Finite Group Databasebeta

← #25064626

Subgroups — #25064626

Order 11008.

984 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D43C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3C2×#14582954C211yesmaximal, characteristic, complemented
4#19133225C212yesmaximal, complemented
5#19133223C212yesmaximal, complemented
6#19133220C212yesmaximal, complemented
7#19133217C212yesmaximal, complemented
8#19133184C211yesmaximal, characteristic, complemented
9#19133183C211yesmaximal, characteristic, complemented
10#19133181C211yesmaximal, characteristic, complemented
11C43×#1524C211yesmaximal, characteristic, complemented
12#14583436C411yescharacteristic
13#14583435C411yescharacteristic
14#14583434C2211yescharacteristic
15#14583433C2211yescharacteristic
16#14583432—21no—
17#14583431C411yescharacteristic
18#14583430C411yescharacteristic
19#14583429—21no—
20#14583428C2211yescharacteristic
21#14583427—21no—
22#14583426—21no—
23#126×D43—21no—
24#125×D43C2211yescharacteristic
25#124×D43C2211yescharacteristic
26#123×D43—21no—
27C22⋊Q8×D43C411yescharacteristic
28#121×D43C411yescharacteristic
29C4×Q8×D43C411yescharacteristic
30C4×D4×D43—21no—
31C4×D4×D43C411yescharacteristic
32#117×D43—21no—
33C2×C42×D43C2211yescharacteristic
34#14582954—21no—
35#14582954—21no—
36#14582954C2212yes—
37#14582954C2212yes—
38#14582954C2212yescomplemented
39#14582954C2212yescomplemented
40#14582950—21no—
41#14582950—21no—
42#14582922—21no—
43C2×Dic43⋊C8—21no—
44#14582862—21no—
45C2×(C2×D43)⋊C8—21no—
46C4×#10621877C2211yescharacteristic, complemented
47C2×#13063236C2211yescharacteristic, complemented
48#14582641C2212yescomplemented
49#14582640C2212yescomplemented
50#14582640C2212yescomplemented
51#14582639C2212yescomplemented
52#14582638C2212yescomplemented
53#14582638C2212yescomplemented
54C43×#529C2211yescharacteristic
55C4×M16×C43C2211yescharacteristic, complemented
56C2×#97×C43C2211yescharacteristic, complemented
57C43×#330C2212yescomplemented
58C43×#329C2212yescomplemented
59C2×Q8×D43C2×C411yescharacteristic
60C2×D4×D43—21no—
61C2×D4×D43C2×C411yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43C2×C411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C2×#10621877—21no—
67C22×C43⋊C8—21no—
68#13063320—21no—
69#13063320—21no—
70#13063320—21no—
71#13063319—21no—
72#13063318—21no—
73#13063318—21no—
74#13063318—21no—
75#13063317C2311yescharacteristic
76#13063316C2×C411yescharacteristic
77#13063316C2×C411yescharacteristic
78#13063315—21no—
79#13063315—21no—
80#13063314C2×C411yescharacteristic
81#13063313C2311yescharacteristic
82#13063312C2×C411yescharacteristic
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#13063304C2×C411yescharacteristic
94#13063303—21no—
95#13063302—21no—
96#13063301C2×C411yescharacteristic
97#13063300C2×C411yescharacteristic
98#13063299C2×C411yescharacteristic
99#13063298—21no—
100#13063297—21no—
101#13063296C2×C411yescharacteristic
102Q8×Dic43C2×C411yescharacteristic
103C4×Dic86—21no—
104C4×Dic86C2×C411yescharacteristic
105#13063290—21no—
106#13063290C2×C411yescharacteristic
107C4×D172—21no—
108C4×D172C2×C411yescharacteristic
109D4×Dic43—21no—
110D4×Dic43C2×C411yescharacteristic
111#13063287—21no—
112#13063287C2×C411yescharacteristic
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×Dic43C2×C411yescharacteristic
138C2×C4×Dic43D411yescharacteristic
139C2×C4×Dic43D411yescharacteristic
140C42×D43—21no—
141C42×D43C2×C411yescharacteristic
142C42×D43C2×C411yescharacteristic
143C42×D43D411yescharacteristic
144C42×D43D411yescharacteristic
145C42×D43D411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43C2311yescharacteristic
148C42×D43C2311yescharacteristic
149Dic43⋊C8—22no—
150Dic43⋊C8—22no—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153(C2×D43)⋊C8—22no—
154(C2×D43)⋊C8—22no—
155(C2×D43)⋊C8—22no—
156(C2×D43)⋊C8—22no—
157#13063236—21no—
158#13063236C2312yes—
159#13063236C2312yes—
160C4×C43⋊C8—21no—
161C2×M16×C43—21no—
162C22×C8×C43—21no—
163#126×C43—21no—
164#125×C43C2311yescharacteristic
165#124×C43C2311yescharacteristic
166#123×C43—21no—
167C22⋊Q8×C43C2×C411yescharacteristic
168#121×C43C2×C411yescharacteristic
169C4×Q8×C43C2×C411yescharacteristic
170C4×D4×C43—21no—
171C4×D4×C43C2×C411yescharacteristic
172#117×C43—21no—
173C2×C42×C43C2311yescharacteristic
174#97×C43—21no—
175#97×C43C2312yes—
176#97×C43C2312yes—
177C4×C8×C43—21no—
178C23×D43—21no—
179C23×D43C22⋊C411yescharacteristic
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43C22×C411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C22×Dic43—21no—
191C22×Dic43C22⋊C411yescharacteristic
192C22×Dic43C22⋊C411yescharacteristic
193C22×Dic43C22⋊C411yescharacteristic
194Q8×D43—42no—
195D4×D43—44no—
196D4×D43—42no—
197C2×D172—21no—
198C2×D172C22×C411yescharacteristic
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43—44no—
208C2×C4×D43C22⋊C411yescharacteristic
209C2×C4×D43C22⋊C411yescharacteristic
210C2×C4×D43C22⋊C411yescharacteristic
211C2×C4×D43C22⋊C411yescharacteristic
212C2×C4×D43C22⋊C411yescharacteristic
213C2×C4×D43C22⋊C411yescharacteristic
214C2×C4×D43C22×C411yescharacteristic
215C2×C4×D43C22×C411yescharacteristic
216C2×C4×D43C2×D411yescharacteristic
217C2×C4×D43C2×D411yescharacteristic
218C2×C4×D43C2×D411yescharacteristic
219C2×C4×D43C2×D411yescharacteristic
220C2×Dic86—21no—
221C2×Dic86C22×C411yescharacteristic
222M16×C43—42no—
223C2×C8×C43—22no—
224C2×C8×C43—22no—
225C2×C8×C43—42no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43C22×C411yescharacteristic
231C4⋊C4×C43C22×C411yescharacteristic
232C22⋊C4×C43—21no—
233C22⋊C4×C43—21no—
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C42×C43—21no—
238C42×C43C22×C411yescharacteristic
239C42×C43C2×D411yescharacteristic
240C42×C43C2×D411yescharacteristic
241C42×C43C2411yescharacteristic
242C22⋊Dic43—21no—
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247(C2×D43)⋊C4—21no—
248(C2×D43)⋊C4—21no—
249(C2×D43)⋊C4—21no—
250(C2×D43)⋊C4—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—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43C22×C411yescharacteristic
262C4⋊Dic43C22×C411yescharacteristic
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273C4×Dic43—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43C22⋊C411yescharacteristic
277C4×Dic43C22⋊C411yescharacteristic
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22×C411yescharacteristic
283C4×Dic43C22×C411yescharacteristic
284C4×Dic43C2×D411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288#10621877—42no—
289C2×C43⋊C8—22no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8—42no—
292C23×C43—21no—
293C23×C43C2×C22⋊C411yescharacteristic
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—21no—
297C22×D43—41no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43C2×C22⋊C411yescharacteristic
302C22×D43C2×C22⋊C411yescharacteristic
303Q8×C43—41no—
304D4×C43—41no—
305D4×C43—42no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—41no—
312C2×C4×C43—42no—
313C2×C4×C43C2×C22⋊C411yescharacteristic
314C2×C4×C43C2×C22⋊C411yescharacteristic
315C2×C4×C43C2×C22⋊C411yescharacteristic
316C2×C4×C43C23×C411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C22⋊D43—42no—
320C22⋊D43—42no—
321C22⋊D43—42no—
322C2×Dic43—22no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—42no—
329C2×Dic43C2×C22⋊C411yescharacteristic
330C2×Dic43C2×C22⋊C411yescharacteristic
331C2×Dic43C2×C22⋊C411yescharacteristic
332C2×Dic43C2×C22⋊C411yescharacteristic
333C2×Dic43C2×C22⋊C411yescharacteristic
334C2×Dic43C2×C22⋊C411yescharacteristic
335D172—41no—
336D172—42no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—41no—
342C4×D43—41no—
343C4×D43—41no—
344C4×D43—41no—
345C4×D43—41no—
346C4×D43—41no—
347C4×D43—41no—
348C4×D43—41no—
349C4×D43—42no—
350C4×D43—42no—
351C4×D43—42no—
352C4×D43—42no—
353C4×D43—42no—
354Dic86—42no—
355Dic86—41no—
356C8×C43—42no—
357C8×C43—42no—
358C43⋊C8—42no—
359C43⋊C8—42no—
360#17659—431nomaximal, Sylow
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43#42112yes—
367C22×C43C22×C22⋊C411yescharacteristic
368C2×D43—21no—
369C2×D43—21no—
370C2×D43—21no—
371C2×D43—21no—
372C2×D43—21no—
373C2×D43—44no—
374C2×D43—41no—
375C2×D43—41no—
376C2×D43—41no—
377C2×D43—84no—
378C2×D43#41312yes—
379C4×C43—21no—
380C4×C43—21no—
381C4×C43—21no—
382C4×C43—21no—
383C4×C43—21no—
384C4×C43—41no—
385C4×C43—41no—
386C4×C43—41no—
387C4×C43#42112yes—
388Dic43—21no—
389Dic43—21no—
390Dic43—21no—
391Dic43—21no—
392Dic43—21no—
393Dic43—21no—
394Dic43—41no—
395Dic43—41no—
396Dic43—41no—
397C2×#529—431no—
398#2920—431no—
399C2×#432—431no—
400#1535—432no—
401#1535—432no—
402#1534—432no—
403#1533—432no—
404#1524—431no—
405#1524—431no—
406#1524—431no—
407#1524D4311yescharacteristic, complemented
408C2×C43—22no—
409C2×C43—81no—
410C2×C43C2×#41311yescharacteristic
411C2×C43C2×#42111yescharacteristic
412C2×C43C2×#42111yescharacteristic
413D43—22no—
414D43—41no—
415D43—81no—
416#529—431no—
417#529—431no—
418#529—431no—
419#529—431no—
420#529—431no—
421#529—431no—
422#529—431no—
423#529—861no—
424#529—861no—
425#529—861no—
426#529—861no—
427#529C2×D4311yescharacteristic
428C2×#126—861no—
429C2×#125—431no—
430C2×#124—431no—
431C2×#123—861no—
432C2×C22⋊Q8—431no—
433C2×#121—431no—
434C2×C4×Q8—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×#117—861no—
438C22×C42—431no—
439#432—432no—
440#432—432no—
441#432—432no—
442#432—432no—
443#432—861no—
444#432—861no—
445#431—861no—
446#431—861no—
447#423—861no—
448C2×C4⋊C8—861no—
449#407—861no—
450C2×C22⋊C8—861no—
451C4×M16—431no—
452C4×M16C2×D4311yescharacteristic, complemented
453C2×#97—431no—
454C2×#97C2×D4311yescharacteristic, complemented
455#330—432no—
456#330—432no—
457#330—432no—
458#330C2×D4312yescomplemented
459#329—432no—
460#329—432no—
461#329—432no—
462#329C2×D4312yescomplemented
463C43#1765911yescharacteristic, complemented, Sylow
464C22×Q8—431no—
465C22×D4—431no—
466C22×D4—861no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C23×C4—861no—
471C2×M16—21no—
472C2×M16—861no—
473C22×C8—21no—
474C22×C8—861no—
475#126—21no—
476#126—861no—
477#126—861no—
478#126—861no—
479#126—861no—
480#126—861no—
481#126—861no—
482#126—861no—
483#125—431no—
484#125—431no—
485#125—431no—
486#125—861no—
487#125—861no—
488#125C22×D4311yescharacteristic
489#124—431no—
490#124—431no—
491#124—431no—
492#124—861no—
493#124—861no—
494#124C22×D4311yescharacteristic
495#123—21no—
496#123—861no—
497#123—861no—
498#123—861no—
499#123—861no—
500#123—861no—
501#123—861no—
502#123—861no—
503C22⋊Q8—431no—
504C22⋊Q8—431no—
505C22⋊Q8—431no—
506C22⋊Q8—861no—
507C22⋊Q8—861no—
508C22⋊Q8C4×D4311yescharacteristic
509#121—431no—
510#121—431no—
511#121—431no—
512#121—861no—
513#121—861no—
514#121C4×D4311yescharacteristic
515C4×Q8—431no—
516C4×Q8—431no—
517C4×Q8—431no—
518C4×Q8—861no—
519C4×Q8—861no—
520C4×Q8C4×D4311yescharacteristic
521C4×D4—21no—
522C4×D4—431no—
523C4×D4—431no—
524C4×D4—431no—
525C4×D4—861no—
526C4×D4—861no—
527C4×D4—861no—
528C4×D4—861no—
529C4×D4—861no—
530C4×D4—861no—
531C4×D4—861no—
532C4×D4—861no—
533C4×D4—861no—
534C4×D4C4×D4311yescharacteristic
535#117—21no—
536#117—861no—
537#117—861no—
538#117—861no—
539#117—861no—
540#117—861no—
541#117—861no—
542#117—861no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C42—431no—
555C2×C42—431no—
556C2×C42—431no—
557C2×C42—431no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—431no—
561C2×C42—431no—
562C2×C42—431no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—861no—
566C2×C42C22×D4311yescharacteristic
567C4⋊C8—862no—
568C4⋊C8—862no—
569C4⋊C8—862no—
570C4⋊C8—862no—
571C22⋊C8—862no—
572C22⋊C8—862no—
573C22⋊C8—862no—
574C22⋊C8—862no—
575#97—21no—
576#97—432no—
577#97—432no—
578#97—861no—
579#97C22×D4312yes—
580#97C22×D4312yes—
581C4×C8—21no—
582C4×C8—861no—
583C24—431no—
584C24—861no—
585C2×Q8—431no—
586C2×Q8—861no—
587C2×Q8—1722no—
588C2×Q8C2×C4×D4311yescharacteristic
589C2×D4—21no—
590C2×D4—431no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—1722no—
596C2×D4—1724no—
597C2×D4C2×C4×D4311yescharacteristic
598C22×C4—21no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—1722no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4—1724no—
624C22×C4C2×C4×D4311yescharacteristic
625C22×C4D4×D4311yescharacteristic
626C22×C4D4×D4311yescharacteristic
627M16—42no—
628M16—1722no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—42no—
632C2×C8—862no—
633C2×C8—862no—
634C2×C8—1722no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—431no—
640C4⋊C4—431no—
641C4⋊C4—861no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4C2×C4×D4311yescharacteristic
656C4⋊C4C2×C4×D4311yescharacteristic
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—861no—
663C22⋊C4—861no—
664C22⋊C4—861no—
665C22⋊C4—861no—
666C22⋊C4—861no—
667C22⋊C4—861no—
668C22⋊C4—861no—
669C22⋊C4—861no—
670C22⋊C4—861no—
671C22⋊C4—861no—
672C22⋊C4—861no—
673C22⋊C4—861no—
674C22⋊C4—861no—
675C22⋊C4—861no—
676C22⋊C4—861no—
677C42—21no—
678C42—431no—
679C42—431no—
680C42—431no—
681C42—431no—
682C42—431no—
683C42—431no—
684C42—431no—
685C42—431no—
686C42—431no—
687C42—431no—
688C42—431no—
689C42—431no—
690C42—861no—
691C42—861no—
692C42—861no—
693C42C2×C4×D4311yescharacteristic
694C42D4×D4311yescharacteristic
695C42D4×D4311yescharacteristic
696C42C23×D4311yescharacteristic
697C23—21no—
698C23—431no—
699C23—431no—
700C23—862no—
701C23—862no—
702C23—861no—
703C23—1721no—
704C23—1722no—
705C23—1722no—
706C23—1722no—
707C23C22⋊C4×D4311yescharacteristic
708Q8—41no—
709Q8—1721no—
710Q8—1722no—
711D4—41no—
712D4—42no—
713D4—1721no—
714D4—1722no—
715D4—1722no—
716D4—1722no—
717D4—1722no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—431no—
726C2×C4—431no—
727C2×C4—431no—
728C2×C4—431no—
729C2×C4—431no—
730C2×C4—431no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4—1722no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1722no—
754C2×C4—1722no—
755C2×C4C22⋊C4×D4311yescharacteristic
756C2×C4C22⋊C4×D4311yescharacteristic
757C2×C4C22⋊C4×D4311yescharacteristic
758C2×C4C22×C4×D4311yescharacteristic
759C2×C4C2×D4×D4311yescharacteristic
760C2×C4C2×D4×D4311yescharacteristic
761C8—42no—
762C8—42no—
763C8—1722no—
764C8—1722no—
765C22—21no—
766C22—21no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—432no—
771C22—861no—
772C22—861no—
773C22—861no—
774C22—861no—
775C22—861no—
776C22—3444no—
777C22—1724no—
778C22—1721no—
779C22—1721no—
780C22—1721no—
781C22#1458291412yes—
782C22C2×C22⋊C4×D4311yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—861no—
792C4—861no—
793C4—861no—
794C4—861no—
795C4—861no—
796C4—861no—
797C4—1721no—
798C4—1721no—
799C4—1721no—
800C4#1458291412yes—
801C2—22no—
802C2—81no—
803C2—862no—
804C2—3441no—
805C2—1721no—
806C2#413×D4311yescharacteristic
807C2C2×#1458291411yescharacteristic
808C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1524C2
socleC22×C43C22×C22⋊C4
prime radical#121×D43C4
cosocleC42×C43C24
hypercenter#1524D43
hypocenterC43#17659
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1524

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. C2×#14582954C2semidirect
4. #19133225C2semidirect
5. #19133223C2semidirect
6. #19133220C2semidirect
7. #19133217C2semidirect
8. #19133184C2semidirect
9. #19133183C2semidirect
10. #19133181C2semidirect
11. C43×#1524C2semidirect
38. #14582954C22semidirect
39. #14582954C22semidirect
46. C4×#10621877C22semidirect
47. C2×#13063236C22semidirect
48. #14582641C22semidirect
49. #14582640C22semidirect
50. #14582640C22semidirect
51. #14582639C22semidirect
52. #14582638C22semidirect
53. #14582638C22semidirect
55. C4×M16×C43C22semidirect
56. C2×#97×C43C22semidirect
57. C43×#330C22semidirect
58. C43×#329C22semidirect
407. #1524D43semidirect
452. C4×M16C2×D43semidirect
454. C2×#97C2×D43semidirect
458. #330C2×D43semidirect
462. #329C2×D43semidirect
463. C43#17659semidirect

Maximal subgroups

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

subgroupindex
#529×D432
#191432262
C2×#145829542
#191332252
#191332232
#191332202
#191332172
#191331842
#191331832
#191331812
C43×#15242
#1765943