Finite Group Databasebeta

← C3⋊D3×#343 #11783387

Subgroups — C3⋊D3×#343 #11783387

Order 1152.

1296 conjugacy classes of subgroups; only the 261 normal subgroups are shown.

normal subgroups only

This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 261 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
1C2×M16×C3⋊D3C212yesmaximal
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
3C32×#343C211yesmaximal, characteristic, complemented
4#10589420C212yesmaximal, complemented
5#10589396C211yesmaximal, characteristic, complemented
6D3×#343—34nomaximal
7C22×C4×C3⋊D3C412yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C32×M16C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×#3750C412yes—
13C2×#3748C2212yes—
14M16×C3⋊D3—24no—
15M16×C3⋊D3C418yescomplemented
16C2×#3743—22no—
17C2×C8×C3⋊D3—22no—
18C4⋊C4×C3⋊D3—22no—
19C4⋊C4×C3⋊D3—22no—
20C2×D3×M16—38no—
21C2×D3×C4⋊C4—34no—
22C3×#343D314yescomplemented
23#4554—38no—
24#4530—34no—
25C23×C3⋊D3C2×C411yescharacteristic
26C22×C32×C4C2×C412yes—
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3C2×C412yes—
29C22×C3⋊Dic3C2×C411yescharacteristic
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3—44no—
33C2×C4×C3⋊D3C2×C414yes—
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3D412yes—
36C2×C4×C3⋊D3D412yes—
37C2×C4×C3⋊D3Q812yes—
38C32×M16—22no—
39C32×M16C2×C414yescomplemented
40C2×C32×C8—22no—
41C32×C4⋊C4—22no—
42C4⋊(C3⋊Dic3)—22no—
43#3750—24no—
44#3748—22no—
45#3748C2×C414yescomplemented
46C2×C3⋊(C3⋊C8)—22no—
47#3743—28no—
48C8×C3⋊D3—28no—
49C2×#343—91noSylow
50C22×C4×D3—34no—
51C22×C4×D3—38no—
52C2×C3×M16C2×D318yes—
53C2×C3×C4⋊C4C2×D314yes—
54C2×C4⋊Dic3—34no—
55C2×Dic3⋊C4—38no—
56C2×#208—38no—
57D3×M16—332no—
58D3×M16—616no—
59C2×ΓL(1,𝔽25)—68no—
60C2×D3×C8—68no—
61D3×C4⋊C4—68no—
62D3×C4⋊C4—68no—
63C23×C32C22×C411yescharacteristic
64C22×C3⋊D3—22no—
65C22×C3⋊D3—22no—
66C22×C3⋊D3C4212yes—
67C22×C3⋊D3C22⋊C411yescharacteristic
68C22×C3⋊D3C22⋊C411yescharacteristic
69C22×C3⋊D3C4⋊C412yes—
70C2×C32×C4—22no—
71C2×C32×C4—42no—
72C2×C32×C4C22×C412yes—
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4C2×D412yes—
75C2×C32×C4C2×Q811yescharacteristic
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—42no—
78C2×C3⋊Dic3C4212yes—
79C2×C3⋊Dic3C22⋊C412yes—
80C2×C3⋊Dic3C4⋊C412yes—
81C4×C3⋊D3—44no—
82C4×C3⋊D3—44no—
83C4×C3⋊D3C22⋊C414yes—
84C4×C3⋊D3C22⋊C414yes—
85C4×C3⋊D3C4⋊C414yes—
86C4×C3⋊D3C4⋊C414yes—
87C32×C8—24no—
88C3⋊(C3⋊C8)—24no—
89C22×M16—92no—
90C22×C4⋊C4—91no—
91#343—92no—
92#343—91no—
93#343C3⋊D311yescharacteristic, direct product factor
94C23×D3—34no—
95C22×C3×C4C4×D318yes—
96C22×C3×C4C22×D314yes—
97C22×Dic3—34no—
98C22×Dic3—38no—
99C2×C4×D3—316no—
100C2×C4×D3—38no—
101C2×C4×D3—38no—
102C2×C4×D3—38no—
103C2×C4×D3—38no—
104C2×C4×D3—68no—
105C2×C4×D3—68no—
106C2×C4×D3—1216no—
107C3×M16—28no—
108C3×M16C4×D3116yescomplemented
109C2×C3×C8—28no—
110C3×C4⋊C4—28no—
111C4⋊Dic3—68no—
112Dic3⋊C4—616no—
113#208—316no—
114#208—68no—
115C2×C3⋊C8—68no—
116ΓL(1,𝔽25)—632no—
117D3×C8—632no—
118C22×C32—21no—
119C22×C32—21no—
120C22×C32C2×C4211yescharacteristic
121C22×C32C2×C22⋊C411yescharacteristic
122C22×C32C2×C4⋊C411yescharacteristic
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C2×C3⋊D3—24no—
126C2×C3⋊D3—24no—
127C2×C3⋊D3#9512yes—
128C2×C3⋊D3#9512yes—
129C2×C3⋊D3#10012yes—
130C2×C3⋊D3#10112yes—
131C32×C4—42no—
132C32×C4C2×C22⋊C412yes—
133C32×C4C2×C4⋊C412yes—
134C3⋊Dic3—42no—
135C3⋊Dic3#9514yes—
136C23×C4—91no—
137C23×C4—92no—
138C2×M16—92no—
139C2×M16—98no—
140C2×M16—182no—
141C2×M16—184no—
142C2×M16C2×C3⋊D312yes—
143C22×C8—182no—
144C2×C4⋊C4—92no—
145C2×C4⋊C4—91no—
146C2×C4⋊C4—182no—
147C2×C4⋊C4—182no—
148C2×C4⋊C4C2×C3⋊D311yescharacteristic
149C23×C3C2×C4×D314yes—
150C22×D3—34no—
151C22×D3—38no—
152C22×D3—34no—
153C22×D3—38no—
154C22×D3—68no—
155C22×D3—68no—
156C2×C3×C4—28no—
157C2×C3×C4—48no—
158C2×C3×C4C2×C4×D318yes—
159C2×C3×C4D3×D414yes—
160C2×C3×C4D3×D418yes—
161C2×C3×C4D3×Q814yes—
162C2×Dic3—38no—
163C2×Dic3—38no—
164C2×Dic3—38no—
165C2×Dic3—68no—
166C2×Dic3—128no—
167C4×D3—316no—
168C4×D3—316no—
169C4×D3—316no—
170C4×D3—316no—
171C4×D3—1216no—
172C4×D3—1216no—
173C3×C8—216no—
174C3⋊C8—616no—
175C2×C32—21no—
176C2×C32—21no—
177C2×C32C2×#9511yescharacteristic
178C2×C32C2×#10011yescharacteristic
179C2×C32C2×#10111yescharacteristic
180C3⋊D3—22no—
181C3⋊D3#34314yesdirect product factor
182C24—91no—
183C22×C4—91no—
184C22×C4—94no—
185C22×C4—92no—
186C22×C4—92no—
187C22×C4—92no—
188C22×C4—92no—
189C22×C4—92no—
190C22×C4—182no—
191C22×C4—182no—
192C22×C4—364no—
193C22×C4C4×C3⋊D312yes—
194C22×C4C22×C3⋊D311yescharacteristic
195M16—22no—
196M16—94no—
197M16—188no—
198M16—182no—
199M16C4×C3⋊D314yescomplemented
200C2×C8—22no—
201C2×C8—188no—
202C2×C8—182no—
203C4⋊C4—22no—
204C4⋊C4—184no—
205C4⋊C4—182no—
206C22×C3—24no—
207C22×C3—24no—
208C22×C3C42×D314yes—
209C22×C3D3×C22⋊C414yes—
210C22×C3D3×C4⋊C414yes—
211C2×D3—38no—
212C2×D3—38no—
213C2×D3—38no—
214C2×D3—38no—
215C2×D3—616no—
216C2×D3—616no—
217C2×D3—64no—
218C2×D3—64no—
219C3×C4—48no—
220C3×C4D3×C22⋊C418yes—
221C3×C4D3×C4⋊C418yes—
222Dic3—316no—
223Dic3—128no—
224C32C2×#34311yescharacteristic, complemented, Sylow
225C23—91no—
226C23—92no—
227C23—91no—
228C23—92no—
229C23—182no—
230C23—182no—
231C23C2×C4×C3⋊D311yescharacteristic
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—92no—
235C2×C4—92no—
236C2×C4—92no—
237C2×C4—94no—
238C2×C4—94no—
239C2×C4—94no—
240C2×C4—94no—
241C2×C4—182no—
242C2×C4—364no—
243C2×C4—364no—
244C2×C4—362no—
245C2×C4C2×C4×C3⋊D312yes—
246C2×C4D4×C3⋊D311yescharacteristic
247C2×C4D4×C3⋊D312yes—
248C2×C4Q8×C3⋊D311yescharacteristic
249C8—24no—
250C8—184no—
251C2×C3—24no—
252C2×C3—24no—
253C2×C3D3×#9514yes—
254C2×C3D3×#10014yes—
255C2×C3D3×#10114yes—
256D3—316no—
257D3—68no—
258C22—21no—
259C22—21no—
260C22—92no—
261C22—92no—
262C22—92no—
263C22—92no—
264C22—184no—
265C22—184no—
266C22—181no—
267C22—181no—
268C22C42×C3⋊D311yescharacteristic
269C22C22⋊C4×C3⋊D311yescharacteristic
270C22C4⋊C4×C3⋊D311yescharacteristic
271C4—42no—
272C4—94no—
273C4—362no—
274C4C22⋊C4×C3⋊D312yes—
275C4C4⋊C4×C3⋊D312yes—
276C3D3×#34314yescomplemented
277C2—21no—
278C2—21no—
279C2—94no—
280C2—182no—
281C2C3⋊D3×#9511yescharacteristic
282C2C3⋊D3×#10011yescharacteristic
283C2C3⋊D3×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C2×C42
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenter#343C3⋊D3
hypocenterC32C2×#343
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. C32×#343C2semidirect
4. #10589420C2semidirect
5. #10589396C2semidirect
15. M16×C3⋊D3C4semidirect
22. C3×#343D3semidirect
39. C32×M16C2×C4semidirect
45. #3748C2×C4semidirect
93. #343C3⋊D3direct (N × H)
108. C3×M16C4×D3semidirect
181. C3⋊D3#343direct (N × H)
199. M16C4×C3⋊D3semidirect
224. C32C2×#343semidirect
276. C3D3×#343semidirect

Maximal subgroups

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

subgroupindex
C2×M16×C3⋊D32
C2×C4⋊C4×C3⋊D32
C32×#3432
#105894202
#105893962
D3×#3433