Finite Group Databasebeta

← #6434435

Subgroups — #6434435

Order 512.

2072 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36631C211yesmaximal, characteristic, complemented
2C2×C4×#124C211yesmaximal, characteristic, complemented
3#30134C214yesmaximal, complemented
4#30082C212yesmaximal, complemented
5#30045C212yesmaximal, complemented
6#29953C211yesmaximal, characteristic, complemented
7#29952C211yesmaximal, characteristic, complemented
8#29912C212yesmaximal, complemented
9#29713C211yesmaximal, characteristic, complemented
10#29712C211yesmaximal, characteristic
11#29623C212yesmaximal, complemented
12#23817C212yesmaximal, complemented
13#23796C212yesmaximal, complemented
14#23680C214yesmaximal, complemented
15C4×#448C212yesmaximal, complemented
16C4×#447C212yesmaximal, complemented
17#20777C211yesmaximal, characteristic, complemented
18C2×#529—21no—
19C22×#124C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C2×#448C2212yes—
23C2×#447C2212yes—
24C2×C4×SD16C2214yescomplemented
25C2×C4×D8C2214yes—
26#2861—21no—
27#2860—21no—
28#2860C2212yescomplemented
29#2859C2211yescharacteristic, complemented
30#2858C2211yescharacteristic, complemented
31#2857C2211yescharacteristic
32#2856C2211yescharacteristic
33#2854—21no—
34#2854C2212yes—
35#2850—21no—
36C4×C4⋊Q8C2211yescharacteristic, complemented
37C4×#127C2211yescharacteristic, complemented
38C4×#124—21no—
39C4×#124—21no—
40C4×#124—21no—
41C4×#124—21no—
42C4×#124—21no—
43C4×#124C2212yes—
44C4×#124C2212yes—
45C4×#124C2212yes—
46C4×#124C2212yes—
47C4×#121—21no—
48C4×#121C2212yes—
49C2×#391C2211yescharacteristic
50#2293—21no—
51#2293C2212yescomplemented
52C2×#390C2211yescharacteristic
53C2×#388—21no—
54C2×#388—21no—
55C2×#382C2211yescharacteristic
56C2×C4×C22⋊C4—21no—
57C2×C4×C22⋊C4—21no—
58C2×C43C2211yescharacteristic
59#2101C2214yescomplemented
60#2095C2212yescomplemented
61#2094C2212yes—
62#2092C2214yescomplemented
63#2085C2214yescomplemented
64#2073C2214yescomplemented
65#2072C2212yescomplemented
66#2071C2212yes—
67#2068C2214yescomplemented
68#2065C2214yes—
69#2055C2214yescomplemented
70#2054C2214yes—
71#2042C2214yes—
72#2042C2214yes—
73#2024C2212yescomplemented
74#2023C2212yes—
75#2014C2212yescomplemented
76#2012C2214yes—
77#2012C2214yes—
78#2011C2212yes—
79#1880C2214yescomplemented
80#1879C2214yes—
81#1874C2212yes—
82#1874C2212yes—
83#1865C2214yescomplemented
84#1862C2214yes—
85#1853C2212yes—
86#1852C2212yes—
87#1839C2212yescomplemented
88#1831C2212yescomplemented
89#1817C2212yes—
90#1797C2211yescharacteristic
91#1797C2211yescharacteristic
92#1787C2212yes—
93#1786C2212yes—
94C4×C4⋊C8C2212yescomplemented
95C4×#103C2214yescomplemented
96C4×#102C2214yes—
97C4×C22⋊C8C2212yes—
98#1744C2212yescomplemented
99C23×Q8C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C22×SD16C2314yes—
103C22×D8C2314yes—
104C2×C4⋊Q8C2311yescharacteristic
105C2×#127C2311yescharacteristic
106#529—48no—
107C2×#126—22no—
108C2×#125—21no—
109C2×#124—24no—
110C2×#124—24no—
111C2×#124—21no—
112C2×#124—21no—
113C2×#124—21no—
114C2×#124—21no—
115C2×#124C2312yes—
116C2×#124C2312yes—
117C2×#123—22no—
118C2×C22⋊Q8—21no—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121C2312yes—
122C2×C4×Q8—21no—
123C2×C4×Q8—21no—
124C2×C4×Q8—21no—
125C2×C4×Q8—44no—
126C2×C4×Q8C2312yes—
127C2×C4×Q8C2312yes—
128C2×C4×D4—22no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—44no—
134C2×C4×D4C2312yes—
135C2×C4×D4C2312yes—
136C2×C4×D4C2312yes—
137C2×#117—22no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C42—21no—
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#448—28no—
155#447—28no—
156C4×SD16—48no—
157C4×D8—48no—
158C2×#107C2314yes—
159C2×#106C2314yes—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2312yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172C2×C4×C8C2314yes—
173#391—21no—
174#391—21no—
175#391—21no—
176#391—21no—
177#391C2312yes—
178#391C2312yes—
179#390—21no—
180#390—21no—
181#390—21no—
182#390—21no—
183#390—21no—
184#390—21no—
185#390—21no—
186#390—21no—
187#390C2312yes—
188#390C2312yes—
189#390C2312yes—
190#390C2312yes—
191#390C2312yes—
192#390C2312yes—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389C2312yes—
198#389C2312yes—
199#389C2312yes—
200#389C2312yes—
201#388—22no—
202#388—22no—
203#388—22no—
204#388—22no—
205#388—22no—
206#388—22no—
207#388—22no—
208#388—22no—
209#388—22no—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#386—22no—
218#386—22no—
219#384C2311yescharacteristic
220#384C2311yescharacteristic
221#382—21no—
222#382—21no—
223#382—21no—
224#382C2312yes—
225#382C2312yes—
226#380—21no—
227#380C2312yes—
228C4×C4⋊C4—21no—
229C4×C4⋊C4C2312yes—
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—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C2×#95—21no—
241C2×#95—21no—
242C2×#95—21no—
243C2×#95—21no—
244C43D411yescharacteristic
245C43D411yescharacteristic
246C43D411yescharacteristic
247C43D411yescharacteristic
248C43C2311yescharacteristic
249C43C2311yescharacteristic
250C43C2311yescharacteristic
251C43C2311yescharacteristic
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#336C2312yes—
257#336C2312yes—
258#336C2314yes—
259#336C2314yes—
260#336C2314yes—
261C25—21no—
262C22×Q8—21no—
263C22×Q8—21no—
264C22×Q8—22no—
265C22×Q8—42no—
266C22×Q8—42no—
267C22×Q8#4114yes—
268C22×Q8C2412yes—
269C22×D4—22no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4—22no—
274C22×D4—42no—
275C22×D4—42no—
276C22×D4#4114yes—
277C22×D4C2412yes—
278C22×D4C2412yes—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
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
295C2×SD16—28no—
296C2×SD16—44no—
297C2×SD16—44no—
298C2×D8—28no—
299C2×D8—44no—
300C2×D8—44no—
301C22×C8C2414yes—
302C22×C8C2414yes—
303C4⋊Q8—42no—
304#127—42no—
305#126—48no—
306#125—44no—
307#124—28no—
308#124—28no—
309#124—24no—
310#124—24no—
311#124—24no—
312#124—24no—
313#124—44no—
314#124—44no—
315#123—48no—
316C22⋊Q8—44no—
317#121—24no—
318#121—24no—
319#121—44no—
320#121—44no—
321C4×Q8—28no—
322C4×Q8—44no—
323C4×Q8—44no—
324C4×Q8—44no—
325C4×Q8—44no—
326C4×D4—28no—
327C4×D4—28no—
328C4×D4—44no—
329C4×D4—44no—
330C4×D4—44no—
331C4×D4—44no—
332C4×D4—44no—
333C4×D4—48no—
334#117—48no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
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×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—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—44no—
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×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422#107—44no—
423#106—44no—
424C4⋊C8—42no—
425C4⋊C8—42no—
426#103—28no—
427#103—44no—
428#103—44no—
429#102—28no—
430#102—44no—
431#102—44no—
432#102—44no—
433#102—44no—
434C22⋊C8—24no—
435C22⋊C8—24no—
436C4×C8—28no—
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—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451C24—24no—
452C24—22no—
453C24—22no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24C22×D411yescharacteristic
461C2×Q8—24no—
462C2×Q8—22no—
463C2×Q8—24no—
464C2×Q8—24no—
465C2×Q8—48no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—48no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8C2×#4114yes—
473C2×D4—24no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—48no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—48no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4C2×#4114yes—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
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—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—816no—
538C22×C4#13514yes—
539C22×C4AGL(1,ℤ/8)14yes—
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×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4C2511yescharacteristic
556SD16—416no—
557D8—416no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8—24no—
561C2×C8—24no—
562C2×C8—24no—
563C2×C8—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—44no—
579C4⋊C4—42no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—44no—
583C22⋊C4—28no—
584C22⋊C4—28no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—44no—
588C22⋊C4—44no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C42—22no—
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—22no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42H(5,𝔽2)14yes—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—24no—
642C23—48no—
643C23—48no—
644C23—48no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—84no—
659C23—84no—
660C23—84no—
661C23—84no—
662C23#52512yes—
663C23C2×#13512yes—
664C23C2×AGL(1,ℤ/8)12yes—
665C23C23×D411yescharacteristic
666Q8—28no—
667Q8—48no—
668Q8—44no—
669Q8—84no—
670D4—28no—
671D4—48no—
672D4—44no—
673D4—44no—
674D4—44no—
675D4—84no—
676D4—84no—
677D4—88no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
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—24no—
691C2×C4—24no—
692C2×C4—28no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—24no—
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—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—48no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
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—88no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—88no—
739C2×C4—88no—
740C2×C4#52512yes—
741C2×C4#53512yes—
742C2×C4#53512yes—
743C2×C4C2×#13512yes—
744C2×C4C2×#13512yes—
745C2×C4C2×AGL(1,ℤ/8)12yes—
746C2×C4C2×AGL(1,ℤ/8)12yes—
747C2×C4#57512yes—
748C2×C4#57512yes—
749C2×C4C22×#4111yescharacteristic
750C2×C4C22×#4111yescharacteristic
751C2×C4C2×H(5,𝔽2)12yes—
752C2×C4#58512yes—
753C8—44no—
754C8—44no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—816no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22#310614yes—
777C22C2×#52511yescharacteristic
778C22C2×#53511yescharacteristic
779C22#344911yescharacteristic
780C22C22×#13511yescharacteristic
781C22C22×AGL(1,ℤ/8)11yescharacteristic
782C22C2×#57511yescharacteristic
783C22C2×#57511yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—41no—
791C4—44no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4#321314yes—
803C4#345912yes—
804C4#345912yes—
805C2—24no—
806C2—84no—
807C2—162no—
808C2#3459311yescharacteristic
809C2C2×#310611yescharacteristic
810C2#6055911yescharacteristic
811C2#6078211yescharacteristic
812C2C2×#321311yescharacteristic
813C2#6094511yescharacteristic
814C2#6094911yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radical#29712C2
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. #36631C2semidirect
2. C2×C4×#124C2semidirect
3. #30134C2semidirect
4. #30082C2semidirect
5. #30045C2semidirect
6. #29953C2semidirect
7. #29952C2semidirect
8. #29912C2semidirect
9. #29713C2semidirect
11. #29623C2semidirect
12. #23817C2semidirect
13. #23796C2semidirect
14. #23680C2semidirect
15. C4×#448C2semidirect
16. C4×#447C2semidirect
17. #20777C2semidirect
24. C2×C4×SD16C22semidirect
28. #2860C22semidirect
29. #2859C22semidirect
30. #2858C22semidirect
36. C4×C4⋊Q8C22semidirect
37. C4×#127C22semidirect
51. #2293C22semidirect
59. #2101C22semidirect
60. #2095C22semidirect
62. #2092C22semidirect
63. #2085C22semidirect
64. #2073C22semidirect
65. #2072C22semidirect
67. #2068C22semidirect
69. #2055C22semidirect
73. #2024C22semidirect
75. #2014C22semidirect
79. #1880C22semidirect
83. #1865C22semidirect
87. #1839C22semidirect
88. #1831C22semidirect
94. C4×C4⋊C8C22semidirect
95. C4×#103C22semidirect
98. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#366312
C2×C4×#1242
#301342
#300822
#300452
#299532
#299522
#299122
#297132
#297122
#296232
#238172
#237962
#236802
C4×#4482
C4×#4472
#207772