Finite Group Databasebeta

← Dic3×#994 #11923389

Subgroups — Dic3×#994 #11923389

Order 1152.

795 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 795 conjugacy classes of subgroups — too many to draw. Only its 137 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×#994C211yesmaximal, characteristic
2#5827⋊C3C213yesmaximal, complemented
3Dic3×#41⋊C3C213yesmaximal, complemented
4Dic3×H(5,𝔽2)C311yesmaximal, characteristic, complemented
5C4×#994—31nomaximal
6C3×#994C414yescomplemented
7C2×C3×#41⋊C3C2213yes—
8C3×Q8×Dic3—41nomaximal
9Dic3×SL(2,𝔽3)C2211yescharacteristic, complemented
10Dic3×SL(2,𝔽3)C2213yescomplemented
11C2×C3×H(5,𝔽2)C2×C311yescharacteristic
12C2×#994—21no—
13C2×#994D311yescharacteristic
14#5827—31no—
15#5827C2×C313yes—
16Dic3×#41—31no—
17Dic3×#41C2×C313yes—
18#5798—33no—
19C2×D4×Dic3—33no—
20#520⋊C3—33no—
21C4×#41⋊C3—33no—
22C2×C32×Q8—41no—
23C3×#41⋊C3C2×C416yescomplemented
24C2×C3×SL(2,𝔽3)C2311yescharacteristic
25C3×C4⋊Dic3—43no—
26C3×C4×Dic3—43no—
27C4×H(5,𝔽2)—31noSylow
28C3×H(5,𝔽2)—34no—
29C3×H(5,𝔽2)C3×C414yescomplemented
30C2×C3×#41—31no—
31C2×C3×#41C22×C313yes—
32C22×C3×D4—33no—
33C23×Dic3—32no—
34#994—24no—
35#994Dic314yesdirect product factor
36C2×#41⋊C3—23no—
37C2×#41⋊C3C2×D313yes—
38C3×C4×Q8—121no—
39C2×#217—36no—
40Q8×Dic3—31no—
41Q8×Dic3A411yescharacteristic
42Q8×Dic3C22×C311yescharacteristic
43Q8×Dic3C22×C313yes—
44D4×Dic3—36no—
45D4×Dic3—33no—
46D4×Dic3—33no—
47D4×Dic3—36no—
48D4×Dic3—33no—
49D4×Dic3—33no—
50#926—33no—
51#926—33no—
52C2×C4⋊Dic3—33no—
53C2×C4×Dic3—33no—
54C4×SL(2,𝔽3)—31no—
55C4×SL(2,𝔽3)—33no—
56C32×Q8—44no—
57C2×C32×C4—43no—
58C2×C3×Dic3—41no—
59C2×C3×Dic3—43no—
60C3×SL(2,𝔽3)C22×C411yescharacteristic, complemented
61C2×H(5,𝔽2)C3×D311yescharacteristic
62#520—33no—
63#520—91no—
64#518—93no—
65C4×#41—33no—
66C4×#41—91no—
67C2×C4×D4—93no—
68C24×C3—32no—
69C3×#41—34no—
70C3×#41—34no—
71C3×#41—36no—
72C3×#41C2×C3×C416yes—
73C2×C3×Q8—41no—
74C2×C3×Q8—81no—
75C2×C3×Q8C2×A411yescharacteristic
76C2×C3×Q8C23×C311yescharacteristic
77C2×C3×D4—33no—
78C2×C3×D4—312no—
79C2×C3×D4—312no—
80C2×C3×D4—33no—
81C22×C3×C4—33no—
82C22×Dic3—36no—
83C22×Dic3—33no—
84C22×Dic3—33no—
85C22×Dic3—124no—
86#41⋊C3—26no—
87#41⋊C3C2×Dic316yescomplemented
88C2×SL(2,𝔽3)—21no—
89C2×SL(2,𝔽3)C22×D311yescharacteristic
90C3×C4⋊C4—123no—
91C3×C42—123no—
92#217—36no—
93#217—36no—
94C4⋊Dic3—33no—
95C4⋊Dic3—33no—
96C4⋊Dic3—31no—
97C4⋊Dic3C2×A413yes—
98C4×Dic3—33no—
99C4×Dic3—31no—
100C4×Dic3—33no—
101C4×Dic3C2×A413yes—
102C22×C32—41no—
103C32×C4—46no—
104C3×Dic3—42no—
105C3×Dic3—83no—
106H(5,𝔽2)—34no—
107H(5,𝔽2)C3×Dic314yescomplemented
108C2×#41—31no—
109C2×#41C2×C3×D313yes—
110C22×D4—33no—
111C23×C4—92no—
112C4×Q8—31no—
113C4×Q8—31no—
114C4×Q8—33no—
115C4×Q8—91no—
116C4×D4—93no—
117C4×D4—93no—
118C4×D4—96no—
119C4×D4—93no—
120C4×D4—93no—
121C4×D4—96no—
122#117—93no—
123#117—93no—
124C2×C4⋊C4—93no—
125C2×C22⋊C4—96no—
126C2×C42—93no—
127C23×C3—38no—
128C23×C3—33no—
129C23×C3—122no—
130C23×C3—122no—
131C3×Q8—31no—
132C3×Q8—44no—
133C3×Q8—84no—
134C3×Q8C4×A414yes—
135C3×Q8C22×C3×C411yescharacteristic
136C3×D4—36no—
137C3×D4—36no—
138C3×D4—312no—
139C2×C3×C4—31no—
140C2×C3×C4—36no—
141C2×C3×C4—36no—
142C2×C3×C4—43no—
143C2×C3×C4—83no—
144C2×C3×C4—121no—
145C2×C3×C4—123no—
146C2×C3×C4C22×A413yes—
147C2×Dic3—31no—
148C2×Dic3—33no—
149C2×Dic3—66no—
150C2×Dic3—123no—
151C2×Dic3—126no—
152C2×Dic3C22×A413yes—
153C2×Dic3C22×A411yescharacteristic
154SL(2,𝔽3)—21no—
155SL(2,𝔽3)C22×Dic311yescharacteristic, complemented
156C2×C32—41no—
157C2×C32—41no—
158C2×C32—41no—
159C24—32no—
160#41—34no—
161#41—34no—
162#41—36no—
163#41C2×C3×Dic316yes—
164C2×Q8D3×A411yescharacteristic
165C2×Q8C22×C3×D311yescharacteristic
166C2×D4—33no—
167C2×D4—312no—
168C2×D4—312no—
169C2×D4—33no—
170C22×C4—33no—
171C22×C4—93no—
172C22×C4—93no—
173C22×C4—96no—
174C22×C4—364no—
175C4⋊C4—33no—
176C4⋊C4—93no—
177C4⋊C4—91no—
178C4⋊C4—93no—
179C22⋊C4—96no—
180C22⋊C4—96no—
181C42—33no—
182C42—91no—
183C42—93no—
184C42—93no—
185C22×C3—36no—
186C22×C3—41no—
187C22×C3—63no—
188C22×C3—63no—
189C22×C3—81no—
190C22×C3—128no—
191C22×C3C23×A411yescharacteristic
192C3×C4—31no—
193C3×C4—31no—
194C3×C4—46no—
195C3×C4—86no—
196C3×C4—122no—
197C3×C4—243no—
198C3×C4C2×C4×A416yes—
199Dic3—23no—
200Dic3—63no—
201Dic3—61no—
202Dic3#99412yesdirect product factor
203C32—41noSylow
204C23—38no—
205C23—33no—
206C23—122no—
207C23—122no—
208Q8—31no—
209Q8Dic3×A414yes—
210Q8C22×C3×Dic311yescharacteristic
211D4—36no—
212D4—36no—
213D4—312no—
214C2×C4—31no—
215C2×C4—31no—
216C2×C4—36no—
217C2×C4—36no—
218C2×C4—33no—
219C2×C4—91no—
220C2×C4—93no—
221C2×C4—186no—
222C2×C4—363no—
223C2×C4—366no—
224C2×C4C2×D3×A413yes—
225C2×C3—41no—
226C2×C3—41no—
227C2×C3—41no—
228C2×C3—66no—
229C2×C3—81no—
230C2×C3—81no—
231C2×C3—81no—
232C2×C3C22×C4×A411yescharacteristic
233C2×C3C2×#99411yescharacteristic
234C2×C3#594511yescharacteristic
235C22—36no—
236C22—63no—
237C22—63no—
238C22—128no—
239C22C22×D3×A411yescharacteristic
240C4—32no—
241C4—31no—
242C4—31no—
243C4—63no—
244C4—183no—
245C4—181no—
246C4C2×Dic3×A416yes—
247C3—41no—
248C3—81no—
249C3C4×#99411yescharacteristic, complemented
250C2—66no—
251C2D3×#99411yescharacteristic
252C2#1059662311yescharacteristic
253C2C22×Dic3×A411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, hypocenterC3×Q8C22×C3×C4
FittingC2×C3×H(5,𝔽2)C2×C3
socleC22×C3C23×A4
prime radicalC2×C3×#994C2
cosocleC2×C3×Q8C23×C3
hypercenterC2×Q8D3×A4
LCSG ▷ C3×Q8
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #5827⋊C3C2semidirect
3. Dic3×#41⋊C3C2semidirect
4. Dic3×H(5,𝔽2)C3semidirect
6. C3×#994C4semidirect
9. Dic3×SL(2,𝔽3)C22semidirect
10. Dic3×SL(2,𝔽3)C22semidirect
23. C3×#41⋊C3C2×C4semidirect
29. C3×H(5,𝔽2)C3×C4semidirect
35. #994Dic3direct (N × H)
60. C3×SL(2,𝔽3)C22×C4semidirect
87. #41⋊C3C2×Dic3semidirect
107. H(5,𝔽2)C3×Dic3semidirect
155. SL(2,𝔽3)C22×Dic3semidirect
202. Dic3#994direct (N × H)
249. C3C4×#994semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9942
#5827⋊C32
Dic3×#41⋊C32
Dic3×H(5,𝔽2)3
C4×#9943
C3×Q8×Dic34