Finite Group Databasebeta

← #72270520

Subgroups — #72270520

Order 1536.

1564 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10947849C211yesmaximal, characteristic, complemented
2#10795562C211yesmaximal, characteristic, complemented
3#10713827C212yesmaximal, complemented
4#10713459C212yesmaximal, complemented
5#10712662C211yesmaximal, characteristic, complemented
6#10712652C211yesmaximal, characteristic, complemented
7#10712647C211yesmaximal, characteristic, complemented
8#10712637C211yesmaximal, characteristic, complemented
9#10710471C212yesmaximal, complemented
10#10710457C212yesmaximal, complemented
11C3×#60698C211yesmaximal, characteristic
12#495573—31nomaximal, Sylow
13C3×#3460—21no—
14C3×#3184C412yescomplemented
15C3×#3183C412yescomplemented
16C3×#3180—22no—
17C3×#3179—22no—
18C3×#3176C412yescomplemented
19C3×#3173C412yescomplemented
20C3×#3163C2211yescharacteristic
21C3×#3155C2211yescharacteristic
22C3×#3136—21no—
23C3×#3062—21no—
24C3×#3060C2211yescharacteristic
25C3×#3058C2211yescharacteristic
26C3×C4×AGL(1,ℤ/8)—21no—
27C3×#2943C2211yescharacteristic
28C2×C3×#442C2211yescharacteristic
29C3×#2875C2211yescharacteristic
30#83780C2211yescharacteristic
31#83780C2211yescharacteristic
32#72080C2212yes—
33#72076C2212yes—
34C2×#4563C2212yes—
35#72033C2212yes—
36#72014C2211yescharacteristic
37#72012C2211yescharacteristic
38#72011—21no—
39#71644—21no—
40#69896C2212yes—
41#69895—21no—
42#69884—22no—
43#69884C2212yes—
44#69871—21no—
45#69829C2212yes—
46C2×#4466—22no—
47C2×#4466C2212yes—
48#67727C2212yes—
49#67725C2212yes—
50#67721C2212yes—
51#67720C2212yes—
52#60698D311yescharacteristic
53#33329—31no—
54#20788—31no—
55#13291—32no—
56#13215—32no—
57#13079—31no—
58#13077—31no—
59#13076—31no—
60#13074—31no—
61#12649—32no—
62#12647—32no—
63C2×C3×AGL(1,ℤ/8)—21no—
64C2×C3×#135C2311yescharacteristic
65C22×C3×D8C2311yescharacteristic
66C2×C3×#131D411yescharacteristic
67C2×C3×#131C2311yescharacteristic
68C3×#544—21no—
69C3×#542—22no—
70C3×#542—41no—
71C3×#540—22no—
72C3×#540—41no—
73C3×#538—42no—
74C3×#537—21no—
75C3×#535—21no—
76C3×#535—21no—
77C3×#532—22no—
78C3×#532—41no—
79C3×#529—22no—
80C3×#529—41no—
81C3×#525—42no—
82C3×C4×#41—21no—
83C3×C4×#41D411yescharacteristic
84C2×C3×C4×D4—21no—
85C3×#501—22no—
86C3×#499C2×C412yes—
87C3×#498C2×C412yes—
88C3×#496—22no—
89C3×#495C2×C412yes—
90C3×#493C2×C412yes—
91C3×#490—22no—
92C3×#489—22no—
93C3×#488—22no—
94C3×#486—22no—
95C3×#470C2×C412yes—
96C3×#469—22no—
97C3×#469C2×C412yes—
98C3×#469C2×C412yes—
99C3×#469C2×C412yes—
100C3×#468—22no—
101C3×#466—22no—
102C3×#466—22no—
103C3×#465—22no—
104C3×#465—22no—
105C3×#442—22no—
106C3×#442—21no—
107C3×#442—21no—
108C3×#442C2×C412yes—
109C3×#442C2×C411yescharacteristic
110C3×#442C2×C412yes—
111C3×#442C2×C411yescharacteristic
112C3×#441C2×C411yescharacteristic
113C3×#441C2×C411yescharacteristic
114C3×#440—22no—
115C3×#440—21no—
116C3×#440—21no—
117C3×C4×SD16—22no—
118C3×C4×D8—22no—
119C3×#428—21no—
120C3×#427C2311yescharacteristic
121C2×C3×#106C2311yescharacteristic
122C3×#418—21no—
123C3×#417—21no—
124C3×#416—21no—
125C2×C3×#102—21no—
126C3×#405C2×C412yes—
127C3×#405D411yescharacteristic
128C3×#405D412yes—
129C3×#405C2311yescharacteristic
130C3×C4×M16C2×C412yes—
131C3×C4×M16D411yescharacteristic
132C2×C3×#97D412yes—
133C2×C3×#97C2311yescharacteristic
134#5240—21no—
135#5237—21no—
136#5140—24no—
137#5140—24no—
138C2×#819C2312yes—
139#5106C2312yes—
140#5101—22no—
141C2×#812—22no—
142C2×#812—22no—
143C2×#812C2312yes—
144C2×#812C2312yes—
145#4567—24no—
146#4566—24no—
147#4563—24no—
148#4562—24no—
149C3⋊#338—21no—
150#4557—21no—
151#4556—22no—
152#4531—22no—
153#4523—22no—
154#4466—22no—
155#4466—24no—
156#4466—22no—
157#3460—21no—
158#3407—31no—
159#3407—31no—
160#3184Dic312yescomplemented
161#3183Dic312yescomplemented
162#3180—22no—
163#3179—22no—
164#3176Dic312yescomplemented
165#3173Dic312yescomplemented
166#3163C2×D311yescharacteristic
167#3155C2×D311yescharacteristic
168#3136—21no—
169#3062—21no—
170#3060C2×D311yescharacteristic
171#3058C2×D311yescharacteristic
172C4×AGL(1,ℤ/8)—21no—
173#2943C2×D311yescharacteristic
174C2×#442C2×D311yescharacteristic
175#2875C2×D311yescharacteristic
176C2×#361—32no—
177#2145—32no—
178#2143—32no—
179#2140—32no—
180#2110—32no—
181#2110—62no—
182C2×#347—32no—
183C2×#347—62no—
184#1841—61no—
185#1833—32no—
186#1827—61no—
187#1813—31no—
188#1812—31no—
189#1773—32no—
190#1757—61no—
191#1747—61no—
192#1389—32no—
193#1386—32no—
194#1384—32no—
195#1383—32no—
196C2×C3×#41—21no—
197C2×C3×#41—42no—
198C2×C3×#41C2×D411yescharacteristic
199C22×C3×D4—21no—
200C23×C3×C4—41no—
201C3×AGL(1,ℤ/8)—44no—
202C3×#135—22no—
203C3×#135—22no—
204C2×C3×Q16C22×C411yescharacteristic
205C2×C3×SD16—22no—
206C2×C3×SD16—21no—
207C2×C3×D8—22no—
208C2×C3×D8—21no—
209C2×C3×D8—22no—
210C2×C3×D8—22no—
211C2×C3×D8C22×C412yes—
212C2×C3×D8C22×C411yescharacteristic
213C3×#131—22no—
214C3×#131—22no—
215C3×#131—42no—
216C2×C3×M16C22⋊C412yes—
217C2×C3×M16C22×C412yes—
218C2×C3×M16C2×D411yescharacteristic
219C2×C3×M16C2×D411yescharacteristic
220C22×C3×C8C22⋊C412yes—
221C22×C3×C8C2×D411yescharacteristic
222C22×C3×C8C2×D412yes—
223C22×C3×C8C2411yescharacteristic
224C3×C4⋊Q8—22no—
225C3×C4⋊Q8—41no—
226C3×#127—22no—
227C3×#127—41no—
228C3×#126—42no—
229C3×#126—42no—
230C3×#125—22no—
231C3×#125—41no—
232C3×#124—22no—
233C3×#124—42no—
234C3×#124—42no—
235C3×#124—41no—
236C3×#123—42no—
237C3×#123—42no—
238C3×#123—42no—
239C3×#123—42no—
240C3×C22⋊Q8—22no—
241C3×C22⋊Q8—42no—
242C3×C22⋊Q8—42no—
243C3×C22⋊Q8—41no—
244C3×#121—22no—
245C3×#121—22no—
246C3×#121—22no—
247C3×#121—42no—
248C3×#121—42no—
249C3×#121—41no—
250C3×#121—41no—
251C3×#121—42no—
252C3×#121—42no—
253C3×#121—41no—
254C3×#120—42no—
255C3×#120—42no—
256C3×C4×Q8—21no—
257C3×C4×Q8—21no—
258C3×C4×Q8—21no—
259C3×C4×D4—22no—
260C3×C4×D4—21no—
261C3×C4×D4—21no—
262C3×C4×D4—22no—
263C3×C4×D4—22no—
264C3×C4×D4—21no—
265C3×C4×D4—41no—
266C3×C4×D4—41no—
267C3×C4×D4—42no—
268C3×C4×D4—41no—
269C3×C4×D4—41no—
270C3×C4×D4—42no—
271C3×#117—21no—
272C3×#117—41no—
273C3×#117—42no—
274C3×#117C22⋊C412yes—
275C3×#117C2×D411yescharacteristic
276C2×C3×C4⋊C4—21no—
277C2×C3×C22⋊C4—41no—
278C2×C3×C42—41no—
279C2×C3×C42C22⋊C412yes—
280C2×C3×C42C2×D411yescharacteristic
281#926—22no—
282C2×#208—22no—
283C3×#107—22no—
284C3×#107—21no—
285C3×#106—22no—
286C3×#106—21no—
287C3×#106C22×C412yes—
288C3×#106C22×C411yescharacteristic
289C3×#106C22×C411yescharacteristic
290C3×#103—21no—
291C3×#103—21no—
292C3×#103—22no—
293C3×#102—22no—
294C3×#102—22no—
295C3×#102—21no—
296C3×#102—21no—
297C3×#102—22no—
298C3×#102—22no—
299C3×#102—22no—
300C3×#97C22⋊C412yes—
301C3×#97C22⋊C412yes—
302C3×#97C22×C411yescharacteristic
303C3×#97C22×C411yescharacteristic
304C3×#97C2×D411yescharacteristic
305C3×#97C2×D412yes—
306C3×#97C2×D411yescharacteristic
307C3×C4×C8C22⋊C412yes—
308C3×C4×C8C22⋊C412yes—
309C3×C4×C8C22×C412yes—
310#836—41no—
311#834—42no—
312#833—41no—
313#819—22no—
314#819—22no—
315#818—22no—
316#817—22no—
317#815—42no—
318C8×Dic3—42no—
319#812—24no—
320#812—24no—
321#812—22no—
322#812—22no—
323#812—22no—
324#812#4114yescomplemented
325C2×C3⋊C16—24no—
326C2×C3⋊C16—24no—
327C2×C3⋊C16—22no—
328C2×C3⋊C16#4114yescomplemented
329C2×AGL(1,ℤ/8)—21no—
330C2×#135C22×D311yescharacteristic
331C22×D8C22×D311yescharacteristic
332C2×#131#6711yescharacteristic
333C2×#131C22×D311yescharacteristic
334#544—21no—
335#542—22no—
336#542—41no—
337#540—22no—
338#540—41no—
339#538—42no—
340#537—21no—
341#535—21no—
342#535—21no—
343#532—22no—
344#532—41no—
345#529—22no—
346#529—41no—
347#525—42no—
348C4×#41—21no—
349C4×#41#6711yescharacteristic
350C2×C4×D4—21no—
351#504—64no—
352#504—64no—
353C2×M32—32no—
354C2×M32—32no—
355C2×M32—62no—
356C2×M32—62no—
357#501—22no—
358#499C2×Dic312yes—
359#498C2×Dic312yes—
360#496—22no—
361#495C2×Dic312yes—
362#493C2×Dic312yes—
363#490—22no—
364#489—22no—
365#488—22no—
366#486—22no—
367#470C2×Dic312yes—
368#469—22no—
369#469C2×Dic312yes—
370#469C2×Dic312yes—
371#469C2×Dic312yes—
372#468—22no—
373#466—22no—
374#466—22no—
375#465—22no—
376#465—22no—
377#442—22no—
378#442—21no—
379#442—21no—
380#442C2×Dic312yes—
381#442C2×Dic311yescharacteristic
382#442C2×Dic312yes—
383#442C2×Dic311yescharacteristic
384#441C2×Dic311yescharacteristic
385#441C2×Dic311yescharacteristic
386#440—22no—
387#440—21no—
388#440—21no—
389C4×SD16—22no—
390C4×D8—22no—
391C2×#108—32no—
392#428—21no—
393#427—32no—
394#427C22×D311yescharacteristic
395C2×#106C22×D311yescharacteristic
396#418—21no—
397#417—21no—
398#416—21no—
399C2×#102—21no—
400#413—61no—
401#410—61no—
402#405—62no—
403#405C2×Dic312yes—
404#405#6711yescharacteristic
405#405#6712yes—
406#405C22×D311yescharacteristic
407C4×M16C2×Dic312yes—
408C4×M16#6711yescharacteristic
409C2×#97#6712yes—
410C2×#97C22×D311yescharacteristic
411#361—64no—
412#360—64no—
413#359—64no—
414#357—64no—
415#347—62no—
416#347—62no—
417#347—64no—
418#344—62no—
419#339—62no—
420#338—61no—
421H(3,ℤ/4)—61no—
422H(3,ℤ/4)—62no—
423C24×C3—41no—
424C3×#41—22no—
425C3×#41—22no—
426C3×#41—42no—
427C3×#41—42no—
428C3×#41—164no—
429C2×C3×Q8—21no—
430C2×C3×Q8—42no—
431C2×C3×Q8AGL(1,ℤ/8)11yescharacteristic
432C2×C3×D4—22no—
433C2×C3×D4—21no—
434C2×C3×D4—42no—
435C2×C3×D4—42no—
436C2×C3×D4—41no—
437C2×C3×D4—42no—
438C2×C3×D4—42no—
439C2×C3×D4—42no—
440C2×C3×D4—42no—
441C2×C3×D4—41no—
442C2×C3×D4—42no—
443C2×C3×D4AGL(1,ℤ/8)11yescharacteristic
444C2×C3×D4AGL(1,ℤ/8)12yes—
445C22×C3×C4—21no—
446C22×C3×C4—22no—
447C22×C3×C4—41no—
448C22×C3×C4—42no—
449C22×C3×C4—41no—
450C22×C3×C4—42no—
451C22×C3×C4—41no—
452C22×C3×C4—41no—
453C22×C3×C4—162no—
454C22×C3×C4C2×C22⋊C412yes—
455C22×C3×C4C22×D411yescharacteristic
456C3×Q16—22no—
457C3×SD16—44no—
458C3×SD16—41no—
459C3×SD16—41no—
460C3×D8—24no—
461C3×D8—22no—
462C3×D8—44no—
463C3×D8—41no—
464C3×D8—41no—
465C3×M16—22no—
466C3×M16—22no—
467C3×M16—24no—
468C3×M16—42no—
469C2×C3×C8—22no—
470C2×C3×C8—22no—
471C2×C3×C8—22no—
472C2×C3×C8—42no—
473C2×C3×C8C2×C22⋊C412yes—
474C2×C3×C8C2×C22⋊C411yescharacteristic
475C2×C3×C8C2×C22⋊C412yes—
476C2×C3×C8C2×C22⋊C411yescharacteristic
477C2×C3×C8C23×C411yescharacteristic
478C2×C3×C8C22×D411yescharacteristic
479C2×C3×C8C2×#4112yes—
480C2×C3×C8C2×#4112yes—
481C3×C4⋊C4—21no—
482C3×C4⋊C4—22no—
483C3×C4⋊C4—22no—
484C3×C4⋊C4—21no—
485C3×C4⋊C4—21no—
486C3×C4⋊C4—41no—
487C3×C4⋊C4—41no—
488C3×C4⋊C4—42no—
489C3×C4⋊C4—42no—
490C3×C4⋊C4—42no—
491C3×C4⋊C4—41no—
492C3×C4⋊C4—42no—
493C3×C22⋊C4—21no—
494C3×C22⋊C4—22no—
495C3×C22⋊C4—42no—
496C3×C22⋊C4—42no—
497C3×C22⋊C4—41no—
498C3×C22⋊C4—41no—
499C3×C22⋊C4—42no—
500C3×C22⋊C4—42no—
501C3×C22⋊C4—41no—
502C3×C22⋊C4—42no—
503C3×C22⋊C4—42no—
504C3×C22⋊C4—42no—
505C3×C22⋊C4—42no—
506C3×C42—21no—
507C3×C42—22no—
508C3×C42—41no—
509C3×C42—41no—
510C3×C42—41no—
511C3×C42C2×C22⋊C411yescharacteristic
512C3×C42C2×C22⋊C412yes—
513C3×C42C2×C22⋊C411yescharacteristic
514#217—42no—
515C4⋊Dic3—42no—
516C4×Dic3—42no—
517#208—42no—
518#208—42no—
519C2×C3⋊C8—42no—
520C3⋊C16—24no—
521C3⋊C16—24no—
522C2×#41—21no—
523C2×#41—42no—
524C2×#41C2×#6711yescharacteristic
525C22×D4—21no—
526C23×C4—41no—
527AGL(1,ℤ/8)—44no—
528#135—22no—
529#135—22no—
530C2×Q16C22×Dic311yescharacteristic
531C2×SD16—22no—
532C2×SD16—21no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—21no—
537C2×D8C22×Dic312yes—
538C2×D8C22×Dic311yescharacteristic
539#131—22no—
540#131—22no—
541#131—42no—
542C2×M16—62no—
543C2×M16#21712yes—
544C2×M16C22×Dic312yes—
545C2×M16C2×#6711yescharacteristic
546C2×M16C2×#6711yescharacteristic
547C22×C8#21712yes—
548C22×C8C2×#6711yescharacteristic
549C22×C8C2×#6712yes—
550C22×C8C23×D311yescharacteristic
551C4⋊Q8—22no—
552C4⋊Q8—41no—
553#127—22no—
554#127—41no—
555#126—42no—
556#126—42no—
557#125—22no—
558#125—41no—
559#124—22no—
560#124—42no—
561#124—42no—
562#124—41no—
563#123—42no—
564#123—42no—
565#123—42no—
566#123—42no—
567C22⋊Q8—22no—
568C22⋊Q8—42no—
569C22⋊Q8—42no—
570C22⋊Q8—41no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—42no—
575#121—42no—
576#121—41no—
577#121—41no—
578#121—42no—
579#121—42no—
580#121—41no—
581#120—42no—
582#120—42no—
583C4×Q8—21no—
584C4×Q8—21no—
585C4×Q8—21no—
586C4×D4—22no—
587C4×D4—21no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—42no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—42no—
598#117—21no—
599#117—41no—
600#117—42no—
601#117—62no—
602#117#21712yes—
603#117C2×#6711yescharacteristic
604C2×C4⋊C4—21no—
605C2×C22⋊C4—41no—
606C2×C42—41no—
607C2×C42#21712yes—
608C2×C42C2×#6711yescharacteristic
609M32—34no—
610M32—64no—
611M32—64no—
612M32—62no—
613M32—62no—
614M32—62no—
615C2×C16—34no—
616C2×C16—64no—
617C2×C16—64no—
618C2×C16—62no—
619#108—62no—
620#108—62no—
621#107—22no—
622#107—21no—
623#107—62no—
624#106—22no—
625#106—21no—
626#106—62no—
627#106C22×Dic312yes—
628#106C22×Dic311yescharacteristic
629#106C22×Dic311yescharacteristic
630#103—21no—
631#103—21no—
632#103—22no—
633#102—22no—
634#102—22no—
635#102—21no—
636#102—21no—
637#102—22no—
638#102—22no—
639#102—22no—
640#101—121no—
641#100—121no—
642#99—122no—
643#97—122no—
644#97#21712yes—
645#97#21712yes—
646#97C22×Dic311yescharacteristic
647#97C22×Dic311yescharacteristic
648#97C2×#6711yescharacteristic
649#97C2×#6712yes—
650#97C2×#6711yescharacteristic
651C4×C8—122no—
652C4×C8#21712yes—
653C4×C8#21712yes—
654C4×C8C22×Dic312yes—
655C23×C3—42no—
656C23×C3—41no—
657C23×C3—82no—
658C23×C3—161no—
659C23×C3—161no—
660C23×C3#41812yes—
661C23×C3C2×AGL(1,ℤ/8)11yescharacteristic
662C3×Q8—22no—
663C3×Q8—41no—
664C3×Q8—41no—
665C3×Q8—162no—
666C3×D4—24no—
667C3×D4—22no—
668C3×D4—41no—
669C3×D4—42no—
670C3×D4—42no—
671C3×D4—41no—
672C3×D4—82no—
673C3×D4—82no—
674C3×D4—162no—
675C3×D4—162no—
676C3×D4—162no—
677C3×D4—162no—
678C3×D4—162no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—22no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—42no—
688C2×C3×C4—81no—
689C2×C3×C4—82no—
690C2×C3×C4—84no—
691C2×C3×C4—82no—
692C2×C3×C4—82no—
693C2×C3×C4—161no—
694C2×C3×C4—162no—
695C2×C3×C4—161no—
696C2×C3×C4#41812yes—
697C2×C3×C4C22×C22⋊C411yescharacteristic
698C2×C3×C4#53212yes—
699C2×C3×C4C2×AGL(1,ℤ/8)11yescharacteristic
700C2×C3×C4#57512yes—
701C2×Dic3—82no—
702C3×C8—21no—
703C3×C8—21no—
704C3×C8—22no—
705C3×C8—22no—
706C3×C8C4×#4112yes—
707C3×C8#52511yescharacteristic
708C3×C8#52511yescharacteristic
709C3⋊C8—82no—
710C24—41no—
711#41—22no—
712#41—22no—
713#41—42no—
714#41—42no—
715#41—164no—
716C2×Q8—21no—
717C2×Q8—42no—
718C2×Q8#93211yescharacteristic
719C2×D4—22no—
720C2×D4—21no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—41no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—41no—
728C2×D4—42no—
729C2×D4—42no—
730C2×D4#93212yes—
731C2×D4#93211yescharacteristic
732C22×C4—22no—
733C22×C4—21no—
734C22×C4—41no—
735C22×C4—42no—
736C22×C4—41no—
737C22×C4—42no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—162no—
741C22×C4C2×#21712yes—
742C22×C4C22×#6711yescharacteristic
743Q16—22no—
744SD16—44no—
745SD16—41no—
746SD16—41no—
747D8—24no—
748D8—22no—
749D8—44no—
750D8—41no—
751D8—41no—
752M16—22no—
753M16—22no—
754M16—24no—
755M16—42no—
756M16—122no—
757M16—122no—
758C2×C8—22no—
759C2×C8—22no—
760C2×C8—22no—
761C2×C8—42no—
762C2×C8—122no—
763C2×C8C2×#21712yes—
764C2×C8C2×#21711yescharacteristic
765C2×C8C2×#21712yes—
766C2×C8C2×#21711yescharacteristic
767C2×C8D3×#4112yes—
768C2×C8D3×#4112yes—
769C2×C8C23×Dic311yescharacteristic
770C2×C8C22×#6711yescharacteristic
771C4⋊C4—22no—
772C4⋊C4—21no—
773C4⋊C4—22no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—42no—
779C4⋊C4—42no—
780C4⋊C4—42no—
781C4⋊C4—42no—
782C4⋊C4—41no—
783C4⋊C4—122no—
784C22⋊C4—22no—
785C22⋊C4—21no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C22⋊C4—41no—
789C22⋊C4—41no—
790C22⋊C4—42no—
791C22⋊C4—42no—
792C22⋊C4—42no—
793C22⋊C4—41no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—122no—
798C42—22no—
799C42—21no—
800C42—41no—
801C42—41no—
802C42—41no—
803C42—122no—
804C42C2×#21711yescharacteristic
805C42C2×#21712yes—
806C42C2×#21711yescharacteristic
807C16—64no—
808C16—64no—
809C22×C3—22no—
810C22×C3—41no—
811C22×C3—42no—
812C22×C3—82no—
813C22×C3—81no—
814C22×C3—81no—
815C22×C3—82no—
816C22×C3—81no—
817C22×C3—82no—
818C22×C3—164no—
819C22×C3C2×#41811yescharacteristic
820C22×C3#318012yes—
821C3×C4—22no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—42no—
825C3×C4—82no—
826C3×C4—81no—
827C3×C4—81no—
828C3×C4—81no—
829C3×C4#229711yescharacteristic
830C3×C4#289611yescharacteristic
831C3×C4#318012yes—
832Dic3—162no—
833C23—42no—
834C23—41no—
835C23—82no—
836C23—161no—
837C23—161no—
838C23#521512yes—
839C23C2×#93211yescharacteristic
840Q8—22no—
841Q8—41no—
842Q8—41no—
843Q8—162no—
844D4—24no—
845D4—22no—
846D4—41no—
847D4—42no—
848D4—42no—
849D4—41no—
850D4—82no—
851D4—82no—
852D4—162no—
853D4—162no—
854D4—162no—
855D4—162no—
856D4—162no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—81no—
867C2×C4—82no—
868C2×C4—84no—
869C2×C4—82no—
870C2×C4—82no—
871C2×C4—162no—
872C2×C4—161no—
873C2×C4—161no—
874C2×C4—242no—
875C2×C4#521512yes—
876C2×C4C2×#93211yescharacteristic
877C2×C4#582212yes—
878C2×C4#583212yes—
879C2×C4C22×#21711yescharacteristic
880C8—21no—
881C8—21no—
882C8—22no—
883C8—22no—
884C8—242no—
885C8Dic3×#4112yes—
886C8#582811yescharacteristic
887C8#582811yescharacteristic
888C2×C3—22no—
889C2×C3—21no—
890C2×C3—42no—
891C2×C3—161no—
892C2×C3—162no—
893C2×C3#2140811yescharacteristic
894C22—22no—
895C22—41no—
896C22—42no—
897C22—82no—
898C22—81no—
899C22—81no—
900C22—82no—
901C22—81no—
902C22—82no—
903C22—164no—
904C22#8329312yes—
905C22C2×#521511yescharacteristic
906C4—22no—
907C4—41no—
908C4—41no—
909C4—42no—
910C4—82no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4—482no—
915C4#8329312yes—
916C4#8407211yescharacteristic
917C4#8408611yescharacteristic
918C3#49557311yescharacteristic, complemented, Sylow
919C2—21no—
920C2—22no—
921C2—42no—
922C2—162no—
923C2—161no—
924C2#1080042511yescharacteristic
subgroupG/H
centerC2#10800425
commutatorC2×C3×C8C23×C4
FrattiniC22×C8C23×D3
Fitting, prime radicalC3×#60698C2
socleC2×C3#21408
cosocleC22×C3×C8C24
hypercenter#60698D3
hypocenterC3#495573
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2875 ◁ #60698

Complements

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

NH ≅ G/Ntype
1. #10947849C2semidirect
2. #10795562C2semidirect
3. #10713827C2semidirect
4. #10713459C2semidirect
5. #10712662C2semidirect
6. #10712652C2semidirect
7. #10712647C2semidirect
8. #10712637C2semidirect
9. #10710471C2semidirect
10. #10710457C2semidirect
14. C3×#3184C4semidirect
15. C3×#3183C4semidirect
18. C3×#3176C4semidirect
19. C3×#3173C4semidirect
160. #3184Dic3semidirect
161. #3183Dic3semidirect
164. #3176Dic3semidirect
165. #3173Dic3semidirect
324. #812#41semidirect
328. C2×C3⋊C16#41semidirect
918. C3#495573semidirect

Maximal subgroups

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

subgroupindex
#109478492
#107955622
#107138272
#107134592
#107126622
#107126522
#107126472
#107126372
#107104712
#107104572
C3×#606982
#4955733