Finite Group Databasebeta

← #6520484

Subgroups — #6520484

Order 512.

2448 conjugacy classes of subgroups.

The subgroup lattice has 1426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3257C211yesmaximal, characteristic, complemented
2C2×#3224C211yesmaximal, characteristic, complemented
3C2×#3119C211yesmaximal, characteristic, complemented
4C2×#3045C211yesmaximal, characteristic, complemented
5#37302C211yesmaximal, characteristic, complemented
6#35623C211yesmaximal, characteristic, complemented
7#28480C211yesmaximal, characteristic, complemented
8#28475C211yesmaximal, characteristic, complemented
9#28468C211yesmaximal, characteristic, complemented
10#28467C211yesmaximal, characteristic, complemented
11#28457C211yesmaximal, characteristic, complemented
12#28454C211yesmaximal, characteristic, complemented
13#28448C211yesmaximal, characteristic, complemented
14#28448C211yesmaximal, characteristic, complemented
15#28436C211yesmaximal, characteristic, complemented
16#28422C211yesmaximal, characteristic, complemented
17#28420C211yesmaximal, characteristic, complemented
18#28413C211yesmaximal, characteristic, complemented
19#28392C211yesmaximal, characteristic, complemented
20#28387C211yesmaximal, characteristic, complemented
21#28379C211yesmaximal, characteristic, complemented
22#28379C211yesmaximal, characteristic, complemented
23#28366C211yesmaximal, characteristic, complemented
24#28354C211yesmaximal, characteristic, complemented
25#28344C211yesmaximal, characteristic, complemented
26#28341C211yesmaximal, characteristic, complemented
27#25794C211yesmaximal, characteristic, complemented
28#25791C211yesmaximal, characteristic, complemented
29#25787C211yesmaximal, characteristic, complemented
30#25785C211yesmaximal, characteristic, complemented
31#20554C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C22×#135C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#540C2211yescharacteristic
36C2×#535C2211yescharacteristic
37C2×#520C2211yescharacteristic
38#3257—28no—
39#3224—28no—
40C2×#497C2211yescharacteristic, complemented
41C2×#496C2211yescharacteristic
42C2×#496C2211yescharacteristic
43C2×#496C2211yescharacteristic
44C2×#496C2211yescharacteristic, complemented
45C2×#496C2211yescharacteristic, complemented
46C2×#496C2211yescharacteristic, complemented
47C2×#495C2211yescharacteristic
48C2×#493C2211yescharacteristic
49C2×#492C2211yescharacteristic
50C2×#489C2211yescharacteristic
51C2×#486C2211yescharacteristic
52#3119—28no—
53C2×#481C2211yescharacteristic
54C2×#480C2211yescharacteristic
55C2×#479C2211yescharacteristic, complemented
56C2×#479C2211yescharacteristic, complemented
57C2×#478C2211yescharacteristic, complemented
58C2×#478C2211yescharacteristic, complemented
59C2×#476C2211yescharacteristic, complemented
60C2×#474C2211yescharacteristic, complemented
61C2×#469C2211yescharacteristic
62C2×#468C2211yescharacteristic
63C2×#466C2211yescharacteristic
64C2×#465C2211yescharacteristic
65#3045—28no—
66C2×#464C2211yescharacteristic
67C2×#464C2211yescharacteristic
68C2×#464C2211yescharacteristic
69C2×#460C2211yescharacteristic
70C2×#460C2211yescharacteristic
71C2×#460C2211yescharacteristic
72C2×#460C2211yescharacteristic, complemented
73C2×#460C2211yescharacteristic, complemented
74C2×#463C2211yescharacteristic
75C2×#463C2211yescharacteristic
76C2×#463C2211yescharacteristic
77C2×#463C2211yescharacteristic, complemented
78C2×#463C2211yescharacteristic, complemented
79C2×#459C2211yescharacteristic
80C2×#459C2211yescharacteristic
81C2×#459C2211yescharacteristic
82C2×#459C2211yescharacteristic, complemented
83C2×#459C2211yescharacteristic, complemented
84C2×#452C2211yescharacteristic
85C2×#449C2211yescharacteristic
86C2×#449C2211yescharacteristic
87C2×#449C2211yescharacteristic
88C2×#450C2211yescharacteristic
89C2×#447C2211yescharacteristic
90C2×#442C2211yescharacteristic, complemented
91C2×#440C2211yescharacteristic, complemented
92C2×C4×SD16C2211yescharacteristic, complemented
93C2×C4×D8C2211yescharacteristic, complemented
94C2×#433C2211yescharacteristic
95C2×#424C2211yescharacteristic
96C2×#417C2211yescharacteristic
97C22×#102C2211yescharacteristic
98#2867C2211yescharacteristic
99#2861C2211yescharacteristic
100#2673—22no—
101#2673—22no—
102#2669—22no—
103#2669—22no—
104#2657C2211yescharacteristic
105#2641C2211yescharacteristic
106#2568C2211yescharacteristic, complemented
107#2563C2211yescharacteristic, complemented
108#2545C2211yescharacteristic, complemented
109#2544C2211yescharacteristic
110#2544C2211yescharacteristic
111#2544C2211yescharacteristic, complemented
112#2541C2211yescharacteristic
113#2541C2211yescharacteristic
114#2504C2211yescharacteristic
115#2503C2211yescharacteristic
116#2481—22no—
117#2477—22no—
118#2459—22no—
119#2457—22no—
120#2433C2211yescharacteristic
121#2433C2211yescharacteristic
122#2432C2211yescharacteristic
123#2431C2211yescharacteristic
124#2431C2211yescharacteristic
125#2431C2211yescharacteristic
126#2328C2211yescharacteristic, complemented
127#2327C2211yescharacteristic, complemented
128C4×#124C2211yescharacteristic, complemented
129C4×#124C2211yescharacteristic, complemented
130#2298C2211yescharacteristic
131#2097C2211yescharacteristic, complemented
132#2097C2211yescharacteristic, complemented
133#2092C2211yescharacteristic
134#2092C2211yescharacteristic
135#2092C2211yescharacteristic
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2015C2211yescharacteristic, complemented
140#2015C2211yescharacteristic, complemented
141#2015C2211yescharacteristic, complemented
142#2015C2211yescharacteristic, complemented
143#2014C2211yescharacteristic
144#2014C2211yescharacteristic
145#2014C2211yescharacteristic
146#2014C2211yescharacteristic
147#2014C2211yescharacteristic, complemented
148#2014C2211yescharacteristic, complemented
149#2013C2211yescharacteristic
150#2013C2211yescharacteristic, complemented
151#2012C2211yescharacteristic
152#2012C2211yescharacteristic
153#2012C2211yescharacteristic, complemented
154#2012C2211yescharacteristic, complemented
155#2011C2211yescharacteristic
156#2011C2211yescharacteristic
157#2011C2211yescharacteristic
158#2011C2211yescharacteristic
159#2011C2211yescharacteristic
160#2011C2211yescharacteristic, complemented
161#2011C2211yescharacteristic, complemented
162#2011C2211yescharacteristic, complemented
163#1973C2211yescharacteristic
164#1973C2211yescharacteristic
165#1973C2211yescharacteristic
166#1973C2211yescharacteristic, complemented
167#1973C2211yescharacteristic, complemented
168#1973C2211yescharacteristic, complemented
169#1972C2211yescharacteristic
170#1972C2211yescharacteristic
171#1972C2211yescharacteristic
172#1972C2211yescharacteristic, complemented
173#1971C2211yescharacteristic, complemented
174#1971C2211yescharacteristic, complemented
175#1970C2211yescharacteristic
176#1970C2211yescharacteristic, complemented
177#1968C2211yescharacteristic
178#1968C2211yescharacteristic, complemented
179#1961C2211yescharacteristic
180#1961C2211yescharacteristic
181#1961C2211yescharacteristic
182#1961C2211yescharacteristic
183#1961C2211yescharacteristic, complemented
184#1961C2211yescharacteristic, complemented
185#1958C2211yescharacteristic, complemented
186#1958C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189#1770C2211yescharacteristic, complemented
190#1770C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1768C2211yescharacteristic, complemented
193#1767C2211yescharacteristic, complemented
194#1767C2211yescharacteristic, complemented
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C2×AGL(1,ℤ/8)—24no—
203C2×AGL(1,ℤ/8)—42no—
204C2×AGL(1,ℤ/8)—42no—
205C2×#135—24no—
206C2×#135—42no—
207C2×#135—42no—
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×D8C2311yescharacteristic
226C22×D8C2311yescharacteristic
227C22×D8C2311yescharacteristic
228C22×D8C2311yescharacteristic
229C22×D8C2311yescharacteristic
230C22×D8C2311yescharacteristic
231C22×D8C2311yescharacteristic
232C22×M16C2311yescharacteristic
233C23×C8C2311yescharacteristic
234#542—24no—
235#542—24no—
236#540—24no—
237#540—24no—
238#535—24no—
239#535—24no—
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2311yescharacteristic
242C2×#127—22no—
243C2×#127—22no—
244C2×#127C2311yescharacteristic
245C2×#127C2311yescharacteristic
246C2×#127C2311yescharacteristic
247C2×#127C2311yescharacteristic
248C2×#127C2311yescharacteristic
249C2×#127C2311yescharacteristic
250C2×#127C2311yescharacteristic
251C2×#127C2311yescharacteristic
252C2×#127C2311yescharacteristic
253C2×#127C2311yescharacteristic
254C2×#126—21no—
255C2×#125C2311yescharacteristic
256C2×#124—21no—
257C2×#124C2311yescharacteristic
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2311yescharacteristic
263C2×#124C2311yescharacteristic
264C2×#123—21no—
265C2×#123—21no—
266C2×#123—21no—
267C2×C22⋊Q8—21no—
268C2×C22⋊Q8C2311yescharacteristic
269C2×#121—21no—
270C2×#121—21no—
271C2×#121—22no—
272C2×#121—22no—
273C2×#121—21no—
274C2×#121—21no—
275C2×#121C2311yescharacteristic
276C2×#121C2311yescharacteristic
277C2×#121C2311yescharacteristic
278C2×#120—21no—
279C2×#120—21no—
280C2×#120—22no—
281C2×#120—22no—
282#520—24no—
283#520—24no—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×D4—21no—
288C2×C4×D4—21no—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2311yescharacteristic
294C2×#117—21no—
295C2×#117C2311yescharacteristic
296C22×C4⋊C4—21no—
297C22×C4⋊C4C2311yescharacteristic
298#497—42no—
299#496—24no—
300#496—42no—
301#496—42no—
302#496—42no—
303#496—42no—
304#496—42no—
305#495—24no—
306#493—42no—
307#492—42no—
308#489—24no—
309#486—24no—
310#481—24no—
311#480—24no—
312#479—24no—
313#479—24no—
314#478—24no—
315#478—24no—
316#476—24no—
317#474—24no—
318#469—24no—
319#468—24no—
320#466—24no—
321#465—24no—
322#464—24no—
323#464—24no—
324#464—24no—
325#463—24no—
326#463—24no—
327#463—24no—
328#463—24no—
329#463—24no—
330#460—24no—
331#460—24no—
332#460—24no—
333#460—24no—
334#460—24no—
335#459—24no—
336#459—24no—
337#459—24no—
338#459—24no—
339#459—24no—
340#452—24no—
341#450—24no—
342#449—24no—
343#449—24no—
344#449—24no—
345#447—24no—
346#442—24no—
347#440—24no—
348C4×SD16—24no—
349C4×D8—24no—
350#433D418yescomplemented
351C2×#107C2311yescharacteristic
352C2×#107C2311yescharacteristic
353C2×#107C2311yescharacteristic
354C2×#107C2311yescharacteristic
355C2×#106C2311yescharacteristic
356C2×#106C2311yescharacteristic
357C2×#106C2311yescharacteristic
358C2×#106C2311yescharacteristic
359#424D418yescomplemented
360C2×C4⋊C8C2311yescharacteristic
361C2×C4⋊C8C2311yescharacteristic
362C2×C4⋊C8C2311yescharacteristic
363C2×C4⋊C8C2311yescharacteristic
364C2×C4⋊C8C2311yescharacteristic
365C2×C4⋊C8C2311yescharacteristic
366#417—24no—
367C2×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
374C2×#103C2311yescharacteristic
375C2×#102—24no—
376C2×#102C2311yescharacteristic
377C2×#102C2311yescharacteristic
378C2×#102C2311yescharacteristic
379C2×#102C2311yescharacteristic
380C2×#102C2311yescharacteristic
381C2×#102C2311yescharacteristic
382C2×#102C2311yescharacteristic
383C2×#102C2311yescharacteristic
384C2×#102C2311yescharacteristic
385C2×#102C2311yescharacteristic
386C2×#102C2311yescharacteristic
387C2×#102C2311yescharacteristic
388C2×#102C2311yescharacteristic
389C2×#102C2311yescharacteristic
390C2×#102C2311yescharacteristic
391C2×#102C2311yescharacteristic
392C2×#102C2311yescharacteristic
393C2×#102C2311yescharacteristic
394C2×#102C2311yescharacteristic
395C2×#102C2311yescharacteristic
396C2×#102C2311yescharacteristic
397C2×#102C2311yescharacteristic
398C2×#102C2311yescharacteristic
399C2×#102C2311yescharacteristic
400C2×C22⋊C8C2311yescharacteristic
401C2×C22⋊C8C2311yescharacteristic
402C2×#97C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×#97C2311yescharacteristic
405C2×#97C2311yescharacteristic
406C2×#97C2311yescharacteristic
407C2×#97C2311yescharacteristic
408C2×#97C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410C2×C4×C8C2311yescharacteristic
411C2×C4×C8C2311yescharacteristic
412#400—22no—
413#400—22no—
414#397—22no—
415#396—22no—
416#394—22no—
417#394—22no—
418#394—22no—
419#394—22no—
420#394—22no—
421#394—22no—
422#393—22no—
423#392—22no—
424#392—22no—
425#392—22no—
426#392—22no—
427#392—22no—
428#392—22no—
429#392—22no—
430#392—22no—
431#392—22no—
432#391—22no—
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#390C2311yescharacteristic
449#388—22no—
450#388—22no—
451#388—22no—
452#388—22no—
453#388—22no—
454#388D412yes—
455#388D412yes—
456#387—22no—
457#387—22no—
458#387D412yes—
459#387D412yes—
460#386—22no—
461#386—22no—
462#386—22no—
463#386—22no—
464#386—22no—
465#386—22no—
466#386—22no—
467#386—22no—
468#386—22no—
469#385—22no—
470#382C2311yescharacteristic
471#382C2311yescharacteristic
472#382C2311yescharacteristic
473#382C2311yescharacteristic
474#381—22no—
475#380—22no—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C22⋊C4—22no—
479C4×C22⋊C4—22no—
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376C2311yescharacteristic
483C43C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492C25—21no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C22×Q8—21no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—22no—
526C22×D4—22no—
527C22×D4—22no—
528C22×D4—22no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C2411yescharacteristic
550AGL(1,ℤ/8)—416no—
551#135—416no—
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16—41no—
582C2×SD16—41no—
583C2×SD16—41no—
584C2×SD16—41no—
585C2×SD16—41no—
586C2×SD16—41no—
587C2×SD16—41no—
588C2×SD16—41no—
589C2×SD16—41no—
590C2×SD16—41no—
591C2×SD16—41no—
592C2×SD16—41no—
593C2×SD16—41no—
594C2×D8—22no—
595C2×D8—22no—
596C2×D8—22no—
597C2×D8—22no—
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—22no—
603C2×D8—22no—
604C2×D8—22no—
605C2×D8—22no—
606C2×D8—22no—
607C2×D8—22no—
608C2×D8—22no—
609C2×D8—41no—
610C2×D8—41no—
611C2×D8—41no—
612C2×D8—41no—
613C2×D8—41no—
614C2×D8—41no—
615C2×D8—41no—
616C2×D8—41no—
617C2×D8—41no—
618C2×D8—41no—
619C2×D8—41no—
620C2×D8—41no—
621C2×D8—41no—
622C2×D8—41no—
623C2×D8—41no—
624C2×M16—41no—
625C2×M16—41no—
626C2×M16C2×D414yes—
627C22×C8—41no—
628C22×C8—41no—
629C22×C8C2×D414yes—
630C22×C8C2411yescharacteristic
631C22×C8C2411yescharacteristic
632C22×C8C2411yescharacteristic
633C22×C8C2411yescharacteristic
634C22×C8C2411yescharacteristic
635C22×C8C2411yescharacteristic
636C22×C8C2411yescharacteristic
637C22×C8C2411yescharacteristic
638C4⋊Q8—22no—
639C4⋊Q8—22no—
640C4⋊Q8—22no—
641C4⋊Q8—41no—
642#127—22no—
643#127—22no—
644#127—22no—
645#127—22no—
646#127—22no—
647#127—22no—
648#127—22no—
649#127—41no—
650#127—41no—
651#127—41no—
652#127—41no—
653#127—41no—
654#127—41no—
655#127—41no—
656#127—41no—
657#127—41no—
658#127—41no—
659#127—41no—
660#127—41no—
661#127—41no—
662#127—84no—
663#127—84no—
664#126—44no—
665#125—22no—
666#125—22no—
667#124—22no—
668#124—22no—
669#124—22no—
670#124—22no—
671#124—22no—
672#124—22no—
673#124—22no—
674#124—22no—
675#124—41no—
676#124—41no—
677#124—41no—
678#124—41no—
679#124—41no—
680#124—41no—
681#124—44no—
682#123—44no—
683#123—44no—
684#123—44no—
685C22⋊Q8—22no—
686C22⋊Q8—22no—
687C22⋊Q8—44no—
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—22no—
693#121—22no—
694#121—44no—
695#121—44no—
696#121—44no—
697#121—44no—
698#121—84no—
699#121—84no—
700#120—44no—
701#120—44no—
702#120—84no—
703#120—84no—
704C4×Q8—22no—
705C4×Q8—22no—
706C4×Q8—22no—
707C4×Q8—22no—
708C4×Q8—22no—
709C4×Q8—22no—
710C4×D4—22no—
711C4×D4—22no—
712C4×D4—22no—
713C4×D4—22no—
714C4×D4—22no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—22no—
718C4×D4—22no—
719C4×D4—22no—
720C4×D4—44no—
721C4×D4—44no—
722#117—44no—
723#117C2×D414yes—
724#117C2×D414yes—
725C2×C4⋊C4—22no—
726C2×C4⋊C4—22no—
727C2×C4⋊C4—21no—
728C2×C4⋊C4—21no—
729C2×C4⋊C4—21no—
730C2×C4⋊C4—21no—
731C2×C4⋊C4—21no—
732C2×C4⋊C4—21no—
733C2×C4⋊C4—21no—
734C2×C4⋊C4—21no—
735C2×C4⋊C4—22no—
736C2×C4⋊C4—44no—
737C2×C4⋊C4C2×D412yes—
738C2×C4⋊C4C2×D412yes—
739C2×C4⋊C4C2×D411yescharacteristic
740C2×C4⋊C4C2×D411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—21no—
755C2×C22⋊C4—21no—
756C2×C22⋊C4—21no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—21no—
760C2×C22⋊C4—21no—
761C2×C22⋊C4—21no—
762C2×C22⋊C4—21no—
763C2×C22⋊C4—21no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4C2×D412yes—
777C2×C22⋊C4C2×D412yes—
778C2×C22⋊C4C2×D411yescharacteristic
779C2×C22⋊C4C2×D411yescharacteristic
780C2×C42—21no—
781C2×C42—21no—
782C2×C42—21no—
783C2×C42C2×D412yes—
784C2×C42C2×D412yes—
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790C2×C42C2411yescharacteristic
791#107—22no—
792#107—22no—
793#107—22no—
794#107—22no—
795#106—22no—
796#106—22no—
797#106—22no—
798#106—22no—
799C4⋊C8C2×D414yes—
800C4⋊C8C2×D414yes—
801C4⋊C8C2×D414yes—
802C4⋊C8C2×D414yes—
803C4⋊C8C2×D414yes—
804C4⋊C8C2×D414yes—
805#103—22no—
806#103—22no—
807#103—22no—
808#103—22no—
809#103—22no—
810#103—22no—
811#103—22no—
812#103—22no—
813#102—22no—
814#102—22no—
815#102—22no—
816#102—22no—
817#102—22no—
818#102—22no—
819#102—22no—
820#102—22no—
821#102—22no—
822#102—22no—
823#102—22no—
824#102—22no—
825#102—22no—
826#102—22no—
827#102—22no—
828#102—22no—
829#102—22no—
830#102—22no—
831#102—22no—
832#102—22no—
833#102—22no—
834#102—22no—
835#102—22no—
836#102—22no—
837C22⋊C8C2×D414yes—
838C22⋊C8C2×D414yes—
839#97—41no—
840#97—41no—
841#97—41no—
842#97—41no—
843#97—41no—
844#97—41no—
845#97C2×D414yes—
846C4×C8—41no—
847C4×C8—41no—
848C4×C8C2×D414yes—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—22no—
855#95—22no—
856#95—22no—
857#95—22no—
858#95—22no—
859#95C2×D412yes—
860#95C2×D412yes—
861#95C2×D412yes—
862#95C2×D412yes—
863#95C2×D412yes—
864#95C2×D412yes—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—42no—
873C24—81no—
874C24—81no—
875C24—82no—
876C24—82no—
877C24C22×D411yescharacteristic
878#41—28no—
879#41—44no—
880#41—44no—
881#41—44no—
882#41—44no—
883#41—44no—
884#41—82no—
885#41—82no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—42no—
904C2×Q8—82no—
905C2×Q8H(5,𝔽2)12yes—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—21no—
933C2×D4—21no—
934C2×D4—21no—
935C2×D4—21no—
936C2×D4—21no—
937C2×D4—21no—
938C2×D4—21no—
939C2×D4—21no—
940C2×D4—21no—
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—21no—
944C2×D4—21no—
945C2×D4—21no—
946C2×D4—21no—
947C2×D4—42no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—42no—
963C2×D4—42no—
964C2×D4—42no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—42no—
968C2×D4—82no—
969C2×D4—82no—
970C2×D4—81no—
971C2×D4—81no—
972C2×D4—82no—
973C2×D4—82no—
974C2×D4—82no—
975C2×D4—82no—
976C2×D4—82no—
977C2×D4—82no—
978C2×D4—82no—
979C2×D4—82no—
980C2×D4—82no—
981C2×D4—82no—
982C2×D4—82no—
983C2×D4—82no—
984C2×D4—82no—
985C2×D4—82no—
986C2×D4—82no—
987C2×D4—82no—
988C2×D4—82no—
989C2×D4—82no—
990C2×D4—82no—
991C2×D4—82no—
992C2×D4—82no—
993C2×D4—82no—
994C2×D4—81no—
995C2×D4—81no—
996C2×D4—82no—
997C2×D4—82no—
998C2×D4—82no—
999C2×D4H(5,𝔽2)12yes—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4—21no—
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—21no—
1011C22×C4—21no—
1012C22×C4—21no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—81no—
1024C22×C4—81no—
1025C22×C4—82no—
1026C22×C4—82no—
1027C22×C4—82no—
1028C22×C4—82no—
1029C22×C4—82no—
1030C22×C4—82no—
1031C22×C4C22×D412yes—
1032C22×C4C22×D412yes—
1033C22×C4C22×D412yes—
1034C22×C4C22×D412yes—
1035C22×C4C22×D411yescharacteristic
1036C22×C4C22×D411yescharacteristic
1037C22×C4C22×D411yescharacteristic
1038C22×C4C22×D411yescharacteristic
1039C22×C4C22×D411yescharacteristic
1040C22×C4C22×D412yes—
1041C22×C4C22×D412yes—
1042C22×C4C2511yescharacteristic
1043Q16—44no—
1044Q16—82no—
1045SD16—44no—
1046SD16—44no—
1047SD16—44no—
1048SD16—44no—
1049SD16—44no—
1050SD16—44no—
1051SD16—82no—
1052SD16—82no—
1053SD16—82no—
1054SD16—82no—
1055SD16—82no—
1056SD16—82no—
1057D8—44no—
1058D8—44no—
1059D8—44no—
1060D8—44no—
1061D8—44no—
1062D8—82no—
1063D8—82no—
1064D8—82no—
1065D8—82no—
1066D8—82no—
1067M16—44no—
1068C2×C8—21no—
1069C2×C8—21no—
1070C2×C8—21no—
1071C2×C8—21no—
1072C2×C8—21no—
1073C2×C8—21no—
1074C2×C8—21no—
1075C2×C8—21no—
1076C2×C8—21no—
1077C2×C8—21no—
1078C2×C8—21no—
1079C2×C8—21no—
1080C2×C8—21no—
1081C2×C8—21no—
1082C2×C8—21no—
1083C2×C8—21no—
1084C2×C8—44no—
1085C2×C8C22×D412yes—
1086C2×C8C22×D412yes—
1087C2×C8C22×D412yes—
1088C2×C8C22×D412yes—
1089C2×C8C22×D412yes—
1090C2×C8C22×D412yes—
1091C2×C8C22×D412yes—
1092C2×C8C22×D412yes—
1093C4⋊C4—21no—
1094C4⋊C4—21no—
1095C4⋊C4—21no—
1096C4⋊C4—21no—
1097C4⋊C4—21no—
1098C4⋊C4—21no—
1099C4⋊C4—21no—
1100C4⋊C4—21no—
1101C4⋊C4—21no—
1102C4⋊C4—21no—
1103C4⋊C4—21no—
1104C4⋊C4—21no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4#12714yes—
1117C4⋊C4#12714yes—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—82no—
1140C22⋊C4—82no—
1141C22⋊C4—82no—
1142C22⋊C4—82no—
1143C22⋊C4—82no—
1144C22⋊C4—82no—
1145C22⋊C4—82no—
1146C22⋊C4—82no—
1147C22⋊C4—82no—
1148C22⋊C4—82no—
1149C22⋊C4#12714yes—
1150C22⋊C4#12714yes—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—21no—
1156C42—21no—
1157C42—21no—
1158C42—21no—
1159C42—42no—
1160C42—42no—
1161C42—42no—
1162C42—42no—
1163C42—42no—
1164C42C22×D412yes—
1165C42C22×D412yes—
1166C42C22×D412yes—
1167C42C22×D412yes—
1168C23—22no—
1169C23—22no—
1170C23—21no—
1171C23—21no—
1172C23—22no—
1173C23—42no—
1174C23—42no—
1175C23—41no—
1176C23—41no—
1177C23—42no—
1178C23—42no—
1179C23—42no—
1180C23—42no—
1181C23—42no—
1182C23—42no—
1183C23—42no—
1184C23—42no—
1185C23—42no—
1186C23—42no—
1187C23—42no—
1188C23—42no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—41no—
1206C23—41no—
1207C23—84no—
1208C23—162no—
1209C23—162no—
1210C23—164no—
1211C23—164no—
1212C23C2×#12712yes—
1213C23C23×D411yescharacteristic
1214Q8—22no—
1215Q8—22no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—41no—
1220Q8—41no—
1221Q8—41no—
1222Q8—41no—
1223Q8—41no—
1224Q8—41no—
1225Q8—41no—
1226Q8—162no—
1227D4—22no—
1228D4—22no—
1229D4—48no—
1230D4—41no—
1231D4—41no—
1232D4—41no—
1233D4—41no—
1234D4—41no—
1235D4—41no—
1236D4—41no—
1237D4—41no—
1238D4—41no—
1239D4—41no—
1240D4—41no—
1241D4—41no—
1242D4—41no—
1243D4—41no—
1244D4—41no—
1245D4—41no—
1246D4—41no—
1247D4—41no—
1248D4—41no—
1249D4—41no—
1250D4—41no—
1251D4—41no—
1252D4—41no—
1253D4—41no—
1254D4—41no—
1255D4—41no—
1256D4—84no—
1257D4—84no—
1258D4—162no—
1259D4—162no—
1260D4—162no—
1261D4—162no—
1262D4—162no—
1263D4—162no—
1264D4—164no—
1265D4—164no—
1266D4—164no—
1267D4—164no—
1268D4—164no—
1269D4—164no—
1270D4—164no—
1271D4—162no—
1272D4—162no—
1273D4—162no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—48no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—42no—
1301C2×C4—42no—
1302C2×C4—42no—
1303C2×C4—42no—
1304C2×C4—42no—
1305C2×C4—42no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—84no—
1319C2×C4—162no—
1320C2×C4—162no—
1321C2×C4—162no—
1322C2×C4—162no—
1323C2×C4—162no—
1324C2×C4—162no—
1325C2×C4C2×#12712yes—
1326C2×C4C2×#12712yes—
1327C2×C4C2×#12712yes—
1328C2×C4C2×#12712yes—
1329C2×C4C2×#12712yes—
1330C2×C4C23×D411yescharacteristic
1331C2×C4C23×D411yescharacteristic
1332C2×C4C2×H(5,𝔽2)11yescharacteristic
1333C2×C4C2×H(5,𝔽2)11yescharacteristic
1334C2×C4#58511yescharacteristic
1335C2×C4#58511yescharacteristic
1336C8—22no—
1337C8—22no—
1338C8—22no—
1339C8—22no—
1340C8—22no—
1341C8—22no—
1342C8—22no—
1343C8—22no—
1344C22—22no—
1345C22—22no—
1346C22—22no—
1347C22—42no—
1348C22—42no—
1349C22—44no—
1350C22—42no—
1351C22—82no—
1352C22—81no—
1353C22—81no—
1354C22—82no—
1355C22—82no—
1356C22—82no—
1357C22—82no—
1358C22—82no—
1359C22—82no—
1360C22—82no—
1361C22—82no—
1362C22—82no—
1363C22—82no—
1364C22—82no—
1365C22—82no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—168no—
1385C22C22×#12711yescharacteristic
1386C22#348811yescharacteristic
1387C22#348811yescharacteristic
1388C22#358512yes—
1389C22#358512yes—
1390C4—22no—
1391C4—22no—
1392C4—22no—
1393C4—22no—
1394C4—22no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4#348411yescharacteristic
1409C4#348711yescharacteristic
1410C4#348811yescharacteristic
1411C4#348811yescharacteristic
1412C2—42no—
1413C2—82no—
1414C2—161no—
1415C2—161no—
1416C2—161no—
1417C2—161no—
1418C2—161no—
1419C2—161no—
1420C2#3556511yescharacteristic
1421C2#6065011yescharacteristic
1422C2#6065011yescharacteristic
1423C2#6207912yes—
1424C2#6208112yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3257C2semidirect
2. C2×#3224C2semidirect
3. C2×#3119C2semidirect
4. C2×#3045C2semidirect
5. #37302C2semidirect
6. #35623C2semidirect
7. #28480C2semidirect
8. #28475C2semidirect
9. #28468C2semidirect
10. #28467C2semidirect
11. #28457C2semidirect
12. #28454C2semidirect
13. #28448C2semidirect
14. #28448C2semidirect
15. #28436C2semidirect
16. #28422C2semidirect
17. #28420C2semidirect
18. #28413C2semidirect
19. #28392C2semidirect
20. #28387C2semidirect
21. #28379C2semidirect
22. #28379C2semidirect
23. #28366C2semidirect
24. #28354C2semidirect
25. #28344C2semidirect
26. #28341C2semidirect
27. #25794C2semidirect
28. #25791C2semidirect
29. #25787C2semidirect
30. #25785C2semidirect
31. #20554C2semidirect
40. C2×#497C22semidirect
44. C2×#496C22semidirect
45. C2×#496C22semidirect
46. C2×#496C22semidirect
55. C2×#479C22semidirect
56. C2×#479C22semidirect
57. C2×#478C22semidirect
58. C2×#478C22semidirect
59. C2×#476C22semidirect
60. C2×#474C22semidirect
72. C2×#460C22semidirect
73. C2×#460C22semidirect
77. C2×#463C22semidirect
78. C2×#463C22semidirect
82. C2×#459C22semidirect
83. C2×#459C22semidirect
90. C2×#442C22semidirect
91. C2×#440C22semidirect
92. C2×C4×SD16C22semidirect
93. C2×C4×D8C22semidirect
106. #2568C22semidirect
107. #2563C22semidirect
108. #2545C22semidirect
111. #2544C22semidirect
126. #2328C22semidirect
127. #2327C22semidirect
128. C4×#124C22semidirect
129. C4×#124C22semidirect
131. #2097C22semidirect
132. #2097C22semidirect
137. #2092C22semidirect
138. #2092C22semidirect
139. #2015C22semidirect
140. #2015C22semidirect
141. #2015C22semidirect
142. #2015C22semidirect
147. #2014C22semidirect
148. #2014C22semidirect
150. #2013C22semidirect
153. #2012C22semidirect
154. #2012C22semidirect
160. #2011C22semidirect
161. #2011C22semidirect
162. #2011C22semidirect
166. #1973C22semidirect
167. #1973C22semidirect
168. #1973C22semidirect
172. #1972C22semidirect
173. #1971C22semidirect
174. #1971C22semidirect
176. #1970C22semidirect
178. #1968C22semidirect
183. #1961C22semidirect
184. #1961C22semidirect
185. #1958C22semidirect
186. #1958C22semidirect
187. #1771C22semidirect
188. #1771C22semidirect
189. #1770C22semidirect
190. #1770C22semidirect
191. #1768C22semidirect
192. #1768C22semidirect
193. #1767C22semidirect
194. #1767C22semidirect
350. #433D4semidirect
359. #424D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32572
C2×#32242
C2×#31192
C2×#30452
#373022
#356232
#284802
#284752
#284682
#284672
#284572
#284542
#284482
#284362
#284222
#284202
#284132
#283922
#283872
#283792
#283662
#283542
#283442
#283412
#257942
#257912
#257872
#257852
#205542