Finite Group Databasebeta

← C3⋊D3×#490 #11873561

Subgroups — C3⋊D3×#490 #11873561

Order 1152.

1464 conjugacy classes of subgroups; only the 225 normal subgroups are shown.

normal subgroups only

This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#127C211yesmaximal, characteristic
2C3⋊D3×#125C211yesmaximal, characteristic, complemented
3C32×#490C211yesmaximal, characteristic, complemented
4#10592770C211yesmaximal, characteristic, complemented
5#10592766C211yesmaximal, characteristic, complemented
6C3⋊D3×#102C214yesmaximal, complemented
7#10592463C214yesmaximal, complemented
8#10592412C211yesmaximal, characteristic, complemented
9C3⋊D3×#97C211yesmaximal, characteristic, complemented
10D3×#490—34nomaximal
11C2×D4×C3⋊D3—22no—
12C2×D4×C3⋊D3C2212yes—
13C32×#127C2211yescharacteristic
14C32×#125C2211yescharacteristic, complemented
15#64149—22no—
16#64149C2212yes—
17C2×C8×C3⋊D3C2212yes—
18C4⋊C4×C3⋊D3—22no—
19C4⋊C4×C3⋊D3C2212yes—
20#64099C2212yescomplemented
21#64098—22no—
22#64083C2211yescharacteristic
23C42×C3⋊D3C2211yescharacteristic
24#64079C2211yescharacteristic, complemented
25C32×#102C2214yescomplemented
26C32×#97C2211yescharacteristic, complemented
27#63659C2214yescomplemented
28#63648C2214yescomplemented
29#63642C2212yescomplemented
30#63636C2214yescomplemented
31#63630C2211yescharacteristic, complemented
32D3×#127—34no—
33D3×#125—34no—
34C3×#490D314yescomplemented
35#5071—34no—
36#5067—34no—
37D3×#102—316no—
38#4764—316no—
39#4713—34no—
40D3×#97—34no—
41C23×C3⋊D3—22no—
42C2×C32×D4—22no—
43C2×C32×D4C2312yes—
44C2×#638—24no—
45C2×#638—22no—
46D4×C3⋊D3—28no—
47D4×C3⋊D3—48no—
48C2×C4⋊(C3⋊D3)—22no—
49C2×C4⋊(C3⋊D3)C2312yes—
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3D412yes—
52C2×C4×C3⋊D3C2311yescharacteristic
53C2×C32×C8C2312yes—
54C32×C4⋊C4—22no—
55C32×C4⋊C4C2312yes—
56C32×C42C2311yescharacteristic
57C4⋊(C3⋊Dic3)—22no—
58C4⋊(C3⋊Dic3)C2312yes—
59#3750—22no—
60#3750—22no—
61#3750—22no—
62C4×C3⋊Dic3D412yes—
63C4×C3⋊Dic3C2311yescharacteristic
64C2×C3⋊(C3⋊C8)C2312yes—
65C8×C3⋊D3—24no—
66C2×#490—91noSylow
67C2×D3×D4—38no—
68C2×D3×D4—68no—
69C3×#127C2×D314yes—
70C3×#125C2×D314yescomplemented
71#940—38no—
72#940—68no—
73C2×D3×C8—38no—
74D3×C4⋊C4—38no—
75D3×C4⋊C4—68no—
76#890—38no—
77#889—68no—
78#874—34no—
79C42×D3—34no—
80#870—34no—
81C3×#102C2×D3116yescomplemented
82C3×#97C2×D314yescomplemented
83#832—316no—
84#821—316no—
85#815—38no—
86#809—316no—
87#803—34no—
88C23×C32—22no—
89C22×C3⋊D3—22no—
90C22×C3⋊D3—44no—
91C22×C3⋊D3—48no—
92C22×C3⋊D3C2×D411yescharacteristic
93C32×D4—24no—
94C32×D4—44no—
95C2×C32×C4—22no—
96C2×C32×C4C2×D412yes—
97C2×C32×C4C2411yescharacteristic
98#638—48no—
99#638—44no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3C2×D412yes—
102C2×C3⋊Dic3C2×D411yescharacteristic
103C4⋊(C3⋊D3)—24no—
104C4⋊(C3⋊D3)—44no—
105C4×C3⋊D3—24no—
106C4×C3⋊D3—44no—
107C4×C3⋊D3#4114yes—
108C32×C8—22no—
109C3⋊(C3⋊C8)—22no—
110C2×#127—91no—
111C2×#125—91no—
112#490—91no—
113#490—91no—
114#490—94no—
115#490—91no—
116#490C3⋊D311yescharacteristic, direct product factor
117C2×#102—94no—
118C2×#97—91no—
119C23×D3—68no—
120C2×C3×D4—28no—
121C2×C3×D4C22×D318yes—
122C2×#67—616no—
123C2×#67—68no—
124D3×D4—632no—
125D3×D4—1232no—
126C2×D12—38no—
127C2×D12—68no—
128C2×C4×D3—34no—
129C2×C4×D3—38no—
130C2×C4×D3—68no—
131C2×C3×C8C22×D318yes—
132C3×C4⋊C4—28no—
133C3×C4⋊C4C22×D318yes—
134C3×C42C22×D314yes—
135C4⋊Dic3—38no—
136C4⋊Dic3—68no—
137Dic3⋊C4—68no—
138Dic3⋊C4—68no—
139Dic3⋊C4—68no—
140C4×Dic3—38no—
141C4×Dic3—34no—
142C2×C3⋊C8—38no—
143D3×C8—616no—
144C22×C32—42no—
145C22×C32—44no—
146C22×C32C22×D411yescharacteristic
147C2×C3⋊D3—42no—
148C2×C3⋊D3—44no—
149C2×C3⋊D3—88no—
150C2×C3⋊D3#12412yes—
151C2×C3⋊D3AGL(1,ℤ/8)14yes—
152C32×C4—22no—
153C32×C4—42no—
154C32×C4C2×#4112yes—
155C3⋊Dic3—22no—
156C3⋊Dic3—42no—
157C3⋊Dic3#12412yes—
158C22×D4—92no—
159C22×D4—182no—
160C22×C8—92no—
161#127—92no—
162#127—91no—
163#127—182no—
164#127C2×C3⋊D311yescharacteristic
165#125—92no—
166#125—91no—
167#125—182no—
168#125C2×C3⋊D311yescharacteristic, complemented
169C2×C4⋊C4—92no—
170C2×C4⋊C4—182no—
171C2×C42—91no—
172#102—94no—
173#102—94no—
174#102—94no—
175#102C2×C3⋊D314yescomplemented
176#97—92no—
177#97—91no—
178#97C2×C3⋊D311yescharacteristic, complemented
179C23×C3—28no—
180C22×D3—34no—
181C22×D3—68no—
182C22×D3—1216no—
183C22×D3—1232no—
184C3×D4—216no—
185C3×D4—416no—
186C2×C3×C4—28no—
187C2×C3×C4D3×D418yes—
188C2×C3×C4C23×D314yes—
189#67—1216no—
190#67—1232no—
191C2×Dic3—34no—
192C2×Dic3—38no—
193C2×Dic3—68no—
194D12—616no—
195D12—1216no—
196C4×D3—316no—
197C4×D3—616no—
198C4×D3—1216no—
199C3×C8—28no—
200C3⋊C8—68no—
201C2×C32—82no—
202C2×C32C2×#12411yescharacteristic
203C2×C32C2×AGL(1,ℤ/8)12yes—
204C3⋊D3—82no—
205C3⋊D3#49014yesdirect product factor
206C24—182no—
207C2×D4—22no—
208C2×D4—92no—
209C2×D4—188no—
210C2×D4—184no—
211C2×D4—182no—
212C2×D4—182no—
213C2×D4—368no—
214C2×D4C22×C3⋊D312yes—
215C22×C4—91no—
216C22×C4—92no—
217C22×C4—182no—
218C2×C8—92no—
219C2×C8—184no—
220C2×C8C22×C3⋊D312yes—
221C4⋊C4—22no—
222C4⋊C4—92no—
223C4⋊C4—182no—
224C4⋊C4—182no—
225C4⋊C4—182no—
226C4⋊C4—182no—
227C4⋊C4C22×C3⋊D312yes—
228C42—91no—
229C42—92no—
230C42C22×C3⋊D311yescharacteristic
231C22×C3—48no—
232C22×C3—416no—
233C22×C3C2×D3×D414yes—
234C2×D3—38no—
235C2×D3—316no—
236C2×D3—128no—
237C2×D3—1216no—
238C2×D3—2432no—
239C3×C4—28no—
240C3×C4—48no—
241C3×C4D3×#4118yes—
242Dic3—38no—
243Dic3—68no—
244Dic3—128no—
245C32C2×#49011yescharacteristic, complemented, Sylow
246C23—22no—
247C23—91no—
248C23—182no—
249C23—364no—
250C23—368no—
251D4—24no—
252D4—44no—
253D4—184no—
254D4—364no—
255D4—364no—
256D4—368no—
257C2×C4—22no—
258C2×C4—91no—
259C2×C4—94no—
260C2×C4—92no—
261C2×C4—184no—
262C2×C4—182no—
263C2×C4—364no—
264C2×C4D4×C3⋊D312yes—
265C2×C4C23×C3⋊D311yescharacteristic
266C8—22no—
267C8—182no—
268C2×C3—88no—
269C2×C3D3×#12414yes—
270C2×C3D3×AGL(1,ℤ/8)18yes—
271D3—316no—
272D3—248no—
273C22—42no—
274C22—44no—
275C22—92no—
276C22—94no—
277C22—362no—
278C22—364no—
279C22—728no—
280C22C2×D4×C3⋊D311yescharacteristic
281C4—22no—
282C4—42no—
283C4—92no—
284C4—182no—
285C4—362no—
286C4#41×C3⋊D312yes—
287C3D3×#49014yescomplemented
288C2—82no—
289C2—94no—
290C2—722no—
291C2C3⋊D3×#12411yescharacteristic
292C2C3⋊D3×AGL(1,ℤ/8)12yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#490C2
socleC22×C32C22×D4
prime radicalC3⋊D3×#127C2
hypercenter#490C3⋊D3
hypocenterC32C2×#490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#125C2semidirect
3. C32×#490C2semidirect
4. #10592770C2semidirect
5. #10592766C2semidirect
6. C3⋊D3×#102C2semidirect
7. #10592463C2semidirect
8. #10592412C2semidirect
9. C3⋊D3×#97C2semidirect
14. C32×#125C22semidirect
20. #64099C22semidirect
24. #64079C22semidirect
25. C32×#102C22semidirect
26. C32×#97C22semidirect
27. #63659C22semidirect
28. #63648C22semidirect
29. #63642C22semidirect
30. #63636C22semidirect
31. #63630C22semidirect
34. C3×#490D3semidirect
70. C3×#125C2×D3semidirect
81. C3×#102C2×D3semidirect
82. C3×#97C2×D3semidirect
116. #490C3⋊D3direct (N × H)
168. #125C2×C3⋊D3semidirect
175. #102C2×C3⋊D3semidirect
178. #97C2×C3⋊D3semidirect
205. C3⋊D3#490direct (N × H)
245. C32C2×#490semidirect
287. C3D3×#490semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1272
C3⋊D3×#1252
C32×#4902
#105927702
#105927662
C3⋊D3×#1022
#105924632
#105924122
C3⋊D3×#972
D3×#4903