Finite Group Databasebeta

← C3⋊D3×#324 #11773726

Subgroups — C3⋊D3×#324 #11773726

Order 1152.

984 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 984 conjugacy classes of subgroups — too many to draw. Only its 163 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×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C3⋊D3×C22⋊C8C212yesmaximal
3C32×#324C211yesmaximal, characteristic, complemented
4#10589394C211yesmaximal, characteristic, complemented
5#10589335C212yesmaximal, complemented
6D3×#324—34nomaximal
7C22×C4×C3⋊D3C411yescharacteristic
8C22×C4×C3⋊D3C411yescharacteristic
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C411yescharacteristic
12C2×#3750C411yescharacteristic
13C2×#3750C2211yescharacteristic
14C2×C8×C3⋊D3—22no—
15C4⋊C4×C3⋊D3—22no—
16C4⋊C4×C3⋊D3—22no—
17C32×C22⋊C8C2212yes—
18#63657C2212yes—
19#63647—22no—
20C2×D3×C4⋊C4—34no—
21D3×C22⋊C8—38no—
22C3×#324D314yescomplemented
23#4528—34no—
24#4469—38no—
25C23×C3⋊D3C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3—42no—
38C2×C4×C3⋊D3—42no—
39C2×C4×C3⋊D3C814yescomplemented
40C2×C4×C3⋊D3D412yes—
41C2×C4×C3⋊D3D412yes—
42C2×C32×C8—22no—
43C32×C4⋊C4—22no—
44C4⋊(C3⋊Dic3)—22no—
45#3750—22no—
46#3750—22no—
47C2×C3⋊(C3⋊C8)—22no—
48C8×C3⋊D3—44no—
49C2×#324—91noSylow
50C22×C4×D3—34no—
51C22×C4×D3—34no—
52C22×C4×D3—34no—
53C2×C3×C4⋊C4C2×D314yes—
54C2×C4⋊Dic3—34no—
55C2×Dic3⋊C4—34no—
56C2×Dic3⋊C4—34no—
57C2×D3×C8—68no—
58D3×C4⋊C4—68no—
59D3×C4⋊C4—68no—
60C3×C22⋊C8C2×D318yes—
61#830—38no—
62(C2×D3)⋊C8—68no—
63C23×C32C22×C411yescharacteristic
64C22×C3⋊D3—22no—
65C22×C3⋊D3—22no—
66C22×C3⋊D3C22⋊C411yescharacteristic
67C22×C3⋊D3C22⋊C411yescharacteristic
68C22×C3⋊D3C2×C812yes—
69C22×C3⋊D3M1612yes—
70C2×C32×C4—21no—
71C2×C32×C4—21no—
72C2×C32×C4—21no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4C2×C812yescomplemented
76C2×C32×C4C2×D412yes—
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3C22⋊C412yes—
83C2×C3⋊Dic3C2×C812yescomplemented
84C4×C3⋊D3—24no—
85C4×C3⋊D3—24no—
86C4×C3⋊D3—24no—
87C4×C3⋊D3—42no—
88C4×C3⋊D3—42no—
89C4×C3⋊D3—42no—
90C32×C8—42no—
91C3⋊(C3⋊C8)—42no—
92C22×C4⋊C4—91no—
93C2×C22⋊C8—92no—
94#324—91no—
95#324—92no—
96#324C3⋊D311yescharacteristic, direct product factor
97C23×D3—34no—
98C22×C3×C4C4×D314yes—
99C22×C3×C4C4×D314yes—
100C22×C3×C4C22×D314yes—
101C22×Dic3—34no—
102C22×Dic3—34no—
103C22×Dic3—34no—
104C2×C4×D3—316no—
105C2×C4×D3—38no—
106C2×C4×D3—38no—
107C2×C4×D3—64no—
108C2×C4×D3—64no—
109C2×C4×D3—68no—
110C2×C4×D3—64no—
111C2×C4×D3—64no—
112C2×C4×D3—128no—
113C2×C4×D3—128no—
114C2×C3×C8—28no—
115C3×C4⋊C4—28no—
116C4⋊Dic3—68no—
117Dic3⋊C4—68no—
118Dic3⋊C4—68no—
119C2×C3⋊C8—68no—
120D3×C8—1216no—
121C22×C32—21no—
122C22×C32—21no—
123C22×C32C2×C22⋊C411yescharacteristic
124C22×C32C22×C811yescharacteristic
125C22×C32C2×M1611yescharacteristic
126C2×C3⋊D3—21no—
127C2×C3⋊D3—21no—
128C2×C3⋊D3—24no—
129C2×C3⋊D3—24no—
130C2×C3⋊D3C22⋊C812yes—
131C2×C3⋊D3C22⋊C812yes—
132C2×C3⋊D3#9912yes—
133C2×C3⋊D3#10112yes—
134C32×C4—22no—
135C32×C4—22no—
136C32×C4—41no—
137C3⋊Dic3—22no—
138C3⋊Dic3—22no—
139C3⋊Dic3—41no—
140C23×C4—91no—
141C23×C4—91no—
142C23×C4—91no—
143C22×C8—182no—
144C2×C4⋊C4—91no—
145C2×C4⋊C4—91no—
146C2×C4⋊C4—91no—
147C2×C4⋊C4—182no—
148C2×C4⋊C4—182no—
149C2×C4⋊C4C2×C3⋊D311yescharacteristic
150C22⋊C8—92no—
151C22⋊C8—182no—
152C22⋊C8C2×C3⋊D312yes—
153C23×C3C2×C4×D314yes—
154C22×D3—34no—
155C22×D3—34no—
156C22×D3—38no—
157C22×D3—38no—
158C22×D3—68no—
159C22×D3—68no—
160C2×C3×C4—24no—
161C2×C3×C4—24no—
162C2×C3×C4—24no—
163C2×C3×C4—44no—
164C2×C3×C4—44no—
165C2×C3×C4D3×C818yescomplemented
166C2×C3×C4D3×D418yes—
167C2×Dic3—38no—
168C2×Dic3—38no—
169C2×Dic3—64no—
170C2×Dic3—64no—
171C2×Dic3—64no—
172C2×Dic3—124no—
173C2×Dic3—124no—
174C4×D3—616no—
175C4×D3—616no—
176C4×D3—616no—
177C4×D3—128no—
178C4×D3—128no—
179C4×D3—128no—
180C3×C8—48no—
181C3⋊C8—128no—
182C2×C32—21no—
183C2×C32—21no—
184C2×C32C2×C22⋊C811yescharacteristic
185C2×C32C2×#9911yescharacteristic
186C2×C32C2×#10111yescharacteristic
187C3⋊D3—22no—
188C3⋊D3#32414yesdirect product factor
189C24—91no—
190C22×C4—91no—
191C22×C4—91no—
192C22×C4—94no—
193C22×C4—92no—
194C22×C4—92no—
195C22×C4—91no—
196C22×C4—181no—
197C22×C4—181no—
198C22×C4—182no—
199C22×C4—181no—
200C22×C4—181no—
201C22×C4—362no—
202C22×C4—362no—
203C22×C4C4×C3⋊D311yescharacteristic
204C22×C4C4×C3⋊D311yescharacteristic
205C22×C4C22×C3⋊D311yescharacteristic
206C2×C8—22no—
207C2×C8—182no—
208C2×C8—364no—
209C4⋊C4—22no—
210C4⋊C4—182no—
211C4⋊C4—182no—
212C4⋊C4—182no—
213C22×C3—24no—
214C22×C3—24no—
215C22×C3D3×C22⋊C414yes—
216C22×C3C2×D3×C814yes—
217C22×C3D3×M1614yes—
218C2×D3—38no—
219C2×D3—38no—
220C2×D3—38no—
221C2×D3—38no—
222C2×D3—616no—
223C2×D3—616no—
224C2×D3—64no—
225C2×D3—64no—
226C3×C4—28no—
227C3×C4—28no—
228C3×C4—44no—
229Dic3—68no—
230Dic3—68no—
231Dic3—124no—
232C32C2×#32411yescharacteristic, complemented, Sylow
233C23—91no—
234C23—91no—
235C23—92no—
236C23—92no—
237C23—182no—
238C23—182no—
239C23C2×C4×C3⋊D311yescharacteristic
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—92no—
246C2×C4—92no—
247C2×C4—184no—
248C2×C4—184no—
249C2×C4—184no—
250C2×C4—181no—
251C2×C4—181no—
252C2×C4—181no—
253C2×C4—362no—
254C2×C4—362no—
255C2×C4—362no—
256C2×C4—361no—
257C2×C4—361no—
258C2×C4C8×C3⋊D312yescomplemented
259C2×C4D4×C3⋊D312yes—
260C8—42no—
261C8—362no—
262C2×C3—24no—
263C2×C3—24no—
264C2×C3D3×C22⋊C814yes—
265C2×C3D3×#9914yes—
266C2×C3D3×#10114yes—
267D3—316no—
268D3—68no—
269C22—21no—
270C22—21no—
271C22—92no—
272C22—92no—
273C22—92no—
274C22—92no—
275C22—184no—
276C22—184no—
277C22—181no—
278C22—181no—
279C22C22⋊C4×C3⋊D311yescharacteristic
280C22C2×C8×C3⋊D311yescharacteristic
281C22M16×C3⋊D311yescharacteristic
282C4—22no—
283C4—22no—
284C4—41no—
285C4—182no—
286C4—182no—
287C4—361no—
288C3D3×#32414yescomplemented
289C2—21no—
290C2—21no—
291C2—94no—
292C2—182no—
293C2C3⋊D3×C22⋊C811yescharacteristic
294C2C3⋊D3×#9911yescharacteristic
295C2C3⋊D3×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C22×C8
FrattiniC22×C4C22×C3⋊D3
FittingC32×#324C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenter#324C3⋊D3
hypocenterC32C2×#324
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
3. C32×#324C2semidirect
4. #10589394C2semidirect
5. #10589335C2semidirect
22. C3×#324D3semidirect
39. C2×C4×C3⋊D3C8semidirect
75. C2×C32×C4C2×C8semidirect
83. C2×C3⋊Dic3C2×C8semidirect
96. #324C3⋊D3direct (N × H)
165. C2×C3×C4D3×C8semidirect
188. C3⋊D3#324direct (N × H)
232. C32C2×#324semidirect
258. C2×C4C8×C3⋊D3semidirect
288. C3D3×#324semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C3⋊D3×C22⋊C82
C32×#3242
#105893942
#105893352
D3×#3243