Finite Group Databasebeta

← #6498779

Subgroups — #6498779

Order 512.

2129 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3244C211yesmaximal, characteristic, complemented
2C2×#3243C211yesmaximal, characteristic, complemented
3C2×#3224C211yesmaximal, characteristic, complemented
4C2×#3224C211yesmaximal, characteristic, complemented
5#35331C211yesmaximal, characteristic, complemented
6#35264C211yesmaximal, characteristic, complemented
7#33247C211yesmaximal, characteristic, complemented
8#33245C211yesmaximal, characteristic, complemented
9#33243C211yesmaximal, characteristic, complemented
10#33243C211yesmaximal, characteristic, complemented
11#30286C211yesmaximal, characteristic, complemented
12#30278C211yesmaximal, characteristic, complemented
13#30268C211yesmaximal, characteristic, complemented
14#30264C211yesmaximal, characteristic, complemented
15#28396C211yesmaximal, characteristic, complemented
16#28393C211yesmaximal, characteristic, complemented
17#28392C211yesmaximal, characteristic, complemented
18#28387C211yesmaximal, characteristic, complemented
19#28383C211yesmaximal, characteristic, complemented
20#28379C211yesmaximal, characteristic, complemented
21#28376C211yesmaximal, characteristic, complemented
22#28371C211yesmaximal, characteristic, complemented
23#28326C211yesmaximal, characteristic, complemented
24#28325C211yesmaximal, characteristic, complemented
25#28320C211yesmaximal, characteristic, complemented
26#28319C211yesmaximal, characteristic, complemented
27#28318C211yesmaximal, characteristic, complemented
28#28312C211yesmaximal, characteristic, complemented
29#28309C211yesmaximal, characteristic, complemented
30#28303C211yesmaximal, characteristic, complemented
31#20468C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#535C2211yescharacteristic
36#3244—28no—
37#3243—28no—
38#3224—28no—
39#3224—28no—
40C2×#501C2211yescharacteristic, complemented
41C2×#501C2211yescharacteristic, complemented
42C2×#500C2211yescharacteristic, complemented
43C2×#498C2211yescharacteristic, complemented
44C2×#496C2211yescharacteristic
45C2×#496C2211yescharacteristic
46C2×#495C2211yescharacteristic
47C2×#495C2211yescharacteristic
48C2×#489C2211yescharacteristic
49C2×#489C2211yescharacteristic
50C2×#489C2211yescharacteristic, complemented
51C2×#489C2211yescharacteristic, complemented
52C2×#488C2211yescharacteristic, complemented
53C2×#488C2211yescharacteristic, complemented
54C2×#486C2211yescharacteristic
55C2×#486C2211yescharacteristic
56C2×#484C2211yescharacteristic
57C2×#481C2211yescharacteristic
58C2×#485C2211yescharacteristic
59C2×#485C2211yescharacteristic
60C2×#482C2211yescharacteristic
61C2×#482C2211yescharacteristic
62C2×#483C2211yescharacteristic
63C2×#480C2211yescharacteristic
64C2×#479C2211yescharacteristic, complemented
65C2×#479C2211yescharacteristic, complemented
66C2×#477C2211yescharacteristic, complemented
67C2×#475C2211yescharacteristic, complemented
68C2×#478C2211yescharacteristic, complemented
69C2×#478C2211yescharacteristic, complemented
70C2×#476C2211yescharacteristic, complemented
71C2×#474C2211yescharacteristic, complemented
72C2×#464C2211yescharacteristic
73C2×#464C2211yescharacteristic
74C2×#460C2211yescharacteristic
75C2×#460C2211yescharacteristic
76C2×#463C2211yescharacteristic
77C2×#463C2211yescharacteristic
78C2×#459C2211yescharacteristic
79C2×#459C2211yescharacteristic
80C2×#452C2211yescharacteristic
81C2×#452C2211yescharacteristic
82C2×#449C2211yescharacteristic
83C2×#449C2211yescharacteristic
84C2×#450C2211yescharacteristic
85C2×#450C2211yescharacteristic
86C2×#447C2211yescharacteristic
87C2×#447C2211yescharacteristic
88C2×#433C2211yescharacteristic
89C2×#433C2211yescharacteristic
90#2862C2211yescharacteristic, complemented
91#2861C2211yescharacteristic
92#2861C2211yescharacteristic
93#2858C2211yescharacteristic
94#2858C2211yescharacteristic
95#2858C2211yescharacteristic, complemented
96#2850C2211yescharacteristic
97#2850C2211yescharacteristic
98#2641C2211yescharacteristic
99#2641C2211yescharacteristic
100#2640C2211yescharacteristic
101#2640C2211yescharacteristic
102#2640C2211yescharacteristic, complemented
103#2640C2211yescharacteristic, complemented
104#2621C2211yescharacteristic
105#2619C2211yescharacteristic
106#2560—22no—
107#2560—22no—
108#2557—22no—
109#2557—22no—
110#2491—22no—
111#2490—22no—
112#2472—22no—
113#2472—22no—
114#2328C2211yescharacteristic, complemented
115#2327C2211yescharacteristic, complemented
116#2311C2211yescharacteristic
117#2309C2211yescharacteristic
118C4×#124C2211yescharacteristic, complemented
119C4×#124C2211yescharacteristic, complemented
120#2297C2211yescharacteristic
121C2×#390C2211yescharacteristic
122C4×#117C2211yescharacteristic
123#2097C2211yescharacteristic, complemented
124#2097C2211yescharacteristic, complemented
125#2097C2211yescharacteristic, complemented
126#2097C2211yescharacteristic, complemented
127#2092C2211yescharacteristic
128#2092C2211yescharacteristic
129#2092C2211yescharacteristic
130#2092C2211yescharacteristic
131#2092C2211yescharacteristic
132#2092C2211yescharacteristic
133#2092C2211yescharacteristic
134#2092C2211yescharacteristic
135#2092C2211yescharacteristic, complemented
136#2092C2211yescharacteristic, complemented
137#2092C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2016C2211yescharacteristic, complemented
140#2015C2211yescharacteristic, complemented
141#2015C2211yescharacteristic, complemented
142#2014C2211yescharacteristic, complemented
143#2013C2211yescharacteristic
144#2013C2211yescharacteristic
145#2013C2211yescharacteristic, complemented
146#2012C2211yescharacteristic
147#2012C2211yescharacteristic
148#2012C2211yescharacteristic
149#2012C2211yescharacteristic
150#2012C2211yescharacteristic, complemented
151#2012C2211yescharacteristic, complemented
152#2011C2211yescharacteristic
153#2011C2211yescharacteristic
154#2011C2211yescharacteristic, complemented
155#1973C2211yescharacteristic
156#1973C2211yescharacteristic
157#1973C2211yescharacteristic
158#1973C2211yescharacteristic
159#1973C2211yescharacteristic, complemented
160#1973C2211yescharacteristic, complemented
161#1973C2211yescharacteristic, complemented
162#1973C2211yescharacteristic, complemented
163#1972C2211yescharacteristic
164#1972C2211yescharacteristic
165#1972C2211yescharacteristic
166#1972C2211yescharacteristic
167#1972C2211yescharacteristic, complemented
168#1972C2211yescharacteristic, complemented
169#1971C2211yescharacteristic, complemented
170#1971C2211yescharacteristic, complemented
171#1970C2211yescharacteristic
172#1970C2211yescharacteristic
173#1970C2211yescharacteristic
174#1970C2211yescharacteristic
175#1970C2211yescharacteristic, complemented
176#1970C2211yescharacteristic, complemented
177#1969C2211yescharacteristic, complemented
178#1969C2211yescharacteristic, complemented
179#1968C2211yescharacteristic
180#1968C2211yescharacteristic
181#1968C2211yescharacteristic
182#1968C2211yescharacteristic
183#1968C2211yescharacteristic, complemented
184#1968C2211yescharacteristic, complemented
185#1968C2211yescharacteristic, complemented
186#1968C2211yescharacteristic, complemented
187#1768C2211yescharacteristic, complemented
188#1768C2211yescharacteristic, complemented
189#1767C2211yescharacteristic, complemented
190C4×C4⋊C8C2211yescharacteristic, complemented
191#1750C2211yescharacteristic
192#1750C2211yescharacteristic
193#1749C2211yescharacteristic
194C4×C22⋊C8C2211yescharacteristic
195#1745C2211yescharacteristic, complemented
196#1744C2211yescharacteristic, complemented
197#1726C2211yescharacteristic, complemented
198#1726C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×D4C2311yescharacteristic
201C22×Q16C2311yescharacteristic
202C22×Q16C2311yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
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#542—24no—
222#542—24no—
223#535—24no—
224#535—24no—
225C2×C4⋊Q8—21no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×#127C2311yescharacteristic
232C2×#127C2311yescharacteristic
233C2×#127C2311yescharacteristic
234C2×#126—21no—
235C2×#126—21no—
236C2×#125—21no—
237C2×#125C2311yescharacteristic
238C2×#125C2311yescharacteristic
239C2×#124—21no—
240C2×#124—21no—
241C2×#124—22no—
242C2×#124—22no—
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#123—21no—
250C2×#123—21no—
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8—21no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8C2311yescharacteristic
256C2×C22⋊Q8C2311yescharacteristic
257C2×#121—21no—
258C2×#121—21no—
259C2×#121C2311yescharacteristic
260C2×#121C2311yescharacteristic
261C2×#120—21no—
262C2×#120—21no—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C22⋊C4—22no—
272C22×C42C2311yescharacteristic
273#501—24no—
274#501—24no—
275#500—24no—
276#498—24no—
277#496—24no—
278#496—24no—
279#495—24no—
280#495—24no—
281#489—24no—
282#489—24no—
283#489—24no—
284#489—24no—
285#488—24no—
286#488—24no—
287#486—24no—
288#486—24no—
289#485—24no—
290#485—24no—
291#484—24no—
292#483—24no—
293#482—24no—
294#482—24no—
295#481—24no—
296#480—24no—
297#479—24no—
298#479—24no—
299#478—24no—
300#478—24no—
301#477—24no—
302#476—24no—
303#475—24no—
304#474—24no—
305#464—24no—
306#464—24no—
307#463—24no—
308#463—24no—
309#460—24no—
310#460—24no—
311#459—24no—
312#459—24no—
313#452—24no—
314#452—24no—
315#450—24no—
316#450—24no—
317#449—24no—
318#449—24no—
319#447—24no—
320#447—24no—
321#433D418yescomplemented
322#433D418yescomplemented
323C2×#107C2311yescharacteristic
324C2×#107C2311yescharacteristic
325C2×#107C2311yescharacteristic
326C2×#107C2311yescharacteristic
327C2×#107C2311yescharacteristic
328C2×#107C2311yescharacteristic
329C2×#107C2311yescharacteristic
330C2×#107C2311yescharacteristic
331C2×#106C2311yescharacteristic
332C2×#106C2311yescharacteristic
333C2×#106C2311yescharacteristic
334C2×#106C2311yescharacteristic
335C2×#106C2311yescharacteristic
336C2×#106C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×C4⋊C8C2311yescharacteristic
340C2×C4⋊C8C2311yescharacteristic
341C2×C4⋊C8C2311yescharacteristic
342C2×C4⋊C8C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#103C2311yescharacteristic
350C2×#103C2311yescharacteristic
351C2×#103C2311yescharacteristic
352C2×#103C2311yescharacteristic
353C2×#103C2311yescharacteristic
354C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
376C2×C22⋊C8C2311yescharacteristic
377C2×C22⋊C8C2311yescharacteristic
378C2×C22⋊C8C2311yescharacteristic
379C2×#97C2311yescharacteristic
380C2×#97C2311yescharacteristic
381C2×#97C2311yescharacteristic
382C2×#97C2311yescharacteristic
383C2×#97C2311yescharacteristic
384C2×#97C2311yescharacteristic
385C2×C4×C8C2311yescharacteristic
386C2×C4×C8C2311yescharacteristic
387C2×C4×C8C2311yescharacteristic
388C2×C4×C8C2311yescharacteristic
389C2×C4×C8C2311yescharacteristic
390C2×C4×C8C2311yescharacteristic
391#398—22no—
392#397—22no—
393#397—22no—
394#397—22no—
395#397—22no—
396#397—22no—
397#394—22no—
398#394—22no—
399#394—22no—
400#394—22no—
401#394—22no—
402#393—22no—
403#393—22no—
404#393—22no—
405#393—22no—
406#392—22no—
407#391—22no—
408#391—22no—
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#391C2311yescharacteristic
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#388—22no—
440#388—22no—
441#388—22no—
442#388—22no—
443#388—22no—
444#388—22no—
445#388—22no—
446#388—22no—
447#387—22no—
448#387—22no—
449#386—22no—
450#386—22no—
451#386—22no—
452#386—22no—
453#386—22no—
454#386—22no—
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#380—22no—
460#379—22no—
461C4×C4⋊C4D412yes—
462C4×C4⋊C4D412yes—
463C4×C22⋊C4—22no—
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×Q8—21no—
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2×D412yes—
519C23×C4C2411yescharacteristic
520C2×Q16—22no—
521C2×Q16—22no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
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×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
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—
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C4⋊Q8—22no—
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579C4⋊Q8—22no—
580C4⋊Q8—22no—
581C4⋊Q8—22no—
582C4⋊Q8—22no—
583C4⋊Q8—22no—
584C4⋊Q8—41no—
585C4⋊Q8—41no—
586C4⋊Q8—44no—
587#127—22no—
588#127—22no—
589#127—22no—
590#127—22no—
591#127—41no—
592#127—41no—
593#126—44no—
594#126—44no—
595#125—22no—
596#125—22no—
597#125—22no—
598#125—22no—
599#125—44no—
600#124—22no—
601#124—22no—
602#124—22no—
603#124—22no—
604#124—22no—
605#124—22no—
606#124—22no—
607#124—22no—
608#124—41no—
609#124—41no—
610#124—41no—
611#124—41no—
612#124—44no—
613#124—44no—
614#124—84no—
615#124—84no—
616#123—44no—
617#123—44no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—22no—
621C22⋊Q8—22no—
622C22⋊Q8—44no—
623C22⋊Q8—44no—
624C22⋊Q8—44no—
625C22⋊Q8—44no—
626#121—22no—
627#121—22no—
628#121—22no—
629#121—22no—
630#121—44no—
631#121—44no—
632#120—44no—
633#120—44no—
634C4×Q8—22no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—22no—
638C4×D4—22no—
639C4×D4—22no—
640C4×D4—22no—
641C4×D4—22no—
642#117—22no—
643#117—22no—
644#117—41no—
645#117—41no—
646#117C2×D414yes—
647#117C2×D414yes—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—21no—
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—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4C2×D412yes—
665C2×C4⋊C4C2×D411yescharacteristic
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×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
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—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
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—84no—
709C2×C22⋊C4C2×D412yes—
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42C2×D412yes—
718C2×C42C2×D412yes—
719C2×C42C2×D412yes—
720C2×C42C2×D412yes—
721C2×C42C2×D412yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
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#106—22no—
737#106—22no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744C4⋊C8C2×D414yes—
745C4⋊C8C2×D414yes—
746C4⋊C8C2×D414yes—
747C4⋊C8C2×D414yes—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—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—
780C22⋊C8C2×D414yes—
781C22⋊C8C2×D414yes—
782C22⋊C8C2×D414yes—
783C22⋊C8C2×D414yes—
784#97—41no—
785#97—41no—
786#97—41no—
787#97—41no—
788#97C2×D414yes—
789#97C2×D414yes—
790C4×C8—41no—
791C4×C8—41no—
792C4×C8—41no—
793C4×C8—41no—
794C4×C8C2×D414yes—
795C4×C8C2×D414yes—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—22no—
801#95—22no—
802#95—22no—
803#95—22no—
804#95—22no—
805#95—22no—
806#95—22no—
807#95—22no—
808#95C2×D412yes—
809#95C2×D412yes—
810#95C2×D412yes—
811#95C2×D412yes—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—82no—
821C24—82no—
822C24C22×D411yescharacteristic
823#41—82no—
824#41—82no—
825#41—82no—
826#41—82no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
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—21no—
844C2×Q8—21no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8—42no—
848C2×Q8—42no—
849C2×Q8—82no—
850C2×Q8—82no—
851C2×Q8—82no—
852C2×Q8—82no—
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—42no—
884C2×D4—42no—
885C2×D4—44no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
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—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
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—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—82no—
933C22×C4—82no—
934C22×C4—82no—
935C22×C4C22×D412yes—
936C22×C4C22×D412yes—
937C22×C4C22×D412yes—
938C22×C4C22×D412yes—
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D412yes—
945C22×C4C22×D412yes—
946C22×C4C2511yescharacteristic
947Q16—82no—
948Q16—82no—
949SD16—82no—
950SD16—82no—
951SD16—82no—
952SD16—82no—
953SD16—82no—
954SD16—82no—
955SD16—82no—
956SD16—82no—
957D8—82no—
958D8—82no—
959D8—82no—
960D8—82no—
961D8—82no—
962D8—82no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
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×C8C22×D412yes—
980C2×C8C22×D412yes—
981C2×C8C22×D412yes—
982C2×C8C22×D412yes—
983C2×C8C22×D412yes—
984C2×C8C22×D412yes—
985C2×C8C22×D412yes—
986C2×C8C22×D412yes—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—42no—
1004C4⋊C4—44no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4#12714yes—
1019C4⋊C4#12714yes—
1020C22⋊C4—42no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
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—82no—
1042C22⋊C4—82no—
1043C22⋊C4—82no—
1044C22⋊C4—82no—
1045C22⋊C4—82no—
1046C22⋊C4—82no—
1047C22⋊C4—82no—
1048C22⋊C4—82no—
1049C22⋊C4—82no—
1050C22⋊C4—82no—
1051C22⋊C4—82no—
1052C22⋊C4—82no—
1053C22⋊C4—82no—
1054C22⋊C4#12714yes—
1055C22⋊C4#12714yes—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—42no—
1065C42—42no—
1066C42—42no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—42no—
1072C42C22×D412yes—
1073C42C22×D412yes—
1074C42C22×D412yes—
1075C42C22×D412yes—
1076C23—22no—
1077C23—22no—
1078C23—21no—
1079C23—21no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—84no—
1106C23—88no—
1107C23—162no—
1108C23—162no—
1109C23—164no—
1110C23C2×#12712yes—
1111C23C23×D411yescharacteristic
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—162no—
1125Q8—162no—
1126Q8—162no—
1127Q8—162no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—84no—
1149D4—84no—
1150D4—162no—
1151D4—162no—
1152D4—162no—
1153D4—162no—
1154D4—164no—
1155D4—162no—
1156D4—162no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4—162no—
1207C2×C4—162no—
1208C2×C4—162no—
1209C2×C4C2×#12712yes—
1210C2×C4C2×#12712yes—
1211C2×C4C2×#12712yes—
1212C2×C4C2×#12712yes—
1213C2×C4C2×#12712yes—
1214C2×C4C23×D411yescharacteristic
1215C2×C4C23×D411yescharacteristic
1216C2×C4#58511yescharacteristic
1217C2×C4#58511yescharacteristic
1218C2×C4#58511yescharacteristic
1219C2×C4#58511yescharacteristic
1220C8—22no—
1221C8—22no—
1222C8—22no—
1223C8—22no—
1224C8—22no—
1225C8—22no—
1226C8—22no—
1227C8—22no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22—42no—
1232C22—42no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—82no—
1239C22—82no—
1240C22—82no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—168no—
1259C22C22×#12711yescharacteristic
1260C22#344911yescharacteristic
1261C22#344911yescharacteristic
1262C22#358412yes—
1263C22#358512yes—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—22no—
1269C4—42no—
1270C4—42no—
1271C4—42no—
1272C4—42no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4#350011yescharacteristic
1285C4#350011yescharacteristic
1286C4#350011yescharacteristic
1287C4#350011yescharacteristic
1288C2—42no—
1289C2—161no—
1290C2—161no—
1291C2—161no—
1292C2—161no—
1293C2—161no—
1294C2#3532911yescharacteristic
1295C2#6064911yescharacteristic
1296C2#6065011yescharacteristic
1297C2#6098512yes—
1298C2#6099812yes—
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×#3243C2semidirect
3. C2×#3224C2semidirect
4. C2×#3224C2semidirect
5. #35331C2semidirect
6. #35264C2semidirect
7. #33247C2semidirect
8. #33245C2semidirect
9. #33243C2semidirect
10. #33243C2semidirect
11. #30286C2semidirect
12. #30278C2semidirect
13. #30268C2semidirect
14. #30264C2semidirect
15. #28396C2semidirect
16. #28393C2semidirect
17. #28392C2semidirect
18. #28387C2semidirect
19. #28383C2semidirect
20. #28379C2semidirect
21. #28376C2semidirect
22. #28371C2semidirect
23. #28326C2semidirect
24. #28325C2semidirect
25. #28320C2semidirect
26. #28319C2semidirect
27. #28318C2semidirect
28. #28312C2semidirect
29. #28309C2semidirect
30. #28303C2semidirect
31. #20468C2semidirect
40. C2×#501C22semidirect
41. C2×#501C22semidirect
42. C2×#500C22semidirect
43. C2×#498C22semidirect
50. C2×#489C22semidirect
51. C2×#489C22semidirect
52. C2×#488C22semidirect
53. C2×#488C22semidirect
64. C2×#479C22semidirect
65. C2×#479C22semidirect
66. C2×#477C22semidirect
67. C2×#475C22semidirect
68. C2×#478C22semidirect
69. C2×#478C22semidirect
70. C2×#476C22semidirect
71. C2×#474C22semidirect
90. #2862C22semidirect
95. #2858C22semidirect
102. #2640C22semidirect
103. #2640C22semidirect
114. #2328C22semidirect
115. #2327C22semidirect
118. C4×#124C22semidirect
119. C4×#124C22semidirect
123. #2097C22semidirect
124. #2097C22semidirect
125. #2097C22semidirect
126. #2097C22semidirect
135. #2092C22semidirect
136. #2092C22semidirect
137. #2092C22semidirect
138. #2092C22semidirect
139. #2016C22semidirect
140. #2015C22semidirect
141. #2015C22semidirect
142. #2014C22semidirect
145. #2013C22semidirect
150. #2012C22semidirect
151. #2012C22semidirect
154. #2011C22semidirect
159. #1973C22semidirect
160. #1973C22semidirect
161. #1973C22semidirect
162. #1973C22semidirect
167. #1972C22semidirect
168. #1972C22semidirect
169. #1971C22semidirect
170. #1971C22semidirect
175. #1970C22semidirect
176. #1970C22semidirect
177. #1969C22semidirect
178. #1969C22semidirect
183. #1968C22semidirect
184. #1968C22semidirect
185. #1968C22semidirect
186. #1968C22semidirect
187. #1768C22semidirect
188. #1768C22semidirect
189. #1767C22semidirect
190. C4×C4⋊C8C22semidirect
195. #1745C22semidirect
196. #1744C22semidirect
197. #1726C22semidirect
198. #1726C22semidirect
321. #433D4semidirect
322. #433D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32442
C2×#32432
C2×#32242
#353312
#352642
#332472
#332452
#332432
#302862
#302782
#302682
#302642
#283962
#283932
#283922
#283872
#283832
#283792
#283762
#283712
#283262
#283252
#283202
#283192
#283182
#283122
#283092
#283032
#204682