Finite Group Databasebeta

← #6569785

Subgroups — #6569785

Order 512.

2288 conjugacy classes of subgroups.

The subgroup lattice has 1307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3345C211yesmaximal, characteristic, complemented
2C2×#3334C211yesmaximal, characteristic, complemented
3C2×#3306C211yesmaximal, characteristic, complemented
4C2×#3297C211yesmaximal, characteristic, complemented
5#38082C211yesmaximal, characteristic, complemented
6#37864C211yesmaximal, characteristic, complemented
7#30289C211yesmaximal, characteristic, complemented
8#30253C211yesmaximal, characteristic, complemented
9#30243C211yesmaximal, characteristic, complemented
10#28544C211yesmaximal, characteristic, complemented
11#28528C211yesmaximal, characteristic, complemented
12#28525C211yesmaximal, characteristic, complemented
13#28422C211yesmaximal, characteristic, complemented
14#28405C211yesmaximal, characteristic, complemented
15#28393C211yesmaximal, characteristic, complemented
16#28354C211yesmaximal, characteristic, complemented
17#28341C211yesmaximal, characteristic, complemented
18#28337C211yesmaximal, characteristic, complemented
19#28329C211yesmaximal, characteristic, complemented
20#28325C211yesmaximal, characteristic, complemented
21#28301C211yesmaximal, characteristic, complemented
22#27942C211yesmaximal, characteristic, complemented
23#27939C211yesmaximal, characteristic, complemented
24#27932C211yesmaximal, characteristic, complemented
25#27926C211yesmaximal, characteristic, complemented
26#27923C211yesmaximal, characteristic, complemented
27#27912C211yesmaximal, characteristic, complemented
28#23810C211yesmaximal, characteristic, complemented
29#23737C211yesmaximal, characteristic, complemented
30C2×#2092C211yesmaximal, characteristic, complemented
31#20557C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×#546C2211yescharacteristic
36#3345—28no—
37#3334—28no—
38#3306—28no—
39#3297—28no—
40C2×#501C2211yescharacteristic, complemented
41C2×#500C2211yescharacteristic, complemented
42C2×#489C2211yescharacteristic
43C2×#488C2211yescharacteristic
44C2×#484C2211yescharacteristic
45C2×#481C2211yescharacteristic
46C2×#481C2211yescharacteristic
47C2×#481C2211yescharacteristic, complemented
48C2×#482C2211yescharacteristic
49C2×#482C2211yescharacteristic, complemented
50C2×#483C2211yescharacteristic
51C2×#480C2211yescharacteristic
52C2×#480C2211yescharacteristic
53C2×#480C2211yescharacteristic
54C2×#480C2211yescharacteristic, complemented
55C2×#480C2211yescharacteristic, complemented
56C2×#478C2211yescharacteristic
57C2×#478C2211yescharacteristic, complemented
58C2×#476C2211yescharacteristic
59C2×#476C2211yescharacteristic, complemented
60C2×#474C2211yescharacteristic, complemented
61C2×#474C2211yescharacteristic, complemented
62C2×#469C2211yescharacteristic
63C2×#469C2211yescharacteristic, complemented
64C2×#466C2211yescharacteristic
65C2×#466C2211yescharacteristic
66C2×#466C2211yescharacteristic
67C2×#466C2211yescharacteristic, complemented
68C2×#465C2211yescharacteristic
69C2×#465C2211yescharacteristic
70C2×#463C2211yescharacteristic
71C2×#463C2211yescharacteristic
72C2×#449C2211yescharacteristic
73C2×#449C2211yescharacteristic
74C2×#447C2211yescharacteristic
75C2×#447C2211yescharacteristic
76C2×#442C2211yescharacteristic
77C2×#442C2211yescharacteristic, complemented
78C2×C4×D8C2211yescharacteristic
79C2×C4×D8C2211yescharacteristic, complemented
80C2×#435C2211yescharacteristic
81C2×C8×D4C2211yescharacteristic
82C2×#428C2211yescharacteristic, complemented
83C22×#107C2211yescharacteristic
84C22×#107C2211yescharacteristic, complemented
85C22×#106C2211yescharacteristic
86C2×#417C2211yescharacteristic
87C2×#416C2211yescharacteristic
88C22×#102C2211yescharacteristic
89C22×#102C2211yescharacteristic
90#2856C2211yescharacteristic
91#2850C2211yescharacteristic
92#2723—22no—
93#2706—22no—
94#2703—22no—
95#2696—22no—
96#2660C2211yescharacteristic, complemented
97#2640C2211yescharacteristic
98#2619C2211yescharacteristic
99#2619C2211yescharacteristic, complemented
100#2566C2211yescharacteristic, complemented
101#2563C2211yescharacteristic
102#2563C2211yescharacteristic, complemented
103#2544C2211yescharacteristic
104#2504C2211yescharacteristic
105#2504C2211yescharacteristic
106#2504C2211yescharacteristic, complemented
107#2503C2211yescharacteristic
108#2501C2211yescharacteristic
109#2500C2211yescharacteristic, complemented
110#2433C2211yescharacteristic
111#2431C2211yescharacteristic
112#2430—22no—
113#2425—22no—
114#2412—22no—
115#2404—22no—
116#2328C2211yescharacteristic
117#2328C2211yescharacteristic, complemented
118#2317C2211yescharacteristic, complemented
119#2311C2211yescharacteristic
120C2×#390C2211yescharacteristic
121#2290C2211yescharacteristic
122C2×#382C2211yescharacteristic
123#2097C2211yescharacteristic, complemented
124#2097C2211yescharacteristic, complemented
125#2097C2211yescharacteristic, complemented
126#2097C2211yescharacteristic, complemented
127#2095C2211yescharacteristic, complemented
128#2095C2211yescharacteristic, complemented
129#2095C2211yescharacteristic, complemented
130#2094C2211yescharacteristic, complemented
131#2093C2211yescharacteristic
132#2093C2211yescharacteristic
133#2093C2211yescharacteristic
134#2093C2211yescharacteristic
135#2092C2211yescharacteristic
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic
140#2092C2211yescharacteristic
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#2014C2211yescharacteristic, complemented
154#2012C2211yescharacteristic, complemented
155#2012C2211yescharacteristic, complemented
156#2011C2211yescharacteristic
157#2011C2211yescharacteristic
158#2011C2211yescharacteristic
159#2011C2211yescharacteristic
160#2011C2211yescharacteristic
161#2011C2211yescharacteristic
162#2011C2211yescharacteristic, complemented
163#1973C2211yescharacteristic, complemented
164#1973C2211yescharacteristic, complemented
165#1972C2211yescharacteristic
166#1972C2211yescharacteristic
167#1970C2211yescharacteristic
168#1970C2211yescharacteristic
169#1970C2211yescharacteristic
170#1970C2211yescharacteristic
171#1970C2211yescharacteristic
172#1970C2211yescharacteristic
173#1968C2211yescharacteristic, complemented
174#1968C2211yescharacteristic, complemented
175#1961C2211yescharacteristic
176#1961C2211yescharacteristic
177#1958C2211yescharacteristic, complemented
178#1958C2211yescharacteristic, complemented
179#1957C2211yescharacteristic
180#1957C2211yescharacteristic
181#1847C2211yescharacteristic, complemented
182#1847C2211yescharacteristic, complemented
183#1846C2211yescharacteristic, complemented
184#1846C2211yescharacteristic, complemented
185#1846C2211yescharacteristic, complemented
186#1846C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188C8×C4⋊C4C2211yescharacteristic, complemented
189#1768C2211yescharacteristic, complemented
190#1753C2211yescharacteristic, complemented
191#1752C2211yescharacteristic
192C8×C22⋊C4C2211yescharacteristic
193C8×C22⋊C4C2211yescharacteristic, complemented
194#1750C2211yescharacteristic, complemented
195C4×C22⋊C8C2211yescharacteristic
196#1746C2211yescharacteristic, complemented
197#1729C2211yescharacteristic, complemented
198C2×#336C2211yescharacteristic
199C22×#41—21no—
200C22×#41—21no—
201C22×#41C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#553—24no—
216#553—24no—
217#547—24no—
218#547—24no—
219#547—24no—
220#547—24no—
221#546—24no—
222#546—24no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#126—21no—
229C2×#125C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×#123—21no—
236C2×#123—21no—
237C2×#123—21no—
238C2×#123—22no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8C2311yescharacteristic
242C2×#121—21no—
243C2×#121—22no—
244C2×#121—21no—
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×#121C2311yescharacteristic
252C2×#120—21no—
253C2×#120—22no—
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C22⋊C4—22no—
268C22×C22⋊C4—21no—
269C22×C42C2311yescharacteristic
270#501—24no—
271#500—24no—
272#489—24no—
273#488—24no—
274#484—24no—
275#483—24no—
276#482—24no—
277#482—24no—
278#481—24no—
279#481—24no—
280#481—24no—
281#480—24no—
282#480—24no—
283#480—24no—
284#480—24no—
285#480—24no—
286#478—24no—
287#478—24no—
288#476—24no—
289#476—24no—
290#474—24no—
291#474—24no—
292#469—24no—
293#469—24no—
294#466—24no—
295#466—24no—
296#466—24no—
297#466—24no—
298#465—24no—
299#465—24no—
300#463—24no—
301#463—24no—
302#449—24no—
303#449—24no—
304#447—24no—
305#447—24no—
306#442—24no—
307#442—24no—
308C4×D8—24no—
309C4×D8—24no—
310#435D418yescomplemented
311C8×D4D418yescomplemented
312#428—24no—
313C2×#107—24no—
314C2×#107—24no—
315C2×#107C2311yescharacteristic
316C2×#107C2311yescharacteristic
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×#106C2311yescharacteristic
331C2×#106C2311yescharacteristic
332C2×#106C2311yescharacteristic
333C2×#106C2311yescharacteristic
334C2×#106C2311yescharacteristic
335C2×#106C2311yescharacteristic
336C2×#106C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×C4⋊C8C2311yescharacteristic
341C2×C4⋊C8C2311yescharacteristic
342#417—24no—
343#416—24no—
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#103C2311yescharacteristic
350C2×#102—24no—
351C2×#102—24no—
352C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
379C2×C22⋊C8C2311yescharacteristic
380C2×C22⋊C8C2311yescharacteristic
381C2×C22⋊C8C2311yescharacteristic
382C2×#97C2311yescharacteristic
383C2×#97C2311yescharacteristic
384C2×#97C2311yescharacteristic
385C2×C4×C8C2311yescharacteristic
386C2×C4×C8C2311yescharacteristic
387C2×C4×C8C2311yescharacteristic
388C2×C4×C8C2311yescharacteristic
389C2×C4×C8C2311yescharacteristic
390#400—22no—
391#399—22no—
392#398—22no—
393#397—22no—
394#397—22no—
395#397—22no—
396#397—22no—
397#396—22no—
398#395—22no—
399#394—22no—
400#394—22no—
401#394—22no—
402#394—22no—
403#393—22no—
404#393—22no—
405#393—22no—
406#392—22no—
407#392—22no—
408#392—22no—
409#392—22no—
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
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#390C2311yescharacteristic
428#389—22no—
429#388—22no—
430#388—22no—
431#388D412yes—
432#387D412yes—
433#386—22no—
434#386—22no—
435#386—22no—
436#386—22no—
437#386—22no—
438#386—22no—
439#386—22no—
440#386—22no—
441#386—22no—
442#386—22no—
443#386—22no—
444#386D412yes—
445#385—22no—
446#385—22no—
447#385D412yes—
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#382—22no—
452#382C2311yescharacteristic
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#381—22no—
462#380—22no—
463#380—22no—
464#380—22no—
465C4×C4⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468#376C2311yescharacteristic
469C2×#95—22no—
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480C25—21no—
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—44no—
488C2×#41—44no—
489C2×#41—84no—
490C2×#41—84no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C2×D412yes—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C2×M16—41no—
556C2×M16—41no—
557C2×M16C2×D414yes—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8C2×D414yes—
565C22×C8C2×D414yes—
566C22×C8C2×D414yes—
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C4⋊Q8—22no—
576C4⋊Q8—22no—
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579#127—22no—
580#127—41no—
581#127—41no—
582#127—41no—
583#127—41no—
584#127—41no—
585#126—44no—
586#125—22no—
587#125—22no—
588#124—22no—
589#124—22no—
590#124—41no—
591#124—41no—
592#123—44no—
593#123—44no—
594#123—44no—
595#123—44no—
596#123—44no—
597#123—44no—
598#123—84no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
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—22no—
615#121—22no—
616#121—22no—
617#121—44no—
618#121—44no—
619#121—84no—
620#120—44no—
621#120—84no—
622C4×D4—22no—
623C4×D4—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—41no—
636#117—41no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
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—21no—
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—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4C2×D412yes—
661C2×C4⋊C4C2×D412yes—
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
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—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—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—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—44no—
703C2×C22⋊C4—84no—
704C2×C22⋊C4C2×D412yes—
705C2×C22⋊C4C2×D412yes—
706C2×C22⋊C4C2×D412yes—
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—41no—
711C2×C42—41no—
712C2×C42C2×D412yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
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#107—22no—
730#107—22no—
731#107—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—
741#106—22no—
742C4⋊C8C2×D414yes—
743C4⋊C8C2×D414yes—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#102—22no—
751#102—22no—
752#102—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—
775#102—22no—
776C22⋊C8C2×D414yes—
777C22⋊C8C2×D414yes—
778C22⋊C8C2×D414yes—
779C22⋊C8C2×D414yes—
780#97—41no—
781#97—41no—
782#97C2×D414yes—
783C4×C8—41no—
784C4×C8—41no—
785C4×C8—41no—
786C4×C8—41no—
787C4×C8C2×D414yes—
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#95—22no—
798#95—22no—
799#95—22no—
800#95C2×D412yes—
801#95C2×D412yes—
802#95C2×D412yes—
803#95C2×D412yes—
804#95C2×D412yes—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—42no—
811C24—42no—
812C24—44no—
813C24—81no—
814C24—82no—
815C24C22×D411yescharacteristic
816C24C22×D411yescharacteristic
817#41—44no—
818#41—44no—
819#41—82no—
820#41—82no—
821#41—816no—
822#41—816no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—42no—
830C2×Q8—42no—
831C2×Q8—82no—
832C2×Q8—82no—
833C2×D4—24no—
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—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—42no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—82no—
882C2×D4—82no—
883C2×D4—81no—
884C2×D4—82no—
885C2×D4—82no—
886C2×D4—82no—
887C2×D4—82no—
888C2×D4—82no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—81no—
892C2×D4—82no—
893C2×D4—82no—
894C2×D4—82no—
895C2×D4—82no—
896C2×D4#12714yes—
897C2×D42−1+412yes—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—24no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—81no—
934C22×C4—82no—
935C22×C4—82no—
936C22×C4—82no—
937C22×C4—82no—
938C22×C4—82no—
939C22×C4—82no—
940C22×C4—82no—
941C22×C4C22×D412yes—
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×C4C2511yescharacteristic
954SD16—82no—
955SD16—82no—
956D8—44no—
957D8—44no—
958D8—44no—
959D8—44no—
960D8—82no—
961D8—82no—
962M16—44no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—44no—
980C2×C8—44no—
981C2×C8—44no—
982C2×C8C22×D412yes—
983C2×C8C22×D412yes—
984C2×C8C22×D412yes—
985C2×C8C22×D412yes—
986C2×C8C22×D412yes—
987C2×C8C22×D412yes—
988C2×C8C22×D412yes—
989C2×C8C22×D412yes—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—82no—
1023C4⋊C4—82no—
1024C4⋊C4—82no—
1025C4⋊C4#12714yes—
1026C22⋊C4—24no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—82no—
1045C22⋊C4—82no—
1046C22⋊C4—82no—
1047C22⋊C4—82no—
1048C22⋊C4—82no—
1049C22⋊C4—82no—
1050C22⋊C4—82no—
1051C22⋊C4—82no—
1052C22⋊C4—82no—
1053C22⋊C4—82no—
1054C22⋊C4—82no—
1055C22⋊C4—82no—
1056C22⋊C4—82no—
1057C22⋊C4—82no—
1058C22⋊C4#12714yes—
1059C22⋊C4#12714yes—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—42no—
1069C42—42no—
1070C42C22×D412yes—
1071C42C22×D412yes—
1072C23—22no—
1073C23—21no—
1074C23—21no—
1075C23—22no—
1076C23—21no—
1077C23—21no—
1078C23—22no—
1079C23—22no—
1080C23—42no—
1081C23—41no—
1082C23—41no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
1104C23—84no—
1105C23—88no—
1106C23—84no—
1107C23—164no—
1108C23—162no—
1109C23C2×#12712yes—
1110C23C2×#12712yes—
1111C23#57614yes—
1112C23C23×D411yescharacteristic
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—84no—
1118Q8—84no—
1119D4—28no—
1120D4—22no—
1121D4—22no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—84no—
1141D4—84no—
1142D4—84no—
1143D4—84no—
1144D4—84no—
1145D4—84no—
1146D4—84no—
1147D4—164no—
1148D4—164no—
1149D4—164no—
1150D4—162no—
1151D4—162no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—84no—
1202C2×C4—84no—
1203C2×C4—84no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4—84no—
1207C2×C4—84no—
1208C2×C4—84no—
1209C2×C4—162no—
1210C2×C4—162no—
1211C2×C4—162no—
1212C2×C4C2×#12712yes—
1213C2×C4C2×#12712yes—
1214C2×C4C2×#12712yes—
1215C2×C4C2×#12712yes—
1216C2×C4C23×D411yescharacteristic
1217C2×C4C23×D411yescharacteristic
1218C2×C4C2×2−1+411yescharacteristic
1219C2×C4#58511yescharacteristic
1220C2×C4#58511yescharacteristic
1221C2×C4#58511yescharacteristic
1222C8—22no—
1223C8—22no—
1224C8—22no—
1225C8—22no—
1226C8—22no—
1227C8—22no—
1228C8—22no—
1229C8—22no—
1230C22—24no—
1231C22—24no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—42no—
1238C22—42no—
1239C22—44no—
1240C22—42no—
1241C22—82no—
1242C22—81no—
1243C22—81no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—168no—
1265C22#315514yes—
1266C22C22×#12711yescharacteristic
1267C22#348511yescharacteristic
1268C22#348911yescharacteristic
1269C22C2×#57612yes—
1270C22#358412yes—
1271C4—22no—
1272C4—22no—
1273C4—22no—
1274C4—22no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4#348511yescharacteristic
1291C4#348511yescharacteristic
1292C4#348911yescharacteristic
1293C4#348911yescharacteristic
1294C2—24no—
1295C2—42no—
1296C2—82no—
1297C2—161no—
1298C2—161no—
1299C2—161no—
1300C2—161no—
1301C2#3606011yescharacteristic
1302C2C2×#315511yescharacteristic
1303C2#6064911yescharacteristic
1304C2#6177212yes—
1305C2#6221112yes—
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×#3334C2semidirect
3. C2×#3306C2semidirect
4. C2×#3297C2semidirect
5. #38082C2semidirect
6. #37864C2semidirect
7. #30289C2semidirect
8. #30253C2semidirect
9. #30243C2semidirect
10. #28544C2semidirect
11. #28528C2semidirect
12. #28525C2semidirect
13. #28422C2semidirect
14. #28405C2semidirect
15. #28393C2semidirect
16. #28354C2semidirect
17. #28341C2semidirect
18. #28337C2semidirect
19. #28329C2semidirect
20. #28325C2semidirect
21. #28301C2semidirect
22. #27942C2semidirect
23. #27939C2semidirect
24. #27932C2semidirect
25. #27926C2semidirect
26. #27923C2semidirect
27. #27912C2semidirect
28. #23810C2semidirect
29. #23737C2semidirect
30. C2×#2092C2semidirect
31. #20557C2semidirect
40. C2×#501C22semidirect
41. C2×#500C22semidirect
47. C2×#481C22semidirect
49. C2×#482C22semidirect
54. C2×#480C22semidirect
55. C2×#480C22semidirect
57. C2×#478C22semidirect
59. C2×#476C22semidirect
60. C2×#474C22semidirect
61. C2×#474C22semidirect
63. C2×#469C22semidirect
67. C2×#466C22semidirect
77. C2×#442C22semidirect
79. C2×C4×D8C22semidirect
82. C2×#428C22semidirect
84. C22×#107C22semidirect
96. #2660C22semidirect
99. #2619C22semidirect
100. #2566C22semidirect
102. #2563C22semidirect
106. #2504C22semidirect
109. #2500C22semidirect
117. #2328C22semidirect
118. #2317C22semidirect
123. #2097C22semidirect
124. #2097C22semidirect
125. #2097C22semidirect
126. #2097C22semidirect
127. #2095C22semidirect
128. #2095C22semidirect
129. #2095C22semidirect
130. #2094C22semidirect
145. #2092C22semidirect
146. #2092C22semidirect
147. #2092C22semidirect
148. #2092C22semidirect
149. #2092C22semidirect
150. #2092C22semidirect
151. #2092C22semidirect
152. #2092C22semidirect
153. #2014C22semidirect
154. #2012C22semidirect
155. #2012C22semidirect
162. #2011C22semidirect
163. #1973C22semidirect
164. #1973C22semidirect
173. #1968C22semidirect
174. #1968C22semidirect
177. #1958C22semidirect
178. #1958C22semidirect
181. #1847C22semidirect
182. #1847C22semidirect
183. #1846C22semidirect
184. #1846C22semidirect
185. #1846C22semidirect
186. #1846C22semidirect
187. #1771C22semidirect
188. C8×C4⋊C4C22semidirect
189. #1768C22semidirect
190. #1753C22semidirect
193. C8×C22⋊C4C22semidirect
194. #1750C22semidirect
196. #1746C22semidirect
197. #1729C22semidirect
310. #435D4semidirect
311. 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×#33342
C2×#33062
C2×#32972
#380822
#378642
#302892
#302532
#302432
#285442
#285282
#285252
#284222
#284052
#283932
#283542
#283412
#283372
#283292
#283252
#283012
#279422
#279392
#279322
#279262
#279232
#279122
#238102
#237372
C2×#20922
#205572