Finite Group Databasebeta

← C4×#15689305 #26222183

Subgroups — C4×#15689305 #26222183

Order 12032.

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×#13094072C211yesmaximal, characteristic
2C2×#15689305C211yesmaximal, characteristic
3C4×#13094055C212yesmaximal, complemented
4#20243782C211yesmaximal, characteristic, complemented
5#20243760C212yesmaximal, complemented
6#20243613C212yesmaximal, complemented
7#20243602C211yesmaximal, characteristic, complemented
8#20243346C211yesmaximal, characteristic
9C4×#13093952C212yesmaximal, complemented
10C4×#13093943C211yesmaximal, characteristic, complemented
11C4×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
12C2×#13094072C2211yescharacteristic
13C2×#13094055C2212yes—
14#15689605—22no—
15#15689604—22no—
16#15689604C2212yes—
17#15689601C2211yescharacteristic
18#15689599—22no—
19C4×#10625354—22no—
20C4×#10625350—22no—
21C4×#10625350C2212yes—
22C4×Q8×D47—22no—
23#15689305C418yesdirect product factor
24#15689228—22no—
25#15689221—22no—
26C4×#10625337—22no—
27C4×#10625336—22no—
28#15689163C2212yes—
29C2×#13093952C2212yes—
30C2×#13093952C2212yes—
31#15689132C2212yes—
32#15689122C2212yes—
33C2×#13093943C2211yescharacteristic
34C2×#13093943C2211yescharacteristic
35C4×#10625329C2212yes—
36#15688892C2212yes—
37#15688883C2212yes—
38#15688883C2212yes—
39C2×C4⋊Q8×C47C2211yescharacteristic
40C2×C4×Q8×C47C2211yescharacteristic
41C2×C4×Q8×C47C2211yescharacteristic
42C47×#391C2211yescharacteristic
43C47×#391C2211yescharacteristic
44C47×#389—22no—
45C47×#384C2211yescharacteristic
46C4×C4⋊C4×C47—22no—
47C43×C47C2211yescharacteristic
48#13094072—22no—
49#13094072—24no—
50#13094072C2×C414yes—
51C2×#10625354—22no—
52C2×#10625350—22no—
53C2×#10625350C2312yes—
54C2×Q8×D47—22no—
55#13094055—24no—
56#13094055C2×C418yescomplemented
57C2×#10625337—22no—
58C2×#10625336—22no—
59C2×#10625329C2312yes—
60C2×#10625329C2312yes—
61Q8×Dic47—22no—
62Q8×Dic47—22no—
63C4×Dic94—22no—
64C4×Dic94—22no—
65C4×Dic94D412yes—
66C4×Dic94D412yes—
67#13093989—24no—
68#13093989—22no—
69C4×D188—22no—
70C4×D188—22no—
71C4×D188D412yes—
72C4×D188D412yes—
73#13093986—24no—
74#13093986—22no—
75C4×C22⋊D47—22no—
76C4×C22⋊D47—24no—
77C4×C22⋊D47—22no—
78#13093983—22no—
79#13093983C2312yes—
80#13093982—24no—
81#13093982—22no—
82#13093981—24no—
83#13093981—22no—
84C4⋊C4×D47—24no—
85C4⋊C4×D47—22no—
86C42×D47—24no—
87C42×D47—22no—
88#13093957—22no—
89#13093955—22no—
90#13093952—24no—
91#13093952C2×C418yescomplemented
92#13093948—22no—
93#13093948—22no—
94#13093947—22no—
95#13093944—22no—
96#13093943—22no—
97#13093943C2×C414yescomplemented
98#13093935—22no—
99C4×C47⋊C8—22no—
100C22×Q8×C47C2311yescharacteristic
101C22×Q8×C47C2311yescharacteristic
102C4⋊Q8×C47—22no—
103C4⋊Q8×C47C2×C414yescomplemented
104C4×Q8×C47—22no—
105C4×Q8×C47—22no—
106C4×Q8×C47—22no—
107C4×Q8×C47—22no—
108C2×C4⋊C4×C47—22no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—22no—
111C2×C4⋊C4×C47D412yes—
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C42×C47—21no—
115C2×C42×C47—21no—
116C2×C42×C47—21no—
117C2×C42×C47D412yes—
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121#95×C47—22no—
122#95×C47—22no—
123C2×Q8×C47—22no—
124C2×Q8×C47—22no—
125C2×Q8×C47—21no—
126C2×Q8×C47—22no—
127C2×Q8×C47—22no—
128C2×Q8×C47C22×C412yes—
129C2×Q8×C47C22×C412yes—
130C2×Q8×C47#4112yes—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D412yes—
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2411yescharacteristic
140C2×C22⋊D47—22no—
141#10625354—28no—
142#10625354—28no—
143Q8×D47—28no—
144Q8×D47—28no—
145#10625350—28no—
146#10625350—28no—
147#10625350—22no—
148#10625350—22no—
149#10625350C22×C414yes—
150#10625350#4114yes—
151C2×D188—22no—
152C2×D188C2×D412yes—
153C2×C4×D47—24no—
154C2×C4×D47—22no—
155C2×C4×D47—22no—
156C2×C4×D47—24no—
157C2×C4×D47—22no—
158C2×Dic94—22no—
159C2×Dic94C2×D412yes—
160C4⋊C4×C47—28no—
161C4⋊C4×C47—24no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—44no—
165C4⋊C4×C47—42no—
166C42×C47—24no—
167C42×C47—22no—
168C42×C47—22no—
169C42×C47—21no—
170C42×C47—22no—
171C42×C47—42no—
172C42×C47—41no—
173C42×C47—41no—
174C42×C47C22×C412yes—
175C42×C47C2×D412yes—
176C42×C47C2×D412yes—
177C22⋊Dic47—22no—
178#10625337—28no—
179#10625336—28no—
180(C2×D47)⋊C4—24no—
181(C2×D47)⋊C4—22no—
182(C2×D47)⋊C4—22no—
183C4⋊Dic47—22no—
184C4⋊Dic47—22no—
185C4⋊Dic47C2×D412yes—
186C4⋊Dic47C2×D412yes—
187Dic47⋊C4—24no—
188Dic47⋊C4—22no—
189Dic47⋊C4—22no—
190C4×Dic47—24no—
191C4×Dic47—24no—
192C4×Dic47—22no—
193C4×Dic47—22no—
194C4×Dic47—22no—
195#10625329—22no—
196#10625329—22no—
197#10625329—22no—
198#10625329C22×C414yes—
199C2×C47⋊C8—22no—
200C2×C47⋊C8—22no—
201C23×C47C22×D411yescharacteristic
202C22×D47—22no—
203Q8×C47—24no—
204Q8×C47—24no—
205Q8×C47—24no—
206Q8×C47—42no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—41no—
224C2×C4×C47C4×D414yes—
225C2×C4×C47#12012yes—
226C2×C4×C47#12011yescharacteristic
227C2×C4×C47#12011yescharacteristic
228C2×C4×C47C23×C411yescharacteristic
229C2×C4×C47C22×D412yes—
230C2×C4×C47C2×#4112yes—
231C2×C4×C47C2×#4111yescharacteristic
232C22⋊D47—24no—
233C22⋊D47—24no—
234C2×Dic47—22no—
235C2×Dic47—22no—
236C2×Dic47—22no—
237D188—28no—
238D188—22no—
239D188C4×D414yes—
240C4×D47—216no—
241C4×D47—24no—
242C4×D47—24no—
243C4×D47—44no—
244C4×D47—82no—
245C4×D47—84no—
246Dic94—28no—
247Dic94—22no—
248Dic94C4×D414yes—
249C47⋊C8—24no—
250C47⋊C8—42no—
251C4×#456—471nomaximal, Sylow
252C22×C47—21no—
253C22×C47—21no—
254C22×C47C2×C4×D411yescharacteristic
255C22×C47C2×#12011yescharacteristic
256C22×C47#52511yescharacteristic
257C2×D47—24no—
258C2×D47—42no—
259C2×D47—42no—
260C4×C47—24no—
261C4×C47—21no—
262C4×C47—22no—
263C4×C47—24no—
264C4×C47—42no—
265C4×C47—42no—
266C4×C47—42no—
267C4×C47—81no—
268C4×C47#45612yescomplemented
269C4×C47C2×C4×D412yes—
270C4×C47#52512yes—
271Dic47—24no—
272Dic47—42no—
273Dic47—42no—
274C4×2−1+4—471no—
275C2×#456—471no—
276C4×#137—472no—
277C4×C4⋊Q8D4711yescharacteristic, complemented
278#1886—471no—
279#1882—472no—
280#1859—472no—
281#1857—471no—
282#1793—471no—
283C4×#104—472no—
284C4×#101—471no—
285C2×C47—21no—
286C2×C47—21no—
287C2×C47C4×#12011yescharacteristic
288C2×C47C2×#45611yescharacteristic
289C2×C47#301811yescharacteristic
290D47—44no—
291C2×2−1+4—471no—
292C2×#137—472no—
293C2×C4⋊Q8C2×D4711yescharacteristic
294#520—472no—
295#520—942no—
296#520—942no—
297#519—471no—
298#519—942no—
299C4×#41—472no—
300C4×#41—942no—
301C4×#41—942no—
302C2×C4×Q8—942no—
303C2×C4×Q8C2×D4711yescharacteristic
304C2×C4×Q8C2×D4711yescharacteristic
305#456—478no—
306#441—942no—
307#440—942no—
308C4×Q16—942no—
309C4×SD16—942no—
310#428—472no—
311C2×#104—472no—
312C2×#104—472no—
313#419—472no—
314#417—472no—
315C2×#101—471no—
316C2×#101—471no—
317C4×M16—472no—
318#391C2×D4711yescharacteristic
319#391C2×D4711yescharacteristic
320#389—22no—
321#384C2×D4711yescharacteristic
322C4×C4⋊C4—22no—
323C43C2×D4711yescharacteristic
324#343—472no—
325#339—472no—
326#339—472no—
327C47C4×#45611yescharacteristic, complemented, Sylow
3282−1+4—474no—
3292−1+4—944no—
3302−1+4—942no—
331C2×#41—472no—
332C2×#41—942no—
333C2×#41—942no—
334C22×Q8—942no—
335C22×Q8C22×D4711yescharacteristic
336C22×Q8C22×D4711yescharacteristic
337#137—478no—
338#137—944no—
339C2×Q16—942no—
340C2×SD16—942no—
341C2×M16—472no—
342C2×M16—472no—
343C4⋊Q8—22no—
344C4⋊Q8C4×D4714yescomplemented
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—472no—
350C4×Q8—472no—
351C4×Q8—942no—
352C4×Q8—942no—
353C4×Q8—942no—
354C4×Q8—944no—
355C4×Q8—942no—
356C4×Q8—942no—
357C4×D4—472no—
358C4×D4—472no—
359C4×D4—942no—
360C4×D4—942no—
361C4×D4—942no—
362C4×D4—944no—
363C4×D4—942no—
364C4×D4—942no—
365C4×D4—944no—
366#117—472no—
367#117—944no—
368#117—942no—
369#117—944no—
370#117—942no—
371#117—942no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—942no—
376C2×C4⋊C4—944no—
377C2×C4⋊C4C22⋊D4712yes—
378C2×C4⋊C4C22×D4711yescharacteristic
379C2×C4⋊C4C22×D4711yescharacteristic
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—944no—
384C2×C42—942no—
385C2×C42C22⋊D4712yes—
386C2×C42C22×D4711yescharacteristic
387C2×C42C22×D4711yescharacteristic
388C2×C42C22×D4711yescharacteristic
389#107—942no—
390#106—942no—
391#104—478no—
392#104—944no—
393#103—942no—
394#103—942no—
395#103—942no—
396#102—942no—
397#101—474no—
398#101—942no—
399#97—942no—
400C4×C8—942no—
401#95—22no—
402#95—22no—
403#41—474no—
404#41—474no—
405#41—948no—
406#41—948no—
407#41—948no—
408#41—948no—
409#41—942no—
410#41—942no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—472no—
417C2×Q8—942no—
418C2×Q8—948no—
419C2×Q8—948no—
420C2×Q8C2×C4×D4712yes—
421C2×Q8C2×C4×D4712yes—
422C2×Q8#1062535012yes—
423C2×D4—472no—
424C2×D4—942no—
425C2×D4—942no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—944no—
431C22×C4—944no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4C2×C22⋊D4712yes—
436C22×C4C2×C22⋊D4711yescharacteristic
437C22×C4C2×C22⋊D4712yes—
438C22×C4C2×C22⋊D4711yescharacteristic
439C22×C4C23×D4711yescharacteristic
440Q16—948no—
441SD16—948no—
442M16—474no—
443M16—942no—
444M16—942no—
445M16—942no—
446C2×C8—942no—
447C2×C8—942no—
448C4⋊C4—28no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—44no—
453C4⋊C4—42no—
454C4⋊C4—472no—
455C4⋊C4—472no—
456C4⋊C4—944no—
457C4⋊C4—942no—
458C4⋊C4—942no—
459C4⋊C4—942no—
460C4⋊C4—942no—
461C22⋊C4—944no—
462C22⋊C4—942no—
463C22⋊C4—942no—
464C22⋊C4—942no—
465C42—24no—
466C42—22no—
467C42—22no—
468C42—21no—
469C42—22no—
470C42—42no—
471C42—41no—
472C42—41no—
473C42—944no—
474C42—944no—
475C42—942no—
476C42—942no—
477C42—942no—
478C42C2×C4×D4712yes—
479C42D4×D4712yes—
480C42D4×D4712yes—
481C23—942no—
482C23C22×C22⋊D4711yescharacteristic
483Q8—24no—
484Q8—24no—
485Q8—24no—
486Q8—42no—
487Q8—474no—
488Q8—948no—
489Q8—942no—
490D4—474no—
491D4—948no—
492D4—944no—
493D4—944no—
494D4—942no—
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—9416no—
513C2×C4—942no—
514C2×C4—944no—
515C2×C4—944no—
516C2×C4—942no—
517C2×C4—942no—
518C2×C4—3762no—
519C2×C4—3764no—
520C2×C4—1884no—
521C2×C4C4×C22⋊D4714yes—
522C2×C4#1309399211yescharacteristic
523C2×C4#1309399212yes—
524C2×C4#1309399211yescharacteristic
525C2×C4C22×C4×D4711yescharacteristic
526C2×C4C2×D4×D4712yes—
527C2×C4#41×D4712yes—
528C2×C4C2×#1062535011yescharacteristic
529C8—944no—
530C8—1882no—
531C22—21no—
532C22—21no—
533C22—944no—
534C22—1882no—
535C22—1882no—
536C22C2×C4×C22⋊D4711yescharacteristic
537C22C2×#1309399211yescharacteristic
538C22#1568963011yescharacteristic
539C4—24no—
540C4—21no—
541C4—22no—
542C4—24no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—81no—
547C4—944no—
548C4—1882no—
549C4—1882no—
550C4#1568930512yesdirect product factor
551C4C4×D4×D4712yes—
552C4#1568963212yes—
553C2—21no—
554C2—21no—
555C2—1884no—
556C2C4×#1309399211yescharacteristic
557C2C2×#1568930511yescharacteristic
558C2#2025273611yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×C4⋊Q8×C47C2
socleC22×C47C2×#120
prime radicalC2×#13094072C22
cosocleC22×C4×C47C24
hypercenterC4×C4⋊Q8D47
hypocenterC47C4×#456
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C4×#13094055C2semidirect
4. #20243782C2semidirect
5. #20243760C2semidirect
6. #20243613C2semidirect
7. #20243602C2semidirect
9. C4×#13093952C2semidirect
10. C4×#13093943C2semidirect
11. C4×C4⋊Q8×C47C2semidirect
23. #15689305C4direct (N × H)
56. #13094055C2×C4semidirect
91. #13093952C2×C4semidirect
97. #13093943C2×C4semidirect
103. C4⋊Q8×C47C2×C4semidirect
268. C4×C47#456semidirect
277. C4×C4⋊Q8D47semidirect
327. C47C4×#456semidirect
344. C4⋊Q8C4×D47semidirect
550. C4#15689305direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130940722
C2×#156893052
C4×#130940552
#202437822
#202437602
#202436132
#202436022
#202433462
C4×#130939522
C4×#130939432
C4×C4⋊Q8×C472
C4×#45647