Finite Group Databasebeta

← #6435282

Subgroups — #6435282

Order 512.

1750 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36645C211yesmaximal, characteristic, complemented
2C4×#529C211yesmaximal, characteristic
3#30116C212yesmaximal, complemented
4#30113C212yesmaximal
5#30067C212yesmaximal, complemented
6#30046C212yesmaximal, complemented
7#29983C211yesmaximal, characteristic, complemented
8#29980C211yesmaximal, characteristic, complemented
9#29926C212yesmaximal, complemented
10#29799C211yesmaximal, characteristic, complemented
11#29798C211yesmaximal, characteristic, complemented
12#29665C212yesmaximal
13#23820C212yesmaximal, complemented
14#23797C212yesmaximal, complemented
15#23571C212yesmaximal, complemented
16#23568C212yesmaximal
17C4×#462C212yesmaximal, complemented
18C4×#461C212yesmaximal, complemented
19#20777C211yesmaximal, characteristic, complemented
20C2×#533C2212yes—
21C2×#529C2211yescharacteristic
22C2×#462C2212yes—
23C2×#461C2212yes—
24C2×C4×Q16C2214yes—
25C2×C4×SD16C2214yes—
26#2868C2211yescharacteristic
27#2868C2211yescharacteristic
28#2862C2212yes—
29#2859—21no—
30#2859—21no—
31#2857—21no—
32#2857—21no—
33#2857C2212yes—
34#2857C2212yes—
35C4×C4⋊Q8—21no—
36C4×C4⋊Q8—21no—
37C4×C4⋊Q8C2212yes—
38C4×C4⋊Q8C2212yes—
39C4×#125C2211yescharacteristic
40C4×#125C2211yescharacteristic
41C4×#126—21no—
42C4×#126—21no—
43C4×#124C2211yescharacteristic
44C4×#124C2211yescharacteristic
45C4×C22⋊Q8C2211yescharacteristic
46C4×C22⋊Q8C2211yescharacteristic
47C4×#123—21no—
48C4×#123—21no—
49C4×#121C2211yescharacteristic
50C4×#121C2211yescharacteristic
51#2298—21no—
52#2295C2211yescharacteristic
53#2293C2211yescharacteristic
54#2290—21no—
55#2285—21no—
56#2285—21no—
57#2283C2211yescharacteristic
58C42×Q8C2211yescharacteristic
59C42×D4—21no—
60C42×D4C2211yescharacteristic
61C4×#117—21no—
62C2×C43C2211yescharacteristic
63#2099C2212yes—
64#2099C2212yes—
65#2097C2214yes—
66#2096C2212yes—
67#2093C2212yes—
68#2074C2214yes—
69#2058C2212yes—
70#2057C2212yes—
71#2043C2212yes—
72#2043C2212yes—
73#2043C2212yes—
74#2043C2212yes—
75#2036C2214yes—
76#2035C2214yes—
77#2026C2214yes—
78#2024C2212yes—
79#2023C2212yes—
80#2016C2212yes—
81#2016C2212yes—
82#2015C2214yes—
83#2013C2212yes—
84#2013C2212yes—
85#2001C2214yes—
86#2000C2214yes—
87#1981C2212yes—
88#1981C2212yes—
89#1948C2212yes—
90#1947C2212yes—
91#1928C2214yes—
92#1927C2214yes—
93#1878C2214yes—
94#1877C2214yes—
95#1839C2212yes—
96#1831C2211yescharacteristic
97#1831C2211yescharacteristic
98#1817C2212yes—
99#1803C2212yes—
100#1802C2212yes—
101#1797C2212yes—
102C4×C4⋊C8C2212yes—
103C4×#103C2214yes—
104C4×#103C2214yes—
105C4×C22⋊C8C2212yes—
106#1744C2212yes—
107C22×Q16C2314yes—
108C22×SD16C2314yes—
109#533—48no—
110C2×C4⋊Q8—21no—
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8C2312yes—
113C2×C4⋊Q8C2312yes—
114C2×C4⋊Q8C2312yes—
115C2×C4⋊Q8C2312yes—
116#529—24no—
117#529—24no—
118C2×#126—21no—
119C2×#125—22no—
120C2×#125C2311yescharacteristic
121C2×#124C2311yescharacteristic
122C2×#123—21no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8C2311yescharacteristic
125C2×C22⋊Q8C2314yes—
126C2×#121C2311yescharacteristic
127C2×C4×Q8—22no—
128C2×C4×Q8C2314yes—
129C2×C4×Q8C2311yescharacteristic
130C2×C4×Q8C2311yescharacteristic
131C2×C4×Q8C2311yescharacteristic
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4C2311yescharacteristic
136C2×C4×D4C2311yescharacteristic
137C2×C4×D4C2311yescharacteristic
138C2×#117—22no—
139C2×#117—21no—
140C2×#117—21no—
141C22×C42—21no—
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149#462—28no—
150#461—28no—
151C4×Q16—48no—
152C4×SD16—48no—
153C2×#107C2314yes—
154C2×#106C2314yes—
155C2×C4⋊C8C2312yes—
156C2×C4⋊C8C2312yes—
157C2×#103C2314yes—
158C2×#103C2314yes—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#102C2314yes—
165C2×C22⋊C8C2314yes—
166C2×C4×C8C2314yes—
167#391—22no—
168#391—22no—
169#391C2314yes—
170#391C2314yes—
171#391C2311yescharacteristic
172#391C2311yescharacteristic
173#390C2311yescharacteristic
174#390C2311yescharacteristic
175#389—22no—
176#389—22no—
177#389—22no—
178#389—22no—
179#389—22no—
180#389—22no—
181#389—22no—
182#389—22no—
183#389C2311yescharacteristic
184#389C2311yescharacteristic
185#389C2311yescharacteristic
186#389C2311yescharacteristic
187#388—21no—
188#388—21no—
189#388—21no—
190#388—21no—
191#388—21no—
192#388—21no—
193#388—21no—
194#388—21no—
195#387—21no—
196#387—21no—
197#387—21no—
198#387—21no—
199#387—21no—
200#387—21no—
201#387—21no—
202#387—21no—
203#386—21no—
204#386—21no—
205#385—21no—
206#385—21no—
207#384—21no—
208#384—21no—
209#384—21no—
210#384—21no—
211#384—21no—
212#384—21no—
213#384C2312yes—
214#384C2312yes—
215#383—21no—
216#382—22no—
217#382—22no—
218#382C2311yescharacteristic
219#382C2311yescharacteristic
220#381—21no—
221#380—22no—
222#380—22no—
223#380—22no—
224#380—22no—
225#380C2311yescharacteristic
226#380C2311yescharacteristic
227C4×C4⋊C4—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4—22no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4C2311yescharacteristic
242C4×C4⋊C4C2311yescharacteristic
243C4×C4⋊C4C2311yescharacteristic
244C4×C4⋊C4C2311yescharacteristic
245C4×C4⋊C4C2311yescharacteristic
246C4×C4⋊C4C2311yescharacteristic
247C4×C22⋊C4—21no—
248C4×C22⋊C4—21no—
249C4×C22⋊C4—21no—
250C4×C22⋊C4—21no—
251C4×C22⋊C4—21no—
252C4×C22⋊C4—21no—
253C4×C22⋊C4—21no—
254C4×C22⋊C4—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260#376—21no—
261#376—21no—
262C43—21no—
263C43D411yescharacteristic
264C43D411yescharacteristic
265C43D411yescharacteristic
266C43D411yescharacteristic
267C43C2311yescharacteristic
268C43C2311yescharacteristic
269C43C2311yescharacteristic
270C43C2311yescharacteristic
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#336C2314yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280#336C2314yes—
281C22×Q8—22no—
282C22×Q8C2414yes—
283C22×Q8C2411yescharacteristic
284C22×D4—21no—
285C22×D4C2411yescharacteristic
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2411yescharacteristic
296C2×Q16—28no—
297C2×Q16—44no—
298C2×Q16—44no—
299C2×SD16—28no—
300C2×SD16—44no—
301C2×SD16—44no—
302C22×C8C2414yes—
303C22×C8C2414yes—
304C4⋊Q8—24no—
305C4⋊Q8—24no—
306C4⋊Q8—44no—
307C4⋊Q8—44no—
308C4⋊Q8—44no—
309C4⋊Q8—44no—
310C4⋊Q8—44no—
311#126—28no—
312#125—22no—
313#125—22no—
314#125—48no—
315#124—22no—
316#124—22no—
317#123—28no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8—44no—
321C22⋊Q8—44no—
322C22⋊Q8—48no—
323#121—22no—
324#121—22no—
325C4×Q8—22no—
326C4×Q8—28no—
327C4×Q8—28no—
328C4×Q8—24no—
329C4×Q8—42no—
330C4×Q8—48no—
331C4×Q8#4114yes—
332C4×D4—28no—
333C4×D4—22no—
334C4×D4—24no—
335C4×D4—42no—
336C4×D4—44no—
337C4×D4—44no—
338C4×D4#4114yes—
339#117—28no—
340#117—48no—
341#117—44no—
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—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4C2411yescharacteristic
366C2×C4⋊C4C2411yescharacteristic
367C2×C4⋊C4C2414yes—
368C2×C4⋊C4C2411yescharacteristic
369C2×C4⋊C4C2411yescharacteristic
370C2×C4⋊C4C2411yescharacteristic
371C2×C4⋊C4C2411yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—24no—
387C2×C42—21no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—24no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—24no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—44no—
405C2×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433#107—44no—
434#106—44no—
435C4⋊C8—24no—
436C4⋊C8—24no—
437#103—28no—
438#103—28no—
439#103—44no—
440#103—44no—
441#103—44no—
442#103—44no—
443#103—44no—
444#102—44no—
445C22⋊C8—44no—
446C4×C8—28no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—24no—
468#95—24no—
469#95—24no—
470#95—24no—
471C24—21no—
472C24C22×D411yescharacteristic
473C2×Q8—21no—
474C2×Q8—24no—
475C2×Q8—24no—
476C2×Q8—22no—
477C2×Q8—24no—
478C2×Q8—24no—
479C2×Q8—22no—
480C2×Q8—24no—
481C2×Q8—24no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8C2×#4112yes—
486C2×D4—24no—
487C2×D4—21no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4C2×#4112yes—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4#13714yes—
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×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C2511yescharacteristic
547Q16—416no—
548SD16—416no—
549C2×C8—24no—
550C2×C8—24no—
551C2×C8—24no—
552C2×C8—24no—
553C2×C8—24no—
554C2×C8—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—24no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—42no—
570C4⋊C4—48no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—42no—
578C4⋊C4—48no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—44no—
586C4⋊C4C2×#4112yes—
587C4⋊C4C2×#4112yes—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—42no—
594C22⋊C4—48no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C42—22no—
603C42—22no—
604C42—24no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
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—22no—
622C42—22no—
623C42—22no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—42no—
629C42—42no—
630C42—48no—
631C42—42no—
632C42—42no—
633C42—42no—
634C42—42no—
635C42—42no—
636C42—42no—
637C42#13514yes—
638C42#13714yes—
639C42C2×#4112yes—
640C42C2×#4112yes—
641C42H(5,𝔽2)14yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23C2×#13712yes—
656C23C23×D411yescharacteristic
657Q8—24no—
658Q8—42no—
659Q8—44no—
660Q8—44no—
661Q8—44no—
662Q8—44no—
663Q8—88no—
664D4—24no—
665D4—48no—
666D4—42no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
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—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—44no—
708C2×C4—48no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—44no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—44no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4#52512yes—
732C2×C4#52512yes—
733C2×C4#53512yes—
734C2×C4#53512yes—
735C2×C4C2×#13512yes—
736C2×C4C2×#13512yes—
737C2×C4C2×#13512yes—
738C2×C4C2×#13712yes—
739C2×C4C2×#13712yes—
740C2×C4C2×#13712yes—
741C2×C4C2×#13712yes—
742C2×C4C2×#13712yes—
743C2×C4#57512yes—
744C2×C4C22×#4111yescharacteristic
745C2×C4C22×#4111yescharacteristic
746C2×C4C2×H(5,𝔽2)12yes—
747C2×C4#58512yes—
748C8—44no—
749C8—44no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22C2×#52511yescharacteristic
765C22C2×#53511yescharacteristic
766C22#344911yescharacteristic
767C22C22×#13511yescharacteristic
768C22C22×#13711yescharacteristic
769C22C22×#13711yescharacteristic
770C22C2×#57511yescharacteristic
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—41no—
779C4—41no—
780C4—42no—
781C4—41no—
782C4—42no—
783C4—41no—
784C4—42no—
785C4—81no—
786C4—81no—
787C4—84no—
788C4—81no—
789C4—84no—
790C4—81no—
791C4#310714yes—
792C4#321814yes—
793C4#346012yes—
794C4#346012yes—
795C2—42no—
796C2—82no—
797C2#3460911yescharacteristic
798C2C2×#310711yescharacteristic
799C2#6056211yescharacteristic
800C2#6078211yescharacteristic
801C2C2×#321811yescharacteristic
802C2#6094711yescharacteristic
803C2#6095011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#121C23
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. #36645C2semidirect
3. #30116C2semidirect
5. #30067C2semidirect
6. #30046C2semidirect
7. #29983C2semidirect
8. #29980C2semidirect
9. #29926C2semidirect
10. #29799C2semidirect
11. #29798C2semidirect
13. #23820C2semidirect
14. #23797C2semidirect
15. #23571C2semidirect
17. C4×#462C2semidirect
18. C4×#461C2semidirect
19. #20777C2semidirect

Maximal subgroups

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

subgroupindex
#366452
C4×#5292
#301162
#301132
#300672
#300462
#299832
#299802
#299262
#297992
#297982
#296652
#238202
#237972
#235712
#235682
C4×#4622
C4×#4612
#207772