Finite Group Databasebeta

← D43×#1512 #25063835

Subgroups — D43×#1512 #25063835

Order 11008.

1098 conjugacy classes of subgroups.

The subgroup lattice has 852 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
3#382×D43C211yesmaximal, characteristic, complemented
4#19133134C211yesmaximal, characteristic, complemented
5#19133133C211yesmaximal, characteristic, complemented
6#19133132C212yesmaximal, complemented
7#19133131C211yesmaximal, characteristic, complemented
8#19133130C212yesmaximal, complemented
9#328×D43C212yesmaximal, complemented
10#327×D43C212yesmaximal
11C43×#1512C211yesmaximal, 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×D43C2211yescharacteristic
35#14582956C2211yescharacteristic, complemented
36#14582955—21no—
37#14582954—21no—
38#14582953C2212yescomplemented
39C4⋊C8×D43—21no—
40C22⋊C8×D43C2212yes—
41#97×D43—21no—
42#14582765C2211yescharacteristic, complemented
43#14582764—21no—
44#14582763—21no—
45#14582763C2212yescomplemented
46#95×D43—21no—
47#95×D43C2212yes—
48#14582637C2212yescomplemented
49#14582636C2212yescomplemented
50#14582635C2212yescomplemented
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#529C2211yescharacteristic
55C43×#432C2211yescharacteristic, complemented
56C43×#382C2211yescharacteristic, complemented
57C43×#328C2212yescomplemented
58C43×#327C2212yes—
59C2×Q8×D43C2×C411yescharacteristic
60C2×D4×D43—21no—
61C2×D4×D43C2×C411yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—22no—
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—21no—
129C4⋊C4×D43—21no—
130C4⋊C4×D43—21no—
131C4⋊C4×D43—21no—
132C4⋊C4×D43—44no—
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×Dic43D411yescharacteristic
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43C2311yescharacteristic
143C42×D43—21no—
144C42×D43C2×C411yescharacteristic
145C42×D43C2×C411yescharacteristic
146C42×D43C2×C411yescharacteristic
147C42×D43C2×C411yescharacteristic
148C42×D43D411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43D411yescharacteristic
151C42×D43D411yescharacteristic
152C4⋊(C43⋊C8)—21no—
153Dic43⋊C8—22no—
154C22⋊(C43⋊C8)C2312yes—
155(C2×D43)⋊C8—22no—
156#13063236—21no—
157#13063235—22no—
158C43⋊#95—21no—
159C43⋊#95—22no—
160C43⋊#95—22no—
161C43⋊#95C2312yes—
162#126×C43—21no—
163#125×C43C2×C411yescharacteristic, complemented
164#124×C43C2×C411yescharacteristic, complemented
165#123×C43—21no—
166C22⋊Q8×C43C2311yescharacteristic
167#121×C43C2311yescharacteristic
168C4×Q8×C43C2×C411yescharacteristic, complemented
169C4×D4×C43—21no—
170C4×D4×C43C2×C411yescharacteristic, complemented
171#117×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C42×C43C2311yescharacteristic
174C4⋊C8×C43—21no—
175C22⋊C8×C43C2312yes—
176#97×C43—21no—
177#95×C43—21no—
178#95×C43C2312yes—
179C23×D43—21no—
180C23×D43C2×D411yescharacteristic
181C2×Q8×C43C22×C411yescharacteristic
182C2×D4×C43—21no—
183C2×D4×C43C22×C411yescharacteristic
184C22×C4×C43—21no—
185C22×C4×C43—22no—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C22×Dic43—21no—
193C22×Dic43—22no—
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197Q8×D43—42no—
198D4×D43—42no—
199D4×D43—42no—
200D4×D43—42no—
201C2×D172—21no—
202C2×D172C22×C411yescharacteristic
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—42no—
211C2×C4×D43—42no—
212C2×C4×D43—44no—
213C2×C4×D43—44no—
214C2×C4×D43—44no—
215C2×C4×D43—44no—
216C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
227C2×C4×D43C2×D411yescharacteristic
228C2×Dic86—21no—
229C2×Dic86C22×C411yescharacteristic
230C2×C8×C43—22no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—42no—
236C4⋊C4×C43C22×C411yescharacteristic
237C4⋊C4×C43C22×C411yescharacteristic
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C22⋊C4×C43—21no—
241C22⋊C4×C43—21no—
242C22⋊C4×C43—21no—
243C42×C43—21no—
244C42×C43C22×C411yescharacteristic
245C42×C43C22×C411yescharacteristic
246C42×C43C2×D411yescharacteristic
247C42×C43C2×D411yescharacteristic
248C22⋊Dic43—21no—
249C22⋊Dic43—21no—
250C22⋊Dic43—21no—
251C22⋊Dic43—21no—
252C22⋊Dic43—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—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—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—42no—
268C4⋊Dic43C22×C411yescharacteristic
269C4⋊Dic43C22×C411yescharacteristic
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275Dic43⋊C4—21no—
276Dic43⋊C4—21no—
277Dic43⋊C4—21no—
278Dic43⋊C4—21no—
279Dic43⋊C4—21no—
280Dic43⋊C4—44no—
281C4×Dic43—21no—
282C4×Dic43—21no—
283C4×Dic43—21no—
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22⋊C411yescharacteristic
286C4×Dic43C22⋊C411yescharacteristic
287C4×Dic43C22⋊C411yescharacteristic
288C4×Dic43C22⋊C411yescharacteristic
289C4×Dic43C22⋊C411yescharacteristic
290C4×Dic43C22⋊C411yescharacteristic
291C4×Dic43C22⋊C411yescharacteristic
292C4×Dic43C22×C411yescharacteristic
293C4×Dic43C22×C411yescharacteristic
294C4×Dic43C2×D411yescharacteristic
295C4×Dic43C2×D411yescharacteristic
296C2×C43⋊C8—22no—
297C8×D43—44no—
298C23×C43—21no—
299C23×C43C22×D411yescharacteristic
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—21no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43C2×C22⋊C411yescharacteristic
307C22×D43C2×C22⋊C411yescharacteristic
308C22×D43AGL(1,ℤ/8)12yes—
309C22×D43#13712yes—
310Q8×C43—41no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—41no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—42no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43C2×C22⋊C411yescharacteristic
326C2×C4×C43C2×C22⋊C411yescharacteristic
327C2×C4×C43C2×C22⋊C411yescharacteristic
328C2×C4×C43C2×C22⋊C411yescharacteristic
329C2×C4×C43C23×C411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C22⋊D43—42no—
332C22⋊D43—41no—
333C22⋊D43—41no—
334C22⋊D43—42no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43C2×C22⋊C411yescharacteristic
347C2×Dic43C2×C22⋊C411yescharacteristic
348C2×Dic43C2×C22⋊C411yescharacteristic
349C2×Dic43C2×C22⋊C411yescharacteristic
350C2×Dic43C2×C22⋊C411yescharacteristic
351C2×Dic43C2×C22⋊C411yescharacteristic
352D172—41no—
353D172—42no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—41no—
363C4×D43—41no—
364C4×D43—41no—
365C4×D43—41no—
366C4×D43—42no—
367C4×D43—42no—
368C4×D43—42no—
369C4×D43—42no—
370C4×D43—42no—
371C4×D43—88no—
372Dic86—42no—
373Dic86—41no—
374C8×C43—42no—
375C43⋊C8—42no—
376C2×#1512—431nomaximal, Sylow
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43C22×C22⋊C411yescharacteristic
383C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C43C2×#13711yescharacteristic
385C2×D43—21no—
386C2×D43—21no—
387C2×D43—24no—
388C2×D43—24no—
389C2×D43—41no—
390C2×D43—41no—
391C2×D43—41no—
392C2×D43—84no—
393C2×D43#41012yes—
394C2×D43#41712yes—
395C2×D43#41712yes—
396C2×D43#42112yes—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—41no—
404C4×C43—41no—
405C4×C43—41no—
406C4×C43—82no—
407Dic43—21no—
408Dic43—21no—
409Dic43—21no—
410Dic43—21no—
411Dic43—21no—
412Dic43—21no—
413Dic43—41no—
414Dic43—41no—
415Dic43—41no—
416Dic43—82no—
417C2×#529—431no—
418C2×#432—431no—
419C2×#382—431no—
420#1512—431no—
421#1512—431no—
422#1512—432no—
423#1512—432no—
424#1512—431no—
425#1512D4311yescharacteristic, direct product factor
426C2×#328—432no—
427C2×#327—432no—
428C2×C43—21no—
429C2×C43—21no—
430C2×C43—81no—
431C2×C43C2×#41011yescharacteristic
432C2×C43C2×#41711yescharacteristic
433C2×C43C2×#42111yescharacteristic
434D43—22no—
435D43—81no—
436D43#151214yesdirect product factor
437#529—431no—
438#529—431no—
439#529—431no—
440#529—431no—
441#529—431no—
442#529—431no—
443#529—431no—
444#529—861no—
445#529—861no—
446#529—861no—
447#529—861no—
448#529C2×D4311yescharacteristic
449C2×#126—861no—
450C2×#125—431no—
451C2×#124—431no—
452C2×#123—861no—
453C2×C22⋊Q8—431no—
454C2×#121—431no—
455C2×C4×Q8—431no—
456C2×C4×D4—431no—
457C2×C4×D4—861no—
458C2×#117—861no—
459C22×C4⋊C4—861no—
460C22×C42—431no—
461#432—431no—
462#432—432no—
463#432—861no—
464#432—861no—
465#432C2×D4311yescharacteristic, complemented
466C2×C4⋊C8—861no—
467C2×C22⋊C8—432no—
468C2×#97—861no—
469#382—431no—
470#382—432no—
471#382—861no—
472#382—861no—
473#382C2×D4311yescharacteristic, complemented
474C2×#95—432no—
475C2×#95—861no—
476#328—432no—
477#328—432no—
478#328—432no—
479#328C2×D4312yescomplemented
480#327—432no—
481#327—432no—
482#327—432no—
483#327C2×D4312yes—
484C43C2×#151211yescharacteristic, complemented, Sylow
485C22×Q8—431no—
486C22×D4—431no—
487C22×D4—861no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—431no—
491C23×C4—861no—
492C23×C4—862no—
493C22×C8—862no—
494#126—21no—
495#126—861no—
496#126—861no—
497#126—861no—
498#126—861no—
499#126—861no—
500#126—861no—
501#126—861no—
502#125—431no—
503#125—431no—
504#125—431no—
505#125—861no—
506#125—861no—
507#125C4×D4311yescharacteristic, complemented
508#124—431no—
509#124—431no—
510#124—431no—
511#124—861no—
512#124—861no—
513#124C4×D4311yescharacteristic, complemented
514#123—21no—
515#123—861no—
516#123—861no—
517#123—861no—
518#123—861no—
519#123—861no—
520#123—861no—
521#123—861no—
522C22⋊Q8—431no—
523C22⋊Q8—431no—
524C22⋊Q8—431no—
525C22⋊Q8—861no—
526C22⋊Q8—861no—
527C22⋊Q8C22×D4311yescharacteristic
528#121—431no—
529#121—431no—
530#121—431no—
531#121—861no—
532#121—861no—
533#121C22×D4311yescharacteristic
534C4×Q8—431no—
535C4×Q8—431no—
536C4×Q8—431no—
537C4×Q8—861no—
538C4×Q8—861no—
539C4×Q8C4×D4311yescharacteristic, complemented
540C4×D4—21no—
541C4×D4—431no—
542C4×D4—431no—
543C4×D4—431no—
544C4×D4—861no—
545C4×D4—861no—
546C4×D4—861no—
547C4×D4—861no—
548C4×D4—861no—
549C4×D4—861no—
550C4×D4—861no—
551C4×D4—861no—
552C4×D4—861no—
553C4×D4C4×D4311yescharacteristic, complemented
554#117—21no—
555#117—861no—
556#117—861no—
557#117—861no—
558#117—861no—
559#117—861no—
560#117—861no—
561#117—861no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4—862no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—1724no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—431no—
580C2×C42—431no—
581C2×C42—431no—
582C2×C42—431no—
583C2×C42—431no—
584C2×C42—431no—
585C2×C42—431no—
586C2×C42—431no—
587C2×C42—431no—
588C2×C42—861no—
589C2×C42C22×D4311yescharacteristic
590C4⋊C8—21no—
591C4⋊C8—862no—
592C4⋊C8—861no—
593C22⋊C8—432no—
594C22⋊C8—862no—
595C22⋊C8C22×D4312yes—
596#97—21no—
597#97—862no—
598#97—861no—
599#95—21no—
600#95—432no—
601#95—862no—
602#95—862no—
603#95—861no—
604#95C22×D4312yes—
605C24—431no—
606C24—861no—
607C2×Q8—431no—
608C2×Q8—861no—
609C2×Q8—1722no—
610C2×Q8C2×C4×D4311yescharacteristic
611C2×D4—21no—
612C2×D4—431no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—1722no—
618C2×D4—1722no—
619C2×D4—1722no—
620C2×D4C2×C4×D4311yescharacteristic
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
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—861no—
639C22×C4—862no—
640C22×C4—862no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—862no—
647C22×C4—1722no—
648C22×C4—1722no—
649C22×C4—1724no—
650C22×C4—1724no—
651C22×C4—1724no—
652C22×C4—1724no—
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656C2×C8—22no—
657C2×C8—862no—
658C2×C8—1724no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—431no—
665C4⋊C4—431no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—861no—
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—1722no—
681C4⋊C4—1724no—
682C4⋊C4C2×C4×D4311yescharacteristic
683C4⋊C4C2×C4×D4311yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—861no—
690C22⋊C4—861no—
691C22⋊C4—861no—
692C22⋊C4—861no—
693C22⋊C4—861no—
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—
704C42—21no—
705C42—431no—
706C42—431no—
707C42—431no—
708C42—431no—
709C42—431no—
710C42—431no—
711C42—431no—
712C42—431no—
713C42—431no—
714C42—431no—
715C42—431no—
716C42—431no—
717C42—861no—
718C42—861no—
719C42—861no—
720C42C2×C4×D4311yescharacteristic
721C42C2×C4×D4311yescharacteristic
722C42D4×D4311yescharacteristic
723C42D4×D4311yescharacteristic
724C23—21no—
725C23—431no—
726C23—431no—
727C23—432no—
728C23—432no—
729C23—862no—
730C23—862no—
731C23—861no—
732C23—1722no—
733C23—1722no—
734C23—1722no—
735C23C2×D4×D4311yescharacteristic
736Q8—41no—
737Q8—1721no—
738Q8—1722no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—1721no—
743D4—1722no—
744D4—1722no—
745D4—1722no—
746D4—1721no—
747D4—1721no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—431no—
760C2×C4—431no—
761C2×C4—431no—
762C2×C4—431no—
763C2×C4—431no—
764C2×C4—431no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—861no—
774C2×C4—861no—
775C2×C4—861no—
776C2×C4—861no—
777C2×C4—861no—
778C2×C4—3448no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1722no—
784C2×C4—1722no—
785C2×C4—1722no—
786C2×C4—1722no—
787C2×C4—1722no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1722no—
791C2×C4—1722no—
792C2×C4—1722no—
793C2×C4—1722no—
794C2×C4C22⋊C4×D4311yescharacteristic
795C2×C4C22⋊C4×D4311yescharacteristic
796C2×C4C22⋊C4×D4311yescharacteristic
797C2×C4C22⋊C4×D4311yescharacteristic
798C2×C4C22×C4×D4311yescharacteristic
799C2×C4C2×D4×D4311yescharacteristic
800C8—42no—
801C8—1722no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—432no—
808C22—432no—
809C22—432no—
810C22—432no—
811C22—864no—
812C22—864no—
813C22—861no—
814C22—861no—
815C22—3444no—
816C22—1721no—
817C22—1721no—
818C22—1721no—
819C22C2×C22⋊C4×D4311yescharacteristic
820C22AGL(1,ℤ/8)×D4311yescharacteristic
821C22#137×D4311yescharacteristic
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—82no—
832C4—861no—
833C4—861no—
834C4—861no—
835C4—861no—
836C4—861no—
837C4—861no—
838C4—3442no—
839C4—1721no—
840C4—1721no—
841C4—1721no—
842C2—21no—
843C2—21no—
844C2—81no—
845C2—434no—
846C2—862no—
847C2—3441no—
848C2#410×D4311yescharacteristic
849C2#417×D4311yescharacteristic
850C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1512C2
socleC22×C43C22×C22⋊C4
prime radical#121×D43C22
cosocleC22×C4×C43C24
hypercenter#1512D43
hypocenterC43C2×#1512
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1512

Complements

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

NH ≅ G/Ntype
2. #432×D43C2semidirect
3. #382×D43C2semidirect
4. #19133134C2semidirect
5. #19133133C2semidirect
6. #19133132C2semidirect
7. #19133131C2semidirect
8. #19133130C2semidirect
9. #328×D43C2semidirect
11. C43×#1512C2semidirect
12. #14583436C4semidirect
14. #14583434C4semidirect
17. #14583431C4semidirect
20. #14583428C4semidirect
24. #125×D43C4semidirect
25. #124×D43C4semidirect
29. C4×Q8×D43C4semidirect
31. C4×D4×D43C4semidirect
35. #14582956C22semidirect
38. #14582953C22semidirect
42. #14582765C22semidirect
45. #14582763C22semidirect
48. #14582637C22semidirect
49. #14582636C22semidirect
50. #14582635C22semidirect
55. C43×#432C22semidirect
56. C43×#382C22semidirect
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
163. #125×C43C2×C4semidirect
164. #124×C43C2×C4semidirect
168. C4×Q8×C43C2×C4semidirect
170. C4×D4×C43C2×C4semidirect
425. #1512D43direct (N × H)
436. D43#1512direct (N × H)
465. #432C2×D43semidirect
473. #382C2×D43semidirect
479. #328C2×D43semidirect
484. C43C2×#1512semidirect
507. #125C4×D43semidirect
513. #124C4×D43semidirect
539. C4×Q8C4×D43semidirect
553. 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
#382×D432
#191331342
#191331332
#191331322
#191331312
#191331302
#328×D432
#327×D432
C43×#15122
C2×#151243