Finite Group Databasebeta

← C3⋊D3×#355 #11796448

Subgroups — C3⋊D3×#355 #11796448

Order 1152.

780 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 109 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×#124C211yesmaximal, characteristic
2C3⋊D3×#101C212yesmaximal, complemented
3C32×#355C211yesmaximal, characteristic, complemented
4#10589408C211yesmaximal, characteristic, complemented
5#10589343C212yesmaximal, complemented
6D3×#355—34nomaximal
7C2×Q8×C3⋊D3C2211yescharacteristic
8C2×D4×C3⋊D3C411yescharacteristic
9C32×#124C2211yescharacteristic
10#64156C2211yescharacteristic
11#64145C411yescharacteristic
12M16×C3⋊D3—22no—
13#64094—22no—
14C22⋊C4×C3⋊D3—22no—
15#64084C411yescharacteristic
16C42×C3⋊D3C411yescharacteristic
17C32×#101C2212yescomplemented
18#63663C2212yescomplemented
19#63651—22no—
20D3×#124—34no—
21D3×#101—38no—
22C3×#355D314yescomplemented
23#4542—34no—
24#4477—38no—
25C23×C3⋊D3—21no—
26C2×C32×Q8C2311yescharacteristic
27C2×C32×D4C2×C411yescharacteristic
28C2×#638—21no—
29Q8×C3⋊D3—41no—
30Q8×C3⋊D3—41no—
31D4×C3⋊D3—41no—
32D4×C3⋊D3—41no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3D412yes—
37C2×#634C2×C411yescharacteristic
38C2×#634D412yes—
39C32×M16—22no—
40C32×C22⋊C4—22no—
41C32×C42C2×C411yescharacteristic
42#3757—22no—
43#3752—22no—
44#3752—22no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3C2×C411yescharacteristic
47#3748—22no—
48#3743—42no—
49C8×C3⋊D3—42no—
50C2×#355—91noSylow
51C2×D3×Q8—34no—
52C2×D3×D4—34no—
53C3×#124C2×D314yes—
54#947—34no—
55#936—34no—
56D3×M16—68no—
57#885—68no—
58D3×C22⋊C4—68no—
59#875—34no—
60C42×D3—34no—
61C3×#101C2×D318yescomplemented
62#836—38no—
63#824—68no—
64C23×C32—21no—
65C22×C3⋊D3—21no—
66C22×C3⋊D3—44no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3—41no—
69C22×C3⋊D3C22⋊C411yescharacteristic
70C32×Q8—41no—
71C32×D4—41no—
72C2×C32×C4—21no—
73C2×C32×C4C22×C411yescharacteristic
74C2×C32×C4C2×D412yes—
75#638—42no—
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C22⋊C412yes—
79C4⋊(C3⋊D3)—41no—
80C4×C3⋊D3—22no—
81C4×C3⋊D3—22no—
82C4×C3⋊D3—21no—
83C4×C3⋊D3—21no—
84C4×C3⋊D3—42no—
85#634—41no—
86#634—42no—
87C32×C8—42no—
88C3⋊(C3⋊C8)—42no—
89C2×#124—91no—
90C2×#101—92no—
91#355—91no—
92#355—92no—
93#355C3⋊D311yescharacteristic, direct product factor
94C23×D3—64no—
95C2×C3×Q8C22×D314yes—
96C2×C3×D4C4×D314yes—
97C2×#67—64no—
98D3×Q8—124no—
99D3×Q8—124no—
100D3×D4—124no—
101D3×D4—124no—
102C2×D12—34no—
103C2×C4×D3—34no—
104C2×C4×D3—38no—
105C2×C4×D3—64no—
106C2×Dic6—34no—
107C2×Dic6—38no—
108C3×M16—28no—
109C3×C22⋊C4—28no—
110C3×C42C4×D314yes—
111#217—68no—
112(C2×D3)⋊C4—68no—
113(C2×D3)⋊C4—68no—
114C4×Dic3—34no—
115C4×Dic3—64no—
116#208—68no—
117ΓL(1,𝔽25)—128no—
118D3×C8—128no—
119C22×C32—42no—
120C22×C32—41no—
121C22×C32C2×C22⋊C411yescharacteristic
122C2×C3⋊D3—22no—
123C2×C3⋊D3—42no—
124C2×C3⋊D3—41no—
125C2×C3⋊D3—82no—
126C2×C3⋊D3—82no—
127C2×C3⋊D3#9911yescharacteristic
128C2×C3⋊D3#9911yescharacteristic
129C32×C4—22no—
130C32×C4—21no—
131C32×C4—41no—
132C3⋊Dic3—22no—
133C3⋊Dic3—21no—
134C3⋊Dic3—41no—
135C22×Q8—91no—
136C22×D4—91no—
137C2×M16—182no—
138#124—91no—
139#124—91no—
140#124—91no—
141#124—182no—
142#124C2×C3⋊D311yescharacteristic
143C2×C22⋊C4—182no—
144C2×C42—91no—
145#101—92no—
146#101—182no—
147#101C2×C3⋊D312yescomplemented
148C23×C3—24no—
149C22×D3—34no—
150C22×D3—64no—
151C22×D3—124no—
152C22×D3—124no—
153C22×D3—1216no—
154C3×Q8—44no—
155C3×D4—44no—
156C2×C3×C4—24no—
157C2×C3×C4C2×C4×D314yes—
158C2×C3×C4D3×D418yes—
159#67—128no—
160C2×Dic3—34no—
161C2×Dic3—38no—
162C2×Dic3—64no—
163D12—124no—
164C4×D3—68no—
165C4×D3—68no—
166C4×D3—64no—
167C4×D3—64no—
168C4×D3—128no—
169Dic6—128no—
170Dic6—124no—
171C3×C8—48no—
172C3⋊C8—128no—
173C2×C32—21no—
174C2×C32—81no—
175C2×C32C2×#9911yescharacteristic
176C3⋊D3—21no—
177C3⋊D3—81no—
178C3⋊D3#35512yesdirect product factor
179C24—181no—
180C2×Q8—91no—
181C2×Q8—92no—
182C2×Q8—361no—
183C2×Q8—361no—
184C2×Q8C22×C3⋊D311yescharacteristic
185C2×D4—91no—
186C2×D4—181no—
187C2×D4—361no—
188C2×D4—361no—
189C2×D4C4×C3⋊D311yescharacteristic
190C22×C4—91no—
191C22×C4—92no—
192C22×C4—181no—
193M16—22no—
194M16—182no—
195M16—362no—
196C2×C8—362no—
197C22⋊C4—22no—
198C22⋊C4—182no—
199C22⋊C4—182no—
200C22⋊C4—182no—
201C42—91no—
202C42—181no—
203C42C4×C3⋊D311yescharacteristic
204C22×C3—48no—
205C22×C3—44no—
206C22×C3D3×C22⋊C414yes—
207C2×D3—34no—
208C2×D3—34no—
209C2×D3—68no—
210C2×D3—128no—
211C2×D3—124no—
212C2×D3—248no—
213C2×D3—248no—
214C3×C4—28no—
215C3×C4—24no—
216C3×C4—44no—
217Dic3—64no—
218Dic3—68no—
219Dic3—124no—
220C32C2×#35511yescharacteristic, complemented, Sylow
221C23—21no—
222C23—91no—
223C23—181no—
224C23—361no—
225C23—361no—
226C23—364no—
227Q8—41no—
228Q8—362no—
229Q8—361no—
230D4—41no—
231D4—361no—
232D4—362no—
233C2×C4—21no—
234C2×C4—91no—
235C2×C4—92no—
236C2×C4—182no—
237C2×C4—182no—
238C2×C4—181no—
239C2×C4—181no—
240C2×C4—181no—
241C2×C4—362no—
242C2×C4C2×C4×C3⋊D311yescharacteristic
243C2×C4D4×C3⋊D312yes—
244C8—42no—
245C8—362no—
246C2×C3—24no—
247C2×C3—84no—
248C2×C3D3×#9914yes—
249D3—38no—
250D3—64no—
251D3—244no—
252C22—42no—
253C22—41no—
254C22—91no—
255C22—91no—
256C22—182no—
257C22—362no—
258C22—361no—
259C22—722no—
260C22—722no—
261C22C22⋊C4×C3⋊D311yescharacteristic
262C4—22no—
263C4—21no—
264C4—41no—
265C4—181no—
266C4—182no—
267C4—361no—
268C3D3×#35514yescomplemented
269C2—21no—
270C2—81no—
271C2—92no—
272C2—181no—
273C2—721no—
274C2C3⋊D3×#9911yescharacteristic
subgroupG/H
centerC2C3⋊D3×#99
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C22×C3⋊D3
FittingC32×#355C2
socleC2×C32C2×#99
prime radicalC2×D4×C3⋊D3C4
cosocleC2×C32×Q8C23
hypercenter#355C3⋊D3
hypocenterC32C2×#355
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#101C2semidirect
3. C32×#355C2semidirect
4. #10589408C2semidirect
5. #10589343C2semidirect
17. C32×#101C22semidirect
18. #63663C22semidirect
22. C3×#355D3semidirect
61. C3×#101C2×D3semidirect
93. #355C3⋊D3direct (N × H)
147. #101C2×C3⋊D3semidirect
178. C3⋊D3#355direct (N × H)
220. C32C2×#355semidirect
268. C3D3×#355semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1242
C3⋊D3×#1012
C32×#3552
#105894082
#105893432
D3×#3553