Finite Group Databasebeta

← #6520506

Subgroups — #6520506

Order 512.

2395 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3224C211yesmaximal, characteristic, complemented
2C2×#3224C211yesmaximal, characteristic, complemented
3C2×#3125C211yesmaximal, characteristic, complemented
4C2×#3124C211yesmaximal, characteristic, complemented
5#37421C211yesmaximal, characteristic, complemented
6#35533C211yesmaximal, characteristic, complemented
7#28481C211yesmaximal, characteristic, complemented
8#28480C211yesmaximal, characteristic, complemented
9#28475C211yesmaximal, characteristic, complemented
10#28474C211yesmaximal, characteristic, complemented
11#28469C211yesmaximal, characteristic, complemented
12#28468C211yesmaximal, characteristic, complemented
13#28465C211yesmaximal, characteristic, complemented
14#28464C211yesmaximal, characteristic, complemented
15#28436C211yesmaximal, characteristic, complemented
16#28434C211yesmaximal, characteristic, complemented
17#28424C211yesmaximal, characteristic, complemented
18#28422C211yesmaximal, characteristic, complemented
19#28420C211yesmaximal, characteristic, complemented
20#28413C211yesmaximal, characteristic, complemented
21#28402C211yesmaximal, characteristic, complemented
22#28399C211yesmaximal, characteristic, complemented
23#28326C211yesmaximal, characteristic, complemented
24#28325C211yesmaximal, characteristic, complemented
25#28312C211yesmaximal, characteristic, complemented
26#28303C211yesmaximal, characteristic, complemented
27#25734C211yesmaximal, characteristic, complemented
28#25732C211yesmaximal, characteristic, complemented
29#25727C211yesmaximal, characteristic, complemented
30#25723C211yesmaximal, characteristic, complemented
31#20541C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#535C2211yescharacteristic
35C2×#535C2211yescharacteristic
36C2×#532C2211yescharacteristic
37C2×#520C2211yescharacteristic
38#3224—28no—
39#3224—28no—
40C2×#497C2211yescharacteristic
41C2×#497C2211yescharacteristic, complemented
42C2×#496C2211yescharacteristic
43C2×#496C2211yescharacteristic
44C2×#496C2211yescharacteristic
45C2×#496C2211yescharacteristic, complemented
46C2×#495C2211yescharacteristic
47C2×#495C2211yescharacteristic
48C2×#495C2211yescharacteristic, complemented
49C2×#495C2211yescharacteristic, complemented
50C2×#493C2211yescharacteristic
51C2×#492C2211yescharacteristic
52C2×#489C2211yescharacteristic
53C2×#489C2211yescharacteristic
54C2×#486C2211yescharacteristic
55C2×#486C2211yescharacteristic
56#3125—28no—
57#3124—28no—
58C2×#484C2211yescharacteristic
59C2×#481C2211yescharacteristic
60C2×#483C2211yescharacteristic
61C2×#480C2211yescharacteristic
62C2×#477C2211yescharacteristic, complemented
63C2×#475C2211yescharacteristic, complemented
64C2×#476C2211yescharacteristic, complemented
65C2×#474C2211yescharacteristic, complemented
66C2×#464C2211yescharacteristic
67C2×#464C2211yescharacteristic
68C2×#464C2211yescharacteristic, complemented
69C2×#464C2211yescharacteristic, complemented
70C2×#460C2211yescharacteristic
71C2×#460C2211yescharacteristic
72C2×#463C2211yescharacteristic
73C2×#463C2211yescharacteristic
74C2×#463C2211yescharacteristic, complemented
75C2×#463C2211yescharacteristic, complemented
76C2×#459C2211yescharacteristic
77C2×#459C2211yescharacteristic
78C2×#452C2211yescharacteristic
79C2×#452C2211yescharacteristic
80C2×#452C2211yescharacteristic
81C2×#452C2211yescharacteristic
82C2×#449C2211yescharacteristic
83C2×#449C2211yescharacteristic
84C2×#449C2211yescharacteristic
85C2×#449C2211yescharacteristic
86C2×#450C2211yescharacteristic
87C2×#450C2211yescharacteristic
88C2×#447C2211yescharacteristic
89C2×#447C2211yescharacteristic
90C2×#442C2211yescharacteristic, complemented
91C2×#441C2211yescharacteristic, complemented
92C2×#440C2211yescharacteristic, complemented
93C2×#440C2211yescharacteristic, complemented
94C2×C4×Q16C2211yescharacteristic, complemented
95C2×C4×SD16C2211yescharacteristic, complemented
96C2×C4×SD16C2211yescharacteristic, complemented
97C2×C4×D8C2211yescharacteristic, complemented
98C2×#433C2211yescharacteristic
99C2×#433C2211yescharacteristic
100#2850C2211yescharacteristic
101#2850C2211yescharacteristic
102#2712—22no—
103#2702—22no—
104#2702—22no—
105#2693—22no—
106#2621C2211yescharacteristic
107#2619C2211yescharacteristic
108#2568C2211yescharacteristic, complemented
109#2568C2211yescharacteristic, complemented
110#2563C2211yescharacteristic, complemented
111#2563C2211yescharacteristic, complemented
112#2548C2211yescharacteristic
113#2548C2211yescharacteristic
114#2545C2211yescharacteristic
115#2545C2211yescharacteristic
116#2545C2211yescharacteristic, complemented
117#2545C2211yescharacteristic, complemented
118#2544C2211yescharacteristic
119#2544C2211yescharacteristic
120#2544C2211yescharacteristic, complemented
121#2544C2211yescharacteristic, complemented
122#2541C2211yescharacteristic
123#2541C2211yescharacteristic
124#2424—22no—
125#2424—22no—
126#2416—22no—
127#2414—22no—
128#2311C2211yescharacteristic
129#2296C2211yescharacteristic
130C2×#390C2211yescharacteristic
131#2097C2211yescharacteristic, complemented
132#2097C2211yescharacteristic, complemented
133#2092C2211yescharacteristic
134#2092C2211yescharacteristic
135#2092C2211yescharacteristic
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2016C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic, complemented
144#2015C2211yescharacteristic, complemented
145#2014C2211yescharacteristic
146#2014C2211yescharacteristic
147#2014C2211yescharacteristic, complemented
148#2014C2211yescharacteristic, complemented
149#2013C2211yescharacteristic, complemented
150#2013C2211yescharacteristic, complemented
151#2012C2211yescharacteristic
152#2012C2211yescharacteristic
153#2012C2211yescharacteristic
154#2012C2211yescharacteristic
155#2012C2211yescharacteristic
156#2012C2211yescharacteristic
157#2012C2211yescharacteristic, complemented
158#2012C2211yescharacteristic, complemented
159#2011C2211yescharacteristic
160#2011C2211yescharacteristic
161#2011C2211yescharacteristic, complemented
162#2011C2211yescharacteristic, complemented
163#1973C2211yescharacteristic
164#1973C2211yescharacteristic
165#1973C2211yescharacteristic, complemented
166#1973C2211yescharacteristic, complemented
167#1972C2211yescharacteristic
168#1972C2211yescharacteristic
169#1972C2211yescharacteristic, complemented
170#1971C2211yescharacteristic, complemented
171#1970C2211yescharacteristic
172#1970C2211yescharacteristic
173#1970C2211yescharacteristic, complemented
174#1969C2211yescharacteristic, complemented
175#1968C2211yescharacteristic
176#1968C2211yescharacteristic
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1961C2211yescharacteristic
180#1961C2211yescharacteristic
181#1961C2211yescharacteristic, complemented
182#1960C2211yescharacteristic, complemented
183#1958C2211yescharacteristic
184#1958C2211yescharacteristic
185#1958C2211yescharacteristic, complemented
186#1958C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1770C2211yescharacteristic, complemented
192#1770C2211yescharacteristic, complemented
193C8×C4⋊C4C2211yescharacteristic, complemented
194C8×C4⋊C4C2211yescharacteristic, complemented
195#1750C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic
198C4×C22⋊C8C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C22×Q16C2311yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×D8C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C22×D8C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×D8C2311yescharacteristic
226#542—24no—
227#542—24no—
228#542—24no—
229#542—24no—
230#535—24no—
231#535—24no—
232#535—42no—
233#535—42no—
234#532—42no—
235#532—42no—
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×#127C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#127C2311yescharacteristic
243C2×#127C2311yescharacteristic
244C2×#127C2311yescharacteristic
245C2×#127C2311yescharacteristic
246C2×#126—21no—
247C2×#126—21no—
248C2×#124—21no—
249C2×#124—21no—
250C2×#124C2311yescharacteristic
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#124C2311yescharacteristic
254C2×#124C2311yescharacteristic
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#124C2311yescharacteristic
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#123—21no—
261C2×#123—21no—
262C2×C22⋊Q8—21no—
263C2×C22⋊Q8—21no—
264C2×C22⋊Q8C2311yescharacteristic
265C2×C22⋊Q8C2311yescharacteristic
266C2×#121—22no—
267C2×#121—21no—
268C2×#121—22no—
269C2×#121—21no—
270C2×#121—22no—
271C2×#121—22no—
272C2×#121C2311yescharacteristic
273C2×#121C2311yescharacteristic
274C2×#120—21no—
275C2×#120—21no—
276C2×#120—22no—
277#520—24no—
278#520—24no—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×D4—21no—
284C2×C4×D4—21no—
285C2×C4×D4—22no—
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2311yescharacteristic
290C2×#117—21no—
291C2×#117C2311yescharacteristic
292C2×#117C2311yescharacteristic
293C22×C4⋊C4—21no—
294C22×C4⋊C4C2311yescharacteristic
295C22×C22⋊C4—22no—
296C22×C42C2311yescharacteristic
297#497—42no—
298#497—42no—
299#496—24no—
300#496—24no—
301#496—42no—
302#496—42no—
303#495—24no—
304#495—24no—
305#495—42no—
306#495—42no—
307#493—42no—
308#492—42no—
309#489—24no—
310#489—24no—
311#486—24no—
312#486—24no—
313#484—24no—
314#483—24no—
315#481—24no—
316#480—24no—
317#477—24no—
318#476—24no—
319#475—24no—
320#474—24no—
321#464—24no—
322#464—24no—
323#464—24no—
324#464—24no—
325#463—24no—
326#463—24no—
327#463—24no—
328#463—24no—
329#460—24no—
330#460—24no—
331#459—24no—
332#459—24no—
333#452—24no—
334#452—24no—
335#452—24no—
336#452—24no—
337#450—24no—
338#450—24no—
339#449—24no—
340#449—24no—
341#449—24no—
342#449—24no—
343#447—24no—
344#447—24no—
345#442—24no—
346#441—24no—
347#440—24no—
348#440—24no—
349C4×Q16—24no—
350C4×SD16—24no—
351C4×SD16—24no—
352C4×D8—24no—
353#433D418yescomplemented
354#433D418yescomplemented
355C2×#107C2311yescharacteristic
356C2×#107C2311yescharacteristic
357C2×#107C2311yescharacteristic
358C2×#107C2311yescharacteristic
359C2×#106C2311yescharacteristic
360C2×#106C2311yescharacteristic
361C2×#106C2311yescharacteristic
362C2×#106C2311yescharacteristic
363C2×C4⋊C8C2311yescharacteristic
364C2×C4⋊C8C2311yescharacteristic
365C2×C4⋊C8C2311yescharacteristic
366C2×C4⋊C8C2311yescharacteristic
367C2×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
374C2×#103C2311yescharacteristic
375C2×#103C2311yescharacteristic
376C2×#103C2311yescharacteristic
377C2×#103C2311yescharacteristic
378C2×#103C2311yescharacteristic
379C2×#102C2311yescharacteristic
380C2×#102C2311yescharacteristic
381C2×#102C2311yescharacteristic
382C2×#102C2311yescharacteristic
383C2×#102C2311yescharacteristic
384C2×#102C2311yescharacteristic
385C2×#102C2311yescharacteristic
386C2×#102C2311yescharacteristic
387C2×#102C2311yescharacteristic
388C2×#102C2311yescharacteristic
389C2×#102C2311yescharacteristic
390C2×#102C2311yescharacteristic
391C2×#102C2311yescharacteristic
392C2×#102C2311yescharacteristic
393C2×#102C2311yescharacteristic
394C2×#102C2311yescharacteristic
395C2×#102C2311yescharacteristic
396C2×#102C2311yescharacteristic
397C2×#102C2311yescharacteristic
398C2×#102C2311yescharacteristic
399C2×C22⋊C8C2311yescharacteristic
400C2×C22⋊C8C2311yescharacteristic
401C2×C22⋊C8C2311yescharacteristic
402C2×C22⋊C8C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×#97C2311yescharacteristic
405C2×#97C2311yescharacteristic
406C2×#97C2311yescharacteristic
407C2×#97C2311yescharacteristic
408C2×#97C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410C2×C4×C8C2311yescharacteristic
411C2×C4×C8C2311yescharacteristic
412C2×C4×C8C2311yescharacteristic
413C2×C4×C8C2311yescharacteristic
414C2×C4×C8C2311yescharacteristic
415#400—22no—
416#400—22no—
417#398—22no—
418#397—22no—
419#396—22no—
420#396—22no—
421#396—22no—
422#396—22no—
423#394—22no—
424#394—22no—
425#394—22no—
426#394—22no—
427#394—22no—
428#394—22no—
429#394—22no—
430#393—22no—
431#393—22no—
432#392—22no—
433#392—22no—
434#392—22no—
435#391—22no—
436#391—22no—
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#391C2311yescharacteristic
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#391C2311yescharacteristic
443#390—22no—
444#390—22no—
445#390—22no—
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#390C2311yescharacteristic
449#390C2311yescharacteristic
450#390C2311yescharacteristic
451#390C2311yescharacteristic
452#390C2311yescharacteristic
453#390C2311yescharacteristic
454#390C2311yescharacteristic
455#390C2311yescharacteristic
456#389D412yes—
457#389D412yes—
458#388—22no—
459#388—22no—
460#388—22no—
461#388—22no—
462#388—22no—
463#388—22no—
464#386—22no—
465#386—22no—
466#386—22no—
467#386—22no—
468#386—22no—
469#386—22no—
470#386—22no—
471#385D412yes—
472#385D412yes—
473#382C2311yescharacteristic
474#382C2311yescharacteristic
475#382C2311yescharacteristic
476#382C2311yescharacteristic
477#380—22no—
478#380—22no—
479#380—22no—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492C25—21no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—22no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C2×D412yes—
544C23×C4C2411yescharacteristic
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16—41no—
582C2×SD16—41no—
583C2×SD16—41no—
584C2×SD16—41no—
585C2×SD16—41no—
586C2×SD16—41no—
587C2×SD16—41no—
588C2×SD16—41no—
589C2×SD16—41no—
590C2×SD16—41no—
591C2×SD16—41no—
592C2×SD16—41no—
593C2×D8—22no—
594C2×D8—22no—
595C2×D8—22no—
596C2×D8—22no—
597C2×D8—22no—
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—22no—
603C2×D8—41no—
604C2×D8—41no—
605C2×D8—41no—
606C2×D8—41no—
607C2×D8—41no—
608C2×D8—41no—
609C2×D8—41no—
610C2×D8—41no—
611C2×D8—41no—
612C2×D8—41no—
613C2×D8—41no—
614C2×D8—41no—
615C2×D8—41no—
616C2×D8—41no—
617C22×C8C2411yescharacteristic
618C22×C8C2411yescharacteristic
619C22×C8C2411yescharacteristic
620C22×C8C2411yescharacteristic
621C22×C8C2411yescharacteristic
622C22×C8C2411yescharacteristic
623C22×C8C2411yescharacteristic
624C22×C8C2411yescharacteristic
625C4⋊Q8—22no—
626C4⋊Q8—22no—
627C4⋊Q8—22no—
628C4⋊Q8—22no—
629C4⋊Q8—22no—
630C4⋊Q8—41no—
631C4⋊Q8—41no—
632C4⋊Q8—41no—
633#127—22no—
634#127—22no—
635#127—22no—
636#127—22no—
637#127—22no—
638#127—22no—
639#127—22no—
640#127—41no—
641#127—41no—
642#127—41no—
643#127—41no—
644#127—41no—
645#126—44no—
646#126—44no—
647#124—22no—
648#124—22no—
649#124—22no—
650#124—22no—
651#124—22no—
652#124—22no—
653#124—22no—
654#124—22no—
655#124—22no—
656#124—22no—
657#124—22no—
658#124—22no—
659#124—41no—
660#124—41no—
661#124—41no—
662#124—41no—
663#124—41no—
664#124—41no—
665#124—41no—
666#124—41no—
667#124—44no—
668#124—44no—
669#123—44no—
670#123—44no—
671C22⋊Q8—22no—
672C22⋊Q8—22no—
673C22⋊Q8—22no—
674C22⋊Q8—22no—
675C22⋊Q8—44no—
676C22⋊Q8—44no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—22no—
681#121—48no—
682#121—48no—
683#121—44no—
684#121—44no—
685#121—84no—
686#121—84no—
687#120—48no—
688#120—44no—
689#120—44no—
690C4×Q8—22no—
691C4×Q8—22no—
692C4×Q8—22no—
693C4×Q8—22no—
694C4×Q8—22no—
695C4×Q8—22no—
696C4×Q8—22no—
697C4×Q8—22no—
698C4×D4—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—22no—
706C4×D4—48no—
707C4×D4—44no—
708C4×D4—44no—
709#117—41no—
710#117—41no—
711#117—44no—
712#117C2×D414yes—
713#117C2×D414yes—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—21no—
721C2×C4⋊C4—21no—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4—21no—
725C2×C4⋊C4—21no—
726C2×C4⋊C4—22no—
727C2×C4⋊C4—44no—
728C2×C4⋊C4C2×D412yes—
729C2×C4⋊C4C2×D412yes—
730C2×C4⋊C4C2×D412yes—
731C2×C4⋊C4C2×D412yes—
732C2×C4⋊C4C2×D412yes—
733C2×C4⋊C4C2×D411yescharacteristic
734C2×C4⋊C4C2×D411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—21no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—21no—
758C2×C22⋊C4—21no—
759C2×C22⋊C4—21no—
760C2×C22⋊C4—21no—
761C2×C22⋊C4—21no—
762C2×C22⋊C4—21no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—84no—
774C2×C22⋊C4C2×D412yes—
775C2×C22⋊C4C2×D411yescharacteristic
776C2×C22⋊C4C2×D411yescharacteristic
777C2×C42—21no—
778C2×C42—21no—
779C2×C42—21no—
780C2×C42—21no—
781C2×C42—41no—
782C2×C42—41no—
783C2×C42C2×D412yes—
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790#107—22no—
791#107—22no—
792#107—22no—
793#107—22no—
794#106—22no—
795#106—22no—
796#106—22no—
797#106—22no—
798C4⋊C8C2×D414yes—
799C4⋊C8C2×D414yes—
800C4⋊C8C2×D414yes—
801C4⋊C8C2×D414yes—
802#103—22no—
803#103—22no—
804#103—22no—
805#103—22no—
806#103—22no—
807#103—22no—
808#103—22no—
809#103—22no—
810#103—22no—
811#103—22no—
812#103—22no—
813#103—22no—
814#102—22no—
815#102—22no—
816#102—22no—
817#102—22no—
818#102—22no—
819#102—22no—
820#102—22no—
821#102—22no—
822#102—22no—
823#102—22no—
824#102—22no—
825#102—22no—
826#102—22no—
827#102—22no—
828#102—22no—
829#102—22no—
830#102—22no—
831#102—22no—
832#102—22no—
833#102—22no—
834C22⋊C8C2×D414yes—
835C22⋊C8C2×D414yes—
836C22⋊C8C2×D414yes—
837C22⋊C8C2×D414yes—
838#97—41no—
839#97—41no—
840#97—41no—
841#97—41no—
842#97C2×D414yes—
843#97C2×D414yes—
844C4×C8—41no—
845C4×C8—41no—
846C4×C8—41no—
847C4×C8—41no—
848C4×C8C2×D414yes—
849C4×C8C2×D414yes—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—22no—
855#95—22no—
856#95—22no—
857#95—22no—
858#95—22no—
859#95—22no—
860#95C2×D412yes—
861#95C2×D412yes—
862#95C2×D412yes—
863#95C2×D412yes—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—42no—
871C24—42no—
872C24—42no—
873C24—82no—
874C24—82no—
875C24C22×D411yescharacteristic
876#41—44no—
877#41—44no—
878#41—44no—
879#41—44no—
880#41—82no—
881#41—82no—
882#41—82no—
883#41—82no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—42no—
908C2×Q8—42no—
909C2×Q8—82no—
910C2×Q8—82no—
911C2×Q8H(5,𝔽2)12yes—
912C2×D4—24no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—21no—
933C2×D4—21no—
934C2×D4—21no—
935C2×D4—21no—
936C2×D4—21no—
937C2×D4—21no—
938C2×D4—21no—
939C2×D4—21no—
940C2×D4—21no—
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—21no—
944C2×D4—21no—
945C2×D4—21no—
946C2×D4—21no—
947C2×D4—21no—
948C2×D4—44no—
949C2×D4—42no—
950C2×D4—44no—
951C2×D4—42no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—42no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—42no—
963C2×D4—42no—
964C2×D4—42no—
965C2×D4—42no—
966C2×D4—82no—
967C2×D4—82no—
968C2×D4—82no—
969C2×D4—82no—
970C2×D4—82no—
971C2×D4—82no—
972C2×D4—82no—
973C2×D4—82no—
974C2×D4—82no—
975C2×D4—82no—
976C2×D4—82no—
977C2×D4—82no—
978C2×D4—82no—
979C2×D4—82no—
980C2×D4—82no—
981C2×D4—82no—
982C2×D4—82no—
983C2×D4—82no—
984C2×D4H(5,𝔽2)12yes—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—24no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—82no—
1014C22×C4—82no—
1015C22×C4—82no—
1016C22×C4—82no—
1017C22×C4—82no—
1018C22×C4C22×D412yes—
1019C22×C4C22×D412yes—
1020C22×C4C22×D412yes—
1021C22×C4C22×D412yes—
1022C22×C4C22×D411yescharacteristic
1023C22×C4C22×D411yescharacteristic
1024C22×C4C22×D411yescharacteristic
1025C22×C4C22×D411yescharacteristic
1026C22×C4C22×D411yescharacteristic
1027C22×C4C22×D412yes—
1028C22×C4C22×D412yes—
1029C22×C4C2511yescharacteristic
1030Q16—44no—
1031Q16—44no—
1032Q16—82no—
1033Q16—82no—
1034SD16—44no—
1035SD16—44no—
1036SD16—44no—
1037SD16—44no—
1038SD16—82no—
1039SD16—82no—
1040SD16—82no—
1041SD16—82no—
1042SD16—82no—
1043SD16—82no—
1044SD16—82no—
1045SD16—82no—
1046D8—44no—
1047D8—44no—
1048D8—82no—
1049D8—82no—
1050D8—82no—
1051D8—82no—
1052D8—82no—
1053D8—82no—
1054C2×C8—21no—
1055C2×C8—21no—
1056C2×C8—21no—
1057C2×C8—21no—
1058C2×C8—21no—
1059C2×C8—21no—
1060C2×C8—21no—
1061C2×C8—21no—
1062C2×C8—21no—
1063C2×C8—21no—
1064C2×C8—21no—
1065C2×C8—21no—
1066C2×C8—21no—
1067C2×C8—21no—
1068C2×C8—21no—
1069C2×C8—21no—
1070C2×C8C22×D412yes—
1071C2×C8C22×D412yes—
1072C2×C8C22×D412yes—
1073C2×C8C22×D412yes—
1074C2×C8C22×D412yes—
1075C2×C8C22×D412yes—
1076C2×C8C22×D412yes—
1077C2×C8C22×D412yes—
1078C4⋊C4—21no—
1079C4⋊C4—21no—
1080C4⋊C4—21no—
1081C4⋊C4—21no—
1082C4⋊C4—21no—
1083C4⋊C4—21no—
1084C4⋊C4—21no—
1085C4⋊C4—21no—
1086C4⋊C4—21no—
1087C4⋊C4—21no—
1088C4⋊C4—21no—
1089C4⋊C4—21no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—82no—
1106C4⋊C4#12714yes—
1107C4⋊C4#12714yes—
1108C22⋊C4—42no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—82no—
1132C22⋊C4—82no—
1133C22⋊C4—82no—
1134C22⋊C4—82no—
1135C22⋊C4—82no—
1136C22⋊C4—82no—
1137C22⋊C4—82no—
1138C22⋊C4—82no—
1139C22⋊C4—82no—
1140C22⋊C4—82no—
1141C22⋊C4#12714yes—
1142C22⋊C4#12714yes—
1143C42—21no—
1144C42—21no—
1145C42—21no—
1146C42—21no—
1147C42—21no—
1148C42—21no—
1149C42—21no—
1150C42—21no—
1151C42—42no—
1152C42—42no—
1153C42—42no—
1154C42—42no—
1155C42—42no—
1156C42C22×D412yes—
1157C42C22×D412yes—
1158C42C22×D412yes—
1159C42C22×D412yes—
1160C23—22no—
1161C23—22no—
1162C23—21no—
1163C23—21no—
1164C23—22no—
1165C23—42no—
1166C23—42no—
1167C23—41no—
1168C23—41no—
1169C23—42no—
1170C23—42no—
1171C23—42no—
1172C23—42no—
1173C23—42no—
1174C23—42no—
1175C23—42no—
1176C23—42no—
1177C23—42no—
1178C23—42no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—84no—
1195C23—88no—
1196C23—162no—
1197C23—162no—
1198C23—164no—
1199C23C2×#12712yes—
1200C23C23×D411yescharacteristic
1201Q8—22no—
1202Q8—22no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—41no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—162no—
1218Q8—162no—
1219D4—22no—
1220D4—22no—
1221D4—48no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—41no—
1231D4—41no—
1232D4—41no—
1233D4—41no—
1234D4—41no—
1235D4—41no—
1236D4—41no—
1237D4—41no—
1238D4—41no—
1239D4—41no—
1240D4—41no—
1241D4—41no—
1242D4—41no—
1243D4—41no—
1244D4—84no—
1245D4—88no—
1246D4—84no—
1247D4—162no—
1248D4—162no—
1249D4—162no—
1250D4—162no—
1251D4—164no—
1252D4—164no—
1253D4—164no—
1254D4—162no—
1255D4—162no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—48no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—42no—
1283C2×C4—42no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—42no—
1287C2×C4—42no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—84no—
1304C2×C4—84no—
1305C2×C4—162no—
1306C2×C4—162no—
1307C2×C4—162no—
1308C2×C4—162no—
1309C2×C4—162no—
1310C2×C4C2×#12712yes—
1311C2×C4C2×#12712yes—
1312C2×C4C2×#12712yes—
1313C2×C4C2×#12712yes—
1314C2×C4C2×#12712yes—
1315C2×C4C23×D411yescharacteristic
1316C2×C4C23×D411yescharacteristic
1317C2×C4C2×H(5,𝔽2)11yescharacteristic
1318C2×C4C2×H(5,𝔽2)11yescharacteristic
1319C2×C4#58511yescharacteristic
1320C2×C4#58511yescharacteristic
1321C8—22no—
1322C8—22no—
1323C8—22no—
1324C8—22no—
1325C8—22no—
1326C8—22no—
1327C8—22no—
1328C8—22no—
1329C22—22no—
1330C22—22no—
1331C22—22no—
1332C22—42no—
1333C22—42no—
1334C22—44no—
1335C22—42no—
1336C22—82no—
1337C22—81no—
1338C22—81no—
1339C22—82no—
1340C22—82no—
1341C22—82no—
1342C22—82no—
1343C22—82no—
1344C22—82no—
1345C22—82no—
1346C22—82no—
1347C22—82no—
1348C22—82no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—168no—
1365C22C22×#12711yescharacteristic
1366C22#348411yescharacteristic
1367C22#348711yescharacteristic
1368C22#358412yes—
1369C22#358512yes—
1370C4—22no—
1371C4—22no—
1372C4—22no—
1373C4—22no—
1374C4—22no—
1375C4—42no—
1376C4—42no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4#348811yescharacteristic
1390C4#348811yescharacteristic
1391C4#348811yescharacteristic
1392C4#348811yescharacteristic
1393C2—42no—
1394C2—82no—
1395C2—161no—
1396C2—161no—
1397C2—161no—
1398C2—161no—
1399C2—161no—
1400C2#3556511yescharacteristic
1401C2#6064911yescharacteristic
1402C2#6065011yescharacteristic
1403C2#6162512yes—
1404C2#6191912yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3224C2semidirect
2. C2×#3224C2semidirect
3. C2×#3125C2semidirect
4. C2×#3124C2semidirect
5. #37421C2semidirect
6. #35533C2semidirect
7. #28481C2semidirect
8. #28480C2semidirect
9. #28475C2semidirect
10. #28474C2semidirect
11. #28469C2semidirect
12. #28468C2semidirect
13. #28465C2semidirect
14. #28464C2semidirect
15. #28436C2semidirect
16. #28434C2semidirect
17. #28424C2semidirect
18. #28422C2semidirect
19. #28420C2semidirect
20. #28413C2semidirect
21. #28402C2semidirect
22. #28399C2semidirect
23. #28326C2semidirect
24. #28325C2semidirect
25. #28312C2semidirect
26. #28303C2semidirect
27. #25734C2semidirect
28. #25732C2semidirect
29. #25727C2semidirect
30. #25723C2semidirect
31. #20541C2semidirect
41. C2×#497C22semidirect
45. C2×#496C22semidirect
48. C2×#495C22semidirect
49. C2×#495C22semidirect
62. C2×#477C22semidirect
63. C2×#475C22semidirect
64. C2×#476C22semidirect
65. C2×#474C22semidirect
68. C2×#464C22semidirect
69. C2×#464C22semidirect
74. C2×#463C22semidirect
75. C2×#463C22semidirect
90. C2×#442C22semidirect
91. C2×#441C22semidirect
92. C2×#440C22semidirect
93. C2×#440C22semidirect
94. C2×C4×Q16C22semidirect
95. C2×C4×SD16C22semidirect
96. C2×C4×SD16C22semidirect
97. C2×C4×D8C22semidirect
108. #2568C22semidirect
109. #2568C22semidirect
110. #2563C22semidirect
111. #2563C22semidirect
116. #2545C22semidirect
117. #2545C22semidirect
120. #2544C22semidirect
121. #2544C22semidirect
131. #2097C22semidirect
132. #2097C22semidirect
137. #2092C22semidirect
138. #2092C22semidirect
139. #2016C22semidirect
140. #2016C22semidirect
143. #2015C22semidirect
144. #2015C22semidirect
147. #2014C22semidirect
148. #2014C22semidirect
149. #2013C22semidirect
150. #2013C22semidirect
157. #2012C22semidirect
158. #2012C22semidirect
161. #2011C22semidirect
162. #2011C22semidirect
165. #1973C22semidirect
166. #1973C22semidirect
169. #1972C22semidirect
170. #1971C22semidirect
173. #1970C22semidirect
174. #1969C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
181. #1961C22semidirect
182. #1960C22semidirect
185. #1958C22semidirect
186. #1958C22semidirect
187. #1771C22semidirect
188. #1771C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1770C22semidirect
192. #1770C22semidirect
193. C8×C4⋊C4C22semidirect
194. C8×C4⋊C4C22semidirect
353. #433D4semidirect
354. #433D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32242
C2×#31252
C2×#31242
#374212
#355332
#284812
#284802
#284752
#284742
#284692
#284682
#284652
#284642
#284362
#284342
#284242
#284222
#284202
#284132
#284022
#283992
#283262
#283252
#283122
#283032
#257342
#257322
#257272
#257232
#205412