Finite Group Databasebeta

← #69565

Subgroups — #69565

Order 384.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#5479C211yesmaximal, characteristic
2C3×#383C211yesmaximal, characteristic, complemented
3#4925C211yesmaximal, characteristic, complemented
4#4452C212yesmaximal, complemented
5#4451C212yesmaximal
6#1521—31nomaximal, Sylow
7C2×C3×C42C2211yescharacteristic
8#930C2211yescharacteristic
9#929—21no—
10C4×#67—21no—
11#924C2211yescharacteristic
12#876—21no—
13#875C411yescharacteristic, complemented
14C4×D12C411yescharacteristic, complemented
15#872—21no—
16#870C411yescharacteristic, complemented
17C4×Dic6C411yescharacteristic, complemented
18C3×#95—21no—
19C3×#95—21no—
20C3×#95C2212yes—
21#830C2212yes—
22C4⋊(C3⋊C8)—21no—
23C4×C3⋊C8—21no—
24#529—31no—
25#431—31no—
26#383D311yescharacteristic, complemented
27#328—32no—
28#327—32no—
29C22×C3×C4—22no—
30C22×C3×C4D411yescharacteristic
31C22×C3×C4D411yescharacteristic
32C22×C3×C4C2311yescharacteristic
33C2×#67—21no—
34C2×D12C2×C411yescharacteristic
35C2×C4×D3—21no—
36C2×Dic6C2×C411yescharacteristic
37C3×C42C2×C411yescharacteristic
38C3×C42C2×C411yescharacteristic
39C3×C42D411yescharacteristic
40C3×C42D411yescharacteristic
41#217—21no—
42(C2×D3)⋊C4—21no—
43(C2×D3)⋊C4—21no—
44(C2×D3)⋊C4—21no—
45(C2×D3)⋊C4—21no—
46C4⋊Dic3C2×C411yescharacteristic
47C4⋊Dic3C2×C411yescharacteristic
48Dic3⋊C4—21no—
49Dic3⋊C4—21no—
50Dic3⋊C4—21no—
51Dic3⋊C4—21no—
52C4×Dic3—21no—
53C2×C3⋊C8—22no—
54#126—61no—
55#125—31no—
56#124—31no—
57#123—61no—
58C22⋊Q8—31no—
59#121—31no—
60C4×Q8—31no—
61C4×D4—31no—
62C4×D4—61no—
63#117—61no—
64C2×C42C2×D311yescharacteristic
65C4⋊C8—61no—
66C22⋊C8—32no—
67C4×C8—61no—
68#95—21no—
69#95—21no—
70#95C2×D312yes—
71C23×C3C2×D411yescharacteristic
72C22×D3—21no—
73C2×C3×C4—22no—
74C2×C3×C4—41no—
75C2×C3×C4—41no—
76C2×C3×C4—42no—
77C2×C3×C4—42no—
78C2×C3×C4—42no—
79C2×C3×C4C22⋊C411yescharacteristic
80C2×C3×C4C22⋊C411yescharacteristic
81C2×C3×C4C22⋊C411yescharacteristic
82C2×C3×C4C22⋊C411yescharacteristic
83C2×C3×C4C22×C411yescharacteristic
84C2×C3×C4C2×D411yescharacteristic
85#67—42no—
86C2×Dic3—21no—
87C2×Dic3—21no—
88C2×Dic3—21no—
89D12—41no—
90C4×D3—42no—
91Dic6—41no—
92C3⋊C8—42no—
93C2×Q8—31no—
94C2×D4—31no—
95C2×D4—61no—
96C22×C4—22no—
97C22×C4—61no—
98C22×C4#6711yescharacteristic
99C22×C4#6711yescharacteristic
100C22×C4C22×D311yescharacteristic
101C2×C8—62no—
102C4⋊C4—31no—
103C4⋊C4—31no—
104C4⋊C4—61no—
105C4⋊C4—61no—
106C4⋊C4—61no—
107C4⋊C4—61no—
108C22⋊C4—61no—
109C22⋊C4—61no—
110C22⋊C4—61no—
111C22⋊C4—61no—
112C22⋊C4—61no—
113C42—61no—
114C42C4×D311yescharacteristic
115C42C4×D311yescharacteristic
116C42D1211yescharacteristic
117C42D1211yescharacteristic
118C22×C3—21no—
119C22×C3—21no—
120C22×C3C2×C22⋊C411yescharacteristic
121C22×C3#13512yes—
122C2×D3—41no—
123C2×D3—41no—
124C2×D3—41no—
125C3×C4—21no—
126C3×C4—21no—
127C3×C4—21no—
128C3×C4—21no—
129C3×C4—21no—
130C3×C4—21no—
131C3×C4—82no—
132Dic3—41no—
133Dic3—41no—
134Dic3—41no—
135C23—61no—
136C23C2×#6711yescharacteristic
137Q8—121no—
138D4—121no—
139D4—122no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—61no—
147C2×C4—61no—
148C2×C4—61no—
149C2×C4—122no—
150C2×C4(C2×D3)⋊C411yescharacteristic
151C2×C4(C2×D3)⋊C411yescharacteristic
152C2×C4(C2×D3)⋊C411yescharacteristic
153C2×C4(C2×D3)⋊C411yescharacteristic
154C2×C4C2×C4×D311yescharacteristic
155C2×C4C2×D1211yescharacteristic
156C8—122no—
157C2×C3—22no—
158C2×C3#41011yescharacteristic
159C2×C3#41611yescharacteristic
160C2×C3#42111yescharacteristic
161D3—81no—
162C22—21no—
163C22—21no—
164C22—121no—
165C22—121no—
166C22—121no—
167C22C2×(C2×D3)⋊C411yescharacteristic
168C22#95012yes—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—82no—
176C4—121no—
177C4—121no—
178C4—121no—
179C3#152111yescharacteristic, complemented, Sylow
180C2—22no—
181C2—241no—
182C2#500211yescharacteristic
183C2#500511yescharacteristic
184C2#500611yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C4
FrattiniC22×C4C22×D3
FittingC3×#383C2
socleC22×C3C2×C22⋊C4
prime radical#930C22
cosocleC22×C3×C4C23
hypercenter#383D3
hypocenterC3#1521
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. C3×#383C2semidirect
3. #4925C2semidirect
4. #4452C2semidirect
13. #875C4semidirect
14. C4×D12C4semidirect
16. #870C4semidirect
17. C4×Dic6C4semidirect
26. #383D3semidirect
179. C3#1521semidirect

Maximal subgroups

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

subgroupindex
#54792
C3×#3832
#49252
#44522
#44512
#15213