Finite Group Databasebeta

← #76605

Subgroups — #76605

Order 384.

332 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 117 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×#391C211yesmaximal, characteristic
2#5230C212yesmaximal
3#4986C211yesmaximal, characteristic
4#4981C211yesmaximal, characteristic
5#4933C212yesmaximal
6C3⋊#401C212yesmaximal
7#4660C212yesmaximal
8#4658C212yesmaximal
9#4657C212yesmaximal
10#2833—31nomaximal, Sylow
11C22×C3×Q8C2211yescharacteristic
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C3×C42C2211yescharacteristic
14C2×C4⋊Dic3C2211yescharacteristic
15C2×C4⋊Dic3C2211yescharacteristic
16C2×Dic3⋊C4C2212yes—
17C2×Dic3⋊C4C2212yes—
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C3×#95C2212yes—
21C3×#95C2212yes—
22C3⋊#95C2212yes—
23C3⋊#95C2212yes—
24C3⋊#95C2211yescharacteristic
25C3⋊#95C2212yes—
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2212yes—
29C3⋊#95C2212yes—
30C3⋊#95C2211yescharacteristic
31C3⋊#95C2212yes—
32#401—32no—
33#400—31no—
34#400—32no—
35#400—32no—
36#398—31no—
37#398—32no—
38#395—32no—
39#391D311yescharacteristic
40#387—32no—
41C2×C3×Q8—22no—
42C2×C3×Q8—41no—
43C2×C3×Q8—41no—
44C22×C3×C4C2312yes—
45C22×C3×C4C2311yescharacteristic
46C22×C3×C4C2311yescharacteristic
47C22×C3×C4C2312yes—
48C22×C3×C4C2311yescharacteristic
49C22×Dic3C2312yes—
50C22×Dic3C2312yes—
51C22×Dic3C2312yes—
52C22×Dic3C2312yes—
53C3×C4⋊C4—41no—
54C3×C42—41no—
55C4⋊Dic3—41no—
56C4⋊Dic3—41no—
57Dic3⋊C4—24no—
58Dic3⋊C4—42no—
59Dic3⋊C4—42no—
60Dic3⋊C4—42no—
61C22×Q8C2×D311yescharacteristic
62C2×C4⋊C4—32no—
63C2×C4⋊C4—32no—
64C2×C4⋊C4—32no—
65C2×C4⋊C4—32no—
66C2×C4⋊C4—31no—
67C2×C4⋊C4—31no—
68C2×C4⋊C4C2×D311yescharacteristic
69C2×C42C2×D311yescharacteristic
70#95—32no—
71#95—32no—
72#95—32no—
73#95—32no—
74#95—32no—
75#95—32no—
76#95—32no—
77#95—32no—
78#95—31no—
79#95—31no—
80#95C2×D312yes—
81#95C2×D312yes—
82C23×C3C2411yescharacteristic
83C3×Q8—44no—
84C2×C3×C4—21no—
85C2×C3×C4—21no—
86C2×C3×C4—22no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—21no—
91C2×C3×C4—21no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×C3×C4#4112yes—
97C2×Dic3—22no—
98C2×Dic3—22no—
99C2×Dic3—22no—
100C2×Dic3—22no—
101C2×Dic3—22no—
102C2×Dic3—22no—
103C2×Dic3—22no—
104C2×Dic3—22no—
105C2×Dic3—24no—
106C2×Dic3—22no—
107C2×Dic3—22no—
108C2×Q8—22no—
109C2×Q8—41no—
110C2×Q8—41no—
111C22×C4—32no—
112C22×C4—32no—
113C22×C4—32no—
114C22×C4—32no—
115C22×C4C22×D312yes—
116C22×C4C22×D311yescharacteristic
117C22×C4C22×D311yescharacteristic
118C22×C4C22×D312yes—
119C22×C4C22×D311yescharacteristic
120C4⋊C4—41no—
121C4⋊C4—64no—
122C4⋊C4—122no—
123C4⋊C4—122no—
124C4⋊C4—122no—
125C4⋊C4—121no—
126C4⋊C4—121no—
127C42—41no—
128C22×C3C2×#4111yescharacteristic
129C22×C3H(5,𝔽2)11yescharacteristic
130C22×C3H(5,𝔽2)11yescharacteristic
131C22×C32−1+412yes—
132C22×C32−1+412yes—
133C3×C4—22no—
134C3×C4—42no—
135C3×C4—42no—
136C3×C4—41no—
137C3×C4—41no—
138Dic3—42no—
139Dic3—42no—
140Dic3—42no—
141Dic3—42no—
142C23C23×D311yescharacteristic
143Q8—44no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—62no—
157C2×C4—62no—
158C2×C4—62no—
159C2×C4—62no—
160C2×C4—62no—
161C2×C4—62no—
162C2×C4—62no—
163C2×C4—64no—
164C2×C4—62no—
165C2×C4—62no—
166C2×C4—62no—
167C2×C4#23512yes—
168C2×C3#53811yescharacteristic
169C2×C3#54112yes—
170C2×C3#56312yes—
171C2×C3#56311yescharacteristic
172C2×C3#56311yescharacteristic
173C22C2×#23511yescharacteristic
174C22#100411yescharacteristic
175C22#100411yescharacteristic
176C22#100712yes—
177C22#101012yes—
178C4—22no—
179C4—42no—
180C4—41no—
181C4—41no—
182C4—42no—
183C4—122no—
184C4—122no—
185C4—122no—
186C4—122no—
187C3#283311yescharacteristic, complemented, Sylow
188C2#549411yescharacteristic
189C2#558312yes—
190C2#564612yes—
191C2#567211yescharacteristic
192C2#573511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#391C2
hypercenter#391D3
hypocenterC3#2833
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
187. C3#2833semidirect

Maximal subgroups

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

subgroupindex
C3×#3912
#52302
#49862
#49812
#49332
C3⋊#4012
#46602
#46582
#46572
#28333