Finite Group Databasebeta

← D3×#63773 #13166402

Subgroups — D3×#63773 #13166402

Order 1728.

376 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 78 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×D3×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2#11723098C211yesmaximal, characteristic, complemented
3C3×#63773C211yesmaximal, characteristic, complemented
4#11722720C212yesmaximal, complemented
5D3×#3708C212yesmaximal, complemented
6C2×#63773—31nomaximal
7C2×C32×C4×D3C411yescharacteristic
8C2×C3⋊(C3⋊(C3⋊C8))C411yescharacteristic
9C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
10D3×C3⋊(C3⋊C8)C411yescharacteristic
11D3×C3⋊(C3⋊C8)C411yescharacteristic
12D3×C3⋊(C3⋊C8)C2211yescharacteristic
13D3×C3⋊(C3⋊C8)C2211yescharacteristic
14C3⋊#3708C2212yescomplemented
15C3×#3708C2212yescomplemented
16C22×C3⋊(C3⋊C8)—31no—
17C2×D3×C3⋊C8—62no—
18#63773—31no—
19#63773—32no—
20#63773D311yescharacteristic, direct product factor
21C2×#3708—32no—
22C22×C32×D3C811yescharacteristic
23C2×C33×C4C2×C411yescharacteristic
24C2×C32×Dic3C811yescharacteristic
25C32×C4×D3C811yescharacteristic
26C32×C4×D3C811yescharacteristic
27C32×C4×D3C2×C411yescharacteristic
28C32×C4×D3C2×C411yescharacteristic
29C3⋊(C3⋊(C3⋊C8))C2×C411yescharacteristic
30C3⋊(C3⋊(C3⋊C8))C2×C411yescharacteristic
31C3×C3⋊(C3⋊C8)C2×C411yescharacteristic
32C3×C3⋊(C3⋊C8)C2311yescharacteristic
33D3×M32—91nomaximal
34C22×C32×C4—31no—
35C2×C3×C4×D3—22no—
36C2×C3⋊(C3⋊C8)—31no—
37C2×C3⋊(C3⋊C8)—31no—
38C2×C3⋊(C3⋊C8)—31no—
39C2×C3⋊(C3⋊C8)—31no—
40C2×C3⋊(C3⋊C8)—31no—
41C2×C3⋊(C3⋊C8)—62no—
42C2×C3⋊(C3⋊C8)—122no—
43C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
44C2×C3×C3⋊C8—62no—
45D3×C3⋊C8—62no—
46D3×C3⋊C8—62no—
47D3×C3⋊C8—62no—
48D3×C3⋊C8—62no—
49#3708—32no—
50#3708C2×D312yescomplemented
51C22×C33C2×C811yescharacteristic
52C2×C32×D3—22no—
53C2×C32×D3C2×C811yescharacteristic
54C2×C32×D3C2×C811yescharacteristic
55C33×C4C2×C811yescharacteristic
56C33×C4C22×C411yescharacteristic
57C32×Dic3C2×C811yescharacteristic
58C32×Dic3C2×C811yescharacteristic
59C22×C3⋊C8—182no—
60C2×D3×C8—91no—
61C3×M32—91no—
62#812—91no—
63#798—92no—
64D3×C16—92no—
65C23×C32—31no—
66C22×C3×D3—22no—
67C2×C32×C4—22no—
68C2×C32×C4—31no—
69C2×C32×C4—31no—
70C2×C32×C4—31no—
71C2×C32×C4—31no—
72C2×C32×C4—31no—
73C2×C32×C4—42no—
74C2×C32×C4C4×D311yescharacteristic
75C2×C3×Dic3—22no—
76C3×C4×D3—22no—
77C3×C4×D3—22no—
78C3×C4×D3—22no—
79C3×C4×D3—22no—
80C3⋊(C3⋊C8)—31no—
81C3⋊(C3⋊C8)—31no—
82C3⋊(C3⋊C8)—62no—
83C3⋊(C3⋊C8)—62no—
84C3⋊(C3⋊C8)—122no—
85C3⋊(C3⋊C8)—122no—
86C3⋊(C3⋊C8)C4×D311yescharacteristic
87C3⋊(C3⋊C8)C22×D311yescharacteristic
88C3×C3⋊C8—62no—
89C3×C3⋊C8—62no—
90C2×M32—271noSylow
91C2×C33—21no—
92C2×C33C22×C811yescharacteristic
93C32×D3—21no—
94C32×D3M3212yescomplemented
95C22×C3×C4—62no—
96C2×C4×D3#15711yescharacteristic
97C2×C3×C8—91no—
98C2×C3⋊C8—62no—
99C2×C3⋊C8—91no—
100C2×C3⋊C8—182no—
101C2×C3⋊C8—182no—
102C2×C3⋊C8—182no—
103C2×C3⋊C8—182no—
104C2×C3⋊C8—182no—
105C2×C3⋊C8—362no—
106D3×C8—91no—
107D3×C8—91no—
108D3×C8—91no—
109D3×C8—91no—
110C3×C16—92no—
111C3⋊C16—92no—
112C22×C32—22no—
113C22×C32—31no—
114C22×C32—31no—
115C22×C32—42no—
116C22×C32—62no—
117C22×C32D3×C811yescharacteristic
118C2×C3×D3—28no—
119C2×C3×D3—22no—
120C2×C3×D3—22no—
121C32×C4—22no—
122C32×C4—22no—
123C32×C4—31no—
124C32×C4—31no—
125C32×C4—42no—
126C32×C4—42no—
127C32×C4D3×C811yescharacteristic
128C32×C4C2×C4×D311yescharacteristic
129C3×Dic3—22no—
130C3×Dic3—22no—
131C22×C8—271no—
132M32—91no—
133M32—272no—
134M32—271no—
135C2×C16—272no—
136C33C2×M3211yescharacteristic, complemented, Sylow
137C23×C3—62no—
138C22×D3#62211yescharacteristic
139C2×C3×C4—22no—
140C2×C3×C4—42no—
141C2×C3×C4—62no—
142C2×C3×C4—62no—
143C2×C3×C4—62no—
144C2×C3×C4—62no—
145C2×C3×C4—62no—
146C2×C3×C4C2×#15711yescharacteristic
147C2×Dic3#62211yescharacteristic
148C4×D3#62211yescharacteristic
149C4×D3#62211yescharacteristic
150C4×D3C2×#15711yescharacteristic
151C4×D3C2×#15711yescharacteristic
152C3×C8—91no—
153C3×C8—91no—
154C3⋊C8—62no—
155C3⋊C8—62no—
156C3⋊C8—91no—
157C3⋊C8—91no—
158C3⋊C8—182no—
159C3⋊C8—182no—
160C3⋊C8—362no—
161C3⋊C8—362no—
162C2×C32—21no—
163C2×C32—24no—
164C2×C32—22no—
165C2×C32—32no—
166C2×C32—44no—
167C2×C32—42no—
168C2×C32—61no—
169C2×C32C2×D3×C811yescharacteristic
170C3×D3—24no—
171C3×D3—24no—
172C22×C4—31no—
173C2×C8—91no—
174C2×C8—271no—
175C2×C8—271no—
176C2×C8—271no—
177C2×C8—271no—
178C2×C8—271no—
179C16—92no—
180C16—272no—
181C22×C3—22no—
182C22×C3—42no—
183C22×C3—62no—
184C22×C3—62no—
185C22×C3—68no—
186C22×C3C2×#62211yescharacteristic
187C2×D3—22no—
188C2×D3C2×#62211yescharacteristic
189C2×D3C2×#62211yescharacteristic
190C3×C4—22no—
191C3×C4—22no—
192C3×C4—42no—
193C3×C4—42no—
194C3×C4—62no—
195C3×C4—62no—
196C3×C4C2×#62211yescharacteristic
197C3×C4C22×#15711yescharacteristic
198Dic3C2×#62211yescharacteristic
199Dic3C2×#62211yescharacteristic
200C32—22no—
201C32—42no—
202C32D3×M3211yescharacteristic, complemented
203C23—31no—
204C2×C4—31no—
205C2×C4—31no—
206C2×C4—31no—
207C2×C4—31no—
208C2×C4—31no—
209C2×C4D3×#15711yescharacteristic
210C8—91no—
211C8—91no—
212C8—271no—
213C8—271no—
214C2×C3—24no—
215C2×C3—21no—
216C2×C3—22no—
217C2×C3—44no—
218C2×C3—42no—
219C2×C3—64no—
220C2×C3—64no—
221C2×C3C22×#62211yescharacteristic
222D3—21no—
223D3#6377312yesdirect product factor
224C22—31no—
225C22—31no—
226C22—62no—
227C22D3×#62211yescharacteristic
228C4—31no—
229C4—31no—
230C4D3×#62211yescharacteristic
231C4C2×D3×#15711yescharacteristic
232C3—22no—
233C3—42no—
234C3C2×#6377311yescharacteristic, complemented
235C2—21no—
236C2—32no—
237C2—61no—
238C2C2×D3×#62211yescharacteristic
subgroupG/H
center, FrattiniC4C2×D3×#157
commutator, socleC2×C33C22×C8
FittingC2×C33×C4C2×C4
prime radicalC22×C32×D3C8
cosocleC3×C3⋊(C3⋊C8)C23
hypercenterC2×C4D3×#157
hypocenterC33C2×M32
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723098C2semidirect
3. C3×#63773C2semidirect
4. #11722720C2semidirect
5. D3×#3708C2semidirect
14. C3⋊#3708C22semidirect
15. C3×#3708C22semidirect
20. #63773D3direct (N × H)
50. #3708C2×D3semidirect
94. C32×D3M32semidirect
136. C33C2×M32semidirect
202. C32D3×M32semidirect
223. D3#63773direct (N × H)
234. C3C2×#63773semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C3⋊(C3⋊C8)2
#117230982
C3×#637732
#117227202
D3×#37082
C2×#637733
D3×M329