Finite Group Databasebeta

← #25063842

Subgroups — #25063842

Order 11008.

1024 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D43C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3#19136987C211yesmaximal, characteristic, complemented
4#19133132C212yesmaximal, complemented
5#19133130C212yesmaximal, complemented
6#19133126C212yesmaximal, complemented
7#19133122C212yesmaximal
8#19133082C211yesmaximal, characteristic, complemented
9#19133081C211yesmaximal, characteristic, complemented
10#19133079C211yesmaximal, characteristic, complemented
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×D43C2211yescharacteristic
34#14582955—21no—
35#14582953C2212yescomplemented
36#14582952C2211yescharacteristic, complemented
37#14582950—21no—
38#14582921—21no—
39#14582861C2212yes—
40C4×#10621872—21no—
41#14582766—21no—
42#14582763C2212yescomplemented
43#14582761C2212yes—
44#14582758—21no—
45C4×Dic43⋊C4—21no—
46C4×(C2×D43)⋊C4—21no—
47#14582745C2211yescharacteristic, complemented
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—21no—
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C2×#10621872—22no—
67#13063320—21no—
68#13063320—21no—
69#13063320—21no—
70#13063319—21no—
71#13063318—21no—
72#13063318—21no—
73#13063318—21no—
74#13063317C2×C411yescharacteristic
75#13063316C2×C411yescharacteristic
76#13063316C2×C411yescharacteristic
77#13063315—21no—
78#13063315—21no—
79#13063314C2×C411yescharacteristic
80#13063313C2×C411yescharacteristic
81#13063312C2×C411yescharacteristic
82#13063311—21no—
83#13063311—21no—
84#13063310—21no—
85#13063310—21no—
86#13063309—21no—
87#13063308—21no—
88#13063307—21no—
89#13063307—21no—
90#13063306—21no—
91#13063305C2×C411yescharacteristic
92#13063304C2311yescharacteristic
93#13063303—21no—
94#13063302—21no—
95#13063301C2×C411yescharacteristic
96#13063300C2×C411yescharacteristic
97#13063299C2311yescharacteristic
98#13063298—21no—
99#13063297—21no—
100#13063296C2×C411yescharacteristic
101Q8×Dic43C2×C411yescharacteristic
102C4×Dic86—21no—
103C4×Dic86C2×C411yescharacteristic
104#13063290—21no—
105#13063290C2×C411yescharacteristic
106C4×D172—21no—
107C4×D172C2×C411yescharacteristic
108D4×Dic43—21no—
109D4×Dic43C2×C411yescharacteristic
110#13063287—21no—
111#13063287C2×C411yescharacteristic
112C4×C22⋊D43—21no—
113C4×C22⋊D43—21no—
114C4×C22⋊D43—21no—
115(C22⋊D43)⋊C4—21no—
116(C22⋊D43)⋊C4—21no—
117(C22⋊D43)⋊C4—21no—
118#13063284—21no—
119#13063283—21no—
120#13063283—21no—
121#13063282—21no—
122#13063282—21no—
123#13063281—21no—
124#13063281—21no—
125C2×Dic43⋊C4—22no—
126C4⋊C4×D43—21no—
127C4⋊C4×D43—21no—
128C4⋊C4×D43—21no—
129C4⋊C4×D43—21no—
130C4⋊C4×D43C2×C411yescharacteristic
131C4⋊C4×D43C2×C411yescharacteristic
132C2×(C2×D43)⋊C4—22no—
133C22⋊C4×D43—21no—
134C22⋊C4×D43—21no—
135C22⋊C4×D43—21no—
136C22⋊C4×D43—21no—
137C22⋊C4×D43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43D411yescharacteristic
140C2×C4×Dic43D411yescharacteristic
141C2×C4×Dic43C2311yescharacteristic
142C42×D43—21no—
143C42×D43C2×C411yescharacteristic
144C42×D43C2×C411yescharacteristic
145C42×D43C2×C411yescharacteristic
146C42×D43C2×C411yescharacteristic
147C42×D43D411yescharacteristic
148C42×D43D411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43D411yescharacteristic
151C4⋊(C43⋊C8)—21no—
152Dic43⋊C8—22no—
153C22⋊(C43⋊C8)C2312yes—
154(C2×D43)⋊C8—22no—
155#13063235—22no—
156C4×C43⋊C8—21no—
157C43⋊#95—21no—
158C43⋊#95—22no—
159C43⋊#95—22no—
160C43⋊#95C2312yes—
161#126×C43—21no—
162#125×C43C2×C411yescharacteristic
163#124×C43C2×C411yescharacteristic
164#123×C43—21no—
165C22⋊Q8×C43C2311yescharacteristic
166#121×C43C2311yescharacteristic
167C4×Q8×C43C2×C411yescharacteristic
168C4×D4×C43—21no—
169C4×D4×C43C2×C411yescharacteristic
170#117×C43—21no—
171C2×C42×C43—21no—
172C2×C42×C43C2311yescharacteristic
173C4⋊C8×C43—21no—
174C22⋊C8×C43C2312yes—
175C4×C8×C43—21no—
176#95×C43—21no—
177#95×C43C2312yes—
178C23×D43—21no—
179C23×D43C2×D411yescharacteristic
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43—22no—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C22×Dic43—21no—
192C22×Dic43—22no—
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196Q8×D43—42no—
197D4×D43—44no—
198D4×D43—42no—
199C2×D172—21no—
200C2×D172C22×C411yescharacteristic
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—42no—
209C2×C4×D43—44no—
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×D43C22⋊C411yescharacteristic
218C2×C4×D43C22×C411yescharacteristic
219C2×C4×D43C22×C411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×Dic86—21no—
223C2×Dic86C22×C411yescharacteristic
224C2×C8×C43—22no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43C22×C411yescharacteristic
230C4⋊C4×C43C22×C411yescharacteristic
231C22⋊C4×C43—21no—
232C22⋊C4×C43—21no—
233C22⋊C4×C43—21no—
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C42×C43—21no—
237C42×C43—42no—
238C42×C43C22×C411yescharacteristic
239C42×C43C22×C411yescharacteristic
240C42×C43C2×D411yescharacteristic
241C42×C43C2×D411yescharacteristic
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—
257(C2×D43)⋊C4—44no—
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—
274Dic43⋊C4—44no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—42no—
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22⋊C411yescharacteristic
286C4×Dic43C22⋊C411yescharacteristic
287C4×Dic43C22×C411yescharacteristic
288C4×Dic43C22×C411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290C4×Dic43C2×D411yescharacteristic
291C2×C43⋊C8—22no—
292#10621872—44no—
293C23×C43—21no—
294C23×C43C22×D411yescharacteristic
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—21no—
298C22×D43—41no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43C2×C22⋊C411yescharacteristic
303C22×D43C2×C22⋊C411yescharacteristic
304Q8×C43—41no—
305D4×C43—41no—
306D4×C43—42no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—41no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43C2×C22⋊C411yescharacteristic
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C23×C411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C22⋊D43—42no—
324C22⋊D43—42no—
325C22⋊D43—42no—
326C2×Dic43—22no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43C2×C22⋊C411yescharacteristic
337C2×Dic43C2×C22⋊C411yescharacteristic
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341C2×Dic43C2×C22⋊C411yescharacteristic
342D172—41no—
343D172—42no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—41no—
351C4×D43—41no—
352C4×D43—41no—
353C4×D43—41no—
354C4×D43—41no—
355C4×D43—41no—
356C4×D43—42no—
357C4×D43—42no—
358C4×D43—42no—
359C4×D43—42no—
360C4×D43—42no—
361Dic86—42no—
362Dic86—41no—
363C8×C43—42no—
364C43⋊C8—42no—
365#17554—431nomaximal, Sylow
366C22×C43—21no—
367C22×C43—21no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43C22×C22⋊C411yescharacteristic
372C22×C43#57512yes—
373C2×D43—21no—
374C2×D43—21no—
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—44no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—84no—
383C2×D43#41012yes—
384C4×C43—21no—
385C4×C43—21no—
386C4×C43—21no—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43—82no—
393C4×C43#42112yes—
394Dic43—21no—
395Dic43—21no—
396Dic43—21no—
397Dic43—21no—
398Dic43—21no—
399Dic43—21no—
400Dic43—41no—
401Dic43—41no—
402Dic43—41no—
403Dic43—82no—
404C2×#529—431no—
405#2920—431no—
406#2283—431no—
407#1512—432no—
408#1512—432no—
409#1511—432no—
410#1510—432no—
411#1500—431no—
412#1500—431no—
413#1500—431no—
414#1500D4311yescharacteristic, complemented
415C2×C43—22no—
416C2×C43—81no—
417C2×C43C2×#41011yescharacteristic
418C2×C43#289611yescharacteristic
419C2×C43C2×#42111yescharacteristic
420D43—22no—
421D43—41no—
422D43—81no—
423#529—431no—
424#529—431no—
425#529—431no—
426#529—431no—
427#529—431no—
428#529—431no—
429#529—431no—
430#529—861no—
431#529—861no—
432#529—861no—
433#529—861no—
434#529C2×D4311yescharacteristic
435C2×#126—861no—
436C2×#125—431no—
437C2×#124—431no—
438C2×#123—861no—
439C2×C22⋊Q8—431no—
440C2×#121—431no—
441C2×C4×Q8—431no—
442C2×C4×D4—431no—
443C2×C4×D4—861no—
444C2×#117—861no—
445C22×C42—431no—
446#432—432no—
447#432—861no—
448#431—431no—
449#431—861no—
450#431C2×D4311yescharacteristic, complemented
451#423—861no—
452#407—432no—
453C4×M16—861no—
454#383—861no—
455#382—432no—
456#381—432no—
457#380—861no—
458C4×C4⋊C4—861no—
459C4×C22⋊C4—861no—
460#376—431no—
461#376C2×D4311yescharacteristic, complemented
462#328—432no—
463#328—432no—
464#328—432no—
465#328C2×D4312yescomplemented
466#327—432no—
467#327—432no—
468#327—432no—
469#327C2×D4312yes—
470C43#1755411yescharacteristic, complemented, Sylow
471C22×Q8—431no—
472C22×D4—431no—
473C22×D4—861no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—861no—
478C2×M16—862no—
479#126—21no—
480#126—861no—
481#126—861no—
482#126—861no—
483#126—861no—
484#126—861no—
485#126—861no—
486#126—861no—
487#125—431no—
488#125—431no—
489#125—431no—
490#125—861no—
491#125—861no—
492#125C4×D4311yescharacteristic
493#124—431no—
494#124—431no—
495#124—431no—
496#124—861no—
497#124—861no—
498#124C4×D4311yescharacteristic
499#123—21no—
500#123—861no—
501#123—861no—
502#123—861no—
503#123—861no—
504#123—861no—
505#123—861no—
506#123—861no—
507C22⋊Q8—431no—
508C22⋊Q8—431no—
509C22⋊Q8—431no—
510C22⋊Q8—861no—
511C22⋊Q8—861no—
512C22⋊Q8C22×D4311yescharacteristic
513#121—431no—
514#121—431no—
515#121—431no—
516#121—861no—
517#121—861no—
518#121C22×D4311yescharacteristic
519C4×Q8—431no—
520C4×Q8—431no—
521C4×Q8—431no—
522C4×Q8—861no—
523C4×Q8—861no—
524C4×Q8C4×D4311yescharacteristic
525C4×D4—21no—
526C4×D4—431no—
527C4×D4—431no—
528C4×D4—431no—
529C4×D4—861no—
530C4×D4—861no—
531C4×D4—861no—
532C4×D4—861no—
533C4×D4—861no—
534C4×D4—861no—
535C4×D4—861no—
536C4×D4—861no—
537C4×D4—861no—
538C4×D4C4×D4311yescharacteristic
539#117—21no—
540#117—861no—
541#117—861no—
542#117—861no—
543#117—861no—
544#117—861no—
545#117—861no—
546#117—861no—
547C2×C4⋊C4—431no—
548C2×C4⋊C4—431no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—862no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—862no—
560C2×C42—21no—
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—431no—
572C2×C42—861no—
573C2×C42—861no—
574C2×C42C22×D4311yescharacteristic
575C4⋊C8—21no—
576C4⋊C8—862no—
577C4⋊C8—861no—
578C22⋊C8—432no—
579C22⋊C8—862no—
580C22⋊C8C22×D4312yes—
581#97—862no—
582C4×C8—21no—
583C4×C8—861no—
584#95—21no—
585#95—432no—
586#95—862no—
587#95—862no—
588#95—861no—
589#95C22×D4312yes—
590C24—431no—
591C24—861no—
592C2×Q8—431no—
593C2×Q8—861no—
594C2×Q8—1722no—
595C2×Q8C2×C4×D4311yescharacteristic
596C2×D4—21no—
597C2×D4—431no—
598C2×D4—861no—
599C2×D4—861no—
600C2×D4—861no—
601C2×D4—861no—
602C2×D4—1722no—
603C2×D4—1724no—
604C2×D4C2×C4×D4311yescharacteristic
605C22×C4—21no—
606C22×C4—22no—
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—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—862no—
629C22×C4—1722no—
630C22×C4—1722no—
631C22×C4—1722no—
632C22×C4—1724no—
633C22×C4D4×D4311yescharacteristic
634C22×C4D4×D4311yescharacteristic
635C22×C4C23×D4311yescharacteristic
636M16—1724no—
637C2×C8—22no—
638C2×C8—862no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—431no—
644C4⋊C4—431no—
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⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—1724no—
660C4⋊C4C2×C4×D4311yescharacteristic
661C4⋊C4C2×C4×D4311yescharacteristic
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
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—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—1724no—
683C42—21no—
684C42—42no—
685C42—431no—
686C42—431no—
687C42—431no—
688C42—431no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—861no—
698C42—861no—
699C42—861no—
700C42—1722no—
701C42C2×C4×D4311yescharacteristic
702C42C2×C4×D4311yescharacteristic
703C42D4×D4311yescharacteristic
704C42D4×D4311yescharacteristic
705C23—21no—
706C23—431no—
707C23—431no—
708C23—862no—
709C23—862no—
710C23—861no—
711C23—1721no—
712C23—1722no—
713C23—1722no—
714C23—1722no—
715C23C2×D4×D4311yescharacteristic
716Q8—41no—
717Q8—1721no—
718Q8—1722no—
719D4—41no—
720D4—42no—
721D4—1721no—
722D4—1722no—
723D4—1722no—
724D4—1722no—
725D4—1722no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—431no—
737C2×C4—431no—
738C2×C4—431no—
739C2×C4—431no—
740C2×C4—431no—
741C2×C4—431no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4C22⋊C4×D4311yescharacteristic
770C2×C4C22⋊C4×D4311yescharacteristic
771C2×C4C22⋊C4×D4311yescharacteristic
772C2×C4C22⋊C4×D4311yescharacteristic
773C2×C4C22×C4×D4311yescharacteristic
774C2×C4C2×D4×D4311yescharacteristic
775C8—42no—
776C8—1722no—
777C22—21no—
778C22—21no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—432no—
783C22—861no—
784C22—861no—
785C22—861no—
786C22—861no—
787C22—861no—
788C22—3444no—
789C22—1724no—
790C22—1721no—
791C22—1721no—
792C22—1721no—
793C22C2×C22⋊C4×D4311yescharacteristic
794C22#1458369612yes—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—82no—
804C4—861no—
805C4—861no—
806C4—861no—
807C4—861no—
808C4—861no—
809C4—861no—
810C4—3442no—
811C4—1721no—
812C4—1721no—
813C4—1721no—
814C4#1458291412yes—
815C2—22no—
816C2—81no—
817C2—862no—
818C2—3441no—
819C2—1721no—
820C2#410×D4311yescharacteristic
821C2#1914311011yescharacteristic
822C2C2×#1458291411yescharacteristic
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
hypocenterC43#17554
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. #19143223C2semidirect
3. #19136987C2semidirect
4. #19133132C2semidirect
5. #19133130C2semidirect
6. #19133126C2semidirect
8. #19133082C2semidirect
9. #19133081C2semidirect
10. #19133079C2semidirect
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. #14582953C22semidirect
36. #14582952C22semidirect
42. #14582763C22semidirect
47. #14582745C22semidirect
48. #14582637C22semidirect
49. #14582636C22semidirect
50. #14582635C22semidirect
55. C43×#431C22semidirect
56. C43×#376C22semidirect
57. C43×#328C22semidirect
414. #1500D43semidirect
450. #431C2×D43semidirect
461. #376C2×D43semidirect
465. #328C2×D43semidirect
470. C43#17554semidirect

Maximal subgroups

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

subgroupindex
#529×D432
#191432232
#191369872
#191331322
#191331302
#191331262
#191331222
#191330822
#191330812
#191330792
C43×#15002
#1755443