Finite Group Databasebeta

← C3×#1468 #72183

Subgroups — C3×#1468 #72183

Order 384.

280 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 92 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×#123C211yesmaximal, characteristic
2C3×#407C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊C8C211yesmaximal, characteristic, complemented
4C3×#324C212yesmaximal, complemented
5C3×#323C212yesmaximal, complemented
6#1468C311yesmaximal, characteristic, direct product factor, Sylow
7C22×C3×D4C411yescharacteristic
8C23×C3×C4C2211yescharacteristic
9C2×C3×M16—21no—
10C22×C3×C8—21no—
11C3×#123—21no—
12C3×#123—21no—
13C3×#123—21no—
14C3×#123—21no—
15C2×C3×C4⋊C4C411yescharacteristic
16C2×C3×C4⋊C4C2211yescharacteristic
17C2×C3×C22⋊C4C411yescharacteristic
18C2×C3×C22⋊C4C411yescharacteristic
19C2×C3×C22⋊C4C2211yescharacteristic
20C3×C22⋊C8—21no—
21C3×C22⋊C8—21no—
22C3×C22⋊C8C2212yes—
23C3×C22⋊C8C2212yes—
24C2×#123C2×C311yescharacteristic
25#407C2×C311yescharacteristic, complemented
26C2×C22⋊C8C2×C311yescharacteristic, complemented
27#324C2×C312yescomplemented
28#323C2×C312yescomplemented
29C24×C3C2×C411yescharacteristic
30C24×C3C2×C411yescharacteristic
31C2×C3×D4—21no—
32C2×C3×D4—21no—
33C2×C3×D4—42no—
34C22×C3×C4—42no—
35C22×C3×C4C2×C411yescharacteristic
36C22×C3×C4C2×C411yescharacteristic
37C22×C3×C4C2×C411yescharacteristic
38C22×C3×C4C2×C411yescharacteristic
39C22×C3×C4D411yescharacteristic
40C22×C3×C4D411yescharacteristic
41C22×C3×C4D411yescharacteristic
42C22×C3×C4D411yescharacteristic
43C22×C3×C4C2311yescharacteristic
44C3×M16—42no—
45C2×C3×C8—22no—
46C2×C3×C8—22no—
47C2×C3×C8—42no—
48C3×C4⋊C4—21no—
49C3×C4⋊C4—21no—
50C3×C4⋊C4—21no—
51C3×C4⋊C4—21no—
52C3×C22⋊C4—21no—
53C3×C22⋊C4—21no—
54C3×C22⋊C4—21no—
55C3×C22⋊C4—21no—
56C3×C22⋊C4—21no—
57C3×C22⋊C4—21no—
58C22×D4C3×C411yescharacteristic
59C23×C4C22×C311yescharacteristic
60C2×M16—21no—
61C22×C8—21no—
62#123—21no—
63#123—21no—
64#123—21no—
65#123—21no—
66C2×C4⋊C4C3×C411yescharacteristic
67C2×C4⋊C4C22×C311yescharacteristic
68C2×C22⋊C4C3×C411yescharacteristic
69C2×C22⋊C4C3×C411yescharacteristic
70C2×C22⋊C4C22×C311yescharacteristic
71C22⋊C8—21no—
72C22⋊C8—21no—
73C22⋊C8C22×C312yes—
74C22⋊C8C22×C312yes—
75C23×C3—22no—
76C23×C3—22no—
77C23×C3—21no—
78C23×C3—22no—
79C23×C3—41no—
80C23×C3—41no—
81C23×C3—41no—
82C23×C3C22⋊C411yescharacteristic
83C23×C3C22⋊C411yescharacteristic
84C23×C3C22×C411yescharacteristic
85C3×D4—42no—
86C3×D4—42no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—21no—
90C2×C3×C4—21no—
91C2×C3×C4—21no—
92C2×C3×C4—22no—
93C2×C3×C4—41no—
94C2×C3×C4—41no—
95C2×C3×C4—41no—
96C2×C3×C4—41no—
97C2×C3×C4—41no—
98C2×C3×C4—41no—
99C2×C3×C4C22⋊C411yescharacteristic
100C2×C3×C4C22⋊C411yescharacteristic
101C2×C3×C4C2×D411yescharacteristic
102C2×C3×C4C2×D411yescharacteristic
103C3×C8—42no—
104C3×C8—42no—
105C24C2×C3×C411yescharacteristic
106C24C2×C3×C411yescharacteristic
107C2×D4—21no—
108C2×D4—21no—
109C2×D4—42no—
110C22×C4—42no—
111C22×C4C2×C3×C411yescharacteristic
112C22×C4C2×C3×C411yescharacteristic
113C22×C4C2×C3×C411yescharacteristic
114C22×C4C2×C3×C411yescharacteristic
115C22×C4C3×D411yescharacteristic
116C22×C4C3×D411yescharacteristic
117C22×C4C3×D411yescharacteristic
118C22×C4C3×D411yescharacteristic
119C22×C4C23×C311yescharacteristic
120M16—42no—
121C2×C8—22no—
122C2×C8—22no—
123C2×C8—42no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C22⋊C4—21no—
129C22⋊C4—21no—
130C22⋊C4—21no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22×C3—21no—
135C22×C3—21no—
136C22×C3—21no—
137C22×C3—21no—
138C22×C3—21no—
139C22×C3—21no—
140C22×C3—21no—
141C22×C3—44no—
142C22×C3—41no—
143C22×C3—41no—
144C22×C3—41no—
145C22×C3—82no—
146C22×C3#9912yes—
147C22×C3C2×C22⋊C411yescharacteristic
148C22×C3#13112yes—
149C3×C4—21no—
150C3×C4—21no—
151C3×C4—21no—
152C3×C4—21no—
153C3×C4—41no—
154C3×C4—41no—
155C3×C4—41no—
156C23—22no—
157C23—22no—
158C23—21no—
159C23—22no—
160C23—41no—
161C23—41no—
162C23—41no—
163C23C3×C22⋊C411yescharacteristic
164C23C3×C22⋊C411yescharacteristic
165C23C22×C3×C411yescharacteristic
166D4—42no—
167D4—42no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4C3×C22⋊C411yescharacteristic
181C2×C4C3×C22⋊C411yescharacteristic
182C2×C4C2×C3×D411yescharacteristic
183C2×C4C2×C3×D411yescharacteristic
184C8—42no—
185C8—42no—
186C2×C3—22no—
187C2×C3—22no—
188C2×C3—41no—
189C2×C3—81no—
190C2×C3#40811yescharacteristic
191C2×C3C2×#9911yescharacteristic
192C2×C3#41311yescharacteristic
193C22—21no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—44no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—82no—
205C22C3×#9912yes—
206C22C2×C3×C22⋊C411yescharacteristic
207C22C3×#13112yes—
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—41no—
213C4—41no—
214C4—41no—
215C3#146811yescharacteristic, direct product factor, Sylow
216C2—22no—
217C2—22no—
218C2—41no—
219C2—81no—
220C2C3×#40811yescharacteristic
221C2C2×C3×#9911yescharacteristic
222C2C3×#41311yescharacteristic
subgroupG/H
center, socleC22×C3C2×C22⋊C4
commutatorC23C22×C3×C4
Frattini, cosocleC22×C4C23×C3
prime radicalC22×C3×D4C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#407C2semidirect
3. C2×C3×C22⋊C8C2semidirect
4. C3×#324C2semidirect
5. C3×#323C2semidirect
6. #1468C3direct (N × H)
25. #407C2×C3semidirect
26. C2×C22⋊C8C2×C3semidirect
27. #324C2×C3semidirect
28. #323C2×C3semidirect
215. C3#1468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1232
C3×#4072
C2×C3×C22⋊C82
C3×#3242
C3×#3232
#14683