Finite Group Databasebeta

← #71249

Subgroups — #71249

Order 384.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#5699C211yesmaximal, characteristic, complemented
2C3×#490C211yesmaximal, characteristic, complemented
3#5074C211yesmaximal, characteristic
4#5071C211yesmaximal, characteristic, complemented
5#4543C211yesmaximal, characteristic, complemented
6#4465C211yesmaximal, characteristic, complemented
7#4464C211yesmaximal, characteristic, complemented
8#1657—31nomaximal, Sylow
9C3×#127C2211yescharacteristic
10C3×#125C2211yescharacteristic
11C2×#214—21no—
12C2×#213—21no—
13#898—21no—
14#898—21no—
15#897—21no—
16#896—21no—
17#894—21no—
18#888—21no—
19#875C2211yescharacteristic
20#870C2211yescharacteristic
21C3×#102—21no—
22C3×#102—21no—
23C3×#97C2211yescharacteristic
24#832—21no—
25#832—21no—
26#803C2211yescharacteristic
27#803C2211yescharacteristic
28#563—31no—
29#496—31no—
30#490—31no—
31#490D311yescharacteristic, complemented
32#330—31no—
33#330—31no—
34#329—31no—
35C2×C3×D4—21no—
36C2×C3×D4—21no—
37C2×C3×D4—21no—
38C2×D12D411yescharacteristic
39C2×C4×D3—21no—
40C2×Dic6—21no—
41C2×Dic6D411yescharacteristic
42C2×C3×C8—21no—
43C3×C4⋊C4—21no—
44C3×C4⋊C4—21no—
45C3×C4⋊C4D411yescharacteristic
46C3×C4⋊C4D411yescharacteristic
47C3×C42C2311yescharacteristic
48#214—42no—
49#213—42no—
50(C2×D3)⋊C4—21no—
51(C2×D3)⋊C4—21no—
52(C2×D3)⋊C4—21no—
53(C2×D3)⋊C4—21no—
54(C2×D3)⋊C4—21no—
55C4⋊Dic3—21no—
56C4⋊Dic3D411yescharacteristic
57C4⋊Dic3D411yescharacteristic
58Dic3⋊C4—21no—
59Dic3⋊C4—21no—
60Dic3⋊C4—21no—
61C4×Dic3—21no—
62C2×C3⋊C8—21no—
63C2×C3⋊C8—21no—
64C2×SD16—61no—
65C2×D8—61no—
66C4⋊Q8—61no—
67#127C2×D311yescharacteristic
68#126—61no—
69#126—61no—
70#125—31no—
71#125C2×D311yescharacteristic
72#124—31no—
73#123—61no—
74C22⋊Q8—61no—
75C22⋊Q8—61no—
76#102—21no—
77#102—21no—
78#102—61no—
79#102—61no—
80#97—31no—
81#97—31no—
82#97C2×D311yescharacteristic
83C23×C3—41no—
84C22×D3—21no—
85C3×D4—41no—
86C3×D4—41no—
87C3×D4—42no—
88C3×D4—42no—
89C2×C3×C4—21no—
90C2×C3×C4—21no—
91C2×C3×C4C2×D411yescharacteristic
92C2×C3×C4C2×D411yescharacteristic
93C2×C3×C4C2×D411yescharacteristic
94C2×Dic3—21no—
95C2×Dic3—21no—
96C2×Dic3—21no—
97D12—41no—
98C4×D3—81no—
99Dic6—41no—
100Dic6—81no—
101C3×C8—41no—
102C3⋊C8—22no—
103C3⋊C8—41no—
104C2×Q8—31no—
105C2×Q8—61no—
106C2×D4—21no—
107C2×D4—21no—
108C2×D4—21no—
109C2×D4—31no—
110C22×C4—61no—
111SD16—122no—
112D8—122no—
113C2×C8—21no—
114C2×C8—61no—
115C2×C8—61no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—31no—
119C4⋊C4—31no—
120C4⋊C4—61no—
121C4⋊C4—61no—
122C4⋊C4—61no—
123C4⋊C4—61no—
124C4⋊C4#6711yescharacteristic
125C4⋊C4#6711yescharacteristic
126C22⋊C4—61no—
127C22⋊C4—61no—
128C22⋊C4—61no—
129C22⋊C4—61no—
130C22⋊C4—61no—
131C42—61no—
132C42C22×D311yescharacteristic
133C22×C3—81no—
134C22×C3—81no—
135C22×C3—81no—
136C22×C3#12011yescharacteristic
137C2×D3—41no—
138C2×D3—41no—
139C2×D3—41no—
140C3×C4—21no—
141C3×C4—21no—
142C3×C4—21no—
143C3×C4—41no—
144C3×C4—41no—
145Dic3—41no—
146Dic3—41no—
147Dic3—41no—
148C23—41no—
149C23—61no—
150Q8—121no—
151Q8—241no—
152D4—41no—
153D4—41no—
154D4—42no—
155D4—42no—
156D4—121no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—61no—
160C2×C4—61no—
161C2×C4—61no—
162C2×C4—241no—
163C2×C4D3×D411yescharacteristic
164C2×C4D3×D411yescharacteristic
165C2×C4C2×#6711yescharacteristic
166C8—41no—
167C8—62no—
168C8—121no—
169C2×C3—161no—
170C2×C3#45311yescharacteristic
171C2×C3#45411yescharacteristic
172C2×C3#45411yescharacteristic
173D3—81no—
174C22—81no—
175C22—81no—
176C22—81no—
177C22—121no—
178C22—121no—
179C22—121no—
180C22#93711yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—121no—
187C4—121no—
188C4—121no—
189C3#165711yescharacteristic, complemented, Sylow
190C2—161no—
191C2—241no—
192C2#506211yescharacteristic
193C2#519811yescharacteristic
194C2#520111yescharacteristic
subgroupG/H
centerC22#937
commutator, cosocleC3×C42C23
FrattiniC42C22×D3
FittingC3×#490C2
socleC22×C3#120
prime radical#5074C2
hypercenter#490D3
hypocenterC3#1657
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #5699C2semidirect
2. C3×#490C2semidirect
4. #5071C2semidirect
5. #4543C2semidirect
6. #4465C2semidirect
7. #4464C2semidirect
31. #490D3semidirect
189. C3#1657semidirect

Maximal subgroups

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

subgroupindex
#56992
C3×#4902
#50742
#50712
#45432
#44652
#44642
#16573