Finite Group Databasebeta

← #71230

Subgroups — #71230

Order 384.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#5730C211yesmaximal, characteristic
2C3×#487C211yesmaximal, characteristic, complemented
3#5094C211yesmaximal, characteristic, complemented
4#5083C211yesmaximal, characteristic
5#4546C211yesmaximal, characteristic, complemented
6#4459C211yesmaximal, characteristic
7#4456C211yesmaximal, characteristic, complemented
8#1643—31nomaximal, Sylow
9C3×C4⋊Q8C2211yescharacteristic
10C3×C4⋊Q8C2211yescharacteristic
11#946—22no—
12C2×#215—21no—
13#897—21no—
14#893—21no—
15D3×C4⋊C4—21no—
16#890—21no—
17C4×D12C2211yescharacteristic
18C4×Dic6C2211yescharacteristic
19C3×#103—22no—
20C3×C4×C8C2211yescharacteristic
21#835—21no—
22#810—21no—
23#808—21no—
24C4⋊(C3⋊C8)C2211yescharacteristic
25C4⋊(C3⋊C8)C2211yescharacteristic
26#554—31no—
27#487D311yescharacteristic, complemented
28#475—31no—
29#461—31no—
30#333—31no—
31Q8⋊C8—31no—
32D4⋊C8—31no—
33C2×C3×Q8—21no—
34C2×C3×Q8D412yes—
35C2×D12D411yescharacteristic
36C2×C4×D3—21no—
37C2×C4×D3—22no—
38C2×Dic6D411yescharacteristic
39C2×C3×C8—21no—
40C3×C4⋊C4—21no—
41C3×C4⋊C4—21no—
42C3×C4⋊C4—21no—
43C3×C4⋊C4—21no—
44C3×C42C2311yescharacteristic
45#215—42no—
46(C2×D3)⋊C4—22no—
47(C2×D3)⋊C4—21no—
48C4⋊Dic3—22no—
49C4⋊Dic3D411yescharacteristic
50C4⋊Dic3D411yescharacteristic
51Dic3⋊C4—22no—
52Dic3⋊C4—21no—
53C4×Dic3—21no—
54C2×C3⋊C8—21no—
55C2×C3⋊C8—21no—
56C2×SD16—61no—
57C4⋊Q8C2×D311yescharacteristic
58C4⋊Q8C2×D311yescharacteristic
59#125—61no—
60C22⋊Q8—61no—
61C22⋊Q8—62no—
62C4×Q8—31no—
63C4×D4—31no—
64C4×D4—61no—
65C2×C4⋊C4—61no—
66#106—61no—
67C4⋊C8—31no—
68C4⋊C8—31no—
69#103—22no—
70#103—61no—
71#103—61no—
72C4×C8C2×D311yescharacteristic
73C22×D3—21no—
74C3×Q8—42no—
75C3×Q8—41no—
76C3×Q8—41no—
77C2×C3×C4—22no—
78C2×C3×C4—41no—
79C2×C3×C4C2×D411yescharacteristic
80C2×C3×C4C2×D411yescharacteristic
81C2×C3×C4C2×D411yescharacteristic
82C2×Dic3—21no—
83C2×Dic3—21no—
84C2×Dic3—21no—
85D12—21no—
86D12SD1612yes—
87C4×D3—41no—
88C4×D3—41no—
89C4×D3—82no—
90Dic6—21no—
91Dic6—21no—
92C3×C8—41no—
93C3⋊C8—41no—
94C3⋊C8—41no—
95C2×Q8—21no—
96C2×Q8—31no—
97C2×Q8#6712yes—
98C2×D4—31no—
99C22×C4—62no—
100C22×C4—61no—
101SD16—122no—
102C2×C8—21no—
103C2×C8—61no—
104C2×C8—61no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—31no—
110C4⋊C4—31no—
111C4⋊C4—62no—
112C4⋊C4—62no—
113C4⋊C4—61no—
114C22⋊C4—62no—
115C22⋊C4—61no—
116C42—61no—
117C42C22×D311yescharacteristic
118C22×C3#12011yescharacteristic
119C2×D3—22no—
120C2×D3—41no—
121C2×D3—41no—
122C3×C4—21no—
123C3×C4—42no—
124C3×C4—81no—
125C3×C4C2×SD1611yescharacteristic
126C3×C4#13511yescharacteristic
127C3×C4#13711yescharacteristic
128C3×C4#13711yescharacteristic
129Dic3—41no—
130Dic3—41no—
131Dic3—41no—
132C23—61no—
133Q8—42no—
134Q8—41no—
135Q8—41no—
136Q8—61no—
137Q8—61no—
138D4—32no—
139D4—61no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—61no—
143C2×C4—61no—
144C2×C4—61no—
145C2×C4—121no—
146C2×C4—121no—
147C2×C4—242no—
148C2×C4D3×D411yescharacteristic
149C2×C4D3×D411yescharacteristic
150C2×C4C2×#6711yescharacteristic
151C8—41no—
152C8—121no—
153C8—121no—
154C2×C3#44811yescharacteristic
155C2×C3#45211yescharacteristic
156C2×C3#45511yescharacteristic
157D3—42no—
158C22—62no—
159C22—121no—
160C22—121no—
161C22#93711yescharacteristic
162C4—21no—
163C4—42no—
164C4—81no—
165C4—121no—
166C4—121no—
167C4—121no—
168C4D3×SD1611yescharacteristic
169C4#91511yescharacteristic
170C4#91811yescharacteristic
171C4#91911yescharacteristic
172C3#164311yescharacteristic, complemented, Sylow
173C2—122no—
174C2#506111yescharacteristic
175C2#517011yescharacteristic
176C2#518711yescharacteristic
subgroupG/H
centerC22#937
commutator, cosocleC3×C42C23
FrattiniC42C22×D3
FittingC3×#487C2
socleC22×C3#120
prime radicalC2×D12D4
hypercenter#487D3
hypocenterC3#1643
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C3×#487C2semidirect
3. #5094C2semidirect
5. #4546C2semidirect
7. #4456C2semidirect
27. #487D3semidirect
172. C3#1643semidirect

Maximal subgroups

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

subgroupindex
#57302
C3×#4872
#50942
#50832
#45462
#44592
#44562
#16433