Finite Group Databasebeta

← #6660700

Subgroups — #6660700

Order 512.

2048 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#32728C214yesmaximal, complemented
4#30244C212yesmaximal, complemented
5#30188C212yesmaximal, complemented
6#29955C212yesmaximal, complemented
7#29922C211yesmaximal, characteristic, complemented
8#29920C211yesmaximal, characteristic, complemented
9#29717C212yesmaximal, complemented
10#29664C211yesmaximal, characteristic, complemented
11#29661C211yesmaximal, characteristic, complemented
12#27682C212yesmaximal, complemented
13#24753C212yesmaximal, complemented
14#24752C212yesmaximal, complemented
15#24383C214yesmaximal, complemented
16#24213C212yesmaximal, complemented
17C2×#1797C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×#525C2212yes—
21C23×C42C2211yescharacteristic
22C2×#467C2214yes—
23C2×#465C2214yes—
24C2×#462C2212yescomplemented
25C2×#460C2212yescomplemented
26C2×#452C2214yes—
27C22×C4⋊C8C2212yes—
28C22×C22⋊C8C2212yes—
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2856C2211yescharacteristic
36#2856C2211yescharacteristic
37#2855—21no—
38#2855C2212yes—
39#2854—21no—
40#2854—21no—
41#2851—21no—
42#2851—21no—
43#2850C2212yes—
44#2850C2212yes—
45#2848—21no—
46#2848C2212yes—
47#2847—21no—
48#2847—21no—
49C4×C22⋊Q8—21no—
50C4×C22⋊Q8—21no—
51C4×C22⋊Q8C2212yes—
52C4×C22⋊Q8C2212yes—
53C4×#121—21no—
54C4×#121—21no—
55C4×#121—21no—
56C4×#121—21no—
57#2297C2212yes—
58#2296—21no—
59#2285C2211yescharacteristic
60#2285C2211yescharacteristic
61#2280—21no—
62#2101C2214yescomplemented
63#2097C2214yescomplemented
64#2096C2212yescomplemented
65#2093C2212yescomplemented
66#2072C2212yescomplemented
67#2071C2212yescomplemented
68#2068C2214yescomplemented
69#2065C2214yescomplemented
70#2056C2214yescomplemented
71#2055C2214yescomplemented
72#2042C2214yescomplemented
73#2035C2214yes—
74#2033C2214yes—
75#2024C2212yescomplemented
76#2023C2212yescomplemented
77#2016C2212yescomplemented
78#2015C2214yescomplemented
79#2013C2212yescomplemented
80#2001C2214yes—
81#2000C2214yes—
82#1982C2212yescomplemented
83#1981C2212yescomplemented
84#1948C2212yescomplemented
85#1947C2212yescomplemented
86#1893C2214yes—
87#1892C2214yes—
88#1873C2214yes—
89#1854C2214yes—
90#1803C2212yescomplemented
91#1803C2212yescomplemented
92#1797C2212yes—
93#1797C2212yes—
94#1797C2212yes—
95#1797C2211yescharacteristic
96#1797C2211yescharacteristic
97#1788C2214yes—
98C2×#336C2212yes—
99C22×#41C2312yes—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C22×Q16C2314yes—
104C22×SD16C2314yes—
105C23×C8C2314yes—
106#533—44no—
107#532—44no—
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2311yescharacteristic
110C2×C4⋊Q8C2311yescharacteristic
111C2×#127C2311yescharacteristic
112C2×#125—21no—
113C2×#124C2312yes—
114#525—48no—
115C2×#123—22no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8C2312yes—
120C2×C22⋊Q8C2312yes—
121C2×C22⋊Q8C2312yes—
122C2×C22⋊Q8C2312yes—
123C2×C22⋊Q8C2312yes—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121—21no—
128C2×#121—21no—
129C2×#121—21no—
130C2×#121C2312yes—
131C2×#121C2312yes—
132C2×#120—22no—
133C2×C4×Q8—21no—
134C2×C4×Q8C2312yes—
135C2×C4×D4—22no—
136C2×C4×D4—22no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×#117—21no—
140C2×#117—21no—
141C2×#117C2312yes—
142C22×C42—44no—
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#467—48no—
156#465—48no—
157#462—44no—
158#460—44no—
159#452—48no—
160C2×#107C2314yes—
161C2×#106C2314yes—
162C2×C4⋊C8—44no—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×C22⋊C8—44no—
175C2×C22⋊C8C2314yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178#391—21no—
179#391—21no—
180#391C2312yes—
181#391C2312yes—
182#391C2312yes—
183#391C2312yes—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390C2312yes—
189#390C2312yes—
190#389—21no—
191#389—21no—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389C2312yes—
201#389C2312yes—
202#388—22no—
203#388—22no—
204#388—22no—
205#388—22no—
206#387—22no—
207#387—22no—
208#387—22no—
209#387—22no—
210#386—22no—
211#386—22no—
212#386—22no—
213#386—22no—
214#386—22no—
215#386—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#385—22no—
220#385—22no—
221#385—22no—
222#384C2311yescharacteristic
223#384C2311yescharacteristic
224#384C2311yescharacteristic
225#384C2311yescharacteristic
226#382—21no—
227#382C2312yes—
228#381—22no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380—21no—
235#380—21no—
236#380—21no—
237#380—21no—
238#380—21no—
239#380—21no—
240#380—21no—
241#380—21no—
242#380C2312yes—
243#380C2312yes—
244#380C2312yes—
245#379—22no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—22no—
250C4×C4⋊C4—22no—
251C4×C4⋊C4C2312yes—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—22no—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#336C2312yes—
261#336C2312yes—
262#336C2314yes—
263C25C2×D411yescharacteristic
264C2×#41—24no—
265C2×#41—24no—
266C2×#41—44no—
267C2×#41—44no—
268C22×Q8—21no—
269C22×Q8C2412yes—
270C22×Q8C2412yes—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4C2412yes—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—42no—
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
306C2×Q16—44no—
307C2×Q16—44no—
308C2×Q16—44no—
309C2×SD16—44no—
310C2×SD16—44no—
311C2×SD16—44no—
312C22×C8—28no—
313C22×C8—44no—
314C22×C8—44no—
315C22×C8C2414yes—
316C22×C8C2414yes—
317C4⋊Q8—24no—
318C4⋊Q8—42no—
319C4⋊Q8—42no—
320#127—24no—
321#125—44no—
322#124—44no—
323#123—48no—
324C22⋊Q8—28no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329C22⋊Q8—44no—
330C22⋊Q8—42no—
331C22⋊Q8—42no—
332C22⋊Q8—44no—
333C22⋊Q8—44no—
334C22⋊Q8—44no—
335#121—28no—
336#121—44no—
337#121—44no—
338#121—44no—
339#121—44no—
340#121—44no—
341#121—44no—
342#121—44no—
343#120—48no—
344C4×Q8—24no—
345C4×Q8—24no—
346C4×Q8—44no—
347C4×D4—44no—
348C4×D4—44no—
349C4×D4—48no—
350C4×D4—48no—
351#117—44no—
352#117—44no—
353#117—44no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428#107—44no—
429#106—44no—
430C4⋊C8—24no—
431C4⋊C8—24no—
432C4⋊C8—44no—
433#103—44no—
434#103—44no—
435#103—44no—
436#103—44no—
437#103—44no—
438#102—44no—
439#102—44no—
440#102—44no—
441C22⋊C8—28no—
442C22⋊C8—42no—
443C22⋊C8—42no—
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—
459#95—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—41no—
467C24—41no—
468C24C22×D411yescharacteristic
469C24C22×D411yescharacteristic
470C24C22×D411yescharacteristic
471#41—88no—
472#41—88no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×D4—22no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—22no—
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—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
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—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
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—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—416no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—416no—
570C22×C4—44no—
571C22×C4#13514yes—
572C22×C4#13714yes—
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
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×C4H(5,𝔽2)14yes—
585C22×C4H(5,𝔽2)12yes—
586C22×C42−1+412yes—
587C22×C4C2511yescharacteristic
588Q16—88no—
589SD16—88no—
590C2×C8—24no—
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—24no—
594C2×C8—24no—
595C2×C8—24no—
596C2×C8—88no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—22no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—44no—
659C42—44no—
660C42—44no—
661C42H(5,𝔽2)14yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—28no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23#53512yes—
693C23#53712yes—
694C23C2×#13512yes—
695C23C2×#13712yes—
696C23#57512yes—
697C23C23×D411yescharacteristic
698Q8—42no—
699Q8—42no—
700Q8—44no—
701Q8—42no—
702Q8—42no—
703Q8—44no—
704Q8—84no—
705D4—44no—
706D4—44no—
707D4—84no—
708D4—88no—
709D4—88no—
710D4—88no—
711D4—84no—
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—28no—
725C2×C4—28no—
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—88no—
779C2×C4#53412yes—
780C2×C4#53412yes—
781C2×C4#53512yes—
782C2×C4#53712yes—
783C2×C4C2×#13512yes—
784C2×C4C2×#13512yes—
785C2×C4C2×#13712yes—
786C2×C4C2×#13712yes—
787C2×C4#57512yes—
788C2×C4C2×H(5,𝔽2)12yes—
789C2×C4C2×H(5,𝔽2)12yes—
790C2×C4C2×H(5,𝔽2)11yescharacteristic
791C2×C4C2×2−1+411yescharacteristic
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#321614yes—
823C22C2×#53411yescharacteristic
824C22C2×#53511yescharacteristic
825C22C2×#53711yescharacteristic
826C22C22×#13511yescharacteristic
827C22C22×#13711yescharacteristic
828C22C2×#57511yescharacteristic
829C22C2×#57511yescharacteristic
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—22no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4#319014yes—
848C4#353612yes—
849C4#353712yes—
850C2—24no—
851C2—42no—
852C2—42no—
853C2—162no—
854C2#3743911yescharacteristic
855C2C2×#319011yescharacteristic
856C2#6075211yescharacteristic
857C2#6078211yescharacteristic
858C2C2×#321611yescharacteristic
859C2#6090011yescharacteristic
860C2#6091811yescharacteristic
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
1. #36625C2semidirect
3. #32728C2semidirect
4. #30244C2semidirect
5. #30188C2semidirect
6. #29955C2semidirect
7. #29922C2semidirect
8. #29920C2semidirect
9. #29717C2semidirect
10. #29664C2semidirect
11. #29661C2semidirect
12. #27682C2semidirect
13. #24753C2semidirect
14. #24752C2semidirect
15. #24383C2semidirect
16. #24213C2semidirect
17. C2×#1797C2semidirect
24. C2×#462C22semidirect
25. C2×#460C22semidirect
62. #2101C22semidirect
63. #2097C22semidirect
64. #2096C22semidirect
65. #2093C22semidirect
66. #2072C22semidirect
67. #2071C22semidirect
68. #2068C22semidirect
69. #2065C22semidirect
70. #2056C22semidirect
71. #2055C22semidirect
72. #2042C22semidirect
75. #2024C22semidirect
76. #2023C22semidirect
77. #2016C22semidirect
78. #2015C22semidirect
79. #2013C22semidirect
82. #1982C22semidirect
83. #1981C22semidirect
84. #1948C22semidirect
85. #1947C22semidirect
90. #1803C22semidirect
91. #1803C22semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#327282
#302442
#301882
#299552
#299222
#299202
#297172
#296642
#296612
#276822
#247532
#247522
#243832
#242132
C2×#17972