Finite Group Databasebeta

← #25102291

Subgroups — #25102291

Order 11008.

1552 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583367C211yesmaximal, characteristic, complemented
2C2×#14583042C211yesmaximal, characteristic
3C2×#14583008C211yesmaximal, characteristic, complemented
4C2×#14582996C211yesmaximal, characteristic, complemented
5#121×Dic43C211yesmaximal, characteristic, complemented
6#19134947C211yesmaximal, characteristic, complemented
7#19134940C211yesmaximal, characteristic, complemented
8#19134864C211yesmaximal, characteristic, complemented
9#19134843C211yesmaximal, characteristic, complemented
10#19134794C211yesmaximal, characteristic, complemented
11#19134536C211yesmaximal, characteristic, complemented
12#19134424C211yesmaximal, characteristic, complemented
13#19134419C211yesmaximal, characteristic, complemented
14#19134359C211yesmaximal, characteristic, complemented
15C43×#1875C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19#14583367—24no—
20#14583367—24no—
21C2×#13063290C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×D4×Dic43—21no—
24C2×D4×Dic43C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×(C22⋊D43)⋊C4—21no—
28C2×(C22⋊D43)⋊C4—21no—
29C2×#13063282—21no—
30C22×C4×Dic43C2211yescharacteristic
31C2×C42×D43—21no—
32#14583042C418yescomplemented
33#14583008—24no—
34#14582996—24no—
35C2×#13063258C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×#13063235C2211yescharacteristic
45C2×#13063235C2211yescharacteristic
46#14582802C2211yescharacteristic
47#14582798C2211yescharacteristic
48#14582792—21no—
49#14582779—21no—
50#14582759C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic
52C22⋊C4×Dic43—21no—
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×#121×C43C2211yescharacteristic
58C2×#117×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C23×Dic43—21no—
74C23×Dic43D411yescharacteristic
75C23×Dic43D411yescharacteristic
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C22×C4×D43—21no—
79C2×#10621883—22no—
80C2×#10621883—22no—
81C2×#10621883C2×C414yescomplemented
82C2×#10621882—22no—
83C2×#10621882—22no—
84C2×#10621882C2×C414yescomplemented
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87#13063290—22no—
88#13063290—22no—
89#13063290—22no—
90#13063290D414yescomplemented
91D4×Dic43—22no—
92D4×Dic43—22no—
93D4×Dic43—44no—
94#13063287—22no—
95#13063287—22no—
96#13063287—22no—
97#13063287D414yescomplemented
98(C22⋊D43)⋊C4—28no—
99(C22⋊D43)⋊C4—28no—
100#13063282—28no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—22no—
115C2×C4×Dic43—22no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43D411yescharacteristic
118C2×C4×Dic43D411yescharacteristic
119C2×C4×Dic43C2311yescharacteristic
120C2×C4×Dic43C2311yescharacteristic
121C42×D43—28no—
122#13063258—22no—
123#13063256—22no—
124#13063250—22no—
125#13063250—22no—
126#13063248C2×C414yescomplemented
127#13063247—22no—
128#13063247—22no—
129#13063245C2×C414yescomplemented
130C22⋊(C43⋊C8)C2×C414yescomplemented
131#13063235—22no—
132#13063235—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C22×D4×C43—21no—
137C22×D4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141#121×C43—22no—
142#121×C43C2×C414yescomplemented
143#117×C43—22no—
144#117×C43—22no—
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C42×C43—21no—
151#102×C43—22no—
152#102×C43—22no—
153C22⋊C8×C43—22no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C23×D43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—24no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43C22×C412yes—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C22×C412yes—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43#4112yes—
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—24no—
178C2×C22⋊D43—24no—
179C2×C22⋊D43—24no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—41no—
187C22×Dic43—41no—
188C22×Dic43—41no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196#10621898—28no—
197#10621898—28no—
198#10621898—28no—
199#10621898—28no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172C22×C412yes—
204C2×D172C2×D412yes—
205C2×D172#4112yes—
206C2×C4×D43—24no—
207C2×C4×D43—24no—
208C2×C4×D43—24no—
209C2×C4×D43—24no—
210C2×C4×D43—24no—
211C2×C4×D43—42no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C2×C4×D43—42no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86C22×C412yes—
219C2×Dic86C2×D412yes—
220C2×Dic86#4112yes—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43C22×C412yes—
231C4⋊C4×C43C2×D412yes—
232C4⋊C4×C43C2×D412yes—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—24no—
235C42×C43—24no—
236C22⋊Dic43—42no—
237C22⋊Dic43—42no—
238C22⋊Dic43—42no—
239C22⋊Dic43—42no—
240#10621883—28no—
241#10621882—28no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—42no—
249Dic43⋊C4—24no—
250Dic43⋊C4—24no—
251C4×Dic43—24no—
252C4×Dic43—21no—
253C4×Dic43—21no—
254C4×Dic43—22no—
255C4×Dic43—24no—
256C4×Dic43—22no—
257C4×Dic43—42no—
258C4×Dic43C2×D412yes—
259C4×Dic43C2×D412yes—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8C22×C412yes—
265C2×C43⋊C8C22×C412yes—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—22no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43C4×D412yes—
280C23×C43C22×D411yescharacteristic
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—48no—
291D4×C43—41no—
292D4×C43—41no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43C4×D412yes—
309C2×C4×C43C23×C411yescharacteristic
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C22⋊D43—216no—
316C2×Dic43—22no—
317C2×Dic43—21no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—44no—
329C2×Dic43—44no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—84no—
337C2×Dic43#12012yes—
338C2×Dic43#12012yes—
339C2×Dic43AGL(1,ℤ/8)12yes—
340D172—22no—
341D172—22no—
342D172—22no—
343D172C4×D414yescomplemented
344C4×D43—216no—
345C4×D43—48no—
346C4×D43—48no—
347Dic86—22no—
348Dic86—22no—
349Dic86—22no—
350Dic86C4×D414yescomplemented
351C8×C43—41no—
352C8×C43—41no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355#21456—431nomaximal, Sylow
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43C2×C4×D411yescharacteristic
371C22×C43C2×#12011yescharacteristic
372C22×C43#52511yescharacteristic
373C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C43#57511yescharacteristic
375C22×C43#57511yescharacteristic
376C22×C43#57511yescharacteristic
377C2×D43—24no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C4×C43—22no—
385C4×C43—42no—
386C4×C43—42no—
387C4×C43—42no—
388C4×C43C2×C4×D411yescharacteristic
389C4×C43C2×C4×D411yescharacteristic
390C4×C43#52511yescharacteristic
391C4×C43#52511yescharacteristic
392Dic43—22no—
393Dic43—22no—
394Dic43—22no—
395Dic43—24no—
396Dic43—41no—
397Dic43—81no—
398Dic43—81no—
399C2×C4×#41—431no—
400C2×#449—431no—
401C2×#442—431no—
402C2×#440—431no—
403C4×#121—431no—
404#1880—431no—
405#1879—431no—
406#1875D4311yescharacteristic, complemented
407#1865—431no—
408#1862—431no—
409#1854—431no—
410#1788—431no—
411#1763—431no—
412#1762—431no—
413#1749—431no—
414C2×C43—42no—
415C2×C43—82no—
416C2×C43C4×#12011yescharacteristic
417C2×C43#294311yescharacteristic
418C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
419C2×C43#300511yescharacteristic
420C2×C43#300611yescharacteristic
421C2×C43#311111yescharacteristic
422C2×C43#311511yescharacteristic
423D43—44no—
424C22×#41—431no—
425C22×SD16—431no—
426C22×D8—431no—
427C2×#121C2×D4311yescharacteristic
428C4×#41—864no—
429C4×#41—864no—
430C2×C4×Q8—431no—
431C2×C4×Q8—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435C2×C4×D4—861no—
436C2×C4×D4—861no—
437C2×C4×D4—861no—
438C2×#117—861no—
439C2×#117C2×D4311yescharacteristic
440C22×C42—431no—
441C22×C42—861no—
442#449—438no—
443#442—864no—
444#440—864no—
445C2×#107—431no—
446C2×#106—431no—
447C2×#103—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102C2×D4311yescharacteristic
454C2×#102C2×D4311yescharacteristic
455C2×C22⋊C8—431no—
456C2×C22⋊C8C2×D4311yescharacteristic
457C2×#97—431no—
458C2×#97—431no—
459#390—431no—
460#389—431no—
461#388—861no—
462#386—861no—
463#380—431no—
464C4×C4⋊C4—431no—
465C4×C22⋊C4—861no—
466#340—431no—
467#340—431no—
468#340C2×D4311yescharacteristic
469#340C2×D4311yescharacteristic
470#336—431no—
471#336—431no—
472C43#2145611yescharacteristic, complemented, Sylow
473C2×#41—434no—
474C2×#41—862no—
475C2×#41—862no—
476C2×#41—862no—
477C2×#41—862no—
478C2×#41—862no—
479C22×Q8—431no—
480C22×D4—21no—
481C22×D4—431no—
482C22×D4—861no—
483C22×D4C22×D4311yescharacteristic
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—861no—
487C23×C4—861no—
488C23×C4—861no—
489C23×C4—861no—
490C23×C4C22×D4311yescharacteristic
491C2×SD16—434no—
492C2×SD16—862no—
493C2×SD16—862no—
494C2×D8—434no—
495C2×D8—862no—
496C2×D8—862no—
497C22×C8—431no—
498C22×C8—431no—
499C22×C8C22×D4311yescharacteristic
500C22×C8C22×D4311yescharacteristic
501#121—22no—
502#121C4×D4314yescomplemented
503C4×Q8—434no—
504C4×Q8—862no—
505C4×Q8—862no—
506C4×Q8—862no—
507C4×D4—434no—
508C4×D4—862no—
509C4×D4—862no—
510C4×D4—862no—
511C4×D4—868no—
512C4×D4—868no—
513C4×D4—862no—
514C4×D4—862no—
515C4×D4—1724no—
516#117—22no—
517#117—22no—
518#117—868no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C42—21no—
536C2×C42—431no—
537C2×C42—431no—
538C2×C42—431no—
539C2×C42—431no—
540C2×C42—868no—
541C2×C42—862no—
542C2×C42—862no—
543C2×C42—861no—
544C2×C42—861no—
545C2×C42—861no—
546#107—862no—
547#106—862no—
548#103—434no—
549#103—862no—
550#103—862no—
551#102—22no—
552#102—22no—
553#102—434no—
554#102—862no—
555#102—862no—
556C22⋊C8—22no—
557C22⋊C8—434no—
558#97—862no—
559#97—862no—
560#95—861no—
561#95—861no—
562#95—861no—
563C24—21no—
564C24—861no—
565C24D4×D4311yescharacteristic
566#41—868no—
567#41—868no—
568#41—868no—
569#41—868no—
570C2×Q8—432no—
571C2×Q8—432no—
572C2×Q8—432no—
573C2×Q8—861no—
574C2×Q8—861no—
575C2×Q8—861no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—432no—
585C2×D4—432no—
586C2×D4—432no—
587C2×D4—864no—
588C2×D4—864no—
589C2×D4—864no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4C2×C4×D4312yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—864no—
606C22×C4—864no—
607C22×C4—864no—
608C22×C4—864no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—861no—
613C22×C4—864no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—1722no—
617C22×C4—1722no—
618C22×C4—1722no—
619C22×C4—1722no—
620C22×C4—1722no—
621C22×C4—1721no—
622C22×C4—1721no—
623C22×C4—1721no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4C2×C4×D4312yes—
627C22×C4D4×D4311yescharacteristic
628C22×C4#1062190012yes—
629C22×C4C23×D4311yescharacteristic
630SD16—868no—
631D8—868no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—432no—
639C2×C8—432no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—864no—
648C4⋊C4—864no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—1722no—
654C4⋊C4C2×C4×D4312yes—
655C4⋊C4D4×D4312yes—
656C4⋊C4D4×D4312yes—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—1722no—
662C22⋊C4—1722no—
663C22⋊C4—1722no—
664C22⋊C4—1722no—
665C42—24no—
666C42—432no—
667C42—432no—
668C42—862no—
669C42—862no—
670C42—864no—
671C42—864no—
672C42—861no—
673C42—861no—
674C42—1722no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—22no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—862no—
689C23—862no—
690C23—862no—
691C23—1721no—
692C23—1721no—
693C23—1721no—
694C23—1721no—
695C23(C22⋊D43)⋊C412yes—
696C23C2×D4×D4311yescharacteristic
697Q8—434no—
698Q8—862no—
699Q8—862no—
700Q8—862no—
701D4—22no—
702D4—22no—
703D4—48no—
704D4—41no—
705D4—41no—
706D4—434no—
707D4—8616no—
708D4—862no—
709D4—862no—
710D4—862no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—432no—
727C2×C4—432no—
728C2×C4—432no—
729C2×C4—8616no—
730C2×C4—862no—
731C2×C4—861no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—3444no—
743C2×C4—1728no—
744C2×C4—1728no—
745C2×C4—1724no—
746C2×C4—1724no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4(C22⋊D43)⋊C412yes—
754C2×C4C22×C4×D4311yescharacteristic
755C2×C4C2×D4×D4311yescharacteristic
756C2×C4C2×D4×D4311yescharacteristic
757C2×C4#41×D4311yescharacteristic
758C2×C4#41×D4311yescharacteristic
759C2×C4C2×#1062190011yescharacteristic
760C8—41no—
761C8—41no—
762C8—862no—
763C8—862no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—864no—
779C22—1722no—
780C22—1722no—
781C22—1722no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22C2×(C22⋊D43)⋊C411yescharacteristic
786C22#120×D4311yescharacteristic
787C22#1458340711yescharacteristic
788C22AGL(1,ℤ/8)×D4311yescharacteristic
789C22#1458369511yescharacteristic
790C22#1458369611yescharacteristic
791C22#1458369611yescharacteristic
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—864no—
797C4—862no—
798C4—862no—
799C4—862no—
800C4—3441no—
801C4—3441no—
802C4—1721no—
803C4C4×D4×D4311yescharacteristic
804C4C4×D4×D4311yescharacteristic
805C4#1458340911yescharacteristic
806C4#1458340911yescharacteristic
807C2—42no—
808C2—82no—
809C2—1724no—
810C2#1913710011yescharacteristic
811C2#1914339111yescharacteristic
812C2#1914339911yescharacteristic
813C2#1914383311yescharacteristic
814C2#1914384411yescharacteristic
815C2#1914469911yescharacteristic
816C2#1914474111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1875C2
socleC23×C43C22×D4
prime radicalC2×#14583042C2
cosocleC22×C4×C43C24
hypercenter#1875D43
hypocenterC43#21456
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. C2×#14583367C2semidirect
3. C2×#14583008C2semidirect
4. C2×#14582996C2semidirect
5. #121×Dic43C2semidirect
6. #19134947C2semidirect
7. #19134940C2semidirect
8. #19134864C2semidirect
9. #19134843C2semidirect
10. #19134794C2semidirect
11. #19134536C2semidirect
12. #19134424C2semidirect
13. #19134419C2semidirect
14. #19134359C2semidirect
15. C43×#1875C2semidirect
32. #14583042C4semidirect
69. C2×#10621898C2×C4semidirect
81. C2×#10621883C2×C4semidirect
84. C2×#10621882C2×C4semidirect
90. #13063290D4semidirect
97. #13063287D4semidirect
126. #13063248C2×C4semidirect
129. #13063245C2×C4semidirect
130. C22⋊(C43⋊C8)C2×C4semidirect
142. #121×C43C2×C4semidirect
343. D172C4×D4semidirect
350. Dic86C4×D4semidirect
406. #1875D43semidirect
472. C43#21456semidirect
502. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833672
C2×#145830422
C2×#145830082
C2×#145829962
#121×Dic432
#191349472
#191349402
#191348642
#191348432
#191347942
#191345362
#191344242
#191344192
#191343592
C43×#18752
#2145643