Finite Group Databasebeta

← #6467176

Subgroups — #6467176

Order 512.

2073 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3126C211yesmaximal, characteristic, complemented
2C2×#3119C211yesmaximal, characteristic
3#34276C211yesmaximal, characteristic, complemented
4C4×#540C211yesmaximal, characteristic, complemented
5#28294C211yesmaximal, characteristic, complemented
6#28293C211yesmaximal, characteristic, complemented
7#28260C211yesmaximal, characteristic, complemented
8#28257C211yesmaximal, characteristic, complemented
9#28209C211yesmaximal, characteristic, complemented
10#28208C211yesmaximal, characteristic, complemented
11#28160C211yesmaximal, characteristic, complemented
12#28158C211yesmaximal, characteristic, complemented
13#28119C211yesmaximal, characteristic, complemented
14#28118C211yesmaximal, characteristic, complemented
15#28116C211yesmaximal, characteristic, complemented
16#28115C211yesmaximal, characteristic, complemented
17#27655C211yesmaximal, characteristic, complemented
18#27654C211yesmaximal, characteristic, complemented
19#24219C211yesmaximal, characteristic, complemented
20#24219C211yesmaximal, characteristic, complemented
21#23693C211yesmaximal, characteristic, complemented
22#23692C211yesmaximal, characteristic, complemented
23#23689C211yesmaximal, characteristic, complemented
24#23689C211yesmaximal, characteristic, complemented
25#21507C211yesmaximal, characteristic, complemented
26#21504C211yesmaximal, characteristic, complemented
27C4×#463C211yesmaximal, characteristic, complemented
28C4×#461C211yesmaximal, characteristic, complemented
29#20813C211yesmaximal, characteristic, complemented
30#20746C211yesmaximal, characteristic, complemented
31#20745C211yesmaximal, characteristic, complemented
32C2×#540C2211yescharacteristic
33C2×#536C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#519C2211yescharacteristic
36#3126—28no—
37#3119—28no—
38C2×#481C2211yescharacteristic
39C2×#482C2211yescharacteristic
40C2×#482C2211yescharacteristic
41C2×#480C2211yescharacteristic
42C2×#479C2211yescharacteristic
43C2×#479C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#478C2211yescharacteristic
46C2×#460C2211yescharacteristic
47C2×#460C2211yescharacteristic
48C2×#460C2211yescharacteristic
49C2×#463C2211yescharacteristic
50C2×#463C2211yescharacteristic
51C2×#461C2211yescharacteristic
52C2×#461C2211yescharacteristic
53C2×#459C2211yescharacteristic
54C2×#449C2211yescharacteristic
55C2×#449C2211yescharacteristic
56C2×#448C2211yescharacteristic
57C2×#448C2211yescharacteristic
58C2×#442C2211yescharacteristic
59C2×#440C2211yescharacteristic
60C2×#440C2211yescharacteristic
61C2×#440C2211yescharacteristic
62C2×C4×SD16C2211yescharacteristic
63C2×C4×SD16C2211yescharacteristic
64C2×C4×SD16C2211yescharacteristic
65C2×C4×D8C2211yescharacteristic
66C2×#433C2211yescharacteristic
67C2×#433C2211yescharacteristic
68#2362—21no—
69#2362—21no—
70#2360—21no—
71#2360—21no—
72#2359—21no—
73#2359—21no—
74#2359—21no—
75#2359—21no—
76#2335—21no—
77#2335—21no—
78#2333—21no—
79#2333—21no—
80#2330C2211yescharacteristic
81#2328C2211yescharacteristic
82#2327C2211yescharacteristic
83#2327C2211yescharacteristic
84#2326C2211yescharacteristic
85#2326C2211yescharacteristic
86#2324C2211yescharacteristic
87#2324C2211yescharacteristic
88#2319C2211yescharacteristic
89#2319C2211yescharacteristic
90#2317C2211yescharacteristic
91#2314C2211yescharacteristic
92C4×C4⋊Q8C2211yescharacteristic
93C4×C4⋊Q8C2211yescharacteristic
94C4×#127C2211yescharacteristic
95C4×#125C2211yescharacteristic
96C4×#124C2211yescharacteristic
97C4×#124C2211yescharacteristic
98C4×#123—21no—
99C4×#123—21no—
100C4×#121—21no—
101C4×#121—21no—
102C4×#121C2211yescharacteristic
103C4×#121C2211yescharacteristic
104#2297C2211yescharacteristic
105C2×#391C2211yescharacteristic
106C42×D4C2211yescharacteristic
107C42×D4C2211yescharacteristic
108C4×#117C2211yescharacteristic
109#2085C2211yescharacteristic
110#2085C2211yescharacteristic
111#2084C2211yescharacteristic
112#2083C2211yescharacteristic
113#2073C2211yescharacteristic
114#2073C2211yescharacteristic
115#2071C2211yescharacteristic
116#2071C2211yescharacteristic
117#2068C2211yescharacteristic
118#2068C2211yescharacteristic
119#2068C2211yescharacteristic
120#2067C2211yescharacteristic
121#2066C2211yescharacteristic
122#2066C2211yescharacteristic
123#2066C2211yescharacteristic
124#2065C2211yescharacteristic
125#2055C2211yescharacteristic
126#2055C2211yescharacteristic
127#2055C2211yescharacteristic
128#2055C2211yescharacteristic
129#2055C2211yescharacteristic
130#2055C2211yescharacteristic
131#2054C2211yescharacteristic
132#2054C2211yescharacteristic
133#2043C2211yescharacteristic
134#2043C2211yescharacteristic
135#2042C2211yescharacteristic
136#2042C2211yescharacteristic
137#2013C2211yescharacteristic
138#2013C2211yescharacteristic
139#2012C2211yescharacteristic
140#2012C2211yescharacteristic
141#1983C2211yescharacteristic
142#1983C2211yescharacteristic
143#1981C2211yescharacteristic
144#1981C2211yescharacteristic
145#1949C2211yescharacteristic
146#1949C2211yescharacteristic
147#1948C2211yescharacteristic
148#1947C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1928C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1926C2211yescharacteristic
156#1925C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1877C2211yescharacteristic
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1843C2211yescharacteristic
166#1843C2211yescharacteristic
167#1831C2211yescharacteristic
168#1831C2211yescharacteristic
169#1825C2211yescharacteristic
170#1825C2211yescharacteristic
171#1824C2211yescharacteristic
172#1823C2211yescharacteristic
173#1805C2211yescharacteristic
174#1805C2211yescharacteristic
175#1805C2211yescharacteristic
176#1804C2211yescharacteristic
177#1804C2211yescharacteristic
178#1804C2211yescharacteristic
179#1803C2211yescharacteristic
180#1803C2211yescharacteristic
181#1803C2211yescharacteristic
182#1802C2211yescharacteristic
183#1802C2211yescharacteristic
184#1802C2211yescharacteristic
185#1798C2211yescharacteristic
186#1798C2211yescharacteristic
187#1797C2211yescharacteristic
188#1797C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1787C2211yescharacteristic
192#1787C2211yescharacteristic
193#1768C2211yescharacteristic
194#1768C2211yescharacteristic
195#1767C2211yescharacteristic
196C4×C4⋊C8C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C4×#103C2211yescharacteristic
204C4×#102C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215#540—24no—
216#540D418yes—
217#536—24no—
218#536—24no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235#520—24no—
236#520—24no—
237#519—24no—
238#519—24no—
239C2×C4×Q8—21no—
240C2×C4×Q8—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117—21no—
262C2×#117—21no—
263C2×#117—21no—
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C22×C4⋊C4—21no—
268C22×C4⋊C4C2311yescharacteristic
269C22×C42—21no—
270C22×C42—21no—
271C22×C42C2311yescharacteristic
272#482—24no—
273#482—24no—
274#481—24no—
275#480—24no—
276#479—24no—
277#479—24no—
278#479—24no—
279#478—24no—
280#463—24no—
281#463—24no—
282#461—24no—
283#461—24no—
284#460—24no—
285#460—24no—
286#460—24no—
287#459—24no—
288#449—24no—
289#449—24no—
290#448—24no—
291#448—24no—
292#442—24no—
293#440—24no—
294#440—24no—
295#440—24no—
296C4×SD16—24no—
297C4×SD16—24no—
298C4×SD16—24no—
299C4×D8—24no—
300#433—24no—
301#433—24no—
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×C22⋊C8C2311yescharacteristic
355C2×C22⋊C8C2311yescharacteristic
356C2×C22⋊C8C2311yescharacteristic
357C2×C22⋊C8C2311yescharacteristic
358C2×#97C2311yescharacteristic
359C2×#97C2311yescharacteristic
360C2×C4×C8C2311yescharacteristic
361C2×C4×C8C2311yescharacteristic
362#391—21no—
363#391—21no—
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#382C2311yescharacteristic
446#382C2311yescharacteristic
447#382C2311yescharacteristic
448#381—21no—
449#381—21no—
450#380—21no—
451#380—21no—
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454C4×C4⋊C4—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4D411yescharacteristic
461C4×C4⋊C4D411yescharacteristic
462C4×C4⋊C4D411yescharacteristic
463C4×C4⋊C4D411yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4—21no—
475C4×C22⋊C4—21no—
476C4×C22⋊C4—21no—
477C4×C22⋊C4—21no—
478C4×C22⋊C4—21no—
479C4×C22⋊C4—21no—
480C4×C22⋊C4—21no—
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483C4×C22⋊C4—21no—
484C4×C22⋊C4D411yescharacteristic
485C4×C22⋊C4D411yescharacteristic
486C4×C22⋊C4D411yescharacteristic
487C4×C22⋊C4D411yescharacteristic
488#376C2311yescharacteristic
489#376C2311yescharacteristic
490C2×#95—21no—
491C2×#95—21no—
492C43C2311yescharacteristic
493C43C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C22×Q8—22no—
525C22×Q8—22no—
526C22×Q8—21no—
527C22×Q8—22no—
528C22×Q8—22no—
529C22×Q8—41no—
530C22×Q8—41no—
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C2×D411yescharacteristic
554C23×C4C2×D411yescharacteristic
555C23×C4C2411yescharacteristic
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—41no—
579C2×D8—41no—
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C4⋊Q8—22no—
589C4⋊Q8—22no—
590C4⋊Q8—22no—
591C4⋊Q8#4114yes—
592#127—22no—
593#127C2×D414yes—
594#125—22no—
595#125C2×D414yes—
596#124—22no—
597#124—22no—
598#124—22no—
599#124#4114yes—
600#123—28no—
601#123—28no—
602#123—28no—
603#123—28no—
604C22⋊Q8—28no—
605C22⋊Q8—28no—
606#121—22no—
607#121—22no—
608#121—28no—
609#121—28no—
610#121C2×D414yes—
611#121C2×D414yes—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—22no—
617C4×Q8—22no—
618C4×Q8—22no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8—22no—
622C4×Q8—22no—
623C4×Q8—22no—
624C4×Q8—44no—
625C4×Q8—44no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—44no—
641C4×D4—44no—
642C4×D4—82no—
643C4×D4—82no—
644C4×D4—82no—
645C4×D4—82no—
646C4×D4C2×D414yes—
647C4×D4C2×D414yes—
648#117—22no—
649#117—22no—
650#117—22no—
651#117—22no—
652#117—44no—
653#117—44no—
654#117—44no—
655#117C2×D414yes—
656#117#4114yes—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—44no—
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—41no—
744C2×C42—41no—
745C2×C42—82no—
746C2×C42—82no—
747C2×C42C2×D411yescharacteristic
748C2×C42C2×D411yescharacteristic
749C2×C42C2×D411yescharacteristic
750C2×C42C2×D411yescharacteristic
751C2×C42C2×D411yescharacteristic
752C2×C42C2×D411yescharacteristic
753C2×C42C2×D411yescharacteristic
754C2×C42C2×D411yescharacteristic
755C2×C42C2×D411yescharacteristic
756C2×C42C2×D411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763#107—22no—
764#107—22no—
765#107—22no—
766#107—22no—
767#106—22no—
768#106—22no—
769#106—22no—
770#106—22no—
771C4⋊C8—22no—
772C4⋊C8—22no—
773C4⋊C8—22no—
774C4⋊C8—22no—
775C4⋊C8—22no—
776C4⋊C8—22no—
777C4⋊C8—22no—
778C4⋊C8—22no—
779C4⋊C8—41no—
780C4⋊C8—41no—
781C4⋊C8—41no—
782C4⋊C8—41no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—41no—
796#103—41no—
797#103—41no—
798#103—41no—
799#103—41no—
800#103—41no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—22no—
810#102—22no—
811#102—22no—
812#102—22no—
813#102—41no—
814#102—41no—
815C22⋊C8—22no—
816C22⋊C8—22no—
817C22⋊C8—22no—
818C22⋊C8—22no—
819#97—22no—
820#97—22no—
821C4×C8—22no—
822C4×C8—22no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95C2×D411yescharacteristic
854#95C2×D411yescharacteristic
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861C24—21no—
862C24—21no—
863C24—21no—
864C24C22×D411yescharacteristic
865#41—44no—
866#41—44no—
867#41—44no—
868#41—44no—
869C2×Q8—24no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—44no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8C2×#4112yes—
892C2×Q8C2×#4112yes—
893C2×Q8C2×#4112yes—
894C2×D4—24no—
895C2×D4—24no—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—24no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4C22×D412yes—
925C2×D4C22×D412yes—
926C2×D4C2×#4112yes—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—22no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D412yes—
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C2×#4112yes—
998C22×C4C2511yescharacteristic
999SD16—44no—
1000SD16—44no—
1001SD16—44no—
1002SD16—44no—
1003SD16—44no—
1004SD16—44no—
1005D8—44no—
1006D8—44no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4#12114yes—
1075C4⋊C4#12114yes—
1076C4⋊C4C22×D412yes—
1077C4⋊C4C22×D412yes—
1078C22⋊C4—24no—
1079C22⋊C4—24no—
1080C22⋊C4—24no—
1081C22⋊C4—24no—
1082C22⋊C4—24no—
1083C22⋊C4—24no—
1084C22⋊C4—24no—
1085C22⋊C4—24no—
1086C22⋊C4—22no—
1087C22⋊C4—22no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4#12114yes—
1110C22⋊C4#12114yes—
1111C42—22no—
1112C42—22no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—41no—
1120C42—41no—
1121C42—41no—
1122C42—41no—
1123C42—41no—
1124C42—41no—
1125C42—41no—
1126C42—41no—
1127C42—42no—
1128C42—42no—
1129C42—42no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42—42no—
1136C42—81no—
1137C42—81no—
1138C42—81no—
1139C42—81no—
1140C42C22×D412yes—
1141C42C22×D412yes—
1142C42C2×#4112yes—
1143C42C2×#4112yes—
1144C42C2×#4112yes—
1145C42C2×#4112yes—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—22no—
1153C23—22no—
1154C23—22no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23C2×#12112yes—
1174C23C23×D411yescharacteristic
1175Q8—22no—
1176Q8—22no—
1177Q8—22no—
1178Q8—22no—
1179Q8—22no—
1180Q8—22no—
1181Q8—48no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188D4—22no—
1189D4—22no—
1190D4—22no—
1191D4—22no—
1192D4—22no—
1193D4—22no—
1194D4—48no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—84no—
1202D4—84no—
1203D4—84no—
1204D4—84no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—48no—
1246C2×C4—48no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—82no—
1282C2×C4—84no—
1283C2×C4—84no—
1284C2×C4—84no—
1285C2×C4—84no—
1286C2×C4—84no—
1287C2×C4—84no—
1288C2×C4—82no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4C2×#12112yes—
1293C2×C4C2×#12112yes—
1294C2×C4C2×#12112yes—
1295C2×C4C2×#12112yes—
1296C2×C4C2×#12112yes—
1297C2×C4#52512yes—
1298C2×C4#52512yes—
1299C2×C4#57712yes—
1300C2×C4C23×D411yescharacteristic
1301C2×C4C22×#4111yescharacteristic
1302C2×C4C22×#4111yescharacteristic
1303C2×C4C22×#4111yescharacteristic
1304C2×C4#58511yescharacteristic
1305C2×C4#58511yescharacteristic
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C22—22no—
1315C22—22no—
1316C22—22no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22C22×#12111yescharacteristic
1343C22C2×#52511yescharacteristic
1344C22#344911yescharacteristic
1345C22C2×#57711yescharacteristic
1346C22#358411yescharacteristic
1347C22#358511yescharacteristic
1348C22#358611yescharacteristic
1349C4—22no—
1350C4—22no—
1351C4—22no—
1352C4—22no—
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—42no—
1358C4—42no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—42no—
1363C4—42no—
1364C4—42no—
1365C4—41no—
1366C4—41no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4D4×#4111yescharacteristic
1376C4D4×#4111yescharacteristic
1377C4#347511yescharacteristic
1378C4#347511yescharacteristic
1379C2—42no—
1380C2—82no—
1381C2—82no—
1382C2—82no—
1383C2#3493511yescharacteristic
1384C2#6042911yescharacteristic
1385C2#6043011yescharacteristic
1386C2#6057211yescharacteristic
1387C2#6057611yescharacteristic
1388C2#6097911yescharacteristic
1389C2#6098411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3119C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3126C2semidirect
3. #34276C2semidirect
4. C4×#540C2semidirect
5. #28294C2semidirect
6. #28293C2semidirect
7. #28260C2semidirect
8. #28257C2semidirect
9. #28209C2semidirect
10. #28208C2semidirect
11. #28160C2semidirect
12. #28158C2semidirect
13. #28119C2semidirect
14. #28118C2semidirect
15. #28116C2semidirect
16. #28115C2semidirect
17. #27655C2semidirect
18. #27654C2semidirect
19. #24219C2semidirect
20. #24219C2semidirect
21. #23693C2semidirect
22. #23692C2semidirect
23. #23689C2semidirect
24. #23689C2semidirect
25. #21507C2semidirect
26. #21504C2semidirect
27. C4×#463C2semidirect
28. C4×#461C2semidirect
29. #20813C2semidirect
30. #20746C2semidirect
31. #20745C2semidirect

Maximal subgroups

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

subgroupindex
C2×#31262
C2×#31192
#342762
C4×#5402
#282942
#282932
#282602
#282572
#282092
#282082
#281602
#281582
#281192
#281182
#281162
#281152
#276552
#276542
#242192
#236932
#236922
#236892
#215072
#215042
C4×#4632
C4×#4612
#208132
#207462
#207452