Finite Group Databasebeta

← #6471429

Subgroups — #6471429

Order 512.

3332 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35005C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
3#32956C211yesmaximal, characteristic, complemented
4#32902C211yesmaximal, characteristic, complemented
5#32878C212yesmaximal, complemented
6#29952C211yesmaximal, characteristic, complemented
7#29892C212yesmaximal, complemented
8#29712C211yesmaximal, characteristic, complemented
9#27539C214yesmaximal, complemented
10#27243C214yesmaximal, complemented
11#25168C214yesmaximal, complemented
12#24913C214yesmaximal, complemented
13#22046C212yesmaximal, complemented
14#21906C211yesmaximal, characteristic, complemented
15#21452C212yesmaximal, complemented
16C24×D4C2211yescharacteristic
17C2×#538—21no—
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C23×C22⋊C4—21no—
21C2×#476C2212yescomplemented
22C2×#459C2212yescomplemented
23C2×#447C2212yes—
24C2×#447C2212yes—
25C2×#447C2214yes—
26C2×#447C2214yes—
27C2×#442C2214yescomplemented
28#2857C2211yescharacteristic, complemented
29#2856C2211yescharacteristic, complemented
30#2847C2212yes—
31#2639—21no—
32#2617—21no—
33#2559—22no—
34#2557—22no—
35#2496C2212yescomplemented
36#2491C2212yescomplemented
37#2428C2212yescomplemented
38#2422C2212yescomplemented
39D4×C22⋊C4—22no—
40D4×C22⋊C4—22no—
41D4×C22⋊C4C2214yes—
42D4×C22⋊C4C2214yes—
43#2325—21no—
44C4×#121C2212yescomplemented
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#386—21no—
48C2×#386—21no—
49C2×#380C2211yescharacteristic
50C2×#379—21no—
51C2×C4×C22⋊C4C2211yescharacteristic
52#2094C2212yescomplemented
53#2077C2214yescomplemented
54#2077C2214yescomplemented
55#2071C2212yescomplemented
56#2065C2214yescomplemented
57#2054C2214yescomplemented
58#2034C2214yescomplemented
59#2034C2214yescomplemented
60#2023C2212yescomplemented
61#2011C2212yescomplemented
62#1972C2214yescomplemented
63#1936C2214yescomplemented
64#1926C2214yescomplemented
65#1924C2214yescomplemented
66#1924C2214yescomplemented
67#1879C2214yescomplemented
68#1879C2214yescomplemented
69#1879C2214yescomplemented
70#1874C2212yescomplemented
71#1874C2212yescomplemented
72#1864C2214yescomplemented
73#1864C2214yescomplemented
74#1853C2212yescomplemented
75#1853C2212yescomplemented
76#1802C2212yescomplemented
77#1802C2212yescomplemented
78#1797C2211yescharacteristic, complemented
79#1797C2211yescharacteristic, complemented
80#1786C2212yes—
81#1786C2214yes—
82#1786C2214yes—
83#1786C2212yes—
84#1779C2212yes—
85#1762C2214yescomplemented
86#1749C2212yescomplemented
87C26—21no—
88C23×D4—24no—
89C23×D4—24no—
90C23×D4—22no—
91C23×D4—21no—
92C23×D4—44no—
93C23×D4—44no—
94C23×D4C2311yescharacteristic
95C23×D4C2314yes—
96C23×D4C2311yescharacteristic
97C24×C4—21no—
98C24×C4—21no—
99C24×C4C2311yescharacteristic
100C22×D8C2314yes—
101C22×D8C2314yes—
102#538—48no—
103C2×C4⋊Q8C2311yescharacteristic, complemented
104C2×#127C2311yescharacteristic, complemented
105C2×#126—22no—
106C2×#124—22no—
107C2×#123—22no—
108C2×C22⋊Q8—21no—
109C2×#121—21no—
110C2×#121—21no—
111C2×#121—22no—
112C2×#121C2312yes—
113C2×#121C2312yes—
114C2×#121C2312yes—
115C2×#120—22no—
116C2×C4×D4—22no—
117C2×C4×D4—22no—
118C2×C4×D4—21no—
119C2×C4×D4—21no—
120C2×C4×D4—44no—
121C2×C4×D4—44no—
122C2×C4×D4C2312yes—
123C2×C4×D4C2312yes—
124C2×C4×D4C2314yes—
125C2×C4×D4C2312yescomplemented
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—48no—
138C22×C22⋊C4D411yescharacteristic
139C22×C22⋊C4D411yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142#476—44no—
143#459—44no—
144#447—28no—
145#447—28no—
146#447—48no—
147#447—48no—
148#442—48no—
149C2×#106C2314yescomplemented
150C2×#106C2314yescomplemented
151C2×C4⋊C8C2312yescomplemented
152C2×C4⋊C8C2312yescomplemented
153C2×#102C2314yes—
154C2×#102C2314yes—
155C2×#102C2314yes—
156C2×#102C2314yes—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yescomplemented
160C2×#102C2314yescomplemented
161C2×C22⋊C8C2312yes—
162C2×C22⋊C8C2312yes—
163C2×C22⋊C8C2314yes—
164C2×C22⋊C8C2314yes—
165C2×#97C2314yescomplemented
166#400—22no—
167#397—22no—
168#397—22no—
169#394—22no—
170#394—22no—
171#394—22no—
172#393—22no—
173#392—22no—
174#391—21no—
175#390—22no—
176#390—21no—
177#390—21no—
178#390—21no—
179#390—21no—
180#390C2312yes—
181#390C2312yes—
182#390C2314yes—
183#390C2312yescomplemented
184#390C2312yescomplemented
185#389—21no—
186#389C2312yescomplemented
187#389C2312yescomplemented
188#388—22no—
189#388—22no—
190#387—22no—
191#386—22no—
192#386—22no—
193#386—22no—
194#386—22no—
195#386—22no—
196#386—24no—
197#386—24no—
198#386—24no—
199#386—24no—
200#385—22no—
201#384C2311yescharacteristic, complemented
202#384C2311yescharacteristic, complemented
203#380—21no—
204#380—22no—
205#380C2312yes—
206#380C2312yes—
207#380C2314yes—
208#380C2312yes—
209#379—24no—
210#379—24no—
211C4×C4⋊C4C2312yescomplemented
212C4×C22⋊C4—22no—
213C4×C22⋊C4D412yes—
214C4×C22⋊C4D412yes—
215C4×C22⋊C4C2312yes—
216C4×C22⋊C4C2312yes—
217C2×#95—21no—
218C2×#95D411yescharacteristic
219C2×#95D411yescharacteristic
220#340C2314yescomplemented
221#340C2314yescomplemented
222#340C2314yescomplemented
223#340C2314yescomplemented
224#336C2312yescomplemented
225#336C2312yescomplemented
226#336C2314yescomplemented
227C25—21no—
228C25—28no—
229C25—21no—
230C25—24no—
231C25—44no—
232C25—44no—
233C25—44no—
234C25—44no—
235C25—82no—
236C25—82no—
237C25C2×D411yescharacteristic
238C22×Q8—21no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—28no—
242C22×D4—216no—
243C22×D4—28no—
244C22×D4—28no—
245C22×D4—28no—
246C22×D4—28no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—21no—
251C22×D4—24no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—42no—
258C22×D4—42no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—48no—
262C22×D4—48no—
263C22×D4—432no—
264C22×D4—432no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4#4114yes—
268C22×D4#4114yes—
269C22×D4C2412yes—
270C22×D4C2412yes—
271C22×D4C2412yes—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—44no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—82no—
287C23×C4—82no—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D412yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C2×D8—28no—
297C2×D8—28no—
298C2×D8—28no—
299C2×D8—28no—
300C2×D8—44no—
301C2×D8—44no—
302C22×C8C2414yes—
303C22×C8C2414yes—
304C4⋊Q8—42no—
305#127—42no—
306#126—48no—
307#124—48no—
308#123—48no—
309C22⋊Q8—44no—
310#121—24no—
311#121—24no—
312#121—48no—
313#121—44no—
314#121—44no—
315#121—44no—
316#121—44no—
317#120—48no—
318C4×D4—28no—
319C4×D4—24no—
320C4×D4—24no—
321C4×D4—44no—
322C4×D4—42no—
323C4×D4—42no—
324C4×D4—44no—
325C4×D4—48no—
326C4×D4—44no—
327C4×D4—44no—
328C4×D4—48no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4C2412yes—
341C2×C4⋊C4C2412yes—
342C2×C4⋊C4C2412yes—
343C2×C4⋊C4C2412yes—
344C2×C4⋊C4C2412yes—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
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—416no—
369C2×C22⋊C4—416no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—82no—
376C2×C22⋊C4—82no—
377C2×C22⋊C4C2×D412yes—
378C2×C22⋊C4C2×D412yes—
379C2×C22⋊C4C2×D412yes—
380C2×C22⋊C4C2×D412yes—
381C2×C42—22no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42C2×D412yes—
385C2×C42C2×D411yescharacteristic
386C2×C42C2×D411yescharacteristic
387C2×C42C2412yes—
388C2×C42C2411yescharacteristic
389C2×C42C2411yescharacteristic
390#106—44no—
391#106—44no—
392C4⋊C8—42no—
393C4⋊C8—42no—
394#102—28no—
395#102—28no—
396#102—28no—
397#102—28no—
398#102—44no—
399#102—44no—
400#102—44no—
401#102—44no—
402C22⋊C8—24no—
403C22⋊C8—24no—
404C22⋊C8—44no—
405C22⋊C8—44no—
406#97—44no—
407#95—24no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95C2×D412yes—
415#95C2×D412yes—
416#95C2×D412yes—
417#95C2×D412yes—
418C24—24no—
419C24—24no—
420C24—22no—
421C24—24no—
422C24—22no—
423C24—22no—
424C24—216no—
425C24—24no—
426C24—22no—
427C24—22no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—48no—
433C24—48no—
434C24—42no—
435C24—42no—
436C24—48no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—432no—
442C24—432no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—48no—
447C24—42no—
448C24—84no—
449C24—84no—
450C24—816no—
451C24—816no—
452C24—816no—
453C24—816no—
454C24—816no—
455C24AGL(1,ℤ/8)14yes—
456C24C22×D412yes—
457C24C22×D411yescharacteristic
458C2×Q8—42no—
459C2×Q8—81no—
460C2×Q8—81no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—216no—
464C2×D4—216no—
465C2×D4—216no—
466C2×D4—24no—
467C2×D4—24no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—48no—
484C2×D4—42no—
485C2×D4—416no—
486C2×D4—416no—
487C2×D4—464no—
488C2×D4—416no—
489C2×D4—432no—
490C2×D4—416no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—42no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4—81no—
500C2×D4—81no—
501C2×D4—82no—
502C2×D4—82no—
503C2×D4—82no—
504C2×D4—82no—
505C2×D4C2×#4114yes—
506C2×D4C2×#4114yes—
507C2×D4H(5,𝔽2)14yes—
508C2×D4H(5,𝔽2)14yes—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—42no—
528C22×C4—42no—
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—48no—
538C22×C4—48no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—44no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4—84no—
555C22×C4—82no—
556C22×C4—82no—
557C22×C4—816no—
558C22×C4—816no—
559C22×C4AGL(1,ℤ/8)14yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4C2511yescharacteristic
571D8—416no—
572D8—88no—
573C2×C8—24no—
574C2×C8—24no—
575C2×C8—24no—
576C2×C8—24no—
577C2×C8—24no—
578C2×C8—24no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—81no—
594C4⋊C4—81no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—48no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—48no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—48no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—82no—
614C22⋊C4—84no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C22⋊C4—82no—
620C42—24no—
621C42—22no—
622C42—22no—
623C42—41no—
624C42—41no—
625C42—42no—
626C42—44no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—216no—
632C23—22no—
633C23—22no—
634C23—28no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—48no—
647C23—48no—
648C23—48no—
649C23—48no—
650C23—48no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—48no—
655C23—432no—
656C23—432no—
657C23—48no—
658C23—42no—
659C23—42no—
660C23—48no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—816no—
678C23—816no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—816no—
684C23—8128no—
685C23—816no—
686C23—816no—
687C23#52512yes—
688C23C2×AGL(1,ℤ/8)14yes—
689C23C2×AGL(1,ℤ/8)12yes—
690C23C2×AGL(1,ℤ/8)12yes—
691C23C23×D411yescharacteristic
692Q8—162no—
693D4—216no—
694D4—24no—
695D4—24no—
696D4—24no—
697D4—28no—
698D4—48no—
699D4—432no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—88no—
704D4—162no—
705D4—162no—
706D4—164no—
707D4—164no—
708D4#53818yescomplemented
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—44no—
733C2×C4—48no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—88no—
754C2×C4—88no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4—816no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4—164no—
761C2×C4#52512yes—
762C2×C4C2×AGL(1,ℤ/8)12yes—
763C2×C4C2×AGL(1,ℤ/8)12yes—
764C2×C4C22×#4111yescharacteristic
765C2×C4C22×#4111yescharacteristic
766C2×C4C2×H(5,𝔽2)12yes—
767C2×C4C2×H(5,𝔽2)12yes—
768C8—44no—
769C8—44no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—28no—
780C22—432no—
781C22—416no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—44no—
788C22—42no—
789C22—42no—
790C22—44no—
791C22—42no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—816no—
796C22—864no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22#310914yes—
809C22C2×#52511yescharacteristic
810C22#348411yescharacteristic
811C22#348411yescharacteristic
812C22C22×AGL(1,ℤ/8)11yescharacteristic
813C22C22×AGL(1,ℤ/8)11yescharacteristic
814C22#358511yescharacteristic
815C22#358511yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—42no—
820C4—41no—
821C4—41no—
822C4—42no—
823C4—42no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4C2×#53812yes—
830C4#349012yes—
831C2—24no—
832C2—44no—
833C2—48no—
834C2—84no—
835C2—162no—
836C2#3498811yescharacteristic
837C2C2×#310911yescharacteristic
838C2#6056411yescharacteristic
839C2#6156911yescharacteristic
840C2#6156911yescharacteristic
841C2#6157111yescharacteristic
842C2#6158211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #35005C2semidirect
2. C2×D4×C22⋊C4C2semidirect
3. #32956C2semidirect
4. #32902C2semidirect
5. #32878C2semidirect
6. #29952C2semidirect
7. #29892C2semidirect
8. #29712C2semidirect
9. #27539C2semidirect
10. #27243C2semidirect
11. #25168C2semidirect
12. #24913C2semidirect
13. #22046C2semidirect
14. #21906C2semidirect
15. #21452C2semidirect
21. C2×#476C22semidirect
22. C2×#459C22semidirect
27. C2×#442C22semidirect
28. #2857C22semidirect
29. #2856C22semidirect
35. #2496C22semidirect
36. #2491C22semidirect
37. #2428C22semidirect
38. #2422C22semidirect
44. C4×#121C22semidirect
52. #2094C22semidirect
53. #2077C22semidirect
54. #2077C22semidirect
55. #2071C22semidirect
56. #2065C22semidirect
57. #2054C22semidirect
58. #2034C22semidirect
59. #2034C22semidirect
60. #2023C22semidirect
61. #2011C22semidirect
62. #1972C22semidirect
63. #1936C22semidirect
64. #1926C22semidirect
65. #1924C22semidirect
66. #1924C22semidirect
67. #1879C22semidirect
68. #1879C22semidirect
69. #1879C22semidirect
70. #1874C22semidirect
71. #1874C22semidirect
72. #1864C22semidirect
73. #1864C22semidirect
74. #1853C22semidirect
75. #1853C22semidirect
76. #1802C22semidirect
77. #1802C22semidirect
78. #1797C22semidirect
79. #1797C22semidirect
85. #1762C22semidirect
86. #1749C22semidirect
103. C2×C4⋊Q8C23semidirect
104. C2×#127C23semidirect
125. C2×C4×D4C23semidirect
149. C2×#106C23semidirect
150. C2×#106C23semidirect
151. C2×C4⋊C8C23semidirect
152. C2×C4⋊C8C23semidirect
159. C2×#102C23semidirect
160. C2×#102C23semidirect
165. C2×#97C23semidirect
183. #390C23semidirect
184. #390C23semidirect
186. #389C23semidirect
187. #389C23semidirect
201. #384C23semidirect
202. #384C23semidirect
211. C4×C4⋊C4C23semidirect
220. #340C23semidirect
221. #340C23semidirect
222. #340C23semidirect
223. #340C23semidirect
224. #336C23semidirect
225. #336C23semidirect
226. #336C23semidirect
708. D4#538semidirect

Maximal subgroups

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

subgroupindex
#350052
C2×D4×C22⋊C42
#329562
#329022
#328782
#299522
#298922
#297122
#275392
#272432
#251682
#249132
#220462
#219062
#214522