Finite Group Databasebeta

← #6569808

Subgroups — #6569808

Order 512.

2189 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3351C211yesmaximal, characteristic, complemented
2C2×#3349C211yesmaximal, characteristic, complemented
3C2×#3324C211yesmaximal, characteristic, complemented
4C2×#3318C211yesmaximal, characteristic
5#38084C211yesmaximal, characteristic, complemented
6#37870C211yesmaximal, characteristic, complemented
7#30287C211yesmaximal, characteristic, complemented
8#30255C211yesmaximal, characteristic, complemented
9#30249C211yesmaximal, characteristic, complemented
10#28544C211yesmaximal, characteristic, complemented
11#28533C211yesmaximal, characteristic, complemented
12#28523C211yesmaximal, characteristic, complemented
13#28431C211yesmaximal, characteristic, complemented
14#28399C211yesmaximal, characteristic, complemented
15#28389C211yesmaximal, characteristic, complemented
16#28361C211yesmaximal, characteristic, complemented
17#28357C211yesmaximal, characteristic, complemented
18#28357C211yesmaximal, characteristic, complemented
19#28330C211yesmaximal, characteristic, complemented
20#28321C211yesmaximal, characteristic, complemented
21#28303C211yesmaximal, characteristic, complemented
22#27946C211yesmaximal, characteristic, complemented
23#27944C211yesmaximal, characteristic, complemented
24#27941C211yesmaximal, characteristic, complemented
25#27928C211yesmaximal, characteristic, complemented
26#27920C211yesmaximal, characteristic, complemented
27#27911C211yesmaximal, characteristic, complemented
28#23813C211yesmaximal, characteristic, complemented
29#23735C211yesmaximal, characteristic, complemented
30#23731C211yesmaximal, characteristic, complemented
31#20561C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#552C2211yescharacteristic
35C2×D42C2211yescharacteristic
36#3351—28no—
37#3349—28no—
38#3324—28no—
39#3318—28no—
40C2×#501C2211yescharacteristic, complemented
41C2×#499C2211yescharacteristic, complemented
42C2×#490C2211yescharacteristic
43C2×#486C2211yescharacteristic
44C2×#484C2211yescharacteristic, complemented
45C2×#481C2211yescharacteristic
46C2×#481C2211yescharacteristic, complemented
47C2×#485C2211yescharacteristic, complemented
48C2×#485C2211yescharacteristic, complemented
49C2×#485C2211yescharacteristic, complemented
50C2×#485C2211yescharacteristic, complemented
51C2×#482C2211yescharacteristic
52C2×#482C2211yescharacteristic
53C2×#482C2211yescharacteristic
54C2×#482C2211yescharacteristic, complemented
55C2×#483C2211yescharacteristic, complemented
56C2×#479C2211yescharacteristic, complemented
57C2×#479C2211yescharacteristic, complemented
58C2×#477C2211yescharacteristic, complemented
59C2×#478C2211yescharacteristic
60C2×#478C2211yescharacteristic, complemented
61C2×#474C2211yescharacteristic
62C2×#470C2211yescharacteristic, complemented
63C2×#469C2211yescharacteristic
64C2×#468C2211yescharacteristic
65C2×#468C2211yescharacteristic
66C2×#468C2211yescharacteristic, complemented
67C2×#468C2211yescharacteristic, complemented
68C2×#467C2211yescharacteristic, complemented
69C2×#466C2211yescharacteristic
70C2×#460C2211yescharacteristic
71C2×#459C2211yescharacteristic
72C2×#450C2211yescharacteristic
73C2×#450C2211yescharacteristic
74C2×#447C2211yescharacteristic
75C2×#447C2211yescharacteristic
76C2×#442C2211yescharacteristic
77C2×#441C2211yescharacteristic, complemented
78C2×C4×SD16C2211yescharacteristic
79C2×C4×SD16C2211yescharacteristic, complemented
80C2×#436C2211yescharacteristic
81C2×#435C2211yescharacteristic
82C2×#428C2211yescharacteristic, complemented
83C2×#428C2211yescharacteristic, complemented
84C2×#428C2211yescharacteristic, complemented
85C2×#427C2211yescharacteristic, complemented
86C2×#418C2211yescharacteristic
87C2×#418C2211yescharacteristic
88C2×#418C2211yescharacteristic
89C22×#102C2211yescharacteristic
90#2850C2211yescharacteristic
91#2850C2211yescharacteristic, complemented
92#2711—22no—
93#2695—22no—
94#2686—22no—
95#2685—22no—
96#2660C2211yescharacteristic, complemented
97#2641C2211yescharacteristic
98#2620C2211yescharacteristic
99#2620C2211yescharacteristic, complemented
100#2566C2211yescharacteristic
101#2565C2211yescharacteristic, complemented
102#2563C2211yescharacteristic, complemented
103#2548C2211yescharacteristic
104#2503C2211yescharacteristic, complemented
105#2501C2211yescharacteristic
106#2500C2211yescharacteristic
107#2500C2211yescharacteristic, complemented
108#2500C2211yescharacteristic, complemented
109#2499C2211yescharacteristic, complemented
110#2469—22no—
111#2468—22no—
112#2435C2211yescharacteristic
113#2435C2211yescharacteristic
114#2411—22no—
115#2405—22no—
116#2326C2211yescharacteristic
117#2326C2211yescharacteristic, complemented
118#2317C2211yescharacteristic, complemented
119#2309C2211yescharacteristic
120C2×#390C2211yescharacteristic
121#2290C2211yescharacteristic
122#2285C2211yescharacteristic, complemented
123#2097C2211yescharacteristic, complemented
124#2097C2211yescharacteristic, complemented
125#2096C2211yescharacteristic, complemented
126#2096C2211yescharacteristic, complemented
127#2095C2211yescharacteristic, complemented
128#2095C2211yescharacteristic, complemented
129#2094C2211yescharacteristic
130#2094C2211yescharacteristic, complemented
131#2094C2211yescharacteristic, complemented
132#2094C2211yescharacteristic, complemented
133#2094C2211yescharacteristic, complemented
134#2094C2211yescharacteristic, complemented
135#2093C2211yescharacteristic
136#2093C2211yescharacteristic
137#2093C2211yescharacteristic, complemented
138#2093C2211yescharacteristic, complemented
139#2093C2211yescharacteristic, complemented
140#2093C2211yescharacteristic, complemented
141#2092C2211yescharacteristic
142#2092C2211yescharacteristic
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#2015C2211yescharacteristic
154#2015C2211yescharacteristic, complemented
155#2015C2211yescharacteristic, complemented
156#2015C2211yescharacteristic, complemented
157#2012C2211yescharacteristic
158#2012C2211yescharacteristic
159#2012C2211yescharacteristic, complemented
160#2012C2211yescharacteristic, complemented
161#2012C2211yescharacteristic, complemented
162#2012C2211yescharacteristic, complemented
163#1973C2211yescharacteristic, complemented
164#1973C2211yescharacteristic, complemented
165#1972C2211yescharacteristic
166#1972C2211yescharacteristic, complemented
167#1970C2211yescharacteristic
168#1970C2211yescharacteristic, complemented
169#1970C2211yescharacteristic, complemented
170#1970C2211yescharacteristic, complemented
171#1968C2211yescharacteristic
172#1968C2211yescharacteristic
173#1968C2211yescharacteristic, complemented
174#1968C2211yescharacteristic, complemented
175#1959C2211yescharacteristic
176#1959C2211yescharacteristic, complemented
177#1958C2211yescharacteristic
178#1958C2211yescharacteristic, complemented
179#1958C2211yescharacteristic, complemented
180#1958C2211yescharacteristic, complemented
181#1847C2211yescharacteristic, complemented
182#1847C2211yescharacteristic, complemented
183#1846C2211yescharacteristic, complemented
184#1846C2211yescharacteristic, complemented
185#1845C2211yescharacteristic, complemented
186#1844C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188C8×C4⋊C4C2211yescharacteristic, complemented
189#1768C2211yescharacteristic, complemented
190#1753C2211yescharacteristic, complemented
191#1753C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193C8×C22⋊C4C2211yescharacteristic, complemented
194#1750C2211yescharacteristic, complemented
195C4×C22⋊C8C2211yescharacteristic, complemented
196#1746C2211yescharacteristic, complemented
197#1729C2211yescharacteristic, complemented
198#1728C2211yescharacteristic, complemented
199C23×D4—21no—
200C23×D4C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C22×Q16C2311yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#556—24no—
215#556—24no—
216#553—24no—
217#553—24no—
218#552—24no—
219#552—24no—
220D42—24no—
221D42—24no—
222C2×C4⋊Q8C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#126—21no—
225C2×#126—21no—
226C2×#126—21no—
227C2×#126—21no—
228C2×#125—21no—
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#124—21no—
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#123—21no—
237C2×#123—21no—
238C2×#123—22no—
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×#121—21no—
244C2×#121—21no—
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×#120—21no—
251C2×C4×Q8—21no—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117—21no—
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C22⋊C4—22no—
267C22×C42C2311yescharacteristic
268#501—24no—
269#499—24no—
270#490—24no—
271#486—24no—
272#485—24no—
273#485—24no—
274#485—24no—
275#485—24no—
276#484—24no—
277#483—24no—
278#482—24no—
279#482—24no—
280#482—24no—
281#482—24no—
282#481—24no—
283#481—24no—
284#479—24no—
285#479—24no—
286#478—24no—
287#478—24no—
288#477—24no—
289#474—24no—
290#470—24no—
291#469—24no—
292#468—24no—
293#468—24no—
294#468—24no—
295#468—24no—
296#467—24no—
297#466—24no—
298#460—24no—
299#459—24no—
300#450—24no—
301#450—24no—
302#447—24no—
303#447—24no—
304#442—24no—
305#441—24no—
306C4×SD16—24no—
307C4×SD16—24no—
308#436D418yes—
309#435D418yes—
310#428—24no—
311#428—24no—
312#428—24no—
313#427—24no—
314C2×#107C2311yescharacteristic
315C2×#107C2311yescharacteristic
316C2×#107C2311yescharacteristic
317C2×#107C2311yescharacteristic
318C2×#107C2311yescharacteristic
319C2×#107C2311yescharacteristic
320C2×#107C2311yescharacteristic
321C2×#107C2311yescharacteristic
322C2×#107C2311yescharacteristic
323C2×#107C2311yescharacteristic
324C2×#107C2311yescharacteristic
325C2×#107C2311yescharacteristic
326C2×#106C2311yescharacteristic
327C2×#106C2311yescharacteristic
328C2×#106C2311yescharacteristic
329C2×#106C2311yescharacteristic
330C2×#106C2311yescharacteristic
331C2×#106C2311yescharacteristic
332C2×#106C2311yescharacteristic
333C2×#106C2311yescharacteristic
334C2×#106C2311yescharacteristic
335C2×#106C2311yescharacteristic
336C2×#106C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×C4⋊C8C2311yescharacteristic
339C2×C4⋊C8C2311yescharacteristic
340#418—24no—
341#418—24no—
342#418—24no—
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#103C2311yescharacteristic
350C2×#103C2311yescharacteristic
351C2×#103C2311yescharacteristic
352C2×#103C2311yescharacteristic
353C2×#102—24no—
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×C22⋊C8C2311yescharacteristic
377C2×C22⋊C8C2311yescharacteristic
378C2×C22⋊C8C2311yescharacteristic
379C2×C22⋊C8C2311yescharacteristic
380C2×#97C2311yescharacteristic
381C2×#97C2311yescharacteristic
382C2×#97C2311yescharacteristic
383C2×C4×C8C2311yescharacteristic
384C2×C4×C8C2311yescharacteristic
385C2×C4×C8C2311yescharacteristic
386C2×C4×C8C2311yescharacteristic
387C2×C4×C8C2311yescharacteristic
388#400—22no—
389#399—22no—
390#398—22no—
391#398—22no—
392#397—22no—
393#396—22no—
394#396—22no—
395#396—22no—
396#395—22no—
397#394—22no—
398#394—22no—
399#394—22no—
400#394—22no—
401#394—22no—
402#394—22no—
403#394—22no—
404#394—22no—
405#394—22no—
406#394—22no—
407#393—22no—
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#390—22no—
413#390—22no—
414#390—22no—
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#390C2311yescharacteristic
423#390C2311yescharacteristic
424#390C2311yescharacteristic
425#390C2311yescharacteristic
426#390C2311yescharacteristic
427#389—22no—
428#388—22no—
429#388—22no—
430#388—22no—
431#388—22no—
432#388—22no—
433#388—22no—
434#388—22no—
435#388D412yes—
436#387—22no—
437#387—22no—
438#387D412yes—
439#386—22no—
440#386—22no—
441#386D412yes—
442#385—22no—
443#385—22no—
444#385—22no—
445#385—22no—
446#385D412yes—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#381—22no—
460#380—22no—
461#380—22no—
462#379—22no—
463#379—22no—
464#379—22no—
465C4×C4⋊C4—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—
482C22×Q8—21no—
483C22×Q8C2411yescharacteristic
484C22×Q8C2411yescharacteristic
485C22×D4—22no—
486C22×D4—22no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—22no—
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—44no—
506C22×D4—84no—
507C22×D4C2×D411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2×D412yes—
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C2×Q16—22no—
520C2×Q16—41no—
521C2×Q16—41no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16C2×D414yes—
550C2×M16C2×D414yes—
551C2×M16C2×D414yes—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8C2×D414yes—
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C4⋊Q8—22no—
564C4⋊Q8—22no—
565#127—22no—
566#127—22no—
567#126—44no—
568#126—44no—
569#126—44no—
570#126—44no—
571#125—22no—
572#125—22no—
573#125—22no—
574#125—22no—
575#125—44no—
576#124—22no—
577#124—41no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—44no—
585#123—44no—
586#123—44no—
587#123—84no—
588C22⋊Q8—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—44no—
605#121—44no—
606#120—44no—
607#120—44no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—44no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—44no—
618C4×D4C2×D414yes—
619C4×D4C2×D414yes—
620#117—22no—
621#117—22no—
622#117—22no—
623#117—22no—
624#117—22no—
625#117—22no—
626#117—22no—
627#117—22no—
628#117—41no—
629#117—41no—
630#117—44no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4C2×D412yes—
655C2×C4⋊C4C2×D412yes—
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—84no—
698C2×C22⋊C4C2×D412yes—
699C2×C22⋊C4C2×D412yes—
700C2×C22⋊C4C2×D412yes—
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—41no—
710C2×C42—41no—
711C2×C42C2×D412yes—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—22no—
718#107—22no—
719#107—22no—
720#107—22no—
721#107—22no—
722#107—22no—
723#107—22no—
724#107—22no—
725#107—22no—
726#107—22no—
727#107—22no—
728#107—22no—
729#106—22no—
730#106—22no—
731#106—22no—
732#106—22no—
733#106—22no—
734#106—22no—
735#106—22no—
736#106—22no—
737#106—22no—
738#106—22no—
739#106—22no—
740#106—22no—
741C4⋊C8C2×D414yes—
742C4⋊C8C2×D414yes—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#102—22no—
754#102—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—
775C22⋊C8C2×D414yes—
776C22⋊C8C2×D414yes—
777C22⋊C8C2×D414yes—
778C22⋊C8C2×D414yes—
779#97—41no—
780#97—41no—
781#97C2×D414yes—
782C4×C8—41no—
783C4×C8—41no—
784C4×C8—41no—
785C4×C8—41no—
786C4×C8C2×D414yes—
787#95—22no—
788#95—22no—
789#95—22no—
790#95—22no—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95C2×D412yes—
798#95C2×D412yes—
799#95C2×D412yes—
800#95C2×D412yes—
801#95C2×D412yes—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—42no—
807C24—42no—
808C24—44no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—82no—
814C24—82no—
815C24—82no—
816C24C22×D411yescharacteristic
817C24C22×D411yescharacteristic
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—42no—
831C2×Q8—82no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
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—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—44no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—82no—
872C2×D4—82no—
873C2×D4—82no—
874C2×D4—82no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—82no—
878C2×D4—82no—
879C2×D4—82no—
880C2×D4—82no—
881C2×D4—82no—
882C2×D4—816no—
883C2×D4#12714yes—
884C2×D42−1+412yes—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—44no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—82no—
914C22×C4—82no—
915C22×C4—82no—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D412yes—
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D412yes—
925C22×C4C22×D412yes—
926C22×C4C22×D412yes—
927C22×C4C22×D412yes—
928C22×C4C2511yescharacteristic
929Q16—44no—
930SD16—44no—
931SD16—44no—
932SD16—82no—
933SD16—82no—
934D8—44no—
935D8—82no—
936D8—82no—
937M16—44no—
938M16—44no—
939M16—44no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—44no—
957C2×C8C22×D412yes—
958C2×C8C22×D412yes—
959C2×C8C22×D412yes—
960C2×C8C22×D412yes—
961C2×C8C22×D412yes—
962C2×C8C22×D412yes—
963C2×C8C22×D412yes—
964C2×C8C22×D412yes—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—82no—
1001C4⋊C4—82no—
1002C4⋊C4—82no—
1003C4⋊C4—82no—
1004C4⋊C4—82no—
1005C4⋊C4—82no—
1006C4⋊C4#12714yes—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—82no—
1027C22⋊C4—82no—
1028C22⋊C4—82no—
1029C22⋊C4—82no—
1030C22⋊C4—82no—
1031C22⋊C4—82no—
1032C22⋊C4—82no—
1033C22⋊C4—82no—
1034C22⋊C4—82no—
1035C22⋊C4—82no—
1036C22⋊C4—82no—
1037C22⋊C4—82no—
1038C22⋊C4—82no—
1039C22⋊C4—82no—
1040C22⋊C4#12714yes—
1041C22⋊C4#12714yes—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—42no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—42no—
1056C42—42no—
1057C42C22×D412yes—
1058C42C22×D412yes—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—22no—
1068C23—42no—
1069C23—42no—
1070C23—41no—
1071C23—41no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—84no—
1088C23—84no—
1089C23—84no—
1090C23—84no—
1091C23—88no—
1092C23—162no—
1093C23—162no—
1094C23—164no—
1095C23—164no—
1096C23—164no—
1097C23C2×#12712yes—
1098C23C2×#12712yes—
1099C23C23×D411yescharacteristic
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—84no—
1109D4—22no—
1110D4—22no—
1111D4—44no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—84no—
1127D4—84no—
1128D4—84no—
1129D4—84no—
1130D4—84no—
1131D4—84no—
1132D4—162no—
1133D4—162no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—84no—
1187C2×C4—84no—
1188C2×C4—84no—
1189C2×C4—162no—
1190C2×C4—162no—
1191C2×C4C2×#12712yes—
1192C2×C4C2×#12712yes—
1193C2×C4C2×#12712yes—
1194C2×C4C2×#12712yes—
1195C2×C4C23×D411yescharacteristic
1196C2×C4C23×D411yescharacteristic
1197C2×C4C2×2−1+411yescharacteristic
1198C2×C4#58511yescharacteristic
1199C2×C4#58511yescharacteristic
1200C2×C4#58511yescharacteristic
1201C8—22no—
1202C8—22no—
1203C8—22no—
1204C8—22no—
1205C8—22no—
1206C8—22no—
1207C8—22no—
1208C8—22no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—44no—
1221C22—82no—
1222C22—81no—
1223C22—81no—
1224C22—82no—
1225C22—82no—
1226C22—82no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—82no—
1231C22—82no—
1232C22—82no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—168no—
1240C22—168no—
1241C22C22×#12711yescharacteristic
1242C22#348511yescharacteristic
1243C22#348911yescharacteristic
1244C22#358412yes—
1245C22#358512yes—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—42no—
1251C4—42no—
1252C4—42no—
1253C4—42no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4#348511yescharacteristic
1267C4#348511yescharacteristic
1268C4#348911yescharacteristic
1269C4#348911yescharacteristic
1270C2—42no—
1271C2—42no—
1272C2—82no—
1273C2—161no—
1274C2—161no—
1275C2—161no—
1276C2#3606011yescharacteristic
1277C2#6064411yescharacteristic
1278C2#6064911yescharacteristic
1279C2#6174912yes—
1280C2#6217512yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3318C2
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×#3351C2semidirect
2. C2×#3349C2semidirect
3. C2×#3324C2semidirect
5. #38084C2semidirect
6. #37870C2semidirect
7. #30287C2semidirect
8. #30255C2semidirect
9. #30249C2semidirect
10. #28544C2semidirect
11. #28533C2semidirect
12. #28523C2semidirect
13. #28431C2semidirect
14. #28399C2semidirect
15. #28389C2semidirect
16. #28361C2semidirect
17. #28357C2semidirect
18. #28357C2semidirect
19. #28330C2semidirect
20. #28321C2semidirect
21. #28303C2semidirect
22. #27946C2semidirect
23. #27944C2semidirect
24. #27941C2semidirect
25. #27928C2semidirect
26. #27920C2semidirect
27. #27911C2semidirect
28. #23813C2semidirect
29. #23735C2semidirect
30. #23731C2semidirect
31. #20561C2semidirect
40. C2×#501C22semidirect
41. C2×#499C22semidirect
44. C2×#484C22semidirect
46. C2×#481C22semidirect
47. C2×#485C22semidirect
48. C2×#485C22semidirect
49. C2×#485C22semidirect
50. C2×#485C22semidirect
54. C2×#482C22semidirect
55. C2×#483C22semidirect
56. C2×#479C22semidirect
57. C2×#479C22semidirect
58. C2×#477C22semidirect
60. C2×#478C22semidirect
62. C2×#470C22semidirect
66. C2×#468C22semidirect
67. C2×#468C22semidirect
68. C2×#467C22semidirect
77. C2×#441C22semidirect
79. C2×C4×SD16C22semidirect
82. C2×#428C22semidirect
83. C2×#428C22semidirect
84. C2×#428C22semidirect
85. C2×#427C22semidirect
91. #2850C22semidirect
96. #2660C22semidirect
99. #2620C22semidirect
101. #2565C22semidirect
102. #2563C22semidirect
104. #2503C22semidirect
107. #2500C22semidirect
108. #2500C22semidirect
109. #2499C22semidirect
117. #2326C22semidirect
118. #2317C22semidirect
122. #2285C22semidirect
123. #2097C22semidirect
124. #2097C22semidirect
125. #2096C22semidirect
126. #2096C22semidirect
127. #2095C22semidirect
128. #2095C22semidirect
130. #2094C22semidirect
131. #2094C22semidirect
132. #2094C22semidirect
133. #2094C22semidirect
134. #2094C22semidirect
137. #2093C22semidirect
138. #2093C22semidirect
139. #2093C22semidirect
140. #2093C22semidirect
145. #2092C22semidirect
146. #2092C22semidirect
147. #2092C22semidirect
148. #2092C22semidirect
149. #2092C22semidirect
150. #2092C22semidirect
151. #2092C22semidirect
152. #2092C22semidirect
154. #2015C22semidirect
155. #2015C22semidirect
156. #2015C22semidirect
159. #2012C22semidirect
160. #2012C22semidirect
161. #2012C22semidirect
162. #2012C22semidirect
163. #1973C22semidirect
164. #1973C22semidirect
166. #1972C22semidirect
168. #1970C22semidirect
169. #1970C22semidirect
170. #1970C22semidirect
173. #1968C22semidirect
174. #1968C22semidirect
176. #1959C22semidirect
178. #1958C22semidirect
179. #1958C22semidirect
180. #1958C22semidirect
181. #1847C22semidirect
182. #1847C22semidirect
183. #1846C22semidirect
184. #1846C22semidirect
185. #1845C22semidirect
186. #1844C22semidirect
187. #1771C22semidirect
188. C8×C4⋊C4C22semidirect
189. #1768C22semidirect
190. #1753C22semidirect
191. #1753C22semidirect
192. #1753C22semidirect
193. C8×C22⋊C4C22semidirect
194. #1750C22semidirect
195. C4×C22⋊C8C22semidirect
196. #1746C22semidirect
197. #1729C22semidirect
198. #1728C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33512
C2×#33492
C2×#33242
C2×#33182
#380842
#378702
#302872
#302552
#302492
#285442
#285332
#285232
#284312
#283992
#283892
#283612
#283572
#283302
#283212
#283032
#279462
#279442
#279412
#279282
#279202
#279112
#238132
#237352
#237312
#205612