Finite Group Databasebeta

← AGL(1,ℤ/8)×C3⋊Dic3 #11860270

Subgroups — AGL(1,ℤ/8)×C3⋊Dic3 #11860270

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×AGL(1,ℤ/8)C211yesmaximal, characteristic
2#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#10592931C211yesmaximal, characteristic, complemented
5#10592914C211yesmaximal, characteristic, complemented
6#10592863C212yesmaximal, complemented
7SD16×C3⋊Dic3C212yesmaximal, complemented
8#10592851C212yesmaximal, complemented
9D8×C3⋊Dic3C212yesmaximal, complemented
10#10592820C211yesmaximal, characteristic, complemented
11M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
12Dic3×AGL(1,ℤ/8)—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3—21no—
16C32×AGL(1,ℤ/8)C418yescomplemented
17C2×C32×SD16C2212yes—
18C2×C32×D8C2212yes—
19C2×C32×M16C2211yescharacteristic
20C2×#3757—21no—
21Q8×C3⋊Dic3C2211yescharacteristic, complemented
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23D4×C3⋊Dic3—21no—
24D4×C3⋊Dic3—21no—
25D4×C3⋊Dic3—21no—
26D4×C3⋊Dic3—21no—
27D4×C3⋊Dic3C2212yes—
28D4×C3⋊Dic3C2212yes—
29D4×C3⋊Dic3C2211yescharacteristic, complemented
30D4×C3⋊Dic3C2211yescharacteristic, complemented
31#64135—21no—
32#64135C2211yescharacteristic
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
34C2×C4×C3⋊Dic3—21no—
35C2×C4×C3⋊Dic3C2211yescharacteristic
36C2×#3748C2211yescharacteristic
37#63662C2212yescomplemented
38#63659C2212yes—
39#63659C2212yes—
40#63659C2212yescomplemented
41#63645C2212yescomplemented
42#63644C2212yescomplemented
43#63642C2212yescomplemented
44C8×C3⋊Dic3C2212yescomplemented
45C2×C3×AGL(1,ℤ/8)D314yes—
46Dic3×#41—34no—
47C2×D4×Dic3—34no—
48#5232—34no—
49#5215—34no—
50#5164—38no—
51Dic3×SD16—38no—
52#5152—38no—
53Dic3×D8—38no—
54#5121—34no—
55Dic3×M16—34no—
56C24×C32—21no—
57C32×#41—22no—
58C32×#41C2×C414yescomplemented
59C2×C32×Q8C2311yescharacteristic
60C2×C32×D4—21no—
61C2×C32×D4—21no—
62C2×C32×D4—22no—
63C2×C32×D4C2×C414yescomplemented
64C2×C32×D4C2312yes—
65C2×C32×D4C2311yescharacteristic
66C22×C32×C4—21no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C22×C3⋊Dic3—22no—
70C22×C3⋊Dic3—22no—
71C22×C3⋊Dic3—21no—
72C22×C3⋊Dic3—21no—
73C22×C3⋊Dic3—44no—
74C22×C3⋊Dic3D411yescharacteristic
75C22×C3⋊Dic3D411yescharacteristic
76C32×SD16C2×C418yescomplemented
77C32×D8C2×C418yescomplemented
78C32×M16C2×C414yescomplemented
79C2×C32×C8C2312yes—
80#3757—21no—
81#3757—21no—
82#3757—21no—
83#3757—22no—
84#3757—22no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2312yes—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C4×C3⋊Dic3—21no—
92C4×C3⋊Dic3—21no—
93C4×C3⋊Dic3—21no—
94C4×C3⋊Dic3D411yescharacteristic
95C4×C3⋊Dic3D411yescharacteristic
96C4×C3⋊Dic3C2311yescharacteristic
97C4×C3⋊Dic3C2311yescharacteristic
98#3748—22no—
99C2×C3⋊(C3⋊C8)C2312yes—
100C4×AGL(1,ℤ/8)—91noSylow
101C2×C3×#41C2×D314yes—
102C22×C3×D4C2×D314yes—
103C23×Dic3—64no—
104C3×AGL(1,ℤ/8)Dic3132yescomplemented
105C2×C3×SD16C2×D318yes—
106C2×C3×D8C2×D318yes—
107C2×C3×M16C2×D314yes—
108C2×#217—64no—
109Q8×Dic3—34no—
110Q8×Dic3—34no—
111D4×Dic3—34no—
112D4×Dic3—38no—
113D4×Dic3—34no—
114D4×Dic3—38no—
115D4×Dic3—64no—
116D4×Dic3—64no—
117D4×Dic3—64no—
118D4×Dic3—64no—
119#926—34no—
120#926—64no—
121C2×C4⋊Dic3—34no—
122C2×C4×Dic3—34no—
123C2×C4×Dic3—64no—
124C2×#208—34no—
125#835—38no—
126#832—38no—
127#832—38no—
128#832—38no—
129#818—38no—
130#817—38no—
131#815—38no—
132C8×Dic3—38no—
133C23×C32—24no—
134C23×C32—22no—
135C23×C32—21no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32C2×D411yescharacteristic
139C32×Q8—21no—
140C32×Q8C22×C412yescomplemented
141C32×D4—24no—
142C32×D4—24no—
143C32×D4—22no—
144C32×D4—21no—
145C32×D4C22×C414yes—
146C32×D4C22×C412yescomplemented
147C2×C32×C4—21no—
148C2×C32×C4—24no—
149C2×C32×C4C22×C412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4112yes—
152C2×C32×C4C2411yescharacteristic
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—41no—
158C2×C3⋊Dic3—42no—
159C2×C3⋊Dic3—44no—
160C2×C3⋊Dic3—42no—
161C2×C3⋊Dic3—42no—
162C2×C3⋊Dic3—44no—
163C2×C3⋊Dic3C2×D411yescharacteristic
164C2×C3⋊Dic3C2×D411yescharacteristic
165C2×C3⋊Dic3C2×D411yescharacteristic
166C2×C3⋊Dic3C2×D411yescharacteristic
167C32×C8C22×C414yescomplemented
168C3⋊(C3⋊C8)—22no—
169C2×AGL(1,ℤ/8)C3⋊D311yescharacteristic
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×M16—91no—
180C24×C3—24no—
181C3×#41—28no—
182C3×#41C2×Dic3116yescomplemented
183C2×C3×Q8C22×D314yes—
184C2×C3×D4—24no—
185C2×C3×D4—24no—
186C2×C3×D4—28no—
187C2×C3×D4C2×Dic3116yescomplemented
188C2×C3×D4C22×D318yes—
189C2×C3×D4C22×D314yes—
190C22×C3×C4—24no—
191C22×C3×C4C22×D314yes—
192C22×Dic3—34no—
193C22×Dic3—34no—
194C22×Dic3—64no—
195C22×Dic3—64no—
196C22×Dic3—68no—
197C22×Dic3—68no—
198C22×Dic3—64no—
199C22×Dic3—1216no—
200C3×SD16C2×Dic3132yescomplemented
201C3×D8C2×Dic3132yescomplemented
202C3×M16C2×Dic3116yescomplemented
203C2×C3×C8C22×D318yes—
204#217—64no—
205#217—64no—
206#217—68no—
207#217—68no—
208#217—64no—
209C4⋊Dic3—34no—
210C4⋊Dic3—38no—
211C4⋊Dic3—34no—
212C4⋊Dic3—64no—
213C4⋊Dic3—64no—
214C4⋊Dic3—64no—
215C4×Dic3—34no—
216C4×Dic3—34no—
217C4×Dic3—34no—
218C4×Dic3—34no—
219C4×Dic3—64no—
220C4×Dic3—64no—
221C4×Dic3—64no—
222#208—68no—
223C2×C3⋊C8—38no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32—22no—
227C22×C32—24no—
228C22×C32—48no—
229C22×C32—42no—
230C22×C32—41no—
231C22×C32—41no—
232C22×C32—42no—
233C22×C32C4×D412yes—
234C22×C32C22×D411yescharacteristic
235C32×C4—22no—
236C32×C4C4×D412yes—
237C32×C4C23×C411yescharacteristic
238C32×C4C2×#4111yescharacteristic
239C3⋊Dic3—21no—
240C3⋊Dic3—21no—
241C3⋊Dic3—21no—
242C3⋊Dic3—41no—
243C3⋊Dic3—42no—
244C3⋊Dic3—41no—
245C3⋊Dic3AGL(1,ℤ/8)12yesdirect product factor
246C2×#41C2×C3⋊D311yescharacteristic
247C22×D4C2×C3⋊D311yescharacteristic
248C23×C4—181no—
249AGL(1,ℤ/8)C3⋊Dic318yesdirect product factor
250C2×SD16C2×C3⋊D312yes—
251C2×D8C2×C3⋊D312yes—
252C2×M16—91no—
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—91no—
269C2×C42—181no—
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—24no—
280C23×C3—28no—
281C23×C3—48no—
282C23×C3—48no—
283C23×C3D3×D414yes—
284C3×Q8—24no—
285C3×Q8C22×Dic318yescomplemented
286C3×D4—216no—
287C3×D4—216no—
288C3×D4—28no—
289C3×D4—24no—
290C3×D4C22×Dic3116yes—
291C3×D4C22×Dic318yescomplemented
292C2×C3×C4—24no—
293C2×C3×C4—216no—
294C2×C3×C4D3×D414yes—
295C2×C3×C4#23718yes—
296C2×C3×C4C22×Dic318yes—
297C2×C3×C4C23×D314yes—
298C2×Dic3—34no—
299C2×Dic3—34no—
300C2×Dic3—34no—
301C2×Dic3—34no—
302C2×Dic3—68no—
303C2×Dic3—64no—
304C2×Dic3—64no—
305C2×Dic3—68no—
306C2×Dic3—128no—
307C2×Dic3—1216no—
308C2×Dic3—124no—
309C2×Dic3—128no—
310C2×Dic3—1216no—
311C2×Dic3—128no—
312C3×C8C22×Dic3116yescomplemented
313C3⋊C8—68no—
314C2×C32—22no—
315C2×C32—42no—
316C2×C32—44no—
317C2×C32C2×C4×D411yescharacteristic
318C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
319C2×C32#57511yescharacteristic
320C24—21no—
321#41—22no—
322#41C2×C3⋊Dic314yescomplemented
323C2×Q8C22×C3⋊D311yescharacteristic
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—22no—
327C2×D4C2×C3⋊Dic314yescomplemented
328C2×D4C22×C3⋊D312yes—
329C2×D4C22×C3⋊D311yescharacteristic
330C22×C4—21no—
331C22×C4—91no—
332C22×C4—91no—
333C22×C4—181no—
334C22×C4—181no—
335C22×C4—182no—
336C22×C4—182no—
337C22×C4—181no—
338C22×C4—364no—
339C22×C4C22×C3⋊D311yescharacteristic
340SD16C2×C3⋊Dic318yescomplemented
341D8C2×C3⋊Dic318yescomplemented
342M16—182no—
343M16C2×C3⋊Dic314yescomplemented
344C2×C8—92no—
345C2×C8C22×C3⋊D312yes—
346C4⋊C4—91no—
347C4⋊C4—91no—
348C4⋊C4—92no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C22⋊C4—182no—
353C22⋊C4—182no—
354C22⋊C4—181no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C42—91no—
358C42—91no—
359C42—91no—
360C42—91no—
361C42—181no—
362C42—181no—
363C42—181no—
364C22×C3—24no—
365C22×C3—24no—
366C22×C3—28no—
367C22×C3—216no—
368C22×C3—432no—
369C22×C3—48no—
370C22×C3—44no—
371C22×C3—44no—
372C22×C3—48no—
373C22×C3D4×Dic318yes—
374C22×C3C2×D3×D414yes—
375C3×C4—28no—
376C3×C4D4×Dic318yes—
377C3×C4C2×#23714yes—
378C3×C4C23×Dic314yes—
379Dic3—38no—
380Dic3—64no—
381Dic3—64no—
382Dic3—64no—
383Dic3—128no—
384Dic3—124no—
385Dic3—124no—
386C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
387C23—21no—
388C23—22no—
389C23—24no—
390C23—42no—
391C23—42no—
392C23D4×C3⋊D311yescharacteristic
393Q8—21no—
394Q8C22×C3⋊Dic312yescomplemented
395D4—24no—
396D4—22no—
397D4—21no—
398D4—24no—
399D4C22×C3⋊Dic314yes—
400D4C22×C3⋊Dic312yescomplemented
401C2×C4—21no—
402C2×C4—24no—
403C2×C4—91no—
404C2×C4—91no—
405C2×C4—91no—
406C2×C4—91no—
407C2×C4—182no—
408C2×C4—181no—
409C2×C4—181no—
410C2×C4—182no—
411C2×C4—364no—
412C2×C4—362no—
413C2×C4—361no—
414C2×C4—364no—
415C2×C4—362no—
416C2×C4—362no—
417C2×C4D4×C3⋊D311yescharacteristic
418C2×C4#383012yes—
419C2×C4C22×C3⋊Dic312yes—
420C2×C4C23×C3⋊D311yescharacteristic
421C8—182no—
422C8C22×C3⋊Dic314yescomplemented
423C2×C3—28no—
424C2×C3—416no—
425C2×C3—48no—
426C2×C3D3×AGL(1,ℤ/8)14yes—
427C2×C3#577314yes—
428C2×C3C2×D4×Dic314yes—
429C22—21no—
430C22—21no—
431C22—22no—
432C22—24no—
433C22—48no—
434C22—42no—
435C22—41no—
436C22—41no—
437C22—42no—
438C22D4×C3⋊Dic312yes—
439C22C2×D4×C3⋊D311yescharacteristic
440C4—22no—
441C4—92no—
442C4—181no—
443C4—181no—
444C4—181no—
445C4—362no—
446C4—361no—
447C4—361no—
448C4D4×C3⋊Dic312yes—
449C4C2×#383011yescharacteristic
450C4C23×C3⋊Dic311yescharacteristic
451C3Dic3×AGL(1,ℤ/8)14yescomplemented
452C2—22no—
453C2—44no—
454C2—42no—
455C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
456C2#1059624411yescharacteristic
457C2C2×D4×C3⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
Fitting, prime radicalC2×C32×AGL(1,ℤ/8)C2
socleC22×C32C22×D4
cosocleC2×C32×C4C24
hypercenterC2×AGL(1,ℤ/8)C3⋊D3
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
2. #41×C3⋊Dic3C2semidirect
3. C2×D4×C3⋊Dic3C2semidirect
4. #10592931C2semidirect
5. #10592914C2semidirect
6. #10592863C2semidirect
7. SD16×C3⋊Dic3C2semidirect
8. #10592851C2semidirect
9. D8×C3⋊Dic3C2semidirect
10. #10592820C2semidirect
11. M16×C3⋊Dic3C2semidirect
16. C32×AGL(1,ℤ/8)C4semidirect
21. Q8×C3⋊Dic3C22semidirect
22. Q8×C3⋊Dic3C22semidirect
29. D4×C3⋊Dic3C22semidirect
30. D4×C3⋊Dic3C22semidirect
37. #63662C22semidirect
40. #63659C22semidirect
41. #63645C22semidirect
42. #63644C22semidirect
43. #63642C22semidirect
44. C8×C3⋊Dic3C22semidirect
58. C32×#41C2×C4semidirect
63. C2×C32×D4C2×C4semidirect
76. C32×SD16C2×C4semidirect
77. C32×D8C2×C4semidirect
78. C32×M16C2×C4semidirect
104. C3×AGL(1,ℤ/8)Dic3semidirect
140. C32×Q8C22×C4semidirect
146. C32×D4C22×C4semidirect
167. C32×C8C22×C4semidirect
182. C3×#41C2×Dic3semidirect
187. C2×C3×D4C2×Dic3semidirect
200. C3×SD16C2×Dic3semidirect
201. C3×D8C2×Dic3semidirect
202. C3×M16C2×Dic3semidirect
245. C3⋊Dic3AGL(1,ℤ/8)direct (N × H)
249. AGL(1,ℤ/8)C3⋊Dic3direct (N × H)
285. C3×Q8C22×Dic3semidirect
291. C3×D4C22×Dic3semidirect
312. C3×C8C22×Dic3semidirect
322. #41C2×C3⋊Dic3semidirect
327. C2×D4C2×C3⋊Dic3semidirect
340. SD16C2×C3⋊Dic3semidirect
341. D8C2×C3⋊Dic3semidirect
343. M16C2×C3⋊Dic3semidirect
386. C32C4×AGL(1,ℤ/8)semidirect
394. Q8C22×C3⋊Dic3semidirect
400. D4C22×C3⋊Dic3semidirect
422. C8C22×C3⋊Dic3semidirect
451. C3Dic3×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×C32×AGL(1,ℤ/8)2
#41×C3⋊Dic32
C2×D4×C3⋊Dic32
#105929312
#105929142
#105928632
SD16×C3⋊Dic32
#105928512
D8×C3⋊Dic32
#105928202
M16×C3⋊Dic32
Dic3×AGL(1,ℤ/8)3