Finite Group Databasebeta

← #6569775

Subgroups — #6569775

Order 512.

2346 conjugacy classes of subgroups.

The subgroup lattice has 1317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3345C211yesmaximal, characteristic, complemented
2C2×#3337C211yesmaximal, characteristic, complemented
3C2×#3310C211yesmaximal, characteristic, complemented
4C2×#3294C211yesmaximal, characteristic, complemented
5#38080C211yesmaximal, characteristic, complemented
6#37863C211yesmaximal, characteristic, complemented
7#30287C211yesmaximal, characteristic, complemented
8#30251C211yesmaximal, characteristic, complemented
9#30243C211yesmaximal, characteristic, complemented
10#28543C211yesmaximal, characteristic, complemented
11#28534C211yesmaximal, characteristic, complemented
12#28525C211yesmaximal, characteristic, complemented
13#28421C211yesmaximal, characteristic, complemented
14#28404C211yesmaximal, characteristic, complemented
15#28389C211yesmaximal, characteristic, complemented
16#28353C211yesmaximal, characteristic, complemented
17#28344C211yesmaximal, characteristic, complemented
18#28332C211yesmaximal, characteristic, complemented
19#28329C211yesmaximal, characteristic, complemented
20#28321C211yesmaximal, characteristic, complemented
21#28303C211yesmaximal, characteristic, complemented
22#27945C211yesmaximal, characteristic, complemented
23#27934C211yesmaximal, characteristic, complemented
24#27928C211yesmaximal, characteristic, complemented
25#27926C211yesmaximal, characteristic, complemented
26#27923C211yesmaximal, characteristic, complemented
27#27909C211yesmaximal, characteristic, complemented
28#23808C211yesmaximal, characteristic, complemented
29#23735C211yesmaximal, characteristic, complemented
30C2×#2094C211yesmaximal, characteristic, complemented
31#20557C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×D42C2211yescharacteristic
36#3345—28no—
37#3337—28no—
38#3310—28no—
39#3294—28no—
40C2×#501C2211yescharacteristic, complemented
41C2×#499C2211yescharacteristic, complemented
42C2×#490C2211yescharacteristic
43C2×#486C2211yescharacteristic
44C2×#484C2211yescharacteristic, complemented
45C2×#481C2211yescharacteristic, complemented
46C2×#481C2211yescharacteristic, complemented
47C2×#485C2211yescharacteristic, complemented
48C2×#482C2211yescharacteristic
49C2×#482C2211yescharacteristic, complemented
50C2×#482C2211yescharacteristic, complemented
51C2×#480C2211yescharacteristic
52C2×#480C2211yescharacteristic
53C2×#480C2211yescharacteristic
54C2×#480C2211yescharacteristic, complemented
55C2×#480C2211yescharacteristic, complemented
56C2×#479C2211yescharacteristic, complemented
57C2×#478C2211yescharacteristic
58C2×#478C2211yescharacteristic, complemented
59C2×#478C2211yescharacteristic, complemented
60C2×#476C2211yescharacteristic, complemented
61C2×#474C2211yescharacteristic
62C2×#469C2211yescharacteristic, complemented
63C2×#468C2211yescharacteristic
64C2×#466C2211yescharacteristic
65C2×#466C2211yescharacteristic
66C2×#466C2211yescharacteristic, complemented
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic, complemented
69C2×#465C2211yescharacteristic, complemented
70C2×#460C2211yescharacteristic
71C2×#459C2211yescharacteristic
72C2×#450C2211yescharacteristic
73C2×#450C2211yescharacteristic
74C2×#447C2211yescharacteristic
75C2×#447C2211yescharacteristic
76C2×#442C2211yescharacteristic, complemented
77C2×#440C2211yescharacteristic
78C2×C4×SD16C2211yescharacteristic, complemented
79C2×C4×D8C2211yescharacteristic
80C2×#435C2211yescharacteristic
81C2×C8×D4C2211yescharacteristic
82C2×#428C2211yescharacteristic, complemented
83C2×#427C2211yescharacteristic, complemented
84C22×#106C2211yescharacteristic, complemented
85C22×#106C2211yescharacteristic, complemented
86C2×#418C2211yescharacteristic
87C22×#102C2211yescharacteristic
88C22×#102C2211yescharacteristic
89C22×#102C2211yescharacteristic
90#2856C2211yescharacteristic
91#2850C2211yescharacteristic, complemented
92#2720—22no—
93#2718—22no—
94#2714—22no—
95#2678—22no—
96#2660C2211yescharacteristic, complemented
97#2641C2211yescharacteristic
98#2620C2211yescharacteristic, complemented
99#2619C2211yescharacteristic
100#2567C2211yescharacteristic, complemented
101#2566C2211yescharacteristic
102#2566C2211yescharacteristic, complemented
103#2541C2211yescharacteristic
104#2504C2211yescharacteristic
105#2503C2211yescharacteristic, complemented
106#2502C2211yescharacteristic, complemented
107#2501C2211yescharacteristic, complemented
108#2500C2211yescharacteristic
109#2500C2211yescharacteristic, complemented
110#2433C2211yescharacteristic
111#2433C2211yescharacteristic
112#2424—22no—
113#2413—22no—
114#2410—22no—
115#2406—22no—
116#2328C2211yescharacteristic
117#2326C2211yescharacteristic, complemented
118#2317C2211yescharacteristic, complemented
119#2309C2211yescharacteristic
120C2×#390C2211yescharacteristic
121#2290C2211yescharacteristic
122C2×#384C2211yescharacteristic, complemented
123#2097C2211yescharacteristic, complemented
124#2097C2211yescharacteristic, complemented
125#2095C2211yescharacteristic, complemented
126#2094C2211yescharacteristic
127#2094C2211yescharacteristic
128#2094C2211yescharacteristic
129#2094C2211yescharacteristic
130#2094C2211yescharacteristic, complemented
131#2094C2211yescharacteristic, complemented
132#2094C2211yescharacteristic, complemented
133#2094C2211yescharacteristic, complemented
134#2094C2211yescharacteristic, complemented
135#2094C2211yescharacteristic, complemented
136#2094C2211yescharacteristic, complemented
137#2093C2211yescharacteristic
138#2093C2211yescharacteristic, complemented
139#2093C2211yescharacteristic, complemented
140#2093C2211yescharacteristic, complemented
141#2093C2211yescharacteristic, complemented
142#2093C2211yescharacteristic, complemented
143#2092C2211yescharacteristic
144#2092C2211yescharacteristic
145#2092C2211yescharacteristic, complemented
146#2092C2211yescharacteristic, complemented
147#2092C2211yescharacteristic, complemented
148#2092C2211yescharacteristic, complemented
149#2092C2211yescharacteristic, complemented
150#2092C2211yescharacteristic, complemented
151#2092C2211yescharacteristic, complemented
152#2092C2211yescharacteristic, complemented
153#2014C2211yescharacteristic
154#2014C2211yescharacteristic, complemented
155#2014C2211yescharacteristic, complemented
156#2012C2211yescharacteristic
157#2012C2211yescharacteristic, complemented
158#2012C2211yescharacteristic, complemented
159#2012C2211yescharacteristic, complemented
160#2011C2211yescharacteristic
161#2011C2211yescharacteristic, complemented
162#2011C2211yescharacteristic, complemented
163#1973C2211yescharacteristic
164#1973C2211yescharacteristic, complemented
165#1972C2211yescharacteristic, complemented
166#1972C2211yescharacteristic, complemented
167#1970C2211yescharacteristic
168#1970C2211yescharacteristic
169#1970C2211yescharacteristic, complemented
170#1970C2211yescharacteristic, complemented
171#1968C2211yescharacteristic
172#1968C2211yescharacteristic, complemented
173#1968C2211yescharacteristic, complemented
174#1968C2211yescharacteristic, complemented
175#1961C2211yescharacteristic
176#1961C2211yescharacteristic, complemented
177#1957C2211yescharacteristic
178#1957C2211yescharacteristic, complemented
179#1957C2211yescharacteristic, complemented
180#1957C2211yescharacteristic, complemented
181#1847C2211yescharacteristic, complemented
182#1847C2211yescharacteristic, complemented
183#1846C2211yescharacteristic, complemented
184#1846C2211yescharacteristic, complemented
185#1845C2211yescharacteristic, complemented
186#1845C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188C8×C4⋊C4C2211yescharacteristic, complemented
189#1768C2211yescharacteristic, complemented
190#1753C2211yescharacteristic, complemented
191#1752C2211yescharacteristic, complemented
192C8×C22⋊C4C2211yescharacteristic, complemented
193C8×C22⋊C4C2211yescharacteristic, complemented
194#1750C2211yescharacteristic, complemented
195C4×C22⋊C8C2211yescharacteristic, complemented
196#1746C2211yescharacteristic, complemented
197#1729C2211yescharacteristic, complemented
198C2×#336C2211yescharacteristic, complemented
199C22×#41—21no—
200C23×D4—21no—
201C23×D4C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#553—24no—
216#553—24no—
217#552—24no—
218#552—24no—
219#547—24no—
220#547—24no—
221D42—24no—
222D42—24no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#126—21no—
229C2×#126—21no—
230C2×#125—21no—
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#123—21no—
235C2×#123—21no—
236C2×#123—21no—
237C2×#123—21no—
238C2×#123—22no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×#121—21no—
243C2×#121—22no—
244C2×#121—21no—
245C2×#121—22no—
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×#121C2311yescharacteristic
252C2×#120—21no—
253C2×#120—21no—
254C2×#120—22no—
255C2×#120—22no—
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×#117—21no—
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C22×C4⋊C4—22no—
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C22⋊C4—22no—
272C22×C42C2311yescharacteristic
273#501—24no—
274#499—24no—
275#490—24no—
276#486—24no—
277#485—24no—
278#484—24no—
279#482—24no—
280#482—24no—
281#482—24no—
282#481—24no—
283#481—24no—
284#480—24no—
285#480—24no—
286#480—24no—
287#480—24no—
288#480—24no—
289#479—24no—
290#478—24no—
291#478—24no—
292#478—24no—
293#476—24no—
294#474—24no—
295#469—24no—
296#468—24no—
297#466—24no—
298#466—24no—
299#466—24no—
300#465—24no—
301#465—24no—
302#465—24no—
303#460—24no—
304#459—24no—
305#450—24no—
306#450—24no—
307#447—24no—
308#447—24no—
309#442—24no—
310#440—24no—
311C4×SD16—24no—
312C4×D8—24no—
313#435D418yescomplemented
314C8×D4D418yescomplemented
315#428—24no—
316#427—24no—
317C2×#107C2311yescharacteristic
318C2×#107C2311yescharacteristic
319C2×#107C2311yescharacteristic
320C2×#107C2311yescharacteristic
321C2×#107C2311yescharacteristic
322C2×#107C2311yescharacteristic
323C2×#107C2311yescharacteristic
324C2×#107C2311yescharacteristic
325C2×#107C2311yescharacteristic
326C2×#107C2311yescharacteristic
327C2×#107C2311yescharacteristic
328C2×#107C2311yescharacteristic
329C2×#106—24no—
330C2×#106—24no—
331C2×#106C2311yescharacteristic
332C2×#106C2311yescharacteristic
333C2×#106C2311yescharacteristic
334C2×#106C2311yescharacteristic
335C2×#106C2311yescharacteristic
336C2×#106C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×C4⋊C8C2311yescharacteristic
344C2×C4⋊C8C2311yescharacteristic
345#418—24no—
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#103C2311yescharacteristic
350C2×#102—24no—
351C2×#102—24no—
352C2×#102—24no—
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×#102C2311yescharacteristic
358C2×#102C2311yescharacteristic
359C2×#102C2311yescharacteristic
360C2×#102C2311yescharacteristic
361C2×#102C2311yescharacteristic
362C2×#102C2311yescharacteristic
363C2×#102C2311yescharacteristic
364C2×#102C2311yescharacteristic
365C2×#102C2311yescharacteristic
366C2×#102C2311yescharacteristic
367C2×#102C2311yescharacteristic
368C2×#102C2311yescharacteristic
369C2×#102C2311yescharacteristic
370C2×#102C2311yescharacteristic
371C2×#102C2311yescharacteristic
372C2×#102C2311yescharacteristic
373C2×#102C2311yescharacteristic
374C2×#102C2311yescharacteristic
375C2×#102C2311yescharacteristic
376C2×#102C2311yescharacteristic
377C2×#102C2311yescharacteristic
378C2×#102C2311yescharacteristic
379C2×#102C2311yescharacteristic
380C2×#102C2311yescharacteristic
381C2×C22⋊C8C2311yescharacteristic
382C2×C22⋊C8C2311yescharacteristic
383C2×C22⋊C8C2311yescharacteristic
384C2×C22⋊C8C2311yescharacteristic
385C2×#97C2311yescharacteristic
386C2×#97C2311yescharacteristic
387C2×#97C2311yescharacteristic
388C2×C4×C8C2311yescharacteristic
389C2×C4×C8C2311yescharacteristic
390C2×C4×C8C2311yescharacteristic
391C2×C4×C8C2311yescharacteristic
392C2×C4×C8C2311yescharacteristic
393#400—22no—
394#399—22no—
395#398—22no—
396#398—22no—
397#397—22no—
398#396—22no—
399#396—22no—
400#396—22no—
401#395—22no—
402#395—22no—
403#394—22no—
404#394—22no—
405#394—22no—
406#394—22no—
407#394—22no—
408#394—22no—
409#392—22no—
410#392—22no—
411#392—22no—
412#392—22no—
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#390—22no—
417#390—22no—
418#390—22no—
419#390C2311yescharacteristic
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#390C2311yescharacteristic
423#390C2311yescharacteristic
424#390C2311yescharacteristic
425#390C2311yescharacteristic
426#390C2311yescharacteristic
427#390C2311yescharacteristic
428#390C2311yescharacteristic
429#390C2311yescharacteristic
430#390C2311yescharacteristic
431#390C2311yescharacteristic
432#389—22no—
433#389—22no—
434#388—22no—
435#388—22no—
436#388—22no—
437#388—22no—
438#388D412yes—
439#387D412yes—
440#386—22no—
441#386—22no—
442#386—22no—
443#386—22no—
444#386D412yes—
445#385—22no—
446#385—22no—
447#385—22no—
448#385—22no—
449#385—22no—
450#385D412yes—
451#384—22no—
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#382C2311yescharacteristic
464#381—22no—
465#379—22no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469#376C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480C25—21no—
481C25—21no—
482C2×#41—44no—
483C2×#41—84no—
484C22×Q8—21no—
485C22×Q8C2411yescharacteristic
486C22×D4—22no—
487C22×D4—22no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—22no—
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—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—44no—
512C22×D4—84no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2×D412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×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×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16C2×D414yes—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8C2×D414yes—
563C22×C8C2×D414yes—
564C22×C8C2×D414yes—
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—22no—
575#127—22no—
576#127—22no—
577#127—22no—
578#127—41no—
579#127—41no—
580#127—41no—
581#127—41no—
582#127—41no—
583#126—44no—
584#126—44no—
585#125—22no—
586#125—22no—
587#125—22no—
588#125—22no—
589#125—44no—
590#124—41no—
591#124—41no—
592#123—44no—
593#123—44no—
594#123—44no—
595#123—44no—
596#123—84no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—44no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—22no—
611#121—22no—
612#121—22no—
613#121—22no—
614#121—44no—
615#121—44no—
616#121—84no—
617#121—84no—
618#120—44no—
619#120—44no—
620#120—84no—
621#120—84no—
622C4×Q8—22no—
623C4×Q8—22no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—44no—
631C4×D4C2×D414yes—
632C4×D4C2×D414yes—
633#117—22no—
634#117—22no—
635#117—22no—
636#117—22no—
637#117—41no—
638#117—41no—
639#117—44no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
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—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—84no—
668C2×C4⋊C4C2×D412yes—
669C2×C4⋊C4C2×D412yes—
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
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×D412yes—
711C2×C22⋊C4C2×D412yes—
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—41no—
718C2×C42—41no—
719C2×C42C2×D412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725#107—22no—
726#107—22no—
727#107—22no—
728#107—22no—
729#107—22no—
730#107—22no—
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—22no—
736#107—22no—
737#106—22no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—22no—
746#106—22no—
747#106—22no—
748#106—22no—
749C4⋊C8C2×D414yes—
750C4⋊C8C2×D414yes—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783C22⋊C8C2×D414yes—
784C22⋊C8C2×D414yes—
785C22⋊C8C2×D414yes—
786C22⋊C8C2×D414yes—
787#97—41no—
788#97—41no—
789#97C2×D414yes—
790C4×C8—41no—
791C4×C8—41no—
792C4×C8—41no—
793C4×C8—41no—
794C4×C8C2×D414yes—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—22no—
801#95—22no—
802#95—22no—
803#95C2×D412yes—
804#95C2×D412yes—
805#95C2×D412yes—
806#95C2×D412yes—
807#95C2×D412yes—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—42no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—44no—
818C24—82no—
819C24—81no—
820C24—81no—
821C24—82no—
822C24—82no—
823C24C22×D411yescharacteristic
824C24C22×D411yescharacteristic
825#41—816no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—42no—
833C2×Q8—82no—
834C2×D4—24no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—44no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—44no—
885C2×D4—82no—
886C2×D4—82no—
887C2×D4—82no—
888C2×D4—82no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—82no—
892C2×D4—82no—
893C2×D4—82no—
894C2×D4—82no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—82no—
899C2×D4—82no—
900C2×D4—82no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—816no—
904C2×D4#12714yes—
905C2×D42−1+412yes—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—24no—
915C22×C4—24no—
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—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—82no—
938C22×C4—82no—
939C22×C4—82no—
940C22×C4—82no—
941C22×C4—82no—
942C22×C4C22×D412yes—
943C22×C4C22×D412yes—
944C22×C4C22×D412yes—
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D412yes—
950C22×C4C22×D412yes—
951C22×C4C22×D412yes—
952C22×C4C22×D412yes—
953C22×C4C22×D412yes—
954C22×C4C2511yescharacteristic
955SD16—44no—
956SD16—44no—
957SD16—82no—
958SD16—82no—
959D8—44no—
960D8—44no—
961D8—82no—
962D8—82no—
963M16—44no—
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×C8—21no—
980C2×C8—44no—
981C2×C8—44no—
982C2×C8—44no—
983C2×C8C22×D412yes—
984C2×C8C22×D412yes—
985C2×C8C22×D412yes—
986C2×C8C22×D412yes—
987C2×C8C22×D412yes—
988C2×C8C22×D412yes—
989C2×C8C22×D412yes—
990C2×C8C22×D412yes—
991C4⋊C4—24no—
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—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—82no—
1026C4⋊C4—82no—
1027C4⋊C4—82no—
1028C4⋊C4—82no—
1029C4⋊C4—82no—
1030C4⋊C4—82no—
1031C4⋊C4—82no—
1032C4⋊C4#12714yes—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—42no—
1036C22⋊C4—44no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—82no—
1054C22⋊C4—82no—
1055C22⋊C4—82no—
1056C22⋊C4—82no—
1057C22⋊C4—82no—
1058C22⋊C4—82no—
1059C22⋊C4—82no—
1060C22⋊C4—82no—
1061C22⋊C4—82no—
1062C22⋊C4—82no—
1063C22⋊C4#12714yes—
1064C22⋊C4#12714yes—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42C22×D412yes—
1078C42C22×D412yes—
1079C23—21no—
1080C23—21no—
1081C23—22no—
1082C23—21no—
1083C23—21no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—41no—
1088C23—41no—
1089C23—42no—
1090C23—42no—
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—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—42no—
1111C23—84no—
1112C23—84no—
1113C23—88no—
1114C23—84no—
1115C23—84no—
1116C23—164no—
1117C23—162no—
1118C23—162no—
1119C23—164no—
1120C23—164no—
1121C23C2×#12712yes—
1122C23C2×#12712yes—
1123C23#57614yes—
1124C23C23×D411yescharacteristic
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—84no—
1130D4—28no—
1131D4—22no—
1132D4—22no—
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—41no—
1149D4—41no—
1150D4—41no—
1151D4—84no—
1152D4—84no—
1153D4—84no—
1154D4—84no—
1155D4—84no—
1156D4—84no—
1157D4—84no—
1158D4—84no—
1159D4—164no—
1160D4—162no—
1161D4—164no—
1162D4—164no—
1163D4—162no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
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—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—48no—
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—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—84no—
1217C2×C4—84no—
1218C2×C4—162no—
1219C2×C4—162no—
1220C2×C4C2×#12712yes—
1221C2×C4C2×#12712yes—
1222C2×C4C2×#12712yes—
1223C2×C4C2×#12712yes—
1224C2×C4#57714yes—
1225C2×C4C23×D411yescharacteristic
1226C2×C4C23×D411yescharacteristic
1227C2×C4C2×2−1+411yescharacteristic
1228C2×C4#58511yescharacteristic
1229C2×C4#58511yescharacteristic
1230C2×C4#58511yescharacteristic
1231C8—22no—
1232C8—22no—
1233C8—22no—
1234C8—22no—
1235C8—22no—
1236C8—22no—
1237C8—22no—
1238C8—22no—
1239C22—24no—
1240C22—22no—
1241C22—22no—
1242C22—24no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—44no—
1250C22—82no—
1251C22—81no—
1252C22—81no—
1253C22—82no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—168no—
1274C22—168no—
1275C22#315514yes—
1276C22C22×#12711yescharacteristic
1277C22#348511yescharacteristic
1278C22#348911yescharacteristic
1279C22C2×#57612yes—
1280C22C2×#57712yes—
1281C4—24no—
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4#348511yescharacteristic
1301C4#348511yescharacteristic
1302C4#348911yescharacteristic
1303C4#348911yescharacteristic
1304C2—24no—
1305C2—42no—
1306C2—82no—
1307C2—161no—
1308C2—161no—
1309C2—161no—
1310C2—161no—
1311C2#3606011yescharacteristic
1312C2C2×#315511yescharacteristic
1313C2#6064611yescharacteristic
1314C2#6176612yes—
1315C2#6220012yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3345C2semidirect
2. C2×#3337C2semidirect
3. C2×#3310C2semidirect
4. C2×#3294C2semidirect
5. #38080C2semidirect
6. #37863C2semidirect
7. #30287C2semidirect
8. #30251C2semidirect
9. #30243C2semidirect
10. #28543C2semidirect
11. #28534C2semidirect
12. #28525C2semidirect
13. #28421C2semidirect
14. #28404C2semidirect
15. #28389C2semidirect
16. #28353C2semidirect
17. #28344C2semidirect
18. #28332C2semidirect
19. #28329C2semidirect
20. #28321C2semidirect
21. #28303C2semidirect
22. #27945C2semidirect
23. #27934C2semidirect
24. #27928C2semidirect
25. #27926C2semidirect
26. #27923C2semidirect
27. #27909C2semidirect
28. #23808C2semidirect
29. #23735C2semidirect
30. C2×#2094C2semidirect
31. #20557C2semidirect
40. C2×#501C22semidirect
41. C2×#499C22semidirect
44. C2×#484C22semidirect
45. C2×#481C22semidirect
46. C2×#481C22semidirect
47. C2×#485C22semidirect
49. C2×#482C22semidirect
50. C2×#482C22semidirect
54. C2×#480C22semidirect
55. C2×#480C22semidirect
56. C2×#479C22semidirect
58. C2×#478C22semidirect
59. C2×#478C22semidirect
60. C2×#476C22semidirect
62. C2×#469C22semidirect
66. C2×#466C22semidirect
68. C2×#465C22semidirect
69. C2×#465C22semidirect
76. C2×#442C22semidirect
78. C2×C4×SD16C22semidirect
82. C2×#428C22semidirect
83. C2×#427C22semidirect
84. C22×#106C22semidirect
85. C22×#106C22semidirect
91. #2850C22semidirect
96. #2660C22semidirect
98. #2620C22semidirect
100. #2567C22semidirect
102. #2566C22semidirect
105. #2503C22semidirect
106. #2502C22semidirect
107. #2501C22semidirect
109. #2500C22semidirect
117. #2326C22semidirect
118. #2317C22semidirect
122. C2×#384C22semidirect
123. #2097C22semidirect
124. #2097C22semidirect
125. #2095C22semidirect
130. #2094C22semidirect
131. #2094C22semidirect
132. #2094C22semidirect
133. #2094C22semidirect
134. #2094C22semidirect
135. #2094C22semidirect
136. #2094C22semidirect
138. #2093C22semidirect
139. #2093C22semidirect
140. #2093C22semidirect
141. #2093C22semidirect
142. #2093C22semidirect
145. #2092C22semidirect
146. #2092C22semidirect
147. #2092C22semidirect
148. #2092C22semidirect
149. #2092C22semidirect
150. #2092C22semidirect
151. #2092C22semidirect
152. #2092C22semidirect
154. #2014C22semidirect
155. #2014C22semidirect
157. #2012C22semidirect
158. #2012C22semidirect
159. #2012C22semidirect
161. #2011C22semidirect
162. #2011C22semidirect
164. #1973C22semidirect
165. #1972C22semidirect
166. #1972C22semidirect
169. #1970C22semidirect
170. #1970C22semidirect
172. #1968C22semidirect
173. #1968C22semidirect
174. #1968C22semidirect
176. #1961C22semidirect
178. #1957C22semidirect
179. #1957C22semidirect
180. #1957C22semidirect
181. #1847C22semidirect
182. #1847C22semidirect
183. #1846C22semidirect
184. #1846C22semidirect
185. #1845C22semidirect
186. #1845C22semidirect
187. #1771C22semidirect
188. C8×C4⋊C4C22semidirect
189. #1768C22semidirect
190. #1753C22semidirect
191. #1752C22semidirect
192. C8×C22⋊C4C22semidirect
193. C8×C22⋊C4C22semidirect
194. #1750C22semidirect
195. C4×C22⋊C8C22semidirect
196. #1746C22semidirect
197. #1729C22semidirect
198. C2×#336C22semidirect
313. #435D4semidirect
314. C8×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33452
C2×#33372
C2×#33102
C2×#32942
#380802
#378632
#302872
#302512
#302432
#285432
#285342
#285252
#284212
#284042
#283892
#283532
#283442
#283322
#283292
#283212
#283032
#279452
#279342
#279282
#279262
#279232
#279092
#238082
#237352
C2×#20942
#205572