Finite Group Databasebeta

← #6475833

Subgroups — #6475833

Order 512.

3418 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
1#36625C211yesmaximal, characteristic, complemented
2C22×#390C211yesmaximal, characteristic
3#32983C212yesmaximal, complemented
4#32881C212yesmaximal
5#29950C212yesmaximal, complemented
6#29714C212yesmaximal, complemented
7#29109C212yesmaximal, complemented
8#28311C212yesmaximal, complemented
9#28123C214yesmaximal, complemented
10#27582C212yesmaximal, complemented
11#24507C214yesmaximal, complemented
12#23933C212yesmaximal, complemented
13#22049C214yesmaximal, complemented
14#20715C211yesmaximal, characteristic, complemented
15C24×D4C2211yescharacteristic
16C2×#533C2211yescharacteristic, complemented
17C23×C4⋊C4C2211yescharacteristic
18C23×C22⋊C4—21no—
19C23×C22⋊C4—21no—
20C23×C42C2211yescharacteristic
21C2×#484C2214yescomplemented
22C2×#450C2214yes—
23C2×#450C2214yes—
24C2×#450C2214yes—
25C2×#432C2212yescomplemented
26#2857C2211yescharacteristic, complemented
27#2857C2211yescharacteristic, complemented
28#2857C2211yescharacteristic, complemented
29#2857C2211yescharacteristic, complemented
30#2855—21no—
31#2855C2212yescomplemented
32#2851—21no—
33#2851—21no—
34#2848—21no—
35#2848C2212yes—
36C4×C22⋊Q8—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8C2212yescomplemented
39C4×C22⋊Q8C2212yescomplemented
40#2296—21no—
41C2×#390—21no—
42C2×#390—21no—
43C2×#390—21no—
44C2×#390—21no—
45C2×#390—21no—
46C2×#390—21no—
47C2×#390C2212yes—
48C2×#390C2212yes—
49C2×#390C2212yes—
50C2×#390C2212yes—
51C2×#390C2212yes—
52C2×#390C2212yes—
53#2285C2211yescharacteristic, complemented
54#2280—21no—
55#2093C2214yescomplemented
56#2071C2214yescomplemented
57#2067C2218yescomplemented
58#2055C2218yescomplemented
59#2023C2214yescomplemented
60#2013C2214yescomplemented
61#1973C2218yescomplemented
62#1936C2218yescomplemented
63#1925C2218yescomplemented
64#1880C2218yescomplemented
65#1872C2214yescomplemented
66#1872C2214yescomplemented
67#1852C2214yescomplemented
68#1852C2214yescomplemented
69#1824C2214yescomplemented
70#1817C2212yescomplemented
71#1797C2212yescomplemented
72#1797C2212yescomplemented
73#1786C2214yes—
74#1786C2214yes—
75#1786C2214yes—
76#1779C2212yes—
77#1749C2212yescomplemented
78#1749C2212yescomplemented
79C26—21no—
80C23×D4—28no—
81C23×D4—21no—
82C23×D4—21no—
83C23×D4—21no—
84C23×D4—44no—
85C23×D4—44no—
86C23×D4C2312yes—
87C23×D4C2312yes—
88C23×D4C2312yes—
89C24×C4—21no—
90C24×C4D411yescharacteristic
91C24×C4D411yescharacteristic
92C24×C4C2311yescharacteristic
93C22×SD16C2318yes—
94#533—44no—
95C2×C4⋊Q8C2311yescharacteristic, complemented
96C2×C4⋊Q8C2311yescharacteristic, complemented
97C2×#125—21no—
98C2×C22⋊Q8—21no—
99C2×C22⋊Q8—21no—
100C2×C22⋊Q8—21no—
101C2×C22⋊Q8C2312yes—
102C2×C22⋊Q8C2312yes—
103C2×C22⋊Q8C2312yes—
104C2×C4×Q8—21no—
105C2×C4×Q8C2312yescomplemented
106C2×#117—21no—
107C2×#117—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—44no—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C22⋊C4—22no—
116C22×C22⋊C4—22no—
117C22×C22⋊C4—22no—
118C22×C22⋊C4—22no—
119C22×C22⋊C4—22no—
120C22×C22⋊C4—22no—
121C22×C22⋊C4—22no—
122C22×C22⋊C4—22no—
123C22×C22⋊C4—22no—
124C22×C22⋊C4—22no—
125C22×C22⋊C4—22no—
126C22×C22⋊C4—22no—
127C22×C22⋊C4—48no—
128C22×C22⋊C4—48no—
129C22×C42—44no—
130C22×C42D411yescharacteristic
131C22×C42D411yescharacteristic
132C22×C42D411yescharacteristic
133C22×C42D411yescharacteristic
134C22×C42D411yescharacteristic
135C22×C42D411yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142#484—48no—
143#450—216no—
144#450—48no—
145#450—48no—
146#432—44no—
147C2×#107C2318yescomplemented
148C2×C4⋊C8C2314yescomplemented
149C2×#103C2318yescomplemented
150C2×#102C2318yes—
151C2×#102C2318yes—
152C2×#102C2318yes—
153C2×C22⋊C8C2314yes—
154C2×C22⋊C8C2314yes—
155C2×C22⋊C8C2314yes—
156C2×#97C2314yescomplemented
157#391—21no—
158#391—21no—
159#391C2312yescomplemented
160#391C2312yescomplemented
161#390—22no—
162#390—22no—
163#390—22no—
164#390—22no—
165#390—22no—
166#390—22no—
167#390—22no—
168#390—22no—
169#390—22no—
170#390—22no—
171#390—22no—
172#390—22no—
173#390C2314yes—
174#390C2314yes—
175#390C2314yes—
176#390C2314yes—
177#389—21no—
178#389—21no—
179#389—21no—
180#389—21no—
181#389—21no—
182#389—21no—
183#389C2312yescomplemented
184#389C2312yescomplemented
185#387—22no—
186#387—22no—
187#387—22no—
188#387—22no—
189#385—22no—
190#385—22no—
191#385—22no—
192#385—22no—
193#385—22no—
194#385—22no—
195#384C2311yescharacteristic, complemented
196#384C2311yescharacteristic, complemented
197#382—21no—
198#381—22no—
199#380—21no—
200#380—21no—
201#380—21no—
202#380—21no—
203#380—21no—
204#380—21no—
205#380—21no—
206#380C2312yes—
207#380C2312yes—
208#380C2312yes—
209#379—22no—
210C4×C4⋊C4—21no—
211C4×C4⋊C4—22no—
212C4×C4⋊C4—22no—
213C4×C4⋊C4C2312yescomplemented
214C4×C22⋊C4—22no—
215C4×C22⋊C4—22no—
216#340C2318yescomplemented
217#340C2318yescomplemented
218#336C2314yescomplemented
219#336C2314yescomplemented
220C25—28no—
221C25—22no—
222C25—22no—
223C25—22no—
224C25—44no—
225C25—44no—
226C25—44no—
227C25—44no—
228C25—44no—
229C25—44no—
230C25C2×D411yescharacteristic
231C22×Q8—21no—
232C22×Q8C2412yes—
233C22×D4—28no—
234C22×D4—28no—
235C22×D4—28no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—24no—
242C22×D4—28no—
243C22×D4—28no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—464no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4#4118yes—
256C22×D4C2414yes—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C2×SD16—216no—
291C2×SD16—48no—
292C2×SD16—48no—
293C22×C8C2418yes—
294C4⋊Q8—42no—
295C4⋊Q8—42no—
296#125—44no—
297C22⋊Q8—28no—
298C22⋊Q8—28no—
299C22⋊Q8—28no—
300C22⋊Q8—44no—
301C22⋊Q8—44no—
302C22⋊Q8—44no—
303C4×Q8—44no—
304C4×Q8—44no—
305#117—44no—
306#117—44no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4C2414yes—
330C2×C4⋊C4C2412yes—
331C2×C4⋊C4C2412yes—
332C2×C4⋊C4C2412yes—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—48no—
348C2×C22⋊C4—48no—
349C2×C22⋊C4—48no—
350C2×C22⋊C4—48no—
351C2×C22⋊C4—48no—
352C2×C22⋊C4—48no—
353C2×C22⋊C4—48no—
354C2×C22⋊C4—48no—
355C2×C22⋊C4—48no—
356C2×C22⋊C4—48no—
357C2×C22⋊C4—48no—
358C2×C22⋊C4—48no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—42no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42C2×D411yescharacteristic
374C2×C42C2×D411yescharacteristic
375C2×C42C2×D411yescharacteristic
376C2×C42C2×D411yescharacteristic
377C2×C42C2×D411yescharacteristic
378C2×C42C2×D411yescharacteristic
379C2×C42C2×D411yescharacteristic
380C2×C42C2×D411yescharacteristic
381C2×C42C2×D411yescharacteristic
382C2×C42C2×D411yescharacteristic
383C2×C42C2×D411yescharacteristic
384C2×C42C2×D411yescharacteristic
385C2×C42C2411yescharacteristic
386C2×C42C2411yescharacteristic
387C2×C42C2411yescharacteristic
388C2×C42C2411yescharacteristic
389#107—48no—
390C4⋊C8—44no—
391#103—48no—
392#102—216no—
393#102—48no—
394#102—48no—
395C22⋊C8—28no—
396C22⋊C8—28no—
397C22⋊C8—28no—
398#97—44no—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—28no—
416C24—28no—
417C24—28no—
418C24—24no—
419C24—44no—
420C24—44no—
421C24—44no—
422C24—44no—
423C24—432no—
424C24—44no—
425C24—44no—
426C24—44no—
427C24—44no—
428C24—432no—
429C24—432no—
430C24—44no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24—44no—
435C24—44no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—44no—
440C24—816no—
441C24—816no—
442C24—816no—
443C24—816no—
444C24#13714yes—
445C24C22×D411yescharacteristic
446C24C22×D411yescharacteristic
447C24C22×D411yescharacteristic
448C2×Q8—24no—
449C2×Q8—24no—
450C2×Q8—24no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8—42no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—24no—
458C2×D4—28no—
459C2×D4—28no—
460C2×D4—416no—
461C2×D4—432no—
462C2×D4—432no—
463C2×D4—432no—
464C2×D4—432no—
465C2×D4—432no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—416no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4C2×#4118yes—
474C22×C4—232no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—416no—
530C22×C4—416no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—816no—
541C22×C4AGL(1,ℤ/8)14yes—
542C22×C4AGL(1,ℤ/8)14yes—
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C2×#4114yes—
555C22×C4H(5,𝔽2)14yes—
556C22×C4H(5,𝔽2)14yes—
557C22×C4C2511yescharacteristic
558SD16—816no—
559C2×C8—28no—
560C2×C8—28no—
561C2×C8—28no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—28no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—44no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—44no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—44no—
587C22⋊C4—44no—
588C22⋊C4—44no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C42—41no—
609C42—41no—
610C42—41no—
611C42—41no—
612C42—44no—
613C42—44no—
614C23—28no—
615C23—28no—
616C23—28no—
617C23—28no—
618C23—28no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—28no—
626C23—28no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—28no—
634C23—416no—
635C23—416no—
636C23—416no—
637C23—416no—
638C23—416no—
639C23—416no—
640C23—416no—
641C23—416no—
642C23—416no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—8128no—
650C23—88no—
651C23—88no—
652C23—88no—
653C23—88no—
654C23—88no—
655C23—88no—
656C23—88no—
657C23—88no—
658C23—88no—
659C23—88no—
660C23—88no—
661C23—88no—
662C23#52512yes—
663C23#53412yes—
664C23#53512yes—
665C23C2×AGL(1,ℤ/8)12yes—
666C23C2×AGL(1,ℤ/8)12yes—
667C23C2×#13712yes—
668C23C2×#13712yes—
669C23C2×#13712yes—
670C23#57512yes—
671C23C23×D411yescharacteristic
672Q8—48no—
673Q8—84no—
674D4—216no—
675D4—416no—
676D4—416no—
677D4—416no—
678D4—48no—
679C2×C4—28no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—28no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—88no—
739C2×C4—88no—
740C2×C4—88no—
741C2×C4#52512yes—
742C2×C4#53412yes—
743C2×C4#53512yes—
744C2×C4C2×AGL(1,ℤ/8)12yes—
745C2×C4C2×AGL(1,ℤ/8)12yes—
746C2×C4C2×AGL(1,ℤ/8)12yes—
747C2×C4C2×AGL(1,ℤ/8)12yes—
748C2×C4C22×#4112yes—
749C2×C4C2×H(5,𝔽2)12yes—
750C2×C4C2×H(5,𝔽2)12yes—
751C8—48no—
752C22—232no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—48no—
772C22—48no—
773C22—48no—
774C22—832no—
775C22—832no—
776C22—832no—
777C22—84no—
778C22—84no—
779C22—84no—
780C22—84no—
781C22#311014yes—
782C22#319314yes—
783C22#321514yes—
784C22C2×#52511yescharacteristic
785C22C2×#53411yescharacteristic
786C22C2×#53511yescharacteristic
787C22C22×AGL(1,ℤ/8)11yescharacteristic
788C22C22×AGL(1,ℤ/8)11yescharacteristic
789C22C22×#13711yescharacteristic
790C22C2×#57511yescharacteristic
791C4—22no—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—82no—
803C4—82no—
804C4—84no—
805C4—82no—
806C4—82no—
807C4#349014yes—
808C2—24no—
809C2—24no—
810C2—24no—
811C2—88no—
812C2#3505011yescharacteristic
813C2C2×#311011yescharacteristic
814C2#6055811yescharacteristic
815C2C2×#319311yescharacteristic
816C2#6075011yescharacteristic
817C2C2×#321511yescharacteristic
818C2#6079811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24×D4C22
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. #36625C2semidirect
3. #32983C2semidirect
5. #29950C2semidirect
6. #29714C2semidirect
7. #29109C2semidirect
8. #28311C2semidirect
9. #28123C2semidirect
10. #27582C2semidirect
11. #24507C2semidirect
12. #23933C2semidirect
13. #22049C2semidirect
14. #20715C2semidirect
16. C2×#533C22semidirect
21. C2×#484C22semidirect
25. C2×#432C22semidirect
26. #2857C22semidirect
27. #2857C22semidirect
28. #2857C22semidirect
29. #2857C22semidirect
31. #2855C22semidirect
38. C4×C22⋊Q8C22semidirect
39. C4×C22⋊Q8C22semidirect
53. #2285C22semidirect
55. #2093C22semidirect
56. #2071C22semidirect
57. #2067C22semidirect
58. #2055C22semidirect
59. #2023C22semidirect
60. #2013C22semidirect
61. #1973C22semidirect
62. #1936C22semidirect
63. #1925C22semidirect
64. #1880C22semidirect
65. #1872C22semidirect
66. #1872C22semidirect
67. #1852C22semidirect
68. #1852C22semidirect
69. #1824C22semidirect
70. #1817C22semidirect
71. #1797C22semidirect
72. #1797C22semidirect
77. #1749C22semidirect
78. #1749C22semidirect
95. C2×C4⋊Q8C23semidirect
96. C2×C4⋊Q8C23semidirect
105. C2×C4×Q8C23semidirect
147. C2×#107C23semidirect
148. C2×C4⋊C8C23semidirect
149. C2×#103C23semidirect
156. C2×#97C23semidirect
159. #391C23semidirect
160. #391C23semidirect
183. #389C23semidirect
184. #389C23semidirect
195. #384C23semidirect
196. #384C23semidirect
213. C4×C4⋊C4C23semidirect
216. #340C23semidirect
217. #340C23semidirect
218. #336C23semidirect
219. #336C23semidirect

Maximal subgroups

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

subgroupindex
#366252
C22×#3902
#329832
#328812
#299502
#297142
#291092
#283112
#281232
#275822
#245072
#239332
#220492
#207152