Finite Group Databasebeta

← #6477242

Subgroups — #6477242

Order 512.

2000 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#33217C212yesmaximal, complemented
4#33052C212yesmaximal, complemented
5#30365C212yesmaximal, complemented
6#30364C212yesmaximal, complemented
7#29157C212yesmaximal, complemented
8#29156C212yesmaximal, complemented
9#27968C211yesmaximal, characteristic, complemented
10#27917C211yesmaximal, characteristic, complemented
11#27881C212yesmaximal, complemented
12#25911C211yesmaximal, characteristic, complemented
13#25818C211yesmaximal, characteristic, complemented
14#25676C212yesmaximal, complemented
15#24555C214yesmaximal, complemented
16#22086C214yesmaximal, complemented
17C2×#1749C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×#525—21no—
21C23×C42C2211yescharacteristic
22C2×#501C2212yescomplemented
23C2×#490C2212yescomplemented
24C2×#482C2214yes—
25C22×C22⋊C8C2212yes—
26C22×#97C2212yes—
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2856C2211yescharacteristic
34#2856C2211yescharacteristic
35#2855—21no—
36#2855—21no—
37#2854—21no—
38#2854C2212yes—
39#2851C2212yes—
40#2851C2212yes—
41#2850—21no—
42#2850—21no—
43#2848—21no—
44#2848—21no—
45#2847—21no—
46#2847C2212yes—
47C4×C22⋊Q8—21no—
48C4×C22⋊Q8—21no—
49C4×C22⋊Q8—21no—
50C4×C22⋊Q8—21no—
51C4×#121—21no—
52C4×#121—21no—
53C4×#121C2212yes—
54C4×#121C2212yes—
55#2297—21no—
56#2296C2212yes—
57#2285C2211yescharacteristic
58#2285C2211yescharacteristic
59#2280C2212yes—
60#2100C2212yescomplemented
61#2099C2212yescomplemented
62#2094C2212yescomplemented
63#2093C2212yescomplemented
64#2077C2214yes—
65#2076C2214yes—
66#2058C2212yescomplemented
67#2057C2212yescomplemented
68#2034C2214yes—
69#2033C2214yes—
70#2023C2212yescomplemented
71#2023C2212yescomplemented
72#1993C2212yescomplemented
73#1992C2212yescomplemented
74#1992C2212yescomplemented
75#1961C2212yescomplemented
76#1944C2214yescomplemented
77#1943C2214yescomplemented
78#1936C2214yescomplemented
79#1936C2214yescomplemented
80#1920C2214yescomplemented
81#1918C2214yescomplemented
82#1893C2214yes—
83#1893C2214yes—
84#1875C2214yes—
85#1864C2214yescomplemented
86#1862C2214yescomplemented
87#1854C2214yes—
88#1847C2212yescomplemented
89#1836C2212yescomplemented
90#1825C2214yes—
91#1808C2214yes—
92#1807C2214yes—
93#1749C2211yescharacteristic
94#1749C2211yescharacteristic
95#1749C2212yes—
96#1749C2212yes—
97#1749C2212yes—
98C2×#336C2212yes—
99C22×#41—21no—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C23×C8C2314yes—
104#533—44no—
105#532—44no—
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×#127C2311yescharacteristic
110C2×#125C2312yes—
111C2×#124—21no—
112#525—48no—
113C2×#123—22no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—21no—
121C2×C22⋊Q8—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×#121C2312yes—
130C2×#120—22no—
131C2×C4×Q8—21no—
132C2×C4×Q8—21no—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—21no—
136C2×C4×D4C2312yes—
137C2×#117—21no—
138C2×#117C2312yes—
139C2×#117C2312yes—
140C22×C42—44no—
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#501—44no—
154#490—44no—
155#482—216no—
156C2×#107C2314yes—
157C2×#107C2314yes—
158C2×#106C2314yes—
159C2×#106C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×C22⋊C8—28no—
165C2×C22⋊C8C2314yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2312yes—
168C2×#97—44no—
169C2×#97C2312yes—
170C2×#97C2312yes—
171C2×#97C2314yes—
172#391—21no—
173#391—21no—
174#391—21no—
175#391—21no—
176#391—21no—
177#391—21no—
178#390—21no—
179#390—21no—
180#390—21no—
181#390—21no—
182#390C2312yes—
183#390C2312yes—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189#389—21no—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#389C2312yes—
196#388—22no—
197#388—22no—
198#388—22no—
199#388—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#386—22no—
205#386—22no—
206#386—22no—
207#386—22no—
208#386—22no—
209#386—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#384C2311yescharacteristic
217#384C2311yescharacteristic
218#384C2311yescharacteristic
219#384C2311yescharacteristic
220#382—21no—
221#382C2312yes—
222#381—22no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#380C2312yes—
238#380C2312yes—
239#379—22no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—22no—
245C4×C4⋊C4C2312yes—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2312yes—
259#336C2312yes—
260#336C2314yes—
261C25C2×D411yescharacteristic
262C2×#41—44no—
263C2×#41—44no—
264C2×#41—44no—
265C22×Q8—21no—
266C22×Q8—21no—
267C22×Q8—21no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4C2412yes—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C22×C8—28no—
303C22×C8—28no—
304C22×C8—44no—
305C22×C8C2414yes—
306C22×C8C2414yes—
307C4⋊Q8—24no—
308C4⋊Q8—42no—
309C4⋊Q8—42no—
310#127—24no—
311#125—24no—
312#125—24no—
313#124—44no—
314#123—48no—
315C22⋊Q8—44no—
316C22⋊Q8—44no—
317C22⋊Q8—44no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320C22⋊Q8—44no—
321C22⋊Q8—44no—
322C22⋊Q8—44no—
323#121—28no—
324#121—28no—
325#121—44no—
326#121—44no—
327#121—44no—
328#121—44no—
329#121—44no—
330#121—44no—
331#120—48no—
332C4×Q8—44no—
333C4×Q8—44no—
334C4×D4—44no—
335C4×D4—44no—
336C4×D4—48no—
337C4×D4—48no—
338#117—28no—
339#117—42no—
340#117—42no—
341#117—44no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
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×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
413C2×C42C2411yescharacteristic
414C2×C42C2411yescharacteristic
415C2×C42C2411yescharacteristic
416#107—28no—
417#107—44no—
418#106—28no—
419#106—44no—
420#102—28no—
421#102—28no—
422#102—44no—
423#102—44no—
424C22⋊C8—24no—
425C22⋊C8—28no—
426C22⋊C8#4118yescomplemented
427#97—24no—
428#97—24no—
429#97—44no—
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—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—41no—
453C24—41no—
454C24C22×D411yescharacteristic
455C24C22×D411yescharacteristic
456C24C22×D411yescharacteristic
457#41—816no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—24no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
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—44no—
483C2×D4—42no—
484C2×D4—42no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
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—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
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—416no—
544C22×C4—416no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—416no—
548C22×C4—44no—
549C22×C4AGL(1,ℤ/8)14yes—
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C2×#4114yes—
562C22×C42−1+414yes—
563C22×C4C2511yescharacteristic
564C2×C8—24no—
565C2×C8—24no—
566C2×C8—24no—
567C2×C8—24no—
568C2×C8—24no—
569C2×C8—416no—
570C2×C8C2×#4118yes—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—24no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—44no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—42no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—44no—
632C42—44no—
633C42—44no—
634C42H(5,𝔽2)14yes—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—28no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23#53212yes—
666C23#53612yes—
667C23C2×AGL(1,ℤ/8)12yes—
668C23#57512yes—
669C23#57512yes—
670C23C23×D411yescharacteristic
671Q8—84no—
672Q8—84no—
673Q8—84no—
674D4—48no—
675D4—84no—
676D4—84no—
677D4—88no—
678D4—88no—
679D4—88no—
680C2×C4—28no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
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—88no—
746C2×C4#53212yes—
747C2×C4#53412yes—
748C2×C4#53412yes—
749C2×C4#53612yes—
750C2×C4C2×AGL(1,ℤ/8)12yes—
751C2×C4C2×AGL(1,ℤ/8)12yes—
752C2×C4#57512yes—
753C2×C4C22×#4112yes—
754C2×C4C2×H(5,𝔽2)12yes—
755C2×C4C2×2−1+412yes—
756C8—28no—
757C8—44no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—416no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22#323514yes—
787C22C2×#53211yescharacteristic
788C22C2×#53411yescharacteristic
789C22C2×#53611yescharacteristic
790C22C22×AGL(1,ℤ/8)11yescharacteristic
791C22C2×#57511yescharacteristic
792C22C2×#57511yescharacteristic
793C22C2×#57511yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—22no—
799C4—22no—
800C4—22no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—82no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4#352014yes—
813C2—24no—
814C2—42no—
815C2—42no—
816C2—162no—
817C2#3508511yescharacteristic
818C2#6068811yescharacteristic
819C2#6070011yescharacteristic
820C2#6075011yescharacteristic
821C2#6075211yescharacteristic
822C2C2×#323511yescharacteristic
823C2#6085411yescharacteristic
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. #33217C2semidirect
4. #33052C2semidirect
5. #30365C2semidirect
6. #30364C2semidirect
7. #29157C2semidirect
8. #29156C2semidirect
9. #27968C2semidirect
10. #27917C2semidirect
11. #27881C2semidirect
12. #25911C2semidirect
13. #25818C2semidirect
14. #25676C2semidirect
15. #24555C2semidirect
16. #22086C2semidirect
17. C2×#1749C2semidirect
22. C2×#501C22semidirect
23. C2×#490C22semidirect
60. #2100C22semidirect
61. #2099C22semidirect
62. #2094C22semidirect
63. #2093C22semidirect
66. #2058C22semidirect
67. #2057C22semidirect
70. #2023C22semidirect
71. #2023C22semidirect
72. #1993C22semidirect
73. #1992C22semidirect
74. #1992C22semidirect
75. #1961C22semidirect
76. #1944C22semidirect
77. #1943C22semidirect
78. #1936C22semidirect
79. #1936C22semidirect
80. #1920C22semidirect
81. #1918C22semidirect
85. #1864C22semidirect
86. #1862C22semidirect
88. #1847C22semidirect
89. #1836C22semidirect
426. C22⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#332172
#330522
#303652
#303642
#291572
#291562
#279682
#279172
#278812
#259112
#258182
#256762
#245552
#220862
C2×#17492