no—
480#41—48no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8C2×#4114yes—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—28no—
490C2×D4—24no—
491C2×D4—216no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—48no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4C2×#4114yes—
510C2×D4C2×#4114yes—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—28no—
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—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—44no—
540C22×C4—432no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C2×#4112yes—
574C22×C4C2×#4114yes—
575C22×C4C2×#4112yes—
576C22×C4H(5,𝔽2)14yes—
577C22×C4C2511yescharacteristic
578SD16—416no—
579D8—416no—
580M16—48no—
581M16—48no—
582C2×C8—24no—
583C2×C8—24no—
584C2×C8—24no—
585C2×C8—24no—
586C2×C8—24no—
587C2×C8—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—24no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4C2×#4114yes—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—44no—
660C42—44no—
661C42—44no—
662C42—44no—
663C42—44no—
664C42AGL(1,ℤ/8)14yescomplemented
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—24no—
670C23—24no—
671C23—48no—
672C23—48no—
673C23—48no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23—84no—
690C23#52512yes—
691C23#52512yes—
692C23#53512yes—
693C23C23×D411yescharacteristic
694Q8—24no—
695Q8—24no—
696Q8—42no—
697Q8—42no—
698D4—24no—
699D4—28no—
700D4—24no—
701D4—48no—
702D4—48no—
703D4—416no—
704D4—48no—
705D4—42no—
706D4—44no—
707D4—42no—
708C2×C4—28no—
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—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
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—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—416no—
746C2×C4—416no—
747C2×C4—44no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—416no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—88no—
767C2×C4—88no—
768C2×C4—84no—
769C2×C4—84no—
770C2×C4#52512yes—
771C2×C4#52512yes—
772C2×C4#53512yes—
773C2×C4#55118yes—
774C2×C4#55318yes—
775C2×C4C2×AGL(1,ℤ/8)12yes—
776C2×C4C2×AGL(1,ℤ/8)12yes—
777C2×C4C2×AGL(1,ℤ/8)12yes—
778C2×C4#57512yes—
779C2×C4#57512yes—
780C2×C4#57512yes—
781C2×C4C22×#4111yescharacteristic
782C2×C4C22×#4112yes—
783C2×C4C22×#4111yescharacteristic
784C2×C4C2×H(5,𝔽2)12yes—
785C8—44no—
786C8—44no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—816no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22#259814yes—
809C22C2×#52511yescharacteristic
810C22C2×#52511yescharacteristic
811C22C2×#53511yescharacteristic
812C22C22×AGL(1,ℤ/8)11yescharacteristic
813C22C2×#57511yescharacteristic
814C22C2×#57511yescharacteristic
815C22C2×#57511yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—44no—
823C4—41no—
824C4—41no—
825C4—44no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4#259814yes—
835C4C2×#55112yes—
836C4C2×#55312yes—
837C2—24no—
838C2—84no—
839C2—84no—
840C2C2×#259811yescharacteristic
841C2#6055811yescharacteristic
842C2#6055911yescharacteristic
843C2#6056111yescharacteristic
844C2#6056311yescharacteristic
845C2#6080311yescharacteristic
846C2#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. C4×#532C2semidirect
2. C2×#2293C2semidirect
3. #29373C2semidirect
4. #29372C2semidirect
5. #29369C2semidirect
6. #29368C2semidirect
7. #29365C2semidirect
8. #29364C2semidirect
9. #23747C2semidirect
10. #23731C2semidirect
11. #23508C2semidirect
13. #21059C2semidirect
14. #20928C2semidirect
15. #20925C2semidirect
16. #20875C2semidirect
17. #20772C2semidirect
28. C4×C4⋊Q8C22semidirect
29. C4×C4⋊Q8C22semidirect
30. C4×#127C22semidirect
31. C4×#127C22semidirect
32. C4×#124C22semidirect
33. C4×#124C22semidirect
61. #2101C22semidirect
62. #2100C22semidirect
63. #2099C22semidirect
67. #2043C22semidirect
68. #2042C22semidirect
69. #2041C22semidirect
73. #1928C22semidirect
74. #1927C22semidirect
75. #1926C22semidirect
76. #1925C22semidirect
85. #1865C22semidirect
86. #1864C22semidirect
87. #1863C22semidirect
88. #1862C22semidirect
89. #1839C22semidirect
90. #1839C22semidirect
91. #1839C22semidirect
92. #1839C22semidirect
664. 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
C4×#5322
C2×#22932
#293732
#293722
#293692
#293682
#293652
#293642
#237472
#237312
#235082
#234282
#210592
#209282
#209252
#208752
#207722