Finite Group Databasebeta

← C4×#64141 #11860264

Subgroups — C4×#64141 #11860264

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×#64141C211yesmaximal, characteristic
3C4×#3828C211yesmaximal, characteristic, complemented
4#10592914C211yesmaximal, characteristic, complemented
5#10592717C212yesmaximal, complemented
6C4×#3754C212yesmaximal, complemented
7#10592713C212yesmaximal, complemented
8C4×#3753C212yesmaximal, complemented
9#10592665C211yesmaximal, characteristic, complemented
10#10592663C211yesmaximal, characteristic, complemented
11C4×#3748C211yesmaximal, characteristic, complemented
12C4×#932—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C32×C4—21no—
15C2×#3828C2211yescharacteristic
16C32×C4×D4—21no—
17C32×C4×D4—21no—
18C32×C4×D4C2212yes—
19C32×C4×D4C2212yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4—21no—
22C2×C32×C42C2211yescharacteristic
23C2×#3754C2212yes—
24#64141C418yesdirect product factor
25C2×#3753C2212yes—
26C4×#638—21no—
27C4×#638—21no—
28#64135C2211yescharacteristic
29C2×#3748C2211yescharacteristic
30C2×#3748C2211yescharacteristic
31C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
32C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
33#64081—21no—
34C42×C3⋊D3—21no—
35C4×#634C2211yescharacteristic, complemented
36C4×#634C2211yescharacteristic, complemented
37#63659C2212yes—
38#63659C2212yes—
39#63637C2212yescomplemented
40#63636C2212yescomplemented
41#63635C2212yescomplemented
42#63634C2212yescomplemented
43#63630C2212yescomplemented
44C4×C3⋊(C3⋊C8)C2212yescomplemented
45C2×C3×C4×D4D314yescomplemented
46C2×#932—34no—
47C4×#235—34no—
48#5215—34no—
49#5018—38no—
50C4×#214—38no—
51#5014—38no—
52C4×#213—38no—
53#4966—34no—
54#4964—34no—
55C4×#208—34no—
56C24×C32—21no—
57C2×C32×D4—21no—
58C2×C32×D4—22no—
59C2×C32×D4C2×C414yescomplemented
60C2×C32×D4C2312yes—
61C22×C32×C4—21no—
62C22×C32×C4—22no—
63C22×C32×C4—22no—
64C22×C32×C4—44no—
65C22×C32×C4D411yescharacteristic
66C22×C32×C4D411yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69#3828—22no—
70#3828C2×C414yescomplemented
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—21no—
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—21no—
75C2×#634C2311yescharacteristic
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78C32×C22⋊C4—22no—
79C32×C22⋊C4—22no—
80C32×C42D411yescharacteristic
81C32×C42D411yescharacteristic
82C32×C42C2311yescharacteristic
83C32×C42C2311yescharacteristic
84#3757—21no—
85#3754C2×C418yescomplemented
86#3753C2×C418yescomplemented
87#3752—21no—
88#3752—21no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91#3750—21no—
92#3750—21no—
93C4×C3⋊Dic3—21no—
94C4×C3⋊Dic3—21no—
95C4×C3⋊Dic3—21no—
96#3748—22no—
97#3748C2×C414yescomplemented
98C2×C3⋊(C3⋊C8)C2312yes—
99C2×C3⋊(C3⋊C8)C2312yes—
100C4×AGL(1,ℤ/8)—91noSylow
101C22×C3×D4C2×D314yes—
102C23×C3×C4—24no—
103C2×#235—34no—
104C3×C4×D4—24no—
105C3×C4×D4—24no—
106C3×C4×D4C2×D318yes—
107C3×C4×D4C2×D318yes—
108C2×C3×C4⋊C4C2×D314yes—
109C2×C3×C22⋊C4—24no—
110C2×C3×C42C2×D314yes—
111C2×#214—38no—
112#932—332no—
113C2×#213—38no—
114C4×#67—64no—
115C4×#67—64no—
116#926—34no—
117C2×#208—34no—
118C2×#208—34no—
119C4×D12—34no—
120C4×D12—34no—
121#872—64no—
122C42×D3—64no—
123C4×Dic6—34no—
124C4×Dic6—34no—
125#832—38no—
126#832—38no—
127#810—38no—
128#809—38no—
129#808—38no—
130#807—38no—
131#803—38no—
132C4×C3⋊C8—38no—
133C23×C32—24no—
134C23×C32—22no—
135C23×C32—42no—
136C23×C32—42no—
137C23×C32C2×D411yescharacteristic
138C22×C3⋊D3—21no—
139C32×D4—24no—
140C32×D4—22no—
141C32×D4C22×C414yes—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4—41no—
145C2×C32×C4—44no—
146C2×C32×C4—42no—
147C2×C32×C4—44no—
148C2×C32×C4C22×C412yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4#4112yes—
155C2×C32×C4C2411yescharacteristic
156#638—24no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C4⋊(C3⋊D3)—21no—
161C4⋊(C3⋊D3)C22×C412yescomplemented
162C4×C3⋊D3—24no—
163C4×C3⋊D3—42no—
164C4×C3⋊D3—42no—
165#634—21no—
166#634C22×C412yescomplemented
167C3⋊(C3⋊C8)—22no—
168C3⋊(C3⋊C8)C22×C414yescomplemented
169C2×AGL(1,ℤ/8)—91no—
170C4×#41—91no—
171C2×C4×D4C3⋊D311yescharacteristic, complemented
172#442—92no—
173#440—92no—
174C4×SD16—92no—
175C4×D8—92no—
176#428—91no—
177#418—91no—
178#417—91no—
179C4×M16—91no—
180C24×C3—24no—
181C2×C3×D4—28no—
182C2×C3×D4—24no—
183C2×C3×D4C4×D3116yescomplemented
184C2×C3×D4C22×D318yes—
185C22×C3×C4—24no—
186C22×C3×C4—28no—
187C22×C3×C4—28no—
188C22×C3×C4—416no—
189C22×C3×C4#6714yes—
190C22×C3×C4#6714yes—
191C22×C3×C4C22×D314yes—
192C2×#67—64no—
193#235—316no—
194#235—68no—
195C2×D12—34no—
196C2×C4×D3—64no—
197C2×C4×D3—64no—
198C2×C4×D3—64no—
199C2×Dic6—34no—
200C3×C4⋊C4—24no—
201C3×C4⋊C4C22×D318yes—
202C3×C22⋊C4—28no—
203C3×C22⋊C4—28no—
204C3×C42#6714yes—
205C3×C42#6714yes—
206C3×C42C22×D314yes—
207C3×C42C22×D314yes—
208#217—64no—
209#214—332no—
210#213—332no—
211(C2×D3)⋊C4—64no—
212(C2×D3)⋊C4—64no—
213C4⋊Dic3—34no—
214C4⋊Dic3—34no—
215Dic3⋊C4—64no—
216Dic3⋊C4—64no—
217C4×Dic3—64no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220#208—316no—
221#208—68no—
222C2×C3⋊C8—38no—
223C2×C3⋊C8—38no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32—24no—
227C22×C32—48no—
228C22×C32—42no—
229C22×C32—42no—
230C22×C32C4×D412yes—
231C22×C32C22×D411yescharacteristic
232C2×C3⋊D3—22no—
233C2×C3⋊D3—41no—
234C2×C3⋊D3—41no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4—21no—
238C32×C4—42no—
239C32×C4C4×D412yes—
240C32×C4AGL(1,ℤ/8)12yescomplemented
241C32×C4C23×C411yescharacteristic
242C32×C4C2×#4111yescharacteristic
243C3⋊Dic3—22no—
244C3⋊Dic3—41no—
245C3⋊Dic3—41no—
246C2×#41—91no—
247C22×D4C2×C3⋊D311yescharacteristic
248C23×C4—21no—
249AGL(1,ℤ/8)—98no—
250C2×SD16—92no—
251C2×D8—92no—
252C2×M16—91no—
253C2×M16—91no—
254C4×Q8—91no—
255C4×Q8—91no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—91no—
259C4×D4—91no—
260C4×D4—181no—
261C4×D4—181no—
262C4×D4C2×C3⋊D312yes—
263C4×D4C2×C3⋊D312yes—
264#117—91no—
265#117—181no—
266C2×C4⋊C4C2×C3⋊D311yescharacteristic
267C2×C22⋊C4—21no—
268C2×C42—181no—
269C2×C42C2×C3⋊D311yescharacteristic
270#107—92no—
271#106—92no—
272#103—92no—
273#102—92no—
274#102—92no—
275#102—92no—
276#97—92no—
277C4×C8—92no—
278C23×C3—216no—
279C23×C3—28no—
280C23×C3—48no—
281C23×C3—48no—
282C23×C3C2×#6714yes—
283C22×D3—64no—
284C3×D4—216no—
285C3×D4—28no—
286C3×D4C2×C4×D3116yes—
287C2×C3×C4—28no—
288C2×C3×C4—28no—
289C2×C3×C4—44no—
290C2×C3×C4—416no—
291C2×C3×C4—48no—
292C2×C3×C4—416no—
293C2×C3×C4C2×C4×D318yes—
294C2×C3×C4#23518yes—
295C2×C3×C4C2×#6714yes—
296C2×C3×C4C2×#6714yes—
297C2×C3×C4C2×#6714yes—
298C2×C3×C4C2×#6714yes—
299C2×C3×C4C2×#6714yes—
300C2×C3×C4C23×D314yes—
301#67—616no—
302C2×Dic3—64no—
303C2×Dic3—64no—
304C2×Dic3—64no—
305D12—38no—
306D12—64no—
307C4×D3—616no—
308C4×D3—128no—
309C4×D3—128no—
310Dic6—38no—
311Dic6—64no—
312C3⋊C8—316no—
313C3⋊C8—68no—
314C2×C32—22no—
315C2×C32—44no—
316C2×C32C2×C4×D411yescharacteristic
317C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
318C2×C32#57511yescharacteristic
319C3⋊D3—42no—
320C24—21no—
321#41—94no—
322#41—182no—
323C2×Q8—91no—
324C2×D4—22no—
325C2×D4—21no—
326C2×D4—91no—
327C2×D4—181no—
328C2×D4C4×C3⋊D314yescomplemented
329C2×D4C22×C3⋊D312yes—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—44no—
334C22×C4—181no—
335C22×C4—181no—
336C22×C4—181no—
337C22×C4#63811yescharacteristic
338C22×C4#63811yescharacteristic
339C22×C4C22×C3⋊D311yescharacteristic
340SD16—98no—
341D8—98no—
342M16—94no—
343M16—182no—
344C2×C8—92no—
345C2×C8—92no—
346C4⋊C4—21no—
347C4⋊C4—91no—
348C4⋊C4—91no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4C22×C3⋊D312yes—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—181no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C42—181no—
358C42—181no—
359C42—181no—
360C42#63811yescharacteristic
361C42#63811yescharacteristic
362C42C22×C3⋊D311yescharacteristic
363C42C22×C3⋊D311yescharacteristic
364C22×C3—24no—
365C22×C3—24no—
366C22×C3—216no—
367C22×C3—432no—
368C22×C3—48no—
369C22×C3—48no—
370C22×C3C4×#6718yes—
371C22×C3C22×#6714yes—
372C2×D3—68no—
373C2×D3—124no—
374C2×D3—124no—
375C3×C4—24no—
376C3×C4—24no—
377C3×C4—24no—
378C3×C4—48no—
379C3×C4C4×#6718yes—
380C3×C4#93218yescomplemented
381C3×C4C22×C4×D314yes—
382C3×C4C2×#23514yes—
383Dic3—68no—
384Dic3—124no—
385Dic3—124no—
386C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
387C23—22no—
388C23—24no—
389C23—42no—
390C23—42no—
391C23—181no—
392C23C2×#63811yescharacteristic
393Q8—92no—
394Q8—181no—
395D4—22no—
396D4—24no—
397D4—92no—
398D4—184no—
399D4—181no—
400D4C2×C4×C3⋊D314yes—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—44no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—181no—
408C2×C4—184no—
409C2×C4—181no—
410C2×C4—181no—
411C2×C4—362no—
412C2×C4—362no—
413C2×C4C2×C4×C3⋊D312yes—
414C2×C4#382812yes—
415C2×C4C2×#63811yescharacteristic
416C2×C4C2×#63811yescharacteristic
417C2×C4C2×#63811yescharacteristic
418C2×C4C2×#63811yescharacteristic
419C2×C4C2×#63811yescharacteristic
420C2×C4C23×C3⋊D311yescharacteristic
421C8—94no—
422C8—182no—
423C2×C3—28no—
424C2×C3—416no—
425C2×C3C2×C4×#6714yes—
426C2×C3C2×#93214yes—
427C2×C3#582214yes—
428D3—128no—
429C22—21no—
430C22—21no—
431C22—24no—
432C22—48no—
433C22—42no—
434C22—42no—
435C22—182no—
436C22—361no—
437C22—361no—
438C22C4×#63812yes—
439C22C22×#63811yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—42no—
444C4—182no—
445C4—361no—
446C4—361no—
447C4C4×#63812yes—
448C4#6414112yesdirect product factor
449C4C22×C4×C3⋊D311yescharacteristic
450C4C2×#382811yescharacteristic
451C3C4×#93214yescomplemented
452C2—22no—
453C2—44no—
454C2—362no—
455C2C2×C4×#63811yescharacteristic
456C2C2×#6414111yescharacteristic
457C2#1059629311yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C4×D4C2
socleC22×C32C22×D4
prime radicalC2×#64141C2
cosocleC2×C32×C4C24
hypercenterC2×C4×D4C3⋊D3
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C4×#3828C2semidirect
4. #10592914C2semidirect
5. #10592717C2semidirect
6. C4×#3754C2semidirect
7. #10592713C2semidirect
8. C4×#3753C2semidirect
9. #10592665C2semidirect
10. #10592663C2semidirect
11. C4×#3748C2semidirect
24. #64141C4direct (N × H)
31. C4×C4⋊(C3⋊D3)C22semidirect
32. C4×C4⋊(C3⋊D3)C22semidirect
35. C4×#634C22semidirect
36. C4×#634C22semidirect
39. #63637C22semidirect
40. #63636C22semidirect
41. #63635C22semidirect
42. #63634C22semidirect
43. #63630C22semidirect
44. C4×C3⋊(C3⋊C8)C22semidirect
45. C2×C3×C4×D4D3semidirect
59. C2×C32×D4C2×C4semidirect
70. #3828C2×C4semidirect
85. #3754C2×C4semidirect
86. #3753C2×C4semidirect
97. #3748C2×C4semidirect
161. C4⋊(C3⋊D3)C22×C4semidirect
166. #634C22×C4semidirect
168. C3⋊(C3⋊C8)C22×C4semidirect
171. C2×C4×D4C3⋊D3semidirect
183. C2×C3×D4C4×D3semidirect
240. C32×C4AGL(1,ℤ/8)semidirect
328. C2×D4C4×C3⋊D3semidirect
380. C3×C4#932semidirect
386. C32C4×AGL(1,ℤ/8)semidirect
448. C4#64141direct (N × H)
451. C3C4×#932semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×#641412
C4×#38282
#105929142
#105927172
C4×#37542
#105927132
C4×#37532
#105926652
#105926632
C4×#37482
C4×#9323