Finite Group Databasebeta

← C3⋊#2104 #68950

Subgroups — C3⋊#2104 #68950

Order 384.

178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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×#342C211yesmaximal, characteristic
2#4527C211yesmaximal, characteristic
3#4527C211yesmaximal, characteristic
4#4527C211yesmaximal, characteristic
5#4527C211yesmaximal, characteristic
6#4526C211yesmaximal, characteristic
7#4526C211yesmaximal, characteristic
8#2104—31nomaximal, Sylow
9C2×C3×C22⋊C4C2211yescharacteristic
10C2×C3×C22⋊C4C2211yescharacteristic
11C2×C3×C22⋊C4C2211yescharacteristic
12C2×#217C2211yescharacteristic
13C2×#217C2211yescharacteristic
14C2×#217C2211yescharacteristic
15C2×#217C2211yescharacteristic
16#342—31no—
17#342—31no—
18#342—31no—
19#342—31no—
20#342—31no—
21#342—31no—
22#342D311yescharacteristic
23C24×C3C2311yescharacteristic
24C22×C3×C4—21no—
25C22×C3×C4—21no—
26C22×C3×C4—21no—
27C22×Dic3—21no—
28C22×Dic3—21no—
29C22×Dic3—21no—
30C22×Dic3—21no—
31C3×C22⋊C4—21no—
32C3×C22⋊C4—21no—
33C3×C22⋊C4—21no—
34C3×C22⋊C4—21no—
35C3×C22⋊C4—21no—
36C3×C22⋊C4—21no—
37#217—21no—
38#217—21no—
39#217—21no—
40#217—21no—
41#217—21no—
42#217—21no—
43#217—21no—
44#217—21no—
45C2×C22⋊C4—31no—
46C2×C22⋊C4—31no—
47C2×C22⋊C4—31no—
48C2×C22⋊C4—31no—
49C2×C22⋊C4C2×D311yescharacteristic
50C2×C22⋊C4C2×D311yescharacteristic
51C2×C22⋊C4C2×D311yescharacteristic
52C23×C3—81no—
53C23×C3#4111yescharacteristic
54C23×C3#4111yescharacteristic
55C23×C3#4111yescharacteristic
56C23×C3#4111yescharacteristic
57C23×C3#4111yescharacteristic
58C23×C3#4111yescharacteristic
59C23×C3#4111yescharacteristic
60C2×C3×C4—41no—
61C2×C3×C4—41no—
62C2×C3×C4—41no—
63C2×C3×C4—81no—
64C2×C3×C4—81no—
65C2×C3×C4—81no—
66C2×Dic3—41no—
67C2×Dic3—41no—
68C2×Dic3—41no—
69C2×Dic3—41no—
70C2×Dic3—81no—
71C2×Dic3—81no—
72C2×Dic3—81no—
73C2×Dic3—81no—
74C24C22×D311yescharacteristic
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—61no—
79C22×C4—61no—
80C22×C4—61no—
81C22×C4—61no—
82C22⋊C4—21no—
83C22⋊C4—21no—
84C22⋊C4—21no—
85C22⋊C4—21no—
86C22⋊C4—21no—
87C22⋊C4—21no—
88C22⋊C4—61no—
89C22⋊C4—61no—
90C22⋊C4—61no—
91C22⋊C4—61no—
92C22⋊C4—61no—
93C22⋊C4—61no—
94C22⋊C4—61no—
95C22⋊C4—61no—
96C22×C3—41no—
97C22×C3—41no—
98C22×C3—41no—
99C22×C3—41no—
100C22×C3—41no—
101C22×C3—41no—
102C22×C3—41no—
103C22×C3#12611yescharacteristic
104C22×C3#12611yescharacteristic
105C22×C3#12611yescharacteristic
106C22×C3#12611yescharacteristic
107C22×C3#12611yescharacteristic
108C22×C3#12611yescharacteristic
109C22×C3#12611yescharacteristic
110C3×C4—81no—
111C3×C4—81no—
112C3×C4—81no—
113Dic3—81no—
114Dic3—81no—
115Dic3—81no—
116Dic3—81no—
117C23—81no—
118C23#23511yescharacteristic
119C23#23511yescharacteristic
120C23#23511yescharacteristic
121C23#23711yescharacteristic
122C23#23711yescharacteristic
123C23#23711yescharacteristic
124C23#23911yescharacteristic
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—81no—
129C2×C4—81no—
130C2×C4—81no—
131C2×C4—121no—
132C2×C4—121no—
133C2×C4—121no—
134C2×C4—121no—
135C2×C4—241no—
136C2×C4—241no—
137C2×C4—241no—
138C2×C4—241no—
139C2×C3—21no—
140C2×C3—21no—
141C2×C3—21no—
142C2×C3—21no—
143C2×C3—21no—
144C2×C3—21no—
145C2×C3—21no—
146C2×C3#40111yescharacteristic
147C22—41no—
148C22—41no—
149C22—41no—
150C22—41no—
151C22—41no—
152C22—41no—
153C22—41no—
154C22#87611yescharacteristic
155C22#87911yescharacteristic
156C22#87911yescharacteristic
157C22#87911yescharacteristic
158C22#89811yescharacteristic
159C22#89811yescharacteristic
160C22#89811yescharacteristic
161C4—81no—
162C4—81no—
163C4—81no—
164C4—241no—
165C4—241no—
166C4—241no—
167C4—241no—
168C3#210411yescharacteristic, complemented, Sylow
169C2—21no—
170C2—21no—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—21no—
175C2—21no—
176C2C3⋊#40111yescharacteristic
subgroupG/H
centerC2C3⋊#401
commutator, prime radical, cosocleC24×C3C23
FrattiniC24C22×D3
FittingC3×#342C2
socleC2×C3#401
hypercenter#342D3
hypocenterC3#2104
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
168. C3#2104semidirect

Maximal subgroups

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

subgroupindex
C3×#3422
#45272
#45262
#21043