Finite Group Databasebeta

← #76603

Subgroups — #76603

Order 384.

368 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 137 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#5229C211yesmaximal, characteristic
3#5229C211yesmaximal, characteristic
4#4982C212yesmaximal
5#4933C212yesmaximal
6#4660C212yesmaximal
7#4657C212yesmaximal
8#4654C212yesmaximal
9#4647C212yesmaximal
10#2809—31nomaximal, Sylow
11C22×C3×Q8C2211yescharacteristic
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C3×C42C2211yescharacteristic
14C2×C4⋊Dic3C2212yes—
15C2×C4⋊Dic3C2211yescharacteristic
16C2×C4⋊Dic3C2211yescharacteristic
17C2×Dic3⋊C4C2212yes—
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2212yes—
20C2×Dic3⋊C4C2212yes—
21C2×C4×Dic3C2211yescharacteristic
22C2×C4×Dic3C2211yescharacteristic
23C3×#95C2212yes—
24C3×#95C2212yes—
25C3⋊#95C2212yes—
26C3⋊#95C2212yes—
27C3⋊#95C2212yes—
28C3⋊#95C2212yes—
29C3⋊#95C2212yes—
30C3⋊#95C2212yes—
31C3⋊#95C2212yes—
32#400—32no—
33#398—32no—
34#398—32no—
35#391—31no—
36#391—31no—
37#391D311yescharacteristic
38#389—32no—
39#387—32no—
40#387—32no—
41C2×C3×Q8—41no—
42C2×C3×Q8—41no—
43C2×C3×Q8Q814yes—
44C22×C3×C4C2312yes—
45C22×C3×C4C2312yes—
46C22×C3×C4C2311yescharacteristic
47C22×C3×C4C2311yescharacteristic
48C22×C3×C4C2311yescharacteristic
49C22×Dic3C2312yes—
50C22×Dic3C2312yes—
51C22×Dic3C2312yes—
52C22×Dic3C2312yes—
53C3×C4⋊C4—41no—
54C3×C42—41no—
55C4⋊Dic3—24no—
56C4⋊Dic3—41no—
57C4⋊Dic3—41no—
58Dic3⋊C4—24no—
59Dic3⋊C4—24no—
60Dic3⋊C4—42no—
61Dic3⋊C4—42no—
62C4×Dic3—41no—
63C4×Dic3—41no—
64C22×Q8C2×D311yescharacteristic
65C2×C4⋊C4—32no—
66C2×C4⋊C4—32no—
67C2×C4⋊C4—32no—
68C2×C4⋊C4—32no—
69C2×C4⋊C4—31no—
70C2×C4⋊C4—31no—
71C2×C4⋊C4—32no—
72C2×C4⋊C4C2×D311yescharacteristic
73C2×C42—31no—
74C2×C42—31no—
75C2×C42C2×D311yescharacteristic
76#95—32no—
77#95—32no—
78#95—32no—
79#95—32no—
80#95—32no—
81#95—32no—
82#95—32no—
83#95C2×D312yes—
84#95C2×D312yes—
85C23×C3C2411yescharacteristic
86C3×Q8—44no—
87C2×C3×C4—21no—
88C2×C3×C4—21no—
89C2×C3×C4—21no—
90C2×C3×C4—21no—
91C2×C3×C4—21no—
92C2×C3×C4—21no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×C3×C4—22no—
99C2×C3×C4C2×Q812yes—
100C2×C3×C4C2×Q812yes—
101C2×C3×C4C2×Q812yes—
102C2×Dic3—22no—
103C2×Dic3—22no—
104C2×Dic3—22no—
105C2×Dic3—22no—
106C2×Dic3—22no—
107C2×Dic3—22no—
108C2×Dic3—22no—
109C2×Dic3—22no—
110C2×Dic3—22no—
111C2×Dic3—24no—
112C2×Dic3#4114yes—
113C2×Q8—41no—
114C2×Q8—41no—
115C2×Q8Dic614yes—
116C22×C4—32no—
117C22×C4—32no—
118C22×C4—32no—
119C22×C4—32no—
120C22×C4C22×D312yes—
121C22×C4C22×D312yes—
122C22×C4C22×D311yescharacteristic
123C22×C4C22×D311yescharacteristic
124C22×C4C22×D311yescharacteristic
125C4⋊C4—41no—
126C4⋊C4—64no—
127C4⋊C4—64no—
128C4⋊C4—64no—
129C4⋊C4—122no—
130C4⋊C4—122no—
131C4⋊C4—121no—
132C4⋊C4—121no—
133C42—41no—
134C42—121no—
135C42—121no—
136C22×C3C22×Q811yescharacteristic
137C22×C3C2×#4112yes—
138C22×C3H(5,𝔽2)11yescharacteristic
139C22×C3H(5,𝔽2)11yescharacteristic
140C22×C32−1+412yes—
141C3×C4—22no—
142C3×C4—22no—
143C3×C4—22no—
144C3×C4—42no—
145C3×C4—42no—
146Dic3—24no—
147Dic3—42no—
148Dic3—42no—
149Dic3—42no—
150C23C23×D311yescharacteristic
151Q8—44no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—34no—
165C2×C4—62no—
166C2×C4—62no—
167C2×C4—62no—
168C2×C4—62no—
169C2×C4—62no—
170C2×C4—62no—
171C2×C4—64no—
172C2×C4—62no—
173C2×C4—62no—
174C2×C4—62no—
175C2×C4C2×Dic612yes—
176C2×C4C2×Dic612yes—
177C2×C4C2×Dic612yes—
178C2×C3#53912yes—
179C2×C3#54311yescharacteristic
180C2×C3#55511yescharacteristic
181C2×C3#55712yes—
182C2×C3#56311yescharacteristic
183C22C22×Dic611yescharacteristic
184C22#100411yescharacteristic
185C22#100411yescharacteristic
186C22#100712yes—
187C22D3×#4112yes—
188C4—22no—
189C4—22no—
190C4—22no—
191C4—42no—
192C4—42no—
193C4—64no—
194C4—122no—
195C4—122no—
196C4—122no—
197C3#280911yescharacteristic, complemented, Sylow
198C2#548311yescharacteristic
199C2#556912yes—
200C2#563812yes—
201C2#567011yescharacteristic
202C2#573511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#391C2
hypercenter#391D3
hypocenterC3#2809
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
197. C3#2809semidirect

Maximal subgroups

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

subgroupindex
C3×#3912
#52292
#49822
#49332
#46602
#46572
#46542
#46472
#28093