Finite Group Databasebeta

← #25064513

Subgroups — #25064513

Order 11008.

1068 conjugacy classes of subgroups.

The subgroup lattice has 816 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×#14582851C211yesmaximal, characteristic, complemented
4#19133201C212yesmaximal, complemented
5#19133199C212yesmaximal, complemented
6#19133195C212yesmaximal, complemented
7#19133191C212yesmaximal, complemented
8#19133184C211yesmaximal, characteristic, complemented
9#19133183C211yesmaximal, characteristic, complemented
10#19133181C211yesmaximal, characteristic, complemented
11C43×#1524C211yesmaximal, characteristic, complemented
12C22×#10621872—21no—
13#14583436C411yescharacteristic
14#14583435C411yescharacteristic
15#14583434C2211yescharacteristic
16#14583433C2211yescharacteristic
17#14583432—21no—
18#14583431C411yescharacteristic
19#14583430C411yescharacteristic
20#14583429—21no—
21#14583428C2211yescharacteristic
22#14583427—21no—
23#14583426—21no—
24#126×D43—21no—
25#125×D43C2211yescharacteristic
26#124×D43C2211yescharacteristic
27#123×D43—21no—
28C22⋊Q8×D43C411yescharacteristic
29#121×D43C411yescharacteristic
30C4×Q8×D43C411yescharacteristic
31C4×D4×D43—21no—
32C4×D4×D43C411yescharacteristic
33#117×D43—21no—
34C2×C42×D43C2211yescharacteristic
35#14582954C2212yes—
36#14582954C2212yescomplemented
37#14582950—21no—
38#14582950—21no—
39#14582922—21no—
40#14582862—21no—
41C4×#10621877C2211yescharacteristic, complemented
42#14582851—21no—
43#14582851—21no—
44#14582851C2212yes—
45#14582851C2212yescomplemented
46C2×#13063236C2211yescharacteristic, complemented
47C2×C8×Dic43—21no—
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—
67C2×#10621872—28no—
68C2×#10621872—22no—
69C2×#10621872—22no—
70C22×C43⋊C8—21no—
71#13063320—21no—
72#13063320—21no—
73#13063320—21no—
74#13063319—21no—
75#13063318—21no—
76#13063318—21no—
77#13063318—21no—
78#13063317C2311yescharacteristic
79#13063316C2×C411yescharacteristic
80#13063316C2×C411yescharacteristic
81#13063315—21no—
82#13063315—21no—
83#13063314C2×C411yescharacteristic
84#13063313C2311yescharacteristic
85#13063312C2×C411yescharacteristic
86#13063311—21no—
87#13063311—21no—
88#13063310—21no—
89#13063310—21no—
90#13063309—21no—
91#13063308—21no—
92#13063307—21no—
93#13063307—21no—
94#13063306—21no—
95#13063305C2×C411yescharacteristic
96#13063304C2×C411yescharacteristic
97#13063303—21no—
98#13063302—21no—
99#13063301C2×C411yescharacteristic
100#13063300C2×C411yescharacteristic
101#13063299C2×C411yescharacteristic
102#13063298—21no—
103#13063297—21no—
104#13063296C2×C411yescharacteristic
105Q8×Dic43C2×C411yescharacteristic
106C4×Dic86—21no—
107C4×Dic86C2×C411yescharacteristic
108#13063290—21no—
109#13063290C2×C411yescharacteristic
110C4×D172—21no—
111C4×D172C2×C411yescharacteristic
112D4×Dic43—21no—
113D4×Dic43C2×C411yescharacteristic
114#13063287—21no—
115#13063287C2×C411yescharacteristic
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119(C22⋊D43)⋊C4—21no—
120(C22⋊D43)⋊C4—21no—
121(C22⋊D43)⋊C4—21no—
122#13063284—21no—
123#13063283—21no—
124#13063283—21no—
125#13063282—21no—
126#13063282—21no—
127#13063281—21no—
128#13063281—21no—
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×Dic43C2×C411yescharacteristic
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C42×D43—21no—
144C42×D43C2×C411yescharacteristic
145C42×D43C2×C411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43D411yescharacteristic
148C42×D43D411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43C2311yescharacteristic
151C42×D43C2311yescharacteristic
152Dic43⋊C8—22no—
153Dic43⋊C8—22no—
154(C2×D43)⋊C8—22no—
155(C2×D43)⋊C8—22no—
156#13063236—21no—
157#13063236C2312yes—
158#13063236C2312yes—
159C4×C43⋊C8—21no—
160C8×Dic43—22no—
161C8×Dic43—22no—
162C2×M16×C43—21no—
163C22×C8×C43—21no—
164#126×C43—21no—
165#125×C43C2311yescharacteristic
166#124×C43C2311yescharacteristic
167#123×C43—21no—
168C22⋊Q8×C43C2×C411yescharacteristic
169#121×C43C2×C411yescharacteristic
170C4×Q8×C43C2×C411yescharacteristic
171C4×D4×C43—21no—
172C4×D4×C43C2×C411yescharacteristic
173#117×C43—21no—
174C2×C42×C43C2311yescharacteristic
175#97×C43—21no—
176#97×C43C2312yes—
177#97×C43C2312yes—
178C4×C8×C43—21no—
179C23×D43—21no—
180C23×D43C22⋊C411yescharacteristic
181C2×Q8×C43C22×C411yescharacteristic
182C2×D4×C43—21no—
183C2×D4×C43C22×C411yescharacteristic
184C22×C4×C43—21no—
185C22×C4×C43C22×C411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C22×Dic43—21no—
192C22×Dic43C22⋊C411yescharacteristic
193C22×Dic43C22⋊C411yescharacteristic
194C22×Dic43C22⋊C411yescharacteristic
195Q8×D43—42no—
196D4×D43—44no—
197D4×D43—42no—
198C2×D172—21no—
199C2×D172C22×C411yescharacteristic
200C2×C4×D43—24no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×C4×D43—44no—
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×D43C22×C411yescharacteristic
217C2×C4×D43C2×D411yescharacteristic
218C2×C4×D43C2×D411yescharacteristic
219C2×C4×D43C2×D411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×Dic86—21no—
222C2×Dic86C22×C411yescharacteristic
223M16×C43—42no—
224C2×C8×C43—24no—
225C2×C8×C43—22no—
226C2×C8×C43—22no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43C22×C411yescharacteristic
232C4⋊C4×C43C22×C411yescharacteristic
233C22⋊C4×C43—21no—
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C42×C43—21no—
239C42×C43C22×C411yescharacteristic
240C42×C43C2×D411yescharacteristic
241C42×C43C2×D411yescharacteristic
242C42×C43C2411yescharacteristic
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—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—
257(C2×D43)⋊C4—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C22×C411yescharacteristic
263C4⋊Dic43C22×C411yescharacteristic
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—
273Dic43⋊C4—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43C22⋊C411yescharacteristic
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22×C411yescharacteristic
284C4×Dic43C22×C411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289#10621877—42no—
290C2×C43⋊C8—24no—
291C2×C43⋊C8—22no—
292C2×C43⋊C8—22no—
293#10621872—28no—
294#10621872—28no—
295C23×C43—21no—
296C23×C43C2×C22⋊C411yescharacteristic
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—21no—
300C22×D43—41no—
301C22×D43—42no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43C2×C22⋊C411yescharacteristic
305C22×D43C2×C22⋊C411yescharacteristic
306Q8×C43—41no—
307D4×C43—41no—
308D4×C43—42no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—41no—
315C2×C4×C43—42no—
316C2×C4×C43C2×C22⋊C411yescharacteristic
317C2×C4×C43C2×C22⋊C411yescharacteristic
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C23×C411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C22⋊D43—42no—
323C22⋊D43—42no—
324C22⋊D43—42no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—42no—
332C2×Dic43C2×C22⋊C411yescharacteristic
333C2×Dic43C2×C22⋊C411yescharacteristic
334C2×Dic43C2×C22⋊C411yescharacteristic
335C2×Dic43C2×C22⋊C411yescharacteristic
336C2×Dic43C2×C22⋊C411yescharacteristic
337C2×Dic43C2×C22⋊C411yescharacteristic
338D172—41no—
339D172—42no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—41no—
346C4×D43—41no—
347C4×D43—41no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—41no—
351C4×D43—42no—
352C4×D43—42no—
353C4×D43—42no—
354C4×D43—42no—
355C4×D43—42no—
356C4×D43#10414yes—
357Dic86—42no—
358Dic86—41no—
359C8×C43—24no—
360C8×C43—42no—
361C43⋊C8—24no—
362C43⋊C8—42no—
363#17642—431nomaximal, Sylow
364C22×C43—21no—
365C22×C43—21no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43#42112yes—
370C22×C43C22×C22⋊C411yescharacteristic
371C2×D43—21no—
372C2×D43—21no—
373C2×D43—21no—
374C2×D43—21no—
375C2×D43—21no—
376C2×D43—44no—
377C2×D43—41no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—84no—
381C2×D43C2×#10412yes—
382C4×C43—21no—
383C4×C43—21no—
384C4×C43—21no—
385C4×C43—21no—
386C4×C43—21no—
387C4×C43—41no—
388C4×C43—41no—
389C4×C43—41no—
390C4×C43C2×#10412yes—
391Dic43—21no—
392Dic43—21no—
393Dic43—21no—
394Dic43—21no—
395Dic43—41no—
396Dic43—41no—
397Dic43—41no—
398Dic43#41312yes—
399Dic43C2×#10412yes—
400C2×#529—431no—
401#2920—431no—
402C2×C4×M16—431no—
403#1529—432no—
404#1529—432no—
405#1528—432no—
406#1527—432no—
407#1524—431no—
408#1524—431no—
409#1524—431no—
410#1524D4311yescharacteristic, complemented
411C2×C43—22no—
412C2×C43—81no—
413C2×C43C2×#41311yescharacteristic
414C2×C43C22×#10411yescharacteristic
415C2×C43C2×#42111yescharacteristic
416D43—22no—
417D43—41no—
418D43—81no—
419C22×M16—861no—
420#529—431no—
421#529—431no—
422#529—431no—
423#529—431no—
424#529—431no—
425#529—431no—
426#529—431no—
427#529—861no—
428#529—861no—
429#529—861no—
430#529—861no—
431#529C2×D4311yescharacteristic
432C2×#126—861no—
433C2×#125—431no—
434C2×#124—431no—
435C2×#123—861no—
436C2×C22⋊Q8—431no—
437C2×#121—431no—
438C2×C4×Q8—431no—
439C2×C4×D4—431no—
440C2×C4×D4—861no—
441C2×#117—861no—
442C22×C42—431no—
443#432—432no—
444#432—432no—
445#431—861no—
446#431—861no—
447#423—861no—
448#407—861no—
449C4×M16—431no—
450C4×M16—432no—
451C4×M16—432no—
452C4×M16—861no—
453C4×M16—861no—
454C4×M16C2×D4311yescharacteristic, complemented
455C2×#97—431no—
456C2×#97C2×D4311yescharacteristic, complemented
457C2×C4×C8—861no—
458#330—432no—
459#330—432no—
460#330—432no—
461#330C2×D4312yescomplemented
462#329—432no—
463#329—432no—
464#329—432no—
465#329C2×D4312yescomplemented
466C43#1764211yescharacteristic, complemented, Sylow
467C22×Q8—431no—
468C22×D4—431no—
469C22×D4—861no—
470C23×C4—431no—
471C23×C4—431no—
472C23×C4—431no—
473C23×C4—861no—
474C2×M16—21no—
475C2×M16—862no—
476C2×M16—862no—
477C2×M16—868no—
478C2×M16—861no—
479C22×C8—21no—
480C22×C8—861no—
481#126—21no—
482#126—861no—
483#126—861no—
484#126—861no—
485#126—861no—
486#126—861no—
487#126—861no—
488#126—861no—
489#125—431no—
490#125—431no—
491#125—431no—
492#125—861no—
493#125—861no—
494#125C22×D4311yescharacteristic
495#124—431no—
496#124—431no—
497#124—431no—
498#124—861no—
499#124—861no—
500#124C22×D4311yescharacteristic
501#123—21no—
502#123—861no—
503#123—861no—
504#123—861no—
505#123—861no—
506#123—861no—
507#123—861no—
508#123—861no—
509C22⋊Q8—431no—
510C22⋊Q8—431no—
511C22⋊Q8—431no—
512C22⋊Q8—861no—
513C22⋊Q8—861no—
514C22⋊Q8C4×D4311yescharacteristic
515#121—431no—
516#121—431no—
517#121—431no—
518#121—861no—
519#121—861no—
520#121C4×D4311yescharacteristic
521C4×Q8—431no—
522C4×Q8—431no—
523C4×Q8—431no—
524C4×Q8—861no—
525C4×Q8—861no—
526C4×Q8C4×D4311yescharacteristic
527C4×D4—21no—
528C4×D4—431no—
529C4×D4—431no—
530C4×D4—431no—
531C4×D4—861no—
532C4×D4—861no—
533C4×D4—861no—
534C4×D4—861no—
535C4×D4—861no—
536C4×D4—861no—
537C4×D4—861no—
538C4×D4—861no—
539C4×D4—861no—
540C4×D4C4×D4311yescharacteristic
541#117—21no—
542#117—861no—
543#117—861no—
544#117—861no—
545#117—861no—
546#117—861no—
547#117—861no—
548#117—861no—
549C2×C4⋊C4—431no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C42—431no—
561C2×C42—431no—
562C2×C42—431no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—861no—
572C2×C42C22×D4311yescharacteristic
573C4⋊C8—862no—
574C4⋊C8—862no—
575C22⋊C8—862no—
576C22⋊C8—862no—
577#97—21no—
578#97—432no—
579#97—432no—
580#97—861no—
581#97C22×D4312yes—
582#97C22×D4312yes—
583C4×C8—21no—
584C4×C8—862no—
585C4×C8—862no—
586C4×C8—861no—
587C24—431no—
588C24—861no—
589C2×Q8—431no—
590C2×Q8—861no—
591C2×Q8—1722no—
592C2×Q8C2×C4×D4311yescharacteristic
593C2×D4—21no—
594C2×D4—431no—
595C2×D4—861no—
596C2×D4—861no—
597C2×D4—861no—
598C2×D4—861no—
599C2×D4—1722no—
600C2×D4—1724no—
601C2×D4C2×C4×D4311yescharacteristic
602C22×C4—21no—
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—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—864no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—1722no—
626C22×C4—1724no—
627C22×C4—1722no—
628C22×C4C2×C4×D4311yescharacteristic
629C22×C4D4×D4311yescharacteristic
630C22×C4D4×D4311yescharacteristic
631M16—42no—
632M16—868no—
633M16—868no—
634M16—1722no—
635C2×C8—24no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—864no—
639C2×C8—862no—
640C2×C8—862no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—431no—
646C4⋊C4—431no—
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⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4C2×C4×D4311yescharacteristic
662C4⋊C4C2×C4×D4311yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
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—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—861no—
683C42—21no—
684C42—431no—
685C42—431no—
686C42—431no—
687C42—431no—
688C42—431no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—861no—
697C42—861no—
698C42—861no—
699C42C2×C4×D4311yescharacteristic
700C42D4×D4311yescharacteristic
701C42D4×D4311yescharacteristic
702C42C23×D4311yescharacteristic
703C23—21no—
704C23—431no—
705C23—431no—
706C23—862no—
707C23—862no—
708C23—861no—
709C23—1721no—
710C23—1722no—
711C23—1722no—
712C23—1722no—
713C23C22⋊C4×D4311yescharacteristic
714Q8—41no—
715Q8—1721no—
716Q8—1722no—
717D4—41no—
718D4—42no—
719D4—1721no—
720D4—1722no—
721D4—1722no—
722D4—1722no—
723D4—1722no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—431no—
732C2×C4—431no—
733C2×C4—434no—
734C2×C4—431no—
735C2×C4—431no—
736C2×C4—431no—
737C2×C4—431no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—861no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1722no—
756C2×C4—1722no—
757C2×C4—1722no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4C22⋊C4×D4311yescharacteristic
762C2×C4C22⋊C4×D4311yescharacteristic
763C2×C4C22⋊C4×D4311yescharacteristic
764C2×C4C22×C4×D4311yescharacteristic
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4C2×D4×D4311yescharacteristic
767C8—24no—
768C8—42no—
769C8—864no—
770C8—1722no—
771C22—21no—
772C22—21no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—432no—
777C22—861no—
778C22—861no—
779C22—861no—
780C22—861no—
781C22—861no—
782C22—3444no—
783C22—1724no—
784C22—1721no—
785C22—1721no—
786C22—1721no—
787C22#1458291412yes—
788C22C2×C22⋊C4×D4311yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—432no—
798C4—432no—
799C4—861no—
800C4—861no—
801C4—861no—
802C4—861no—
803C4—1721no—
804C4—1721no—
805C4—1721no—
806C4#104×D4312yes—
807C2—22no—
808C2—81no—
809C2—862no—
810C2—3441no—
811C2—1721no—
812C2#413×D4311yescharacteristic
813C2C2×#104×D4311yescharacteristic
814C2C2×#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#17642
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×#14582851C2semidirect
4. #19133201C2semidirect
5. #19133199C2semidirect
6. #19133195C2semidirect
7. #19133191C2semidirect
8. #19133184C2semidirect
9. #19133183C2semidirect
10. #19133181C2semidirect
11. C43×#1524C2semidirect
36. #14582954C22semidirect
41. C4×#10621877C22semidirect
45. #14582851C22semidirect
46. 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
410. #1524D43semidirect
454. C4×M16C2×D43semidirect
456. C2×#97C2×D43semidirect
461. #330C2×D43semidirect
465. #329C2×D43semidirect
466. C43#17642semidirect

Maximal subgroups

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

subgroupindex
#529×D432
#191432262
C2×#145828512
#191332012
#191331992
#191331952
#191331912
#191331842
#191331832
#191331812
C43×#15242
#1764243