Finite Group Databasebeta

← C4×#14583081 #25102502

Subgroups — C4×#14583081 #25102502

Order 11008.

1358 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063373C211yesmaximal, characteristic
2C2×#14583081C211yesmaximal, characteristic
3C4×#13063356C212yesmaximal, complemented
4#19134989C211yesmaximal, characteristic, complemented
5#19134967C212yesmaximal, complemented
6#19134820C212yesmaximal, complemented
7#19134809C211yesmaximal, characteristic, complemented
8#19134553C211yesmaximal, characteristic
9C4×#13063253C212yesmaximal, complemented
10C4×#13063244C211yesmaximal, characteristic, complemented
11C4×C4⋊Q8×C43C211yesmaximal, characteristic, complemented
12C2×#13063373C2211yescharacteristic
13C2×#13063356C2212yes—
14#14583381—22no—
15#14583380—22no—
16#14583380C2212yes—
17#14583377C2211yescharacteristic
18#14583375—22no—
19C4×#10621902—22no—
20C4×#10621898—22no—
21C4×#10621898C2212yes—
22C4×Q8×D43—22no—
23#14583081C418yesdirect product factor
24#14583004—22no—
25#14582997—22no—
26C4×#10621885—22no—
27C4×#10621884—22no—
28#14582939C2212yes—
29C2×#13063253C2212yes—
30C2×#13063253C2212yes—
31#14582908C2212yes—
32#14582898C2212yes—
33C2×#13063244C2211yescharacteristic
34C2×#13063244C2211yescharacteristic
35C4×#10621877C2212yes—
36#14582668C2212yes—
37#14582659C2212yes—
38#14582659C2212yes—
39C2×C4⋊Q8×C43C2211yescharacteristic
40C2×C4×Q8×C43C2211yescharacteristic
41C2×C4×Q8×C43C2211yescharacteristic
42C43×#391C2211yescharacteristic
43C43×#391C2211yescharacteristic
44C43×#389—22no—
45C43×#384C2211yescharacteristic
46C4×C4⋊C4×C43—22no—
47C43×C43C2211yescharacteristic
48#13063373—22no—
49#13063373—24no—
50#13063373C2×C414yes—
51C2×#10621902—22no—
52C2×#10621898—22no—
53C2×#10621898C2312yes—
54C2×Q8×D43—22no—
55#13063356—24no—
56#13063356C2×C418yescomplemented
57C2×#10621885—22no—
58C2×#10621884—22no—
59C2×#10621877C2312yes—
60C2×#10621877C2312yes—
61Q8×Dic43—22no—
62Q8×Dic43—22no—
63C4×Dic86—22no—
64C4×Dic86—22no—
65C4×Dic86D412yes—
66C4×Dic86D412yes—
67#13063290—24no—
68#13063290—22no—
69C4×D172—22no—
70C4×D172—22no—
71C4×D172D412yes—
72C4×D172D412yes—
73#13063287—24no—
74#13063287—22no—
75C4×C22⋊D43—22no—
76C4×C22⋊D43—24no—
77C4×C22⋊D43—22no—
78#13063284—22no—
79#13063284C2312yes—
80#13063283—24no—
81#13063283—22no—
82#13063282—24no—
83#13063282—22no—
84C4⋊C4×D43—24no—
85C4⋊C4×D43—22no—
86C42×D43—24no—
87C42×D43—22no—
88#13063258—22no—
89#13063256—22no—
90#13063253—24no—
91#13063253C2×C418yescomplemented
92#13063249—22no—
93#13063249—22no—
94#13063248—22no—
95#13063245—22no—
96#13063244—22no—
97#13063244C2×C414yescomplemented
98#13063236—22no—
99C4×C43⋊C8—22no—
100C22×Q8×C43C2311yescharacteristic
101C22×Q8×C43C2311yescharacteristic
102C4⋊Q8×C43—22no—
103C4⋊Q8×C43C2×C414yescomplemented
104C4×Q8×C43—22no—
105C4×Q8×C43—22no—
106C4×Q8×C43—22no—
107C4×Q8×C43—22no—
108C2×C4⋊C4×C43—22no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43D412yes—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43D412yes—
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#95×C43—22no—
122#95×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×Q8×C43—21no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43C22×C412yes—
129C2×Q8×C43C22×C412yes—
130C2×Q8×C43#4112yes—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D412yes—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C2×C22⋊D43—22no—
141#10621902—28no—
142#10621902—28no—
143Q8×D43—28no—
144Q8×D43—28no—
145#10621898—28no—
146#10621898—28no—
147#10621898—22no—
148#10621898—22no—
149#10621898C22×C414yes—
150#10621898#4114yes—
151C2×D172—22no—
152C2×D172C2×D412yes—
153C2×C4×D43—24no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—24no—
157C2×C4×D43—22no—
158C2×Dic86—22no—
159C2×Dic86C2×D412yes—
160C4⋊C4×C43—28no—
161C4⋊C4×C43—24no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—44no—
165C4⋊C4×C43—42no—
166C42×C43—24no—
167C42×C43—22no—
168C42×C43—22no—
169C42×C43—21no—
170C42×C43—22no—
171C42×C43—42no—
172C42×C43—41no—
173C42×C43—41no—
174C42×C43C22×C412yes—
175C42×C43C2×D412yes—
176C42×C43C2×D412yes—
177C22⋊Dic43—22no—
178#10621885—28no—
179#10621884—28no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—22no—
182(C2×D43)⋊C4—22no—
183C4⋊Dic43—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43C2×D412yes—
186C4⋊Dic43C2×D412yes—
187Dic43⋊C4—24no—
188Dic43⋊C4—22no—
189Dic43⋊C4—22no—
190C4×Dic43—24no—
191C4×Dic43—24no—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195#10621877—22no—
196#10621877—22no—
197#10621877—22no—
198#10621877C22×C414yes—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—22no—
201C23×C43C22×D411yescharacteristic
202C22×D43—22no—
203Q8×C43—24no—
204Q8×C43—24no—
205Q8×C43—24no—
206Q8×C43—42no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—41no—
224C2×C4×C43C4×D414yes—
225C2×C4×C43#12012yes—
226C2×C4×C43#12011yescharacteristic
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43C23×C411yescharacteristic
229C2×C4×C43C22×D412yes—
230C2×C4×C43C2×#4112yes—
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—24no—
233C22⋊D43—24no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237D172—28no—
238D172—22no—
239D172C4×D414yes—
240C4×D43—216no—
241C4×D43—24no—
242C4×D43—24no—
243C4×D43—44no—
244C4×D43—82no—
245C4×D43—84no—
246Dic86—28no—
247Dic86—22no—
248Dic86C4×D414yes—
249C43⋊C8—24no—
250C43⋊C8—42no—
251C4×#456—431nomaximal, Sylow
252C22×C43—21no—
253C22×C43—21no—
254C22×C43C2×C4×D411yescharacteristic
255C22×C43C2×#12011yescharacteristic
256C22×C43#52511yescharacteristic
257C2×D43—24no—
258C2×D43—42no—
259C2×D43—42no—
260C4×C43—24no—
261C4×C43—21no—
262C4×C43—22no—
263C4×C43—24no—
264C4×C43—42no—
265C4×C43—42no—
266C4×C43—42no—
267C4×C43—81no—
268C4×C43#45612yescomplemented
269C4×C43C2×C4×D412yes—
270C4×C43#52512yes—
271Dic43—24no—
272Dic43—42no—
273Dic43—42no—
274C4×2−1+4—431no—
275C2×#456—431no—
276C4×#137—432no—
277C4×C4⋊Q8D4311yescharacteristic, complemented
278#1886—431no—
279#1882—432no—
280#1859—432no—
281#1857—431no—
282#1793—431no—
283C4×#104—432no—
284C4×#101—431no—
285C2×C43—21no—
286C2×C43—21no—
287C2×C43C4×#12011yescharacteristic
288C2×C43C2×#45611yescharacteristic
289C2×C43#301811yescharacteristic
290D43—44no—
291C2×2−1+4—431no—
292C2×#137—432no—
293C2×C4⋊Q8C2×D4311yescharacteristic
294#520—432no—
295#520—862no—
296#520—862no—
297#519—431no—
298#519—862no—
299C4×#41—432no—
300C4×#41—862no—
301C4×#41—862no—
302C2×C4×Q8—862no—
303C2×C4×Q8C2×D4311yescharacteristic
304C2×C4×Q8C2×D4311yescharacteristic
305#456—438no—
306#441—862no—
307#440—862no—
308C4×Q16—862no—
309C4×SD16—862no—
310#428—432no—
311C2×#104—432no—
312C2×#104—432no—
313#419—432no—
314#417—432no—
315C2×#101—431no—
316C2×#101—431no—
317C4×M16—432no—
318#391C2×D4311yescharacteristic
319#391C2×D4311yescharacteristic
320#389—22no—
321#384C2×D4311yescharacteristic
322C4×C4⋊C4—22no—
323C43C2×D4311yescharacteristic
324#343—432no—
325#339—432no—
326#339—432no—
327C43C4×#45611yescharacteristic, complemented, Sylow
3282−1+4—434no—
3292−1+4—864no—
3302−1+4—862no—
331C2×#41—432no—
332C2×#41—862no—
333C2×#41—862no—
334C22×Q8—862no—
335C22×Q8C22×D4311yescharacteristic
336C22×Q8C22×D4311yescharacteristic
337#137—438no—
338#137—864no—
339C2×Q16—862no—
340C2×SD16—862no—
341C2×M16—432no—
342C2×M16—432no—
343C4⋊Q8—22no—
344C4⋊Q8C4×D4314yescomplemented
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—432no—
350C4×Q8—432no—
351C4×Q8—862no—
352C4×Q8—862no—
353C4×Q8—862no—
354C4×Q8—864no—
355C4×Q8—862no—
356C4×Q8—862no—
357C4×D4—432no—
358C4×D4—432no—
359C4×D4—862no—
360C4×D4—862no—
361C4×D4—862no—
362C4×D4—864no—
363C4×D4—862no—
364C4×D4—862no—
365C4×D4—864no—
366#117—432no—
367#117—864no—
368#117—862no—
369#117—864no—
370#117—862no—
371#117—862no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—862no—
376C2×C4⋊C4—864no—
377C2×C4⋊C4C22⋊D4312yes—
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—864no—
384C2×C42—862no—
385C2×C42C22⋊D4312yes—
386C2×C42C22×D4311yescharacteristic
387C2×C42C22×D4311yescharacteristic
388C2×C42C22×D4311yescharacteristic
389#107—862no—
390#106—862no—
391#104—438no—
392#104—864no—
393#103—862no—
394#103—862no—
395#103—862no—
396#102—862no—
397#101—434no—
398#101—862no—
399#97—862no—
400C4×C8—862no—
401#95—22no—
402#95—22no—
403#41—434no—
404#41—434no—
405#41—868no—
406#41—868no—
407#41—868no—
408#41—868no—
409#41—862no—
410#41—862no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—432no—
417C2×Q8—862no—
418C2×Q8—868no—
419C2×Q8—868no—
420C2×Q8C2×C4×D4312yes—
421C2×Q8C2×C4×D4312yes—
422C2×Q8#1062189812yes—
423C2×D4—432no—
424C2×D4—862no—
425C2×D4—862no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—864no—
431C22×C4—864no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4C2×C22⋊D4312yes—
436C22×C4C2×C22⋊D4311yescharacteristic
437C22×C4C2×C22⋊D4312yes—
438C22×C4C2×C22⋊D4311yescharacteristic
439C22×C4C23×D4311yescharacteristic
440Q16—868no—
441SD16—868no—
442M16—434no—
443M16—862no—
444M16—862no—
445M16—862no—
446C2×C8—862no—
447C2×C8—862no—
448C4⋊C4—28no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—44no—
453C4⋊C4—42no—
454C4⋊C4—432no—
455C4⋊C4—432no—
456C4⋊C4—864no—
457C4⋊C4—862no—
458C4⋊C4—862no—
459C4⋊C4—862no—
460C4⋊C4—862no—
461C22⋊C4—864no—
462C22⋊C4—862no—
463C22⋊C4—862no—
464C22⋊C4—862no—
465C42—24no—
466C42—22no—
467C42—22no—
468C42—21no—
469C42—22no—
470C42—42no—
471C42—41no—
472C42—41no—
473C42—864no—
474C42—864no—
475C42—862no—
476C42—862no—
477C42—862no—
478C42C2×C4×D4312yes—
479C42D4×D4312yes—
480C42D4×D4312yes—
481C23—862no—
482C23C22×C22⋊D4311yescharacteristic
483Q8—24no—
484Q8—24no—
485Q8—24no—
486Q8—42no—
487Q8—434no—
488Q8—868no—
489Q8—862no—
490D4—434no—
491D4—868no—
492D4—864no—
493D4—864no—
494D4—862no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—8616no—
513C2×C4—862no—
514C2×C4—864no—
515C2×C4—864no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—3442no—
519C2×C4—3444no—
520C2×C4—1724no—
521C2×C4C4×C22⋊D4314yes—
522C2×C4#1306329311yescharacteristic
523C2×C4#1306329312yes—
524C2×C4#1306329311yescharacteristic
525C2×C4C22×C4×D4311yescharacteristic
526C2×C4C2×D4×D4312yes—
527C2×C4#41×D4312yes—
528C2×C4C2×#1062189811yescharacteristic
529C8—864no—
530C8—1722no—
531C22—21no—
532C22—21no—
533C22—864no—
534C22—1722no—
535C22—1722no—
536C22C2×C4×C22⋊D4311yescharacteristic
537C22C2×#1306329311yescharacteristic
538C22#1458340611yescharacteristic
539C4—24no—
540C4—21no—
541C4—22no—
542C4—24no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—81no—
547C4—864no—
548C4—1722no—
549C4—1722no—
550C4#1458308112yesdirect product factor
551C4C4×D4×D4312yes—
552C4#1458340812yes—
553C2—21no—
554C2—21no—
555C2—1724no—
556C2C4×#1306329311yescharacteristic
557C2C2×#1458308111yescharacteristic
558C2#1914394311yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×C4⋊Q8×C43C2
socleC22×C43C2×#120
prime radicalC2×#13063373C22
cosocleC22×C4×C43C24
hypercenterC4×C4⋊Q8D43
hypocenterC43C4×#456
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C4×#13063356C2semidirect
4. #19134989C2semidirect
5. #19134967C2semidirect
6. #19134820C2semidirect
7. #19134809C2semidirect
9. C4×#13063253C2semidirect
10. C4×#13063244C2semidirect
11. C4×C4⋊Q8×C43C2semidirect
23. #14583081C4direct (N × H)
56. #13063356C2×C4semidirect
91. #13063253C2×C4semidirect
97. #13063244C2×C4semidirect
103. C4⋊Q8×C43C2×C4semidirect
268. C4×C43#456semidirect
277. C4×C4⋊Q8D43semidirect
327. C43C4×#456semidirect
344. C4⋊Q8C4×D43semidirect
550. C4#14583081direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130633732
C2×#145830812
C4×#130633562
#191349892
#191349672
#191348202
#191348092
#191345532
C4×#130632532
C4×#130632442
C4×C4⋊Q8×C432
C4×#45643