Finite Group Databasebeta

← D3×#5067 #11873590

Subgroups — D3×#5067 #11873590

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#125C211yesmaximal, characteristic, complemented
2D3×#874C211yesmaximal, characteristic
3#10592766C211yesmaximal, characteristic, complemented
4C3×#5067C211yesmaximal, characteristic, complemented
5D3×#809C214yesmaximal, complemented
6#10590550C214yesmaximal, complemented
7D3×#803C211yesmaximal, characteristic, complemented
8#10590282C211yesmaximal, characteristic, complemented
9#10590279C211yesmaximal, characteristic, complemented
10C2×#5067—31nomaximal
11D3×#490—31nomaximal
12C2×D3×D12—22no—
13C2×D3×D12C2212yes—
14C32×#125C2211yescharacteristic, complemented
15#64083C2211yescharacteristic
16C3×D3×C4⋊C4—22no—
17C3×D3×C4⋊C4C2212yes—
18C3×#890C2212yescomplemented
19C3×#889—22no—
20C3×#874C2211yescharacteristic
21C3×C42×D3C2211yescharacteristic
22C3×#870C2211yescharacteristic, complemented
23#63911—22no—
24#63911C2212yes—
25C2×D3×C3⋊C8C2212yes—
26#63636C2214yescomplemented
27#63630C2211yescharacteristic, complemented
28C3×#809C2214yescomplemented
29C3×#803C2211yescharacteristic, complemented
30#63564C2214yescomplemented
31#63562C2214yescomplemented
32#63554C2212yescomplemented
33C2×C3×#125—31no—
34D3×#127—31no—
35D3×#125D311yescharacteristic, complemented
36C2×#874—31no—
37C3×#490—31no—
38#5071—31no—
39#5067—31no—
40#5067—31no—
41#5067—31no—
42#5067—34no—
43#5067—31no—
44#5067—61no—
45#5067D311yescharacteristic, direct product factor
46C2×#809—34no—
47C2×#803—31no—
48D3×#102—34no—
49#4764—34no—
50#4713—31no—
51D3×#97—31no—
52C22×D32—22no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C2×C3×D12—22no—
56C2×C3×D12C2312yes—
57C2×C3×C4×D3—22no—
58C2×C3×C4×D3D412yes—
59C2×C3×C4×D3C2311yescharacteristic
60C2×#626—24no—
61C2×#626—22no—
62D3×D12—28no—
63D3×D12—48no—
64C32×C4⋊C4—22no—
65C32×C4⋊C4C2312yes—
66C32×C42C2311yescharacteristic
67C2×C3⋊(C3⋊C8)C2312yes—
68C3×C4⋊Dic3—22no—
69C3×C4⋊Dic3C2312yes—
70C3×Dic3⋊C4—22no—
71C3×Dic3⋊C4—22no—
72C3×Dic3⋊C4—22no—
73C3×C4×Dic3D412yes—
74C3×C4×Dic3C2311yescharacteristic
75C2×C3×C3⋊C8C2312yes—
76D3×C3⋊C8—24no—
77C2×#490—91noSylow
78C2×D3×D4—32no—
79C2×D3×D4—62no—
80C22×D12—32no—
81C22×D12—62no—
82C3×#127—31no—
83C3×#125—21no—
84C3×#125—32no—
85C3×#125—31no—
86C3×#125—62no—
87C3×#125C2×D311yescharacteristic, complemented
88C3×#125C2×D311yescharacteristic, complemented
89C2×C3×C4⋊C4—32no—
90C2×C3×C4⋊C4—62no—
91C2×C3×C42—31no—
92#940—32no—
93#940—62no—
94C22×C3⋊C8—32no—
95C2×D3×C8—32no—
96D3×C4⋊C4—22no—
97D3×C4⋊C4C2×D312yes—
98#890C2×D312yescomplemented
99#889—22no—
100#874—32no—
101#874—31no—
102#874—31no—
103#874—61no—
104#874—62no—
105#874C2×D311yescharacteristic
106C42×D3C2×D311yescharacteristic
107#870C2×D311yescharacteristic, complemented
108C3×#102—34no—
109C3×#97—31no—
110#832—34no—
111#821—34no—
112#815—32no—
113#809—34no—
114#809—34no—
115#809—34no—
116#809—34no—
117#809—64no—
118#809C2×D314yescomplemented
119#803—31no—
120#803—31no—
121#803—32no—
122#803—61no—
123#803C2×D311yescharacteristic, complemented
124C22×C3⋊D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3C2×D411yescharacteristic
127C2×D32—44no—
128C2×D32—48no—
129C2×C32×C4—22no—
130C2×C32×C4C2×D412yes—
131C2×C32×C4C2411yescharacteristic
132C4⋊(C3⋊D3)—24no—
133C4⋊(C3⋊D3)—44no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3C2×D412yes—
136C2×C3×Dic3C2×D411yescharacteristic
137C3×D12—24no—
138C3×D12—44no—
139C3×C4×D3—24no—
140C3×C4×D3—44no—
141C3×C4×D3#4114yes—
142#626—48no—
143#626—44no—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—22no—
146C2×#127—91no—
147C2×#125—31no—
148#490—31no—
149#490—91no—
150#490—94no—
151#490—91no—
152#490—91no—
153C2×#102—94no—
154C2×#97—91no—
155C23×D3—62no—
156C23×D3—62no—
157C2×C3×D4—32no—
158C2×C3×D4—62no—
159C22×C3×C4—31no—
160C22×C3×C4—32no—
161C22×C3×C4—62no—
162C2×#67—64no—
163C2×#67—62no—
164D3×D4—68no—
165D3×D4—128no—
166C2×D12—22no—
167C2×D12—32no—
168C2×D12—32no—
169C2×D12—62no—
170C2×D12—68no—
171C2×D12—64no—
172C2×D12—62no—
173C2×D12—62no—
174C2×D12—62no—
175C2×D12—122no—
176C2×D12—128no—
177C2×D12C22×D312yes—
178C2×C4×D3—22no—
179C2×C4×D3#6712yes—
180C2×C4×D3C22×D311yescharacteristic
181C2×C3×C8—32no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—32no—
186C3×C4⋊C4—42no—
187C3×C4⋊C4—62no—
188C3×C4⋊C4—62no—
189C3×C4⋊C4—62no—
190C3×C4⋊C4—62no—
191C3×C4⋊C4C22×D312yes—
192C3×C4⋊C4C22×D312yes—
193C3×C42—21no—
194C3×C42—32no—
195C3×C42—31no—
196C3×C42C22×D311yescharacteristic
197C3×C42C22×D311yescharacteristic
198C4⋊Dic3—22no—
199C4⋊Dic3C22×D312yes—
200Dic3⋊C4—22no—
201Dic3⋊C4—22no—
202Dic3⋊C4—22no—
203C4×Dic3#6712yes—
204C4×Dic3C22×D311yescharacteristic
205C2×C3⋊C8—32no—
206C2×C3⋊C8—32no—
207C2×C3⋊C8—62no—
208C2×C3⋊C8—64no—
209C2×C3⋊C8C22×D312yes—
210D3×C8—64no—
211C22×C32C22×D411yescharacteristic
212C2×C3⋊D3—42no—
213C2×C3⋊D3—44no—
214C2×C3×D3—42no—
215C2×C3×D3—44no—
216C2×C3×D3#12412yes—
217C2×C3×D3AGL(1,ℤ/8)14yes—
218D32—88no—
219C32×C4—22no—
220C32×C4—42no—
221C32×C4C2×#4112yes—
222C3×Dic3—22no—
223C3×Dic3—42no—
224C3×Dic3#12412yes—
225C22×D4—92no—
226C22×D4—182no—
227C22×C8—92no—
228#127—31no—
229#127—92no—
230#127—91no—
231#127—182no—
232#125—32no—
233#125—31no—
234#125—62no—
235#125D3211yescharacteristic, complemented
236C2×C4⋊C4—32no—
237C2×C4⋊C4—62no—
238C2×C42—31no—
239#102—34no—
240#102—94no—
241#102—94no—
242#102—94no—
243#97—31no—
244#97—92no—
245#97—91no—
246C23×C3—31no—
247C23×C3—62no—
248C22×D3—22no—
249C22×D3—62no—
250C22×D3—62no—
251C22×D3—122no—
252C22×D3—124no—
253C22×D3—128no—
254C22×D3—124no—
255C22×D3—128no—
256C22×D3C2×#6711yescharacteristic
257C3×D4—64no—
258C3×D4—124no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—22no—
263C2×C3×C4—31no—
264C2×C3×C4—34no—
265C2×C3×C4—32no—
266C2×C3×C4—42no—
267C2×C3×C4—64no—
268C2×C3×C4—62no—
269C2×C3×C4—124no—
270C2×C3×C4D3×D412yes—
271C2×C3×C4C2×#6712yes—
272C2×C3×C4C23×D311yescharacteristic
273C2×C3×C4C23×D311yescharacteristic
274#67—128no—
275#67—124no—
276C2×Dic3—22no—
277C2×Dic3C2×#6712yes—
278C2×Dic3C2×#6711yescharacteristic
279D12—24no—
280D12—44no—
281D12—64no—
282D12—64no—
283D12—124no—
284D12—124no—
285D12—124no—
286D12—124no—
287D12—128no—
288D12—244no—
289C4×D3—24no—
290C4×D3—44no—
291C4×D3#23914yes—
292C3×C8—62no—
293C3⋊C8—22no—
294C3⋊C8—62no—
295C3⋊C8—62no—
296C3⋊C8—122no—
297C2×C32C2×#12411yescharacteristic
298C2×C32C2×AGL(1,ℤ/8)12yes—
299C3⋊D3—82no—
300C3×D3—82no—
301C3×D3#49014yescomplemented
302C24—182no—
303C2×D4—32no—
304C2×D4—62no—
305C2×D4—92no—
306C2×D4—188no—
307C2×D4—184no—
308C2×D4—182no—
309C2×D4—182no—
310C2×D4—368no—
311C22×C4—31no—
312C22×C4—32no—
313C22×C4—62no—
314C2×C8—32no—
315C2×C8—92no—
316C2×C8—184no—
317C4⋊C4—22no—
318C4⋊C4—32no—
319C4⋊C4—62no—
320C4⋊C4—62no—
321C4⋊C4—62no—
322C4⋊C4—62no—
323C4⋊C4C2×D3212yes—
324C42—31no—
325C42—32no—
326C42C2×D3211yescharacteristic
327C22×C3—21no—
328C22×C3—32no—
329C22×C3—34no—
330C22×C3—122no—
331C22×C3—124no—
332C22×C3C2×D3×D411yescharacteristic
333C22×C3C22×#6711yescharacteristic
334C2×D3—42no—
335C2×D3—44no—
336C2×D3—122no—
337C2×D3—124no—
338C2×D3—122no—
339C2×D3—124no—
340C2×D3—242no—
341C2×D3—244no—
342C2×D3—248no—
343C2×D3—248no—
344C2×D3#94712yes—
345C2×D3#94914yes—
346C3×C4—22no—
347C3×C4—22no—
348C3×C4—22no—
349C3×C4—32no—
350C3×C4—42no—
351C3×C4—42no—
352C3×C4—42no—
353C3×C4—62no—
354C3×C4—82no—
355C3×C4—122no—
356C3×C4C2×#23912yes—
357C3×C4D3×#4112yes—
358Dic3—22no—
359Dic3—42no—
360Dic3#94712yes—
361C32C2×#49011yescharacteristic, complemented, Sylow
362C23—31no—
363C23—62no—
364C23—182no—
365C23—364no—
366C23—368no—
367D4—64no—
368D4—124no—
369D4—184no—
370D4—364no—
371D4—364no—
372D4—368no—
373C2×C4—22no—
374C2×C4—31no—
375C2×C4—34no—
376C2×C4—32no—
377C2×C4—64no—
378C2×C4—62no—
379C2×C4—124no—
380C2×C4D3×#6712yes—
381C2×C4C22×D3211yescharacteristic
382C8—62no—
383C8—182no—
384C2×C3—21no—
385C2×C3—22no—
386C2×C3—34no—
387C2×C3—242no—
388C2×C3D3×#12411yescharacteristic
389C2×C3D3×AGL(1,ℤ/8)12yes—
390C2×C3C2×#94711yescharacteristic
391C2×C3C2×#94912yes—
392D3—82no—
393D3—242no—
394D3—242no—
395D3—482no—
396D3#506714yesdirect product factor
397C22—32no—
398C22—34no—
399C22—122no—
400C22—124no—
401C22—362no—
402C22—364no—
403C22—728no—
404C22C2×D3×#6711yescharacteristic
405C4—22no—
406C4—32no—
407C4—42no—
408C4—62no—
409C4—122no—
410C4D3×#23912yes—
411C3—21no—
412C3D3×#49011yescharacteristic, complemented
413C3C2×#506711yescharacteristic, complemented
414C2—34no—
415C2—242no—
416C2—722no—
417C2D3×#94711yescharacteristic
418C2D3×#94912yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalD3×#874C2
hypercenter#125D32
hypocenterC32C2×#490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×D3×#125C2semidirect
3. #10592766C2semidirect
4. C3×#5067C2semidirect
5. D3×#809C2semidirect
6. #10590550C2semidirect
7. D3×#803C2semidirect
8. #10590282C2semidirect
9. #10590279C2semidirect
14. C32×#125C22semidirect
18. C3×#890C22semidirect
22. C3×#870C22semidirect
26. #63636C22semidirect
27. #63630C22semidirect
28. C3×#809C22semidirect
29. C3×#803C22semidirect
30. #63564C22semidirect
31. #63562C22semidirect
32. #63554C22semidirect
35. D3×#125D3semidirect
45. #5067D3direct (N × H)
87. C3×#125C2×D3semidirect
88. C3×#125C2×D3semidirect
98. #890C2×D3semidirect
107. #870C2×D3semidirect
118. #809C2×D3semidirect
123. #803C2×D3semidirect
235. #125D32semidirect
301. C3×D3#490semidirect
361. C32C2×#490semidirect
396. D3#5067direct (N × H)
412. C3D3×#490semidirect
413. C3C2×#5067semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1252
D3×#8742
#105927662
C3×#50672
D3×#8092
#105905502
D3×#8032
#105902822
#105902792
C2×#50673
D3×#4903