Finite Group Databasebeta

← D3×#808 #10590570

Subgroups — D3×#808 #10590570

Order 576.

278 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C3×D3×C4⋊C4C211yesmaximal, characteristic
2D3×C4⋊Dic3C211yesmaximal, characteristic
3C2×D3×C3⋊C8C211yesmaximal, characteristic
4#63635C211yesmaximal, characteristic, complemented
5C3×#808C211yesmaximal, characteristic, complemented
6#63574C211yesmaximal, characteristic, complemented
7#63573C211yesmaximal, characteristic, complemented
8C2×#808—31nomaximal
9D3×#106—31nomaximal
10C2×C3×C4×D3—21no—
11C2×C3×C4×D3C2211yescharacteristic
12C2×D3×Dic3—21no—
13C32×C4⋊C4C2211yescharacteristic
14C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×C4⋊Dic3C2211yescharacteristic
17C3×C4⋊Dic3C2211yescharacteristic
18C3×Dic3⋊C4—21no—
19C2×C3×C3⋊C8C2211yescharacteristic
20Dic3⋊Dic3—21no—
21D3×C3⋊C8C414yescomplemented
22C2×C3×C4⋊C4—31no—
23C2×C4⋊Dic3—31no—
24C22×C3⋊C8—31no—
25C2×D3×C8—31no—
26D3×C4⋊C4—31no—
27D3×C4⋊C4D311yescharacteristic
28C3×#106—31no—
29#817—31no—
30#808—31no—
31#808—31no—
32#808—31no—
33#808—31no—
34#808—31no—
35#808—61no—
36#808D311yescharacteristic, direct product factor
37C22×C3×D3D411yescharacteristic
38C2×C32×C4—21no—
39C2×C32×C4C2311yescharacteristic
40C2×C3⋊Dic3—21no—
41C2×C3×Dic3—21no—
42C2×C3×Dic3—21no—
43C2×C3×Dic3D411yescharacteristic
44C3×C4×D3—42no—
45C3×C4×D3C2×C412yes—
46C3×C4×D3Q812yes—
47D3×Dic3—42no—
48C3⋊(C3⋊C8)C2×C412yescomplemented
49C3×C3⋊C8C2×C412yescomplemented
50C2×#106—91noSylow
51C22×C3×C4—31no—
52C22×C3×C4—61no—
53C22×Dic3—61no—
54C2×C4×D3—21no—
55C2×C4×D3—61no—
56C2×C4×D3C2×D311yescharacteristic
57C2×C3×C8—31no—
58C3×C4⋊C4—21no—
59C3×C4⋊C4—31no—
60C3×C4⋊C4—31no—
61C3×C4⋊C4—61no—
62C3×C4⋊C4C2×D311yescharacteristic
63C3×C4⋊C4C2×D311yescharacteristic
64C4⋊Dic3—31no—
65C4⋊Dic3—31no—
66C4⋊Dic3—61no—
67C4⋊Dic3—61no—
68C4⋊Dic3C2×D311yescharacteristic
69C4⋊Dic3C2×D311yescharacteristic
70Dic3⋊C4—21no—
71Dic3⋊C4—61no—
72C2×C3⋊C8—31no—
73C2×C3⋊C8—31no—
74C2×C3⋊C8—34no—
75C2×C3⋊C8—61no—
76C2×C3⋊C8C2×D311yescharacteristic
77D3×C8—34no—
78C22×C32C2×D411yescharacteristic
79C2×C3×D3C4⋊C412yes—
80C2×C3×D3SD1612yes—
81C2×C3×D3SD1612yes—
82C32×C4—41no—
83C32×C4C22×C411yescharacteristic
84C32×C4C2×Q811yescharacteristic
85C3⋊Dic3—41no—
86C3×Dic3—41no—
87C3×Dic3—41no—
88C3×Dic3C4⋊C412yes—
89C22×C8—91no—
90C2×C4⋊C4—31no—
91C2×C4⋊C4—91no—
92#106—31no—
93#106—91no—
94#106—91no—
95#106—91no—
96C23×C3—31no—
97C22×D3#6711yescharacteristic
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—31no—
102C2×C3×C4—32no—
103C2×C3×C4—32no—
104C2×C3×C4—41no—
105C2×C3×C4—61no—
106C2×C3×C4—61no—
107C2×C3×C4—122no—
108C2×C3×C4C22×D311yescharacteristic
109C2×C3×C4C22×D311yescharacteristic
110C2×Dic3—21no—
111C2×Dic3—21no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—121no—
115C2×Dic3—122no—
116C2×Dic3#6711yescharacteristic
117C4×D3—42no—
118C4×D3—122no—
119C4×D3Dic612yes—
120C4×D3C4×D312yes—
121C3×C8—32no—
122C3⋊C8—32no—
123C3⋊C8—32no—
124C3⋊C8—62no—
125C3⋊C8C4×D312yescomplemented
126C2×C32C2×C4⋊C411yescharacteristic
127C2×C32C2×SD1611yescharacteristic
128C2×C32C2×SD1611yescharacteristic
129C3×D3#10614yescomplemented
130C22×C4—31no—
131C22×C4—61no—
132C22×C4—181no—
133C2×C8—31no—
134C2×C8—94no—
135C2×C8—91no—
136C4⋊C4—31no—
137C4⋊C4—31no—
138C4⋊C4—61no—
139C4⋊C4—91no—
140C4⋊C4—181no—
141C4⋊C4D3211yescharacteristic
142C22×C3—21no—
143C22×C3—32no—
144C22×C3—32no—
145C22×C3—32no—
146C22×C3D3×D411yescharacteristic
147C22×C3C2×#6711yescharacteristic
148C2×D3Dic3⋊C412yes—
149C2×D3#21412yes—
150C2×D3#21512yes—
151C3×C4—21no—
152C3×C4—21no—
153C3×C4—32no—
154C3×C4—41no—
155C3×C4—41no—
156C3×C4—81no—
157C3×C4—121no—
158C3×C4—121no—
159C3×C4C2×Dic611yescharacteristic
160C3×C4C2×C4×D311yescharacteristic
161C3×C4C2×C4×D311yescharacteristic
162C3×C4D3×Q811yescharacteristic
163Dic3—41no—
164Dic3—41no—
165Dic3—121no—
166Dic3—121no—
167Dic3—241no—
168Dic3Dic3⋊C412yes—
169C32C2×#10611yescharacteristic, complemented, Sylow
170C23—31no—
171C2×C4—21no—
172C2×C4—31no—
173C2×C4—32no—
174C2×C4—32no—
175C2×C4—61no—
176C2×C4—61no—
177C2×C4—122no—
178C2×C4—181no—
179C2×C4—362no—
180C2×C4C2×D3211yescharacteristic
181C8—32no—
182C8—92no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3—21no—
186C2×C3—34no—
187C2×C3D3×C4⋊C411yescharacteristic
188C2×C3D3×SD1611yescharacteristic
189C2×C3D3×SD1611yescharacteristic
190C2×C3C2×Dic3⋊C411yescharacteristic
191C2×C3C2×#21411yescharacteristic
192C2×C3C2×#21511yescharacteristic
193D3#80814yesdirect product factor
194C22—32no—
195C22—32no—
196C22—32no—
197C22D3×#6711yescharacteristic
198C4—32no—
199C4—41no—
200C4—121no—
201C4—121no—
202C4—361no—
203C4D3×Dic611yescharacteristic
204C4C4×D3211yescharacteristic
205C3—21no—
206C3D3×#10611yescharacteristic, complemented
207C3C2×#80811yescharacteristic, complemented
208C2—34no—
209C2D3×Dic3⋊C411yescharacteristic
210C2D3×#21411yescharacteristic
211C2D3×#21511yescharacteristic
subgroupG/H
centerC22D3×#67
commutatorC32×C4C22×C4
FrattiniC2×C4C2×D32
FittingC32×C4⋊C4C22
socleC22×C32C2×D4
prime radicalC22×C3×D3D4
cosocleC2×C32×C4C23
hypercenterC4⋊C4D32
hypocenterC32C2×#106
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #63635C2semidirect
5. C3×#808C2semidirect
6. #63574C2semidirect
7. #63573C2semidirect
21. D3×C3⋊C8C4semidirect
36. #808D3direct (N × H)
48. C3⋊(C3⋊C8)C2×C4semidirect
49. C3×C3⋊C8C2×C4semidirect
125. C3⋊C8C4×D3semidirect
129. C3×D3#106semidirect
169. C32C2×#106semidirect
193. D3#808direct (N × H)
206. C3D3×#106semidirect
207. C3C2×#808semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊C42
D3×C4⋊Dic32
C2×D3×C3⋊C82
#636352
C3×#8082
#635742
#635732
C2×#8083
D3×#1063