Finite Group Databasebeta

← #6467553

Subgroups — #6467553

Order 512.

2438 conjugacy classes of subgroups.

The subgroup lattice has 1319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3183C211yesmaximal, characteristic, complemented
2C2×#3105C211yesmaximal, characteristic, complemented
3C2×#3102C211yesmaximal, characteristic, complemented
4C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
5#35233C211yesmaximal, characteristic, complemented
6#35211C211yesmaximal, characteristic, complemented
7#28537C211yesmaximal, characteristic, complemented
8#28534C211yesmaximal, characteristic, complemented
9#28467C211yesmaximal, characteristic, complemented
10#28464C211yesmaximal, characteristic, complemented
11#28410C211yesmaximal, characteristic, complemented
12#28409C211yesmaximal, characteristic, complemented
13#28408C211yesmaximal, characteristic, complemented
14#28405C211yesmaximal, characteristic, complemented
15#28364C211yesmaximal, characteristic, complemented
16#28361C211yesmaximal, characteristic, complemented
17#28356C211yesmaximal, characteristic, complemented
18#28353C211yesmaximal, characteristic, complemented
19#27946C211yesmaximal, characteristic, complemented
20#27944C211yesmaximal, characteristic, complemented
21#25793C211yesmaximal, characteristic, complemented
22#25791C211yesmaximal, characteristic, complemented
23#23813C211yesmaximal, characteristic, complemented
24#23810C211yesmaximal, characteristic, complemented
25#23809C211yesmaximal, characteristic, complemented
26#23808C211yesmaximal, characteristic, complemented
27#21704C211yesmaximal, characteristic, complemented
28#21704C211yesmaximal, characteristic, complemented
29#21696C211yesmaximal, characteristic, complemented
30#21695C211yesmaximal, characteristic, complemented
31#20482C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37#3183—28no—
38C2×#499C2211yescharacteristic, complemented
39C2×#496C2211yescharacteristic
40C2×#496C2211yescharacteristic
41C2×#495C2211yescharacteristic
42C2×#495C2211yescharacteristic, complemented
43C2×#492C2211yescharacteristic
44C2×#488C2211yescharacteristic, complemented
45C2×#488C2211yescharacteristic, complemented
46#3105—28no—
47#3102—28no—
48C2×#484C2211yescharacteristic
49C2×#481C2211yescharacteristic
50C2×#485C2211yescharacteristic
51C2×#482C2211yescharacteristic
52C2×#479C2211yescharacteristic, complemented
53C2×#478C2211yescharacteristic
54C2×#478C2211yescharacteristic
55C2×#478C2211yescharacteristic, complemented
56C2×#470C2211yescharacteristic
57C2×#469C2211yescharacteristic
58C2×#468C2211yescharacteristic
59C2×#468C2211yescharacteristic
60C2×#464C2211yescharacteristic, complemented
61C2×#463C2211yescharacteristic
62C2×#463C2211yescharacteristic
63C2×#463C2211yescharacteristic, complemented
64C2×#452C2211yescharacteristic
65C2×#449C2211yescharacteristic
66C2×#450C2211yescharacteristic
67C2×#447C2211yescharacteristic
68C4×AGL(1,ℤ/8)—28no—
69C2×#442C2211yescharacteristic
70C2×#442C2211yescharacteristic
71C2×#442C2211yescharacteristic, complemented
72C2×#441C2211yescharacteristic, complemented
73C2×#440C2211yescharacteristic
74C2×#440C2211yescharacteristic
75C2×#440C2211yescharacteristic, complemented
76C2×#440C2211yescharacteristic, complemented
77C2×C4×Q16C2211yescharacteristic, complemented
78C2×C4×SD16C2211yescharacteristic
79C2×C4×SD16C2211yescharacteristic
80C2×C4×SD16C2211yescharacteristic
81C2×C4×SD16C2211yescharacteristic
82C2×C4×SD16C2211yescharacteristic, complemented
83C2×C4×SD16C2211yescharacteristic, complemented
84C2×C4×D8C2211yescharacteristic
85C2×C4×D8C2211yescharacteristic
86C2×C4×D8C2211yescharacteristic
87C2×C4×D8C2211yescharacteristic
88C2×C4×D8C2211yescharacteristic, complemented
89C2×#431C2211yescharacteristic
90C2×#428C2211yescharacteristic
91C2×#417C2211yescharacteristic
92C2×#418C2211yescharacteristic
93C2×C4×M16C2211yescharacteristic
94#2852—22no—
95#2849—22no—
96#2636—22no—
97#2630—22no—
98#2609—22no—
99#2600—22no—
100#2598—22no—
101#2566C2211yescharacteristic
102#2566C2211yescharacteristic
103#2566C2211yescharacteristic, complemented
104#2565C2211yescharacteristic, complemented
105#2545C2211yescharacteristic, complemented
106#2544C2211yescharacteristic
107#2544C2211yescharacteristic
108#2544C2211yescharacteristic, complemented
109#2534—22no—
110#2503C2211yescharacteristic
111#2501C2211yescharacteristic
112#2500C2211yescharacteristic
113#2499C2211yescharacteristic
114#2435C2211yescharacteristic
115#2433C2211yescharacteristic
116#2432C2211yescharacteristic
117#2431C2211yescharacteristic
118#2328C2211yescharacteristic
119#2328C2211yescharacteristic
120#2328C2211yescharacteristic, complemented
121#2327C2211yescharacteristic, complemented
122#2326C2211yescharacteristic
123#2326C2211yescharacteristic
124#2326C2211yescharacteristic, complemented
125#2326C2211yescharacteristic, complemented
126#2283C2211yescharacteristic
127#2097C2211yescharacteristic, complemented
128#2097C2211yescharacteristic, complemented
129#2096C2211yescharacteristic, complemented
130#2096C2211yescharacteristic, complemented
131#2096C2211yescharacteristic, complemented
132#2095C2211yescharacteristic, complemented
133#2094C2211yescharacteristic
134#2094C2211yescharacteristic
135#2094C2211yescharacteristic, complemented
136#2093C2211yescharacteristic, complemented
137#2092C2211yescharacteristic
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic, complemented
140#2092C2211yescharacteristic, complemented
141#2092C2211yescharacteristic, complemented
142#2092C2211yescharacteristic, complemented
143#2016C2211yescharacteristic, complemented
144#2015C2211yescharacteristic
145#2015C2211yescharacteristic
146#2015C2211yescharacteristic
147#2015C2211yescharacteristic, complemented
148#2014C2211yescharacteristic
149#2013C2211yescharacteristic
150#2012C2211yescharacteristic
151#2012C2211yescharacteristic
152#2012C2211yescharacteristic
153#2012C2211yescharacteristic, complemented
154#2011C2211yescharacteristic
155#2011C2211yescharacteristic
156#2011C2211yescharacteristic
157#2011C2211yescharacteristic
158#2011C2211yescharacteristic, complemented
159#1973C2211yescharacteristic
160#1973C2211yescharacteristic
161#1973C2211yescharacteristic
162#1973C2211yescharacteristic, complemented
163#1973C2211yescharacteristic, complemented
164#1973C2211yescharacteristic, complemented
165#1972C2211yescharacteristic
166#1972C2211yescharacteristic, complemented
167#1970C2211yescharacteristic
168#1970C2211yescharacteristic
169#1970C2211yescharacteristic
170#1969C2211yescharacteristic, complemented
171#1968C2211yescharacteristic
172#1968C2211yescharacteristic, complemented
173#1968C2211yescharacteristic, complemented
174#1968C2211yescharacteristic, complemented
175#1961C2211yescharacteristic
176#1960C2211yescharacteristic, complemented
177#1959C2211yescharacteristic
178#1959C2211yescharacteristic, complemented
179#1958C2211yescharacteristic
180#1958C2211yescharacteristic, complemented
181#1957C2211yescharacteristic
182#1957C2211yescharacteristic, complemented
183#1847C2211yescharacteristic, complemented
184#1847C2211yescharacteristic, complemented
185#1846C2211yescharacteristic, complemented
186#1845C2211yescharacteristic, complemented
187#1770C2211yescharacteristic, complemented
188#1770C2211yescharacteristic, complemented
189C8×C4⋊C4C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1753C2211yescharacteristic
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic
195#1746C2211yescharacteristic, complemented
196#1746C2211yescharacteristic, complemented
197#1726C2211yescharacteristic, complemented
198#1726C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×D4C2311yescharacteristic
201C24×C4—21no—
202C2×AGL(1,ℤ/8)—24no—
203C2×AGL(1,ℤ/8)—24no—
204C2×AGL(1,ℤ/8)—24no—
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×D8C2311yescharacteristic
218C22×D8C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C22×M16C2311yescharacteristic
222C22×M16C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#127C2311yescharacteristic
227#529—24no—
228#529—24no—
229#529—24no—
230#529—24no—
231C2×#126—21no—
232C2×#126—21no—
233C2×#125C2311yescharacteristic
234C2×#125C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#123—21no—
242C2×#123—21no—
243C2×#123—22no—
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#120—22no—
249C4×#41—24no—
250C4×#41—24no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259C2×C4×D4—21no—
260C2×C4×D4—21no—
261C2×C4×D4—24no—
262C2×C4×D4—24no—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×#117—21no—
272C2×#117—21no—
273C2×#117—21no—
274C2×#117C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C22⋊C4—21no—
277C22×C42—21no—
278C22×C42C2311yescharacteristic
279#499—24no—
280#496—24no—
281#496—24no—
282#495—24no—
283#495—24no—
284#492—24no—
285#488—24no—
286#488—24no—
287#485—24no—
288#484—24no—
289#482—24no—
290#481—24no—
291#479—24no—
292#478—24no—
293#478—24no—
294#478—24no—
295#470—24no—
296#469—24no—
297#468—24no—
298#468—24no—
299#464—24no—
300#463—24no—
301#463—24no—
302#463—24no—
303#452—24no—
304#450—24no—
305#449—24no—
306#447—24no—
307#442—24no—
308#442—24no—
309#442—24no—
310#441—24no—
311#440—24no—
312#440—24no—
313#440—24no—
314#440—24no—
315C4×Q16—24no—
316C4×SD16—24no—
317C4×SD16—24no—
318C4×SD16—24no—
319C4×SD16—24no—
320C4×SD16—24no—
321C4×SD16—24no—
322C4×D8—24no—
323C4×D8—24no—
324C4×D8—24no—
325C4×D8—24no—
326C4×D8—24no—
327#431D418yescomplemented
328#428—24no—
329C2×#107C2311yescharacteristic
330C2×#107C2311yescharacteristic
331C2×#107C2311yescharacteristic
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×#106C2311yescharacteristic
345C2×C4⋊C8C2311yescharacteristic
346C2×C4⋊C8C2311yescharacteristic
347#418—24no—
348#417—24no—
349C2×#103C2311yescharacteristic
350C2×#103C2311yescharacteristic
351C2×#103C2311yescharacteristic
352C2×#103C2311yescharacteristic
353C2×#103C2311yescharacteristic
354C2×#103C2311yescharacteristic
355C2×#103C2311yescharacteristic
356C2×#103C2311yescharacteristic
357C2×#103C2311yescharacteristic
358C2×#103C2311yescharacteristic
359C2×#103C2311yescharacteristic
360C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
382C2×C22⋊C8C2311yescharacteristic
383C4×M16D418yescomplemented
384C2×#97C2311yescharacteristic
385C2×#97C2311yescharacteristic
386C2×#97C2311yescharacteristic
387C2×#97C2311yescharacteristic
388C2×#97C2311yescharacteristic
389C2×#97C2311yescharacteristic
390C2×C4×C8C2311yescharacteristic
391C2×C4×C8C2311yescharacteristic
392C2×C4×C8C2311yescharacteristic
393C2×C4×C8C2311yescharacteristic
394C2×C4×C8C2311yescharacteristic
395C2×C4×C8C2311yescharacteristic
396C2×C4×C8C2311yescharacteristic
397C2×C4×C8C2311yescharacteristic
398#400—22no—
399#399—22no—
400#398—22no—
401#397—22no—
402#396—22no—
403#396—22no—
404#396—22no—
405#396—22no—
406#394—22no—
407#394—22no—
408#394—22no—
409#394—22no—
410#394—22no—
411#394—22no—
412#392—22no—
413#392—22no—
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#391C2311yescharacteristic
417#391C2311yescharacteristic
418#391C2311yescharacteristic
419#391C2311yescharacteristic
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#390C2311yescharacteristic
423#390C2311yescharacteristic
424#390C2311yescharacteristic
425#390C2311yescharacteristic
426#390C2311yescharacteristic
427#390C2311yescharacteristic
428#390C2311yescharacteristic
429#390C2311yescharacteristic
430#388—22no—
431#388—22no—
432#388—22no—
433#388—22no—
434#388—22no—
435#388—22no—
436#387—22no—
437#387—22no—
438#387—22no—
439#387—22no—
440#386—22no—
441#386—22no—
442#386—22no—
443#386—22no—
444#386—22no—
445#386—22no—
446#386—22no—
447#386—22no—
448#386—22no—
449#386—22no—
450#385—22no—
451#385—22no—
452#385—22no—
453#385—22no—
454#385—22no—
455#385—22no—
456#385—22no—
457#385—22no—
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#384C2311yescharacteristic
461#384C2311yescharacteristic
462#383D412yes—
463#382D412yes—
464#382C2311yescharacteristic
465#382C2311yescharacteristic
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#381—22no—
469#381D412yes—
470#380D412yes—
471#379—22no—
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
476#376C2311yescharacteristic
477#376C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486C25—21no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—22no—
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×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—44no—
525C23×C4—84no—
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529AGL(1,ℤ/8)—232no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16#4114yes—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—22no—
568C2×D8—22no—
569C2×D8—22no—
570C2×D8—22no—
571C2×D8—22no—
572C2×D8—41no—
573C2×D8—41no—
574C2×D8—41no—
575C2×D8—41no—
576C2×D8—41no—
577C2×D8#4114yes—
578C2×M16—22no—
579C2×M16—22no—
580C2×M16—41no—
581C2×M16—41no—
582C2×M16C2×D414yes—
583C2×M16C2×D414yes—
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C4⋊Q8—22no—
593C4⋊Q8—41no—
594#127—22no—
595#127—22no—
596#127—22no—
597#127—41no—
598#127—41no—
599#127—41no—
600#126—44no—
601#126—44no—
602#125—22no—
603#125—22no—
604#125—22no—
605#125—22no—
606#124—22no—
607#124—22no—
608#124—22no—
609#124—22no—
610#124—22no—
611#124—22no—
612#124—22no—
613#124—22no—
614#124—41no—
615#124—41no—
616#124—41no—
617#124—41no—
618#123—44no—
619#123—44no—
620#123—84no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625#121—22no—
626#121—22no—
627#121—22no—
628#121—22no—
629#120—84no—
630C4×Q8—22no—
631C4×Q8—22no—
632C4×Q8—22no—
633C4×Q8—22no—
634C4×Q8—22no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—22no—
638C4×D4—22no—
639C4×D4—22no—
640C4×D4—22no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—44no—
655C4×D4—44no—
656C4×D4—44no—
657C4×D4—44no—
658C4×D4—44no—
659C4×D4—44no—
660#117—22no—
661#117—22no—
662#117—44no—
663#117—44no—
664#117—44no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4C2×D412yes—
684C2×C4⋊C4C2×D412yes—
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
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—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—44no—
725C2×C22⋊C4C2×D412yes—
726C2×C22⋊C4C2×D412yes—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—44no—
733C2×C42C2×D411yescharacteristic
734C2×C42C2×D411yescharacteristic
735C2×C42C2×D414yes—
736C2×C42C2×D414yes—
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743#107—22no—
744#107—22no—
745#107—22no—
746#107—22no—
747#107—22no—
748#107—22no—
749#107—22no—
750#107—22no—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—22no—
755#106—22no—
756#106—22no—
757#106—22no—
758#106—22no—
759C4⋊C8C2×D414yes—
760C4⋊C8C2×D414yes—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—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—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—22no—
793C22⋊C8C2×D414yes—
794C22⋊C8C2×D414yes—
795#97—22no—
796#97—22no—
797#97—41no—
798#97—41no—
799#97C2×D414yes—
800#97C2×D414yes—
801C4×C8—22no—
802C4×C8—22no—
803C4×C8—41no—
804C4×C8—41no—
805C4×C8C2×D414yes—
806C4×C8C2×D414yes—
807C4×C8C2×D414yes—
808C4×C8C2×D414yes—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95C2×D412yes—
820#95C2×D412yes—
821#95C2×D412yes—
822#95C2×D412yes—
823#95C2×D412yes—
824#95C2×D412yes—
825#95C2×D412yes—
826#95C2×D412yes—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—42no—
833C24—42no—
834C24—44no—
835C24—42no—
836C24—82no—
837C24C22×D411yescharacteristic
838#41—28no—
839#41—44no—
840#41—44no—
841#41—44no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8C2×#4112yes—
860C2×D4—28no—
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—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—44no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—82no—
909C2×D4—82no—
910C2×D4C2×#4112yes—
911C2×D4C2×#4112yes—
912C2×D4C2×#4112yes—
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—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—44no—
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×C4—82no—
948C22×C4—82no—
949C22×C4—82no—
950C22×C4—82no—
951C22×C4—816no—
952C22×C4#12714yes—
953C22×C4#12714yes—
954C22×C4C22×D412yes—
955C22×C4C22×D412yes—
956C22×C4C22×D412yes—
957C22×C4C22×D412yes—
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D412yes—
964C22×C4C22×D412yes—
965C22×C4C2511yescharacteristic
966Q16—44no—
967Q16—44no—
968SD16—28no—
969SD16—28no—
970SD16—44no—
971SD16—44no—
972SD16—44no—
973SD16—44no—
974SD16—44no—
975SD16—44no—
976D8—28no—
977D8—28no—
978D8—44no—
979D8—44no—
980D8—44no—
981D8—44no—
982M16—28no—
983M16—44no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8C22×D412yes—
999C2×C8C22×D412yes—
1000C2×C8C22×D412yes—
1001C2×C8C22×D412yes—
1002C2×C8C22×D412yes—
1003C2×C8C22×D412yes—
1004C2×C8C22×D412yes—
1005C2×C8C22×D412yes—
1006C2×C8C2×#4112yes—
1007C2×C8C2×#4112yes—
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—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—82no—
1039C4⋊C4—82no—
1040C4⋊C4—82no—
1041C4⋊C4—82no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—82no—
1066C22⋊C4—82no—
1067C22⋊C4—82no—
1068C22⋊C4—82no—
1069C22⋊C4—82no—
1070C22⋊C4—82no—
1071C22⋊C4—82no—
1072C22⋊C4—82no—
1073C22⋊C4—82no—
1074C22⋊C4—82no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—42no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—42no—
1088C42#12714yes—
1089C42#12714yes—
1090C42C22×D412yes—
1091C42C22×D412yes—
1092C42C22×D412yes—
1093C42C22×D412yes—
1094C23—22no—
1095C23—22no—
1096C23—21no—
1097C23—21no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—48no—
1102C23—42no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—42no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—84no—
1125C23—84no—
1126C23—88no—
1127C23—88no—
1128C23C2×#12712yes—
1129C23C23×D411yescharacteristic
1130Q8—22no—
1131Q8—22no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142D4—22no—
1143D4—22no—
1144D4—22no—
1145D4—22no—
1146D4—22no—
1147D4—22no—
1148D4—48no—
1149D4—48no—
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—84no—
1166D4—164no—
1167D4—164no—
1168D4—164no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
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—44no—
1193C2×C4—44no—
1194C2×C4—48no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
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—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—84no—
1220C2×C4—84no—
1221C2×C4—84no—
1222C2×C4—84no—
1223C2×C4—84no—
1224C2×C4—84no—
1225C2×C4—84no—
1226C2×C4—84no—
1227C2×C4—84no—
1228C2×C4C2×#12712yes—
1229C2×C4C2×#12712yes—
1230C2×C4C2×#12712yes—
1231C2×C4C2×#12712yes—
1232C2×C4C2×#12712yes—
1233C2×C4C23×D411yescharacteristic
1234C2×C4C23×D411yescharacteristic
1235C2×C4C22×#4111yescharacteristic
1236C2×C4C22×#4111yescharacteristic
1237C2×C4#58511yescharacteristic
1238C2×C4#58511yescharacteristic
1239C8—22no—
1240C8—22no—
1241C8—22no—
1242C8—22no—
1243C8—22no—
1244C8—22no—
1245C8—22no—
1246C8#52514yes—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—42no—
1251C22—42no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—816no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22C22×#12711yescharacteristic
1279C22D4×#4111yescharacteristic
1280C22D4×#4111yescharacteristic
1281C22#358412yes—
1282C22#358512yes—
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—22no—
1287C4—22no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4C2×#52511yescharacteristic
1304C4#344911yescharacteristic
1305C4D4×#4111yescharacteristic
1306C4D4×#4111yescharacteristic
1307C2—42no—
1308C2—82no—
1309C2—82no—
1310C2—82no—
1311C2—161no—
1312C2—161no—
1313C2#3493611yescharacteristic
1314C2#6064311yescharacteristic
1315C2#6064411yescharacteristic
1316C2#6153512yes—
1317C2#6154812yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3183C2semidirect
2. C2×#3105C2semidirect
3. C2×#3102C2semidirect
4. C2×C4×AGL(1,ℤ/8)C2semidirect
5. #35233C2semidirect
6. #35211C2semidirect
7. #28537C2semidirect
8. #28534C2semidirect
9. #28467C2semidirect
10. #28464C2semidirect
11. #28410C2semidirect
12. #28409C2semidirect
13. #28408C2semidirect
14. #28405C2semidirect
15. #28364C2semidirect
16. #28361C2semidirect
17. #28356C2semidirect
18. #28353C2semidirect
19. #27946C2semidirect
20. #27944C2semidirect
21. #25793C2semidirect
22. #25791C2semidirect
23. #23813C2semidirect
24. #23810C2semidirect
25. #23809C2semidirect
26. #23808C2semidirect
27. #21704C2semidirect
28. #21704C2semidirect
29. #21696C2semidirect
30. #21695C2semidirect
31. #20482C2semidirect
38. C2×#499C22semidirect
42. C2×#495C22semidirect
44. C2×#488C22semidirect
45. C2×#488C22semidirect
52. C2×#479C22semidirect
55. C2×#478C22semidirect
60. C2×#464C22semidirect
63. C2×#463C22semidirect
71. C2×#442C22semidirect
72. C2×#441C22semidirect
75. C2×#440C22semidirect
76. C2×#440C22semidirect
77. C2×C4×Q16C22semidirect
82. C2×C4×SD16C22semidirect
83. C2×C4×SD16C22semidirect
88. C2×C4×D8C22semidirect
103. #2566C22semidirect
104. #2565C22semidirect
105. #2545C22semidirect
108. #2544C22semidirect
120. #2328C22semidirect
121. #2327C22semidirect
124. #2326C22semidirect
125. #2326C22semidirect
127. #2097C22semidirect
128. #2097C22semidirect
129. #2096C22semidirect
130. #2096C22semidirect
131. #2096C22semidirect
132. #2095C22semidirect
135. #2094C22semidirect
136. #2093C22semidirect
139. #2092C22semidirect
140. #2092C22semidirect
141. #2092C22semidirect
142. #2092C22semidirect
143. #2016C22semidirect
147. #2015C22semidirect
153. #2012C22semidirect
158. #2011C22semidirect
162. #1973C22semidirect
163. #1973C22semidirect
164. #1973C22semidirect
166. #1972C22semidirect
170. #1969C22semidirect
172. #1968C22semidirect
173. #1968C22semidirect
174. #1968C22semidirect
176. #1960C22semidirect
178. #1959C22semidirect
180. #1958C22semidirect
182. #1957C22semidirect
183. #1847C22semidirect
184. #1847C22semidirect
185. #1846C22semidirect
186. #1845C22semidirect
187. #1770C22semidirect
188. #1770C22semidirect
189. C8×C4⋊C4C22semidirect
190. C8×C4⋊C4C22semidirect
195. #1746C22semidirect
196. #1746C22semidirect
197. #1726C22semidirect
198. #1726C22semidirect
327. #431D4semidirect
383. C4×M16D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31832
C2×#31052
C2×#31022
C2×C4×AGL(1,ℤ/8)2
#352332
#352112
#285372
#285342
#284672
#284642
#284102
#284092
#284082
#284052
#283642
#283612
#283562
#283532
#279462
#279442
#257932
#257912
#238132
#238102
#238092
#238082
#217042
#216962
#216952
#204822