Finite Group Databasebeta

← Dic3⋊(#131⋊C3) #11921333

Subgroups — Dic3⋊(#131⋊C3) #11921333

Order 1152.

287 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 287 conjugacy classes of subgroups — too many to draw. Only its 59 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×C3×#131⋊C3C211yesmaximal, characteristic
2Dic3×#41⋊C3C211yesmaximal, characteristic
3C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic
4#83783C311yesmaximal, characteristic, complemented
5C4⋊(#131⋊C3)—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3×#131⋊C3—21no—
8C3⋊(#131⋊C3)—21no—
9Dic3×SL(2,𝔽3)C411yescharacteristic
10Dic3×SL(2,𝔽3)C411yescharacteristic
11C3×Dic3⋊C8—41nomaximal
12C2×C3×#131C2×C311yescharacteristic
13Dic3×#41C2×C311yescharacteristic
14C2×#948C2×C311yescharacteristic
15C2×#131⋊C3—21no—
16C2×#131⋊C3—31no—
17C2×#131⋊C3D311yescharacteristic
18C4×#41⋊C3—31no—
19#5119—31no—
20#5118—31no—
21#5102—31no—
22C2×Dic3⋊C8—31no—
23C3×#41⋊C3D411yescharacteristic
24C3×#41⋊C3Q811yescharacteristic
25C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
26C2×C32×C8—41no—
27C3×C4×Dic3—41no—
28C2×C3×C3⋊C8—41no—
29#2906—31noSylow
30C2×C3×#41C22×C311yescharacteristic
31C2×#41⋊C3—21no—
32C2×#41⋊C3C2×D311yescharacteristic
33C3×#131—21no—
34C3×#131—61no—
35C2×C3×M16—31no—
36C22×C3×C8—31no—
37#948—21no—
38#948—61no—
39Q8×Dic3C3×C411yescharacteristic
40Q8×Dic3C3×C411yescharacteristic
41D4×Dic3—31no—
42D4×Dic3—31no—
43#926—31no—
44C2×C4×Dic3—31no—
45C2×#208—31no—
46C22×C3⋊C8—31no—
47#131⋊C3—22no—
48#131⋊C3—21no—
49#131⋊C3—61no—
50C4×SL(2,𝔽3)—31no—
51C4×SL(2,𝔽3)—31no—
52C3×C4⋊C8—121no—
53Dic3⋊C8—32no—
54Dic3⋊C8—31no—
55Dic3⋊C8—31no—
56Dic3⋊C8—31no—
57Dic3⋊C8A411yescharacteristic
58C2×C32×C4—41no—
59C2×C3×Dic3—41no—
60C2×C3×Dic3—41no—
61C3×SL(2,𝔽3)C4⋊C411yescharacteristic
62C32×C8—81no—
63C3×C3⋊C8—81no—
64C2×#131—31no—
65C2×#131C3×D311yescharacteristic
66C4×#41—31no—
67#424—91no—
68#424—91no—
69#423—91no—
70C2×C4⋊C8—91no—
71C3×#41—31no—
72C3×#41—31no—
73C3×#41C3×D411yescharacteristic
74C3×#41C3×Q811yescharacteristic
75C2×C3×Q8C2×C3×C411yescharacteristic
76C2×C3×D4—31no—
77C22×C3×C4—31no—
78C22×Dic3—31no—
79C22×Dic3—31no—
80#41⋊C3—21no—
81#41⋊C3—21no—
82#41⋊C3Dic611yescharacteristic
83#41⋊C3#6711yescharacteristic
84C2×SL(2,𝔽3)—21no—
85C2×SL(2,𝔽3)C4×D311yescharacteristic
86C3×M16—61no—
87C3×M16—61no—
88C2×C3×C8—31no—
89C2×C3×C8—41no—
90C2×C3×C8—61no—
91C2×C3×C8—61no—
92C2×C3×C8—81no—
93C2×C3×C8—121no—
94C2×C3×C8C2×A411yescharacteristic
95C3×C42—121no—
96#217—32no—
97C4⋊Dic3—31no—
98C4⋊Dic3—31no—
99C4×Dic3—31no—
100C4×Dic3—31no—
101C4×Dic3—31no—
102C4×Dic3C2×A411yescharacteristic
103#208—61no—
104#208—61no—
105C2×C3⋊C8—31no—
106C2×C3⋊C8—61no—
107C2×C3⋊C8—61no—
108C2×C3⋊C8C2×A411yescharacteristic
109C22×C32—41no—
110C32×C4—41no—
111C32×C4—41no—
112C3×Dic3—42no—
113C3×Dic3—81no—
114C2×#41C2×C3×D311yescharacteristic
115#131—21no—
116#131—61no—
117#131—61no—
118#131—181no—
119C2×M16—31no—
120C2×M16—91no—
121C22×C8—31no—
122C22×C8—91no—
123C4×Q8—31no—
124C4×Q8—31no—
125C4×D4—91no—
126C4×D4—91no—
127#117—91no—
128C2×C42—91no—
129C4⋊C8—31no—
130C4⋊C8—91no—
131C4⋊C8—91no—
132C4⋊C8—92no—
133C4⋊C8—91no—
134C23×C3—31no—
135C3×Q8—31no—
136C3×Q8C3×C4⋊C411yescharacteristic
137C3×D4—31no—
138C3×D4—31no—
139C3×D4—32no—
140C2×C3×C4—31no—
141C2×C3×C4—31no—
142C2×C3×C4—31no—
143C2×C3×C4—31no—
144C2×C3×C4—31no—
145C2×C3×C4—41no—
146C2×C3×C4—81no—
147C2×C3×C4—121no—
148C2×C3×C4—121no—
149C2×C3×C4C22×A411yescharacteristic
150C2×Dic3—31no—
151C2×Dic3—31no—
152C2×Dic3—62no—
153C2×Dic3—121no—
154C2×Dic3C4×A411yescharacteristic
155C2×Dic3C4×A411yescharacteristic
156SL(2,𝔽3)—21no—
157SL(2,𝔽3)Dic3⋊C411yescharacteristic
158C3×C8—21no—
159C3×C8—61no—
160C3×C8—81no—
161C3×C8—82no—
162C3×C8—241no—
163C3⋊C8—21no—
164C3⋊C8—61no—
165C2×C32—41no—
166C2×C32—41no—
167C2×C32—41no—
168#41—31no—
169#41—31no—
170#41C3×Dic611yescharacteristic
171#41C3×#6711yescharacteristic
172C2×Q8C3×C4×D311yescharacteristic
173C2×D4—31no—
174C22×C4—31no—
175C22×C4—91no—
176C22×C4—91no—
177M16—61no—
178M16—61no—
179M16—181no—
180M16—181no—
181C2×C8—31no—
182C2×C8—31no—
183C2×C8—61no—
184C2×C8—61no—
185C2×C8—91no—
186C2×C8—181no—
187C2×C8—181no—
188C2×C8D3×A411yescharacteristic
189C4⋊C4—91no—
190C4⋊C4—91no—
191C22⋊C4—92no—
192C42—31no—
193C42—91no—
194C42—91no—
195C42—91no—
196C22×C3—31no—
197C22×C3—31no—
198C22×C3—41no—
199C22×C3—61no—
200C22×C3—61no—
201C22×C3—81no—
202C22×C3C2×C4×A411yescharacteristic
203C3×C4—31no—
204C3×C4—31no—
205C3×C4—41no—
206C3×C4—41no—
207C3×C4—81no—
208C3×C4—81no—
209C3×C4—122no—
210C3×C4—241no—
211C3×C4D4×A411yescharacteristic
212C3×C4Q8×A411yescharacteristic
213Dic3—21no—
214Dic3—61no—
215Dic3—61no—
216Dic3#131⋊C312yescomplemented
217C32—41noSylow
218C23—31no—
219Q8—31no—
220Q8C3×Dic3⋊C411yescharacteristic
221D4—31no—
222D4—31no—
223D4—32no—
224C2×C4—31no—
225C2×C4—31no—
226C2×C4—31no—
227C2×C4—31no—
228C2×C4—31no—
229C2×C4—31no—
230C2×C4—31no—
231C2×C4—91no—
232C2×C4—91no—
233C2×C4—182no—
234C2×C4—361no—
235C2×C4C2×D3×A411yescharacteristic
236C8—21no—
237C8—61no—
238C8—61no—
239C8—181no—
240C2×C3—41no—
241C2×C3—41no—
242C2×C3—41no—
243C2×C3—61no—
244C2×C3—61no—
245C2×C3—81no—
246C2×C3—81no—
247C2×C3—81no—
248C2×C3A4×C4⋊C411yescharacteristic
249C2×C3C2×#131⋊C311yescharacteristic
250C2×C3#568⋊C311yescharacteristic
251C22—31no—
252C22—31no—
253C22—61no—
254C22—61no—
255C22C4×D3×A411yescharacteristic
256C4—32no—
257C4—31no—
258C4—31no—
259C4—61no—
260C4—181no—
261C4—181no—
262C4A4×Dic611yescharacteristic
263C4A4×#6711yescharacteristic
264C3—41no—
265C3—81no—
266C3C4⋊(#131⋊C3)11yescharacteristic, complemented
267C2—61no—
268C2—61no—
269C2D3×#131⋊C311yescharacteristic
270C2#5750⋊C311yescharacteristic
271C2A4×Dic3⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D3×A4
commutatorC2×C3×Q8C2×C3×C4
FittingC2×C3×#131C2×C3
socleC22×C3C2×C4×A4
prime radicalC2×C3×#41⋊C3C22
cosocleC2×C3×#41C22×C3
hypercenterC2×C8D3×A4
hypocenterC3×Q8C3×C4⋊C4
LCSG ▷ C2×C3×Q8 ▷ C3×Q8
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
4. #83783C3semidirect
216. Dic3#131⋊C3semidirect
266. C3C4⋊(#131⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#131⋊C32
Dic3×#41⋊C32
C2×C3⋊(#131⋊C3)2
#837833
C4⋊(#131⋊C3)3
C3×Dic3⋊C84