Finite Group Databasebeta

← #6520409

Subgroups — #6520409

Order 512.

2448 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3256C211yesmaximal, characteristic, complemented
2C2×#3212C211yesmaximal, characteristic, complemented
3C2×#3105C211yesmaximal, characteristic, complemented
4C2×#3036C211yesmaximal, characteristic, complemented
5#37544C211yesmaximal, characteristic, complemented
6#35233C211yesmaximal, characteristic, complemented
7#28468C211yesmaximal, characteristic, complemented
8#28467C211yesmaximal, characteristic, complemented
9#28465C211yesmaximal, characteristic, complemented
10#28464C211yesmaximal, characteristic, complemented
11#28455C211yesmaximal, characteristic, complemented
12#28454C211yesmaximal, characteristic, complemented
13#28453C211yesmaximal, characteristic, complemented
14#28452C211yesmaximal, characteristic, complemented
15#28410C211yesmaximal, characteristic, complemented
16#28409C211yesmaximal, characteristic, complemented
17#28406C211yesmaximal, characteristic, complemented
18#28405C211yesmaximal, characteristic, complemented
19#28390C211yesmaximal, characteristic, complemented
20#28389C211yesmaximal, characteristic, complemented
21#28388C211yesmaximal, characteristic, complemented
22#28387C211yesmaximal, characteristic, complemented
23#28366C211yesmaximal, characteristic, complemented
24#28364C211yesmaximal, characteristic, complemented
25#28358C211yesmaximal, characteristic, complemented
26#28356C211yesmaximal, characteristic, complemented
27#25796C211yesmaximal, characteristic, complemented
28#25794C211yesmaximal, characteristic, complemented
29#25793C211yesmaximal, characteristic, complemented
30#25791C211yesmaximal, characteristic, complemented
31#20548C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C22×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C2×#529C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38#3256—28no—
39#3212—28no—
40C2×#497C2211yescharacteristic
41C2×#496C2211yescharacteristic
42C2×#496C2211yescharacteristic
43C2×#496C2211yescharacteristic
44C2×#495C2211yescharacteristic
45C2×#495C2211yescharacteristic
46C2×#495C2211yescharacteristic, complemented
47C2×#495C2211yescharacteristic, complemented
48C2×#493C2211yescharacteristic
49C2×#492C2211yescharacteristic
50C2×#488C2211yescharacteristic, complemented
51C2×#488C2211yescharacteristic, complemented
52#3105—28no—
53C2×#484C2211yescharacteristic
54C2×#481C2211yescharacteristic
55C2×#479C2211yescharacteristic, complemented
56C2×#479C2211yescharacteristic, complemented
57C2×#478C2211yescharacteristic
58C2×#478C2211yescharacteristic
59C2×#478C2211yescharacteristic, complemented
60C2×#478C2211yescharacteristic, complemented
61C2×#470C2211yescharacteristic
62C2×#469C2211yescharacteristic
63C2×#468C2211yescharacteristic
64C2×#468C2211yescharacteristic
65#3036—28no—
66C2×#464C2211yescharacteristic, complemented
67C2×#464C2211yescharacteristic, complemented
68C2×#462C2211yescharacteristic, complemented
69C2×#460C2211yescharacteristic, complemented
70C2×#463C2211yescharacteristic
71C2×#463C2211yescharacteristic
72C2×#463C2211yescharacteristic
73C2×#463C2211yescharacteristic
74C2×#463C2211yescharacteristic
75C2×#463C2211yescharacteristic
76C2×#463C2211yescharacteristic, complemented
77C2×#463C2211yescharacteristic, complemented
78C2×#461C2211yescharacteristic
79C2×#461C2211yescharacteristic
80C2×#461C2211yescharacteristic, complemented
81C2×#459C2211yescharacteristic
82C2×#459C2211yescharacteristic
83C2×#459C2211yescharacteristic, complemented
84C2×#452C2211yescharacteristic
85C2×#452C2211yescharacteristic
86C2×#449C2211yescharacteristic
87C2×#449C2211yescharacteristic
88C2×#450C2211yescharacteristic
89C2×#447C2211yescharacteristic
90C2×C4×SD16C2211yescharacteristic
91C2×C4×SD16C2211yescharacteristic
92C2×C4×D8C2211yescharacteristic
93C2×C4×D8C2211yescharacteristic
94C2×#431C2211yescharacteristic
95C2×#423C2211yescharacteristic
96C2×#417C2211yescharacteristic
97C2×#417C2211yescharacteristic
98#2849—22no—
99#2813—22no—
100#2658C2211yescharacteristic, complemented
101#2657C2211yescharacteristic, complemented
102#2642C2211yescharacteristic, complemented
103#2641C2211yescharacteristic, complemented
104#2636—22no—
105#2636—22no—
106#2635—22no—
107#2598—22no—
108#2598—22no—
109#2566C2211yescharacteristic
110#2566C2211yescharacteristic
111#2545C2211yescharacteristic, complemented
112#2545C2211yescharacteristic, complemented
113#2544C2211yescharacteristic
114#2544C2211yescharacteristic
115#2544C2211yescharacteristic, complemented
116#2544C2211yescharacteristic, complemented
117#2534—22no—
118#2503C2211yescharacteristic
119#2501C2211yescharacteristic
120#2435C2211yescharacteristic
121#2433C2211yescharacteristic
122#2432C2211yescharacteristic
123#2432C2211yescharacteristic
124#2431C2211yescharacteristic
125#2431C2211yescharacteristic
126#2328C2211yescharacteristic
127#2328C2211yescharacteristic
128#2326C2211yescharacteristic
129#2326C2211yescharacteristic
130#2283C2211yescharacteristic
131#2097C2211yescharacteristic, complemented
132#2097C2211yescharacteristic, complemented
133#2096C2211yescharacteristic, complemented
134#2095C2211yescharacteristic, complemented
135#2094C2211yescharacteristic, complemented
136#2093C2211yescharacteristic, complemented
137#2092C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2016C2211yescharacteristic, complemented
140#2015C2211yescharacteristic
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic, complemented
143#2015C2211yescharacteristic, complemented
144#2014C2211yescharacteristic
145#2014C2211yescharacteristic
146#2014C2211yescharacteristic, complemented
147#2013C2211yescharacteristic
148#2013C2211yescharacteristic
149#2013C2211yescharacteristic, complemented
150#2012C2211yescharacteristic
151#2012C2211yescharacteristic
152#2012C2211yescharacteristic
153#2012C2211yescharacteristic
154#2012C2211yescharacteristic
155#2012C2211yescharacteristic
156#2012C2211yescharacteristic, complemented
157#2012C2211yescharacteristic, complemented
158#2011C2211yescharacteristic
159#2011C2211yescharacteristic
160#2011C2211yescharacteristic
161#2011C2211yescharacteristic
162#2011C2211yescharacteristic, complemented
163#1973C2211yescharacteristic
164#1973C2211yescharacteristic
165#1973C2211yescharacteristic, complemented
166#1973C2211yescharacteristic, complemented
167#1972C2211yescharacteristic
168#1972C2211yescharacteristic
169#1972C2211yescharacteristic, complemented
170#1971C2211yescharacteristic, complemented
171#1970C2211yescharacteristic
172#1970C2211yescharacteristic
173#1970C2211yescharacteristic, complemented
174#1969C2211yescharacteristic, complemented
175#1968C2211yescharacteristic
176#1968C2211yescharacteristic
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1961C2211yescharacteristic, complemented
180#1960C2211yescharacteristic, complemented
181#1959C2211yescharacteristic, complemented
182#1959C2211yescharacteristic, complemented
183#1958C2211yescharacteristic, complemented
184#1958C2211yescharacteristic, complemented
185#1957C2211yescharacteristic, complemented
186#1956C2211yescharacteristic, complemented
187#1770C2211yescharacteristic, complemented
188#1770C2211yescharacteristic, complemented
189C8×C4⋊C4C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1768C2211yescharacteristic, complemented
193#1768C2211yescharacteristic, complemented
194#1768C2211yescharacteristic, complemented
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C24×C4—21no—
203C2×AGL(1,ℤ/8)—24no—
204C2×AGL(1,ℤ/8)—24no—
205C2×AGL(1,ℤ/8)—42no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C2×AGL(1,ℤ/8)—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
223C22×SD16C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×D8C2311yescharacteristic
226C22×D8C2311yescharacteristic
227C22×D8C2311yescharacteristic
228C22×D8C2311yescharacteristic
229C22×D8C2311yescharacteristic
230C22×D8C2311yescharacteristic
231C22×D8C2311yescharacteristic
232C22×D8C2311yescharacteristic
233C22×M16C2311yescharacteristic
234C22×M16C2311yescharacteristic
235#532—24no—
236#532—24no—
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×#127C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#127C2311yescharacteristic
243C2×#127C2311yescharacteristic
244C2×#127C2311yescharacteristic
245#529—24no—
246#529—24no—
247#529—24no—
248#529—24no—
249C2×#126—21no—
250C2×#126—21no—
251C2×#125C2311yescharacteristic
252C2×#125C2311yescharacteristic
253C2×#124C2311yescharacteristic
254C2×#124C2311yescharacteristic
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#124C2311yescharacteristic
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2311yescharacteristic
263C2×#123—21no—
264C2×#123—21no—
265C2×#123—22no—
266C2×C22⋊Q8C2311yescharacteristic
267C2×C22⋊Q8C2311yescharacteristic
268C2×#121—21no—
269C2×#121—21no—
270C2×#121C2311yescharacteristic
271C2×#121C2311yescharacteristic
272C2×#120—22no—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×D4—21no—
276C2×C4×D4—21no—
277C2×C4×D4—21no—
278C2×C4×D4—21no—
279C2×C4×D4—21no—
280C2×C4×D4—21no—
281C2×C4×D4—24no—
282C2×C4×D4—24no—
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2311yescharacteristic
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2311yescharacteristic
289C2×#117—21no—
290C2×#117—21no—
291C22×C4⋊C4C2311yescharacteristic
292C22×C22⋊C4—21no—
293C22×C42C2311yescharacteristic
294#497—42no—
295#496—42no—
296#496—42no—
297#496—42no—
298#495—24no—
299#495—24no—
300#495—42no—
301#495—42no—
302#493—42no—
303#492—42no—
304#488—24no—
305#488—24no—
306#484—24no—
307#481—24no—
308#479—24no—
309#479—24no—
310#478—24no—
311#478—24no—
312#478—24no—
313#478—24no—
314#470—24no—
315#469—24no—
316#468—24no—
317#468—24no—
318#464—24no—
319#464—24no—
320#463—24no—
321#463—24no—
322#463—24no—
323#463—24no—
324#463—24no—
325#463—24no—
326#463—24no—
327#463—24no—
328#462—24no—
329#461—24no—
330#461—24no—
331#461—24no—
332#460—24no—
333#459—24no—
334#459—24no—
335#459—24no—
336#452—24no—
337#452—24no—
338#450—24no—
339#449—24no—
340#449—24no—
341#447—24no—
342C4×SD16—24no—
343C4×SD16—24no—
344C4×D8—24no—
345C4×D8—24no—
346#431D418yescomplemented
347C2×#107C2311yescharacteristic
348C2×#107C2311yescharacteristic
349C2×#107C2311yescharacteristic
350C2×#107C2311yescharacteristic
351C2×#106C2311yescharacteristic
352C2×#106C2311yescharacteristic
353C2×#106C2311yescharacteristic
354C2×#106C2311yescharacteristic
355#423D418yescomplemented
356C2×C4⋊C8C2311yescharacteristic
357C2×C4⋊C8C2311yescharacteristic
358C2×C4⋊C8C2311yescharacteristic
359C2×C4⋊C8C2311yescharacteristic
360C2×C4⋊C8C2311yescharacteristic
361C2×C4⋊C8C2311yescharacteristic
362#417—24no—
363#417—24no—
364C2×#103C2311yescharacteristic
365C2×#103C2311yescharacteristic
366C2×#103C2311yescharacteristic
367C2×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
374C2×#103C2311yescharacteristic
375C2×#103C2311yescharacteristic
376C2×#103C2311yescharacteristic
377C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
397C2×C22⋊C8C2311yescharacteristic
398C2×#97C2311yescharacteristic
399C2×#97C2311yescharacteristic
400C2×#97C2311yescharacteristic
401C2×#97C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404C2×C4×C8C2311yescharacteristic
405C2×C4×C8C2311yescharacteristic
406C2×C4×C8C2311yescharacteristic
407C2×C4×C8C2311yescharacteristic
408#400—22no—
409#400—22no—
410#400—22no—
411#399—22no—
412#399—22no—
413#399—22no—
414#396—22no—
415#396—22no—
416#396—22no—
417#396—22no—
418#394—22no—
419#394—22no—
420#394—22no—
421#394—22no—
422#394—22no—
423#394—22no—
424#394—22no—
425#394—22no—
426#394—22no—
427#392—22no—
428#392—22no—
429#392—22no—
430#392—22no—
431#392—22no—
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#388—22no—
449#388—22no—
450#388—22no—
451#388—22no—
452#386—22no—
453#386—22no—
454#386—22no—
455#386—22no—
456#386—22no—
457#386—22no—
458#386—22no—
459#386—22no—
460#386—22no—
461#386—22no—
462#385—22no—
463#385—22no—
464#385—22no—
465#385—22no—
466#385—22no—
467#385—22no—
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#383D412yes—
471#382D412yes—
472#382C2311yescharacteristic
473#382C2311yescharacteristic
474#381—22no—
475#381D412yes—
476#380D412yes—
477#379—22no—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376C2311yescharacteristic
483#376C2311yescharacteristic
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—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—44no—
542C23×C4—84no—
543C23×C4C2×D411yescharacteristic
544C23×C4C2×D411yescharacteristic
545C23×C4C2411yescharacteristic
546AGL(1,ℤ/8)—416no—
547AGL(1,ℤ/8)—416no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×SD16—22no—
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—41no—
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×D8—22no—
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—41no—
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×M16—41no—
621C2×M16—41no—
622C2×M16—41no—
623C2×M16—41no—
624C2×M16C2×D414yes—
625C2×M16C2×D414yes—
626C22×C8C2411yescharacteristic
627C22×C8C2411yescharacteristic
628C22×C8C2411yescharacteristic
629C22×C8C2411yescharacteristic
630C22×C8C2411yescharacteristic
631C22×C8C2411yescharacteristic
632C22×C8C2411yescharacteristic
633C22×C8C2411yescharacteristic
634C4⋊Q8—22no—
635C4⋊Q8—22no—
636C4⋊Q8—41no—
637C4⋊Q8—41no—
638C4⋊Q8—41no—
639C4⋊Q8—41no—
640#127—22no—
641#127—22no—
642#127—22no—
643#127—22no—
644#127—41no—
645#127—41no—
646#127—41no—
647#127—41no—
648#127—41no—
649#127—41no—
650#126—44no—
651#126—44no—
652#125—22no—
653#125—22no—
654#125—22no—
655#125—22no—
656#124—22no—
657#124—22no—
658#124—22no—
659#124—22no—
660#124—22no—
661#124—22no—
662#124—22no—
663#124—22no—
664#124—22no—
665#124—22no—
666#124—41no—
667#124—41no—
668#124—41no—
669#124—41no—
670#124—41no—
671#124—41no—
672#124—41no—
673#124—41no—
674#124—41no—
675#124—41no—
676#123—44no—
677#123—44no—
678#123—84no—
679C22⋊Q8—22no—
680C22⋊Q8—22no—
681C22⋊Q8—22no—
682C22⋊Q8—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—44no—
688#121—44no—
689#120—84no—
690C4×Q8—22no—
691C4×Q8—22no—
692C4×Q8—22no—
693C4×Q8—22no—
694C4×D4—22no—
695C4×D4—22no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—22no—
706C4×D4—44no—
707C4×D4—44no—
708C4×D4—44no—
709C4×D4—44no—
710C4×D4—44no—
711C4×D4—44no—
712#117—44no—
713#117—44no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4—21no—
721C2×C4⋊C4—21no—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4—21no—
725C2×C4⋊C4—21no—
726C2×C4⋊C4—21no—
727C2×C4⋊C4—22no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4C2×D412yes—
732C2×C4⋊C4C2×D412yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
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—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
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—44no—
774C2×C22⋊C4C2×D412yes—
775C2×C22⋊C4C2×D412yes—
776C2×C42—21no—
777C2×C42—21no—
778C2×C42C2×D411yescharacteristic
779C2×C42C2×D411yescharacteristic
780C2×C42C2×D414yes—
781C2×C42C2×D414yes—
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788#107—22no—
789#107—22no—
790#107—22no—
791#107—22no—
792#106—22no—
793#106—22no—
794#106—22no—
795#106—22no—
796C4⋊C8C2×D414yes—
797C4⋊C8C2×D414yes—
798C4⋊C8C2×D414yes—
799C4⋊C8C2×D414yes—
800C4⋊C8C2×D414yes—
801C4⋊C8C2×D414yes—
802#103—22no—
803#103—22no—
804#103—22no—
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#103—22no—
814#103—22no—
815#103—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—
834C22⋊C8C2×D414yes—
835C22⋊C8C2×D414yes—
836#97—41no—
837#97—41no—
838#97—41no—
839#97—41no—
840C4×C8—41no—
841C4×C8—41no—
842C4×C8—41no—
843C4×C8—41no—
844C4×C8C2×D414yes—
845C4×C8C2×D414yes—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95C2×D412yes—
855#95C2×D412yes—
856#95C2×D412yes—
857#95C2×D412yes—
858#95C2×D412yes—
859#95C2×D412yes—
860#95C2×D412yes—
861#95C2×D412yes—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—42no—
869C24—42no—
870C24—44no—
871C24—42no—
872C24—82no—
873C24C22×D411yescharacteristic
874#41—44no—
875#41—44no—
876#41—44no—
877#41—44no—
878#41—82no—
879#41—82no—
880#41—82no—
881#41—82no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
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—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×D4—28no—
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—44no—
942C2×D4—44no—
943C2×D4—42no—
944C2×D4—42no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—42no—
952C2×D4—42no—
953C2×D4—42no—
954C2×D4—42no—
955C2×D4—42no—
956C2×D4—82no—
957C2×D4—82no—
958C2×D4—82no—
959C2×D4—82no—
960C2×D4—82no—
961C2×D4—82no—
962C2×D4—82no—
963C2×D4—82no—
964C2×D4—82no—
965C2×D4—82no—
966C2×D4—82no—
967C2×D4—82no—
968C2×D4—82no—
969C2×D4—81no—
970C2×D4—81no—
971C2×D4—81no—
972C2×D4—81no—
973C2×D4H(5,𝔽2)12yes—
974C2×D4H(5,𝔽2)12yes—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—44no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—82no—
1002C22×C4—82no—
1003C22×C4—82no—
1004C22×C4—82no—
1005C22×C4—82no—
1006C22×C4—82no—
1007C22×C4—81no—
1008C22×C4—81no—
1009C22×C4—81no—
1010C22×C4—81no—
1011C22×C4—816no—
1012C22×C4#12714yes—
1013C22×C4#12714yes—
1014C22×C4C22×D412yes—
1015C22×C4C22×D412yes—
1016C22×C4C22×D412yes—
1017C22×C4C22×D412yes—
1018C22×C4C22×D411yescharacteristic
1019C22×C4C22×D411yescharacteristic
1020C22×C4C22×D411yescharacteristic
1021C22×C4C22×D411yescharacteristic
1022C22×C4C22×D411yescharacteristic
1023C22×C4C22×D412yes—
1024C22×C4C22×D412yes—
1025C22×C4C2511yescharacteristic
1026Q16—82no—
1027Q16—82no—
1028Q16—82no—
1029SD16—44no—
1030SD16—44no—
1031SD16—44no—
1032SD16—44no—
1033SD16—44no—
1034SD16—44no—
1035SD16—82no—
1036SD16—82no—
1037SD16—82no—
1038SD16—82no—
1039SD16—82no—
1040SD16—82no—
1041D8—44no—
1042D8—44no—
1043D8—44no—
1044D8—44no—
1045D8—44no—
1046D8—44no—
1047D8—82no—
1048D8—82no—
1049D8—82no—
1050M16—44no—
1051M16—44no—
1052C2×C8—21no—
1053C2×C8—21no—
1054C2×C8—21no—
1055C2×C8—21no—
1056C2×C8—21no—
1057C2×C8—21no—
1058C2×C8—21no—
1059C2×C8—21no—
1060C2×C8—21no—
1061C2×C8—21no—
1062C2×C8—21no—
1063C2×C8—21no—
1064C2×C8—21no—
1065C2×C8—21no—
1066C2×C8—21no—
1067C2×C8—21no—
1068C2×C8C22×D412yes—
1069C2×C8C22×D412yes—
1070C2×C8C22×D412yes—
1071C2×C8C22×D412yes—
1072C2×C8C22×D412yes—
1073C2×C8C22×D412yes—
1074C2×C8C22×D412yes—
1075C2×C8C22×D412yes—
1076C4⋊C4—21no—
1077C4⋊C4—21no—
1078C4⋊C4—21no—
1079C4⋊C4—21no—
1080C4⋊C4—21no—
1081C4⋊C4—21no—
1082C4⋊C4—21no—
1083C4⋊C4—21no—
1084C4⋊C4—21no—
1085C4⋊C4—21no—
1086C4⋊C4—21no—
1087C4⋊C4—21no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—82no—
1102C4⋊C4—82no—
1103C4⋊C4—82no—
1104C4⋊C4—82no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—82no—
1128C22⋊C4—82no—
1129C22⋊C4—82no—
1130C22⋊C4—82no—
1131C22⋊C4—82no—
1132C22⋊C4—82no—
1133C22⋊C4—82no—
1134C22⋊C4—82no—
1135C22⋊C4—82no—
1136C22⋊C4—82no—
1137C22⋊C4—82no—
1138C22⋊C4—82no—
1139C22⋊C4—82no—
1140C22⋊C4—82no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—21no—
1145C42—21no—
1146C42—21no—
1147C42—21no—
1148C42—21no—
1149C42—42no—
1150C42—42no—
1151C42#12714yes—
1152C42#12714yes—
1153C42C22×D412yes—
1154C42C22×D412yes—
1155C42C22×D412yes—
1156C42C22×D412yes—
1157C23—22no—
1158C23—22no—
1159C23—21no—
1160C23—21no—
1161C23—22no—
1162C23—22no—
1163C23—48no—
1164C23—42no—
1165C23—42no—
1166C23—42no—
1167C23—42no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—42no—
1173C23—42no—
1174C23—42no—
1175C23—42no—
1176C23—42no—
1177C23—42no—
1178C23—42no—
1179C23—42no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—84no—
1193C23—84no—
1194C23—88no—
1195C23—88no—
1196C23C2×#12712yes—
1197C23C23×D411yescharacteristic
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—41no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214D4—22no—
1215D4—22no—
1216D4—22no—
1217D4—22no—
1218D4—48no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—41no—
1231D4—41no—
1232D4—41no—
1233D4—41no—
1234D4—41no—
1235D4—41no—
1236D4—41no—
1237D4—41no—
1238D4—41no—
1239D4—84no—
1240D4—84no—
1241D4—84no—
1242D4—84no—
1243D4—84no—
1244D4—84no—
1245D4—164no—
1246D4—164no—
1247D4—164no—
1248D4—164no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—44no—
1272C2×C4—44no—
1273C2×C4—42no—
1274C2×C4—42no—
1275C2×C4—42no—
1276C2×C4—42no—
1277C2×C4—42no—
1278C2×C4—42no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—84no—
1298C2×C4—84no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—84no—
1302C2×C4—84no—
1303C2×C4—84no—
1304C2×C4—84no—
1305C2×C4—84no—
1306C2×C4C2×#12712yes—
1307C2×C4C2×#12712yes—
1308C2×C4C2×#12712yes—
1309C2×C4C2×#12712yes—
1310C2×C4C2×#12712yes—
1311C2×C4C23×D411yescharacteristic
1312C2×C4C23×D411yescharacteristic
1313C2×C4C2×H(5,𝔽2)11yescharacteristic
1314C2×C4C2×H(5,𝔽2)11yescharacteristic
1315C2×C4#58511yescharacteristic
1316C2×C4#58511yescharacteristic
1317C8—22no—
1318C8—22no—
1319C8—22no—
1320C8—22no—
1321C8—22no—
1322C8—22no—
1323C8—22no—
1324C8—22no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—42no—
1329C22—42no—
1330C22—44no—
1331C22—44no—
1332C22—42no—
1333C22—42no—
1334C22—816no—
1335C22—82no—
1336C22—82no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—82no—
1342C22—82no—
1343C22—82no—
1344C22—82no—
1345C22—82no—
1346C22—82no—
1347C22—82no—
1348C22—82no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22C22×#12711yescharacteristic
1362C22#348811yescharacteristic
1363C22#348811yescharacteristic
1364C22#358412yes—
1365C22#358512yes—
1366C4—22no—
1367C4—22no—
1368C4—22no—
1369C4—22no—
1370C4—22no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4#348411yescharacteristic
1386C4#348711yescharacteristic
1387C4#348811yescharacteristic
1388C4#348811yescharacteristic
1389C2—42no—
1390C2—82no—
1391C2—82no—
1392C2—161no—
1393C2—161no—
1394C2—161no—
1395C2—161no—
1396C2#3556511yescharacteristic
1397C2#6064311yescharacteristic
1398C2#6064411yescharacteristic
1399C2#6202712yes—
1400C2#6202812yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3256C2semidirect
2. C2×#3212C2semidirect
3. C2×#3105C2semidirect
4. C2×#3036C2semidirect
5. #37544C2semidirect
6. #35233C2semidirect
7. #28468C2semidirect
8. #28467C2semidirect
9. #28465C2semidirect
10. #28464C2semidirect
11. #28455C2semidirect
12. #28454C2semidirect
13. #28453C2semidirect
14. #28452C2semidirect
15. #28410C2semidirect
16. #28409C2semidirect
17. #28406C2semidirect
18. #28405C2semidirect
19. #28390C2semidirect
20. #28389C2semidirect
21. #28388C2semidirect
22. #28387C2semidirect
23. #28366C2semidirect
24. #28364C2semidirect
25. #28358C2semidirect
26. #28356C2semidirect
27. #25796C2semidirect
28. #25794C2semidirect
29. #25793C2semidirect
30. #25791C2semidirect
31. #20548C2semidirect
46. C2×#495C22semidirect
47. C2×#495C22semidirect
50. C2×#488C22semidirect
51. C2×#488C22semidirect
55. C2×#479C22semidirect
56. C2×#479C22semidirect
59. C2×#478C22semidirect
60. C2×#478C22semidirect
66. C2×#464C22semidirect
67. C2×#464C22semidirect
68. C2×#462C22semidirect
69. C2×#460C22semidirect
76. C2×#463C22semidirect
77. C2×#463C22semidirect
80. C2×#461C22semidirect
83. C2×#459C22semidirect
100. #2658C22semidirect
101. #2657C22semidirect
102. #2642C22semidirect
103. #2641C22semidirect
111. #2545C22semidirect
112. #2545C22semidirect
115. #2544C22semidirect
116. #2544C22semidirect
131. #2097C22semidirect
132. #2097C22semidirect
133. #2096C22semidirect
134. #2095C22semidirect
135. #2094C22semidirect
136. #2093C22semidirect
137. #2092C22semidirect
138. #2092C22semidirect
139. #2016C22semidirect
142. #2015C22semidirect
143. #2015C22semidirect
146. #2014C22semidirect
149. #2013C22semidirect
156. #2012C22semidirect
157. #2012C22semidirect
162. #2011C22semidirect
165. #1973C22semidirect
166. #1973C22semidirect
169. #1972C22semidirect
170. #1971C22semidirect
173. #1970C22semidirect
174. #1969C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
179. #1961C22semidirect
180. #1960C22semidirect
181. #1959C22semidirect
182. #1959C22semidirect
183. #1958C22semidirect
184. #1958C22semidirect
185. #1957C22semidirect
186. #1956C22semidirect
187. #1770C22semidirect
188. #1770C22semidirect
189. C8×C4⋊C4C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1768C22semidirect
192. #1768C22semidirect
193. #1768C22semidirect
194. #1768C22semidirect
346. #431D4semidirect
355. #423D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32562
C2×#32122
C2×#31052
C2×#30362
#375442
#352332
#284682
#284672
#284652
#284642
#284552
#284542
#284532
#284522
#284102
#284092
#284062
#284052
#283902
#283892
#283882
#283872
#283662
#283642
#283582
#283562
#257962
#257942
#257932
#257912
#205482