Finite Group Databasebeta

← C3×#1891 #72606

Subgroups — C3×#1891 #72606

Order 384.

342 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 108 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×#568C211yesmaximal, characteristic, complemented
2C3×#525C211yesmaximal, characteristic
3C3×#413C211yesmaximal, characteristic, complemented
4C3×#407C212yesmaximal, complemented
5C3×#344C212yesmaximal, complemented
6#1891C311yesmaximal, characteristic, direct product factor, Sylow
7C2×C3×#41C2211yescharacteristic
8C23×C3×C4C2211yescharacteristic
9C3×#131—24no—
10C2×C3×M16—22no—
11C2×C3×M16C2212yes—
12C2×C3×M16C2212yes—
13C3×#123C412yes—
14C3×C22⋊Q8—21no—
15C3×#121—21no—
16C3×#120C412yes—
17C3×C4×D4—22no—
18C3×#117C2211yescharacteristic
19C3×#101—21no—
20C3×#100—21no—
21C3×C22⋊C8—24no—
22#568C2×C311yescharacteristic, complemented
23#525C2×C311yescharacteristic
24#413C2×C311yescharacteristic, complemented
25#407C2×C312yescomplemented
26#344C2×C312yescomplemented
27C24×C3C2×C411yescharacteristic
28C3×#41—22no—
29C3×#41—22no—
30C2×C3×Q8D411yescharacteristic
31C2×C3×D4—22no—
32C2×C3×D4C2×C412yes—
33C2×C3×D4D411yescharacteristic
34C22×C3×C4—22no—
35C22×C3×C4—21no—
36C22×C3×C4—21no—
37C22×C3×C4—22no—
38C22×C3×C4C2×C411yescharacteristic
39C22×C3×C4D412yes—
40C22×C3×C4C2311yescharacteristic
41C3×M16—24no—
42C3×M16—22no—
43C3×M16—22no—
44C3×M16—22no—
45C3×M16—22no—
46C2×C3×C8—24no—
47C2×C3×C8—22no—
48C2×C3×C8D414yescomplemented
49C3×C4⋊C4—22no—
50C3×C4⋊C4—21no—
51C3×C22⋊C4—22no—
52C3×C22⋊C4—22no—
53C3×C22⋊C4C2×C412yes—
54C3×C42—21no—
55C2×#41C22×C311yescharacteristic
56C23×C4C22×C311yescharacteristic
57#131—24no—
58C2×M16—22no—
59C2×M16C22×C312yes—
60C2×M16C22×C312yes—
61#123C3×C412yes—
62C22⋊Q8—21no—
63#121—21no—
64#120C3×C412yes—
65C4×D4—22no—
66#117C22×C311yescharacteristic
67#101—21no—
68#100—21no—
69C22⋊C8—24no—
70C23×C3—21no—
71C23×C3—22no—
72C23×C3—42no—
73C23×C3C22⋊C412yes—
74C23×C3C22×C411yescharacteristic
75C3×Q8—22no—
76C3×D4—24no—
77C3×D4—22no—
78C3×D4—44no—
79C2×C3×C4—22no—
80C2×C3×C4—22no—
81C2×C3×C4—22no—
82C2×C3×C4—21no—
83C2×C3×C4—22no—
84C2×C3×C4—41no—
85C2×C3×C4—42no—
86C2×C3×C4—41no—
87C2×C3×C4C22⋊C412yes—
88C2×C3×C4C2×D412yes—
89C2×C3×C4C2×D411yescharacteristic
90C2×C3×C4C2×D411yescharacteristic
91C2×C3×C4#4112yes—
92C3×C8—24no—
93C3×C8—42no—
94C24C2×C3×C411yescharacteristic
95#41—22no—
96#41—22no—
97C2×Q8C3×D411yescharacteristic
98C2×D4—22no—
99C2×D4C2×C3×C412yes—
100C2×D4C3×D411yescharacteristic
101C22×C4—22no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—22no—
105C22×C4C2×C3×C411yescharacteristic
106C22×C4C3×D412yes—
107C22×C4C23×C311yescharacteristic
108M16—24no—
109M16—22no—
110M16—22no—
111M16—22no—
112M16—22no—
113C2×C8—24no—
114C2×C8—22no—
115C2×C8C3×D414yescomplemented
116C4⋊C4—22no—
117C4⋊C4—21no—
118C22⋊C4—22no—
119C22⋊C4—22no—
120C22⋊C4C2×C3×C412yes—
121C42—21no—
122C22×C3—22no—
123C22×C3—24no—
124C22×C3—22no—
125C22×C3—41no—
126C22×C3—42no—
127C22×C3—41no—
128C22×C3—42no—
129C22×C3—41no—
130C22×C3C2×C22⋊C411yescharacteristic
131C22×C3C4×D412yes—
132C3×C4—22no—
133C3×C4—42no—
134C3×C4—41no—
135C3×C4#12011yescharacteristic
136C3×C4#12112yes—
137C3×C4#12311yescharacteristic
138C23—21no—
139C23—22no—
140C23—42no—
141C23C3×C22⋊C412yes—
142C23C22×C3×C411yescharacteristic
143Q8—22no—
144D4—24no—
145D4—22no—
146D4—44no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4C3×C22⋊C412yes—
156C2×C4C2×C3×D412yes—
157C2×C4C2×C3×D411yescharacteristic
158C2×C4C2×C3×D411yescharacteristic
159C2×C4C3×#4112yes—
160C8—24no—
161C8—42no—
162C2×C3—21no—
163C2×C3—22no—
164C2×C3—42no—
165C2×C3—42no—
166C2×C3#38611yescharacteristic
167C22—22no—
168C22—24no—
169C22—22no—
170C22—41no—
171C22—42no—
172C22—41no—
173C22—42no—
174C22—41no—
175C22C2×C3×C22⋊C411yescharacteristic
176C22C3×C4×D412yes—
177C4—22no—
178C4—42no—
179C4—41no—
180C4C3×#12011yescharacteristic
181C4C3×#12112yes—
182C4C3×#12311yescharacteristic
183C3#189111yescharacteristic, direct product factor, Sylow
184C2—21no—
185C2—22no—
186C2—42no—
187C2—42no—
188C2C3×#38611yescharacteristic
subgroupG/H
centerC3×C4#120
commutatorC23C22×C3×C4
Frattini, cosocleC22×C4C23×C3
socleC2×C3#386
prime radicalC3×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#568C2semidirect
3. C3×#413C2semidirect
4. C3×#407C2semidirect
5. C3×#344C2semidirect
6. #1891C3direct (N × H)
22. #568C2×C3semidirect
24. #413C2×C3semidirect
25. #407C2×C3semidirect
26. #344C2×C3semidirect
48. C2×C3×C8D4semidirect
115. C2×C8C3×D4semidirect
183. C3#1891direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5682
C3×#5252
C3×#4132
C3×#4072
C3×#3442
#18913