Finite Group Databasebeta

← C4×#64158 #11860258

Subgroups — C4×#64158 #11860258

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
1C32×C4×#41C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic
3C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4#10592931C211yesmaximal, characteristic, complemented
5#10592725C212yesmaximal, complemented
6C4×#3755C212yesmaximal, complemented
7#10592713C212yesmaximal, complemented
8C4×#3753C212yesmaximal, complemented
9#10592700C211yesmaximal, characteristic, complemented
10#10592694C211yesmaximal, characteristic, complemented
11C4×#3748C211yesmaximal, characteristic, complemented
12C4×#949—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C32×C4×Q8C2211yescharacteristic, complemented
17C32×C4×Q8C2211yescharacteristic, complemented
18C32×C4×D4—21no—
19C32×C4×D4—21no—
20C32×C4×D4C2211yescharacteristic, complemented
21C32×C4×D4C2211yescharacteristic, complemented
22C32×#117—21no—
23C32×#117C2211yescharacteristic
24C2×C32×C42—21no—
25C2×C32×C42C2211yescharacteristic
26#64158C418yesdirect product factor
27C2×#3755C2212yes—
28C2×#3753C2212yes—
29C2×#3752—21no—
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×#3748C2211yescharacteristic
32C2×#3748C2211yescharacteristic
33C4×C4⋊(C3⋊D3)—21no—
34C4×C4⋊(C3⋊D3)—21no—
35C4×C4⋊(C3⋊D3)C2212yes—
36C4×C4⋊(C3⋊D3)C2212yes—
37#63662C2212yescomplemented
38#63659C2212yescomplemented
39#63636C2212yes—
40#63636C2212yes—
41#63635C2212yescomplemented
42#63634C2212yescomplemented
43#63630C2212yescomplemented
44C4×C3⋊(C3⋊C8)C2212yescomplemented
45C3×C4×#41D314yescomplemented
46C2×#949—34no—
47C2×C4×D12—34no—
48#5232—34no—
49#5026—38no—
50C4×#215—38no—
51#5014—38no—
52C4×#213—38no—
53#5001—34no—
54#4995—34no—
55C4×#208—34no—
56C23×C3⋊D3—21no—
57C32×#41—22no—
58C32×#41C2×C414yescomplemented
59C2×C32×Q8C2311yescharacteristic
60C2×C32×D4—21no—
61C2×C32×D4C2311yescharacteristic
62C22×C32×C4—21no—
63C22×C32×C4—21no—
64C22×C32×C4—21no—
65C22×C32×C4D411yescharacteristic
66C22×C32×C4D411yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)C2×C414yescomplemented
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—44no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C4⋊C4C2311yescharacteristic
80C32×C22⋊C4—21no—
81C32×C22⋊C4—21no—
82C32×C22⋊C4—21no—
83C32×C42—21no—
84C32×C42—21no—
85C32×C42—21no—
86C32×C42D411yescharacteristic
87C32×C42D411yescharacteristic
88C32×C42C2311yescharacteristic
89C32×C42C2311yescharacteristic
90#3755C2×C418yescomplemented
91#3753C2×C418yescomplemented
92#3752—22no—
93#3752—22no—
94C4⋊(C3⋊Dic3)—21no—
95C4⋊(C3⋊Dic3)C2312yes—
96#3748—22no—
97#3748C2×C414yescomplemented
98C2×C3⋊(C3⋊C8)C2312yes—
99C2×C3⋊(C3⋊C8)C2312yes—
100C4×AGL(1,ℤ/8)—91noSylow
101C2×C3×#41C2×D314yes—
102C22×D12—34no—
103C22×C4×D3—64no—
104C3×C4×Q8C2×D314yescomplemented
105C3×C4×Q8C2×D314yescomplemented
106C3×C4×D4—24no—
107C3×C4×D4—24no—
108C3×C4×D4C2×D314yescomplemented
109C3×C4×D4C2×D314yescomplemented
110C3×#117—24no—
111C3×#117C2×D314yes—
112C2×C3×C42—24no—
113C2×C3×C42C2×D314yes—
114#949—332no—
115C2×#215—38no—
116C2×#213—38no—
117C2×(C2×D3)⋊C4—64no—
118C2×C4⋊Dic3—34no—
119C2×#208—34no—
120C2×#208—34no—
121C4×D12—38no—
122C4×D12—38no—
123C4×D12—64no—
124C4×D12—64no—
125#835—38no—
126#832—38no—
127#809—38no—
128#809—38no—
129#808—38no—
130#807—38no—
131#803—38no—
132C4×C3⋊C8—38no—
133C23×C32—21no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—24no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C32×Q8—21no—
140C32×Q8C22×C412yescomplemented
141C32×D4—24no—
142C32×D4—21no—
143C32×D4C22×C412yescomplemented
144C2×C32×C4—21no—
145C2×C32×C4—24no—
146C2×C32×C4—22no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—41no—
150C2×C32×C4—42no—
151C2×C32×C4—42no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4#4112yes—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—42no—
162C4⋊(C3⋊D3)—24no—
163C4⋊(C3⋊D3)—22no—
164C4⋊(C3⋊D3)C22×C414yes—
165C4×C3⋊D3—44no—
166C4×C3⋊D3—44no—
167C3⋊(C3⋊C8)—22no—
168C3⋊(C3⋊C8)C22×C414yescomplemented
169C2×AGL(1,ℤ/8)—91no—
170C4×#41C3⋊D311yescharacteristic, complemented
171C2×C4×D4—91no—
172#442—92no—
173#440—92no—
174C4×SD16—92no—
175C4×D8—92no—
176#428—91no—
177#418—91no—
178#417—91no—
179C4×M16—91no—
180C23×D3—64no—
181C3×#41—28no—
182C3×#41C4×D3116yescomplemented
183C2×C3×Q8C22×D314yes—
184C2×C3×D4—24no—
185C2×C3×D4C22×D314yes—
186C22×C3×C4—24no—
187C22×C3×C4—24no—
188C22×C3×C4—24no—
189C22×C3×C4#6714yes—
190C22×C3×C4#6714yes—
191C22×C3×C4C22×D314yes—
192C22×Dic3—64no—
193C2×D12—316no—
194C2×D12—38no—
195C2×D12—68no—
196C2×D12—64no—
197C2×C4×D3—68no—
198C2×C4×D3—68no—
199C2×C4×D3—1216no—
200C3×C4⋊C4—24no—
201C3×C4⋊C4—24no—
202C3×C4⋊C4C22×D314yes—
203C3×C4⋊C4C22×D314yes—
204C3×C22⋊C4—24no—
205C3×C22⋊C4—24no—
206C3×C22⋊C4—24no—
207C3×C42—24no—
208C3×C42—24no—
209C3×C42—24no—
210C3×C42#6714yes—
211C3×C42#6714yes—
212C3×C42C22×D314yes—
213C3×C42C22×D314yes—
214#215—332no—
215#213—332no—
216(C2×D3)⋊C4—68no—
217(C2×D3)⋊C4—68no—
218C4⋊Dic3—38no—
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—22no—
227C22×C32—41no—
228C22×C32—41no—
229C22×C32C4×D412yes—
230C22×C32C22×D411yescharacteristic
231C2×C3⋊D3—24no—
232C2×C3⋊D3—48no—
233C2×C3⋊D3—42no—
234C2×C3⋊D3—42no—
235C32×C4—22no—
236C32×C4—21no—
237C32×C4—21no—
238C32×C4—21no—
239C32×C4—41no—
240C32×C4—41no—
241C32×C4C4×D412yes—
242C32×C4AGL(1,ℤ/8)12yescomplemented
243C32×C4C23×C411yescharacteristic
244C32×C4C2×#4111yescharacteristic
245C3⋊Dic3—42no—
246C2×#41C2×C3⋊D311yescharacteristic
247C22×D4—91no—
248C23×C4—181no—
249AGL(1,ℤ/8)—98no—
250C2×SD16—92no—
251C2×D8—92no—
252C2×M16—91no—
253C2×M16—91no—
254C4×Q8C2×C3⋊D311yescharacteristic, complemented
255C4×Q8C2×C3⋊D311yescharacteristic, complemented
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—92no—
259C4×D4—92no—
260C4×D4—181no—
261C4×D4—181no—
262C4×D4C2×C3⋊D311yescharacteristic, complemented
263C4×D4C2×C3⋊D311yescharacteristic, complemented
264#117—21no—
265#117C2×C3⋊D311yescharacteristic
266C2×C4⋊C4—91no—
267C2×C22⋊C4—181no—
268C2×C42—21no—
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—24no—
279C23×C3C2×#6714yes—
280C22×D3—616no—
281C22×D3—68no—
282C22×D3—128no—
283C22×D3—128no—
284C3×Q8—24no—
285C3×Q8C2×C4×D318yescomplemented
286C3×D4—216no—
287C3×D4—24no—
288C3×D4C2×C4×D318yescomplemented
289C2×C3×C4—24no—
290C2×C3×C4—216no—
291C2×C3×C4—28no—
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—44no—
295C2×C3×C4—48no—
296C2×C3×C4—48no—
297C2×C3×C4C2×C4×D318yes—
298C2×C3×C4#23518yes—
299C2×C3×C4C2×#6714yes—
300C2×C3×C4C2×#6714yes—
301C2×C3×C4C2×#6714yes—
302C2×C3×C4C2×#6714yes—
303C2×C3×C4C2×#6714yes—
304C2×C3×C4C23×D314yes—
305C2×Dic3—68no—
306C2×Dic3—128no—
307D12—316no—
308D12—616no—
309D12—68no—
310C4×D3—1216no—
311C4×D3—1216no—
312C3⋊C8—316no—
313C3⋊C8—68no—
314C2×C32—22no—
315C2×C32—42no—
316C2×C32C2×C4×D411yescharacteristic
317C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
318C2×C32#57511yescharacteristic
319C3⋊D3—44no—
320C24—181no—
321#41—22no—
322#41C4×C3⋊D314yescomplemented
323C2×Q8C22×C3⋊D311yescharacteristic
324C2×D4—21no—
325C2×D4—92no—
326C2×D4—94no—
327C2×D4—182no—
328C2×D4—181no—
329C2×D4C22×C3⋊D311yescharacteristic
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—181no—
334C22×C4—182no—
335C22×C4—182no—
336C22×C4—364no—
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—21no—
348C4⋊C4—92no—
349C4⋊C4—181no—
350C4⋊C4C22×C3⋊D311yescharacteristic
351C4⋊C4C22×C3⋊D311yescharacteristic
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—182no—
356C22⋊C4—182no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42#63811yescharacteristic
361C42#63811yescharacteristic
362C42C22×C3⋊D311yescharacteristic
363C42C22×C3⋊D311yescharacteristic
364C22×C3—24no—
365C22×C3—24no—
366C22×C3—28no—
367C22×C3—44no—
368C22×C3—44no—
369C22×C3C4×#6718yes—
370C22×C3C22×#6714yes—
371C2×D3—616no—
372C2×D3—1232no—
373C2×D3—128no—
374C2×D3—128no—
375C3×C4—28no—
376C3×C4—24no—
377C3×C4—24no—
378C3×C4—24no—
379C3×C4—44no—
380C3×C4—44no—
381C3×C4C4×#6718yes—
382C3×C4#94918yescomplemented
383C3×C4C22×C4×D314yes—
384C3×C4C2×#23514yes—
385Dic3—128no—
386C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
387C23—21no—
388C23—182no—
389C23—184no—
390C23—362no—
391C23—362no—
392C23C2×#63811yescharacteristic
393Q8—21no—
394Q8C2×C4×C3⋊D312yescomplemented
395D4—24no—
396D4—21no—
397D4—94no—
398D4—182no—
399D4—184no—
400D4C2×C4×C3⋊D312yescomplemented
401C2×C4—21no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—182no—
410C2×C4—364no—
411C2×C4—362no—
412C2×C4—364no—
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—48no—
425C2×C3C2×C4×#6714yes—
426C2×C3C2×#94914yes—
427C2×C3#582214yes—
428D3—1216no—
429C22—21no—
430C22—21no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—184no—
435C22—368no—
436C22—362no—
437C22—362no—
438C22C4×#63812yes—
439C22C22×#63811yescharacteristic
440C4—22no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—41no—
445C4—41no—
446C4—362no—
447C4C4×#63812yes—
448C4#6415812yesdirect product factor
449C4C22×C4×C3⋊D311yescharacteristic
450C4C2×#382811yescharacteristic
451C3C4×#94914yescomplemented
452C2—22no—
453C2—42no—
454C2—364no—
455C2C2×C4×#63811yescharacteristic
456C2C2×#6415811yescharacteristic
457C2#1059629311yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×#41C2
socleC22×C32C22×D4
prime radicalC2×#64158C2
cosocleC2×C32×C4C24
hypercenterC4×#41C3⋊D3
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C32×C4×#41C2semidirect
3. C2×C4×C4⋊(C3⋊D3)C2semidirect
4. #10592931C2semidirect
5. #10592725C2semidirect
6. C4×#3755C2semidirect
7. #10592713C2semidirect
8. C4×#3753C2semidirect
9. #10592700C2semidirect
10. #10592694C2semidirect
11. C4×#3748C2semidirect
16. C32×C4×Q8C22semidirect
17. C32×C4×Q8C22semidirect
20. C32×C4×D4C22semidirect
21. C32×C4×D4C22semidirect
26. #64158C4direct (N × H)
37. #63662C22semidirect
38. #63659C22semidirect
41. #63635C22semidirect
42. #63634C22semidirect
43. #63630C22semidirect
44. C4×C3⋊(C3⋊C8)C22semidirect
45. C3×C4×#41D3semidirect
58. C32×#41C2×C4semidirect
71. C2×C4⋊(C3⋊D3)C2×C4semidirect
90. #3755C2×C4semidirect
91. #3753C2×C4semidirect
97. #3748C2×C4semidirect
104. C3×C4×Q8C2×D3semidirect
105. C3×C4×Q8C2×D3semidirect
108. C3×C4×D4C2×D3semidirect
109. C3×C4×D4C2×D3semidirect
140. C32×Q8C22×C4semidirect
143. C32×D4C22×C4semidirect
168. C3⋊(C3⋊C8)C22×C4semidirect
170. C4×#41C3⋊D3semidirect
182. C3×#41C4×D3semidirect
242. C32×C4AGL(1,ℤ/8)semidirect
254. C4×Q8C2×C3⋊D3semidirect
255. C4×Q8C2×C3⋊D3semidirect
262. C4×D4C2×C3⋊D3semidirect
263. C4×D4C2×C3⋊D3semidirect
285. C3×Q8C2×C4×D3semidirect
288. C3×D4C2×C4×D3semidirect
322. #41C4×C3⋊D3semidirect
382. C3×C4#949semidirect
386. C32C4×AGL(1,ℤ/8)semidirect
394. Q8C2×C4×C3⋊D3semidirect
400. D4C2×C4×C3⋊D3semidirect
448. C4#64158direct (N × H)
451. C3C4×#949semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C2×#641582
C2×C4×C4⋊(C3⋊D3)2
#105929312
#105927252
C4×#37552
#105927132
C4×#37532
#105927002
#105926942
C4×#37482
C4×#9493