Finite Group Databasebeta

← #6498787

Subgroups — #6498787

Order 512.

2190 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3244C211yesmaximal, characteristic, complemented
2C2×#3241C211yesmaximal, characteristic, complemented
3C2×#3224C211yesmaximal, characteristic, complemented
4C2×#3220C211yesmaximal, characteristic, complemented
5#35276C211yesmaximal, characteristic, complemented
6#35264C211yesmaximal, characteristic, complemented
7#33254C211yesmaximal, characteristic, complemented
8#33253C211yesmaximal, characteristic, complemented
9#33251C211yesmaximal, characteristic, complemented
10#33251C211yesmaximal, characteristic, complemented
11#30290C211yesmaximal, characteristic, complemented
12#30287C211yesmaximal, characteristic, complemented
13#30274C211yesmaximal, characteristic, complemented
14#30270C211yesmaximal, characteristic, complemented
15#28395C211yesmaximal, characteristic, complemented
16#28393C211yesmaximal, characteristic, complemented
17#28389C211yesmaximal, characteristic, complemented
18#28387C211yesmaximal, characteristic, complemented
19#28383C211yesmaximal, characteristic, complemented
20#28381C211yesmaximal, characteristic, complemented
21#28379C211yesmaximal, characteristic, complemented
22#28378C211yesmaximal, characteristic, complemented
23#28328C211yesmaximal, characteristic, complemented
24#28325C211yesmaximal, characteristic, complemented
25#28321C211yesmaximal, characteristic, complemented
26#28319C211yesmaximal, characteristic, complemented
27#28318C211yesmaximal, characteristic, complemented
28#28316C211yesmaximal, characteristic, complemented
29#28312C211yesmaximal, characteristic, complemented
30#28310C211yesmaximal, characteristic, complemented
31#20465C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#540C2211yescharacteristic
35C2×#535C2211yescharacteristic
36#3244—28no—
37#3241—28no—
38#3224—28no—
39#3220—28no—
40C2×#501C2211yescharacteristic, complemented
41C2×#501C2211yescharacteristic, complemented
42C2×#499C2211yescharacteristic, complemented
43C2×#498C2211yescharacteristic, complemented
44C2×#496C2211yescharacteristic
45C2×#496C2211yescharacteristic
46C2×#495C2211yescharacteristic
47C2×#493C2211yescharacteristic
48C2×#490C2211yescharacteristic
49C2×#490C2211yescharacteristic, complemented
50C2×#489C2211yescharacteristic
51C2×#489C2211yescharacteristic, complemented
52C2×#488C2211yescharacteristic
53C2×#488C2211yescharacteristic, complemented
54C2×#486C2211yescharacteristic
55C2×#486C2211yescharacteristic, complemented
56C2×#481C2211yescharacteristic
57C2×#481C2211yescharacteristic
58C2×#485C2211yescharacteristic
59C2×#482C2211yescharacteristic
60C2×#482C2211yescharacteristic
61C2×#482C2211yescharacteristic
62C2×#483C2211yescharacteristic
63C2×#480C2211yescharacteristic
64C2×#479C2211yescharacteristic, complemented
65C2×#475C2211yescharacteristic, complemented
66C2×#478C2211yescharacteristic, complemented
67C2×#478C2211yescharacteristic, complemented
68C2×#478C2211yescharacteristic, complemented
69C2×#476C2211yescharacteristic, complemented
70C2×#476C2211yescharacteristic, complemented
71C2×#474C2211yescharacteristic, complemented
72C2×#464C2211yescharacteristic
73C2×#460C2211yescharacteristic
74C2×#463C2211yescharacteristic
75C2×#463C2211yescharacteristic
76C2×#463C2211yescharacteristic
77C2×#459C2211yescharacteristic
78C2×#459C2211yescharacteristic
79C2×#459C2211yescharacteristic
80C2×#452C2211yescharacteristic
81C2×#449C2211yescharacteristic
82C2×#449C2211yescharacteristic
83C2×#449C2211yescharacteristic
84C2×#450C2211yescharacteristic
85C2×#447C2211yescharacteristic
86C2×#447C2211yescharacteristic
87C2×#447C2211yescharacteristic
88C2×#433C2211yescharacteristic
89C2×#433C2211yescharacteristic
90#2861C2211yescharacteristic
91#2861C2211yescharacteristic
92#2861C2211yescharacteristic, complemented
93#2858C2211yescharacteristic
94#2858C2211yescharacteristic
95#2858C2211yescharacteristic, complemented
96#2856C2211yescharacteristic
97#2850C2211yescharacteristic
98#2660C2211yescharacteristic, complemented
99#2657C2211yescharacteristic, complemented
100#2641C2211yescharacteristic
101#2641C2211yescharacteristic
102#2640C2211yescharacteristic
103#2640C2211yescharacteristic
104#2620C2211yescharacteristic
105#2619C2211yescharacteristic
106#2555—22no—
107#2554—22no—
108#2491—22no—
109#2490—22no—
110#2472—22no—
111#2472—22no—
112#2464—22no—
113#2461—22no—
114#2328C2211yescharacteristic, complemented
115#2326C2211yescharacteristic, complemented
116#2311C2211yescharacteristic
117#2309C2211yescharacteristic
118C4×#127C2211yescharacteristic, complemented
119C4×#124C2211yescharacteristic, complemented
120#2297C2211yescharacteristic
121C2×#390C2211yescharacteristic
122C4×#117C2211yescharacteristic
123#2097C2211yescharacteristic, complemented
124#2097C2211yescharacteristic, complemented
125#2096C2211yescharacteristic, complemented
126#2096C2211yescharacteristic, complemented
127#2094C2211yescharacteristic
128#2094C2211yescharacteristic
129#2094C2211yescharacteristic
130#2094C2211yescharacteristic, complemented
131#2093C2211yescharacteristic
132#2093C2211yescharacteristic, complemented
133#2092C2211yescharacteristic
134#2092C2211yescharacteristic
135#2092C2211yescharacteristic
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2015C2211yescharacteristic, complemented
140#2015C2211yescharacteristic, complemented
141#2014C2211yescharacteristic, complemented
142#2014C2211yescharacteristic, complemented
143#2012C2211yescharacteristic
144#2012C2211yescharacteristic
145#2012C2211yescharacteristic
146#2012C2211yescharacteristic
147#2012C2211yescharacteristic, complemented
148#2012C2211yescharacteristic, complemented
149#2011C2211yescharacteristic
150#2011C2211yescharacteristic
151#2011C2211yescharacteristic
152#2011C2211yescharacteristic
153#2011C2211yescharacteristic, complemented
154#2011C2211yescharacteristic, complemented
155#1973C2211yescharacteristic
156#1973C2211yescharacteristic
157#1973C2211yescharacteristic
158#1973C2211yescharacteristic, complemented
159#1973C2211yescharacteristic, complemented
160#1973C2211yescharacteristic, complemented
161#1973C2211yescharacteristic, complemented
162#1973C2211yescharacteristic, complemented
163#1972C2211yescharacteristic
164#1972C2211yescharacteristic
165#1972C2211yescharacteristic
166#1972C2211yescharacteristic
167#1972C2211yescharacteristic
168#1972C2211yescharacteristic
169#1972C2211yescharacteristic
170#1972C2211yescharacteristic
171#1972C2211yescharacteristic
172#1972C2211yescharacteristic, complemented
173#1972C2211yescharacteristic, complemented
174#1972C2211yescharacteristic, complemented
175#1972C2211yescharacteristic, complemented
176#1972C2211yescharacteristic, complemented
177#1971C2211yescharacteristic, complemented
178#1971C2211yescharacteristic, complemented
179#1970C2211yescharacteristic
180#1970C2211yescharacteristic
181#1970C2211yescharacteristic
182#1970C2211yescharacteristic, complemented
183#1968C2211yescharacteristic
184#1968C2211yescharacteristic, complemented
185#1968C2211yescharacteristic, complemented
186#1968C2211yescharacteristic, complemented
187#1768C2211yescharacteristic, complemented
188#1768C2211yescharacteristic, complemented
189#1767C2211yescharacteristic, complemented
190#1767C2211yescharacteristic, complemented
191#1750C2211yescharacteristic
192#1750C2211yescharacteristic
193#1749C2211yescharacteristic
194#1749C2211yescharacteristic
195#1746C2211yescharacteristic, complemented
196#1746C2211yescharacteristic, complemented
197C4×#97C2211yescharacteristic, complemented
198C4×#97C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×D4C2311yescharacteristic
201C22×Q16C2311yescharacteristic
202C22×SD16C2311yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217#544—24no—
218#544—24no—
219#542—24no—
220#542—24no—
221#540—24no—
222#540—24no—
223#535—24no—
224#535—24no—
225C2×C4⋊Q8—21no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×#127C2311yescharacteristic
230C2×#127C2311yescharacteristic
231C2×#127C2311yescharacteristic
232C2×#127C2311yescharacteristic
233C2×#127C2311yescharacteristic
234C2×#126—21no—
235C2×#125—21no—
236C2×#125C2311yescharacteristic
237C2×#125C2311yescharacteristic
238C2×#125C2311yescharacteristic
239C2×#124—21no—
240C2×#124—22no—
241C2×#124—22no—
242C2×#124—22no—
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#123—21no—
249C2×#123—21no—
250C2×#123—21no—
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8—21no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8C2311yescharacteristic
255C2×#121—22no—
256C2×#121—21no—
257C2×#121—21no—
258C2×#121—21no—
259C2×#121—21no—
260C2×#121C2311yescharacteristic
261C2×#121C2311yescharacteristic
262C2×#121C2311yescharacteristic
263C2×#120—21no—
264C2×#120—21no—
265C2×C4×Q8C2311yescharacteristic
266C2×C4×D4—22no—
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C22⋊C4—22no—
275C22×C42C2311yescharacteristic
276#501—24no—
277#501—24no—
278#499—24no—
279#498—24no—
280#496—24no—
281#496—24no—
282#495—24no—
283#493—24no—
284#490—24no—
285#490—24no—
286#489—24no—
287#489—24no—
288#488—24no—
289#488—24no—
290#486—24no—
291#486—24no—
292#485—24no—
293#483—24no—
294#482—24no—
295#482—24no—
296#482—24no—
297#481—24no—
298#481—24no—
299#480—24no—
300#479—24no—
301#478—24no—
302#478—24no—
303#478—24no—
304#476—24no—
305#476—24no—
306#475—24no—
307#474—24no—
308#464—24no—
309#463—24no—
310#463—24no—
311#463—24no—
312#460—24no—
313#459—24no—
314#459—24no—
315#459—24no—
316#452—24no—
317#450—24no—
318#449—24no—
319#449—24no—
320#449—24no—
321#447—24no—
322#447—24no—
323#447—24no—
324#433D418yescomplemented
325#433D418yescomplemented
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×C4⋊C8C2311yescharacteristic
343C2×C4⋊C8C2311yescharacteristic
344C2×C4⋊C8C2311yescharacteristic
345C2×C4⋊C8C2311yescharacteristic
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#103C2311yescharacteristic
350C2×#103C2311yescharacteristic
351C2×#103C2311yescharacteristic
352C2×#103C2311yescharacteristic
353C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
379C2×C22⋊C8C2311yescharacteristic
380C2×C22⋊C8C2311yescharacteristic
381C2×C22⋊C8C2311yescharacteristic
382C2×#97C2311yescharacteristic
383C2×#97C2311yescharacteristic
384C2×#97C2311yescharacteristic
385C2×#97C2311yescharacteristic
386C2×#97C2311yescharacteristic
387C2×#97C2311yescharacteristic
388C2×#97C2311yescharacteristic
389C2×#97C2311yescharacteristic
390C2×C4×C8C2311yescharacteristic
391C2×C4×C8C2311yescharacteristic
392C2×C4×C8C2311yescharacteristic
393C2×C4×C8C2311yescharacteristic
394#398—22no—
395#397—22no—
396#397—22no—
397#396—22no—
398#395—22no—
399#394—22no—
400#394—22no—
401#394—22no—
402#394—22no—
403#394—22no—
404#394—22no—
405#393—22no—
406#393—22no—
407#392—22no—
408#392—22no—
409#392—22no—
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#390—22no—
417#390—22no—
418#390—22no—
419#390—22no—
420#390—22no—
421#390—22no—
422#390—22no—
423#390C2311yescharacteristic
424#390C2311yescharacteristic
425#390C2311yescharacteristic
426#390C2311yescharacteristic
427#390C2311yescharacteristic
428#390C2311yescharacteristic
429#390C2311yescharacteristic
430#390C2311yescharacteristic
431#390C2311yescharacteristic
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#390C2311yescharacteristic
435#390C2311yescharacteristic
436#390C2311yescharacteristic
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#388—22no—
442#388—22no—
443#388—22no—
444#388—22no—
445#388—22no—
446#388—22no—
447#388—22no—
448#388—22no—
449#388—22no—
450#386—22no—
451#386—22no—
452#386—22no—
453#386—22no—
454#386—22no—
455#385—22no—
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#380—22no—
461#379—22no—
462C4×C4⋊C4D412yes—
463C4×C4⋊C4D412yes—
464C4×C22⋊C4—22no—
465C4×C22⋊C4—22no—
466C4×C22⋊C4D412yes—
467C4×C22⋊C4D412yes—
468#376C2311yescharacteristic
469#376C2311yescharacteristic
470C43C2311yescharacteristic
471C43C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480C25—21no—
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C2×D412yes—
523C23×C4C2411yescharacteristic
524C2×Q16—22no—
525C2×Q16—41no—
526C2×Q16—41no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C2×D8—41no—
565C2×D8—41no—
566C2×D8—41no—
567C2×D8—41no—
568C2×D8—41no—
569C2×D8—41no—
570C2×D8—41no—
571C2×D8—41no—
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C4⋊Q8—22no—
581C4⋊Q8—22no—
582C4⋊Q8—22no—
583C4⋊Q8—22no—
584C4⋊Q8—22no—
585C4⋊Q8—22no—
586C4⋊Q8—44no—
587#127—22no—
588#127—22no—
589#127—22no—
590#127—22no—
591#127—22no—
592#127—22no—
593#127—41no—
594#127—41no—
595#127—41no—
596#127—41no—
597#126—44no—
598#125—22no—
599#125—22no—
600#125—22no—
601#125—22no—
602#125—22no—
603#125—22no—
604#125—44no—
605#124—22no—
606#124—22no—
607#124—22no—
608#124—22no—
609#124—22no—
610#124—22no—
611#124—41no—
612#124—41no—
613#124—41no—
614#124—41no—
615#124—44no—
616#124—84no—
617#124—84no—
618#124—84no—
619#123—44no—
620#123—44no—
621#123—44no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—44no—
625C22⋊Q8—44no—
626C22⋊Q8—44no—
627#121—22no—
628#121—22no—
629#121—22no—
630#121—22no—
631#121—22no—
632#121—22no—
633#121—44no—
634#121—44no—
635#121—44no—
636#121—44no—
637#121—84no—
638#120—44no—
639#120—44no—
640C4×Q8—22no—
641C4×Q8—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—84no—
649#117—22no—
650#117—22no—
651#117—41no—
652#117—41no—
653#117C2×D414yes—
654#117C2×D414yes—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4C2×D412yes—
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
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—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—84no—
717C2×C22⋊C4C2×D412yes—
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—41no—
723C2×C42—41no—
724C2×C42C2×D412yes—
725C2×C42C2×D412yes—
726C2×C42C2×D412yes—
727C2×C42C2×D412yes—
728C2×C42C2×D412yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#107—22no—
736#107—22no—
737#107—22no—
738#107—22no—
739#107—22no—
740#107—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—
753C4⋊C8C2×D414yes—
754C4⋊C8C2×D414yes—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—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—
785#102—22no—
786#102—22no—
787C22⋊C8C2×D414yes—
788C22⋊C8C2×D414yes—
789C22⋊C8C2×D414yes—
790C22⋊C8C2×D414yes—
791#97—41no—
792#97—41no—
793#97—41no—
794#97—41no—
795#97—41no—
796#97—41no—
797#97C2×D414yes—
798#97C2×D414yes—
799C4×C8—41no—
800C4×C8—41no—
801C4×C8C2×D414yes—
802C4×C8C2×D414yes—
803#95—22no—
804#95—22no—
805#95—22no—
806#95—22no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95C2×D412yes—
812#95C2×D412yes—
813#95C2×D412yes—
814#95C2×D412yes—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—42no—
822C24—42no—
823C24—42no—
824C24—82no—
825C24—82no—
826C24C22×D411yescharacteristic
827#41—82no—
828#41—82no—
829#41—82no—
830#41—82no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—82no—
847C2×Q8—82no—
848C2×Q8—82no—
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—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—44no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—44no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
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—82no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—82no—
914C2×D4—82no—
915C2×D4—82no—
916C2×D4—82no—
917C2×D4—82no—
918C2×D4—82no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
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—21no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—82no—
944C22×C4—82no—
945C22×C4—82no—
946C22×C4—82no—
947C22×C4C22×D412yes—
948C22×C4C22×D412yes—
949C22×C4C22×D412yes—
950C22×C4C22×D412yes—
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D412yes—
957C22×C4C22×D412yes—
958C22×C4C2511yescharacteristic
959Q16—82no—
960SD16—82no—
961SD16—82no—
962SD16—82no—
963SD16—82no—
964SD16—82no—
965SD16—82no—
966D8—82no—
967D8—82no—
968D8—82no—
969D8—82no—
970D8—82no—
971D8—82no—
972D8—82no—
973D8—82no—
974D8—82no—
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—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8C22×D412yes—
992C2×C8C22×D412yes—
993C2×C8C22×D412yes—
994C2×C8C22×D412yes—
995C2×C8C22×D412yes—
996C2×C8C22×D412yes—
997C2×C8C22×D412yes—
998C2×C8C22×D412yes—
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—42no—
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—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—82no—
1029C4⋊C4—82no—
1030C4⋊C4#12714yes—
1031C4⋊C4#12714yes—
1032C22⋊C4—42no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
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—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
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—82no—
1067C22⋊C4#12714yes—
1068C22⋊C4#12714yes—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—42no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42—42no—
1082C42—42no—
1083C42—42no—
1084C42C22×D412yes—
1085C42C22×D412yes—
1086C42C22×D412yes—
1087C42C22×D412yes—
1088C23—22no—
1089C23—22no—
1090C23—21no—
1091C23—21no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
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—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—84no—
1123C23—88no—
1124C23—162no—
1125C23—162no—
1126C23—164no—
1127C23C2×#12712yes—
1128C23C23×D411yescharacteristic
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—162no—
1138Q8—162no—
1139Q8—162no—
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—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—84no—
1165D4—88no—
1166D4—84no—
1167D4—162no—
1168D4—162no—
1169D4—162no—
1170D4—162no—
1171D4—162no—
1172D4—162no—
1173D4—164no—
1174D4—162no—
1175D4—162no—
1176D4—162no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
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—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
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—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—84no—
1222C2×C4—84no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4C2×#12712yes—
1228C2×C4C2×#12712yes—
1229C2×C4C2×#12712yes—
1230C2×C4C2×#12712yes—
1231C2×C4C2×#12712yes—
1232C2×C4C23×D411yescharacteristic
1233C2×C4C23×D411yescharacteristic
1234C2×C4#58511yescharacteristic
1235C2×C4#58511yescharacteristic
1236C2×C4#58511yescharacteristic
1237C2×C4#58511yescharacteristic
1238C8—22no—
1239C8—22no—
1240C8—22no—
1241C8—22no—
1242C8—22no—
1243C8—22no—
1244C8—22no—
1245C8—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—42no—
1250C22—42no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
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—168no—
1282C22C22×#12711yescharacteristic
1283C22#344911yescharacteristic
1284C22#344911yescharacteristic
1285C22#358512yes—
1286C22#358512yes—
1287C4—22no—
1288C4—22no—
1289C4—22no—
1290C4—22no—
1291C4—22no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4#350011yescharacteristic
1307C4#350011yescharacteristic
1308C4#350011yescharacteristic
1309C4#350011yescharacteristic
1310C2—42no—
1311C2—161no—
1312C2—161no—
1313C2—161no—
1314C2—161no—
1315C2—161no—
1316C2—161no—
1317C2#3532911yescharacteristic
1318C2#6065011yescharacteristic
1319C2#6065011yescharacteristic
1320C2#6097412yes—
1321C2#6100312yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3244C2semidirect
2. C2×#3241C2semidirect
3. C2×#3224C2semidirect
4. C2×#3220C2semidirect
5. #35276C2semidirect
6. #35264C2semidirect
7. #33254C2semidirect
8. #33253C2semidirect
9. #33251C2semidirect
10. #33251C2semidirect
11. #30290C2semidirect
12. #30287C2semidirect
13. #30274C2semidirect
14. #30270C2semidirect
15. #28395C2semidirect
16. #28393C2semidirect
17. #28389C2semidirect
18. #28387C2semidirect
19. #28383C2semidirect
20. #28381C2semidirect
21. #28379C2semidirect
22. #28378C2semidirect
23. #28328C2semidirect
24. #28325C2semidirect
25. #28321C2semidirect
26. #28319C2semidirect
27. #28318C2semidirect
28. #28316C2semidirect
29. #28312C2semidirect
30. #28310C2semidirect
31. #20465C2semidirect
40. C2×#501C22semidirect
41. C2×#501C22semidirect
42. C2×#499C22semidirect
43. C2×#498C22semidirect
49. C2×#490C22semidirect
51. C2×#489C22semidirect
53. C2×#488C22semidirect
55. C2×#486C22semidirect
64. C2×#479C22semidirect
65. C2×#475C22semidirect
66. C2×#478C22semidirect
67. C2×#478C22semidirect
68. C2×#478C22semidirect
69. C2×#476C22semidirect
70. C2×#476C22semidirect
71. C2×#474C22semidirect
92. #2861C22semidirect
95. #2858C22semidirect
98. #2660C22semidirect
99. #2657C22semidirect
114. #2328C22semidirect
115. #2326C22semidirect
118. C4×#127C22semidirect
119. C4×#124C22semidirect
123. #2097C22semidirect
124. #2097C22semidirect
125. #2096C22semidirect
126. #2096C22semidirect
130. #2094C22semidirect
132. #2093C22semidirect
137. #2092C22semidirect
138. #2092C22semidirect
139. #2015C22semidirect
140. #2015C22semidirect
141. #2014C22semidirect
142. #2014C22semidirect
147. #2012C22semidirect
148. #2012C22semidirect
153. #2011C22semidirect
154. #2011C22semidirect
158. #1973C22semidirect
159. #1973C22semidirect
160. #1973C22semidirect
161. #1973C22semidirect
162. #1973C22semidirect
172. #1972C22semidirect
173. #1972C22semidirect
174. #1972C22semidirect
175. #1972C22semidirect
176. #1972C22semidirect
177. #1971C22semidirect
178. #1971C22semidirect
182. #1970C22semidirect
184. #1968C22semidirect
185. #1968C22semidirect
186. #1968C22semidirect
187. #1768C22semidirect
188. #1768C22semidirect
189. #1767C22semidirect
190. #1767C22semidirect
195. #1746C22semidirect
196. #1746C22semidirect
197. C4×#97C22semidirect
198. C4×#97C22semidirect
324. #433D4semidirect
325. #433D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32442
C2×#32412
C2×#32242
C2×#32202
#352762
#352642
#332542
#332532
#332512
#302902
#302872
#302742
#302702
#283952
#283932
#283892
#283872
#283832
#283812
#283792
#283782
#283282
#283252
#283212
#283192
#283182
#283162
#283122
#283102
#204652