Finite Group Databasebeta

← #6660702

Subgroups — #6660702

Order 512.

2048 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#32725C212yesmaximal, complemented
4#32721C212yesmaximal, complemented
5#30242C211yesmaximal, characteristic, complemented
6#30240C211yesmaximal, characteristic, complemented
7#30187C211yesmaximal, characteristic, complemented
8#30185C211yesmaximal, characteristic, complemented
9#29954C212yesmaximal, complemented
10#29928C212yesmaximal, complemented
11#29717C212yesmaximal, complemented
12#29668C212yesmaximal, complemented
13#27685C212yesmaximal, complemented
14#24755C214yesmaximal, complemented
15#24383C214yesmaximal, complemented
16#24216C212yesmaximal, complemented
17C2×#1797C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×#525C2212yes—
21C23×C42C2211yescharacteristic
22C2×#467C2214yes—
23C2×#465C2214yes—
24C2×#464C2214yescomplemented
25C2×#452C2214yes—
26C22×C4⋊C8C2212yes—
27C22×C22⋊C8C2212yes—
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2856C2211yescharacteristic
35#2856C2211yescharacteristic
36#2855—21no—
37#2855C2212yes—
38#2854—21no—
39#2854—21no—
40#2851—21no—
41#2851—21no—
42#2850C2212yes—
43#2850C2212yes—
44#2848—21no—
45#2848C2212yes—
46#2847—21no—
47#2847—21no—
48C4×C22⋊Q8—21no—
49C4×C22⋊Q8—21no—
50C4×C22⋊Q8C2212yes—
51C4×C22⋊Q8C2212yes—
52C4×#121—21no—
53C4×#121—21no—
54C4×#121—21no—
55C4×#121—21no—
56#2297C2212yes—
57#2296—21no—
58#2285C2211yescharacteristic
59#2285C2211yescharacteristic
60#2280—21no—
61#2100C2212yescomplemented
62#2099C2212yescomplemented
63#2096C2212yescomplemented
64#2095C2212yescomplemented
65#2095C2212yescomplemented
66#2094C2212yescomplemented
67#2072C2212yescomplemented
68#2071C2212yescomplemented
69#2067C2214yescomplemented
70#2066C2214yescomplemented
71#2056C2214yescomplemented
72#2055C2214yescomplemented
73#2043C2212yescomplemented
74#2041C2212yescomplemented
75#2035C2214yes—
76#2033C2214yes—
77#2024C2212yescomplemented
78#2023C2212yescomplemented
79#2016C2212yescomplemented
80#2016C2212yescomplemented
81#2014C2212yescomplemented
82#2013C2212yescomplemented
83#2001C2214yes—
84#2000C2214yes—
85#1983C2214yescomplemented
86#1949C2214yescomplemented
87#1893C2214yes—
88#1892C2214yes—
89#1873C2214yes—
90#1854C2214yes—
91#1805C2214yescomplemented
92#1797C2212yes—
93#1797C2212yes—
94#1797C2212yes—
95#1797C2212yes—
96#1788C2214yes—
97C2×#336C2211yescharacteristic
98C2×#336C2211yescharacteristic
99C22×#41C2312yes—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C22×Q16C2314yes—
104C22×SD16C2314yes—
105C23×C8C2312yes—
106C23×C8C2312yes—
107#533—44no—
108#532—44no—
109C2×C4⋊Q8C2311yescharacteristic
110C2×C4⋊Q8C2311yescharacteristic
111C2×C4⋊Q8C2311yescharacteristic
112C2×#127C2311yescharacteristic
113C2×#125—21no—
114C2×#124C2312yes—
115#525—48no—
116C2×#123—22no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8C2312yes—
121C2×C22⋊Q8C2312yes—
122C2×C22⋊Q8C2312yes—
123C2×C22⋊Q8C2312yes—
124C2×C22⋊Q8C2312yes—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121—21no—
128C2×#121—21no—
129C2×#121—21no—
130C2×#121—21no—
131C2×#121C2312yes—
132C2×#121C2312yes—
133C2×#120—22no—
134C2×C4×Q8—21no—
135C2×C4×Q8C2312yes—
136C2×C4×D4—22no—
137C2×C4×D4—22no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×#117—21no—
141C2×#117—21no—
142C2×#117C2312yes—
143C22×C42—44no—
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#467—48no—
157#465—48no—
158#464—48no—
159#452—48no—
160C2×#107C2314yes—
161C2×#106C2314yes—
162C2×C4⋊C8—44no—
163C2×C4⋊C8C2314yes—
164C2×C4⋊C8C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×C22⋊C8—44no—
174C2×C22⋊C8C2314yes—
175C2×C22⋊C8C2314yes—
176#391—21no—
177#391—21no—
178#391C2312yes—
179#391C2312yes—
180#391C2312yes—
181#391C2312yes—
182#390—21no—
183#390—21no—
184#390—21no—
185#390—21no—
186#390C2312yes—
187#390C2312yes—
188#389—21no—
189#389—21no—
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#389C2312yes—
199#389C2312yes—
200#388—22no—
201#388—22no—
202#388—22no—
203#388—22no—
204#387—22no—
205#387—22no—
206#387—22no—
207#387—22no—
208#386—22no—
209#386—22no—
210#386—22no—
211#386—22no—
212#386—22no—
213#386—22no—
214#385—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#385—22no—
220#384C2311yescharacteristic
221#384C2311yescharacteristic
222#384C2311yescharacteristic
223#384C2311yescharacteristic
224#382—21no—
225#382C2312yes—
226#381—22no—
227#380—21no—
228#380—21no—
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#380C2312yes—
241#380C2312yes—
242#380C2312yes—
243#379—22no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—22no—
248C4×C4⋊C4—22no—
249C4×C4⋊C4C2312yes—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2312yes—
259#336C2312yes—
260#336C2312yes—
261#336C2312yes—
262C25C2×D411yescharacteristic
263C2×#41—24no—
264C2×#41—24no—
265C2×#41—44no—
266C2×#41—44no—
267C22×Q8—21no—
268C22×Q8C2412yes—
269C22×Q8C2412yes—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4C2412yes—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
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
305C2×Q16—44no—
306C2×Q16—44no—
307C2×Q16—44no—
308C2×SD16—44no—
309C2×SD16—44no—
310C2×SD16—44no—
311C22×C8—24no—
312C22×C8—24no—
313C22×C8—42no—
314C22×C8—42no—
315C22×C8—42no—
316C22×C8—42no—
317C22×C8C2414yes—
318C22×C8C2414yes—
319C4⋊Q8—42no—
320C4⋊Q8—42no—
321C4⋊Q8—42no—
322#127—42no—
323#125—44no—
324#124—28no—
325#123—48no—
326C22⋊Q8—28no—
327C22⋊Q8—24no—
328C22⋊Q8—28no—
329C22⋊Q8—24no—
330C22⋊Q8—44no—
331C22⋊Q8—44no—
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—28no—
345C4×Q8—44no—
346C4×D4—44no—
347C4×D4—44no—
348C4×D4—48no—
349C4×D4—48no—
350#117—44no—
351#117—44no—
352#117—44no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C22⋊C4—22no—
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×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—42no—
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×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427#107—44no—
428#106—44no—
429C4⋊C8—28no—
430C4⋊C8—44no—
431#103—44no—
432#103—44no—
433#103—44no—
434#103—44no—
435#103—44no—
436#102—44no—
437#102—44no—
438#102—44no—
439C22⋊C8—28no—
440C22⋊C8—44no—
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—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—41no—
464C24—41no—
465C24C22×D411yescharacteristic
466C24C22×D411yescharacteristic
467C24C22×D411yescharacteristic
468#41—88no—
469#41—88no—
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—24no—
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×D4—22no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—42no—
499C2×D4—42no—
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—21no—
510C22×C4—21no—
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—22no—
534C22×C4—22no—
535C22×C4—21no—
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—48no—
560C22×C4—48no—
561C22×C4—416no—
562C22×C4—416no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4#13514yes—
567C22×C4#13714yes—
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×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4H(5,𝔽2)14yes—
580C22×C4H(5,𝔽2)12yes—
581C22×C42−1+412yes—
582C22×C4C2511yescharacteristic
583Q16—88no—
584SD16—88no—
585C2×C8—24no—
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—24no—
589C2×C8—24no—
590C2×C8—24no—
591C2×C8—84no—
592C2×C8—84no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—42no—
619C4⋊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—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42H(5,𝔽2)14yes—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—28no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23#53512yes—
687C23#53712yes—
688C23C2×#13512yes—
689C23C2×#13712yes—
690C23#57512yes—
691C23C23×D411yescharacteristic
692Q8—44no—
693Q8—44no—
694Q8—44no—
695Q8—44no—
696Q8—84no—
697D4—44no—
698D4—44no—
699D4—84no—
700D4—84no—
701D4—88no—
702D4—88no—
703D4—88no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
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—21no—
723C2×C4—21no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—44no—
735C2×C4—44no—
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—44no—
745C2×C4—44no—
746C2×C4—44no—
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—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—88no—
771C2×C4#53412yes—
772C2×C4#53412yes—
773C2×C4#53512yes—
774C2×C4#53712yes—
775C2×C4C2×#13512yes—
776C2×C4C2×#13512yes—
777C2×C4C2×#13712yes—
778C2×C4C2×#13712yes—
779C2×C4#57512yes—
780C2×C4C2×H(5,𝔽2)12yes—
781C2×C4C2×H(5,𝔽2)12yes—
782C2×C4C2×H(5,𝔽2)11yescharacteristic
783C2×C4C2×2−1+411yescharacteristic
784C8—44no—
785C8—44no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—416no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22#321014yes—
815C22C2×#53411yescharacteristic
816C22C2×#53511yescharacteristic
817C22C2×#53711yescharacteristic
818C22C22×#13511yescharacteristic
819C22C22×#13711yescharacteristic
820C22C2×#57511yescharacteristic
821C22C2×#57511yescharacteristic
822C4—22no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—22no—
827C4—22no—
828C4—22no—
829C4—22no—
830C4—22no—
831C4—41no—
832C4—41no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4#353612yes—
841C4#353712yes—
842C2—24no—
843C2—42no—
844C2—42no—
845C2—162no—
846C2#3743911yescharacteristic
847C2#6073411yescharacteristic
848C2#6075111yescharacteristic
849C2C2×#321011yescharacteristic
850C2#6079011yescharacteristic
851C2#6090011yescharacteristic
852C2#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. #32725C2semidirect
4. #32721C2semidirect
5. #30242C2semidirect
6. #30240C2semidirect
7. #30187C2semidirect
8. #30185C2semidirect
9. #29954C2semidirect
10. #29928C2semidirect
11. #29717C2semidirect
12. #29668C2semidirect
13. #27685C2semidirect
14. #24755C2semidirect
15. #24383C2semidirect
16. #24216C2semidirect
17. C2×#1797C2semidirect
24. C2×#464C22semidirect
61. #2100C22semidirect
62. #2099C22semidirect
63. #2096C22semidirect
64. #2095C22semidirect
65. #2095C22semidirect
66. #2094C22semidirect
67. #2072C22semidirect
68. #2071C22semidirect
69. #2067C22semidirect
70. #2066C22semidirect
71. #2056C22semidirect
72. #2055C22semidirect
73. #2043C22semidirect
74. #2041C22semidirect
77. #2024C22semidirect
78. #2023C22semidirect
79. #2016C22semidirect
80. #2016C22semidirect
81. #2014C22semidirect
82. #2013C22semidirect
85. #1983C22semidirect
86. #1949C22semidirect
91. #1805C22semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#327252
#327212
#302422
#302402
#301872
#301852
#299542
#299282
#297172
#296682
#276852
#247552
#243832
#242162
C2×#17972