Finite Group Databasebeta

← C3×#1473 #72188

Subgroups — C3×#1473 #72188

Order 384.

214 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 88 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×#126C211yesmaximal, characteristic
2C3×#432C211yesmaximal, characteristic, complemented
3C3×#431C211yesmaximal, characteristic, complemented
4C3×#324C212yesmaximal, complemented
5C3×#323C212yesmaximal
6#1473C311yesmaximal, characteristic, direct product factor, Sylow
7C3×#126—21no—
8C3×#126—21no—
9C3×#126—21no—
10C3×#126—21no—
11C2×C3×C4⋊C4C411yescharacteristic
12C2×C3×C4⋊C4C411yescharacteristic
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C22⋊C4C411yescharacteristic
15C2×C3×C22⋊C4C411yescharacteristic
16C2×C3×C22⋊C4C2211yescharacteristic
17C2×C3×C42C2211yescharacteristic
18C3×C4⋊C8—21no—
19C3×C4⋊C8—21no—
20C3×C22⋊C8C2212yes—
21C3×C22⋊C8C2212yes—
22C3×#97—21no—
23C3×C4×C8—21no—
24C2×#126C2×C311yescharacteristic
25#432C2×C311yescharacteristic, complemented
26#431C2×C311yescharacteristic, complemented
27#324C2×C312yescomplemented
28#323C2×C312yes—
29C24×C3C2×C411yescharacteristic
30C22×C3×C4C2×C411yescharacteristic
31C22×C3×C4C2×C411yescharacteristic
32C22×C3×C4C2×C411yescharacteristic
33C22×C3×C4C2×C411yescharacteristic
34C22×C3×C4C2×C411yescharacteristic
35C22×C3×C4C2311yescharacteristic
36C2×C3×C8—22no—
37C2×C3×C8—22no—
38C3×C4⋊C4—21no—
39C3×C4⋊C4—21no—
40C3×C4⋊C4—21no—
41C3×C4⋊C4—21no—
42C3×C4⋊C4—21no—
43C3×C4⋊C4—21no—
44C3×C22⋊C4—21no—
45C3×C22⋊C4—21no—
46C3×C22⋊C4—21no—
47C3×C22⋊C4—21no—
48C3×C22⋊C4—21no—
49C3×C22⋊C4—21no—
50C3×C42D411yescharacteristic
51C3×C42D411yescharacteristic
52C3×C42D411yescharacteristic
53C3×C42D411yescharacteristic
54#126—21no—
55#126—21no—
56#126—21no—
57#126—21no—
58C2×C4⋊C4C3×C411yescharacteristic
59C2×C4⋊C4C3×C411yescharacteristic
60C2×C4⋊C4C22×C311yescharacteristic
61C2×C22⋊C4C3×C411yescharacteristic
62C2×C22⋊C4C3×C411yescharacteristic
63C2×C22⋊C4C22×C311yescharacteristic
64C2×C42C22×C311yescharacteristic
65C4⋊C8—21no—
66C4⋊C8—21no—
67C22⋊C8C22×C312yes—
68C22⋊C8C22×C312yes—
69#97—21no—
70C4×C8—21no—
71C23×C3—21no—
72C23×C3—22no—
73C23×C3—41no—
74C23×C3—41no—
75C23×C3C22×C411yescharacteristic
76C2×C3×C4—22no—
77C2×C3×C4—21no—
78C2×C3×C4—21no—
79C2×C3×C4—21no—
80C2×C3×C4—22no—
81C2×C3×C4—41no—
82C2×C3×C4—41no—
83C2×C3×C4—41no—
84C2×C3×C4—41no—
85C2×C3×C4C22⋊C411yescharacteristic
86C2×C3×C4C22⋊C411yescharacteristic
87C2×C3×C4C22⋊C411yescharacteristic
88C2×C3×C4C22⋊C411yescharacteristic
89C2×C3×C4C2×D411yescharacteristic
90C2×C3×C4C2×D411yescharacteristic
91C3×C8—42no—
92C3×C8—42no—
93C24C2×C3×C411yescharacteristic
94C22×C4C2×C3×C411yescharacteristic
95C22×C4C2×C3×C411yescharacteristic
96C22×C4C2×C3×C411yescharacteristic
97C22×C4C2×C3×C411yescharacteristic
98C22×C4C2×C3×C411yescharacteristic
99C22×C4C23×C311yescharacteristic
100C2×C8—22no—
101C2×C8—22no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C22⋊C4—21no—
109C22⋊C4—21no—
110C22⋊C4—21no—
111C22⋊C4—21no—
112C22⋊C4—21no—
113C22⋊C4—21no—
114C42C3×D411yescharacteristic
115C42C3×D411yescharacteristic
116C42C3×D411yescharacteristic
117C42C3×D411yescharacteristic
118C22×C3—21no—
119C22×C3—21no—
120C22×C3—41no—
121C22×C3—41no—
122C22×C3—41no—
123C22×C3—82no—
124C22×C3C2×C22⋊C411yescharacteristic
125C22×C3#13112yes—
126C3×C4—21no—
127C3×C4—21no—
128C3×C4—21no—
129C3×C4—21no—
130C3×C4—21no—
131C3×C4—21no—
132C3×C4—41no—
133C3×C4—41no—
134C3×C4—41no—
135C23—21no—
136C23—22no—
137C23—41no—
138C23—41no—
139C23C22×C3×C411yescharacteristic
140C2×C4—22no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4C3×C22⋊C411yescharacteristic
150C2×C4C3×C22⋊C411yescharacteristic
151C2×C4C3×C22⋊C411yescharacteristic
152C2×C4C3×C22⋊C411yescharacteristic
153C2×C4C2×C3×D411yescharacteristic
154C2×C4C2×C3×D411yescharacteristic
155C8—42no—
156C8—42no—
157C2×C3—22no—
158C2×C3—81no—
159C2×C3#40811yescharacteristic
160C2×C3#41011yescharacteristic
161C2×C3#41311yescharacteristic
162C22—21no—
163C22—21no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—82no—
168C22C2×C3×C22⋊C411yescharacteristic
169C22C3×#13112yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—41no—
179C3#147311yescharacteristic, direct product factor, Sylow
180C2—22no—
181C2—81no—
182C2C3×#40811yescharacteristic
183C2C3×#41011yescharacteristic
184C2C3×#41311yescharacteristic
subgroupG/H
center, socleC22×C3C2×C22⋊C4
commutatorC23C22×C3×C4
Frattini, cosocleC22×C4C23×C3
prime radicalC24×C3C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#432C2semidirect
3. C3×#431C2semidirect
4. C3×#324C2semidirect
6. #1473C3direct (N × H)
25. #432C2×C3semidirect
26. #431C2×C3semidirect
27. #324C2×C3semidirect
179. C3#1473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1262
C3×#4322
C3×#4312
C3×#3242
C3×#3232
#14733