Finite Group Databasebeta

← #6630378

Subgroups — #6630378

Order 512.

2374 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36635C211yesmaximal, characteristic, complemented
2C2×C42×D4C211yesmaximal, characteristic
3#33201C212yesmaximal, complemented
4#33199C212yesmaximal, complemented
5#33150C212yesmaximal, complemented
6#33149C211yesmaximal, characteristic, complemented
7#33147C211yesmaximal, characteristic, complemented
8#33070C214yesmaximal, complemented
9#32959C212yesmaximal
10#32956C211yesmaximal, characteristic
11#32953C211yesmaximal, characteristic
12C4×#478C214yesmaximal, complemented
13C4×#476C212yesmaximal, complemented
14C4×#474C212yesmaximal, complemented
15#21361C212yesmaximal, complemented
16#20808C211yesmaximal, characteristic, complemented
17#20733C212yesmaximal
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C23×C42—21no—
22C2×#478C2214yes—
23C2×#476C2212yes—
24C2×#474C2212yes—
25C2×#431C2212yes—
26#2864C2212yescomplemented
27#2863—21no—
28#2863—21no—
29#2862C2211yescharacteristic, complemented
30#2859C2211yescharacteristic, complemented
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2855—21no—
34#2855—21no—
35#2851C2212yes—
36C4×C4⋊Q8C2211yescharacteristic, complemented
37C4×C4⋊Q8C2211yescharacteristic, complemented
38C4×#125C2212yescomplemented
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8—21no—
41#2295—21no—
42#2295—21no—
43#2283C2212yes—
44C42×D4—21no—
45C42×D4—21no—
46C42×D4—21no—
47C42×D4—21no—
48C42×D4C2212yes—
49C42×D4C2212yes—
50C42×D4C2212yes—
51C42×D4C2212yes—
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4—21no—
56C2×C4×C22⋊C4—21no—
57C2×C4×C22⋊C4—21no—
58C2×C43C2211yescharacteristic
59#1989C2214yescomplemented
60#1988C2212yescomplemented
61#1987C2212yescomplemented
62#1949C2214yescomplemented
63#1949C2214yescomplemented
64#1949C2214yescomplemented
65#1948C2212yescomplemented
66#1947C2212yescomplemented
67#1921C2214yescomplemented
68#1920C2214yescomplemented
69#1919C2214yescomplemented
70#1918C2214yescomplemented
71#1864C2214yes—
72#1864C2214yes—
73#1862C2214yes—
74#1862C2214yes—
75#1853C2212yes—
76#1853C2212yes—
77#1852C2212yes—
78#1852C2212yes—
79#1842C2212yescomplemented
80#1831C2212yescomplemented
81#1824C2212yes—
82#1824C2212yes—
83#1804C2214yes—
84#1804C2214yes—
85#1804C2214yes—
86#1802C2212yes—
87#1802C2212yes—
88#1797C2211yescharacteristic
89#1797C2211yescharacteristic
90#1797C2212yes—
91#1786C2212yes—
92#1786C2212yes—
93C4×#107C2214yescomplemented
94C4×#106C2214yescomplemented
95C4×C4⋊C8C2212yescomplemented
96C4×C4⋊C8C2212yescomplemented
97C4×#102C2214yes—
98C4×#102C2214yes—
99C23×D4C2311yescharacteristic
100C24×C4—21no—
101C24×C4—21no—
102C24×C4—21no—
103C2×C4⋊Q8C2311yescharacteristic
104C2×C4⋊Q8C2311yescharacteristic
105C2×#125C2312yes—
106C2×C22⋊Q8—21no—
107C2×C22⋊Q8—21no—
108C2×C4×Q8—21no—
109C2×C4×Q8—21no—
110C2×C4×D4—28no—
111C2×C4×D4—28no—
112C2×C4×D4—21no—
113C2×C4×D4—21no—
114C2×C4×D4—21no—
115C2×C4×D4—21no—
116C2×C4×D4—21no—
117C2×C4×D4—21no—
118C2×C4×D4—24no—
119C2×C4×D4Q818yescomplemented
120C2×C4×D4C2312yes—
121C2×C4×D4C2312yes—
122C2×C4×D4C2312yes—
123C2×C4×D4C2312yes—
124C2×C4×D4C2312yes—
125C2×C4×D4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C42—21no—
133C22×C42—21no—
134C22×C42—21no—
135C22×C42—22no—
136C22×C42—22no—
137C22×C42—22no—
138C22×C42—22no—
139C22×C42—48no—
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#478—216no—
148#476—28no—
149#474—28no—
150#431—28no—
151C2×#107C2314yes—
152C2×#107C2314yes—
153C2×#106C2314yes—
154C2×#106C2314yes—
155C2×C4⋊C8C2314yes—
156C2×C4⋊C8C2312yes—
157C2×C4⋊C8C2312yes—
158C2×C4⋊C8C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×C22⋊C8C2312yes—
164C2×C22⋊C8C2312yes—
165C2×C4×C8C2314yes—
166#391—21no—
167#391—21no—
168#391—21no—
169#391—21no—
170#391—21no—
171#391—21no—
172#391—21no—
173#391—21no—
174#389—21no—
175#389—21no—
176#389—21no—
177#389—21no—
178#389—21no—
179#389—21no—
180#389—21no—
181#389—21no—
182#389C2312yes—
183#389C2312yes—
184#389C2312yes—
185#389C2312yes—
186#387—22no—
187#387—22no—
188#387—22no—
189#387—22no—
190#387—22no—
191#387—22no—
192#387—22no—
193#387—22no—
194#385—22no—
195#385—22no—
196#384C2311yescharacteristic
197#384C2311yescharacteristic
198#383—22no—
199#382C2312yes—
200#382C2312yes—
201#382C2312yes—
202#381—22no—
203#380—21no—
204#380—21no—
205#380C2312yes—
206#380C2312yes—
207C4×C4⋊C4—22no—
208C4×C4⋊C4—22no—
209C4×C4⋊C4—21no—
210C4×C4⋊C4—21no—
211C4×C4⋊C4—21no—
212C4×C4⋊C4—21no—
213C4×C4⋊C4—21no—
214C4×C4⋊C4—21no—
215C4×C4⋊C4—21no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4C2312yes—
218C4×C4⋊C4C2312yes—
219C4×C4⋊C4C2312yes—
220C4×C4⋊C4C2312yes—
221C4×C4⋊C4C2312yes—
222C4×C4⋊C4C2312yes—
223C4×C4⋊C4C2312yes—
224C4×C4⋊C4C2312yes—
225C4×C22⋊C4—22no—
226C4×C22⋊C4—22no—
227C4×C22⋊C4—22no—
228C4×C22⋊C4—22no—
229C4×C22⋊C4—22no—
230C4×C22⋊C4—22no—
231C4×C22⋊C4—22no—
232C4×C22⋊C4—22no—
233C4×C22⋊C4—22no—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238#376—22no—
239C2×#95—21no—
240C2×#95—21no—
241C2×#95—21no—
242C43D411yescharacteristic
243C43D411yescharacteristic
244C43D411yescharacteristic
245C43D411yescharacteristic
246C43C2311yescharacteristic
247C43C2311yescharacteristic
248C43C2311yescharacteristic
249C43C2311yescharacteristic
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2312yes—
259#336C2314yes—
260#336C2312yes—
261C25—21no—
262C22×Q8—21no—
263C22×Q8—21no—
264C22×D4—24no—
265C22×D4—24no—
266C22×D4—21no—
267C22×D4—22no—
268C22×D4C2×Q814yes—
269C22×D4C2412yes—
270C23×C4—28no—
271C23×C4—28no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—28no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—44no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2411yescharacteristic
295C22×C8C2414yes—
296C22×C8C2414yes—
297C4⋊Q8—24no—
298C4⋊Q8—24no—
299#125—28no—
300C22⋊Q8—44no—
301C22⋊Q8—44no—
302C4×Q8—44no—
303C4×Q8—44no—
304C4×D4—28no—
305C4×D4—28no—
306C4×D4—28no—
307C4×D4—28no—
308C4×D4—24no—
309C4×D4—24no—
310C4×D4—24no—
311C4×D4—24no—
312C4×D4—28no—
313C4×D4—28no—
314C4×D4—24no—
315C4×D4—24no—
316C4×D4—24no—
317C4×D4—24no—
318C4×D4C2×Q818yes—
319C4×D4C2×Q818yes—
320C4×D4#4118yes—
321C4×D4#4118yes—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4C2×Q814yes—
341C2×C4⋊C4C2412yes—
342C2×C4⋊C4C2412yes—
343C2×C4⋊C4C2412yes—
344C2×C4⋊C4C2412yes—
345C2×C4⋊C4C2412yes—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—42no—
372C2×C42—48no—
373C2×C42—48no—
374C2×C42—48no—
375C2×C42—42no—
376C2×C42—44no—
377C2×C42—44no—
378C2×C42—44no—
379C2×C42—48no—
380C2×C42C2×D411yescharacteristic
381C2×C42C2×D411yescharacteristic
382C2×C42C2×D411yescharacteristic
383C2×C42C2×D411yescharacteristic
384C2×C42C2×D411yescharacteristic
385C2×C42C2×D411yescharacteristic
386C2×C42C2×D411yescharacteristic
387C2×C42C2×D411yescharacteristic
388C2×C42C2×D411yescharacteristic
389C2×C42C2×D411yescharacteristic
390C2×C42C2×D411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×Q814yes—
403C2×C42#4114yes—
404C2×C42C2411yescharacteristic
405C2×C42C2411yescharacteristic
406C2×C42C2411yescharacteristic
407C2×C42C2411yescharacteristic
408C2×C42C2411yescharacteristic
409C2×C42C2411yescharacteristic
410#107—28no—
411#107—28no—
412#106—28no—
413#106—28no—
414C4⋊C8—28no—
415C4⋊C8—24no—
416C4⋊C8—24no—
417C4⋊C8—28no—
418#102—28no—
419#102—28no—
420#102—28no—
421#102—28no—
422C22⋊C8—24no—
423C22⋊C8—24no—
424C4×C8—28no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—22no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24C22×D411yescharacteristic
454C2×Q8—42no—
455C2×Q8—42no—
456C2×Q8—42no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×D4—24no—
461C2×D4—24no—
462C2×D4—216no—
463C2×D4—216no—
464C2×D4—24no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4C22×Q814yes—
469C2×D4C2×#4114yes—
470C2×D4C2×#4114yes—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—432no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—432no—
512C22×C4—432no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4C22⋊Q814yes—
526C22×C4C22⋊Q814yes—
527C22×C4#13514yes—
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×Q812yes—
542C22×C4C2×#4112yes—
543C22×C4C2511yescharacteristic
544C2×C8—24no—
545C2×C8—24no—
546C2×C8—24no—
547C2×C8—24no—
548C2×C8—24no—
549C2×C8—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—42no—
561C4⋊C4—44no—
562C4⋊C4—42no—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—44no—
570C4⋊C4—42no—
571C4⋊C4—44no—
572C4⋊C4C22×Q814yes—
573C4⋊C4C2×#4114yes—
574C4⋊C4C2×#4114yes—
575C22⋊C4—28no—
576C22⋊C4—28no—
577C22⋊C4—28no—
578C22⋊C4—28no—
579C22⋊C4—28no—
580C22⋊C4—28no—
581C22⋊C4—44no—
582C22⋊C4—44no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—44no—
605C42—44no—
606C42—44no—
607C42—44no—
608C42—44no—
609C42—44no—
610C42—44no—
611C42—44no—
612C42C22⋊Q814yes—
613C42C22⋊Q814yes—
614C42AGL(1,ℤ/8)14yes—
615C42C22×Q812yes—
616C42C22×Q812yes—
617C42C2×#4112yes—
618C42C2×#4112yes—
619C42C2×#4114yes—
620C42C2×#4114yes—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—216no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—48no—
630C23—48no—
631C23—48no—
632C23—48no—
633C23—48no—
634C23—48no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23C2×C22⋊Q812yes—
640C23C2×#13512yes—
641C23#57512yes—
642C23C23×D411yescharacteristic
643Q8—84no—
644Q8—84no—
645D4—216no—
646D4—24no—
647D4—24no—
648D4—24no—
649D4#53318yes—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—416no—
686C2×C4—416no—
687C2×C4—416no—
688C2×C4—416no—
689C2×C4—48no—
690C2×C4—48no—
691C2×C4—48no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—416no—
699C2×C4—416no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4C2×C22⋊Q812yes—
713C2×C4C2×C22⋊Q812yes—
714C2×C4C2×C22⋊Q812yes—
715C2×C4C2×C22⋊Q812yes—
716C2×C4C2×C22⋊Q812yes—
717C2×C4#52512yes—
718C2×C4#52512yes—
719C2×C4#52512yes—
720C2×C4#52512yes—
721C2×C4C2×#13512yes—
722C2×C4C2×#13512yes—
723C2×C4C2×AGL(1,ℤ/8)12yes—
724C2×C4C2×AGL(1,ℤ/8)12yes—
725C2×C4C2×AGL(1,ℤ/8)12yes—
726C2×C4#57512yes—
727C2×C4C23×Q811yescharacteristic
728C2×C4C22×#4112yes—
729C2×C4C22×#4112yes—
730C2×C4C22×#4111yescharacteristic
731C8—44no—
732C8—44no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—28no—
740C22—432no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22#307614yes—
748C22C22×C22⋊Q811yescharacteristic
749C22C2×#52511yescharacteristic
750C22C2×#52511yescharacteristic
751C22C22×#13511yescharacteristic
752C22C22×AGL(1,ℤ/8)11yescharacteristic
753C22C2×#57511yescharacteristic
754C22C2×#57511yescharacteristic
755C4—22no—
756C4—22no—
757C4—22no—
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—44no—
765C4—44no—
766C4—41no—
767C4—44no—
768C4—41no—
769C4—82no—
770C4—82no—
771C4—82no—
772C4—82no—
773C4#307714yes—
774C4#310514yes—
775C4C2×#53312yes—
776C4#344412yes—
777C2—24no—
778C2—48no—
779C2#3662511yescharacteristic
780C2C2×#307611yescharacteristic
781C2C2×#307711yescharacteristic
782C2C2×#310511yescharacteristic
783C2#6053611yescharacteristic
784C2#6055811yescharacteristic
785C2#6056311yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36635C2semidirect
3. #33201C2semidirect
4. #33199C2semidirect
5. #33150C2semidirect
6. #33149C2semidirect
7. #33147C2semidirect
8. #33070C2semidirect
12. C4×#478C2semidirect
13. C4×#476C2semidirect
14. C4×#474C2semidirect
15. #21361C2semidirect
16. #20808C2semidirect
26. #2864C22semidirect
29. #2862C22semidirect
30. #2859C22semidirect
36. C4×C4⋊Q8C22semidirect
37. C4×C4⋊Q8C22semidirect
38. C4×#125C22semidirect
59. #1989C22semidirect
60. #1988C22semidirect
61. #1987C22semidirect
62. #1949C22semidirect
63. #1949C22semidirect
64. #1949C22semidirect
65. #1948C22semidirect
66. #1947C22semidirect
67. #1921C22semidirect
68. #1920C22semidirect
69. #1919C22semidirect
70. #1918C22semidirect
79. #1842C22semidirect
80. #1831C22semidirect
93. C4×#107C22semidirect
94. C4×#106C22semidirect
95. C4×C4⋊C8C22semidirect
96. C4×C4⋊C8C22semidirect
119. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#366352
C2×C42×D42
#332012
#331992
#331502
#331492
#331472
#330702
#329592
#329562
#329532
C4×#4782
C4×#4762
C4×#4742
#213612
#208082
#207332