Finite Group Databasebeta

← #6458955

Subgroups — #6458955

Order 512.

2218 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic, complemented
3#27683C212yesmaximal, complemented
4#27650C212yesmaximal, complemented
5#27632C214yesmaximal, complemented
6#27613C211yesmaximal, characteristic, complemented
7#27610C211yesmaximal, characteristic, complemented
8#27602C212yesmaximal, complemented
9#27585C211yesmaximal, characteristic, complemented
10#27582C211yesmaximal, characteristic, complemented
11#24009C212yesmaximal
12#23761C212yesmaximal, complemented
13#23760C212yesmaximal, complemented
14#21582C214yesmaximal, complemented
15#21363C212yesmaximal, complemented
16#20739C212yesmaximal, complemented
17#20715C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4—21no—
20C22×C4×D4C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#482C2214yes—
23C2×#432C2212yes—
24C4×#121—21no—
25C4×#121—21no—
26C4×#121—21no—
27C4×#121—21no—
28C4×#121C2212yes—
29C4×#121C2212yes—
30C4×#121C2212yes—
31C4×#121C2212yes—
32C2×#390C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#388—21no—
35C2×#386—21no—
36#2285C2211yescharacteristic
37#2285C2211yescharacteristic
38#2285C2211yescharacteristic, complemented
39#2285C2211yescharacteristic, complemented
40#2285C2211yescharacteristic, complemented
41#2285C2211yescharacteristic, complemented
42#2283—21no—
43#2283—21no—
44#2283—21no—
45#2283—21no—
46#2283C2212yes—
47#2283C2212yescomplemented
48#2280—21no—
49#2280—21no—
50#2280C2212yes—
51C2×#380C2211yescharacteristic
52C4×#117—21no—
53C4×#117—21no—
54C4×#117C2212yescomplemented
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4—21no—
57#2100C2212yescomplemented
58#2099C2212yescomplemented
59#2094C2212yescomplemented
60#2093C2212yescomplemented
61#2084C2212yescomplemented
62#2083C2212yescomplemented
63#2077C2214yescomplemented
64#2076C2214yescomplemented
65#2071C2212yescomplemented
66#2071C2212yescomplemented
67#2034C2214yes—
68#2033C2214yes—
69#1949C2214yescomplemented
70#1949C2214yescomplemented
71#1926C2214yescomplemented
72#1925C2214yescomplemented
73#1919C2214yescomplemented
74#1918C2214yescomplemented
75#1875C2214yes—
76#1854C2214yescomplemented
77#1853C2212yes—
78#1853C2212yes—
79#1852C2212yes—
80#1852C2212yes—
81#1825C2214yescomplemented
82#1823C2212yes—
83#1823C2212yes—
84#1817C2211yescharacteristic
85#1817C2211yescharacteristic
86#1804C2214yescomplemented
87#1804C2214yescomplemented
88#1797C2212yescomplemented
89#1797C2212yescomplemented
90#1786C2212yes—
91#1786C2212yes—
92#1779C2212yes—
93#1776C2214yescomplemented
94#1776C2214yescomplemented
95#1762C2214yescomplemented
96#1762C2214yescomplemented
97#1749C2212yescomplemented
98#1749C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C2×#121—21no—
106C2×#121—21no—
107C2×#121—28no—
108C2×#121C2312yes—
109C2×#121C2312yes—
110C2×C4×D4—22no—
111C2×C4×D4—22no—
112C2×C4×D4—22no—
113C2×C4×D4—22no—
114C2×C4×D4—21no—
115C2×C4×D4—21no—
116C2×C4×D4—28no—
117C2×C4×D4—48no—
118C2×C4×D4C2312yes—
119C2×C4×D4C2312yes—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—21no—
124C2×#117C2312yes—
125C2×#117C2312yes—
126C22×C4⋊C4—21no—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C42—28no—
136C22×C42—21no—
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149#482—216no—
150#432—28no—
151C2×#107C2314yes—
152C2×#107C2314yes—
153C2×#106C2314yes—
154C2×#106C2314yes—
155C2×C4⋊C8C2314yes—
156C2×#102C2314yes—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×C22⋊C8C2314yes—
161C2×C22⋊C8C2312yes—
162C2×C22⋊C8C2312yes—
163C2×C22⋊C8C2314yes—
164C2×#97C2314yes—
165#390—21no—
166#390—21no—
167#390C2312yes—
168#390C2312yes—
169#389—21no—
170#389—21no—
171#389C2312yes—
172#389C2312yes—
173#388—22no—
174#388—22no—
175#388—22no—
176#388—22no—
177#386—22no—
178#386—22no—
179#386—22no—
180#386—22no—
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#382C2312yes—
192#382C2312yes—
193#381—22no—
194#381—22no—
195#381—22no—
196#380—21no—
197#380—21no—
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#380C2312yes—
207#380C2312yes—
208#380C2312yes—
209#380C2312yes—
210#380C2312yes—
211#380C2312yes—
212#379—22no—
213C4×C4⋊C4—21no—
214C4×C4⋊C4—21no—
215C4×C4⋊C4—21no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4C2312yes—
224C4×C4⋊C4C2312yes—
225C4×C4⋊C4C2312yes—
226C4×C4⋊C4C2312yes—
227C4×C4⋊C4C2312yes—
228C4×C4⋊C4C2312yes—
229C4×C22⋊C4—22no—
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—
239#376—22no—
240#376—22no—
241#376—22no—
242C2×#95—21no—
243C2×#95—21no—
244C2×#95—21no—
245C43—22no—
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#336C2312yes—
255#336C2312yes—
256#336C2312yes—
257#336C2312yes—
258C25—21no—
259C25C2×D411yescharacteristic
260C22×D4—28no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—24no—
264C22×D4—21no—
265C22×D4—24no—
266C22×D4—42no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4C2412yes—
270C23×C4—21no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—44no—
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×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C22×C8C2414yes—
306C22×C8C2414yes—
307#121—28no—
308#121—28no—
309#121—24no—
310#121—24no—
311#121—24no—
312#121#4118yes—
313C4×D4—28no—
314C4×D4—28no—
315C4×D4—48no—
316C4×D4—48no—
317C4×D4—48no—
318C4×D4—48no—
319C4×D4—44no—
320C4×D4—44no—
321#117—28no—
322#117—44no—
323#117—44no—
324#117—44no—
325#117—44no—
326#117—44no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
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—21no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4C2412yes—
345C2×C4⋊C4C2412yes—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
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—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—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
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—44no—
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#4118yes—
405C2×C42C2411yescharacteristic
406C2×C42C2411yescharacteristic
407C2×C42C2411yescharacteristic
408C2×C42C2411yescharacteristic
409#107—28no—
410#107—44no—
411#106—28no—
412#106—44no—
413C4⋊C8—28no—
414#102—28no—
415#102—28no—
416#102—44no—
417#102—44no—
418C22⋊C8—24no—
419C22⋊C8—24no—
420C22⋊C8—28no—
421C22⋊C8—44no—
422#97—28no—
423#95—22no—
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—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—41no—
449C24—41no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24C22×D411yescharacteristic
457C24C22×D411yescharacteristic
458C24C22×D411yescharacteristic
459C2×D4—24no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—24no—
463C2×D4—22no—
464C2×D4—24no—
465C2×D4—416no—
466C2×D4—42no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—432no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—42no—
473C2×D4C2×#4114yes—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
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—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—41no—
530C22×C4—41no—
531C22×C4—416no—
532C22×C4—416no—
533C22×C4—416no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—816no—
549C22×C4#12314yes—
550C22×C4#12314yes—
551C22×C4AGL(1,ℤ/8)14yes—
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×C4C2×#4114yes—
564C22×C4C2×#4114yes—
565C22×C4C2511yescharacteristic
566C2×C8—24no—
567C2×C8—24no—
568C2×C8—24no—
569C2×C8—24no—
570C2×C8—24no—
571C2×C8—24no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4C2×#4114yes—
593C22⋊C4—28no—
594C22⋊C4—28no—
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—
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—22no—
620C42—22no—
621C42—44no—
622C42—44no—
623C42—44no—
624C42—44no—
625C42—44no—
626C42—44no—
627C42—44no—
628C42—44no—
629C42#12314yes—
630C42#12314yes—
631C42C2×#4114yes—
632C42C2×#4114yes—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—28no—
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—24no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—48no—
657C23—48no—
658C23—48no—
659C23—44no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23C2×#12312yes—
671C23#52512yes—
672C23C2×AGL(1,ℤ/8)12yes—
673C23#57512yes—
674C23#57512yes—
675C23C23×D411yescharacteristic
676D4—28no—
677D4—48no—
678D4—416no—
679D4—416no—
680D4—44no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—28no—
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—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—24no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
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—48no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
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—88no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4C2×#12312yes—
750C2×C4C2×#12312yes—
751C2×C4C2×#12312yes—
752C2×C4C2×#12312yes—
753C2×C4C2×#12312yes—
754C2×C4#52512yes—
755C2×C4C2×AGL(1,ℤ/8)12yes—
756C2×C4C2×AGL(1,ℤ/8)12yes—
757C2×C4#57512yes—
758C2×C4C22×#4112yes—
759C2×C4C22×#4112yes—
760C2×C4#58512yes—
761C8—44no—
762C8—44no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—416no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—816no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22#309414yes—
793C22C22×#12311yescharacteristic
794C22C2×#52511yescharacteristic
795C22#344911yescharacteristic
796C22C22×AGL(1,ℤ/8)11yescharacteristic
797C22C2×#57511yescharacteristic
798C22C2×#57511yescharacteristic
799C22C2×#57511yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—22no—
809C4—41no—
810C4—44no—
811C4—41no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4#347514yes—
819C2—24no—
820C2—42no—
821C2—42no—
822C2—84no—
823C2#3480911yescharacteristic
824C2C2×#309411yescharacteristic
825C2#6051111yescharacteristic
826C2#6054611yescharacteristic
827C2#6055811yescharacteristic
828C2#6095911yescharacteristic
829C2#6096511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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
2. #34012C2semidirect
3. #27683C2semidirect
4. #27650C2semidirect
5. #27632C2semidirect
6. #27613C2semidirect
7. #27610C2semidirect
8. #27602C2semidirect
9. #27585C2semidirect
10. #27582C2semidirect
12. #23761C2semidirect
13. #23760C2semidirect
14. #21582C2semidirect
15. #21363C2semidirect
16. #20739C2semidirect
17. #20715C2semidirect
38. #2285C22semidirect
39. #2285C22semidirect
40. #2285C22semidirect
41. #2285C22semidirect
47. #2283C22semidirect
54. C4×#117C22semidirect
57. #2100C22semidirect
58. #2099C22semidirect
59. #2094C22semidirect
60. #2093C22semidirect
61. #2084C22semidirect
62. #2083C22semidirect
63. #2077C22semidirect
64. #2076C22semidirect
65. #2071C22semidirect
66. #2071C22semidirect
69. #1949C22semidirect
70. #1949C22semidirect
71. #1926C22semidirect
72. #1925C22semidirect
73. #1919C22semidirect
74. #1918C22semidirect
76. #1854C22semidirect
81. #1825C22semidirect
86. #1804C22semidirect
87. #1804C22semidirect
88. #1797C22semidirect
89. #1797C22semidirect
93. #1776C22semidirect
94. #1776C22semidirect
95. #1762C22semidirect
96. #1762C22semidirect
97. #1749C22semidirect
98. #1749C22semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1212
#340122
#276832
#276502
#276322
#276132
#276102
#276022
#275852
#275822
#240092
#237612
#237602
#215822
#213632
#207392
#207152