Finite Group Databasebeta

← #69711

Subgroups — #69711

Order 384.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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
1#5515C211yesmaximal, characteristic
2C3×#398C211yesmaximal, characteristic, complemented
3#4971C211yesmaximal, characteristic, complemented
4#4967C211yesmaximal, characteristic
5#4528C211yesmaximal, characteristic, complemented
6#4452C211yesmaximal, characteristic, complemented
7#4451C211yesmaximal, characteristic
8#1609—31nomaximal, Sylow
9C2×C3×C4⋊C4—21no—
10C2×C3×C4⋊C4C2211yescharacteristic
11C2×C3×C4⋊C4C2211yescharacteristic
12#930C2211yescharacteristic
13#929—21no—
14C4×#67—21no—
15#924C2211yescharacteristic
16#898—21no—
17#896—21no—
18#894—21no—
19#889—21no—
20C3×#95—21no—
21C3×#95C2211yescharacteristic
22#830C2211yescharacteristic
23#830C2211yescharacteristic
24#810—21no—
25#809—21no—
26#808—21no—
27#807—21no—
28#539—31no—
29#483—31no—
30#480—31no—
31#398D311yescharacteristic, complemented
32#328—31no—
33#327—31no—
34#324—31no—
35C22×C3×C4—21no—
36C22×C3×C4—21no—
37C22×C3×C4D411yescharacteristic
38C22×C3×C4D411yescharacteristic
39C22×C3×C4C2311yescharacteristic
40C2×#67—21no—
41C2×D12D411yescharacteristic
42C2×C4×D3—21no—
43C2×Dic6D411yescharacteristic
44C3×C4⋊C4—21no—
45C3×C4⋊C4—21no—
46C3×C4⋊C4—21no—
47C3×C4⋊C4—21no—
48C3×C4⋊C4—42no—
49#217—21no—
50(C2×D3)⋊C4—21no—
51(C2×D3)⋊C4—21no—
52(C2×D3)⋊C4—21no—
53(C2×D3)⋊C4—21no—
54C4⋊Dic3D411yescharacteristic
55C4⋊Dic3D411yescharacteristic
56Dic3⋊C4—21no—
57Dic3⋊C4—21no—
58Dic3⋊C4—21no—
59Dic3⋊C4—21no—
60C4×Dic3—21no—
61C2×C3⋊C8—21no—
62C2×C3⋊C8—21no—
63#126—61no—
64#125—61no—
65#123—61no—
66#123—61no—
67C22⋊Q8—31no—
68C22⋊Q8—61no—
69#121—31no—
70C4×D4—61no—
71C2×C4⋊C4—21no—
72C2×C4⋊C4C2×D311yescharacteristic
73C2×C4⋊C4C2×D311yescharacteristic
74#107—61no—
75#106—61no—
76#103—61no—
77#102—61no—
78C22⋊C8—31no—
79C22⋊C8—31no—
80#95—21no—
81#95C2×D311yescharacteristic
82C23×C3C2×D411yescharacteristic
83C22×D3—21no—
84C2×C3×C4—22no—
85C2×C3×C4—21no—
86C2×C3×C4—21no—
87C2×C3×C4—21no—
88C2×C3×C4—21no—
89C2×C3×C4—41no—
90C2×C3×C4—41no—
91C2×C3×C4—41no—
92C2×C3×C4—41no—
93C2×C3×C4—41no—
94C2×C3×C4—41no—
95C2×C3×C4—41no—
96C2×C3×C4C2×D411yescharacteristic
97C2×C3×C4C2×D411yescharacteristic
98#67—41no—
99#67—41no—
100C2×Dic3—21no—
101C2×Dic3—21no—
102C2×Dic3—21no—
103D12—41no—
104C4×D3—81no—
105Dic6—41no—
106C3⋊C8—41no—
107C3⋊C8—41no—
108C2×Q8—31no—
109C2×D4—31no—
110C2×D4—61no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—61no—
114C22×C4#6711yescharacteristic
115C22×C4#6711yescharacteristic
116C22×C4C22×D311yescharacteristic
117C2×C8—61no—
118C2×C8—61no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—31no—
124C4⋊C4—31no—
125C4⋊C4—42no—
126C4⋊C4—61no—
127C4⋊C4—61no—
128C4⋊C4—61no—
129C4⋊C4—61no—
130C22⋊C4—61no—
131C22⋊C4—61no—
132C22⋊C4—61no—
133C22⋊C4—61no—
134C22⋊C4—61no—
135C42—61no—
136C22×C3—21no—
137C22×C3—21no—
138C22×C3#12011yescharacteristic
139C22×C3#13511yescharacteristic
140C22×C3AGL(1,ℤ/8)11yescharacteristic
141C2×D3—41no—
142C2×D3—41no—
143C2×D3—41no—
144C3×C4—21no—
145C3×C4—21no—
146C3×C4—42no—
147C3×C4—41no—
148C3×C4—41no—
149C3×C4—81no—
150Dic3—41no—
151Dic3—41no—
152Dic3—41no—
153C23—61no—
154C23C2×#6711yescharacteristic
155Q8—121no—
156D4—121no—
157D4—121no—
158D4—121no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—61no—
172C2×C4—61no—
173C2×C4—61no—
174C2×C4—241no—
175C2×C4D3×D411yescharacteristic
176C2×C4D3×D411yescharacteristic
177C8—121no—
178C8—121no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3#44911yescharacteristic
182C2×C3#45611yescharacteristic
183C2×C3#45811yescharacteristic
184D3—81no—
185C22—21no—
186C22—21no—
187C22—121no—
188C22—121no—
189C22—121no—
190C22#93211yescharacteristic
191C22#93711yescharacteristic
192C22#95011yescharacteristic
193C4—21no—
194C4—21no—
195C4—42no—
196C4—41no—
197C4—41no—
198C4—81no—
199C4—121no—
200C4—121no—
201C4—121no—
202C3#160911yescharacteristic, complemented, Sylow
203C2—21no—
204C2—21no—
205C2—241no—
206C2#503711yescharacteristic
207C2#505311yescharacteristic
208C2#509511yescharacteristic
subgroupG/H
centerC22#937
commutator, cosocleC22×C3×C4C23
FrattiniC22×C4C22×D3
FittingC3×#398C2
socleC22×C3#120
prime radical#930C22
hypercenter#398D3
hypocenterC3#1609
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C3×#398C2semidirect
3. #4971C2semidirect
5. #4528C2semidirect
6. #4452C2semidirect
31. #398D3semidirect
202. C3#1609semidirect

Maximal subgroups

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

subgroupindex
#55152
C3×#3982
#49712
#49672
#45282
#44522
#44512
#16093