Finite Group Databasebeta

← D3×#3754 #11723549

Subgroups — D3×#3754 #11723549

Order 864.

488 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C32×D3×D4C211yesmaximal, characteristic
2D3×#634C211yesmaximal, characteristic, complemented
3#88861C211yesmaximal, characteristic, complemented
4C3×#3754C211yesmaximal, characteristic, complemented
5#88794C211yesmaximal, characteristic, complemented
6#88792C211yesmaximal, characteristic, complemented
7D3×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#3754—31nomaximal
9D3×#214—34nomaximal
10C22×C32×D3—21no—
11C33×D4C2211yescharacteristic
12#6308C2211yescharacteristic, complemented
13C3×#634C2211yescharacteristic, complemented
14C32×#67—21no—
15C32×D12C2211yescharacteristic
16C32×C4×D3C2211yescharacteristic
17#6293—21no—
18D3×C3⋊Dic3—21no—
19C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
20C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
21C2×C32×D4—31no—
22C2×#634—31no—
23C3×D3×D4D314yes—
24D3×Dic6—34no—
25#3754—31no—
26#3754—34no—
27#3754—31no—
28#3754—31no—
29#3754—64no—
30#3754D311yescharacteristic, direct product factor
31C2×C3⋊(C3⋊C8)—31no—
32C3×#214—34no—
33#3716—34no—
34#3715—34no—
35D3×C3⋊C8—34no—
36C22×C33—21no—
37C2×C32×D3—21no—
38C2×C32×D3—42no—
39C2×C32×D3D411yescharacteristic
40C33×C4C2311yescharacteristic
41C3⋊(C3⋊Dic3)—21no—
42C3×C3⋊Dic3—21no—
43C32×Dic3D411yescharacteristic
44C2×#214—94no—
45D3×SD16—91no—
46C23×C32—61no—
47C22×C3×D3—24no—
48C32×D4—24no—
49C32×D4—31no—
50C32×D4—61no—
51C32×D4C2×D314yes—
52C32×D4C2×D311yescharacteristic
53C2×C32×C4—31no—
54C2×C3⋊Dic3—61no—
55#634—31no—
56#634—34no—
57#634—64no—
58#634—61no—
59#634C2×D311yescharacteristic, complemented
60C3×#67—24no—
61C3×D12C2×D314yes—
62C3×C4×D3C2×D314yes—
63C3×Dic6—34no—
64#627—64no—
65D3×Dic3—64no—
66C3⋊(C3⋊C8)—31no—
67C3⋊(C3⋊C8)—34no—
68C3⋊(C3⋊C8)—64no—
69C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
70C3×C3⋊C8—34no—
71C2×C33—41no—
72C2×C33C2×D411yescharacteristic
73C32×D3—41no—
74C32×D3SD1612yescomplemented
75C2×C3×D4—34no—
76D3×Q8—91no—
77D3×D4C3⋊D311yescharacteristic
78C2×Dic6—94no—
79C3×SD16—91no—
80#215—91no—
81#214—34no—
82#214—94no—
83#214—94no—
84#214—94no—
85#214—91no—
86#214—184no—
87C2×C3⋊C8—94no—
88#204—91no—
89D3×C8—91no—
90C22×C32—21no—
91C22×C32—24no—
92C22×C32—31no—
93C22×C32—44no—
94C22×C32—61no—
95C22×C32—122no—
96C2×C3×D3—24no—
97C2×C3×D3—48no—
98C2×C3×D3#6714yes—
99C32×C4—24no—
100C32×C4—31no—
101C32×C4C22×D314yes—
102C32×C4C22×D311yescharacteristic
103C3⋊Dic3—21no—
104C3⋊Dic3—61no—
105C3⋊Dic3—64no—
106C3⋊Dic3—124no—
107C3×Dic3—64no—
108C3×Dic3#6714yes—
109C2×SD16—271noSylow
110C33C2×SD1611yescharacteristic, complemented, Sylow
111C23×C3—64no—
112C22×D3—21no—
113C3×Q8—91no—
114C3×D4—24no—
115C3×D4—34no—
116C3×D4—64no—
117C3×D4D3214yes—
118C3×D4C2×C3⋊D311yescharacteristic
119C2×C3×C4—34no—
120#67—21no—
121C2×Dic3—184no—
122D12C2×C3⋊D311yescharacteristic
123C4×D3—181no—
124C4×D3C2×C3⋊D311yescharacteristic
125Dic6—34no—
126Dic6—94no—
127Dic6—91no—
128Dic6—184no—
129Dic6—184no—
130Dic6—181no—
131C3×C8—91no—
132C3⋊C8—34no—
133C3⋊C8—94no—
134C3⋊C8—91no—
135C3⋊C8—184no—
136C2×C32—24no—
137C2×C32—32no—
138C2×C32—41no—
139C2×C32—44no—
140C2×C32—84no—
141C2×C32—121no—
142C2×C32D3×D411yescharacteristic
143C2×C32C2×#6714yes—
144C3×D3—44no—
145C3×D3#21418yescomplemented
146C2×Q8—271no—
147C2×D4—31no—
148SD16—91no—
149SD16—271no—
150SD16—271no—
151SD16—271no—
152C2×C8—271no—
153C22×C3—24no—
154C22×C3—21no—
155C22×C3—34no—
156C22×C3—44no—
157C22×C3—64no—
158C22×C3—128no—
159C2×D3—21no—
160C2×D3—42no—
161C2×D3#63811yescharacteristic
162C3×C4—24no—
163C3×C4—34no—
164C3×C4—181no—
165C3×C4C2×D3214yes—
166C3×C4C22×C3⋊D311yescharacteristic
167Dic3—64no—
168Dic3—184no—
169Dic3—181no—
170Dic3—364no—
171Dic3#63811yescharacteristic
172C32—24no—
173C32D3×SD1611yescharacteristic, complemented
174C32C2×#21414yescomplemented
175C23—61no—
176Q8—91no—
177Q8—271no—
178Q8—541no—
179D4—31no—
180D4—61no—
181D4D3×C3⋊D311yescharacteristic
182C2×C4—31no—
183C2×C4—541no—
184C8—91no—
185C8—271no—
186C2×C3—24no—
187C2×C3—38no—
188C2×C3—41no—
189C2×C3—44no—
190C2×C3—84no—
191C2×C3—124no—
192C2×C3D3×#6714yes—
193C2×C3C2×#63811yescharacteristic
194D3—41no—
195D3#375412yesdirect product factor
196C22—21no—
197C22—31no—
198C22—61no—
199C22—122no—
200C4—31no—
201C4—181no—
202C4—541no—
203C4C2×D3×C3⋊D311yescharacteristic
204C3—24no—
205C3D3×#21414yescomplemented
206C3C2×#375411yescharacteristic, complemented
207C2—32no—
208C2—41no—
209C2—121no—
210C2D3×#63811yescharacteristic
subgroupG/H
centerC2D3×#638
commutator, cosocleC33×C4C23
FrattiniC4C2×D3×C3⋊D3
FittingC33×D4C22
socleC2×C33C2×D4
prime radicalC32×D3×D4C2
hypercenterD4D3×C3⋊D3
hypocenterC33C2×SD16
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
2. D3×#634C2semidirect
3. #88861C2semidirect
4. C3×#3754C2semidirect
5. #88794C2semidirect
6. #88792C2semidirect
7. D3×C3⋊(C3⋊C8)C2semidirect
12. #6308C22semidirect
13. C3×#634C22semidirect
19. C3⋊(C3⋊(C3⋊C8))C22semidirect
20. C3×C3⋊(C3⋊C8)C22semidirect
30. #3754D3direct (N × H)
59. #634C2×D3semidirect
69. C3⋊(C3⋊C8)C2×D3semidirect
74. C32×D3SD16semidirect
110. C33C2×SD16semidirect
145. C3×D3#214semidirect
173. C32D3×SD16semidirect
174. C32C2×#214semidirect
195. D3#3754direct (N × H)
205. C3D3×#214semidirect
206. C3C2×#3754semidirect

Maximal subgroups

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

subgroupindex
C32×D3×D42
D3×#6342
#888612
C3×#37542
#887942
#887922
D3×C3⋊(C3⋊C8)2
C2×#37543
D3×#2143