Finite Group Databasebeta

← #25102292

Subgroups — #25102292

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×C4×#10621902C211yesmaximal, characteristic, complemented
2C2×#14583047C211yesmaximal, characteristic
3C2×#14583012C211yesmaximal, characteristic, complemented
4C2×#14582997C211yesmaximal, characteristic, complemented
5C4×#13063300C211yesmaximal, characteristic, complemented
6#19134948C211yesmaximal, characteristic, complemented
7#19134944C211yesmaximal, characteristic, complemented
8#19134916C211yesmaximal, characteristic, complemented
9#19134865C211yesmaximal, characteristic, complemented
10#19134843C211yesmaximal, characteristic, complemented
11#19134795C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic, complemented
13#19134423C211yesmaximal, characteristic, complemented
14#19134358C211yesmaximal, characteristic, complemented
15C43×#1763C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20C4×#10621902—24no—
21C4×#10621902—24no—
22C2×Q8×Dic43C2211yescharacteristic
23C2×C4×D172—21no—
24C2×C4×D172—21no—
25C2×C4×D172C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×#13063287—21no—
28C2×#13063287C2211yescharacteristic
29C2×#13063283—21no—
30C2×#13063283C2211yescharacteristic
31C2×C42×D43—21no—
32C2×C42×D43C2211yescharacteristic
33#14583047C418yescomplemented
34#14583012—24no—
35#14582997—24no—
36C2×#13063258C2211yescharacteristic
37C2×#13063257C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×#13063236C2211yescharacteristic
47#14582800C2211yescharacteristic
48#14582798C2211yescharacteristic
49#14582791—21no—
50#14582777—21no—
51#14582756C2211yescharacteristic
52C4×(C2×D43)⋊C4—21no—
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—22no—
69C2×#10621902C2×C414yescomplemented
70C22×D172—21no—
71C22×D172—21no—
72C22×D172C2311yescharacteristic
73C22×D172C2311yescharacteristic
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C22×C4×D43D411yescharacteristic
79C22×C4×D43D411yescharacteristic
80C22×C4×D43C2311yescharacteristic
81C2×#10621884—22no—
82C2×#10621884—22no—
83C2×#10621884C2×C414yescomplemented
84C2×D344—22no—
85C2×D344—22no—
86C2×D344C2×C414yescomplemented
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89#13063300—22no—
90#13063300C2×C414yescomplemented
91Q8×Dic43—22no—
92Q8×Dic43—22no—
93C4×D172—28no—
94C4×D172—22no—
95C4×D172—22no—
96C4×D172—22no—
97C4×D172—44no—
98C4×D172D414yescomplemented
99#13063287—28no—
100#13063287—22no—
101#13063287—22no—
102#13063283—28no—
103#13063283—22no—
104#13063283—22no—
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43D411yescharacteristic
120C2×C4×Dic43D411yescharacteristic
121C2×C4×Dic43C2311yescharacteristic
122C42×D43—28no—
123C42×D43—22no—
124C42×D43—22no—
125#13063258—22no—
126#13063257—22no—
127#13063249—22no—
128#13063247—22no—
129#13063247—22no—
130#13063245—22no—
131#13063245—22no—
132#13063245C2×C414yescomplemented
133(C2×D43)⋊C8—22no—
134(C2×D43)⋊C8C2×C414yescomplemented
135#13063236—22no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C22×Q8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C4×Q8×C43—22no—
142C4×Q8×C43D414yescomplemented
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43—21no—
149C2×C42×C43C2311yescharacteristic
150#103×C43—22no—
151#103×C43C2×C414yescomplemented
152#97×C43—22no—
153#95×C43—21no—
154C23×D43—21no—
155C23×D43—21no—
156C23×D43C2×D411yescharacteristic
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C22×C412yes—
161C2×Q8×C43C2×D412yes—
162C2×Q8×C43#4112yes—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2411yescharacteristic
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175#10621902—28no—
176#10621902—28no—
177#10621902—28no—
178#10621902—28no—
179C2×D172—24no—
180C2×D172—24no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—24no—
186C2×D172—24no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—42no—
192C2×D172—42no—
193C2×D172C22×C412yes—
194C2×D172C22×C412yes—
195C2×D172C2×D412yes—
196C2×D172#4112yes—
197C2×C4×D43—24no—
198C2×C4×D43—24no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—24no—
204C2×C4×D43—24no—
205C2×C4×D43—22no—
206C2×C4×D43—22no—
207C2×C4×D43—24no—
208C2×C4×D43—22no—
209C2×C4×D43—41no—
210C2×C4×D43—41no—
211C2×C4×D43—41no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C2×C4×D43—42no—
215C2×C4×D43—42no—
216C2×C4×D43—42no—
217C2×C4×D43—42no—
218C2×C4×D43—42no—
219C2×C4×D43C22×C412yes—
220C2×C4×D43#4112yes—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43C22×C412yes—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43C22×C412yes—
233C4⋊C4×C43C2×D412yes—
234C42×C43—24no—
235C42×C43—42no—
236C42×C43C2×D412yes—
237C42×C43C2×D412yes—
238#10621884—28no—
239(C2×D43)⋊C4—24no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—42no—
244(C2×D43)⋊C4—42no—
245(C2×D43)⋊C4—42no—
246(C2×D43)⋊C4—42no—
247C4⋊Dic43—24no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—42no—
252C4⋊Dic43C2×D412yes—
253C4×Dic43—24no—
254C4×Dic43—24no—
255C4×Dic43—22no—
256C4×Dic43—22no—
257C4×Dic43—21no—
258C4×Dic43—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8C22×C412yes—
265D344—28no—
266C23×C43C22×D411yescharacteristic
267C22×D43—22no—
268C22×D43—21no—
269C22×D43—22no—
270C22×D43—21no—
271C22×D43—22no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—22no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43C4×D412yes—
288Q8×C43—22no—
289Q8×C43—22no—
290Q8×C43—22no—
291Q8×C43C4×D414yescomplemented
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—41no—
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×C43#12012yes—
309C2×C4×C43#12012yes—
310C2×C4×C43C23×C411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—22no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43C4×D412yes—
330C2×Dic43AGL(1,ℤ/8)12yes—
331D172—216no—
332D172—22no—
333D172—22no—
334D172—22no—
335D172—22no—
336D172—22no—
337D172—48no—
338D172—41no—
339D172—41no—
340D172C4×D414yescomplemented
341C4×D43—216no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—44no—
347C4×D43—48no—
348C4×D43—44no—
349C4×D43—48no—
350C4×D43—84no—
351C8×C43—22no—
352C8×C43—41no—
353C43⋊C8—22no—
354C43⋊C8—41no—
355#21456—431nomaximal, Sylow
356C22×C43C2×C4×D411yescharacteristic
357C22×C43C2×#12011yescharacteristic
358C22×C43#52511yescharacteristic
359C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C43#57511yescharacteristic
361C22×C43#57511yescharacteristic
362C22×C43#57511yescharacteristic
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—24no—
366C2×D43—22no—
367C2×D43—41no—
368C2×D43—42no—
369C2×D43—41no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—41no—
374C2×D43—42no—
375C2×D43—41no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—81no—
381C2×D43—81no—
382C2×D43—81no—
383C2×D43—81no—
384C4×C43—22no—
385C4×C43—22no—
386C4×C43—24no—
387C4×C43—42no—
388C4×C43—42no—
389C4×C43—81no—
390C4×C43C2×C4×D411yescharacteristic
391C4×C43C2×C4×D411yescharacteristic
392C4×C43#52511yescharacteristic
393C4×C43#52511yescharacteristic
394Dic43—22no—
395Dic43—22no—
396Dic43—41no—
397Dic43—42no—
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#1875—431no—
407#1865—431no—
408#1862—431no—
409#1854—431no—
410#1788—431no—
411#1763D4311yescharacteristic, complemented
412#1762—431no—
413#1749—431no—
414C2×C43C4×#12011yescharacteristic
415C2×C43#294311yescharacteristic
416C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
417C2×C43#300511yescharacteristic
418C2×C43#300611yescharacteristic
419C2×C43#311111yescharacteristic
420C2×C43#311511yescharacteristic
421D43—42no—
422D43—44no—
423D43—82no—
424C22×#41—431no—
425C22×SD16—431no—
426C22×D8—431no—
427C2×#121—431no—
428C4×#41—864no—
429C4×#41—864no—
430C2×C4×Q8—431no—
431C2×C4×Q8C2×D4311yescharacteristic
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—431no—
439C2×#117—861no—
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×#103C2×D4311yescharacteristic
449C2×#103C2×D4311yescharacteristic
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×C22⋊C8—431no—
456C2×C22⋊C8—431no—
457C2×#97—431no—
458C2×#97C2×D4311yescharacteristic
459#390—431no—
460#389—431no—
461#388—861no—
462#386—861no—
463#380—431no—
464C4×C4⋊C4C2×D4311yescharacteristic
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×Q8C22×D4311yescharacteristic
480C22×D4—431no—
481C22×D4—431no—
482C22×D4—861no—
483C22×D4—861no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—431no—
487C23×C4—861no—
488C23×C4—861no—
489C23×C4—861no—
490C23×C4—861no—
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—434no—
502#121—862no—
503C4×Q8—22no—
504C4×Q8—862no—
505C4×Q8—862no—
506C4×Q8D17214yescomplemented
507C4×D4—434no—
508C4×D4—868no—
509C4×D4—862no—
510C4×D4—868no—
511C4×D4—862no—
512C4×D4—862no—
513C4×D4—862no—
514C4×D4—862no—
515C4×D4—1724no—
516#117—862no—
517#117—868no—
518#117—862no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
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—21no—
537C2×C42—431no—
538C2×C42—431no—
539C2×C42—431no—
540C2×C42—868no—
541C2×C42—861no—
542C2×C42—861no—
543C2×C42—862no—
544C2×C42—862no—
545C2×C42C22×D4311yescharacteristic
546#107—862no—
547#106—862no—
548#103—22no—
549#103—862no—
550#103C4×D4314yescomplemented
551#102—434no—
552#102—862no—
553#102—862no—
554#102—862no—
555#102—862no—
556C22⋊C8—434no—
557C22⋊C8—862no—
558#97—22no—
559#97—862no—
560#95—21no—
561#95—861no—
562#95—861no—
563C24—431no—
564C24—861no—
565C24—861no—
566#41—868no—
567#41—868no—
568#41—868no—
569#41—868no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8C2×C4×D4312yes—
574C2×Q8C2×D17212yes—
575C2×Q8#1062189812yes—
576C2×D4—432no—
577C2×D4—432no—
578C2×D4—432no—
579C2×D4—432no—
580C2×D4—864no—
581C2×D4—864no—
582C2×D4—864no—
583C2×D4—864no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—1722no—
593C2×D4—1722no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—432no—
601C22×C4—432no—
602C22×C4—431no—
603C22×C4—864no—
604C22×C4—862no—
605C22×C4—864no—
606C22×C4—864no—
607C22×C4—864no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—864no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—861no—
617C22×C4—1721no—
618C22×C4—1721no—
619C22×C4—1721no—
620C22×C4—1722no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4D4×D4311yescharacteristic
628C22×C4D4×D4311yescharacteristic
629C22×C4C23×D4311yescharacteristic
630SD16—868no—
631D8—868no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—432no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8C2×C4×D4312yes—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—432no—
650C4⋊C4—864no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—1722no—
655C4⋊C4C2×C4×D4312yes—
656C4⋊C4C2×D17212yes—
657C22⋊C4—864no—
658C22⋊C4—864no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—1722no—
662C22⋊C4—1722no—
663C22⋊C4—1722no—
664C22⋊C4—1722no—
665C42—24no—
666C42—42no—
667C42—864no—
668C42—864no—
669C42—862no—
670C42—862no—
671C42—861no—
672C42—861no—
673C42C2×D17212yes—
674C42D4×D4312yes—
675C23—432no—
676C23—862no—
677C23—862no—
678C23—861no—
679C23—862no—
680C23—861no—
681C23—861no—
682C23—861no—
683C23—861no—
684C23—861no—
685C23—862no—
686C23—1721no—
687C23—1721no—
688C23—1721no—
689C23—1721no—
690C23—1721no—
691C23—1721no—
692C23—1721no—
693C23—1721no—
694C23—1721no—
695C23—1721no—
696C23C2×D4×D4311yescharacteristic
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8C4×D17214yescomplemented
701D4—434no—
702D4—8616no—
703D4—862no—
704D4—862no—
705D4—862no—
706D4—862no—
707D4—862no—
708D4—1728no—
709D4—1721no—
710D4—1721no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
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—41no—
727C2×C4—432no—
728C2×C4—432no—
729C2×C4—8616no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—3444no—
743C2×C4—1724no—
744C2×C4—1724no—
745C2×C4—1728no—
746C2×C4—1728no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4#1306329512yes—
753C2×C4#1306329512yes—
754C2×C4C22×C4×D4311yescharacteristic
755C2×C4C2×D4×D4311yescharacteristic
756C2×C4C22×D17211yescharacteristic
757C2×C4#41×D4311yescharacteristic
758C2×C4#41×D4311yescharacteristic
759C2×C4C2×#1062189811yescharacteristic
760C8—22no—
761C8—41no—
762C8—862no—
763C8—1721no—
764C22—864no—
765C22—862no—
766C22—862no—
767C22—862no—
768C22—3441no—
769C22—3441no—
770C22—3441no—
771C22—3441no—
772C22—1722no—
773C22—1722no—
774C22—1722no—
775C22—1721no—
776C22—1722no—
777C22—1721no—
778C22—1722no—
779C22—1721no—
780C22—1722no—
781C22—1721no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22C4×D4×D4311yescharacteristic
786C22C2×#1306329511yescharacteristic
787C22#1458340811yescharacteristic
788C22AGL(1,ℤ/8)×D4311yescharacteristic
789C22#1458369811yescharacteristic
790C22#1458369811yescharacteristic
791C22#1458369811yescharacteristic
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—862no—
799C4—862no—
800C4—3441no—
801C4—1721no—
802C4—1722no—
803C4C4×D4×D4311yescharacteristic
804C4C2×C4×D17211yescharacteristic
805C4#1458340811yescharacteristic
806C4#1458341111yescharacteristic
807C2—3442no—
808C2—1722no—
809C2—1724no—
810C2C4×#1306329511yescharacteristic
811C2#1914339411yescharacteristic
812C2#1914340011yescharacteristic
813C2#1914384111yescharacteristic
814C2#1914384811yescharacteristic
815C2#1914471011yescharacteristic
816C2#1914474411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1763C2
socleC23×C43C22×D4
prime radicalC2×#14583047C2
cosocleC22×C4×C43C24
hypercenter#1763D43
hypocenterC43#21456
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
1. C2×C4×#10621902C2semidirect
3. C2×#14583012C2semidirect
4. C2×#14582997C2semidirect
5. C4×#13063300C2semidirect
6. #19134948C2semidirect
7. #19134944C2semidirect
8. #19134916C2semidirect
9. #19134865C2semidirect
10. #19134843C2semidirect
11. #19134795C2semidirect
12. #19134534C2semidirect
13. #19134423C2semidirect
14. #19134358C2semidirect
15. C43×#1763C2semidirect
33. #14583047C4semidirect
69. C2×#10621902C2×C4semidirect
83. C2×#10621884C2×C4semidirect
86. C2×D344C2×C4semidirect
90. #13063300C2×C4semidirect
98. C4×D172D4semidirect
132. #13063245C2×C4semidirect
134. (C2×D43)⋊C8C2×C4semidirect
142. C4×Q8×C43D4semidirect
151. #103×C43C2×C4semidirect
291. Q8×C43C4×D4semidirect
340. D172C4×D4semidirect
411. #1763D43semidirect
472. C43#21456semidirect
506. C4×Q8D172semidirect
550. #103C4×D43semidirect
700. Q8C4×D172semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219022
C2×#145830472
C2×#145830122
C2×#145829972
C4×#130633002
#191349482
#191349442
#191349162
#191348652
#191348432
#191347952
#191345342
#191344232
#191343582
C43×#17632
#2145643