Finite Group Databasebeta

← #6498412

Subgroups — #6498412

Order 512.

2192 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3234C211yesmaximal, characteristic, complemented
2C2×#3213C211yesmaximal, characteristic
3C2×#2861C211yesmaximal, characteristic, complemented
4C4×#532C211yesmaximal, characteristic, complemented
5#33028C214yesmaximal, complemented
6#29832C214yesmaximal, complemented
7#28659C212yesmaximal, complemented
8#28658C212yesmaximal, complemented
9#28618C212yesmaximal, complemented
10#28618C212yesmaximal, complemented
11#28118C212yesmaximal, complemented
12#28117C212yesmaximal, complemented
13#28115C212yesmaximal, complemented
14#28114C212yesmaximal, complemented
15#21838C211yesmaximal, characteristic, complemented
16#21808C211yesmaximal, characteristic, complemented
17#20810C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C22×#125C2211yescharacteristic
20C22×#124C2211yescharacteristic
21C2×C4×#41—21no—
22#3234—28no—
23#3213—28no—
24C2×#501C2212yescomplemented
25C2×#496C2212yes—
26C2×#490C2212yescomplemented
27C2×#489C2212yes—
28C2×#481C2212yes—
29C2×#480C2212yes—
30C2×#478C2214yescomplemented
31C2×#463C2214yes—
32C2×#448C2212yes—
33C2×#447C2212yes—
34C2×#432C2211yescharacteristic
35C2×#432C2211yescharacteristic
36#2861—21no—
37#2861—21no—
38#2861—21no—
39#2861—21no—
40#2861C2212yes—
41#2861C2212yes—
42#2861C2212yes—
43#2861C2212yes—
44C4×C4⋊Q8C2211yescharacteristic, complemented
45C4×C4⋊Q8C2211yescharacteristic, complemented
46C4×#127C2211yescharacteristic, complemented
47C4×#127C2211yescharacteristic, complemented
48C4×#124—21no—
49C4×#124—21no—
50C4×#121—21no—
51C4×#121—21no—
52C4×#121C2212yes—
53C4×#121C2212yes—
54#2297—21no—
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57#2293—21no—
58#2293C2212yescomplemented
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#388—21no—
62C2×#388—21no—
63C2×#388—21no—
64C2×#388—21no—
65#2285C2211yescharacteristic
66C42×D4—21no—
67C42×D4C2212yescomplemented
68C2×C43C2211yescharacteristic
69#2068C2214yescomplemented
70#2067C2214yes—
71#2066C2214yescomplemented
72#2065C2214yes—
73#2055C2214yescomplemented
74#2055C2214yescomplemented
75#2054C2214yes—
76#2054C2214yes—
77#1992C2212yescomplemented
78#1992C2212yescomplemented
79#1989C2214yescomplemented
80#1983C2214yes—
81#1959C2212yes—
82#1959C2212yes—
83#1928C2214yescomplemented
84#1927C2214yescomplemented
85#1926C2214yes—
86#1925C2214yes—
87#1879C2214yes—
88#1879C2214yes—
89#1877C2214yescomplemented
90#1877C2214yescomplemented
91#1842C2212yescomplemented
92#1831C2212yescomplemented
93#1824C2212yes—
94#1823C2212yes—
95#1797C2212yes—
96#1797C2212yes—
97#1787C2212yes—
98#1786C2212yes—
99#1767C2212yescomplemented
100#1767C2212yescomplemented
101C22×#41—21no—
102C23×Q8C2311yescharacteristic
103C23×D4C2311yescharacteristic
104C22×SD16C2314yes—
105C22×D8C2314yes—
106#532—24no—
107#532D418yes—
108C2×C4⋊Q8C2311yescharacteristic
109C2×#127C2311yescharacteristic
110C2×#125—21no—
111C2×#125—21no—
112C2×#125—24no—
113C2×#125—24no—
114C2×#125C2312yes—
115C2×#125C2312yes—
116C2×#124—21no—
117C2×#124—21no—
118C2×#124—21no—
119C2×#124—24no—
120C2×#124—24no—
121C2×#124C2312yes—
122C2×#124C2312yes—
123C2×#121—21no—
124C2×#121C2312yes—
125C4×#41—48no—
126C2×C4×Q8—21no—
127C2×C4×Q8—21no—
128C2×C4×D4—22no—
129C2×C4×D4—22no—
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4C2312yes—
136C2×C4×D4C2312yes—
137C2×C4×D4C2312yes—
138C2×#117—21no—
139C2×#117—22no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C42—22no—
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#501—28no—
159#496—28no—
160#490—28no—
161#489—28no—
162#481—28no—
163#480—28no—
164#478—216no—
165#463—216no—
166#448—28no—
167#447—28no—
168#432—24no—
169#432—24no—
170C2×#107C2314yes—
171C2×#106C2314yes—
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2314yes—
175C2×C4⋊C8C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×#97C2312yes—
187C2×#97C2312yes—
188#391—21no—
189#391—21no—
190#391—21no—
191#391—21no—
192#391—21no—
193#391—21no—
194#391C2312yes—
195#391C2312yes—
196#391C2312yes—
197#391C2312yes—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390C2312yes—
207#390C2312yes—
208#390C2312yes—
209#390C2312yes—
210#390C2312yes—
211#390C2312yes—
212#389—21no—
213#389—21no—
214#389C2312yes—
215#389C2312yes—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
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#388—22no—
233#388—22no—
234#388—22no—
235#388—22no—
236#386—22no—
237#386—22no—
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#382—21no—
241#380—21no—
242#380C2312yes—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4C2312yes—
247C4×C4⋊C4C2312yes—
248C4×C4⋊C4C2312yes—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C4×C22⋊C4—22no—
255C2×#95—21no—
256C2×#95—21no—
257C2×#95—21no—
258C2×#95—21no—
259C43D411yescharacteristic
260C43D411yescharacteristic
261C43D411yescharacteristic
262C43D411yescharacteristic
263C43C2311yescharacteristic
264C43C2311yescharacteristic
265C43C2311yescharacteristic
266C43C2311yescharacteristic
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#336C2314yes—
272#336C2314yes—
273C25—21no—
274C2×#41—28no—
275C2×#41—44no—
276C2×#41—44no—
277C22×Q8—21no—
278C22×Q8—21no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—42no—
282C22×Q8—42no—
283C22×Q8C2412yes—
284C22×D4—22no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—22no—
288C22×D4—21no—
289C22×D4—22no—
290C22×D4—42no—
291C22×D4—42no—
292C22×D4C2412yes—
293C22×D4C2412yes—
294C23×C4—22no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2411yescharacteristic
307C2×SD16—28no—
308C2×SD16—44no—
309C2×SD16—44no—
310C2×D8—28no—
311C2×D8—44no—
312C2×D8—44no—
313C22×C8C2414yes—
314C22×C8C2414yes—
315C4⋊Q8—22no—
316C4⋊Q8C2×D414yes—
317#127—22no—
318#127C2×D414yes—
319#125—24no—
320#125—24no—
321#125—24no—
322#125—24no—
323#125—44no—
324#125—44no—
325#124—28no—
326#124—24no—
327#124—24no—
328#124—24no—
329#124—24no—
330#124—44no—
331#124—44no—
332#121—28no—
333#121—24no—
334#121C2×D418yes—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×D4—28no—
338C4×D4—24no—
339C4×D4—44no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—44no—
343C4×D4—44no—
344C4×D4—44no—
345C4×D4—48no—
346C4×D4—48no—
347C4×D4C2×D418yes—
348#117—48no—
349#117—44no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
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—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—48no—
410C2×C42—42no—
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×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D414yes—
434C2×C42#4114yes—
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441#107—28no—
442#106—28no—
443C4⋊C8—24no—
444C4⋊C8—24no—
445C4⋊C8—44no—
446C4⋊C8—44no—
447#103—28no—
448#103—44no—
449#103—44no—
450#102—28no—
451#102—28no—
452#102—28no—
453#102—44no—
454#102—44no—
455C22⋊C8—24no—
456C22⋊C8—24no—
457#97—24no—
458#97—24no—
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—
471#95—22no—
472#95—22no—
473C24—22no—
474C24—22no—
475C24—42no—
476C24—42no—
477C24—42no—
478C24—42no—
479C24—42no—
480C24—42no—
481C24—42no—
482C24C22×D411yescharacteristic
483#41—432no—
484C2×Q8—24no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—24no—
488C2×Q8—24no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—84no—
495C2×Q8—84no—
496C2×D4—28no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—24no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—42no—
515C2×D4—84no—
516C2×D4—84no—
517C2×D4C22×D414yes—
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—28no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4#12114yes—
560C22×C4#12114yes—
561C22×C4AGL(1,ℤ/8)14yes—
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×D412yes—
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C2×#4112yes—
577C22×C4C2511yescharacteristic
578SD16—88no—
579D8—88no—
580C2×C8—24no—
581C2×C8—24no—
582C2×C8—24no—
583C2×C8—24no—
584C2×C8—24no—
585C2×C8—24no—
586C4⋊C4—24no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—44no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4C22×D414yes—
607C22⋊C4—28no—
608C22⋊C4—28no—
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—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42#12114yes—
656C42#12114yes—
657C42C22×D412yes—
658C42C22×D412yes—
659C42C2×#4112yes—
660C42C2×#4112yes—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—24no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23C2×#12112yes—
687C23C2×AGL(1,ℤ/8)12yes—
688C23#57512yes—
689C23C23×D411yescharacteristic
690Q8—48no—
691Q8—44no—
692Q8—44no—
693Q8—84no—
694D4—28no—
695D4—48no—
696D4—48no—
697D4—416no—
698D4—44no—
699D4—44no—
700D4—44no—
701D4—84no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
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—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
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—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—416no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—88no—
760C2×C4—88no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4C2×#12112yes—
765C2×C4C2×#12112yes—
766C2×C4C2×#12112yes—
767C2×C4C2×#12112yes—
768C2×C4C2×#12112yes—
769C2×C4C2×AGL(1,ℤ/8)12yes—
770C2×C4C2×AGL(1,ℤ/8)12yes—
771C2×C4#57512yes—
772C2×C4#57512yes—
773C2×C4C23×D411yescharacteristic
774C2×C4C22×#4111yescharacteristic
775C2×C4#58512yes—
776C2×C4#58512yes—
777C8—44no—
778C8—44no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—168no—
800C22#303614yes—
801C22C22×#12111yescharacteristic
802C22#344911yescharacteristic
803C22#344911yescharacteristic
804C22C22×AGL(1,ℤ/8)11yescharacteristic
805C22C2×#57511yescharacteristic
806C22C2×#57511yescharacteristic
807C22C2×#57511yescharacteristic
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—22no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—44no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4#350012yes—
828C4#351012yes—
829C2—24no—
830C2—84no—
831C2—162no—
832C2#3532711yescharacteristic
833C2C2×#303611yescharacteristic
834C2#6041511yescharacteristic
835C2#6094911yescharacteristic
836C2#6095411yescharacteristic
837C2#6095811yescharacteristic
838C2#6095911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3213C2
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. C2×#3234C2semidirect
3. C2×#2861C2semidirect
4. C4×#532C2semidirect
5. #33028C2semidirect
6. #29832C2semidirect
7. #28659C2semidirect
8. #28658C2semidirect
9. #28618C2semidirect
10. #28618C2semidirect
11. #28118C2semidirect
12. #28117C2semidirect
13. #28115C2semidirect
14. #28114C2semidirect
15. #21838C2semidirect
16. #21808C2semidirect
17. #20810C2semidirect
24. C2×#501C22semidirect
26. C2×#490C22semidirect
30. C2×#478C22semidirect
44. C4×C4⋊Q8C22semidirect
45. C4×C4⋊Q8C22semidirect
46. C4×#127C22semidirect
47. C4×#127C22semidirect
58. #2293C22semidirect
67. C42×D4C22semidirect
69. #2068C22semidirect
71. #2066C22semidirect
73. #2055C22semidirect
74. #2055C22semidirect
77. #1992C22semidirect
78. #1992C22semidirect
79. #1989C22semidirect
83. #1928C22semidirect
84. #1927C22semidirect
89. #1877C22semidirect
90. #1877C22semidirect
91. #1842C22semidirect
92. #1831C22semidirect
99. #1767C22semidirect
100. #1767C22semidirect

Maximal subgroups

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

subgroupindex
C2×#32342
C2×#32132
C2×#28612
C4×#5322
#330282
#298322
#286592
#286582
#286182
#281182
#281172
#281152
#281142
#218382
#218082
#208102