Finite Group Databasebeta

← D43×#1509 #25063720

Subgroups — D43×#1509 #25063720

Order 11008.

1206 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D43C211yesmaximal, characteristic
2#432×D43C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#19133121C211yesmaximal, characteristic, complemented
5#19133120C211yesmaximal, characteristic, complemented
6#19133119C212yesmaximal, complemented
7#19133118C211yesmaximal, characteristic, complemented
8#19133117C212yesmaximal, complemented
9#328×D43C212yesmaximal, complemented
10#327×D43C212yesmaximal
11C43×#1509C211yesmaximal, characteristic, complemented
12#14583436C411yescharacteristic, complemented
13#14583435C2211yescharacteristic
14#14583434C411yescharacteristic, complemented
15#14583433C2211yescharacteristic
16#14583432—21no—
17#14583431C411yescharacteristic, complemented
18#14583430C2211yescharacteristic
19#14583429—21no—
20#14583428C411yescharacteristic, complemented
21#14583427—21no—
22#14583426—21no—
23#126×D43—21no—
24#125×D43C411yescharacteristic, complemented
25#124×D43C411yescharacteristic, complemented
26#123×D43—21no—
27C22⋊Q8×D43C2211yescharacteristic
28#121×D43C2211yescharacteristic
29C4×Q8×D43C411yescharacteristic, complemented
30C4×D4×D43—21no—
31C4×D4×D43C411yescharacteristic, complemented
32#117×D43—21no—
33C2×C4⋊C4×D43—21no—
34C2×C42×D43—21no—
35C2×C42×D43C2211yescharacteristic
36#14582956C2211yescharacteristic, complemented
37#14582955—21no—
38#14582954—21no—
39#14582953C2212yescomplemented
40C4⋊C8×D43—21no—
41C22⋊C8×D43C2212yes—
42#97×D43—21no—
43C4⋊C4×Dic43—21no—
44C4×Dic43⋊C4—21no—
45C4×C4⋊Dic43C2211yescharacteristic, complemented
46#14582750C2212yescomplemented
47#95×D43C2212yes—
48#14582637C2212yescomplemented
49#14582636C2212yescomplemented
50#14582635C2212yescomplemented
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#529C2211yescharacteristic
55C43×#432C2211yescharacteristic, complemented
56C4×C4⋊C4×C43C2211yescharacteristic, complemented
57C43×#328C2212yescomplemented
58C43×#327C2212yes—
59C2×Q8×D43C2×C411yescharacteristic
60C2×D4×D43—21no—
61C2×D4×D43C2×C411yescharacteristic
62C22×C4×D43—22no—
63C22×C4×D43—21no—
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C2×C8×D43—22no—
68#13063320—21no—
69#13063320—21no—
70#13063320—21no—
71#13063319—21no—
72#13063318—21no—
73#13063318—21no—
74#13063318—21no—
75#13063317C2×C411yescharacteristic, complemented
76#13063316C2×C411yescharacteristic, complemented
77#13063316C2×C411yescharacteristic, complemented
78#13063315—21no—
79#13063315—21no—
80#13063314C2×C411yescharacteristic, complemented
81#13063313C2×C411yescharacteristic, complemented
82#13063312C2×C411yescharacteristic, complemented
83#13063311—21no—
84#13063311—21no—
85#13063310—21no—
86#13063310—21no—
87#13063309—21no—
88#13063308—21no—
89#13063307—21no—
90#13063307—21no—
91#13063306—21no—
92#13063305C2×C411yescharacteristic
93#13063304C2311yescharacteristic
94#13063303—21no—
95#13063302—21no—
96#13063301C2×C411yescharacteristic
97#13063300C2×C411yescharacteristic
98#13063299C2311yescharacteristic
99#13063298—21no—
100#13063297—21no—
101#13063296C2×C411yescharacteristic
102Q8×Dic43C2×C411yescharacteristic, complemented
103C4×Dic86—21no—
104C4×Dic86C2×C411yescharacteristic, complemented
105#13063290—21no—
106#13063290C2×C411yescharacteristic, complemented
107C4×D172—21no—
108C4×D172C2×C411yescharacteristic, complemented
109D4×Dic43—21no—
110D4×Dic43C2×C411yescharacteristic, complemented
111#13063287—21no—
112#13063287C2×C411yescharacteristic, complemented
113C4×C22⋊D43—21no—
114C4×C22⋊D43—21no—
115C4×C22⋊D43—21no—
116(C22⋊D43)⋊C4—21no—
117(C22⋊D43)⋊C4—21no—
118(C22⋊D43)⋊C4—21no—
119#13063284—21no—
120#13063283—21no—
121#13063283—21no—
122#13063282—21no—
123#13063282—21no—
124#13063281—21no—
125#13063281—21no—
126C2×C4⋊Dic43—21no—
127C2×Dic43⋊C4—22no—
128C4⋊C4×D43—28no—
129C4⋊C4×D43—21no—
130C4⋊C4×D43—21no—
131C4⋊C4×D43—21no—
132C4⋊C4×D43—21no—
133C4⋊C4×D43C2×C411yescharacteristic
134C4⋊C4×D43C2×C411yescharacteristic
135C22⋊C4×D43—21no—
136C22⋊C4×D43—21no—
137C22⋊C4×D43—21no—
138C22⋊C4×D43—21no—
139C22⋊C4×D43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—22no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43C2311yescharacteristic
145C42×D43—21no—
146C42×D43—44no—
147C42×D43C2×C411yescharacteristic
148C42×D43C2×C411yescharacteristic
149C42×D43C2×C411yescharacteristic
150C42×D43C2×C411yescharacteristic
151C42×D43D411yescharacteristic
152C42×D43D411yescharacteristic
153C42×D43D411yescharacteristic
154C42×D43D411yescharacteristic
155C4⋊(C43⋊C8)—21no—
156Dic43⋊C8—22no—
157C22⋊(C43⋊C8)C2312yes—
158(C2×D43)⋊C8—22no—
159#13063236—21no—
160#13063235—22no—
161C43⋊#95—22no—
162C43⋊#95C2312yes—
163#126×C43—21no—
164#125×C43C2×C411yescharacteristic, complemented
165#124×C43C2×C411yescharacteristic, complemented
166#123×C43—21no—
167C22⋊Q8×C43C2311yescharacteristic
168#121×C43C2311yescharacteristic
169C4×Q8×C43C2×C411yescharacteristic, complemented
170C4×D4×C43—21no—
171C4×D4×C43C2×C411yescharacteristic, complemented
172#117×C43—21no—
173C2×C4⋊C4×C43—21no—
174C2×C42×C43—21no—
175C2×C42×C43C2311yescharacteristic
176C4⋊C8×C43—21no—
177C22⋊C8×C43C2312yes—
178#97×C43—21no—
179#95×C43C2312yes—
180C23×D43—21no—
181C23×D43C2×D411yescharacteristic
182C2×Q8×C43C22×C411yescharacteristic
183C2×D4×C43—21no—
184C2×D4×C43C22×C411yescharacteristic
185C22×C4×C43—21no—
186C22×C4×C43—22no—
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C22×Dic43—21no—
194C22×Dic43—22no—
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198Q8×D43—42no—
199D4×D43—42no—
200D4×D43—42no—
201D4×D43—42no—
202C2×D172—21no—
203C2×D172C22×C411yescharacteristic
204C2×C4×D43—24no—
205C2×C4×D43—28no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—22no—
212C2×C4×D43—22no—
213C2×C4×D43—42no—
214C2×C4×D43—44no—
215C2×C4×D43—44no—
216C2×C4×D43—44no—
217C2×C4×D43C22⋊C411yescharacteristic
218C2×C4×D43C22⋊C411yescharacteristic
219C2×C4×D43C22⋊C411yescharacteristic
220C2×C4×D43C22⋊C411yescharacteristic
221C2×C4×D43C22⋊C411yescharacteristic
222C2×C4×D43C22⋊C411yescharacteristic
223C2×C4×D43C22⋊C411yescharacteristic
224C2×C4×D43C22⋊C411yescharacteristic
225C2×C4×D43C22×C411yescharacteristic
226C2×C4×D43C22×C411yescharacteristic
227C2×C4×D43C2×D411yescharacteristic
228C2×C4×D43C2×D411yescharacteristic
229C2×Dic86—21no—
230C2×Dic86C22×C411yescharacteristic
231C2×C8×C43—22no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C22×C411yescharacteristic
238C4⋊C4×C43C22×C411yescharacteristic
239C22⋊C4×C43—21no—
240C22⋊C4×C43—21no—
241C22⋊C4×C43—21no—
242C22⋊C4×C43—21no—
243C22⋊C4×C43—21no—
244C42×C43—21no—
245C42×C43—42no—
246C42×C43C22×C411yescharacteristic
247C42×C43C22×C411yescharacteristic
248C42×C43C2×D411yescharacteristic
249C42×C43C2×D411yescharacteristic
250C22⋊Dic43—21no—
251C22⋊Dic43—21no—
252C22⋊Dic43—21no—
253C22⋊Dic43—21no—
254C22⋊Dic43—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259(C2×D43)⋊C4—21no—
260(C2×D43)⋊C4—21no—
261(C2×D43)⋊C4—21no—
262(C2×D43)⋊C4—21no—
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265C4⋊Dic43—24no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43C22×C411yescharacteristic
271C4⋊Dic43C22×C411yescharacteristic
272Dic43⋊C4—28no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275Dic43⋊C4—21no—
276Dic43⋊C4—21no—
277Dic43⋊C4—21no—
278Dic43⋊C4—21no—
279Dic43⋊C4—21no—
280Dic43⋊C4—21no—
281Dic43⋊C4—21no—
282Dic43⋊C4—21no—
283C4×Dic43—21no—
284C4×Dic43—21no—
285C4×Dic43—21no—
286C4×Dic43—44no—
287C4×Dic43—42no—
288C4×Dic43C22⋊C411yescharacteristic
289C4×Dic43C22⋊C411yescharacteristic
290C4×Dic43C22⋊C411yescharacteristic
291C4×Dic43C22⋊C411yescharacteristic
292C4×Dic43C22⋊C411yescharacteristic
293C4×Dic43C22⋊C411yescharacteristic
294C4×Dic43C22⋊C411yescharacteristic
295C4×Dic43C22⋊C411yescharacteristic
296C4×Dic43C22×C411yescharacteristic
297C4×Dic43C22×C411yescharacteristic
298C4×Dic43C2×D411yescharacteristic
299C4×Dic43C2×D411yescharacteristic
300C2×C43⋊C8—22no—
301C8×D43—44no—
302C23×C43—21no—
303C23×C43C22×D411yescharacteristic
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—21no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43C2×C22⋊C411yescharacteristic
311C22×D43C2×C22⋊C411yescharacteristic
312C22×D43AGL(1,ℤ/8)12yes—
313C22×D43#13712yes—
314Q8×C43—41no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—41no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—22no—
321C2×C4×C43—24no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—41no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43C2×C22⋊C411yescharacteristic
330C2×C4×C43C2×C22⋊C411yescharacteristic
331C2×C4×C43C2×C22⋊C411yescharacteristic
332C2×C4×C43C2×C22⋊C411yescharacteristic
333C2×C4×C43C23×C411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C22⋊D43—42no—
336C22⋊D43—41no—
337C22⋊D43—41no—
338C22⋊D43—42no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—22no—
342C2×Dic43—24no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—41no—
347C2×Dic43—42no—
348C2×Dic43—42no—
349C2×Dic43—42no—
350C2×Dic43C2×C22⋊C411yescharacteristic
351C2×Dic43C2×C22⋊C411yescharacteristic
352C2×Dic43C2×C22⋊C411yescharacteristic
353C2×Dic43C2×C22⋊C411yescharacteristic
354C2×Dic43C2×C22⋊C411yescharacteristic
355C2×Dic43C2×C22⋊C411yescharacteristic
356D172—41no—
357D172—42no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—22no—
364C4×D43—22no—
365C4×D43—22no—
366C4×D43—22no—
367C4×D43—41no—
368C4×D43—41no—
369C4×D43—416no—
370C4×D43—42no—
371C4×D43—42no—
372C4×D43—42no—
373C4×D43—42no—
374C4×D43—42no—
375C4×D43#10414yes—
376Dic86—42no—
377Dic86—41no—
378C8×C43—42no—
379C43⋊C8—42no—
380C2×#1509—431nomaximal, Sylow
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43C22×C22⋊C411yescharacteristic
387C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C43C2×#13711yescharacteristic
389C2×D43—21no—
390C2×D43—21no—
391C2×D43—24no—
392C2×D43—24no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—41no—
396C2×D43—84no—
397C2×D43#41012yes—
398C2×D43#41712yes—
399C2×D43#41712yes—
400C2×D43C2×#10412yes—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—21no—
404C4×C43—21no—
405C4×C43—21no—
406C4×C43—44no—
407C4×C43—41no—
408C4×C43—41no—
409C4×C43—41no—
410C4×C43C2×#10412yes—
411Dic43—21no—
412Dic43—21no—
413Dic43—21no—
414Dic43—21no—
415Dic43—21no—
416Dic43—44no—
417Dic43—41no—
418Dic43—41no—
419Dic43—41no—
420Dic43C2×#10412yes—
421C2×#529—431no—
422C2×#432—431no—
423C2×C4×C4⋊C4—431no—
424#1509—431no—
425#1509—431no—
426#1509—432no—
427#1509—432no—
428#1509—431no—
429#1509D4311yescharacteristic, direct product factor
430C2×#328—432no—
431C2×#327—432no—
432C2×C43—21no—
433C2×C43—21no—
434C2×C43—81no—
435C2×C43C2×#41011yescharacteristic
436C2×C43C2×#41711yescharacteristic
437C2×C43C22×#10411yescharacteristic
438D43—22no—
439D43—81no—
440D43#150914yesdirect product factor
441#529—431no—
442#529—431no—
443#529—431no—
444#529—431no—
445#529—431no—
446#529—431no—
447#529—431no—
448#529—861no—
449#529—861no—
450#529—861no—
451#529—861no—
452#529C2×D4311yescharacteristic
453C2×#126—861no—
454C2×#125—431no—
455C2×#124—431no—
456C2×#123—861no—
457C2×C22⋊Q8—431no—
458C2×#121—431no—
459C2×C4×Q8—431no—
460C2×C4×D4—431no—
461C2×C4×D4—861no—
462C2×#117—861no—
463C22×C4⋊C4—861no—
464C22×C42—431no—
465C22×C42—861no—
466#432—431no—
467#432—432no—
468#432—861no—
469#432—861no—
470#432C2×D4311yescharacteristic, complemented
471C2×C4⋊C8—861no—
472C2×C22⋊C8—432no—
473C2×#97—861no—
474C4×C4⋊C4—431no—
475C4×C4⋊C4—432no—
476C4×C4⋊C4—861no—
477C4×C4⋊C4—861no—
478C4×C4⋊C4C2×D4311yescharacteristic, complemented
479C2×#95—432no—
480#328—432no—
481#328—432no—
482#328—432no—
483#328C2×D4312yescomplemented
484#327—432no—
485#327—432no—
486#327—432no—
487#327C2×D4312yes—
488C43C2×#150911yescharacteristic, complemented, Sylow
489C22×Q8—431no—
490C22×D4—431no—
491C22×D4—861no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—861no—
496C23×C4—862no—
497C22×C8—862no—
498#126—21no—
499#126—861no—
500#126—861no—
501#126—861no—
502#126—861no—
503#126—861no—
504#126—861no—
505#126—861no—
506#125—431no—
507#125—431no—
508#125—431no—
509#125—861no—
510#125—861no—
511#125C4×D4311yescharacteristic, complemented
512#124—431no—
513#124—431no—
514#124—431no—
515#124—861no—
516#124—861no—
517#124C4×D4311yescharacteristic, complemented
518#123—21no—
519#123—861no—
520#123—861no—
521#123—861no—
522#123—861no—
523#123—861no—
524#123—861no—
525#123—861no—
526C22⋊Q8—431no—
527C22⋊Q8—431no—
528C22⋊Q8—431no—
529C22⋊Q8—861no—
530C22⋊Q8—861no—
531C22⋊Q8C22×D4311yescharacteristic
532#121—431no—
533#121—431no—
534#121—431no—
535#121—861no—
536#121—861no—
537#121C22×D4311yescharacteristic
538C4×Q8—431no—
539C4×Q8—431no—
540C4×Q8—431no—
541C4×Q8—861no—
542C4×Q8—861no—
543C4×Q8C4×D4311yescharacteristic, complemented
544C4×D4—21no—
545C4×D4—431no—
546C4×D4—431no—
547C4×D4—431no—
548C4×D4—861no—
549C4×D4—861no—
550C4×D4—861no—
551C4×D4—861no—
552C4×D4—861no—
553C4×D4—861no—
554C4×D4—861no—
555C4×D4—861no—
556C4×D4—861no—
557C4×D4C4×D4311yescharacteristic, complemented
558#117—21no—
559#117—861no—
560#117—861no—
561#117—861no—
562#117—861no—
563#117—861no—
564#117—861no—
565#117—861no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—868no—
574C2×C4⋊C4—862no—
575C2×C4⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C42—21no—
582C2×C42—431no—
583C2×C42—431no—
584C2×C42—431no—
585C2×C42—431no—
586C2×C42—431no—
587C2×C42—431no—
588C2×C42—431no—
589C2×C42—431no—
590C2×C42—431no—
591C2×C42—431no—
592C2×C42—431no—
593C2×C42—861no—
594C2×C42—862no—
595C2×C42—861no—
596C2×C42—1724no—
597C2×C42C22×D4311yescharacteristic
598C4⋊C8—21no—
599C4⋊C8—862no—
600C4⋊C8—861no—
601C22⋊C8—432no—
602C22⋊C8—862no—
603C22⋊C8C22×D4312yes—
604#97—21no—
605#97—862no—
606#97—861no—
607#95—432no—
608#95—862no—
609#95C22×D4312yes—
610C24—431no—
611C24—861no—
612C2×Q8—431no—
613C2×Q8—861no—
614C2×Q8—1722no—
615C2×Q8C2×C4×D4311yescharacteristic
616C2×D4—21no—
617C2×D4—431no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—861no—
621C2×D4—861no—
622C2×D4—1722no—
623C2×D4—1722no—
624C2×D4—1722no—
625C2×D4C2×C4×D4311yescharacteristic
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—864no—
644C22×C4—861no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—868no—
651C22×C4—861no—
652C22×C4—862no—
653C22×C4—861no—
654C22×C4—1724no—
655C22×C4—1722no—
656C22×C4—1724no—
657C22×C4—1724no—
658C22×C4D4×D4311yescharacteristic
659C22×C4D4×D4311yescharacteristic
660C22×C4C23×D4311yescharacteristic
661C2×C8—22no—
662C2×C8—862no—
663C2×C8—1724no—
664C4⋊C4—24no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—431no—
670C4⋊C4—431no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—868no—
682C4⋊C4—864no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4C2×C4×D4311yescharacteristic
688C4⋊C4C2×C4×D4311yescharacteristic
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—861no—
695C22⋊C4—861no—
696C22⋊C4—861no—
697C22⋊C4—861no—
698C22⋊C4—861no—
699C22⋊C4—861no—
700C22⋊C4—861no—
701C22⋊C4—861no—
702C22⋊C4—861no—
703C22⋊C4—861no—
704C22⋊C4—861no—
705C22⋊C4—861no—
706C22⋊C4—861no—
707C22⋊C4—861no—
708C22⋊C4—861no—
709C42—21no—
710C42—42no—
711C42—431no—
712C42—431no—
713C42—431no—
714C42—431no—
715C42—431no—
716C42—431no—
717C42—431no—
718C42—431no—
719C42—431no—
720C42—431no—
721C42—431no—
722C42—431no—
723C42—861no—
724C42—861no—
725C42—861no—
726C42—1722no—
727C42—1724no—
728C42C2×C4×D4311yescharacteristic
729C42C2×C4×D4311yescharacteristic
730C42D4×D4311yescharacteristic
731C42D4×D4311yescharacteristic
732C23—21no—
733C23—431no—
734C23—431no—
735C23—432no—
736C23—432no—
737C23—862no—
738C23—862no—
739C23—861no—
740C23—1722no—
741C23—1722no—
742C23—1722no—
743C23C2×D4×D4311yescharacteristic
744Q8—41no—
745Q8—1721no—
746Q8—1722no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—1721no—
751D4—1722no—
752D4—1722no—
753D4—1722no—
754D4—1721no—
755D4—1721no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—431no—
768C2×C4—434no—
769C2×C4—431no—
770C2×C4—431no—
771C2×C4—431no—
772C2×C4—431no—
773C2×C4—431no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—862no—
786C2×C4—864no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1722no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4—1722no—
796C2×C4—17216no—
797C2×C4—1722no—
798C2×C4—1721no—
799C2×C4—1722no—
800C2×C4—1722no—
801C2×C4—1722no—
802C2×C4C22⋊C4×D4311yescharacteristic
803C2×C4C22⋊C4×D4311yescharacteristic
804C2×C4C22⋊C4×D4311yescharacteristic
805C2×C4C22⋊C4×D4311yescharacteristic
806C2×C4C22×C4×D4311yescharacteristic
807C2×C4C2×D4×D4311yescharacteristic
808C8—42no—
809C8—1722no—
810C22—21no—
811C22—21no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—432no—
816C22—432no—
817C22—432no—
818C22—432no—
819C22—864no—
820C22—864no—
821C22—861no—
822C22—861no—
823C22—3444no—
824C22—1721no—
825C22—1721no—
826C22—1721no—
827C22C2×C22⋊C4×D4311yescharacteristic
828C22AGL(1,ℤ/8)×D4311yescharacteristic
829C22#137×D4311yescharacteristic
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—44no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—432no—
840C4—861no—
841C4—861no—
842C4—861no—
843C4—861no—
844C4—861no—
845C4—1724no—
846C4—1721no—
847C4—1721no—
848C4—1721no—
849C4#104×D4312yes—
850C2—21no—
851C2—21no—
852C2—81no—
853C2—434no—
854C2—862no—
855C2—3441no—
856C2#410×D4311yescharacteristic
857C2#417×D4311yescharacteristic
858C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1509C2
socleC22×C43C22×C22⋊C4
prime radical#121×D43C22
cosocleC22×C4×C43C24
hypercenter#1509D43
hypocenterC43C2×#1509
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #432×D43C2semidirect
3. C4×C4⋊C4×D43C2semidirect
4. #19133121C2semidirect
5. #19133120C2semidirect
6. #19133119C2semidirect
7. #19133118C2semidirect
8. #19133117C2semidirect
9. #328×D43C2semidirect
11. C43×#1509C2semidirect
12. #14583436C4semidirect
14. #14583434C4semidirect
17. #14583431C4semidirect
20. #14583428C4semidirect
24. #125×D43C4semidirect
25. #124×D43C4semidirect
29. C4×Q8×D43C4semidirect
31. C4×D4×D43C4semidirect
36. #14582956C22semidirect
39. #14582953C22semidirect
45. C4×C4⋊Dic43C22semidirect
46. #14582750C22semidirect
48. #14582637C22semidirect
49. #14582636C22semidirect
50. #14582635C22semidirect
55. C43×#432C22semidirect
56. C4×C4⋊C4×C43C22semidirect
57. C43×#328C22semidirect
75. #13063317C2×C4semidirect
76. #13063316C2×C4semidirect
77. #13063316C2×C4semidirect
80. #13063314C2×C4semidirect
81. #13063313C2×C4semidirect
82. #13063312C2×C4semidirect
102. Q8×Dic43C2×C4semidirect
104. C4×Dic86C2×C4semidirect
106. #13063290C2×C4semidirect
108. C4×D172C2×C4semidirect
110. D4×Dic43C2×C4semidirect
112. #13063287C2×C4semidirect
164. #125×C43C2×C4semidirect
165. #124×C43C2×C4semidirect
169. C4×Q8×C43C2×C4semidirect
171. C4×D4×C43C2×C4semidirect
429. #1509D43direct (N × H)
440. D43#1509direct (N × H)
470. #432C2×D43semidirect
478. C4×C4⋊C4C2×D43semidirect
483. #328C2×D43semidirect
488. C43C2×#1509semidirect
511. #125C4×D43semidirect
517. #124C4×D43semidirect
543. C4×Q8C4×D43semidirect
557. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#529×D432
#432×D432
C4×C4⋊C4×D432
#191331212
#191331202
#191331192
#191331182
#191331172
#328×D432
#327×D432
C43×#15092
C2×#150943