Finite Group Databasebeta

← D43×#1500 #25063681

Subgroups — D43×#1500 #25063681

Order 11008.

1182 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D43C211yesmaximal, characteristic
2#431×D43C211yesmaximal, characteristic, complemented
3#376×D43C211yesmaximal, characteristic, complemented
4#19133082C211yesmaximal, characteristic, complemented
5#19133081C211yesmaximal, characteristic, complemented
6#19133080C212yesmaximal, complemented
7#19133079C211yesmaximal, characteristic, complemented
8#19133078C212yesmaximal, complemented
9#328×D43C212yesmaximal, complemented
10#327×D43C212yesmaximal
11C43×#1500C211yesmaximal, 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×C42×D43—21no—
34C2×C42×D43C2211yescharacteristic
35#14582952C2211yescharacteristic, complemented
36#14582951—21no—
37#14582950—21no—
38#14582949C2212yescomplemented
39C4⋊C8×D43—21no—
40C22⋊C8×D43C2212yes—
41C4×C8×D43—21no—
42#14582745—21no—
43#14582745C2211yescharacteristic, complemented
44#14582744—21no—
45#14582744C2212yescomplemented
46#95×D43—21no—
47#95×D43C2212yes—
48#14582637C2212yescomplemented
49#14582636C2212yescomplemented
50#14582635C2212yescomplemented
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#529C2211yescharacteristic
55C43×#431C2211yescharacteristic, complemented
56C43×#376C2211yescharacteristic, 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—
126C4⋊C4×D43—21no—
127C4⋊C4×D43—21no—
128C4⋊C4×D43—21no—
129C4⋊C4×D43—21no—
130C4⋊C4×D43C2×C411yescharacteristic
131C4⋊C4×D43C2×C411yescharacteristic
132C22⋊C4×D43—21no—
133C22⋊C4×D43—21no—
134C22⋊C4×D43—21no—
135C22⋊C4×D43—21no—
136C22⋊C4×D43—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—22no—
139C2×C4×Dic43D411yescharacteristic
140C2×C4×Dic43D411yescharacteristic
141C2×C4×Dic43C2311yescharacteristic
142C42×D43—28no—
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—
156C4×C43⋊C8—21no—
157C8×Dic43—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×C42×C43—21no—
173C2×C42×C43C2311yescharacteristic
174C4⋊C8×C43—21no—
175C22⋊C8×C43C2312yes—
176C4×C8×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—44no—
199D4×D43—42no—
200C2×D172—21no—
201C2×D172C22×C411yescharacteristic
202C2×C4×D43—24no—
203C2×C4×D43—28no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—24no—
210C2×C4×D43—42no—
211C2×C4×D43—44no—
212C2×C4×D43—44no—
213C2×C4×D43—44no—
214C2×C4×D43C22⋊C411yescharacteristic
215C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
225C2×C4×D43C2×D411yescharacteristic
226C2×Dic86—21no—
227C2×Dic86C22×C411yescharacteristic
228C2×C8×C43—22no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43C22×C411yescharacteristic
234C4⋊C4×C43C22×C411yescharacteristic
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C42×C43—24no—
241C42×C43—21no—
242C42×C43C22×C411yescharacteristic
243C42×C43C22×C411yescharacteristic
244C42×C43C2×D411yescharacteristic
245C42×C43C2×D411yescharacteristic
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249C22⋊Dic43—21no—
250C22⋊Dic43—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—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—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43C22×C411yescharacteristic
266C4⋊Dic43C22×C411yescharacteristic
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275Dic43⋊C4—21no—
276Dic43⋊C4—21no—
277C4×Dic43—28no—
278C4×Dic43—24no—
279C4×Dic43—21no—
280C4×Dic43—21no—
281C4×Dic43—21no—
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
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×Dic43C2×D411yescharacteristic
293C4×Dic43C2×D411yescharacteristic
294C2×C43⋊C8—22no—
295C8×D43—44no—
296C23×C43—21no—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—21no—
301C22×D43—42no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43C2×C22⋊C411yescharacteristic
305C22×D43C2×C22⋊C411yescharacteristic
306C22×D43#13514yes—
307Q8×C43—41no—
308D4×C43—41no—
309D4×C43—42no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—24no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—41no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C2×C22⋊C411yescharacteristic
322C2×C4×C43C2×C22⋊C411yescharacteristic
323C2×C4×C43C2×C22⋊C411yescharacteristic
324C2×C4×C43C23×C411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C22⋊D43—42no—
327C22⋊D43—42no—
328C22⋊D43—42no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—24no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—41no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341C2×Dic43C2×C22⋊C411yescharacteristic
342C2×Dic43C2×C22⋊C411yescharacteristic
343C2×Dic43C2×C22⋊C411yescharacteristic
344C2×Dic43C2×C22⋊C411yescharacteristic
345D172—41no—
346D172—42no—
347C4×D43—22no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—41no—
357C4×D43—41no—
358C4×D43—416no—
359C4×D43—42no—
360C4×D43—42no—
361C4×D43—42no—
362C4×D43—42no—
363C4×D43—42no—
364C4×D43#10414yes—
365Dic86—42no—
366Dic86—41no—
367C8×C43—42no—
368C43⋊C8—42no—
369C2×#1500—431nomaximal, Sylow
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43C22×C22⋊C411yescharacteristic
376C22×C43C2×#13512yes—
377C2×D43—21no—
378C2×D43—21no—
379C2×D43—28no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—84no—
384C2×D43#41012yes—
385C2×D43#41612yes—
386C2×D43#41612yes—
387C2×D43C2×#10412yes—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—21no—
391C4×C43—21no—
392C4×C43—21no—
393C4×C43—44no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43—41no—
397C4×C43C2×#10412yes—
398Dic43—21no—
399Dic43—21no—
400Dic43—21no—
401Dic43—21no—
402Dic43—21no—
403Dic43—44no—
404Dic43—41no—
405Dic43—41no—
406Dic43—41no—
407Dic43C2×#10412yes—
408C2×#529—431no—
409C2×#431—431no—
410C2×#376—431no—
411#1500—431no—
412#1500—431no—
413#1500—432no—
414#1500—432no—
415#1500—431no—
416#1500D4311yescharacteristic, direct product factor
417C2×#328—432no—
418C2×#327—432no—
419C2×C43—22no—
420C2×C43—81no—
421C2×C43C2×#41011yescharacteristic
422C2×C43C2×#41611yescharacteristic
423C2×C43C22×#10411yescharacteristic
424D43—22no—
425D43—81no—
426D43#150014yesdirect product factor
427#529—431no—
428#529—431no—
429#529—431no—
430#529—431no—
431#529—431no—
432#529—431no—
433#529—431no—
434#529—861no—
435#529—861no—
436#529—861no—
437#529—861no—
438#529C2×D4311yescharacteristic
439C2×#126—861no—
440C2×#125—431no—
441C2×#124—431no—
442C2×#123—861no—
443C2×C22⋊Q8—431no—
444C2×#121—431no—
445C2×C4×Q8—431no—
446C2×C4×D4—431no—
447C2×C4×D4—861no—
448C2×#117—861no—
449C22×C42—431no—
450C22×C42—861no—
451#431—431no—
452#431—432no—
453#431—861no—
454#431—861no—
455#431C2×D4311yescharacteristic, complemented
456C2×C4⋊C8—861no—
457C2×C22⋊C8—432no—
458C2×C4×C8—861no—
459#376—431no—
460#376—432no—
461#376—861no—
462#376—861no—
463#376C2×D4311yescharacteristic, complemented
464C2×#95—432no—
465C2×#95—861no—
466#328—432no—
467#328—432no—
468#328—432no—
469#328C2×D4312yescomplemented
470#327—432no—
471#327—432no—
472#327—432no—
473#327C2×D4312yes—
474C43C2×#150011yescharacteristic, complemented, Sylow
475C22×Q8—431no—
476C22×D4—431no—
477C22×D4—861no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—861no—
482C23×C4—862no—
483C22×C8—862no—
484#126—21no—
485#126—861no—
486#126—861no—
487#126—861no—
488#126—861no—
489#126—861no—
490#126—861no—
491#126—861no—
492#125—431no—
493#125—431no—
494#125—431no—
495#125—861no—
496#125—861no—
497#125C4×D4311yescharacteristic, complemented
498#124—431no—
499#124—431no—
500#124—431no—
501#124—861no—
502#124—861no—
503#124C4×D4311yescharacteristic, complemented
504#123—21no—
505#123—861no—
506#123—861no—
507#123—861no—
508#123—861no—
509#123—861no—
510#123—861no—
511#123—861no—
512C22⋊Q8—431no—
513C22⋊Q8—431no—
514C22⋊Q8—431no—
515C22⋊Q8—861no—
516C22⋊Q8—861no—
517C22⋊Q8C22×D4311yescharacteristic
518#121—431no—
519#121—431no—
520#121—431no—
521#121—861no—
522#121—861no—
523#121C22×D4311yescharacteristic
524C4×Q8—431no—
525C4×Q8—431no—
526C4×Q8—431no—
527C4×Q8—861no—
528C4×Q8—861no—
529C4×Q8C4×D4311yescharacteristic, complemented
530C4×D4—21no—
531C4×D4—431no—
532C4×D4—431no—
533C4×D4—431no—
534C4×D4—861no—
535C4×D4—861no—
536C4×D4—861no—
537C4×D4—861no—
538C4×D4—861no—
539C4×D4—861no—
540C4×D4—861no—
541C4×D4—861no—
542C4×D4—861no—
543C4×D4C4×D4311yescharacteristic, complemented
544#117—21no—
545#117—861no—
546#117—861no—
547#117—861no—
548#117—861no—
549#117—861no—
550#117—861no—
551#117—861no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C42—21no—
564C2×C42—431no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—431no—
572C2×C42—431no—
573C2×C42—431no—
574C2×C42—431no—
575C2×C42—861no—
576C2×C42—868no—
577C2×C42—862no—
578C2×C42—861no—
579C2×C42C22×D4311yescharacteristic
580C4⋊C8—21no—
581C4⋊C8—862no—
582C4⋊C8—861no—
583C22⋊C8—432no—
584C22⋊C8—862no—
585C22⋊C8C22×D4312yes—
586C4×C8—21no—
587C4×C8—862no—
588C4×C8—861no—
589#95—21no—
590#95—432no—
591#95—862no—
592#95—862no—
593#95—861no—
594#95C22×D4312yes—
595C24—431no—
596C24—861no—
597C2×Q8—431no—
598C2×Q8—861no—
599C2×Q8—1722no—
600C2×Q8C2×C4×D4311yescharacteristic
601C2×D4—21no—
602C2×D4—431no—
603C2×D4—861no—
604C2×D4—861no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—1722no—
608C2×D4—1724no—
609C2×D4C2×C4×D4311yescharacteristic
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—864no—
628C22×C4—861no—
629C22×C4—864no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—868no—
634C22×C4—861no—
635C22×C4—862no—
636C22×C4—861no—
637C22×C4—1724no—
638C22×C4—1722no—
639C22×C4—1724no—
640C22×C4—1724no—
641C22×C4D4×D4311yescharacteristic
642C22×C4D4×D4311yescharacteristic
643C22×C4C23×D4311yescharacteristic
644C2×C8—22no—
645C2×C8—862no—
646C2×C8—1724no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—431no—
652C4⋊C4—431no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4—861no—
667C4⋊C4C2×C4×D4311yescharacteristic
668C4⋊C4C2×C4×D4311yescharacteristic
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—861no—
675C22⋊C4—861no—
676C22⋊C4—861no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—861no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C22⋊C4—861no—
686C22⋊C4—861no—
687C22⋊C4—861no—
688C22⋊C4—861no—
689C42—24no—
690C42—21no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—431no—
699C42—431no—
700C42—431no—
701C42—431no—
702C42—431no—
703C42—861no—
704C42—861no—
705C42—864no—
706C42—868no—
707C42—861no—
708C42C2×C4×D4311yescharacteristic
709C42C2×C4×D4311yescharacteristic
710C42D4×D4311yescharacteristic
711C42D4×D4311yescharacteristic
712C23—21no—
713C23—431no—
714C23—431no—
715C23—434no—
716C23—862no—
717C23—862no—
718C23—861no—
719C23—1722no—
720C23—1722no—
721C23—1722no—
722C23C2×D4×D4311yescharacteristic
723Q8—41no—
724Q8—1721no—
725Q8—1722no—
726D4—41no—
727D4—42no—
728D4—1721no—
729D4—1722no—
730D4—1722no—
731D4—1722no—
732D4—1722no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—431no—
744C2×C4—434no—
745C2×C4—431no—
746C2×C4—431no—
747C2×C4—431no—
748C2×C4—431no—
749C2×C4—431no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—864no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—17216no—
772C2×C4—1722no—
773C2×C4—1721no—
774C2×C4—1722no—
775C2×C4—1722no—
776C2×C4—1722no—
777C2×C4C22⋊C4×D4311yescharacteristic
778C2×C4C22⋊C4×D4311yescharacteristic
779C2×C4C22⋊C4×D4311yescharacteristic
780C2×C4C22⋊C4×D4311yescharacteristic
781C2×C4C22×C4×D4311yescharacteristic
782C2×C4C2×D4×D4311yescharacteristic
783C8—42no—
784C8—1722no—
785C22—21no—
786C22—21no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—432no—
791C22—432no—
792C22—432no—
793C22—432no—
794C22—868no—
795C22—861no—
796C22—861no—
797C22—3444no—
798C22—1721no—
799C22—1721no—
800C22—1721no—
801C22C2×C22⋊C4×D4311yescharacteristic
802C22#135×D4312yes—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—44no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—432no—
813C4—861no—
814C4—861no—
815C4—861no—
816C4—861no—
817C4—861no—
818C4—1724no—
819C4—1721no—
820C4—1721no—
821C4—1721no—
822C4#104×D4312yes—
823C2—22no—
824C2—81no—
825C2—434no—
826C2—862no—
827C2—3441no—
828C2#410×D4311yescharacteristic
829C2#416×D4311yescharacteristic
830C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1500C2
socleC22×C43C22×C22⋊C4
prime radical#121×D43C22
cosocleC22×C4×C43C24
hypercenter#1500D43
hypocenterC43C2×#1500
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #431×D43C2semidirect
3. #376×D43C2semidirect
4. #19133082C2semidirect
5. #19133081C2semidirect
6. #19133080C2semidirect
7. #19133079C2semidirect
8. #19133078C2semidirect
9. #328×D43C2semidirect
11. C43×#1500C2semidirect
12. #14583436C4semidirect
14. #14583434C4semidirect
17. #14583431C4semidirect
20. #14583428C4semidirect
24. #125×D43C4semidirect
25. #124×D43C4semidirect
29. C4×Q8×D43C4semidirect
31. C4×D4×D43C4semidirect
35. #14582952C22semidirect
38. #14582949C22semidirect
43. #14582745C22semidirect
45. #14582744C22semidirect
48. #14582637C22semidirect
49. #14582636C22semidirect
50. #14582635C22semidirect
55. C43×#431C22semidirect
56. C43×#376C22semidirect
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
416. #1500D43direct (N × H)
426. D43#1500direct (N × H)
455. #431C2×D43semidirect
463. #376C2×D43semidirect
469. #328C2×D43semidirect
474. C43C2×#1500semidirect
497. #125C4×D43semidirect
503. #124C4×D43semidirect
529. C4×Q8C4×D43semidirect
543. 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
#431×D432
#376×D432
#191330822
#191330812
#191330802
#191330792
#191330782
#328×D432
#327×D432
C43×#15002
C2×#150043