Finite Group Databasebeta

← C4×#63930 #11859881

Subgroups — C4×#63930 #11859881

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2C2×#63930C211yesmaximal, characteristic
3C4×#3797C211yesmaximal, characteristic, complemented
4C3×C4×#214C212yesmaximal, complemented
5#10591445C212yesmaximal, complemented
6#10591416C211yesmaximal, characteristic
7#10590601C211yesmaximal, characteristic, complemented
8#10590575C211yesmaximal, characteristic, complemented
9#10590483C212yesmaximal, complemented
10C4×#3717C212yesmaximal, complemented
11C4×#3710C211yesmaximal, characteristic, complemented
12C4×D3×SD16—32nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3—21no—
15C2×#3797C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17D4×C3⋊Dic3C2211yescharacteristic
18C4×#638—21no—
19#64102C2211yescharacteristic
20C4⋊C4×C3⋊D3C2211yescharacteristic
21#64090—21no—
22C22⋊C4×C3⋊D3—21no—
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C42×C3⋊D3C2211yescharacteristic
25C2×C3×#214C2212yes—
26C3×C4×Dic6C2212yescomplemented
27#63930C418yesdirect product factor
28C4×#627—21no—
29#63900C2211yescharacteristic
30#63883—21no—
31C4×#624—21no—
32#63843C2212yescomplemented
33#63838—21no—
34C2×#3717C2212yes—
35C2×#3710C2211yescharacteristic
36C2×#3710C2211yescharacteristic
37C3×#832C2212yes—
38C3×#810C2212yescomplemented
39C3×#808C2212yescomplemented
40C3×C4×C3⋊C8C2212yescomplemented
41#63573C2212yescomplemented
42#63566C2212yescomplemented
43#63564C2212yes—
44#63553C2212yescomplemented
45C2×D3×SD16—32no—
46C4×D3×Q8—32no—
47C4×D3×D4—32no—
48C4×D3×D4—61no—
49C3×C4×SD16—32no—
50Dic3×SD16—32no—
51C4×#215—32no—
52C4×#214D312yescomplemented
53D3×#106—32no—
54#4852—32no—
55D3×#103—32no—
56#4788—32no—
57D3×#102—32no—
58#4758—32no—
59C4×#204—32no—
60C4×D3×C8—32no—
61C23×C3⋊D3—21no—
62C2×C32×D4C2311yescharacteristic
63C22×C32×C4—21no—
64C2×#638—21no—
65C22×C3⋊Dic3—21no—
66D4×C3⋊D3—22no—
67D4×C3⋊D3C2×C414yes—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—21no—
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—44no—
73C2×C4×C3⋊D3D411yescharacteristic
74C2×C4×C3⋊D3D411yescharacteristic
75C2×C4×C3⋊D3C2311yescharacteristic
76C2×C3×Dic6C2312yes—
77C2×#627—21no—
78C2×#624—21no—
79C2×#624—21no—
80#3797—22no—
81#3797C2×C414yescomplemented
82C32×C4⋊C4C2311yescharacteristic
83C32×C22⋊C4—21no—
84C32×C42C2311yescharacteristic
85#3757—21no—
86#3752—21no—
87#3752—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89#3750—21no—
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C3×#214C2×C418yescomplemented
94C3×C4⋊Dic3C2312yes—
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—22no—
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2312yes—
99#3724—21no—
100Dic3⋊Dic3—22no—
101Dic32—22no—
102#3717C2×C418yescomplemented
103#3710—22no—
104#3710C2×C414yescomplemented
105C2×C4×SD16—91noSylow
106C2×D3×Q8—32no—
107C2×D3×D4—32no—
108C2×D3×D4—61no—
109C22×C4×D3—62no—
110C22×C4×D3—62no—
111C2×C3×SD16—32no—
112C3×C4×Q8—32no—
113C3×C4×D4—21no—
114C3×C4×D4C2×D312yes—
115Q8×Dic3—32no—
116C2×#215—32no—
117D4×Dic3—32no—
118D4×Dic3—61no—
119C2×#214C2×D312yes—
120C4×#67—62no—
121C4×#67—62no—
122D3×SD16—316no—
123C2×#204—32no—
124C2×D3×C8—32no—
125C2×D3×C8—32no—
126#893—32no—
127#893—61no—
128D3×C4⋊C4—32no—
129D3×C4⋊C4—32no—
130D3×C4⋊C4—61no—
131D3×C4⋊C4—62no—
132#887—32no—
133#887—62no—
134#67⋊C4—62no—
135#67⋊C4—62no—
136D3×C22⋊C4—62no—
137D3×C22⋊C4—62no—
138C4×D12—32no—
139C4×D12—61no—
140C42×D3—32no—
141C42×D3—61no—
142C42×D3—62no—
143C4×Dic6—62no—
144C4×Dic6C2×D312yescomplemented
145C3×#106—32no—
146C3×#103—32no—
147C3×#102—32no—
148C3×C4×C8—32no—
149#835—32no—
150#832C2×D312yes—
151#821—32no—
152#817—32no—
153#816—32no—
154C8×Dic3—32no—
155C8×Dic3—32no—
156#810C2×D312yescomplemented
157#809—32no—
158#808—32no—
159#808C2×D312yescomplemented
160C4×C3⋊C8C2×D312yescomplemented
161C23×C32—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—24no—
164C22×C3⋊D3—42no—
165C22×C3⋊D3—42no—
166C22×C3⋊D3C2×D411yescharacteristic
167C32×D4—21no—
168C32×D4C22×C412yes—
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174#638—24no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—42no—
177C2×C3⋊Dic3C2×D411yescharacteristic
178C2×C3⋊Dic3C2×D411yescharacteristic
179C2×C3⋊Dic3C2×D411yescharacteristic
180C4⋊(C3⋊D3)—21no—
181C4⋊(C3⋊D3)C22×C412yes—
182C4×C3⋊D3—22no—
183C4×C3⋊D3—42no—
184C4×C3⋊D3—42no—
185C4×C3⋊D3—42no—
186C4×C3⋊D3SD1614yescomplemented
187C4×C3⋊D3C22×C412yes—
188C4×C3⋊D3#4112yes—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C3×Dic6—22no—
192C3×Dic6C22×C414yescomplemented
193#627—24no—
194#624—24no—
195#624—42no—
196C3×C3⋊C8—22no—
197C3×C3⋊C8C22×C414yescomplemented
198C22×SD16—91no—
199C2×C4×Q8—91no—
200C2×C4×D4—91no—
201C4×SD16—32no—
202C4×SD16—92no—
203C4×SD16—92no—
204C4×SD16—92no—
205C2×#106—91no—
206C2×#103—91no—
207C2×#102—91no—
208C2×C4×C8—91no—
209C23×D3—62no—
210C23×D3—62no—
211C2×C3×Q8—32no—
212C2×C3×D4—21no—
213C2×C3×D4C22×D312yes—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C2×#67—62no—
217C2×#67—62no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220D3×Q8—38no—
221D3×Q8—64no—
222D3×D4—38no—
223D3×D4—64no—
224D3×D4—64no—
225D3×D4—64no—
226C2×D12—32no—
227C2×D12—61no—
228C2×C4×D3—32no—
229C2×C4×D3—32no—
230C2×C4×D3—32no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—62no—
238C2×C4×D3—62no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—128no—
243C2×C4×D3—128no—
244C2×Dic6—62no—
245C2×Dic6C22×D312yes—
246C3×SD16—38no—
247C2×C3×C8—32no—
248C2×C3×C8—32no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—32no—
251C3×C4⋊C4—62no—
252C3×C4⋊C4C22×D312yes—
253C3×C22⋊C4—22no—
254C3×C22⋊C4—22no—
255C3×C42—21no—
256C3×C42—62no—
257C3×C42C22×D312yes—
258#217—62no—
259#217—62no—
260#215—38no—
261#214C4×D318yescomplemented
262(C2×D3)⋊C4—62no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4—62no—
266C4⋊Dic3—32no—
267C4⋊Dic3—61no—
268C4⋊Dic3—62no—
269C4⋊Dic3C22×D312yes—
270Dic3⋊C4—22no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275C4×Dic3—22no—
276C4×Dic3—32no—
277C4×Dic3—32no—
278C4×Dic3—32no—
279C4×Dic3—61no—
280C4×Dic3—61no—
281C4×Dic3—61no—
282C4×Dic3—62no—
283C4×Dic3—62no—
284C2×C3⋊C8C22×D312yes—
285C2×C3⋊C8C22×D312yes—
286#204—38no—
287D3×C8—38no—
288D3×C8—64no—
289C22×C32—22no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32C22×D411yescharacteristic
293C2×C3⋊D3—22no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C2×C3⋊D3—48no—
297C2×C3⋊D3C4×D412yes—
298C2×C3⋊D3C2×SD1612yes—
299C2×C3⋊D3#13512yes—
300C32×C4—21no—
301C32×C4—41no—
302C32×C4C2×SD1612yescomplemented
303C32×C4C23×C411yescharacteristic
304C32×C4C2×#4111yescharacteristic
305C3⋊Dic3—21no—
306C3⋊Dic3—41no—
307C3⋊Dic3C4×D412yes—
308C3⋊Dic3C2×SD1612yescomplemented
309C3×Dic3—24no—
310C3×Dic3—42no—
311C22×Q8—91no—
312C22×D4—91no—
313C23×C4—181no—
314C2×SD16—32no—
315C2×SD16—92no—
316C2×SD16—98no—
317C22×C8—91no—
318C22×C8—91no—
319C4×Q8—32no—
320C4×Q8—92no—
321C4×Q8—181no—
322C4×Q8—181no—
323C4×D4—91no—
324C4×D4—91no—
325C4×D4—91no—
326C4×D4—181no—
327C4×D4—181no—
328C4×D4D3211yescharacteristic
329C2×C4⋊C4—91no—
330C2×C4⋊C4—91no—
331C2×C4⋊C4—181no—
332C2×C22⋊C4—181no—
333C2×C42—91no—
334C2×C42—181no—
335#106—32no—
336#106—92no—
337#103—32no—
338#103—92no—
339#102—32no—
340#102—92no—
341C4×C8—32no—
342C4×C8—92no—
343C23×C3—22no—
344C23×C3—22no—
345C22×D3—32no—
346C22×D3—61no—
347C22×D3—68no—
348C22×D3—62no—
349C22×D3—68no—
350C22×D3—62no—
351C22×D3—124no—
352C22×D3—124no—
353C22×D3—124no—
354C22×D3—124no—
355C3×Q8—34no—
356C3×Q8—62no—
357C3×D4—22no—
358C3×D4—22no—
359C3×D4—22no—
360C3×D4C2×C4×D314yes—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—44no—
367C2×C3×C4—44no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4D3×D412yes—
371C2×C3×C4D3×D412yes—
372C2×C3×C4C23×D312yes—
373#67—68no—
374#67—68no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—124no—
386C2×Dic3—124no—
387D12—34no—
388D12—62no—
389D12—62no—
390D12—62no—
391C4×D3—38no—
392C4×D3—34no—
393C4×D3—34no—
394C4×D3—64no—
395C4×D3—62no—
396C4×D3—62no—
397C4×D3—68no—
398C4×D3—64no—
399C4×D3—122no—
400C4×D3—124no—
401C4×D3—124no—
402C4×D3—124no—
403C4×D3—124no—
404C4×D3—124no—
405C4×D3—124no—
406C4×D3—124no—
407Dic6—22no—
408Dic6—68no—
409Dic6C2×C4×D314yescomplemented
410C3×C8—34no—
411C3×C8—62no—
412C3⋊C8—22no—
413C3⋊C8C2×C4×D314yescomplemented
414C2×C32—42no—
415C2×C32C2×C4×D411yescharacteristic
416C2×C32C22×SD1611yescharacteristic
417C2×C32C2×#13511yescharacteristic
418C3⋊D3—42no—
419C3⋊D3C4×SD1614yescomplemented
420C24—181no—
421C2×Q8—32no—
422C2×Q8—94no—
423C2×Q8—181no—
424C2×Q8—182no—
425C2×D4—94no—
426C2×D4—91no—
427C2×D4—182no—
428C2×D4—181no—
429C2×D4C2×D3211yescharacteristic
430C22×C4—21no—
431C22×C4—91no—
432C22×C4—91no—
433C22×C4—91no—
434C22×C4—181no—
435C22×C4—181no—
436C22×C4—181no—
437C22×C4—181no—
438C22×C4—181no—
439C22×C4—181no—
440C22×C4—364no—
441SD16—38no—
442SD16—98no—
443C2×C8—32no—
444C2×C8—32no—
445C2×C8—94no—
446C2×C8—182no—
447C4⋊C4—32no—
448C4⋊C4—62no—
449C4⋊C4—91no—
450C4⋊C4—181no—
451C4⋊C4—181no—
452C4⋊C4—182no—
453C4⋊C4C2×D3211yescharacteristic
454C22⋊C4—21no—
455C22⋊C4—181no—
456C22⋊C4—181no—
457C22⋊C4—181no—
458C42—62no—
459C42—91no—
460C42—91no—
461C42—91no—
462C42—182no—
463C42C2×D3211yescharacteristic
464C22×C3—24no—
465C22×C3—24no—
466C22×C3—21no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3C2×D3×D412yes—
472C2×D3—34no—
473C2×D3—34no—
474C2×D3—34no—
475C2×D3—62no—
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—64no—
479C2×D3—64no—
480C2×D3—1216no—
481C2×D3—1216no—
482C2×D3—122no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—122no—
486C3×C4—22no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—22no—
490C3×C4—41no—
491C3×C4—42no—
492C3×C4—42no—
493C3×C4—64no—
494C3×C4—122no—
495C3×C4D3×SD1614yescomplemented
496C3×C4C22×C4×D312yes—
497C3×C4D3×#4112yes—
498Dic3—24no—
499Dic3—34no—
500Dic3—34no—
501Dic3—42no—
502Dic3—62no—
503Dic3—62no—
504Dic3—62no—
505Dic3—121no—
506Dic3—122no—
507Dic3—122no—
508C32C2×C4×SD1611yescharacteristic, complemented, Sylow
509C23—21no—
510C23—91no—
511C23—184no—
512C23—181no—
513C23—362no—
514C23—362no—
515Q8—34no—
516Q8—62no—
517Q8—184no—
518D4—21no—
519D4—92no—
520D4—184no—
521D4—181no—
522D4C4×D3212yes—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—91no—
528C2×C4—91no—
529C2×C4—92no—
530C2×C4—92no—
531C2×C4—94no—
532C2×C4—91no—
533C2×C4—182no—
534C2×C4—184no—
535C2×C4—181no—
536C2×C4—362no—
537C2×C4—362no—
538C2×C4—362no—
539C2×C4—362no—
540C2×C4—362no—
541C2×C4#381111yescharacteristic
542C2×C4#381111yescharacteristic
543C2×C4C22×D3211yescharacteristic
544C8—34no—
545C8—62no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—44no—
550C2×C3—44no—
551C2×C3C4×D3×D412yes—
552C2×C3C2×D3×SD1612yes—
553C2×C3D3×#13512yes—
554D3—38no—
555D3—64no—
556D3—124no—
557D3—124no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—92no—
562C22—92no—
563C22—92no—
564C22—182no—
565C22—368no—
566C22—361no—
567C22—361no—
568C22C2×#381111yescharacteristic
569C4—21no—
570C4—41no—
571C4—64no—
572C4—92no—
573C4—92no—
574C4—122no—
575C4—181no—
576C4—361no—
577C4#6393012yesdirect product factor
578C4C2×C4×D3211yescharacteristic
579C4#6430611yescharacteristic
580C3—21no—
581C3C4×D3×SD1612yescomplemented
582C2—42no—
583C2—94no—
584C2—362no—
585C2C4×#381111yescharacteristic
586C2C2×#6393011yescharacteristic
587C2#1059545911yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32C2×C4×SD16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. C4×#3797C2semidirect
4. C3×C4×#214C2semidirect
5. #10591445C2semidirect
7. #10590601C2semidirect
8. #10590575C2semidirect
9. #10590483C2semidirect
10. C4×#3717C2semidirect
11. C4×#3710C2semidirect
26. C3×C4×Dic6C22semidirect
27. #63930C4direct (N × H)
32. #63843C22semidirect
38. C3×#810C22semidirect
39. C3×#808C22semidirect
40. C3×C4×C3⋊C8C22semidirect
41. #63573C22semidirect
42. #63566C22semidirect
44. #63553C22semidirect
52. C4×#214D3semidirect
81. #3797C2×C4semidirect
93. C3×#214C2×C4semidirect
102. #3717C2×C4semidirect
104. #3710C2×C4semidirect
144. C4×Dic6C2×D3semidirect
156. #810C2×D3semidirect
159. #808C2×D3semidirect
160. C4×C3⋊C8C2×D3semidirect
186. C4×C3⋊D3SD16semidirect
192. C3×Dic6C22×C4semidirect
197. C3×C3⋊C8C22×C4semidirect
261. #214C4×D3semidirect
302. C32×C4C2×SD16semidirect
308. C3⋊Dic3C2×SD16semidirect
409. Dic6C2×C4×D3semidirect
413. C3⋊C8C2×C4×D3semidirect
419. C3⋊D3C4×SD16semidirect
495. C3×C4D3×SD16semidirect
508. C32C2×C4×SD16semidirect
577. C4#63930direct (N × H)
581. C3C4×D3×SD16semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
C2×#639302
C4×#37972
C3×C4×#2142
#105914452
#105914162
#105906012
#105905752
#105904832
C4×#37172
C4×#37102
C4×D3×SD163