Finite Group Databasebeta

← #6569796

Subgroups — #6569796

Order 512.

2321 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3355C211yesmaximal, characteristic, complemented
2C2×#3347C211yesmaximal, characteristic, complemented
3C2×#3325C211yesmaximal, characteristic, complemented
4C2×#3318C211yesmaximal, characteristic, complemented
5#38080C211yesmaximal, characteristic, complemented
6#37869C211yesmaximal, characteristic, complemented
7#30287C211yesmaximal, characteristic, complemented
8#30253C211yesmaximal, characteristic, complemented
9#30247C211yesmaximal, characteristic, complemented
10#28548C211yesmaximal, characteristic, complemented
11#28534C211yesmaximal, characteristic, complemented
12#28525C211yesmaximal, characteristic, complemented
13#28421C211yesmaximal, characteristic, complemented
14#28397C211yesmaximal, characteristic, complemented
15#28387C211yesmaximal, characteristic, complemented
16#28353C211yesmaximal, characteristic, complemented
17#28353C211yesmaximal, characteristic, complemented
18#28353C211yesmaximal, characteristic, complemented
19#28329C211yesmaximal, characteristic, complemented
20#28319C211yesmaximal, characteristic, complemented
21#28301C211yesmaximal, characteristic, complemented
22#27942C211yesmaximal, characteristic, complemented
23#27942C211yesmaximal, characteristic, complemented
24#27941C211yesmaximal, characteristic, complemented
25#27928C211yesmaximal, characteristic, complemented
26#27923C211yesmaximal, characteristic, complemented
27#27907C211yesmaximal, characteristic, complemented
28#23810C211yesmaximal, characteristic, complemented
29#23735C211yesmaximal, characteristic, complemented
30#23731C211yesmaximal, characteristic, complemented
31#20561C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#553C2211yescharacteristic
35C2×D42C2211yescharacteristic
36#3355—28no—
37#3347—28no—
38#3325—28no—
39#3318—28no—
40C2×#501C2211yescharacteristic, complemented
41C2×#499C2211yescharacteristic, complemented
42C2×#490C2211yescharacteristic
43C2×#486C2211yescharacteristic
44C2×#481C2211yescharacteristic
45C2×#482C2211yescharacteristic
46C2×#482C2211yescharacteristic
47C2×#482C2211yescharacteristic
48C2×#482C2211yescharacteristic, complemented
49C2×#482C2211yescharacteristic, complemented
50C2×#482C2211yescharacteristic, complemented
51C2×#482C2211yescharacteristic, complemented
52C2×#482C2211yescharacteristic, complemented
53C2×#480C2211yescharacteristic, complemented
54C2×#480C2211yescharacteristic, complemented
55C2×#480C2211yescharacteristic, complemented
56C2×#478C2211yescharacteristic
57C2×#478C2211yescharacteristic, complemented
58C2×#478C2211yescharacteristic, complemented
59C2×#478C2211yescharacteristic, complemented
60C2×#476C2211yescharacteristic
61C2×#474C2211yescharacteristic, complemented
62C2×#469C2211yescharacteristic
63C2×#469C2211yescharacteristic
64C2×#469C2211yescharacteristic
65C2×#469C2211yescharacteristic, complemented
66C2×#469C2211yescharacteristic, complemented
67C2×#469C2211yescharacteristic, complemented
68C2×#466C2211yescharacteristic
69C2×#466C2211yescharacteristic, complemented
70C2×#459C2211yescharacteristic
71C2×#459C2211yescharacteristic
72C2×#447C2211yescharacteristic
73C2×#447C2211yescharacteristic
74C2×#447C2211yescharacteristic
75C2×#447C2211yescharacteristic
76C2×#442C2211yescharacteristic
77C2×#442C2211yescharacteristic, complemented
78C2×C4×D8C2211yescharacteristic
79C2×C4×D8C2211yescharacteristic, complemented
80C2×#436C2211yescharacteristic
81C2×#435C2211yescharacteristic
82C2×#428C2211yescharacteristic, complemented
83C2×#428C2211yescharacteristic, complemented
84C2×#428C2211yescharacteristic, complemented
85C2×#427C2211yescharacteristic, complemented
86C2×#418C2211yescharacteristic
87C2×#418C2211yescharacteristic
88C2×#418C2211yescharacteristic
89C22×#102C2211yescharacteristic
90#2856C2211yescharacteristic
91#2856C2211yescharacteristic, complemented
92#2714—22no—
93#2678—22no—
94#2672—22no—
95#2671—22no—
96#2660C2211yescharacteristic, complemented
97#2641C2211yescharacteristic
98#2619C2211yescharacteristic
99#2619C2211yescharacteristic, complemented
100#2566C2211yescharacteristic
101#2566C2211yescharacteristic, complemented
102#2542C2211yescharacteristic, complemented
103#2541C2211yescharacteristic
104#2504C2211yescharacteristic
105#2501C2211yescharacteristic, complemented
106#2500C2211yescharacteristic
107#2500C2211yescharacteristic, complemented
108#2500C2211yescharacteristic, complemented
109#2500C2211yescharacteristic, complemented
110#2479—22no—
111#2461—22no—
112#2433C2211yescharacteristic
113#2433C2211yescharacteristic
114#2424—22no—
115#2410—22no—
116#2328C2211yescharacteristic
117#2328C2211yescharacteristic, complemented
118#2317C2211yescharacteristic, complemented
119#2309C2211yescharacteristic
120C2×#390C2211yescharacteristic
121#2290C2211yescharacteristic
122#2285C2211yescharacteristic, complemented
123#2094C2211yescharacteristic
124#2094C2211yescharacteristic
125#2094C2211yescharacteristic, complemented
126#2094C2211yescharacteristic, complemented
127#2094C2211yescharacteristic, complemented
128#2094C2211yescharacteristic, complemented
129#2094C2211yescharacteristic, complemented
130#2094C2211yescharacteristic, complemented
131#2093C2211yescharacteristic
132#2093C2211yescharacteristic
133#2093C2211yescharacteristic, complemented
134#2093C2211yescharacteristic, complemented
135#2093C2211yescharacteristic, complemented
136#2093C2211yescharacteristic, complemented
137#2092C2211yescharacteristic
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic
140#2092C2211yescharacteristic, complemented
141#2092C2211yescharacteristic, complemented
142#2092C2211yescharacteristic, complemented
143#2092C2211yescharacteristic, complemented
144#2092C2211yescharacteristic, complemented
145#2092C2211yescharacteristic, complemented
146#2092C2211yescharacteristic, complemented
147#2092C2211yescharacteristic, complemented
148#2092C2211yescharacteristic, complemented
149#2092C2211yescharacteristic, complemented
150#2092C2211yescharacteristic, complemented
151#2092C2211yescharacteristic, complemented
152#2092C2211yescharacteristic, complemented
153#2011C2211yescharacteristic
154#2011C2211yescharacteristic
155#2011C2211yescharacteristic
156#2011C2211yescharacteristic, complemented
157#2011C2211yescharacteristic, complemented
158#2011C2211yescharacteristic, complemented
159#2011C2211yescharacteristic, complemented
160#2011C2211yescharacteristic, complemented
161#2011C2211yescharacteristic, complemented
162#2011C2211yescharacteristic, complemented
163#1972C2211yescharacteristic
164#1972C2211yescharacteristic, complemented
165#1972C2211yescharacteristic, complemented
166#1972C2211yescharacteristic, complemented
167#1970C2211yescharacteristic
168#1970C2211yescharacteristic
169#1970C2211yescharacteristic
170#1970C2211yescharacteristic, complemented
171#1970C2211yescharacteristic, complemented
172#1970C2211yescharacteristic, complemented
173#1970C2211yescharacteristic, complemented
174#1970C2211yescharacteristic, complemented
175#1961C2211yescharacteristic
176#1961C2211yescharacteristic, complemented
177#1957C2211yescharacteristic
178#1957C2211yescharacteristic, complemented
179#1957C2211yescharacteristic, complemented
180#1957C2211yescharacteristic, complemented
181#1847C2211yescharacteristic, complemented
182#1847C2211yescharacteristic, complemented
183#1846C2211yescharacteristic, complemented
184#1846C2211yescharacteristic, complemented
185#1845C2211yescharacteristic, complemented
186#1844C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188C8×C4⋊C4C2211yescharacteristic, complemented
189#1768C2211yescharacteristic, complemented
190#1753C2211yescharacteristic, complemented
191#1753C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193C8×C22⋊C4C2211yescharacteristic, complemented
194#1750C2211yescharacteristic, complemented
195C4×C22⋊C8C2211yescharacteristic, complemented
196#1746C2211yescharacteristic, complemented
197#1729C2211yescharacteristic, complemented
198#1728C2211yescharacteristic, complemented
199C23×D4—21no—
200C23×D4C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C22×D8C2311yescharacteristic
203C22×D8C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#555—24no—
215#555—24no—
216#553—24no—
217#553—24no—
218#553—24no—
219#553—24no—
220D42—24no—
221D42—24no—
222C2×C4⋊Q8C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#126—21no—
229C2×#126—21no—
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#124—21no—
233C2×#124—21no—
234C2×#123—21no—
235C2×#123—21no—
236C2×#123—22no—
237C2×C22⋊Q8—22no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—22no—
242C2×#121—22no—
243C2×#121—21no—
244C2×#121—22no—
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×#121C2311yescharacteristic
252C2×#121C2311yescharacteristic
253C2×#120—21no—
254C2×#120—21no—
255C2×#120—22no—
256C2×#120—22no—
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×#117—21no—
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C22⋊C4—22no—
273C22×C42C2311yescharacteristic
274#501—24no—
275#499—24no—
276#490—24no—
277#486—24no—
278#482—24no—
279#482—24no—
280#482—24no—
281#482—24no—
282#482—24no—
283#482—24no—
284#482—24no—
285#482—24no—
286#481—24no—
287#480—24no—
288#480—24no—
289#480—24no—
290#478—24no—
291#478—24no—
292#478—24no—
293#478—24no—
294#476—24no—
295#474—24no—
296#469—24no—
297#469—24no—
298#469—24no—
299#469—24no—
300#469—24no—
301#469—24no—
302#466—24no—
303#466—24no—
304#459—24no—
305#459—24no—
306#447—24no—
307#447—24no—
308#447—24no—
309#447—24no—
310#442—24no—
311#442—24no—
312C4×D8—24no—
313C4×D8—24no—
314#436D418yescomplemented
315#435D418yescomplemented
316#428—24no—
317#428—24no—
318#428—24no—
319#427—24no—
320C2×#107C2311yescharacteristic
321C2×#107C2311yescharacteristic
322C2×#107C2311yescharacteristic
323C2×#107C2311yescharacteristic
324C2×#107C2311yescharacteristic
325C2×#107C2311yescharacteristic
326C2×#107C2311yescharacteristic
327C2×#107C2311yescharacteristic
328C2×#107C2311yescharacteristic
329C2×#107C2311yescharacteristic
330C2×#107C2311yescharacteristic
331C2×#107C2311yescharacteristic
332C2×#106C2311yescharacteristic
333C2×#106C2311yescharacteristic
334C2×#106C2311yescharacteristic
335C2×#106C2311yescharacteristic
336C2×#106C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×C4⋊C8C2311yescharacteristic
345C2×C4⋊C8C2311yescharacteristic
346#418—24no—
347#418—24no—
348#418—24no—
349C2×#102—24no—
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×#102C2311yescharacteristic
358C2×#102C2311yescharacteristic
359C2×#102C2311yescharacteristic
360C2×#102C2311yescharacteristic
361C2×#102C2311yescharacteristic
362C2×#102C2311yescharacteristic
363C2×#102C2311yescharacteristic
364C2×#102C2311yescharacteristic
365C2×#102C2311yescharacteristic
366C2×#102C2311yescharacteristic
367C2×#102C2311yescharacteristic
368C2×#102C2311yescharacteristic
369C2×#102C2311yescharacteristic
370C2×#102C2311yescharacteristic
371C2×#102C2311yescharacteristic
372C2×#102C2311yescharacteristic
373C2×#102C2311yescharacteristic
374C2×#102C2311yescharacteristic
375C2×#102C2311yescharacteristic
376C2×#102C2311yescharacteristic
377C2×#102C2311yescharacteristic
378C2×#102C2311yescharacteristic
379C2×#102C2311yescharacteristic
380C2×#102C2311yescharacteristic
381C2×#102C2311yescharacteristic
382C2×C22⋊C8C2311yescharacteristic
383C2×C22⋊C8C2311yescharacteristic
384C2×C22⋊C8C2311yescharacteristic
385C2×C22⋊C8C2311yescharacteristic
386C2×#97C2311yescharacteristic
387C2×#97C2311yescharacteristic
388C2×#97C2311yescharacteristic
389C2×C4×C8C2311yescharacteristic
390C2×C4×C8C2311yescharacteristic
391C2×C4×C8C2311yescharacteristic
392C2×C4×C8C2311yescharacteristic
393C2×C4×C8C2311yescharacteristic
394#399—22no—
395#399—22no—
396#398—22no—
397#397—22no—
398#396—22no—
399#396—22no—
400#395—22no—
401#394—22no—
402#394—22no—
403#394—22no—
404#394—22no—
405#394—22no—
406#394—22no—
407#394—22no—
408#394—22no—
409#392—22no—
410#392—22no—
411#392—22no—
412#392—22no—
413#392—22no—
414#390—22no—
415#390—22no—
416#390—22no—
417#390—22no—
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#390C2311yescharacteristic
423#390C2311yescharacteristic
424#390C2311yescharacteristic
425#390C2311yescharacteristic
426#390C2311yescharacteristic
427#390C2311yescharacteristic
428#390C2311yescharacteristic
429#390C2311yescharacteristic
430#390C2311yescharacteristic
431#390C2311yescharacteristic
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#389—22no—
435#388—22no—
436#388—22no—
437#388—22no—
438#388—22no—
439#388D412yes—
440#387D412yes—
441#386—22no—
442#386—22no—
443#386—22no—
444#386—22no—
445#386—22no—
446#386D412yes—
447#385—22no—
448#385—22no—
449#385—22no—
450#385D412yes—
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#380—22no—
464#379—22no—
465C4×C4⋊C4—22no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469#376C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480C25—21no—
481C25—21no—
482C22×Q8—21no—
483C22×D4—22no—
484C22×D4—22no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—44no—
512C22×D4—84no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2×D412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16—41no—
559C2×M16C2×D414yes—
560C2×M16C2×D414yes—
561C2×M16C2×D414yes—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8C2×D414yes—
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—22no—
575#127—22no—
576#127—22no—
577#127—22no—
578#127—41no—
579#127—41no—
580#127—41no—
581#127—41no—
582#127—41no—
583#127—41no—
584#127—41no—
585#126—44no—
586#126—44no—
587#125—22no—
588#125—22no—
589#125—22no—
590#125—22no—
591#124—44no—
592#124—44no—
593#123—44no—
594#123—44no—
595#123—84no—
596C22⋊Q8—84no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—22no—
611#121—22no—
612#121—22no—
613#121—44no—
614#121—44no—
615#121—44no—
616#121—44no—
617#121—84no—
618#121—84no—
619#121—84no—
620#120—44no—
621#120—44no—
622#120—84no—
623#120—84no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—44no—
633C4×D4—44no—
634C4×D4C2×D414yes—
635C4×D4C2×D414yes—
636#117—22no—
637#117—22no—
638#117—22no—
639#117—22no—
640#117—22no—
641#117—22no—
642#117—22no—
643#117—22no—
644#117—41no—
645#117—41no—
646#117—44no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4C2×D412yes—
665C2×C4⋊C4C2×D412yes—
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—84no—
710C2×C22⋊C4C2×D412yes—
711C2×C22⋊C4C2×D412yes—
712C2×C22⋊C4C2×D412yes—
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—41no—
720C2×C42—41no—
721C2×C42C2×D412yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#107—22no—
728#107—22no—
729#107—22no—
730#107—22no—
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—22no—
736#107—22no—
737#107—22no—
738#107—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—22no—
746#106—22no—
747#106—22no—
748#106—22no—
749#106—22no—
750#106—22no—
751C4⋊C8C2×D414yes—
752C4⋊C8C2×D414yes—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785C22⋊C8C2×D414yes—
786C22⋊C8C2×D414yes—
787C22⋊C8C2×D414yes—
788C22⋊C8C2×D414yes—
789#97—41no—
790#97—41no—
791#97C2×D414yes—
792C4×C8—41no—
793C4×C8—41no—
794C4×C8—41no—
795C4×C8—41no—
796C4×C8C2×D414yes—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—22no—
801#95—22no—
802#95—22no—
803#95C2×D412yes—
804#95C2×D412yes—
805#95C2×D412yes—
806#95C2×D412yes—
807#95C2×D412yes—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—42no—
815C24—42no—
816C24—44no—
817C24—42no—
818C24—42no—
819C24—82no—
820C24—81no—
821C24—81no—
822C24—82no—
823C24—82no—
824C24C22×D411yescharacteristic
825C24C22×D411yescharacteristic
826C2×Q8—42no—
827C2×Q8—82no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—44no—
887C2×D4—82no—
888C2×D4—82no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—82no—
894C2×D4—82no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—82no—
899C2×D4—82no—
900C2×D4—82no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—82no—
909C2×D4—82no—
910C2×D4—816no—
911C2×D4#12714yes—
912C2×D42−1+412yes—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—24no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—82no—
941C22×C4—82no—
942C22×C4—82no—
943C22×C4—82no—
944C22×C4—82no—
945C22×C4—82no—
946C22×C4C22×D412yes—
947C22×C4C22×D412yes—
948C22×C4C22×D412yes—
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D412yes—
954C22×C4C22×D412yes—
955C22×C4C22×D412yes—
956C22×C4C22×D412yes—
957C22×C4C22×D412yes—
958C22×C4C2511yescharacteristic
959D8—44no—
960D8—44no—
961D8—44no—
962D8—44no—
963D8—82no—
964D8—82no—
965D8—82no—
966D8—82no—
967M16—44no—
968M16—44no—
969M16—44no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—44no—
987C2×C8C22×D412yes—
988C2×C8C22×D412yes—
989C2×C8C22×D412yes—
990C2×C8C22×D412yes—
991C2×C8C22×D412yes—
992C2×C8C22×D412yes—
993C2×C8C22×D412yes—
994C2×C8C22×D412yes—
995C4⋊C4—24no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—82no—
1026C4⋊C4—82no—
1027C4⋊C4—82no—
1028C4⋊C4—82no—
1029C4⋊C4—82no—
1030C4⋊C4#12714yes—
1031C22⋊C4—24no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—82no—
1055C22⋊C4—82no—
1056C22⋊C4—82no—
1057C22⋊C4—82no—
1058C22⋊C4—82no—
1059C22⋊C4—82no—
1060C22⋊C4—82no—
1061C22⋊C4—82no—
1062C22⋊C4—82no—
1063C22⋊C4—82no—
1064C22⋊C4—82no—
1065C22⋊C4—82no—
1066C22⋊C4#12714yes—
1067C22⋊C4#12714yes—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—42no—
1077C42—42no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42C22×D412yes—
1082C42C22×D412yes—
1083C23—22no—
1084C23—22no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—42no—
1093C23—41no—
1094C23—41no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—42no—
1117C23—42no—
1118C23—42no—
1119C23—42no—
1120C23—42no—
1121C23—84no—
1122C23—84no—
1123C23—84no—
1124C23—84no—
1125C23—88no—
1126C23—162no—
1127C23—162no—
1128C23—164no—
1129C23—164no—
1130C23—164no—
1131C23C2×#12712yes—
1132C23C2×#12712yes—
1133C23C23×D411yescharacteristic
1134Q8—162no—
1135D4—22no—
1136D4—22no—
1137D4—44no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—84no—
1161D4—84no—
1162D4—84no—
1163D4—84no—
1164D4—84no—
1165D4—84no—
1166D4—84no—
1167D4—164no—
1168D4—162no—
1169D4—164no—
1170D4—164no—
1171D4—164no—
1172D4—162no—
1173D4—162no—
1174D4—162no—
1175D4—162no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—84no—
1222C2×C4—84no—
1223C2×C4—84no—
1224C2×C4—162no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4C2×#12712yes—
1229C2×C4C2×#12712yes—
1230C2×C4C2×#12712yes—
1231C2×C4C2×#12712yes—
1232C2×C4#57614yes—
1233C2×C4C23×D411yescharacteristic
1234C2×C4C23×D411yescharacteristic
1235C2×C4C2×2−1+411yescharacteristic
1236C2×C4#58511yescharacteristic
1237C2×C4#58511yescharacteristic
1238C2×C4#58511yescharacteristic
1239C8—22no—
1240C8—22no—
1241C8—22no—
1242C8—22no—
1243C8—22no—
1244C8—22no—
1245C8—22no—
1246C8—22no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—44no—
1259C22—82no—
1260C22—81no—
1261C22—81no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—168no—
1288C22—168no—
1289C22C22×#12711yescharacteristic
1290C22#348511yescharacteristic
1291C22#348911yescharacteristic
1292C22C2×#57612yes—
1293C22#358512yes—
1294C4—24no—
1295C4—22no—
1296C4—22no—
1297C4—22no—
1298C4—22no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4#348511yescharacteristic
1313C4#348511yescharacteristic
1314C4#348911yescharacteristic
1315C4#348911yescharacteristic
1316C2—42no—
1317C2—42no—
1318C2—82no—
1319C2—161no—
1320C2—161no—
1321C2—161no—
1322C2—161no—
1323C2—161no—
1324C2#3606011yescharacteristic
1325C2#6064411yescharacteristic
1326C2#6064711yescharacteristic
1327C2#6175212yes—
1328C2#6218712yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3355C2semidirect
2. C2×#3347C2semidirect
3. C2×#3325C2semidirect
4. C2×#3318C2semidirect
5. #38080C2semidirect
6. #37869C2semidirect
7. #30287C2semidirect
8. #30253C2semidirect
9. #30247C2semidirect
10. #28548C2semidirect
11. #28534C2semidirect
12. #28525C2semidirect
13. #28421C2semidirect
14. #28397C2semidirect
15. #28387C2semidirect
16. #28353C2semidirect
17. #28353C2semidirect
18. #28353C2semidirect
19. #28329C2semidirect
20. #28319C2semidirect
21. #28301C2semidirect
22. #27942C2semidirect
23. #27942C2semidirect
24. #27941C2semidirect
25. #27928C2semidirect
26. #27923C2semidirect
27. #27907C2semidirect
28. #23810C2semidirect
29. #23735C2semidirect
30. #23731C2semidirect
31. #20561C2semidirect
40. C2×#501C22semidirect
41. C2×#499C22semidirect
48. C2×#482C22semidirect
49. C2×#482C22semidirect
50. C2×#482C22semidirect
51. C2×#482C22semidirect
52. C2×#482C22semidirect
53. C2×#480C22semidirect
54. C2×#480C22semidirect
55. C2×#480C22semidirect
57. C2×#478C22semidirect
58. C2×#478C22semidirect
59. C2×#478C22semidirect
61. C2×#474C22semidirect
65. C2×#469C22semidirect
66. C2×#469C22semidirect
67. C2×#469C22semidirect
69. C2×#466C22semidirect
77. C2×#442C22semidirect
79. C2×C4×D8C22semidirect
82. C2×#428C22semidirect
83. C2×#428C22semidirect
84. C2×#428C22semidirect
85. C2×#427C22semidirect
91. #2856C22semidirect
96. #2660C22semidirect
99. #2619C22semidirect
101. #2566C22semidirect
102. #2542C22semidirect
105. #2501C22semidirect
107. #2500C22semidirect
108. #2500C22semidirect
109. #2500C22semidirect
117. #2328C22semidirect
118. #2317C22semidirect
122. #2285C22semidirect
125. #2094C22semidirect
126. #2094C22semidirect
127. #2094C22semidirect
128. #2094C22semidirect
129. #2094C22semidirect
130. #2094C22semidirect
133. #2093C22semidirect
134. #2093C22semidirect
135. #2093C22semidirect
136. #2093C22semidirect
140. #2092C22semidirect
141. #2092C22semidirect
142. #2092C22semidirect
143. #2092C22semidirect
144. #2092C22semidirect
145. #2092C22semidirect
146. #2092C22semidirect
147. #2092C22semidirect
148. #2092C22semidirect
149. #2092C22semidirect
150. #2092C22semidirect
151. #2092C22semidirect
152. #2092C22semidirect
156. #2011C22semidirect
157. #2011C22semidirect
158. #2011C22semidirect
159. #2011C22semidirect
160. #2011C22semidirect
161. #2011C22semidirect
162. #2011C22semidirect
164. #1972C22semidirect
165. #1972C22semidirect
166. #1972C22semidirect
170. #1970C22semidirect
171. #1970C22semidirect
172. #1970C22semidirect
173. #1970C22semidirect
174. #1970C22semidirect
176. #1961C22semidirect
178. #1957C22semidirect
179. #1957C22semidirect
180. #1957C22semidirect
181. #1847C22semidirect
182. #1847C22semidirect
183. #1846C22semidirect
184. #1846C22semidirect
185. #1845C22semidirect
186. #1844C22semidirect
187. #1771C22semidirect
188. C8×C4⋊C4C22semidirect
189. #1768C22semidirect
190. #1753C22semidirect
191. #1753C22semidirect
192. #1753C22semidirect
193. C8×C22⋊C4C22semidirect
194. #1750C22semidirect
195. C4×C22⋊C8C22semidirect
196. #1746C22semidirect
197. #1729C22semidirect
198. #1728C22semidirect
314. #436D4semidirect
315. #435D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33552
C2×#33472
C2×#33252
C2×#33182
#380802
#378692
#302872
#302532
#302472
#285482
#285342
#285252
#284212
#283972
#283872
#283532
#283292
#283192
#283012
#279422
#279412
#279282
#279232
#279072
#238102
#237352
#237312
#205612