Finite Group Databasebeta

← C4×#14583048 #25102173

Subgroups — C4×#14583048 #25102173

Order 11008.

1880 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic
2C2×#14583048C211yesmaximal, characteristic
3C2×C4×#10621884C211yesmaximal, characteristic, complemented
4C4×#13063301C211yesmaximal, characteristic, complemented
5#19134931C211yesmaximal, characteristic, complemented
6#19134926C211yesmaximal, characteristic, complemented
7#19134899C211yesmaximal, characteristic, complemented
8#19134854C211yesmaximal, characteristic, complemented
9#19134853C211yesmaximal, characteristic, complemented
10#19134786C211yesmaximal, characteristic, complemented
11#19134524C211yesmaximal, characteristic
12C4×#13063247C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic, complemented
14C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C23×C4×D43—21no—
18C22×#10621884C2211yescharacteristic
19C2×#13063301C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×C4×C22⋊D43—21no—
24C2×(C22⋊D43)⋊C4—21no—
25C4×D4×D43—24no—
26C4×D4×D43—24no—
27C2×C4⋊C4×D43C2211yescharacteristic
28C2×C22⋊C4×D43—21no—
29C2×C42×D43C2211yescharacteristic
30#14583048C418yesdirect product factor
31C4×#10621884—24no—
32C2×#13063256C2211yescharacteristic, complemented
33C2×#13063249C2211yescharacteristic, complemented
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic, complemented
42#14582806C2211yescharacteristic, complemented
43#14582795C2211yescharacteristic, complemented
44#14582780—21no—
45#14582770—21no—
46#14582756C2211yescharacteristic
47C4×Dic43⋊C4—21no—
48C4×C4⋊Dic43C2211yescharacteristic, complemented
49C4×(C2×D43)⋊C4—21no—
50#14582662C2211yescharacteristic, complemented
51#14582662C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56C22×SD16×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic, complemented
58C2×C4×D4×C43C2211yescharacteristic
59C4×SD16×C43—24no—
60C2×#106×C43C2211yescharacteristic, complemented
61C2×#103×C43C2211yescharacteristic, complemented
62C2×#102×C43C2211yescharacteristic
63C2×C4×C8×C43C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43—22no—
72C2×D4×D43C2×C414yes—
73C23×Dic43—21no—
74C22×C4×D43—28no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C22×C4×D43—44no—
79C22×C4×D43—44no—
80C22×C4×D43D411yescharacteristic
81C22×C4×D43D411yescharacteristic
82C22×C4×D43C2311yescharacteristic
83C2×#10621884—22no—
84C2×#10621884—22no—
85C2×#10621884C2×C414yescomplemented
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063301—22no—
89#13063301C2×C414yescomplemented
90C4×D172—22no—
91C4×D172D414yes—
92D4×Dic43—22no—
93D4×Dic43—22no—
94#13063287—22no—
95#13063287—22no—
96C4×C22⋊D43—28no—
97(C22⋊D43)⋊C4—28no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C4⋊C4×D43—22no—
105C4⋊C4×D43—22no—
106C2×C22⋊Dic43—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C22⋊C4×D43—28no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43D411yescharacteristic
114C2×C4×Dic43D411yescharacteristic
115C2×C4×Dic43C2311yescharacteristic
116C42×D43—22no—
117C42×D43—22no—
118#13063256—22no—
119#13063249—22no—
120#13063247—22no—
121#13063247C2×C414yescomplemented
122#13063246—22no—
123#13063246C2×C414yescomplemented
124#13063245—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8C2×C414yescomplemented
127C4×C43⋊C8—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C22×Q8×C43C2311yescharacteristic
134C22×D4×C43C2311yescharacteristic
135C23×C4×C43—21no—
136C2×SD16×C43—22no—
137C2×SD16×C43—22no—
138C2×SD16×C43C2×C414yescomplemented
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C4×Q8×C43—22no—
142C4×Q8×C43—22no—
143C4×D4×C43—22no—
144C4×D4×C43D414yes—
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C42×C43—21no—
150C2×C42×C43C2311yescharacteristic
151#106×C43—22no—
152#103×C43—22no—
153#102×C43—22no—
154C4×C8×C43—22no—
155C24×C43—21no—
156C23×D43—24no—
157C23×D43—24no—
158C23×D43—21no—
159C23×D43—24no—
160C23×D43—42no—
161C23×D43—42no—
162C23×D43—42no—
163C23×D43—42no—
164C23×D43C2×D411yescharacteristic
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43C22×C412yescomplemented
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43C22×C412yes—
175C2×D4×C43C2×D412yes—
176C2×D4×C43#4112yes—
177C22×C4×C43—24no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—42no—
182C22×C4×C43—42no—
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—24no—
187C2×C22⋊D43—24no—
188C2×C22⋊D43—24no—
189C22×Dic43—24no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—42no—
194C22×Dic43—42no—
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198D4×D43—28no—
199D4×D43—28no—
200D4×D43—28no—
201D4×D43—28no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172C22×C412yes—
206C2×D172C2×D412yes—
207C2×D172#4112yes—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—21no—
213C2×C4×D43—21no—
214C2×C4×D43—24no—
215C2×C4×D43—24no—
216C2×C4×D43—22no—
217C2×C4×D43—24no—
218C2×C4×D43—22no—
219C2×C4×D43—41no—
220C2×C4×D43—42no—
221C2×C4×D43—432no—
222C2×C4×D43—42no—
223C2×C4×D43—42no—
224C2×C4×D43—42no—
225C2×C4×D43—42no—
226C2×C4×D43—42no—
227C2×C4×D43SD1614yescomplemented
228C2×C4×D43C22×C412yes—
229C2×C4×D43#4112yes—
230SD16×C43—28no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43C22×C412yescomplemented
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—42no—
241C4⋊C4×C43C2×D412yes—
242C22⋊C4×C43—24no—
243C42×C43—42no—
244C42×C43C2×D412yes—
245C42×C43C2×D412yes—
246C22⋊Dic43—24no—
247#10621884—28no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—42no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43C22×C412yescomplemented
257C4⋊Dic43C2×D412yes—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—42no—
261C4×Dic43—22no—
262C4×Dic43—22no—
263C4×Dic43—21no—
264C4×Dic43—21no—
265C4×Dic43—42no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8C22×C412yescomplemented
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43C22×D411yescharacteristic
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—216no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—48no—
289C22×D43—48no—
290C22×D43—48no—
291C22×D43—48no—
292C22×D43—48no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—48no—
298C22×D43C4×D412yes—
299C22×D43C2×SD1612yes—
300C22×D43#13512yes—
301Q8×C43—22no—
302Q8×C43—22no—
303Q8×C43—41no—
304Q8×C43—41no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43C4×D414yes—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—48no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43#12012yes—
322C2×C4×C43#12012yes—
323C2×C4×C43C2×SD1612yes—
324C2×C4×C43AGL(1,ℤ/8)12yes—
325C2×C4×C43C23×C411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C22⋊D43—216no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—22no—
337C2×Dic43—21no—
338C2×Dic43—22no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—48no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43C4×D412yes—
350C2×Dic43C2×SD1612yes—
351D172—22no—
352D172—22no—
353D172—22no—
354D172C4×D414yes—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—28no—
360C4×D43—48no—
361C4×D43—44no—
362C4×D43—48no—
363C4×D43—48no—
364C8×C43—22no—
365C8×C43—41no—
366C43⋊C8—22no—
367C43⋊C8—41no—
368C4×#450—431nomaximal, Sylow
369C22×C43—24no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43C2×C4×D411yescharacteristic
377C22×C43C2×#12011yescharacteristic
378C22×C43#52511yescharacteristic
379C22×C43C22×SD1611yescharacteristic
380C22×C43C2×#13511yescharacteristic
381C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C43#57511yescharacteristic
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—24no—
390C2×D43—432no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43C4×SD1614yescomplemented
398C4×C43—22no—
399C4×C43—42no—
400C4×C43—42no—
401C4×C43—81no—
402C4×C43#45014yescomplemented
403C4×C43C2×C4×D411yescharacteristic
404C4×C43C2×C4×D411yescharacteristic
405C4×C43#52511yescharacteristic
406C4×C43#52511yescharacteristic
407Dic43—22no—
408Dic43—22no—
409Dic43—42no—
410Dic43—42no—
411Dic43—41no—
412Dic43—81no—
413C22×C4×D4—431no—
414C2×#450—431no—
415C2×C4×SD16—431no—
416C2×C4×SD16D4311yescharacteristic, complemented
417C4×C22⋊Q8—431no—
418#1877—431no—
419#1877—431no—
420#1872—431no—
421#1864—431no—
422#1864—431no—
423#1853—431no—
424#1786—431no—
425C4×#102—431no—
426C4×#102—431no—
427C4×C22⋊C8—431no—
428C2×C43—44no—
429C2×C43C4×#12011yescharacteristic
430C2×C43C2×C4×SD1611yescharacteristic
431C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
432C2×C43C2×#45011yescharacteristic
433C2×C43#300211yescharacteristic
434C2×C43#310111yescharacteristic
435C2×C43#310511yescharacteristic
436D43—24no—
437D43—44no—
438C23×D4—431no—
439C24×C4—861no—
440C22×SD16—431no—
441C22×SD16C2×D4311yescharacteristic
442C2×C22⋊Q8—431no—
443C2×C4×Q8C2×D4311yescharacteristic, complemented
444C2×C4×D4—431no—
445C2×C4×D4—431no—
446C2×C4×D4—431no—
447C2×C4×D4—861no—
448C2×C4×D4—861no—
449C2×C4×D4—864no—
450C2×C4×D4—864no—
451C2×C4×D4C2×D4311yescharacteristic
452C22×C4⋊C4—431no—
453C22×C22⋊C4—861no—
454C22×C42—431no—
455#450—438no—
456C4×SD16—24no—
457C4×SD16—864no—
458C2×#106—431no—
459C2×#106C2×D4311yescharacteristic, complemented
460C2×#103—431no—
461C2×#103C2×D4311yescharacteristic, complemented
462C2×#102—431no—
463C2×#102—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102C2×D4311yescharacteristic
468C2×C22⋊C8—431no—
469C2×C22⋊C8—431no—
470C2×C4×C8—431no—
471C2×C4×C8C2×D4311yescharacteristic, complemented
472#391—431no—
473#389—431no—
474#387—861no—
475#385—861no—
476#380—431no—
477C4×C4⋊C4—431no—
478C4×C4⋊C4—861no—
479C4×C22⋊C4—861no—
480#340—431no—
481#340—431no—
482#340—431no—
483#340—431no—
484#336—431no—
485#336—431no—
486C43C4×#45011yescharacteristic, complemented, Sylow
487C25—861no—
488C22×Q8C22×D4311yescharacteristic
489C22×D4—434no—
490C22×D4—431no—
491C22×D4—862no—
492C22×D4—861no—
493C22×D4—862no—
494C22×D4—862no—
495C22×D4—862no—
496C22×D4—862no—
497C22×D4C22×D4311yescharacteristic
498C23×C4—21no—
499C23×C4—431no—
500C23×C4—431no—
501C23×C4—431no—
502C23×C4—861no—
503C23×C4—861no—
504C23×C4—868no—
505C23×C4—861no—
506C23×C4—861no—
507C23×C4—1724no—
508C23×C4—1724no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—434no—
512C2×SD16—862no—
513C2×SD16—862no—
514C2×SD16C4×D4314yescomplemented
515C22×C8—431no—
516C22×C8—431no—
517C22×C8C22×D4311yescharacteristic
518C22×C8C22×D4311yescharacteristic
519C22⋊Q8—434no—
520C22⋊Q8—862no—
521C4×Q8—22no—
522C4×Q8—22no—
523C4×D4—22no—
524C4×D4—434no—
525C4×D4—868no—
526C4×D4—862no—
527C4×D4—862no—
528C4×D4—868no—
529C4×D4—862no—
530C4×D4—862no—
531C4×D4—862no—
532C4×D4C22⋊D4314yes—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—862no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—862no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—868no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C42—21no—
552C2×C42—431no—
553C2×C42—431no—
554C2×C42—431no—
555C2×C42—862no—
556C2×C42—862no—
557C2×C42—861no—
558C2×C42C22×D4311yescharacteristic
559#106—22no—
560#106—862no—
561#103—22no—
562#103—862no—
563#102—22no—
564#102—434no—
565#102—434no—
566#102—862no—
567#102—862no—
568#102—862no—
569C22⋊C8—434no—
570C22⋊C8—862no—
571C4×C8—22no—
572C4×C8—862no—
573#95—861no—
574#95—861no—
575#95—861no—
576#95—861no—
577#95—861no—
578C24—21no—
579C24—431no—
580C24—864no—
581C24—864no—
582C24—864no—
583C24—861no—
584C24—1722no—
585C24—1722no—
586C24—1722no—
587C24—1722no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8C2×C4×D4312yescomplemented
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—432no—
598C2×D4—432no—
599C2×D4—432no—
600C2×D4—864no—
601C2×D4—868no—
602C2×D4—868no—
603C2×D4—868no—
604C2×D4—864no—
605C2×D4—864no—
606C2×D4—868no—
607C2×D4—861no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4C2×C4×D4312yes—
611C2×D4#1062189812yes—
612C2×D4C2×C22⋊D4312yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—434no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—431no—
625C22×C4—862no—
626C22×C4—864no—
627C22×C4—864no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—864no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—862no—
638C22×C4—864no—
639C22×C4—861no—
640C22×C4—1721no—
641C22×C4—1722no—
642C22×C4—1722no—
643C22×C4—17232no—
644C22×C4—1722no—
645C22×C4—1722no—
646C22×C4—1722no—
647C22×C4—1722no—
648C22×C4—1722no—
649C22×C4—1722no—
650C22×C4D4×D4311yescharacteristic
651C22×C4D4×D4311yescharacteristic
652C22×C4C23×D4311yescharacteristic
653SD16—28no—
654SD16—868no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—432no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8C2×C4×D4312yescomplemented
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—432no—
672C4⋊C4—432no—
673C4⋊C4—864no—
674C4⋊C4—864no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—1722no—
680C4⋊C4C2×C22⋊D4312yes—
681C22⋊C4—24no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—1722no—
687C42—42no—
688C42—862no—
689C42—862no—
690C42—861no—
691C42—861no—
692C42—1722no—
693C42D4×D4312yes—
694C42C2×C22⋊D4312yes—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—432no—
703C23—432no—
704C23—432no—
705C23—8616no—
706C23—861no—
707C23—861no—
708C23—861no—
709C23—861no—
710C23—862no—
711C23—862no—
712C23—862no—
713C23—1728no—
714C23—1728no—
715C23—1728no—
716C23—1728no—
717C23—1728no—
718C23—1728no—
719C23—1721no—
720C23—1721no—
721C23—1721no—
722C23—1721no—
723C23C2×D4×D4311yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—41no—
727Q8—41no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—434no—
732D4—8616no—
733D4—862no—
734D4—862no—
735D4—862no—
736D4C4×C22⋊D4314yes—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—48no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—432no—
750C2×C4—432no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—868no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—861no—
762C2×C4—862no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—1724no—
766C2×C4—1728no—
767C2×C4—1728no—
768C2×C4—1728no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1728no—
777C2×C4#1306329312yes—
778C2×C4#1306329312yes—
779C2×C4SD16×D4312yes—
780C2×C4#1306335212yes—
781C2×C4C22×C4×D4311yescharacteristic
782C2×C4C2×D4×D4311yescharacteristic
783C2×C4C22×C22⋊D4311yescharacteristic
784C2×C4#41×D4311yescharacteristic
785C2×C4#41×D4311yescharacteristic
786C2×C4C2×#1062189811yescharacteristic
787C8—22no—
788C8—41no—
789C8—862no—
790C8—1721no—
791C22—24no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—434no—
799C22—862no—
800C22—862no—
801C22—862no—
802C22—862no—
803C22—862no—
804C22—862no—
805C22—864no—
806C22—17232no—
807C22—1722no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22—1722no—
813C22C4×D4×D4311yescharacteristic
814C22C2×#1306329311yescharacteristic
815C22#1458340811yescharacteristic
816C22C2×SD16×D4311yescharacteristic
817C22#135×D4311yescharacteristic
818C22C2×#1306335211yescharacteristic
819C22#1458369611yescharacteristic
820C4—22no—
821C4—42no—
822C4—42no—
823C4—81no—
824C4—862no—
825C4—862no—
826C4—3441no—
827C4—1722no—
828C4—1721no—
829C4—1722no—
830C4#1458304814yesdirect product factor
831C4C4×D4×D4311yescharacteristic
832C4C2×C4×C22⋊D4311yescharacteristic
833C4#1458340611yescharacteristic
834C4#1458340811yescharacteristic
835C2—44no—
836C2—864no—
837C2—1724no—
838C2C4×#1306329311yescharacteristic
839C2C4×SD16×D4311yescharacteristic
840C2C4×#1306335211yescharacteristic
841C2C2×#1458304811yescharacteristic
842C2#1914380911yescharacteristic
843C2#1914460111yescharacteristic
844C2#1914464611yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenterC2×C4×SD16D43
hypocenterC43C4×#450
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
3. C2×C4×#10621884C2semidirect
4. C4×#13063301C2semidirect
5. #19134931C2semidirect
6. #19134926C2semidirect
7. #19134899C2semidirect
8. #19134854C2semidirect
9. #19134853C2semidirect
10. #19134786C2semidirect
12. C4×#13063247C2semidirect
13. C4×#13063246C2semidirect
14. C4×(C2×D43)⋊C8C2semidirect
15. C2×C4×SD16×C43C2semidirect
30. #14583048C4direct (N × H)
32. C2×#13063256C22semidirect
33. C2×#13063249C22semidirect
41. C2×C4×C43⋊C8C22semidirect
42. #14582806C22semidirect
43. #14582795C22semidirect
48. C4×C4⋊Dic43C22semidirect
50. #14582662C22semidirect
51. #14582662C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. #14582653C22semidirect
55. #14582653C22semidirect
57. C2×C4×Q8×C43C22semidirect
60. C2×#106×C43C22semidirect
61. C2×#103×C43C22semidirect
63. C2×C4×C8×C43C22semidirect
85. C2×#10621884C2×C4semidirect
89. #13063301C2×C4semidirect
121. #13063247C2×C4semidirect
123. #13063246C2×C4semidirect
126. (C2×D43)⋊C8C2×C4semidirect
138. C2×SD16×C43C2×C4semidirect
170. C2×Q8×C43C22×C4semidirect
227. C2×C4×D43SD16semidirect
236. C2×C8×C43C22×C4semidirect
256. C4⋊Dic43C22×C4semidirect
271. C2×C43⋊C8C22×C4semidirect
397. C2×D43C4×SD16semidirect
402. C4×C43#450semidirect
416. C2×C4×SD16D43semidirect
443. C2×C4×Q8C2×D43semidirect
459. C2×#106C2×D43semidirect
461. C2×#103C2×D43semidirect
471. C2×C4×C8C2×D43semidirect
486. C43C4×#450semidirect
514. C2×SD16C4×D43semidirect
593. C2×Q8C2×C4×D43semidirect
666. C2×C8C2×C4×D43semidirect
830. C4#14583048direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
C2×#145830482
C2×C4×#106218842
C4×#130633012
#191349312
#191349262
#191348992
#191348542
#191348532
#191347862
#191345242
C4×#130632472
C4×#130632462
C4×(C2×D43)⋊C82
C2×C4×SD16×C432
C4×#45043