Finite Group Databasebeta

← C4×#64117 #11860276

Subgroups — C4×#64117 #11860276

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×#64117C211yesmaximal, characteristic
2C4×#3828C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C32×C4×M16C211yesmaximal, characteristic, complemented
5#10592832C211yesmaximal, characteristic, complemented
6#10592830C211yesmaximal, characteristic, complemented
7#10592820C211yesmaximal, characteristic, complemented
8#10592410C212yesmaximal, complemented
9#10592409C212yesmaximal, complemented
10C4×#3745C212yesmaximal, complemented
11C4×#3744C212yesmaximal, complemented
12C4×#908—34nomaximal
13C2×#3828C2211yescharacteristic
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C2×C32×M16C2211yescharacteristic
17C2×C32×M16C2211yescharacteristic
18C2×C32×C42C2211yescharacteristic
19C4×#638—21no—
20C4×#638—21no—
21C2×#3752—21no—
22#64135C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24#64117C418yesdirect product factor
25C2×#3745C2212yes—
26C2×#3744C2212yes—
27C4×C4⋊(C3⋊D3)—21no—
28C4×C4⋊(C3⋊D3)—21no—
29C4×C4⋊(C3⋊D3)C2212yes—
30C4×C4⋊(C3⋊D3)C2212yes—
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
37C32×#97C2212yescomplemented
38C32×C4×C8C2212yescomplemented
39#63648C2212yes—
40#63648C2212yes—
41#63648C2212yescomplemented
42#63645C2212yescomplemented
43#63644C2212yescomplemented
44#63643C2212yescomplemented
45C2×#908—34no—
46C4×#235—34no—
47C2×C4×D12—34no—
48C3×C4×M16D314yescomplemented
49#5133—34no—
50#5131—34no—
51#5121—34no—
52#4711—38no—
53#4710—38no—
54C4×D24—38no—
55C4×#204—38no—
56C23×C3⋊D3—21no—
57C22×C32×C4D411yescharacteristic
58C22×C32×C4D411yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C2×#638—21no—
61C22×C3⋊Dic3—21no—
62#3828—22no—
63#3828C2×C414yescomplemented
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—22no—
66C2×C4⋊(C3⋊D3)C2×C414yescomplemented
67C2×C4⋊(C3⋊D3)C2312yes—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—21no—
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—44no—
75C2×#634C2311yescharacteristic
76C32×M16—22no—
77C32×M16C2×C414yescomplemented
78C2×C32×C8C2312yes—
79C2×C32×C8C2312yes—
80C32×C42D411yescharacteristic
81C32×C42D411yescharacteristic
82C32×C42C2311yescharacteristic
83C32×C42C2311yescharacteristic
84#3757—21no—
85#3752—21no—
86#3752—21no—
87#3752—22no—
88#3752—22no—
89C4⋊(C3⋊Dic3)—21no—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92C4⋊(C3⋊Dic3)C2312yes—
93#3750—21no—
94#3750—21no—
95C4×C3⋊Dic3—21no—
96C4×C3⋊Dic3—21no—
97C4×C3⋊Dic3—21no—
98#3745C2×C418yescomplemented
99#3744C2×C418yescomplemented
100C4×AGL(1,ℤ/8)—91noSylow
101C2×#235—34no—
102C22×D12—34no—
103C22×C4×D3—64no—
104C2×C3×M16C2×D314yes—
105C2×C3×M16C2×D314yes—
106C2×C3×C42C2×D314yes—
107C4×#67—64no—
108C4×#67—64no—
109C2×(C2×D3)⋊C4—64no—
110#926—34no—
111C2×C4⋊Dic3—34no—
112#908—332no—
113C2×D24—38no—
114C2×#204—38no—
115C4×D12—38no—
116C4×D12—38no—
117C4×D12—34no—
118C4×D12—34no—
119C4×D12—64no—
120C4×D12—64no—
121#872—64no—
122C42×D3—64no—
123C4×Dic6—34no—
124C4×Dic6—34no—
125C3×#97C2×D318yescomplemented
126C3×C4×C8C2×D318yescomplemented
127#821—38no—
128#821—38no—
129#821—38no—
130#818—38no—
131#817—38no—
132#816—38no—
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—24no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C2×C32×C4—22no—
140C2×C32×C4—41no—
141C2×C32×C4C22×C412yes—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149#638—24no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—42no—
155C4⋊(C3⋊D3)—24no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)—21no—
158C4⋊(C3⋊D3)C22×C414yes—
159C4⋊(C3⋊D3)C22×C412yescomplemented
160C4×C3⋊D3—24no—
161C4×C3⋊D3—42no—
162C4×C3⋊D3—44no—
163C4×C3⋊D3—42no—
164C4×C3⋊D3—44no—
165#634—21no—
166#634C22×C412yescomplemented
167C32×C8—22no—
168C32×C8C22×C414yescomplemented
169C2×AGL(1,ℤ/8)—91no—
170C4×#41—91no—
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×M16C3⋊D311yescharacteristic, complemented
180C23×D3—64no—
181C22×C3×C4D1214yes—
182C22×C3×C4D1214yes—
183C22×C3×C4C22×D314yes—
184C2×#67—64no—
185C22×Dic3—64no—
186#235—316no—
187#235—68no—
188C2×D12—316no—
189C2×D12—38no—
190C2×D12—34no—
191C2×D12—64no—
192C2×D12—68no—
193C2×C4×D3—64no—
194C2×C4×D3—64no—
195C2×C4×D3—64no—
196C2×C4×D3—68no—
197C2×C4×D3—68no—
198C2×C4×D3—1216no—
199C2×Dic6—34no—
200C3×M16—28no—
201C3×M16C4×D3116yescomplemented
202C2×C3×C8C22×D318yes—
203C2×C3×C8C22×D318yes—
204C3×C42D1214yes—
205C3×C42D1214yes—
206C3×C42C22×D314yes—
207C3×C42C22×D314yes—
208#217—64no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—64no—
211(C2×D3)⋊C4—68no—
212(C2×D3)⋊C4—68no—
213C4⋊Dic3—38no—
214C4⋊Dic3—34no—
215C4⋊Dic3—34no—
216C4⋊Dic3—64no—
217Dic3⋊C4—64no—
218Dic3⋊C4—64no—
219C4×Dic3—64no—
220C4×Dic3—64no—
221C4×Dic3—64no—
222D24—332no—
223#204—332no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32C4×D412yes—
227C22×C32C22×D411yescharacteristic
228C2×C3⋊D3—22no—
229C2×C3⋊D3—24no—
230C2×C3⋊D3—48no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—41no—
233C2×C3⋊D3—41no—
234C2×C3⋊D3—42no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4—21no—
238C32×C4C4×D412yes—
239C32×C4AGL(1,ℤ/8)12yescomplemented
240C32×C4C23×C411yescharacteristic
241C32×C4C2×#4111yescharacteristic
242C3⋊Dic3—22no—
243C3⋊Dic3—42no—
244C3⋊Dic3—41no—
245C3⋊Dic3—41no—
246C2×#41—91no—
247C22×D4—91no—
248C23×C4—181no—
249AGL(1,ℤ/8)—98no—
250C2×SD16—92no—
251C2×D8—92no—
252C2×M16C2×C3⋊D311yescharacteristic
253C2×M16C2×C3⋊D311yescharacteristic
254C4×Q8—91no—
255C4×Q8—91no—
256C4×D4—92no—
257C4×D4—92no—
258C4×D4—91no—
259C4×D4—91no—
260C4×D4—181no—
261C4×D4—181no—
262C4×D4—181no—
263C4×D4—181no—
264#117—91no—
265#117—181no—
266C2×C4⋊C4—91no—
267C2×C22⋊C4—181no—
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#97C2×C3⋊D312yescomplemented
277C4×C8C2×C3⋊D312yescomplemented
278C23×C3C2×D1214yes—
279C22×D3—616no—
280C22×D3—64no—
281C22×D3—68no—
282C22×D3—128no—
283C22×D3—128no—
284C2×C3×C4—28no—
285C2×C3×C4—44no—
286C2×C3×C4C2×C4×D318yes—
287C2×C3×C4C2×D1214yes—
288C2×C3×C4C2×D1214yes—
289C2×C3×C4C2×D1214yes—
290C2×C3×C4C2×D1214yes—
291C2×C3×C4C2×D1214yes—
292C2×C3×C4#23518yes—
293C2×C3×C4C23×D314yes—
294#67—616no—
295C2×Dic3—64no—
296C2×Dic3—64no—
297C2×Dic3—64no—
298C2×Dic3—68no—
299C2×Dic3—128no—
300D12—316no—
301D12—38no—
302D12—616no—
303D12—68no—
304D12—64no—
305C4×D3—616no—
306C4×D3—128no—
307C4×D3—1216no—
308C4×D3—128no—
309C4×D3—1216no—
310Dic6—38no—
311Dic6—64no—
312C3×C8—28no—
313C3×C8C2×C4×D3116yescomplemented
314C2×C32—22no—
315C2×C32C2×C4×D411yescharacteristic
316C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
317C2×C32#57511yescharacteristic
318C3⋊D3—42no—
319C3⋊D3—44no—
320C24—181no—
321#41—94no—
322#41—182no—
323C2×Q8—91no—
324C2×D4—91no—
325C2×D4—92no—
326C2×D4—94no—
327C2×D4—181no—
328C2×D4—181no—
329C2×D4—182no—
330C22×C4—181no—
331C22×C4—181no—
332C22×C4—181no—
333C22×C4—182no—
334C22×C4—181no—
335C22×C4—182no—
336C22×C4—364no—
337C22×C4C4⋊(C3⋊D3)11yescharacteristic
338C22×C4C4⋊(C3⋊D3)11yescharacteristic
339C22×C4C22×C3⋊D311yescharacteristic
340SD16—98no—
341D8—98no—
342M16—22no—
343M16C4×C3⋊D314yescomplemented
344C2×C8C22×C3⋊D312yes—
345C2×C8C22×C3⋊D312yes—
346C4⋊C4—91no—
347C4⋊C4—91no—
348C4⋊C4—92no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C22⋊C4—181no—
353C22⋊C4—182no—
354C22⋊C4—182no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C42—181no—
358C42—181no—
359C42—181no—
360C42C4⋊(C3⋊D3)11yescharacteristic
361C42C4⋊(C3⋊D3)11yescharacteristic
362C42C22×C3⋊D311yescharacteristic
363C42C22×C3⋊D311yescharacteristic
364C22×C3—24no—
365C22×C3—24no—
366C22×C3C4×D1218yes—
367C22×C3C22×D1214yes—
368C2×D3—68no—
369C2×D3—616no—
370C2×D3—1232no—
371C2×D3—128no—
372C2×D3—124no—
373C2×D3—124no—
374C2×D3—128no—
375C3×C4—24no—
376C3×C4—24no—
377C3×C4—24no—
378C3×C4C4×D1218yes—
379C3×C4#90818yescomplemented
380C3×C4C22×C4×D314yes—
381C3×C4C2×#23514yes—
382Dic3—68no—
383Dic3—128no—
384Dic3—124no—
385Dic3—124no—
386C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
387C23—184no—
388C23—181no—
389C23—182no—
390C23—362no—
391C23—362no—
392C23C2×C4⋊(C3⋊D3)11yescharacteristic
393Q8—92no—
394Q8—181no—
395D4—92no—
396D4—94no—
397D4—184no—
398D4—184no—
399D4—182no—
400D4—181no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—181no—
404C2×C4—184no—
405C2×C4—181no—
406C2×C4—181no—
407C2×C4—182no—
408C2×C4—364no—
409C2×C4—362no—
410C2×C4—362no—
411C2×C4—364no—
412C2×C4—362no—
413C2×C4C2×C4×C3⋊D312yes—
414C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
415C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
416C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
417C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
418C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
419C2×C4#382812yes—
420C2×C4C23×C3⋊D311yescharacteristic
421C8—22no—
422C8C2×C4×C3⋊D314yescomplemented
423C2×C3—28no—
424C2×C3C2×C4×D1214yes—
425C2×C3C2×#90814yes—
426C2×C3#574814yes—
427D3—1216no—
428D3—128no—
429C22—21no—
430C22—21no—
431C22—182no—
432C22—184no—
433C22—368no—
434C22—362no—
435C22—361no—
436C22—361no—
437C22—362no—
438C22C4×C4⋊(C3⋊D3)12yes—
439C22C22×C4⋊(C3⋊D3)11yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—182no—
444C4—362no—
445C4—361no—
446C4—361no—
447C4C4×C4⋊(C3⋊D3)12yes—
448C4#6411712yesdirect product factor
449C4C22×C4×C3⋊D311yescharacteristic
450C4C2×#382811yescharacteristic
451C3C4×#90814yescomplemented
452C2—22no—
453C2—364no—
454C2—362no—
455C2C2×C4×C4⋊(C3⋊D3)11yescharacteristic
456C2C2×#6411711yescharacteristic
457C2#1059621911yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊(C3⋊D3)
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×M16C2
socleC22×C32C22×D4
prime radicalC2×#64117C2
cosocleC2×C32×C4C24
hypercenterC4×M16C3⋊D3
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. C4×#3828C2semidirect
3. C2×C4×C4⋊(C3⋊D3)C2semidirect
4. C32×C4×M16C2semidirect
5. #10592832C2semidirect
6. #10592830C2semidirect
7. #10592820C2semidirect
8. #10592410C2semidirect
9. #10592409C2semidirect
10. C4×#3745C2semidirect
11. C4×#3744C2semidirect
24. #64117C4direct (N × H)
31. C4×C4⋊(C3⋊D3)C22semidirect
32. C4×C4⋊(C3⋊D3)C22semidirect
35. C4×#634C22semidirect
36. C4×#634C22semidirect
37. C32×#97C22semidirect
38. C32×C4×C8C22semidirect
41. #63648C22semidirect
42. #63645C22semidirect
43. #63644C22semidirect
44. #63643C22semidirect
48. C3×C4×M16D3semidirect
63. #3828C2×C4semidirect
66. C2×C4⋊(C3⋊D3)C2×C4semidirect
77. C32×M16C2×C4semidirect
98. #3745C2×C4semidirect
99. #3744C2×C4semidirect
125. C3×#97C2×D3semidirect
126. C3×C4×C8C2×D3semidirect
159. C4⋊(C3⋊D3)C22×C4semidirect
166. #634C22×C4semidirect
168. C32×C8C22×C4semidirect
179. C4×M16C3⋊D3semidirect
201. C3×M16C4×D3semidirect
239. C32×C4AGL(1,ℤ/8)semidirect
276. #97C2×C3⋊D3semidirect
277. C4×C8C2×C3⋊D3semidirect
313. C3×C8C2×C4×D3semidirect
343. M16C4×C3⋊D3semidirect
379. C3×C4#908semidirect
386. C32C4×AGL(1,ℤ/8)semidirect
422. C8C2×C4×C3⋊D3semidirect
448. C4#64117direct (N × H)
451. C3C4×#908semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
C4×#38282
C2×C4×C4⋊(C3⋊D3)2
C32×C4×M162
#105928322
#105928302
#105928202
#105924102
#105924092
C4×#37452
C4×#37442
C4×#9083