Finite Group Databasebeta

← C4×#64146 #11801972

Subgroups — C4×#64146 #11801972

Order 1152.

3672 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C32×C4×D4C211yesmaximal, characteristic, complemented
3C2×#64146C211yesmaximal, characteristic
4C2×C4×#638C212yesmaximal, complemented
5#10592919C211yesmaximal, characteristic, complemented
6C4×#3757C211yesmaximal, characteristic, complemented
7#10592688C212yesmaximal, complemented
8#10592655C212yesmaximal, complemented
9#10592654C211yesmaximal, characteristic, complemented
10#10592645C211yesmaximal, characteristic, complemented
11C4×#3752C212yesmaximal, complemented
12C4×#937—34nomaximal
13C24×C3⋊D3C2211yescharacteristic
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic, complemented
17C22×#638C2212yes—
18C23×C3⋊Dic3C2211yescharacteristic
19C22×C4×C3⋊D3—24no—
20C22×C4×C3⋊D3—28no—
21C22×C4×C3⋊D3C2212yes—
22C22×C4×C3⋊D3C2212yes—
23C32×C4×D4—24no—
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic, complemented
27C2×C32×C42C2211yescharacteristic, complemented
28C2×#3757C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3757C2212yescomplemented
31#64146C418yesdirect product factor
32C4×#638—28no—
33C2×#3752C2212yes—
34C2×#3752C2212yes—
35C2×#3752C2212yes—
36C2×#3750C2212yescomplemented
37C2×C4×C3⋊Dic3C2212yescomplemented
38#63658C2212yescomplemented
39#63658C2212yescomplemented
40#63658C2212yescomplemented
41C23×C4×D3—34no—
42C2×C3×C4×D4D314yescomplemented
43C2×#937—34no—
44C2×C4×#67—38no—
45#5220—34no—
46C4×#217—34no—
47#4989—38no—
48#4956—38no—
49#4955—34no—
50#4946—34no—
51C4×(C2×D3)⋊C4—38no—
52C24×C32C2311yescharacteristic
53C24×C32C2311yescharacteristic
54C23×C3⋊D3—22no—
55C23×C3⋊D3—22no—
56C23×C3⋊D3—24no—
57C23×C3⋊D3—24no—
58C23×C3⋊D3C2×C414yescomplemented
59C23×C3⋊D3C2312yes—
60C2×C32×D4—22no—
61C2×C32×D4—22no—
62C2×C32×D4C2×C414yescomplemented
63C22×C32×C4—24no—
64C22×C32×C4—24no—
65C22×C32×C4—22no—
66C22×C32×C4D414yescomplemented
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×#638—24no—
73C2×#638—24no—
74C2×#638C2×C418yescomplemented
75C22×C3⋊Dic3—22no—
76C22×C3⋊Dic3—24no—
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2312yes—
80C2×C4×C3⋊D3—232no—
81C2×C4×C3⋊D3—24no—
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3—24no—
84C2×C4×C3⋊D3—24no—
85C2×C4×C3⋊D3—24no—
86C2×C4×C3⋊D3D418yescomplemented
87C32×C4⋊C4—22no—
88C32×C22⋊C4—22no—
89C32×C22⋊C4—22no—
90C32×C42—22no—
91#3757—22no—
92#3757—24no—
93#3757C2×C414yescomplemented
94#3752—24no—
95#3752—24no—
96#3752C2×C418yescomplemented
97#3750—24no—
98C4×C3⋊Dic3—24no—
99C4×#120—91noSylow
100C24×D3—34no—
101C22×C3×D4C2×D314yes—
102C23×C3×C4C2×D314yes—
103C23×C3×C4C2×D314yescomplemented
104C22×#67—38no—
105C23×Dic3—34no—
106C22×C4×D3—38no—
107C22×C4×D3—38no—
108C22×C4×D3—632no—
109C22×C4×D3—616no—
110C3×C4×D4—216no—
111C2×C3×C4⋊C4C2×D314yescomplemented
112C2×C3×C22⋊C4C2×D314yes—
113C2×C3×C22⋊C4C2×D314yescomplemented
114C2×C3×C42C2×D314yescomplemented
115C2×#217—34no—
116C2×#217—34no—
117C2×#217—38no—
118#937—332no—
119C4×#67—632no—
120C2×(C2×D3)⋊C4—38no—
121C2×(C2×D3)⋊C4—38no—
122C2×(C2×D3)⋊C4—38no—
123C2×Dic3⋊C4—38no—
124C2×C4×Dic3—38no—
125C3⋊#95—38no—
126C3⋊#95—38no—
127C3⋊#95—38no—
128C23×C32—22no—
129C23×C32—22no—
130C23×C32—22no—
131C23×C32—21no—
132C23×C32—22no—
133C23×C32—21no—
134C23×C32C22×C412yes—
135C23×C32C22×C412yescomplemented
136C23×C32C2×D412yes—
137C23×C32#4112yes—
138C23×C32C2411yescharacteristic
139C22×C3⋊D3—216no—
140C22×C3⋊D3—28no—
141C22×C3⋊D3—28no—
142C22×C3⋊D3—28no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3—216no—
148C22×C3⋊D3C22×C414yes—
149C22×C3⋊D3C2×D414yes—
150C22×C3⋊D3#4114yes—
151C32×D4—28no—
152C2×C32×C4—21no—
153C2×C32×C4—22no—
154C2×C32×C4—21no—
155C2×C32×C4—28no—
156C2×C32×C4—22no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—22no—
160C2×C32×C4—44no—
161C2×C32×C4C22×C412yescomplemented
162C2×C32×C4C2×D414yes—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D412yes—
165#638—216no—
166C2×C3⋊Dic3—28no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3C22×C414yescomplemented
175C2×C3⋊Dic3C2×D414yes—
176C4×C3⋊D3—216no—
177C4×C3⋊D3—216no—
178C24×C4—91no—
179C2×#120—91no—
180C2×C4×D4—92no—
181C2×C4×D4C3⋊D311yescharacteristic, complemented
182#386—91no—
183#386—92no—
184#385—92no—
185#385—91no—
186#379—91no—
187C4×C22⋊C4—91no—
188C4×C22⋊C4—92no—
189C24×C3C22×D314yes—
190C24×C3C22×D314yes—
191C23×D3—38no—
192C23×D3—316no—
193C23×D3—616no—
194C23×D3—616no—
195C23×D3—68no—
196C23×D3—68no—
197C2×C3×D4—28no—
198C2×C3×D4—28no—
199C2×C3×D4C4×D3116yescomplemented
200C22×C3×C4—216no—
201C22×C3×C4—216no—
202C22×C3×C4—28no—
203C22×C3×C4#67116yescomplemented
204C22×C3×C4C22×D314yes—
205C22×C3×C4C22×D314yes—
206C22×C3×C4C22×D314yes—
207C22×C3×C4C22×D314yes—
208C22×C3×C4C22×D314yes—
209C2×#67—332no—
210C2×#67—616no—
211C2×#67—616no—
212C22×Dic3—38no—
213C22×Dic3—38no—
214C22×Dic3—38no—
215C22×Dic3—616no—
216C22×Dic3—68no—
217C2×C4×D3—332no—
218C2×C4×D3—616no—
219C2×C4×D3—616no—
220C2×C4×D3—6128no—
221C2×C4×D3—616no—
222C2×C4×D3—616no—
223C2×C4×D3—616no—
224C3×C4⋊C4—28no—
225C3×C22⋊C4—28no—
226C3×C22⋊C4—28no—
227C3×C42—28no—
228#217—316no—
229#217—616no—
230#217—68no—
231(C2×D3)⋊C4—332no—
232(C2×D3)⋊C4—616no—
233(C2×D3)⋊C4—616no—
234Dic3⋊C4—616no—
235C4×Dic3—616no—
236C22×C32—24no—
237C22×C32—22no—
238C22×C32—22no—
239C22×C32—24no—
240C22×C32—24no—
241C22×C32—22no—
242C22×C32—41no—
243C22×C32—42no—
244C22×C32—41no—
245C22×C32C4×D414yescomplemented
246C22×C32C23×C411yescharacteristic
247C22×C32C22×D412yes—
248C22×C32C22×D411yescharacteristic
249C22×C32C2×#4111yescharacteristic
250C22×C32C2×#4112yes—
251C2×C3⋊D3—232no—
252C2×C3⋊D3—24no—
253C2×C3⋊D3—24no—
254C2×C3⋊D3—24no—
255C2×C3⋊D3—24no—
256C2×C3⋊D3—24no—
257C2×C3⋊D3—24no—
258C2×C3⋊D3C4×D418yescomplemented
259C32×C4—22no—
260C32×C4—22no—
261C32×C4—41no—
262C32×C4—41no—
263C32×C4#12014yescomplemented
264C3⋊Dic3—24no—
265C3⋊Dic3—24no—
266C3⋊Dic3—42no—
267C25—91no—
268C22×D4—92no—
269C22×D4C2×C3⋊D311yescharacteristic
270C23×C4—92no—
271C23×C4—91no—
272C23×C4—92no—
273C23×C4—188no—
274C23×C4—184no—
275C23×C4C2×C3⋊D311yescharacteristic
276C23×C4C2×C3⋊D311yescharacteristic, complemented
277#120—98no—
278C4×D4—24no—
279C4×D4—188no—
280C2×C4⋊C4—92no—
281C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
282C2×C22⋊C4—91no—
283C2×C22⋊C4—92no—
284C2×C22⋊C4—92no—
285C2×C22⋊C4—91no—
286C2×C22⋊C4—92no—
287C2×C22⋊C4—92no—
288C2×C22⋊C4C2×C3⋊D311yescharacteristic
289C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
290C2×C42—92no—
291C2×C42C2×C3⋊D311yescharacteristic, complemented
292#95—92no—
293#95—92no—
294#95—92no—
295C23×C3—28no—
296C23×C3—28no—
297C23×C3—24no—
298C23×C3—28no—
299C23×C3—28no—
300C23×C3—24no—
301C23×C3C2×C4×D318yes—
302C23×C3C2×C4×D318yescomplemented
303C23×C3#23518yes—
304C23×C3C2×#6718yes—
305C23×C3C23×D314yes—
306C22×D3—316no—
307C22×D3—316no—
308C22×D3—316no—
309C22×D3—664no—
310C22×D3—632no—
311C22×D3—664no—
312C22×D3—632no—
313C22×D3—632no—
314C22×D3—68no—
315C22×D3—68no—
316C22×D3—68no—
317C22×D3—68no—
318C3×D4—232no—
319C2×C3×C4—24no—
320C2×C3×C4—28no—
321C2×C3×C4—24no—
322C2×C3×C4—232no—
323C2×C3×C4—28no—
324C2×C3×C4—28no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—416no—
328C2×C3×C4C2×C4×D318yescomplemented
329C2×C3×C4D3×D4116yes—
330C2×C3×C4C2×#6718yes—
331C2×C3×C4C2×#6718yes—
332#67—664no—
333C2×Dic3—316no—
334C2×Dic3—316no—
335C2×Dic3—632no—
336C2×Dic3—68no—
337C2×Dic3—68no—
338C2×Dic3—68no—
339C2×Dic3—68no—
340C2×Dic3—68no—
341C2×Dic3—68no—
342C2×Dic3—68no—
343C4×D3—664no—
344C4×D3—664no—
345C2×C32—24no—
346C2×C32—42no—
347C2×C32C2×C4×D411yescharacteristic
348C2×C32C2×C4×D412yes—
349C2×C32C2×#12011yescharacteristic
350C2×C32#52512yes—
351C2×C32#52511yescharacteristic
352C3⋊D3—28no—
353C24—92no—
354C24—94no—
355C24—184no—
356C24—184no—
357C24—182no—
358C24—182no—
359C24C22×C3⋊D311yescharacteristic
360C24C22×C3⋊D311yescharacteristic
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—98no—
364C2×D4—184no—
365C2×D4—184no—
366C2×D4C4×C3⋊D314yescomplemented
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—92no—
371C22×C4—92no—
372C22×C4—98no—
373C22×C4—92no—
374C22×C4—184no—
375C22×C4—184no—
376C22×C4—1832no—
377C22×C4—184no—
378C22×C4—182no—
379C22×C4—184no—
380C22×C4—184no—
381C22×C4—184no—
382C22×C4#63814yescomplemented
383C22×C4C22×C3⋊D311yescharacteristic
384C22×C4C22×C3⋊D311yescharacteristic
385C22×C4C22×C3⋊D311yescharacteristic
386C22×C4C22×C3⋊D311yescharacteristic
387C22×C4C22×C3⋊D311yescharacteristic
388C4⋊C4—22no—
389C4⋊C4—184no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—94no—
393C22⋊C4—98no—
394C22⋊C4—184no—
395C22⋊C4—184no—
396C22⋊C4—184no—
397C22⋊C4—182no—
398C42—22no—
399C42—184no—
400C22×C3—28no—
401C22×C3—216no—
402C22×C3—216no—
403C22×C3—28no—
404C22×C3—28no—
405C22×C3—216no—
406C22×C3—44no—
407C22×C3—48no—
408C22×C3—44no—
409C22×C3C4×#67116yescomplemented
410C22×C3C22×C4×D314yes—
411C22×C3C2×#23514yes—
412C22×C3C2×D3×D418yes—
413C22×C3D3×#4118yes—
414C22×C3C22×#6714yes—
415C2×D3—332no—
416C2×D3—6128no—
417C2×D3—616no—
418C2×D3—616no—
419C2×D3—616no—
420C2×D3—616no—
421C2×D3—616no—
422C2×D3—616no—
423C3×C4—28no—
424C3×C4—28no—
425C3×C4—44no—
426C3×C4—44no—
427C3×C4#937116yescomplemented
428Dic3—616no—
429Dic3—616no—
430Dic3—128no—
431C32C4×#12011yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—21no—
435C23—22no—
436C23—22no—
437C23—21no—
438C23—94no—
439C23—94no—
440C23—94no—
441C23—1816no—
442C23—188no—
443C23—1816no—
444C23—188no—
445C23—182no—
446C23—182no—
447C23—182no—
448C23—182no—
449C23—188no—
450C23C2×C4×C3⋊D312yes—
451C23C2×C4×C3⋊D312yescomplemented
452C23#382812yes—
453C23C2×#63812yes—
454C23C23×C3⋊D311yescharacteristic
455D4—28no—
456D4—1816no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—28no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—44no—
466C2×C4—94no—
467C2×C4—94no—
468C2×C4—1816no—
469C2×C4—188no—
470C2×C4—182no—
471C2×C4—182no—
472C2×C4—182no—
473C2×C4—182no—
474C2×C4—1816no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—182no—
478C2×C4C2×C4×C3⋊D312yescomplemented
479C2×C4D4×C3⋊D314yes—
480C2×C4C2×#63812yes—
481C2×C4C2×#63812yes—
482C2×C3—216no—
483C2×C3—48no—
484C2×C3C4×D3×D418yes—
485C2×C3#554718yes—
486C2×C3C2×C4×#6714yes—
487C2×C3C2×#93714yes—
488C2×C3#582814yes—
489D3—632no—
490C22—22no—
491C22—24no—
492C22—24no—
493C22—22no—
494C22—22no—
495C22—24no—
496C22—41no—
497C22—42no—
498C22—41no—
499C22—98no—
500C22—1832no—
501C22—184no—
502C22—184no—
503C22—184no—
504C22—184no—
505C22—184no—
506C22—184no—
507C22C4×#63814yescomplemented
508C22C22×C4×C3⋊D311yescharacteristic
509C22C2×#382811yescharacteristic
510C22C2×D4×C3⋊D312yes—
511C22#41×C3⋊D312yes—
512C22C22×#63811yescharacteristic
513C4—22no—
514C4—22no—
515C4—41no—
516C4—41no—
517C4—184no—
518C4—184no—
519C4—362no—
520C4#6414614yesdirect product factor
521C3C4×#93714yescomplemented
522C2—24no—
523C2—42no—
524C2—188no—
525C2C4×D4×C3⋊D312yes—
526C2#1059601812yes—
527C2C2×C4×#63811yescharacteristic
528C2C2×#6414611yescharacteristic
529C2#1059629911yescharacteristic
subgroupG/H
centerC22×C4C22×C3⋊D3
commutatorC22×C32C23×C4
FrattiniC23C23×C3⋊D3
FittingC2×C32×C4×D4C2
socle, cosocleC23×C32C24
prime radicalC2×#64146C2
hypercenterC2×C4×D4C3⋊D3
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C23×C4×C3⋊D3C2semidirect
2. C2×C32×C4×D4C2semidirect
4. C2×C4×#638C2semidirect
5. #10592919C2semidirect
6. C4×#3757C2semidirect
7. #10592688C2semidirect
8. #10592655C2semidirect
9. #10592654C2semidirect
10. #10592645C2semidirect
11. C4×#3752C2semidirect
16. C23×C32×C4C22semidirect
24. C2×C32×C4⋊C4C22semidirect
26. C2×C32×C22⋊C4C22semidirect
27. C2×C32×C42C22semidirect
30. C2×#3757C22semidirect
31. #64146C4direct (N × H)
36. C2×#3750C22semidirect
37. C2×C4×C3⋊Dic3C22semidirect
38. #63658C22semidirect
39. #63658C22semidirect
40. #63658C22semidirect
42. C2×C3×C4×D4D3semidirect
58. C23×C3⋊D3C2×C4semidirect
62. C2×C32×D4C2×C4semidirect
66. C22×C32×C4D4semidirect
74. C2×#638C2×C4semidirect
86. C2×C4×C3⋊D3D4semidirect
93. #3757C2×C4semidirect
96. #3752C2×C4semidirect
103. C23×C3×C4C2×D3semidirect
111. C2×C3×C4⋊C4C2×D3semidirect
113. C2×C3×C22⋊C4C2×D3semidirect
114. C2×C3×C42C2×D3semidirect
135. C23×C32C22×C4semidirect
161. C2×C32×C4C22×C4semidirect
174. C2×C3⋊Dic3C22×C4semidirect
181. C2×C4×D4C3⋊D3semidirect
199. C2×C3×D4C4×D3semidirect
203. C22×C3×C4#67semidirect
245. C22×C32C4×D4semidirect
258. C2×C3⋊D3C4×D4semidirect
263. C32×C4#120semidirect
276. C23×C4C2×C3⋊D3semidirect
281. C2×C4⋊C4C2×C3⋊D3semidirect
289. C2×C22⋊C4C2×C3⋊D3semidirect
291. C2×C42C2×C3⋊D3semidirect
302. C23×C3C2×C4×D3semidirect
328. C2×C3×C4C2×C4×D3semidirect
366. C2×D4C4×C3⋊D3semidirect
382. C22×C4#638semidirect
409. C22×C3C4×#67semidirect
427. C3×C4#937semidirect
431. C32C4×#120semidirect
451. C23C2×C4×C3⋊D3semidirect
478. C2×C4C2×C4×C3⋊D3semidirect
507. C22C4×#638semidirect
520. C4#64146direct (N × H)
521. C3C4×#937semidirect

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C2×C32×C4×D42
C2×#641462
C2×C4×#6382
#105929192
C4×#37572
#105926882
#105926552
#105926542
#105926452
C4×#37522
C4×#9373