Finite Group Databasebeta

← C3×#1527 #72242

Subgroups — C3×#1527 #72242

Order 384.

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

normal subgroups only

This group has 264 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×#124C211yesmaximal, characteristic
2C3×#432C211yesmaximal, characteristic, complemented
3C3×C4×M16C211yesmaximal, characteristic, complemented
4C3×#329C214yesmaximal, complemented
5#1527C311yesmaximal, characteristic, direct product factor, Sylow
6C22×C3×Q8C411yescharacteristic
7C22×C3×D4C411yescharacteristic
8C2×C3×M16—21no—
9C3×#124—21no—
10C3×#124—21no—
11C3×#124C412yes—
12C3×#124C2212yes—
13C2×C3×C22⋊C4—21no—
14C2×C3×C22⋊C4—21no—
15C2×C3×C42C2211yescharacteristic
16C3×C4⋊C8—21no—
17C3×C22⋊C8—21no—
18C3×#97C2212yescomplemented
19C3×#97C2212yescomplemented
20C3×C4×C8—21no—
21C2×#124C2×C311yescharacteristic
22#432C2×C311yescharacteristic, complemented
23C4×M16C2×C311yescharacteristic, complemented
24#329C2×C314yescomplemented
25C24×C3—21no—
26C2×C3×Q8—21no—
27C2×C3×Q8—42no—
28C2×C3×Q8C2×C412yes—
29C2×C3×D4—21no—
30C2×C3×D4—42no—
31C2×C3×D4C2×C412yes—
32C22×C3×C4—21no—
33C22×C3×C4C2×C411yescharacteristic
34C22×C3×C4D411yescharacteristic
35C22×C3×C4D411yescharacteristic
36C3×M16—24no—
37C2×C3×C8—22no—
38C2×C3×C8—22no—
39C3×C22⋊C4—22no—
40C3×C22⋊C4—22no—
41C3×C22⋊C4—22no—
42C3×C22⋊C4—22no—
43C3×C42C2×C411yescharacteristic
44C3×C42D411yescharacteristic
45C3×C42D411yescharacteristic
46C3×C42C2311yescharacteristic
47C22×Q8C3×C411yescharacteristic
48C22×D4C3×C411yescharacteristic
49C2×M16—21no—
50#124—21no—
51#124—21no—
52#124C3×C412yes—
53#124C22×C312yes—
54C2×C22⋊C4—21no—
55C2×C22⋊C4—21no—
56C2×C42C22×C311yescharacteristic
57C4⋊C8—21no—
58C22⋊C8—21no—
59#97C22×C312yescomplemented
60#97C22×C312yescomplemented
61C4×C8—21no—
62C23×C3—22no—
63C23×C3—42no—
64C23×C3—42no—
65C23×C3—42no—
66C23×C3C22⋊C411yescharacteristic
67C3×Q8—42no—
68C3×Q8—42no—
69C3×D4—42no—
70C3×D4—42no—
71C2×C3×C4—22no—
72C2×C3×C4—22no—
73C2×C3×C4—22no—
74C2×C3×C4—41no—
75C2×C3×C4—42no—
76C2×C3×C4C22⋊C411yescharacteristic
77C2×C3×C4C22⋊C411yescharacteristic
78C2×C3×C4C22⋊C411yescharacteristic
79C2×C3×C4C22×C411yescharacteristic
80C2×C3×C4C2×D411yescharacteristic
81C2×C3×C4C2×D411yescharacteristic
82C3×C8—24no—
83C3×C8—42no—
84C24—21no—
85C2×Q8—21no—
86C2×Q8—42no—
87C2×Q8C2×C3×C412yes—
88C2×D4—21no—
89C2×D4—42no—
90C2×D4C2×C3×C412yes—
91C22×C4—21no—
92C22×C4C2×C3×C411yescharacteristic
93C22×C4C3×D411yescharacteristic
94C22×C4C3×D411yescharacteristic
95M16—24no—
96C2×C8—22no—
97C2×C8—22no—
98C22⋊C4—22no—
99C22⋊C4—22no—
100C22⋊C4—22no—
101C22⋊C4—22no—
102C42C2×C3×C411yescharacteristic
103C42C3×D411yescharacteristic
104C42C3×D411yescharacteristic
105C42C23×C311yescharacteristic
106C22×C3—21no—
107C22×C3—21no—
108C22×C3—42no—
109C22×C3—42no—
110C22×C3—42no—
111C22×C3—84no—
112C22×C3#10412yes—
113C22×C3C2×C22⋊C411yescharacteristic
114C3×C4—21no—
115C3×C4—21no—
116C3×C4—21no—
117C3×C4—21no—
118C3×C4—21no—
119C3×C4—42no—
120C3×C4#10012yes—
121C23—22no—
122C23—42no—
123C23—42no—
124C23—42no—
125C23C3×C22⋊C411yescharacteristic
126Q8—42no—
127Q8—42no—
128D4—42no—
129D4—42no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—41no—
134C2×C4—42no—
135C2×C4C3×C22⋊C411yescharacteristic
136C2×C4C3×C22⋊C411yescharacteristic
137C2×C4C3×C22⋊C411yescharacteristic
138C2×C4C22×C3×C411yescharacteristic
139C2×C4C2×C3×D411yescharacteristic
140C2×C4C2×C3×D411yescharacteristic
141C8—24no—
142C8—42no—
143C2×C3—22no—
144C2×C3—82no—
145C2×C3C2×#10011yescharacteristic
146C2×C3C2×#10411yescharacteristic
147C2×C3#42111yescharacteristic
148C22—21no—
149C22—21no—
150C22—42no—
151C22—42no—
152C22—42no—
153C22—84no—
154C22C3×#10412yes—
155C22C2×C3×C22⋊C411yescharacteristic
156C4—21no—
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—42no—
162C4C3×#10012yes—
163C3#152711yescharacteristic, direct product factor, Sylow
164C2—22no—
165C2—82no—
166C2C2×C3×#10011yescharacteristic
167C2C2×C3×#10411yescharacteristic
168C2C3×#42111yescharacteristic
subgroupG/H
center, socleC22×C3C2×C22⋊C4
commutatorC2×C4C22×C3×C4
Frattini, cosocleC42C23×C3
prime radicalC22×C3×D4C4
LCSG ▷ C2×C4 ▷ C22 ▷ 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×C4×M16C2semidirect
4. C3×#329C2semidirect
5. #1527C3direct (N × H)
18. C3×#97C22semidirect
19. C3×#97C22semidirect
22. #432C2×C3semidirect
23. C4×M16C2×C3semidirect
24. #329C2×C3semidirect
59. #97C22×C3semidirect
60. #97C22×C3semidirect
163. C3#1527direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1242
C3×#4322
C3×C4×M162
C3×#3292
#15273