Finite Group Databasebeta

← #6467151

Subgroups — #6467151

Order 512.

2230 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3113C211yesmaximal, characteristic, complemented
2C2×#3110C211yesmaximal, characteristic
3C4×#533C211yesmaximal, characteristic, complemented
4C2×C4×#124C211yesmaximal, characteristic
5#28281C212yesmaximal, complemented
6#28254C212yesmaximal, complemented
7#28203C212yesmaximal, complemented
8#28159C212yesmaximal, complemented
9#28121C212yesmaximal, complemented
10#28120C212yesmaximal
11#27653C212yesmaximal, complemented
12#24217C212yesmaximal
13#23687C214yesmaximal, complemented
14#21508C214yesmaximal, complemented
15#20810C211yesmaximal, characteristic, complemented
16#20740C211yesmaximal, characteristic, complemented
17#20738C211yesmaximal, characteristic
18C2×#533C2211yescharacteristic
19C22×#124C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22#3113—28no—
23#3110—28no—
24C2×#484C2212yes—
25C2×#483C2212yes—
26C2×#475C2212yescomplemented
27C2×#474C2212yes—
28C2×#464C2214yes—
29C2×#462C2212yescomplemented
30C2×#461C2212yes—
31C2×#451C2212yes—
32C2×#450C2212yes—
33C2×#441C2214yescomplemented
34C2×#440C2214yes—
35C2×#432C2211yescharacteristic
36C2×#432C2211yescharacteristic
37C4×C4⋊Q8C2211yescharacteristic, complemented
38C4×C4⋊Q8C2211yescharacteristic, complemented
39C4×C4⋊Q8C2211yescharacteristic, complemented
40C4×C4⋊Q8C2211yescharacteristic, complemented
41C4×#125—21no—
42C4×#125—21no—
43C4×#124—21no—
44C4×#124—21no—
45C4×#124—21no—
46C4×#124—21no—
47C4×#124C2212yes—
48C4×#124C2212yes—
49C4×#124C2212yes—
50C4×#124C2212yes—
51C4×C22⋊Q8—21no—
52C4×C22⋊Q8—21no—
53C4×C22⋊Q8C2212yes—
54C4×C22⋊Q8C2212yes—
55#2296—21no—
56#2295—21no—
57#2295C2212yescomplemented
58C2×#391C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#388—21no—
61C2×#388—21no—
62#2285C2211yescharacteristic
63C2×#382C2211yescharacteristic
64C42×Q8—21no—
65C42×Q8C2212yescomplemented
66C4×#117—21no—
67C2×C4×C22⋊C4—21no—
68C2×C4×C22⋊C4—21no—
69C2×C43C2211yescharacteristic
70#2085C2214yescomplemented
71#2074C2214yescomplemented
72#2068C2214yescomplemented
73#2065C2214yes—
74#2056C2214yescomplemented
75#2055C2214yes—
76#2042C2214yes—
77#2015C2214yes—
78#1983C2214yes—
79#1949C2214yescomplemented
80#1928C2214yescomplemented
81#1926C2214yes—
82#1880C2214yes—
83#1878C2214yescomplemented
84#1842C2212yescomplemented
85#1831C2212yescomplemented
86#1824C2212yes—
87#1823C2212yes—
88#1805C2214yescomplemented
89#1803C2212yescomplemented
90#1803C2212yescomplemented
91#1802C2212yes—
92#1802C2212yes—
93#1797C2212yes—
94#1797C2212yes—
95#1787C2212yes—
96#1786C2212yes—
97#1767C2212yescomplemented
98#1767C2212yescomplemented
99#1763C2214yescomplemented
100#1762C2214yes—
101C23×Q8C2311yescharacteristic
102C23×D4C2311yescharacteristic
103C24×C4—21no—
104C22×Q16C2314yes—
105C22×SD16C2314yes—
106#533—24no—
107#533D418yes—
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2311yescharacteristic
110C2×#125—21no—
111C2×#124—28no—
112C2×#124—21no—
113C2×#124—21no—
114C2×#124C2312yes—
115C2×#124C2312yes—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8C2312yes—
118C2×C4×Q8—21no—
119C2×C4×Q8—21no—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×Q8—21no—
123C2×C4×Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×Q8C2312yes—
126C2×C4×Q8C2312yes—
127C2×C4×Q8C2312yes—
128C2×C4×Q8C2312yes—
129C2×C4×Q8C2312yes—
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—24no—
133C2×C4×D4—24no—
134C2×C4×D4C2312yes—
135C2×C4×D4C2312yes—
136C2×#117—21no—
137C2×#117—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C42—21no—
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#484—28no—
155#483—28no—
156#475—28no—
157#474—28no—
158#464—216no—
159#462—28no—
160#461—28no—
161#451—28no—
162#450—28no—
163#441—216no—
164#440—216no—
165#432—24no—
166#432—24no—
167C2×#107C2314yes—
168C2×#106C2314yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2314yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×#97C2312yes—
184C2×#97C2312yes—
185#391—21no—
186#391—21no—
187#391—21no—
188#391—21no—
189#391C2312yes—
190#391C2312yes—
191#391C2312yes—
192#391C2312yes—
193#390—21no—
194#390—21no—
195#390C2312yes—
196#390C2312yes—
197#389—21no—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389C2312yes—
204#389C2312yes—
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#387—22no—
214#387—22no—
215#387—22no—
216#387—22no—
217#385—22no—
218#385—22no—
219#384C2311yescharacteristic
220#384C2311yescharacteristic
221#382—21no—
222#382—21no—
223#382—21no—
224#382C2312yes—
225#382C2312yes—
226#380—21no—
227#380C2312yes—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
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⋊C4—22no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4C2312yes—
242C4×C4⋊C4C2312yes—
243C4×C4⋊C4C2312yes—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254#376—22no—
255C2×#95—21no—
256C2×#95—21no—
257C2×#95—21no—
258C2×#95—21no—
259C43—22no—
260C43D411yescharacteristic
261C43D411yescharacteristic
262C43D411yescharacteristic
263C43D411yescharacteristic
264C43C2311yescharacteristic
265C43C2311yescharacteristic
266C43C2311yescharacteristic
267C43C2311yescharacteristic
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#336C2314yes—
273#336C2314yes—
274C25—21no—
275C22×Q8—24no—
276C22×Q8—21no—
277C22×Q8—21no—
278C22×Q8—22no—
279C22×Q8—22no—
280C22×Q8—42no—
281C22×Q8C2412yes—
282C22×Q8C2412yes—
283C22×D4—24no—
284C22×D4—21no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—42no—
288C22×D4C2412yes—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4—44no—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2411yescharacteristic
304C2×Q16—28no—
305C2×Q16—28no—
306C2×Q16—44no—
307C2×SD16—28no—
308C2×SD16—28no—
309C2×SD16—44no—
310C22×C8C2414yes—
311C22×C8C2414yes—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8C2×D414yes—
315C4⋊Q8C2×D414yes—
316#125—28no—
317#124—28no—
318#124—28no—
319#124—24no—
320#124—24no—
321#124—24no—
322#124#4118yes—
323C22⋊Q8—28no—
324C22⋊Q8—24no—
325C22⋊Q8C2×D418yes—
326C4×Q8—28no—
327C4×Q8—24no—
328C4×Q8—24no—
329C4×Q8—24no—
330C4×Q8—24no—
331C4×Q8—24no—
332C4×Q8—28no—
333C4×Q8—44no—
334C4×Q8—44no—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×Q8—44no—
338C4×Q8C2×D418yes—
339C4×D4—24no—
340C4×D4—24no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—44no—
344C4×D4—44no—
345#117—28no—
346#117—44no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
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—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—28no—
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—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—44no—
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×C42C2×D411yescharacteristic
428C2×C42C2×D414yes—
429C2×C42#4114yes—
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436#107—28no—
437#106—28no—
438C4⋊C8—24no—
439C4⋊C8—24no—
440C4⋊C8—28no—
441C4⋊C8—44no—
442#103—28no—
443#103—28no—
444#103—28no—
445#103—28no—
446#103—44no—
447#102—28no—
448#102—28no—
449#102—44no—
450C22⋊C8—24no—
451C22⋊C8—24no—
452#97—24no—
453#97—24no—
454#95—22no—
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—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472C24—24no—
473C24—22no—
474C24—42no—
475C24—42no—
476C24—42no—
477C24—42no—
478C24—42no—
479C24—42no—
480C24C22×D411yescharacteristic
481C2×Q8—24no—
482C2×Q8—24no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—24no—
488C2×Q8—22no—
489C2×Q8—24no—
490C2×Q8—22no—
491C2×Q8—48no—
492C2×Q8—48no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8C22×D414yes—
498C2×Q8C2×#4114yes—
499C2×D4—24no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4C2×#4114yes—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
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—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—816no—
550C22×C4#12114yes—
551C22×C4#12114yes—
552C22×C4#13714yes—
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D412yes—
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C2×#4112yes—
568C22×C4C2511yescharacteristic
569Q16—416no—
570SD16—416no—
571C2×C8—24no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—24no—
575C2×C8—24no—
576C2×C8—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—28no—
581C4⋊C4—28no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—24no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4C22×D414yes—
602C22⋊C4—28no—
603C22⋊C4—28no—
604C22⋊C4—28no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C42—28no—
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—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—41no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—44no—
639C42—44no—
640C42—44no—
641C42—44no—
642C42—44no—
643C42—44no—
644C42—44no—
645C42#12114yes—
646C42#12114yes—
647C42C22×D412yes—
648C42C22×D412yes—
649C42C2×#4112yes—
650C42C2×#4112yes—
651C42C2×#4114yes—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—24no—
657C23—48no—
658C23—48no—
659C23—48no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23C2×#12112yes—
671C23C2×#13712yes—
672C23#57512yes—
673C23C23×D411yescharacteristic
674Q8—28no—
675Q8—24no—
676Q8—24no—
677Q8—48no—
678Q8—42no—
679Q8—44no—
680Q8—42no—
681Q8—48no—
682D4—24no—
683D4—24no—
684D4—48no—
685D4—42no—
686D4—42no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—28no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
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—24no—
705C2×C4—24no—
706C2×C4—28no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—24no—
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—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—48no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—88no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—88no—
749C2×C4C2×#12112yes—
750C2×C4C2×#12112yes—
751C2×C4C2×#12112yes—
752C2×C4C2×#12112yes—
753C2×C4C2×#12112yes—
754C2×C4#52512yes—
755C2×C4#52512yes—
756C2×C4C2×#13712yes—
757C2×C4C2×#13712yes—
758C2×C4#57512yes—
759C2×C4#57512yes—
760C2×C4C23×D411yescharacteristic
761C2×C4C22×#4112yes—
762C2×C4C22×#4111yescharacteristic
763C2×C4#58512yes—
764C8—44no—
765C8—44no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—816no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22#303714yes—
781C22C22×#12111yescharacteristic
782C22C2×#52511yescharacteristic
783C22#344911yescharacteristic
784C22C22×#13711yescharacteristic
785C22C2×#57511yescharacteristic
786C22C2×#57511yescharacteristic
787C22C2×#57511yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—41no—
797C4—41no—
798C4—44no—
799C4—44no—
800C4—41no—
801C4—41no—
802C4—44no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4—82no—
807C4#304014yes—
808C4D4×#4112yes—
809C4#347512yes—
810C2—24no—
811C2—84no—
812C2#3493511yescharacteristic
813C2C2×#303711yescharacteristic
814C2C2×#304011yescharacteristic
815C2#6054611yescharacteristic
816C2#6056211yescharacteristic
817C2#6096011yescharacteristic
818C2#6097011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
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×#3113C2semidirect
3. C4×#533C2semidirect
5. #28281C2semidirect
6. #28254C2semidirect
7. #28203C2semidirect
8. #28159C2semidirect
9. #28121C2semidirect
11. #27653C2semidirect
13. #23687C2semidirect
14. #21508C2semidirect
15. #20810C2semidirect
16. #20740C2semidirect
26. C2×#475C22semidirect
29. C2×#462C22semidirect
33. C2×#441C22semidirect
37. C4×C4⋊Q8C22semidirect
38. C4×C4⋊Q8C22semidirect
39. C4×C4⋊Q8C22semidirect
40. C4×C4⋊Q8C22semidirect
57. #2295C22semidirect
65. C42×Q8C22semidirect
70. #2085C22semidirect
71. #2074C22semidirect
72. #2068C22semidirect
74. #2056C22semidirect
79. #1949C22semidirect
80. #1928C22semidirect
83. #1878C22semidirect
84. #1842C22semidirect
85. #1831C22semidirect
88. #1805C22semidirect
89. #1803C22semidirect
90. #1803C22semidirect
97. #1767C22semidirect
98. #1767C22semidirect
99. #1763C22semidirect

Maximal subgroups

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

subgroupindex
C2×#31132
C2×#31102
C4×#5332
C2×C4×#1242
#282812
#282542
#282032
#281592
#281212
#281202
#276532
#242172
#236872
#215082
#208102
#207402
#207382