Finite Group Databasebeta

← #6631366

Subgroups — #6631366

Order 512.

1926 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#32788C211yesmaximal, characteristic, complemented
4#32774C211yesmaximal, characteristic, complemented
5#32770C211yesmaximal, characteristic, complemented
6#32760C211yesmaximal, characteristic, complemented
7#32745C212yesmaximal, complemented
8#32739C212yesmaximal, complemented
9#32723C212yesmaximal, complemented
10#32721C212yesmaximal, complemented
11#32709C214yesmaximal, complemented
12#23757C212yesmaximal, complemented
13#23754C212yesmaximal, complemented
14#23701C214yesmaximal, complemented
15#23570C212yesmaximal, complemented
16#23568C212yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×#525—21no—
21C23×C42C2211yescharacteristic
22C2×C4×SD16C2214yescomplemented
23C2×#431C2212yes—
24#2857C2211yescharacteristic
25#2857C2211yescharacteristic
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2856C2211yescharacteristic
31#2856C2211yescharacteristic
32#2855—21no—
33#2855C2212yes—
34#2854—21no—
35#2854C2212yes—
36#2851—21no—
37#2851—21no—
38#2850—21no—
39#2850—21no—
40#2848—21no—
41#2848C2212yes—
42#2847—21no—
43#2847C2212yes—
44C4×C22⋊Q8—21no—
45C4×C22⋊Q8—21no—
46C4×C22⋊Q8C2212yes—
47C4×C22⋊Q8C2212yes—
48C4×#121—21no—
49C4×#121—21no—
50C4×#121C2212yes—
51C4×#121C2212yes—
52#2297—21no—
53#2296—21no—
54#2285C2211yescharacteristic
55#2285C2211yescharacteristic
56#2280—21no—
57#2100C2212yescomplemented
58#2099C2212yescomplemented
59#2095C2212yescomplemented
60#2093C2212yescomplemented
61#2088C2214yescomplemented
62#2083C2212yescomplemented
63#2083C2212yescomplemented
64#2077C2214yes—
65#2076C2214yes—
66#2075C2214yes—
67#2072C2212yescomplemented
68#2071C2212yescomplemented
69#2068C2214yescomplemented
70#2067C2214yescomplemented
71#2058C2212yescomplemented
72#2058C2212yescomplemented
73#2055C2214yescomplemented
74#2043C2212yescomplemented
75#2041C2212yescomplemented
76#2036C2214yes—
77#2036C2214yes—
78#2035C2214yes—
79#2034C2214yes—
80#2033C2214yes—
81#2033C2214yes—
82#2024C2212yescomplemented
83#2023C2212yescomplemented
84#2014C2212yescomplemented
85#2013C2212yescomplemented
86#2000C2214yes—
87#2000C2214yes—
88#2000C2214yes—
89#1817C2211yescharacteristic
90#1817C2211yescharacteristic
91#1797C2212yes—
92#1797C2212yes—
93#1779C2212yes—
94C4×#107C2214yescomplemented
95C4×#103C2214yescomplemented
96C4×#102C2214yescomplemented
97C4×C22⋊C8C2212yes—
98C4×C22⋊C8C2212yes—
99C22×#41—21no—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C22×SD16C2314yes—
104#533—44no—
105#532—44no—
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×#127C2311yescharacteristic
110C2×#125—21no—
111C2×#124—21no—
112#525—48no—
113C2×#123—22no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8C2312yes—
120C2×C22⋊Q8C2312yes—
121C2×C22⋊Q8C2312yes—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×#121C2312yes—
130C2×#120—22no—
131C2×C4×Q8—21no—
132C2×C4×Q8C2312yes—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—21no—
136C2×C4×D4C2312yes—
137C2×#117—21no—
138C2×#117—21no—
139C2×#117—21no—
140C22×C42—44no—
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C4×SD16—48no—
154#431—44no—
155C2×#107C2314yes—
156C2×#107C2314yes—
157C2×#106C2314yes—
158C2×C4⋊C8C2314yes—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×C22⋊C8C2314yes—
166C2×C22⋊C8C2314yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2312yes—
169C2×C4×C8C2314yes—
170#391—21no—
171#391—21no—
172#391—21no—
173#391—21no—
174#391C2312yes—
175#391C2312yes—
176#390—21no—
177#390—21no—
178#390—21no—
179#390—21no—
180#390C2312yes—
181#390C2312yes—
182#389—21no—
183#389—21no—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189#389—21no—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#389C2312yes—
194#388—22no—
195#388—22no—
196#388—22no—
197#388—22no—
198#387—22no—
199#387—22no—
200#387—22no—
201#387—22no—
202#386—22no—
203#386—22no—
204#386—22no—
205#386—22no—
206#386—22no—
207#386—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#384C2311yescharacteristic
215#384C2311yescharacteristic
216#384C2311yescharacteristic
217#384C2311yescharacteristic
218#382—21no—
219#382—21no—
220#381—22no—
221#380—21no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#379—22no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4C2312yes—
243C4×C4⋊C4C2312yes—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#336C2312yes—
255#336C2312yes—
256#336C2312yes—
257#336C2312yes—
258C25C2×D411yescharacteristic
259C2×#41—44no—
260C2×#41—44no—
261C2×#41—44no—
262C22×Q8—21no—
263C22×Q8—21no—
264C22×Q8C2412yes—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4C2412yes—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
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×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C2×SD16—44no—
300C2×SD16—44no—
301C2×SD16—44no—
302C22×C8C2414yes—
303C22×C8C2414yes—
304C4⋊Q8—42no—
305C4⋊Q8—42no—
306C4⋊Q8—42no—
307#127—42no—
308#125—44no—
309#124—44no—
310#123—48no—
311C22⋊Q8—42no—
312C22⋊Q8—44no—
313C22⋊Q8—42no—
314C22⋊Q8—44no—
315C22⋊Q8—44no—
316C22⋊Q8—44no—
317C22⋊Q8—44no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320#121—42no—
321#121—44no—
322#121—42no—
323#121—44no—
324#121—44no—
325#121—44no—
326#121—44no—
327#121—44no—
328#121—44no—
329#120—48no—
330C4×Q8—28no—
331C4×Q8—44no—
332C4×D4—28no—
333C4×D4—44no—
334C4×D4—48no—
335C4×D4—48no—
336#117—44no—
337#117—44no—
338#117—44no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
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×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2411yescharacteristic
410C2×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412C2×C42C2411yescharacteristic
413#107—44no—
414#107—44no—
415#106—44no—
416C4⋊C8—44no—
417#103—44no—
418#103—44no—
419#103—44no—
420#102—44no—
421#102—44no—
422#102—44no—
423C22⋊C8—44no—
424C22⋊C8—44no—
425C22⋊C8—42no—
426C22⋊C8—42no—
427C4×C8—28no—
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—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—41no—
449C24—41no—
450C24—41no—
451C24—41no—
452C24C22×D411yescharacteristic
453C24C22×D411yescharacteristic
454C24C22×D411yescharacteristic
455#41—816no—
456C2×Q8—24no—
457C2×Q8—22no—
458C2×Q8—24no—
459C2×Q8—22no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×D4—24no—
467C2×D4—22no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—42no—
484C2×D4—42no—
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—22no—
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—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
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—41no—
543C22×C4—416no—
544C22×C4—416no—
545C22×C4—416no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4#13514yes—
550C22×C4AGL(1,ℤ/8)14yes—
551C22×C4#13714yes—
552C22×C4C22×D411yescharacteristic
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×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C2511yescharacteristic
564SD16—416no—
565C2×C8—24no—
566C2×C8—24no—
567C2×C8—24no—
568C2×C8—24no—
569C2×C8—24no—
570C2×C8—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—44no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊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—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—44no—
632C42—44no—
633C42—44no—
634C42H(5,𝔽2)14yes—
635C23—21no—
636C23—21no—
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—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23C2×#13512yes—
668C23C2×AGL(1,ℤ/8)12yes—
669C23C2×#13712yes—
670C23C23×D411yescharacteristic
671Q8—44no—
672Q8—44no—
673Q8—84no—
674Q8—84no—
675D4—44no—
676D4—44no—
677D4—84no—
678D4—84no—
679D4—88no—
680D4—88no—
681D4—88no—
682C2×C4—28no—
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—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
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—44no—
710C2×C4—44no—
711C2×C4—44no—
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—44no—
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×C4—42no—
745C2×C4—88no—
746C2×C4#53412yes—
747C2×C4#53412yes—
748C2×C4C2×#13512yes—
749C2×C4C2×#13512yes—
750C2×C4C2×AGL(1,ℤ/8)12yes—
751C2×C4C2×AGL(1,ℤ/8)12yes—
752C2×C4C2×#13712yes—
753C2×C4C2×#13712yes—
754C2×C4#57512yes—
755C2×C4C2×H(5,𝔽2)12yes—
756C2×C4#58512yes—
757C2×C4#58512yes—
758C8—44no—
759C8—44no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—416no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22C2×#53411yescharacteristic
790C22#344911yescharacteristic
791C22#344911yescharacteristic
792C22C22×#13511yescharacteristic
793C22C22×AGL(1,ℤ/8)11yescharacteristic
794C22C22×#13711yescharacteristic
795C22C2×#57511yescharacteristic
796C4—22no—
797C4—22no—
798C4—22no—
799C4—22no—
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4#319314yes—
814C4#352914yes—
815C2—42no—
816C2—42no—
817C2—42no—
818C2—162no—
819C2#3665211yescharacteristic
820C2#6073411yescharacteristic
821C2C2×#319311yescharacteristic
822C2#6094611yescharacteristic
823C2#6094711yescharacteristic
824C2#6095111yescharacteristic
825C2#6095211yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ 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. #32788C2semidirect
4. #32774C2semidirect
5. #32770C2semidirect
6. #32760C2semidirect
7. #32745C2semidirect
8. #32739C2semidirect
9. #32723C2semidirect
10. #32721C2semidirect
11. #32709C2semidirect
12. #23757C2semidirect
13. #23754C2semidirect
14. #23701C2semidirect
15. #23570C2semidirect
16. #23568C2semidirect
17. #20714C2semidirect
22. C2×C4×SD16C22semidirect
57. #2100C22semidirect
58. #2099C22semidirect
59. #2095C22semidirect
60. #2093C22semidirect
61. #2088C22semidirect
62. #2083C22semidirect
63. #2083C22semidirect
67. #2072C22semidirect
68. #2071C22semidirect
69. #2068C22semidirect
70. #2067C22semidirect
71. #2058C22semidirect
72. #2058C22semidirect
73. #2055C22semidirect
74. #2043C22semidirect
75. #2041C22semidirect
82. #2024C22semidirect
83. #2023C22semidirect
84. #2014C22semidirect
85. #2013C22semidirect
94. C4×#107C22semidirect
95. C4×#103C22semidirect
96. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#327882
#327742
#327702
#327602
#327452
#327392
#327232
#327212
#327092
#237572
#237542
#237012
#235702
#235682
#207142