Finite Group Databasebeta

← #68490

Subgroups — #68490

Order 384.

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

normal subgroups only

This group has 236 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, complemented
2#5085C211yesmaximal, characteristic, complemented
3#4848C211yesmaximal, characteristic, complemented
4#4843C211yesmaximal, characteristic
5C3×#333C211yesmaximal, characteristic, complemented
6#4484C211yesmaximal, characteristic, complemented
7#4483C211yesmaximal, characteristic, complemented
8#1622—31nomaximal, Sylow
9C3×C4⋊Q8C2211yescharacteristic
10#946—22no—
11C2×#215—22no—
12C2×D24—21no—
13C2×#204—21no—
14#897—21no—
15#893—21no—
16D3×C4⋊C4—21no—
17#890—21no—
18#874C2211yescharacteristic
19C4×D12C2211yescharacteristic
20C4×Dic6C2211yescharacteristic
21C3×C4⋊C8C2211yescharacteristic
22C3×C4⋊C8C2211yescharacteristic
23#821—21no—
24#821—21no—
25C4×C3⋊C8C2211yescharacteristic
26#554—31no—
27#492—31no—
28#460—31no—
29#459—31no—
30#333D311yescharacteristic, complemented
31Q8⋊C8—31no—
32D4⋊C8—31no—
33C2×C3×Q8D412yes—
34C2×D12—21no—
35C2×D12—21no—
36C2×D12—21no—
37C2×D12D411yescharacteristic
38C2×C4×D3—21no—
39C2×C4×D3—22no—
40C2×Dic6D411yescharacteristic
41C2×C3×C8—21no—
42C2×C3×C8—21no—
43C3×C4⋊C4—21no—
44C3×C4⋊C4—21no—
45C3×C42C2311yescharacteristic
46#215—44no—
47(C2×D3)⋊C4—22no—
48(C2×D3)⋊C4—21no—
49C4⋊Dic3—22no—
50C4⋊Dic3D411yescharacteristic
51C4⋊Dic3D411yescharacteristic
52Dic3⋊C4—22no—
53Dic3⋊C4—21no—
54C4×Dic3—21no—
55C2×C3⋊C8—21no—
56D24—42no—
57#204—42no—
58C2×SD16—61no—
59C2×SD16—62no—
60C2×D8—61no—
61C4⋊Q8C2×D311yescharacteristic
62#127—31no—
63#125—61no—
64C22⋊Q8—61no—
65C22⋊Q8—62no—
66C4×Q8—31no—
67C4×D4—31no—
68C4×D4—61no—
69C2×C4⋊C4—61no—
70C4⋊C8C2×D311yescharacteristic
71C4⋊C8C2×D311yescharacteristic
72#102—61no—
73#102—61no—
74C4×C8—31no—
75C22×D3—21no—
76C22×D3—41no—
77C3×Q8—42no—
78C2×C3×C4—22no—
79C2×C3×C4C2×D411yescharacteristic
80C2×C3×C4C2×D411yescharacteristic
81C2×C3×C4C2×D411yescharacteristic
82C2×Dic3—21no—
83C2×Dic3—21no—
84C2×Dic3—21no—
85D12—21no—
86D12—42no—
87D12—41no—
88D12—41no—
89D12—41no—
90D12—41no—
91D12SD1612yescomplemented
92C4×D3—41no—
93C4×D3—41no—
94C4×D3—82no—
95Dic6—21no—
96Dic6—21no—
97C3×C8—41no—
98C3×C8—41no—
99C3⋊C8—22no—
100C2×Q8—31no—
101C2×Q8D1212yes—
102C2×D4—31no—
103C2×D4—61no—
104C2×D4—61no—
105C2×D4—61no—
106C22×C4—62no—
107C22×C4—61no—
108SD16—122no—
109SD16—124no—
110D8—122no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—61no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—31no—
117C4⋊C4—31no—
118C4⋊C4—62no—
119C4⋊C4—62no—
120C4⋊C4—61no—
121C22⋊C4—62no—
122C22⋊C4—61no—
123C42—61no—
124C42C22×D311yescharacteristic
125C22×C3#12011yescharacteristic
126C2×D3—22no—
127C2×D3—41no—
128C2×D3—41no—
129C2×D3—81no—
130C2×D3—81no—
131C2×D3—81no—
132C3×C4—21no—
133C3×C4—42no—
134C3×C4C2×SD1611yescharacteristic
135C3×C4#13511yescharacteristic
136C3×C4AGL(1,ℤ/8)11yescharacteristic
137C3×C4#13711yescharacteristic
138Dic3—41no—
139Dic3—41no—
140Dic3—41no—
141C23—61no—
142C23—121no—
143Q8—42no—
144Q8—61no—
145Q8—61no—
146D4—32no—
147D4—61no—
148D4—122no—
149D4—121no—
150D4—121no—
151D4—121no—
152D4—121no—
153C2×C4—22no—
154C2×C4—61no—
155C2×C4—61no—
156C2×C4—61no—
157C2×C4—121no—
158C2×C4—121no—
159C2×C4—242no—
160C2×C4C2×D1211yescharacteristic
161C2×C4D3×D411yescharacteristic
162C2×C4D3×D411yescharacteristic
163C8—41no—
164C8—41no—
165C8—62no—
166C2×C3#44811yescharacteristic
167C2×C3#44911yescharacteristic
168C2×C3#45311yescharacteristic
169D3—42no—
170D3—161no—
171C22—62no—
172C22—121no—
173C22—121no—
174C22—241no—
175C22—241no—
176C22—241no—
177C22#88211yescharacteristic
178C4—21no—
179C4—42no—
180C4—121no—
181C4—121no—
182C4—121no—
183C4D3×SD1611yescharacteristic
184C4#91411yescharacteristic
185C4#91811yescharacteristic
186C4#91911yescharacteristic
187C3#162211yescharacteristic, complemented, Sylow
188C2—122no—
189C2—481no—
190C2#474711yescharacteristic
191C2#480611yescharacteristic
192C2#481011yescharacteristic
subgroupG/H
centerC22#882
commutator, cosocleC3×C42C23
FrattiniC42C22×D3
FittingC3×#333C2
socleC22×C3#120
prime radical#4843C2
hypercenter#333D3
hypocenterC3#1622
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #5730C2semidirect
2. #5085C2semidirect
3. #4848C2semidirect
5. C3×#333C2semidirect
6. #4484C2semidirect
7. #4483C2semidirect
30. #333D3semidirect
91. D12SD16semidirect
187. C3#1622semidirect

Maximal subgroups

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

subgroupindex
#57302
#50852
#48482
#48432
C3×#3332
#44842
#44832
#16223