Finite Group Databasebeta

← #6493619

Subgroups — #6493619

Order 512.

1988 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2C2×#2283C211yesmaximal, characteristic, complemented
3#33109C211yesmaximal, characteristic, complemented
4#33108C211yesmaximal, characteristic, complemented
5#33107C211yesmaximal, characteristic, complemented
6#33106C211yesmaximal, characteristic, complemented
7#29926C212yesmaximal, complemented
8#29925C212yesmaximal, complemented
9#27977C212yesmaximal, complemented
10#27912C212yesmaximal, complemented
11#27893C214yesmaximal, complemented
12#27590C214yesmaximal, complemented
13#24007C212yesmaximal, complemented
14#24004C212yesmaximal, complemented
15#21985C212yesmaximal, complemented
16#21807C212yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525C2212yes—
20C23×C42C2211yescharacteristic
21C2×#484C2212yes—
22C2×#481C2212yes—
23C2×#483C2212yes—
24C2×#480C2212yes—
25C2×#431C2212yes—
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2856C2211yescharacteristic
29#2856C2211yescharacteristic
30#2854—21no—
31#2854—21no—
32#2850C2212yes—
33#2850C2212yes—
34#2847—21no—
35#2847—21no—
36C4×#121—21no—
37C4×#121—21no—
38C4×#121—21no—
39C4×#121—21no—
40#2297C2212yes—
41#2285C2211yescharacteristic
42#2283—21no—
43#2283—21no—
44#2283—21no—
45#2283—21no—
46#2283C2212yes—
47#2283C2212yes—
48#2283C2212yes—
49#2283C2212yes—
50C2×#383—21no—
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#381—21no—
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59C2×#376—21no—
60#2097C2214yescomplemented
61#2092C2214yescomplemented
62#2074C2214yescomplemented
63#2073C2214yescomplemented
64#2036C2214yes—
65#2035C2214yes—
66#2034C2214yes—
67#2033C2214yes—
68#1982C2212yescomplemented
69#1982C2212yescomplemented
70#1981C2212yescomplemented
71#1981C2212yescomplemented
72#1958C2214yescomplemented
73#1958C2214yescomplemented
74#1948C2212yescomplemented
75#1948C2212yescomplemented
76#1947C2212yescomplemented
77#1947C2212yescomplemented
78#1928C2214yescomplemented
79#1927C2214yescomplemented
80#1926C2214yescomplemented
81#1925C2214yescomplemented
82#1874C2212yes—
83#1874C2212yes—
84#1872C2212yes—
85#1872C2212yes—
86#1854C2214yes—
87#1854C2214yes—
88#1846C2214yescomplemented
89#1835C2214yescomplemented
90#1817C2212yes—
91#1797C2211yescharacteristic
92#1797C2211yescharacteristic
93#1797C2212yes—
94#1788C2214yes—
95#1788C2214yes—
96#1779C2212yes—
97C4×C22⋊C8C2212yes—
98C4×C22⋊C8C2212yes—
99C22×#41C2312yes—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103#532—28no—
104C2×C4⋊Q8C2311yescharacteristic
105C2×#127C2311yescharacteristic
106C2×#124C2312yes—
107#525—44no—
108#525—44no—
109C2×#123—22no—
110C2×C22⋊Q8C2312yes—
111C2×C22⋊Q8C2312yes—
112C2×#121—21no—
113C2×#121—21no—
114C2×#121—21no—
115C2×#121—21no—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121C2312yes—
119C2×#121C2312yes—
120C2×#120—22no—
121C2×C4×D4—22no—
122C2×C4×D4—22no—
123C2×C4×D4—21no—
124C2×C4×D4—21no—
125C2×#117C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C42—28no—
133C22×C42—21no—
134C22×C42—21no—
135C22×C42D411yescharacteristic
136C22×C42D411yescharacteristic
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#484—44no—
148#483—44no—
149#481—44no—
150#480—44no—
151#431—28no—
152C2×#107C2314yes—
153C2×#107C2314yes—
154C2×#106C2314yes—
155C2×#106C2314yes—
156C2×C4⋊C8C2312yes—
157C2×C4⋊C8C2312yes—
158C2×#103C2314yes—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2314yes—
169C2×C22⋊C8C2314yes—
170C2×C4×C8C2314yes—
171#391C2312yes—
172#391C2312yes—
173#390—21no—
174#390—21no—
175#390—21no—
176#390—21no—
177#390C2312yes—
178#390C2312yes—
179#389—21no—
180#389—21no—
181#389—21no—
182#389—21no—
183#388—22no—
184#388—22no—
185#388—22no—
186#388—22no—
187#386—22no—
188#386—22no—
189#386—22no—
190#386—22no—
191#386—22no—
192#386—22no—
193#384C2311yescharacteristic
194#384C2311yescharacteristic
195#383—22no—
196#383—22no—
197#383—22no—
198#383—22no—
199#382—21no—
200#382—21no—
201#382—21no—
202#382—21no—
203#382C2312yes—
204#382C2312yes—
205#382C2312yes—
206#382C2312yes—
207#382C2312yes—
208#381—22no—
209#381—22no—
210#381—22no—
211#381—22no—
212#380—21no—
213#380—21no—
214#380—21no—
215#380—21no—
216#380—21no—
217#380—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380—21no—
222#380C2312yes—
223#380C2312yes—
224#380C2312yes—
225#380C2312yes—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4C2312yes—
233C4×C4⋊C4C2312yes—
234C4×C4⋊C4C2312yes—
235C4×C4⋊C4C2312yes—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242#376—22no—
243#376—22no—
244#376—22no—
245#376—22no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2314yes—
259#336C2312yes—
260#336C2312yes—
261C25C2×D411yescharacteristic
262C2×#41—28no—
263C2×#41—42no—
264C2×#41—42no—
265C2×#41—44no—
266C22×Q8C2412yes—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4C2412yes—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—22no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
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×C4C2×D411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C22×C8C2414yes—
307C22×C8C2414yes—
308C4⋊Q8—24no—
309#127—24no—
310#124—28no—
311#123—48no—
312C22⋊Q8—24no—
313C22⋊Q8—24no—
314C22⋊Q8—42no—
315C22⋊Q8—42no—
316#121—24no—
317#121—24no—
318#121—42no—
319#121—42no—
320#121—44no—
321#121—44no—
322#121—44no—
323#121—44no—
324#121—44no—
325#121—44no—
326#120—48no—
327C4×D4—48no—
328C4×D4—48no—
329C4×D4—44no—
330C4×D4—44no—
331#117—42no—
332#117—42no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
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—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
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—24no—
384C2×C42—24no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—44no—
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—44no—
410#107—44no—
411#106—44no—
412#106—44no—
413C4⋊C8—24no—
414C4⋊C8—24no—
415#103—44no—
416#103—44no—
417#103—44no—
418#103—44no—
419#102—44no—
420#102—44no—
421#102—44no—
422#102—44no—
423C22⋊C8—28no—
424C22⋊C8—24no—
425C22⋊C8—24no—
426C22⋊C8—44no—
427C4×C8—28no—
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—
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—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—41no—
457C24—41no—
458C24C22×D411yescharacteristic
459C24C22×D411yescharacteristic
460C24C22×D411yescharacteristic
461#41—88no—
462#41—88no—
463C2×Q8—24no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—24no—
467C2×D4—24no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—24no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
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—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—416no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—416no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—44no—
563C22×C4#12314yes—
564C22×C4#12314yes—
565C22×C4#13514yes—
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C2×#4114yes—
578C22×C4H(5,𝔽2)12yes—
579C22×C4H(5,𝔽2)12yes—
580C22×C4C2511yescharacteristic
581C2×C8—24no—
582C2×C8—24no—
583C2×C8—24no—
584C2×C8—24no—
585C2×C8—24no—
586C2×C8—24no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—44no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—44no—
639C42—44no—
640C42—44no—
641C42—44no—
642C42—44no—
643C42#12314yes—
644C42#12314yes—
645C42C2×#4114yes—
646C42C2×#4114yes—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—28no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23C2×#12312yes—
678C23#53512yes—
679C23C2×#13512yes—
680C23#57512yes—
681C23#57512yes—
682C23C23×D411yescharacteristic
683Q8—44no—
684Q8—44no—
685D4—44no—
686D4—44no—
687D4—84no—
688D4—88no—
689D4—88no—
690D4—88no—
691D4—84no—
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—21no—
703C2×C4—21no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
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—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
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—88no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4C2×#12312yes—
764C2×C4C2×#12312yes—
765C2×C4C2×#12312yes—
766C2×C4C2×#12312yes—
767C2×C4C2×#12312yes—
768C2×C4#53512yes—
769C2×C4C2×#13512yes—
770C2×C4C2×#13512yes—
771C2×C4#57512yes—
772C2×C4C22×#4112yes—
773C2×C4C2×H(5,𝔽2)11yescharacteristic
774C2×C4C2×H(5,𝔽2)11yescharacteristic
775C2×C4#58512yes—
776C8—44no—
777C8—44no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—416no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22#321214yes—
807C22C22×#12311yescharacteristic
808C22C2×#53511yescharacteristic
809C22#344911yescharacteristic
810C22C22×#13511yescharacteristic
811C22C2×#57511yescharacteristic
812C22C2×#57511yescharacteristic
813C22C2×#57511yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4#309114yes—
832C4#349412yes—
833C4#349412yes—
834C2—24no—
835C2—42no—
836C2—42no—
837C2—162no—
838C2#3526211yescharacteristic
839C2C2×#309111yescharacteristic
840C2#6051111yescharacteristic
841C2C2×#321211yescharacteristic
842C2#6080511yescharacteristic
843C2#6094211yescharacteristic
844C2#6097011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
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×#2283C2semidirect
3. #33109C2semidirect
4. #33108C2semidirect
5. #33107C2semidirect
6. #33106C2semidirect
7. #29926C2semidirect
8. #29925C2semidirect
9. #27977C2semidirect
10. #27912C2semidirect
11. #27893C2semidirect
12. #27590C2semidirect
13. #24007C2semidirect
14. #24004C2semidirect
15. #21985C2semidirect
16. #21807C2semidirect
17. #20714C2semidirect
60. #2097C22semidirect
61. #2092C22semidirect
62. #2074C22semidirect
63. #2073C22semidirect
68. #1982C22semidirect
69. #1982C22semidirect
70. #1981C22semidirect
71. #1981C22semidirect
72. #1958C22semidirect
73. #1958C22semidirect
74. #1948C22semidirect
75. #1948C22semidirect
76. #1947C22semidirect
77. #1947C22semidirect
78. #1928C22semidirect
79. #1927C22semidirect
80. #1926C22semidirect
81. #1925C22semidirect
88. #1846C22semidirect
89. #1835C22semidirect

Maximal subgroups

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

subgroupindex
#366242
C2×#22832
#331092
#331082
#331072
#331062
#299262
#299252
#279772
#279122
#278932
#275902
#240072
#240042
#219852
#218072
#207142