Finite Group Databasebeta

← #6493634

Subgroups — #6493634

Order 512.

2008 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2850C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic, complemented
3#33112C214yesmaximal, complemented
4#29924C214yesmaximal, complemented
5#27979C212yesmaximal, complemented
6#27915C212yesmaximal, complemented
7#27895C212yesmaximal, complemented
8#27894C212yesmaximal, complemented
9#27589C212yesmaximal, complemented
10#27588C212yesmaximal, complemented
11#24010C212yesmaximal, complemented
12#24009C212yesmaximal
13#21986C211yesmaximal, characteristic, complemented
14#21986C211yesmaximal, characteristic, complemented
15#21808C211yesmaximal, characteristic, complemented
16#21808C211yesmaximal, characteristic, complemented
17#20715C211yesmaximal, characteristic, complemented
18C22×#124C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#485C2214yescomplemented
23C2×#482C2214yes—
24C2×#432C2211yescharacteristic
25C2×#432C2211yescharacteristic
26#2850—21no—
27#2850—21no—
28#2850—21no—
29#2850—21no—
30#2850C2212yes—
31#2850C2212yes—
32#2850C2212yes—
33#2850C2212yes—
34C2×#391C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#388—21no—
37C2×#388—21no—
38C2×#386—21no—
39C2×#386—21no—
40#2285C2211yescharacteristic
41#2285C2211yescharacteristic
42#2285C2211yescharacteristic, complemented
43#2285C2211yescharacteristic, complemented
44#2285C2211yescharacteristic, complemented
45#2285C2211yescharacteristic, complemented
46#2283—21no—
47#2283—21no—
48#2283—21no—
49#2283—21no—
50#2283C2212yes—
51#2283C2212yescomplemented
52C2×#382C2211yescharacteristic
53#2280—21no—
54#2280—21no—
55#2280C2212yes—
56C4×#117—21no—
57C4×#117—21no—
58C4×#117C2212yescomplemented
59#2097C2214yescomplemented
60#2092C2214yescomplemented
61#2074C2214yescomplemented
62#2073C2214yescomplemented
63#2036C2214yescomplemented
64#2035C2214yescomplemented
65#2034C2214yes—
66#2033C2214yes—
67#1983C2214yescomplemented
68#1983C2214yescomplemented
69#1959C2212yescomplemented
70#1959C2212yescomplemented
71#1959C2212yescomplemented
72#1959C2212yescomplemented
73#1949C2214yescomplemented
74#1949C2214yescomplemented
75#1928C2214yescomplemented
76#1927C2214yescomplemented
77#1926C2214yescomplemented
78#1925C2214yescomplemented
79#1875C2214yes—
80#1873C2214yescomplemented
81#1853C2212yes—
82#1853C2212yes—
83#1852C2212yes—
84#1852C2212yes—
85#1847C2212yescomplemented
86#1847C2212yescomplemented
87#1836C2212yescomplemented
88#1836C2212yescomplemented
89#1817C2212yes—
90#1797C2212yescomplemented
91#1797C2212yescomplemented
92#1787C2212yes—
93#1787C2212yes—
94#1786C2212yes—
95#1786C2212yes—
96#1779C2212yes—
97#1749C2212yescomplemented
98#1749C2212yescomplemented
99C23×Q8C2311yescharacteristic
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C2×#124—21no—
106C2×#124—21no—
107C2×#124—24no—
108C2×#124—24no—
109C2×#124C2312yes—
110C2×#124C2312yes—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—44no—
114C2×C22⋊Q8C2312yes—
115C2×C22⋊Q8C2312yes—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121—44no—
119C2×#121C2312yes—
120C2×#121C2312yes—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—21no—
124C2×#117—21no—
125C2×#117C2312yes—
126C2×#117C2312yes—
127C22×C4⋊C4—21no—
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×C22⋊C4—21no—
136C22×C42—24no—
137C22×C42—24no—
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150#485—48no—
151#482—48no—
152#432—24no—
153#432—24no—
154C2×#107C2314yes—
155C2×#107C2314yes—
156C2×#106C2314yes—
157C2×#106C2314yes—
158C2×C4⋊C8C2312yes—
159C2×C4⋊C8C2312yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×C22⋊C8C2314yes—
169C2×C22⋊C8C2312yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2314yes—
172C2×#97C2312yes—
173C2×#97C2312yes—
174#391—21no—
175#391—21no—
176#391C2312yes—
177#391C2312yes—
178#390—21no—
179#390—21no—
180#390C2312yes—
181#390C2312yes—
182#388—22no—
183#388—22no—
184#388—22no—
185#388—22no—
186#388—22no—
187#388—22no—
188#388—22no—
189#388—22no—
190#386—22no—
191#386—22no—
192#386—22no—
193#386—22no—
194#386—22no—
195#386—22no—
196#386—22no—
197#386—22no—
198#384C2311yescharacteristic
199#384C2311yescharacteristic
200#384C2311yescharacteristic
201#384C2311yescharacteristic
202#383—22no—
203#383—22no—
204#382—21no—
205#382—21no—
206#382—21no—
207#382—21no—
208#382—21no—
209#382—21no—
210#382C2312yes—
211#382C2312yes—
212#382C2312yes—
213#382C2312yes—
214#381—22no—
215#381—22no—
216#381—22no—
217#380—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380—21no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380C2312yes—
226#380C2312yes—
227#380C2312yes—
228#380C2312yes—
229#379—22no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2312yes—
240C4×C4⋊C4C2312yes—
241C4×C4⋊C4C2312yes—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248#376—22no—
249#376—22no—
250#376—22no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254C2×#95—21no—
255C43—22no—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#336C2314yes—
261#336C2314yes—
262C25—21no—
263C25C2×D411yescharacteristic
264C22×Q8—21no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—42no—
268C22×Q8—42no—
269C22×Q8C2412yes—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—21no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—42no—
276C22×D4—42no—
277C22×D4—44no—
278C22×D4—44no—
279C22×D4—44no—
280C22×D4C2412yes—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—24no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
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×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C22×C8C2414yes—
313C22×C8C2414yes—
314#124—24no—
315#124—24no—
316#124—24no—
317#124—24no—
318#124—44no—
319#124—44no—
320C22⋊Q8—28no—
321C22⋊Q8—44no—
322C22⋊Q8—44no—
323C22⋊Q8—44no—
324#121—28no—
325#121—44no—
326#121—44no—
327#121—44no—
328#117—28no—
329#117—44no—
330#117—44no—
331#117—44no—
332#117—44no—
333#117—44no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
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—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
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—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
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×C42#4114yes—
414C2×C42#4114yes—
415C2×C42C2411yescharacteristic
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419#107—44no—
420#107—44no—
421#106—44no—
422#106—44no—
423C4⋊C8—24no—
424C4⋊C8—24no—
425#103—44no—
426#103—44no—
427#103—44no—
428#103—44no—
429#102—44no—
430#102—44no—
431#102—44no—
432#102—44no—
433C22⋊C8—24no—
434C22⋊C8—24no—
435C22⋊C8—28no—
436C22⋊C8—44no—
437#97—24no—
438#97—24no—
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—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—41no—
466C24—41no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24C22×D411yescharacteristic
475C24C22×D411yescharacteristic
476C24C22×D411yescharacteristic
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—84no—
485C2×Q8—84no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—42no—
499C2×D4—84no—
500C2×D4—84no—
501C2×D4—816no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
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—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
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—48no—
562C22×C4—48no—
563C22×C4—416no—
564C22×C4—416no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4#12314yes—
575C22×C4#12314yes—
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C2×#4112yes—
588C22×C4C2×#4112yes—
589C22×C4H(5,𝔽2)14yes—
590C22×C4C2511yescharacteristic
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—24no—
594C2×C8—24no—
595C2×C8—24no—
596C2×C8—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—44no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊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—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—44no—
652C42—44no—
653C42#12314yes—
654C42#12314yes—
655C42C2×#4112yes—
656C42C2×#4112yes—
657C42C2×#4112yes—
658C42C2×#4112yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—28no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23C2×#12312yes—
697C23#53512yes—
698C23#57512yes—
699C23#57512yes—
700C23#57512yes—
701C23C23×D411yescharacteristic
702Q8—44no—
703Q8—44no—
704Q8—84no—
705D4—44no—
706D4—44no—
707D4—84no—
708D4—88no—
709D4—88no—
710C2×C4—28no—
711C2×C4—28no—
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—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—84no—
779C2×C4—84no—
780C2×C4—84no—
781C2×C4C2×#12312yes—
782C2×C4C2×#12312yes—
783C2×C4C2×#12312yes—
784C2×C4C2×#12312yes—
785C2×C4C2×#12312yes—
786C2×C4#53512yes—
787C2×C4#57512yes—
788C2×C4C22×#4111yescharacteristic
789C2×C4C22×#4111yescharacteristic
790C2×C4C2×H(5,𝔽2)12yes—
791C2×C4#58512yes—
792C8—44no—
793C8—44no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—416no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—168no—
823C22#309314yes—
824C22C22×#12311yescharacteristic
825C22C2×#53511yescharacteristic
826C22#344911yescharacteristic
827C22C2×#57511yescharacteristic
828C22C2×#57511yescharacteristic
829C22C2×#57511yescharacteristic
830C22C2×#57511yescharacteristic
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4#349412yes—
850C4#349412yes—
851C2—24no—
852C2—42no—
853C2—42no—
854C2—162no—
855C2#3526211yescharacteristic
856C2C2×#309311yescharacteristic
857C2#6051111yescharacteristic
858C2#6079011yescharacteristic
859C2#6079911yescharacteristic
860C2#6095411yescharacteristic
861C2#6095911yescharacteristic
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. #33112C2semidirect
4. #29924C2semidirect
5. #27979C2semidirect
6. #27915C2semidirect
7. #27895C2semidirect
8. #27894C2semidirect
9. #27589C2semidirect
10. #27588C2semidirect
11. #24010C2semidirect
13. #21986C2semidirect
14. #21986C2semidirect
15. #21808C2semidirect
16. #21808C2semidirect
17. #20715C2semidirect
22. C2×#485C22semidirect
42. #2285C22semidirect
43. #2285C22semidirect
44. #2285C22semidirect
45. #2285C22semidirect
51. #2283C22semidirect
58. C4×#117C22semidirect
59. #2097C22semidirect
60. #2092C22semidirect
61. #2074C22semidirect
62. #2073C22semidirect
63. #2036C22semidirect
64. #2035C22semidirect
67. #1983C22semidirect
68. #1983C22semidirect
69. #1959C22semidirect
70. #1959C22semidirect
71. #1959C22semidirect
72. #1959C22semidirect
73. #1949C22semidirect
74. #1949C22semidirect
75. #1928C22semidirect
76. #1927C22semidirect
77. #1926C22semidirect
78. #1925C22semidirect
80. #1873C22semidirect
85. #1847C22semidirect
86. #1847C22semidirect
87. #1836C22semidirect
88. #1836C22semidirect
90. #1797C22semidirect
91. #1797C22semidirect
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×#28502
#340122
#331122
#299242
#279792
#279152
#278952
#278942
#275892
#275882
#240102
#240092
#219862
#218082
#207152