Finite Group Databasebeta

← #6496033

Subgroups — #6496033

Order 512.

4352 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#532C211yesmaximal, characteristic
2C2×#3234C212yesmaximal, complemented
3C2×#2851C211yesmaximal, characteristic, complemented
4#32959C214yesmaximal, complemented
5#29694C214yesmaximal, complemented
6#25860C212yesmaximal, complemented
7#25816C212yesmaximal, complemented
8#25676C214yesmaximal, complemented
9#24061C212yesmaximal, complemented
10#24060C212yesmaximal, complemented
11#24005C212yesmaximal, complemented
12#24002C212yesmaximal, complemented
13#21865C212yesmaximal, complemented
14#20715C211yesmaximal, characteristic, complemented
15C23×#41—21no—
16C2×#532—21no—
17C2×#532—21no—
18C2×#532—21no—
19C2×#532—21no—
20C2×#532—216no—
21C2×#532C2212yes—
22C2×#532C2212yes—
23C2×#532C2212yes—
24C2×#532C2212yes—
25C22×C4⋊Q8C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C22×#125C2211yescharacteristic, complemented
28C22×#124—21no—
29C22×#121—21no—
30C22×#121C2212yes—
31C22×C4×D4—21no—
32C22×C4×D4C2212yes—
33C23×C42C2211yescharacteristic
34#3234—216no—
35C2×#501C2214yescomplemented
36C2×#490C2214yescomplemented
37C2×#481C2214yescomplemented
38C2×#480C2214yescomplemented
39C2×#478C2218yescomplemented
40C2×#432C2212yescomplemented
41#2851—21no—
42#2851—21no—
43#2851—21no—
44#2851—21no—
45#2851C2212yes—
46#2851C2212yes—
47#2851C2212yescomplemented
48#2851C2212yescomplemented
49C2×#389C2211yescharacteristic, complemented
50C2×#389C2211yescharacteristic, complemented
51C2×#387—21no—
52C2×#387—21no—
53C2×#385—21no—
54C2×#385—21no—
55C2×#382C2211yescharacteristic, complemented
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58#2058C2214yescomplemented
59#2057C2214yescomplemented
60#2041C2214yescomplemented
61#2041C2214yescomplemented
62#2034C2218yescomplemented
63#2033C2218yescomplemented
64#1993C2214yescomplemented
65#1961C2214yescomplemented
66#1874C2214yescomplemented
67#1874C2214yescomplemented
68#1864C2218yescomplemented
69#1862C2218yescomplemented
70#1853C2214yes—
71#1852C2214yes—
72#1817C2212yescomplemented
73#1804C2218yescomplemented
74#1797C2212yes—
75#1797C2212yescomplemented
76#1786C2214yes—
77#1786C2214yes—
78#1779C2212yes—
79#1749C2212yes—
80#1749C2212yescomplemented
81C22×#41—216no—
82C22×#41—22no—
83C22×#41—22no—
84C22×#41—22no—
85C22×#41—22no—
86C22×#41—48no—
87C22×#41—48no—
88C23×Q8—21no—
89C23×D4—22no—
90C23×D4—21no—
91C23×D4—21no—
92C23×D4C2312yes—
93C24×C4—22no—
94C24×C4D411yescharacteristic
95C24×C4D411yescharacteristic
96C24×C4C2311yescharacteristic
97#532—216no—
98#532—216no—
99#532—216no—
100#532—216no—
101#532—28no—
102#532—28no—
103#532—216no—
104#532—216no—
105#532—28no—
106#532D4116yes—
107C2×C4⋊Q8—28no—
108C2×C4⋊Q8—21no—
109C2×C4⋊Q8—21no—
110C2×C4⋊Q8C2312yes—
111C2×C4⋊Q8C2312yes—
112C2×#127—28no—
113C2×#127—21no—
114C2×#127—21no—
115C2×#127C2312yes—
116C2×#127C2312yes—
117C2×#125—21no—
118C2×#125—21no—
119C2×#125—28no—
120C2×#125C2312yes—
121C2×#125C2312yes—
122C2×#124—216no—
123C2×#124—22no—
124C2×#124—22no—
125C2×#124—22no—
126C2×#124—22no—
127C2×#121—216no—
128C2×#121—22no—
129C2×#121—22no—
130C2×#121—22no—
131C2×#121—22no—
132C2×#121—22no—
133C2×#121—22no—
134C2×#121—216no—
135C2×#121C2314yes—
136C2×#121C2314yes—
137C2×C4×D4—216no—
138C2×C4×D4—216no—
139C2×C4×D4—22no—
140C2×C4×D4—22no—
141C2×C4×D4—22no—
142C2×C4×D4—22no—
143C2×C4×D4—22no—
144C2×C4×D4—22no—
145C2×C4×D4C2314yes—
146C2×C4×D4C2314yes—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C22⋊C4—22no—
158C22×C22⋊C4—22no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—21no—
161C22×C42—28no—
162C22×C42D411yescharacteristic
163C22×C42D411yescharacteristic
164C22×C42D411yescharacteristic
165C22×C42D411yescharacteristic
166C22×C42D411yescharacteristic
167C22×C42D411yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174#501—216no—
175#490—216no—
176#481—216no—
177#480—216no—
178#478—232no—
179#432—28no—
180C2×#107C2318yes—
181C2×#106C2318yes—
182C2×C4⋊C8C2314yes—
183C2×#102C2318yes—
184C2×#102C2318yes—
185C2×#102C2318yes—
186C2×#102C2318yes—
187C2×C22⋊C8C2314yes—
188C2×C22⋊C8C2314yes—
189C2×C22⋊C8C2314yes—
190C2×#97C2314yes—
191#389—21no—
192#389—21no—
193#389—21no—
194#389—21no—
195#389C2312yes—
196#389C2312yes—
197#389C2312yes—
198#389C2312yes—
199#387—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#387—22no—
205#387—22no—
206#387—22no—
207#385—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#382—21no—
216#382—21no—
217#382C2312yes—
218#382C2312yes—
219#380—21no—
220#380—21no—
221#380—21no—
222#380—21no—
223#380C2312yes—
224#380C2312yes—
225#380C2312yes—
226#380C2312yes—
227C2×#95—21no—
228C2×#95—21no—
229C2×#95—21no—
230C2×#95—21no—
231C2×#95—21no—
232C2×#95—21no—
233#340C2318yes—
234#340C2318yes—
235#336C2314yes—
236#336C2314yes—
237C25—22no—
238C25C2×D411yescharacteristic
239C2×#41—216no—
240C2×#41—216no—
241C2×#41—216no—
242C2×#41—216no—
243C2×#41—4128no—
244C2×#41—48no—
245C2×#41—48no—
246C2×#41—48no—
247C2×#41—48no—
248C2×#41—48no—
249C2×#41—48no—
250C2×#41—48no—
251C2×#41—48no—
252C22×Q8—28no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—44no—
256C22×Q8—44no—
257C22×D4—28no—
258C22×D4—216no—
259C22×D4—28no—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4—28no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—28no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4—44no—
274C22×D4—48no—
275C22×D4—48no—
276C22×D4C2414yes—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—216no—
281C23×C4—22no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—48no—
295C23×C4—48no—
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C22×C8C2418yes—
315C4⋊Q8—28no—
316C4⋊Q8—28no—
317C4⋊Q8—28no—
318C4⋊Q8—24no—
319C4⋊Q8C2×D418yes—
320#127—28no—
321#127—28no—
322#127—28no—
323#127—24no—
324#127C2×D418yes—
325#125—28no—
326#125—28no—
327#125—44no—
328#125—44no—
329#124—216no—
330#124—216no—
331#124—216no—
332#124—216no—
333#121—216no—
334#121—216no—
335#121—216no—
336#121—216no—
337#121—216no—
338#121—28no—
339#121—216no—
340#121—28no—
341#121—28no—
342#121C2×D4116yes—
343C4×D4—216no—
344C4×D4—216no—
345C4×D4—216no—
346C4×D4—216no—
347C4×D4—216no—
348C4×D4—28no—
349C4×D4—28no—
350C4×D4—216no—
351C4×D4—28no—
352C4×D4C2×D4116yes—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2414yes—
383C2×C22⋊C4—216no—
384C2×C22⋊C4—216no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
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×D418yes—
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423#107—216no—
424#106—216no—
425C4⋊C8—28no—
426#102—216no—
427#102—216no—
428#102—48no—
429#102—48no—
430C22⋊C8—28no—
431C22⋊C8—28no—
432C22⋊C8—44no—
433#97—28no—
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—
444#95—22no—
445#95—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—28no—
451C24—24no—
452C24—41no—
453C24—41no—
454C24—44no—
455C24—44no—
456C24—44no—
457C24—44no—
458C24—44no—
459C24—44no—
460C24AGL(1,ℤ/8)14yes—
461C24C22×D411yescharacteristic
462C24C22×D411yescharacteristic
463C24C22×D411yescharacteristic
464#41—464no—
465#41—464no—
466#41—464no—
467#41—464no—
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—432no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—216no—
478C2×D4—28no—
479C2×D4—216no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—24no—
483C2×D4—28no—
484C2×D4—28no—
485C2×D4—432no—
486C2×D4—432no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—432no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—464no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4C22×D418yes—
504C22×C4—232no—
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—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—28no—
529C22×C4—216no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—216no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—416no—
563C22×C4—416no—
564C22×C4—464no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4#12014yes—
584C22×C4#12014yes—
585C22×C4AGL(1,ℤ/8)14yes—
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D414yes—
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C42−1+414yes—
599C22×C4C2511yescharacteristic
600C2×C8—28no—
601C2×C8—28no—
602C2×C8—28no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—44no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4C22×D418yes—
624C22⋊C4—216no—
625C22⋊C4—216no—
626C22⋊C4—216no—
627C22⋊C4—216no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42#12014yes—
645C42#12014yes—
646C42C22×D414yes—
647C42C22×D414yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—28no—
660C23—28no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—28no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—416no—
671C23—416no—
672C23—416no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—88no—
680C23—88no—
681C23—88no—
682C23—88no—
683C23C2×#12012yes—
684C23#53612yes—
685C23C2×AGL(1,ℤ/8)12yes—
686C23C2×AGL(1,ℤ/8)12yes—
687C23C2×AGL(1,ℤ/8)12yes—
688C23C2×AGL(1,ℤ/8)12yes—
689C23#57512yes—
690C23C23×D411yescharacteristic
691Q8—416no—
692Q8—416no—
693D4—216no—
694D4—416no—
695D4—416no—
696D4—416no—
697D4—416no—
698D4—416no—
699D4—432no—
700D4—432no—
701D4—48no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—28no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—432no—
745C2×C4—432no—
746C2×C4—416no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4C2×#12012yes—
767C2×C4C2×#12012yes—
768C2×C4C2×#12012yes—
769C2×C4C2×#12012yes—
770C2×C4C2×#12012yes—
771C2×C4#53612yes—
772C2×C4C2×AGL(1,ℤ/8)12yes—
773C2×C4C2×AGL(1,ℤ/8)12yes—
774C2×C4#57512yes—
775C2×C4C23×D412yes—
776C2×C4C2×2−1+412yes—
777C2×C4#58512yes—
778C8—48no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—416no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—48no—
800C22—48no—
801C22—48no—
802C22—832no—
803C22—84no—
804C22—84no—
805C22—84no—
806C22—84no—
807C22#300314yes—
808C22#323414yescomplemented
809C22C22×#12011yescharacteristic
810C22C2×#53611yescharacteristic
811C22#344911yescharacteristic
812C22C22×AGL(1,ℤ/8)11yescharacteristic
813C22C22×AGL(1,ℤ/8)11yescharacteristic
814C22C2×#57511yescharacteristic
815C22C2×#57511yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—22no—
823C4—22no—
824C4—22no—
825C4—48no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4#348914yes—
833C2—24no—
834C2—24no—
835C2—42no—
836C2—88no—
837C2#3530511yescharacteristic
838C2C2×#300311yescharacteristic
839C2#6035911yescharacteristic
840C2C2×#323411yescharacteristic
841C2#6086411yescharacteristic
842C2#6094911yescharacteristic
843C2#6095811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#532C2
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. C2×#3234C2semidirect
3. C2×#2851C2semidirect
4. #32959C2semidirect
5. #29694C2semidirect
6. #25860C2semidirect
7. #25816C2semidirect
8. #25676C2semidirect
9. #24061C2semidirect
10. #24060C2semidirect
11. #24005C2semidirect
12. #24002C2semidirect
13. #21865C2semidirect
14. #20715C2semidirect
27. C22×#125C22semidirect
35. C2×#501C22semidirect
36. C2×#490C22semidirect
37. C2×#481C22semidirect
38. C2×#480C22semidirect
39. C2×#478C22semidirect
40. C2×#432C22semidirect
47. #2851C22semidirect
48. #2851C22semidirect
49. C2×#389C22semidirect
50. C2×#389C22semidirect
55. C2×#382C22semidirect
58. #2058C22semidirect
59. #2057C22semidirect
60. #2041C22semidirect
61. #2041C22semidirect
62. #2034C22semidirect
63. #2033C22semidirect
64. #1993C22semidirect
65. #1961C22semidirect
66. #1874C22semidirect
67. #1874C22semidirect
68. #1864C22semidirect
69. #1862C22semidirect
72. #1817C22semidirect
73. #1804C22semidirect
75. #1797C22semidirect
80. #1749C22semidirect
808. C22#3234semidirect

Maximal subgroups

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

subgroupindex
C22×#5322
C2×#32342
C2×#28512
#329592
#296942
#258602
#258162
#256762
#240612
#240602
#240052
#240022
#218652
#207152