Finite Group Databasebeta

← #6493718

Subgroups — #6493718

Order 512.

1752 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic
3#33154C212yesmaximal, complemented
4#33114C212yesmaximal, complemented
5#29941C212yesmaximal, complemented
6#29926C212yesmaximal, complemented
7#27866C214yesmaximal, complemented
8#27682C212yesmaximal, complemented
9#27649C212yesmaximal, complemented
10#27629C212yesmaximal, complemented
11#27628C212yesmaximal, complemented
12#24561C214yesmaximal
13#21964C211yesmaximal, characteristic, complemented
14#21964C211yesmaximal, characteristic, complemented
15#21894C211yesmaximal, characteristic, complemented
16#21894C211yesmaximal, characteristic, complemented
17#20626C211yesmaximal, characteristic
18C2×#533C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C2×#485C2214yes—
21C2×#423C2211yescharacteristic
22C2×#423C2211yescharacteristic
23C2×#407C2212yes—
24#2857C2211yescharacteristic
25#2857C2211yescharacteristic
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2855—21no—
29#2855C2212yes—
30#2851—21no—
31#2851—21no—
32#2848—21no—
33#2848C2212yes—
34C4×C22⋊Q8—21no—
35C4×C22⋊Q8—21no—
36C4×C22⋊Q8C2212yes—
37C4×C22⋊Q8C2212yes—
38#2296—21no—
39#2285C2211yescharacteristic
40#2285C2211yescharacteristic
41#2285C2211yescharacteristic
42#2285C2211yescharacteristic
43#2285C2211yescharacteristic
44#2285C2211yescharacteristic
45#2285C2211yescharacteristic
46#2283—21no—
47#2283—21no—
48#2283—21no—
49#2283—21no—
50#2283C2212yes—
51#2283C2212yes—
52#2280—21no—
53#2280—21no—
54#2280—21no—
55#2280C2212yes—
56C4×#117—21no—
57C4×#117—21no—
58C4×#117C2212yes—
59#2101C2214yescomplemented
60#2097C2214yescomplemented
61#2085C2214yescomplemented
62#2077C2214yes—
63#2076C2214yes—
64#2074C2214yescomplemented
65#2036C2214yes—
66#2035C2214yes—
67#1988C2212yescomplemented
68#1988C2212yescomplemented
69#1981C2212yescomplemented
70#1981C2212yescomplemented
71#1948C2212yescomplemented
72#1948C2212yescomplemented
73#1948C2212yescomplemented
74#1948C2212yescomplemented
75#1947C2212yescomplemented
76#1947C2212yescomplemented
77#1947C2212yescomplemented
78#1947C2212yescomplemented
79#1928C2214yescomplemented
80#1927C2214yescomplemented
81#1921C2214yescomplemented
82#1920C2214yescomplemented
83#1894C2214yes—
84#1894C2214yes—
85#1873C2214yes—
86#1854C2214yes—
87#1825C2214yes—
88#1809C2214yes—
89#1809C2214yes—
90#1803C2212yescomplemented
91#1803C2212yescomplemented
92#1803C2212yescomplemented
93#1803C2212yescomplemented
94#1797C2212yes—
95#1797C2212yes—
96#1797C2212yes—
97#1797C2212yes—
98#1728C2212yes—
99C24×C4D411yescharacteristic
100C24×C4D411yescharacteristic
101C24×C4C2311yescharacteristic
102C22×M16C2312yes—
103C22×M16C2312yes—
104#533—24no—
105#533—24no—
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×#125—21no—
109C2×C22⋊Q8—21no—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8C2312yes—
113C2×C22⋊Q8C2312yes—
114C2×C22⋊Q8C2312yes—
115C2×C4×Q8—21no—
116C2×C4×Q8C2312yes—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117C2312yes—
124C2×#117C2312yes—
125C22×C42—24no—
126C22×C42—24no—
127C22×C42D411yescharacteristic
128C22×C42D411yescharacteristic
129C22×C42D411yescharacteristic
130C22×C42D411yescharacteristic
131C22×C42D411yescharacteristic
132C22×C42D411yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139#485—48no—
140C2×#107C2314yes—
141C2×#107C2314yes—
142C2×#106C2314yes—
143C2×#106C2314yes—
144#423—24no—
145#423—24no—
146C2×C4⋊C8C2312yes—
147C2×C4⋊C8C2312yes—
148C2×C4⋊C8C2312yes—
149C2×C4⋊C8C2312yes—
150C2×#103C2314yes—
151C2×#103C2314yes—
152C2×#103C2314yes—
153C2×#103C2314yes—
154#407—44no—
155C2×C22⋊C8C2314yes—
156C2×C22⋊C8C2314yes—
157#391—21no—
158#391—21no—
159#391C2312yes—
160#391C2312yes—
161#389—21no—
162#389—21no—
163#389—21no—
164#389—21no—
165#389—21no—
166#389—21no—
167#389C2312yes—
168#389C2312yes—
169#387—22no—
170#387—22no—
171#387—22no—
172#387—22no—
173#385—22no—
174#385—22no—
175#385—22no—
176#385—22no—
177#385—22no—
178#385—22no—
179#384C2311yescharacteristic
180#384C2311yescharacteristic
181#384C2311yescharacteristic
182#384C2311yescharacteristic
183#384C2311yescharacteristic
184#384C2311yescharacteristic
185#383—22no—
186#383—22no—
187#382—21no—
188#382—21no—
189#382—21no—
190#382—21no—
191#382—21no—
192#382C2312yes—
193#382C2312yes—
194#381—22no—
195#381—22no—
196#381—22no—
197#381—22no—
198#380—21no—
199#380—21no—
200#380—21no—
201#380—21no—
202#380—21no—
203#380—21no—
204#380—21no—
205#380—21no—
206#380—21no—
207#380—21no—
208#380—21no—
209#380—21no—
210#380—21no—
211#380—21no—
212#380—21no—
213#380C2312yes—
214#380C2312yes—
215#380C2312yes—
216#380C2312yes—
217#380C2312yes—
218#380C2312yes—
219#380C2312yes—
220#379—22no—
221#379—22no—
222C4×C4⋊C4—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⋊C4—22no—
232C4×C4⋊C4—22no—
233C4×C4⋊C4C2312yes—
234C4×C4⋊C4C2312yes—
235C4×C4⋊C4C2312yes—
236C4×C4⋊C4C2312yes—
237C4×C4⋊C4C2312yes—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246#376—22no—
247#376—22no—
248#376—22no—
249C43—22no—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2314yes—
259#336C2314yes—
260C25C2×D411yescharacteristic
261C22×Q8—21no—
262C22×Q8C2412yes—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—41no—
274C23×C4—41no—
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×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C2×M16—24no—
294C2×M16—24no—
295C2×M16—42no—
296C2×M16—42no—
297C2×M16—42no—
298C2×M16—42no—
299C22×C8C2414yes—
300C22×C8C2414yes—
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303C4⋊Q8—22no—
304C4⋊Q8—22no—
305#125—44no—
306C22⋊Q8—24no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—42no—
311C22⋊Q8—42no—
312C22⋊Q8—44no—
313C22⋊Q8—44no—
314C22⋊Q8—44no—
315C4×Q8—24no—
316C4×Q8—24no—
317C4×Q8—44no—
318#117—24no—
319#117—24no—
320#117—42no—
321#117—42no—
322#117—44no—
323#117—44no—
324#117—44no—
325#117—44no—
326#117—44no—
327#117—44no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
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×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42#4114yes—
405C2×C42#4114yes—
406C2×C42C2411yescharacteristic
407C2×C42C2411yescharacteristic
408C2×C42C2411yescharacteristic
409C2×C42C2411yescharacteristic
410#107—44no—
411#107—44no—
412#106—44no—
413#106—44no—
414C4⋊C8—24no—
415C4⋊C8—24no—
416C4⋊C8—24no—
417C4⋊C8—24no—
418#103—44no—
419#103—44no—
420#103—44no—
421#103—44no—
422C22⋊C8—28no—
423C22⋊C8—44no—
424#95—22no—
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—
445#95—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—41no—
450C24—41no—
451C24—41no—
452C24—41no—
453C24C22×D411yescharacteristic
454C24C22×D411yescharacteristic
455C24C22×D411yescharacteristic
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
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—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
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—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—416no—
535C22×C4#12314yes—
536C22×C4#12314yes—
537C22×C4#13714yes—
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4H(5,𝔽2)12yes—
552C22×C42−1+412yes—
553C22×C4C2511yescharacteristic
554M16—84no—
555M16—84no—
556C2×C8—24no—
557C2×C8—24no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8—24no—
561C2×C8—24no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—42no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—44no—
624C42—44no—
625C42—44no—
626C42—44no—
627C42—44no—
628C42—44no—
629C42—44no—
630C42—44no—
631C42#12314yes—
632C42#12314yes—
633C42C2×#4112yes—
634C42C2×#4112yes—
635C42C2×#4112yes—
636C42C2×#4112yes—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23C2×#12312yes—
663C23#53712yes—
664C23C2×#13712yes—
665C23C23×D411yescharacteristic
666Q8—42no—
667Q8—42no—
668Q8—42no—
669Q8—42no—
670Q8—84no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—28no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
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—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
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×C4C2×#12312yes—
745C2×C4C2×#12312yes—
746C2×C4C2×#12312yes—
747C2×C4C2×#12312yes—
748C2×C4C2×#12312yes—
749C2×C4#53712yes—
750C2×C4C2×#13712yes—
751C2×C4C2×#13712yes—
752C2×C4#57512yes—
753C2×C4#57512yes—
754C2×C4#57512yes—
755C2×C4C22×#4111yescharacteristic
756C2×C4C22×#4111yescharacteristic
757C2×C4C2×H(5,𝔽2)11yescharacteristic
758C2×C4C2×2−1+411yescharacteristic
759C2×C4#58511yescharacteristic
760C2×C4#58511yescharacteristic
761C8—44no—
762C8—44no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—416no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22C22×#12311yescharacteristic
786C22C2×#53711yescharacteristic
787C22#344911yescharacteristic
788C22C22×#13711yescharacteristic
789C22C2×#57511yescharacteristic
790C22C2×#57511yescharacteristic
791C22C2×#57511yescharacteristic
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—22no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4#309314yes—
810C4#309514yes—
811C4#349411yescharacteristic
812C4#349411yescharacteristic
813C4#349511yescharacteristic
814C4#349511yescharacteristic
815C2—42no—
816C2—42no—
817C2—42no—
818C2#3526311yescharacteristic
819C2C2×#309311yescharacteristic
820C2C2×#309511yescharacteristic
821C2#6090711yescharacteristic
822C2#6091811yescharacteristic
823C2#6095211yescharacteristic
824C2#6096711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
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
3. #33154C2semidirect
4. #33114C2semidirect
5. #29941C2semidirect
6. #29926C2semidirect
7. #27866C2semidirect
8. #27682C2semidirect
9. #27649C2semidirect
10. #27629C2semidirect
11. #27628C2semidirect
13. #21964C2semidirect
14. #21964C2semidirect
15. #21894C2semidirect
16. #21894C2semidirect
59. #2101C22semidirect
60. #2097C22semidirect
61. #2085C22semidirect
64. #2074C22semidirect
67. #1988C22semidirect
68. #1988C22semidirect
69. #1981C22semidirect
70. #1981C22semidirect
71. #1948C22semidirect
72. #1948C22semidirect
73. #1948C22semidirect
74. #1948C22semidirect
75. #1947C22semidirect
76. #1947C22semidirect
77. #1947C22semidirect
78. #1947C22semidirect
79. #1928C22semidirect
80. #1927C22semidirect
81. #1921C22semidirect
82. #1920C22semidirect
90. #1803C22semidirect
91. #1803C22semidirect
92. #1803C22semidirect
93. #1803C22semidirect

Maximal subgroups

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

subgroupindex
#366252
#340122
#331542
#331142
#299412
#299262
#278662
#276822
#276492
#276292
#276282
#245612
#219642
#218942
#206262