Finite Group Databasebeta

← #71016

Subgroups — #71016

Order 384.

236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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#5543C211yesmaximal, characteristic, complemented
2C3×#459C211yesmaximal, characteristic
3#5076C211yesmaximal, characteristic, complemented
4#5075C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#4484C211yesmaximal, characteristic, complemented
7#4481C211yesmaximal, characteristic, complemented
8#1622—31nomaximal, Sylow
9C2×C3×D8—21no—
10C3×#127C2211yescharacteristic
11C3×C4×D4C2211yescharacteristic
12D4×Dic3—21no—
13C2×#214—21no—
14C2×#214—22no—
15C2×C4⋊Dic3—21no—
16#924—21no—
17#890—21no—
18#878—22no—
19#869C2211yescharacteristic
20C4×Dic6C2211yescharacteristic
21C3×C4⋊C8C2211yescharacteristic
22C3×#102—21no—
23#832—21no—
24C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C3⋊C8C2211yescharacteristic
26#554—31no—
27#492—31no—
28#460—31no—
29#459D311yescharacteristic
30#333—31no—
31Q8⋊C8—31no—
32D4⋊C8—31no—
33C2×C3×D4—21no—
34C2×C3×D4—21no—
35C2×C3×D4—21no—
36C2×C3×D4D411yescharacteristic
37C22×C3×C4—21no—
38C22×Dic3—22no—
39C2×Dic6D411yescharacteristic
40C2×Dic6D412yes—
41C3×D8—42no—
42C2×C3×C8—21no—
43C3×C4⋊C4D411yescharacteristic
44C3×C22⋊C4—21no—
45C3×C42C2311yescharacteristic
46#217—22no—
47#214—44no—
48#214—42no—
49C4⋊Dic3—22no—
50C4⋊Dic3—21no—
51C4⋊Dic3—21no—
52C4⋊Dic3D411yescharacteristic
53Dic3⋊C4—22no—
54Dic3⋊C4—21no—
55C4×Dic3—21no—
56C2×C3⋊C8—21no—
57C2×C3⋊C8—21no—
58C2×SD16—61no—
59C2×SD16—62no—
60C2×D8—21no—
61C4⋊Q8—31no—
62#127C2×D311yescharacteristic
63#125—61no—
64C22⋊Q8—62no—
65C22⋊Q8—61no—
66C4×Q8—31no—
67C4×D4—61no—
68C4×D4C2×D311yescharacteristic
69C2×C4⋊C4—61no—
70C4⋊C8—31no—
71C4⋊C8C2×D311yescharacteristic
72#102—21no—
73#102—61no—
74C4×C8—31no—
75C23×C3—21no—
76C23×C3—41no—
77C3×D4—21no—
78C3×D4—42no—
79C3×D4—41no—
80C3×D4—41no—
81C3×D4—41no—
82C3×D4—41no—
83C3×D4SD1612yescomplemented
84C2×C3×C4—21no—
85C2×C3×C4—41no—
86C2×C3×C4—41no—
87C2×C3×C4C2×D411yescharacteristic
88C2×C3×C4C2×D411yescharacteristic
89C2×C3×C4C2×D411yescharacteristic
90C2×Dic3—21no—
91C2×Dic3—21no—
92C2×Dic3—22no—
93C2×Dic3—82no—
94Dic6—21no—
95Dic6—21no—
96Dic6—42no—
97C3×C8—41no—
98C3⋊C8—22no—
99C3⋊C8—41no—
100C2×Q8—31no—
101C2×Q8—32no—
102C2×D4—21no—
103C2×D4—21no—
104C2×D4—21no—
105C2×D4#6711yescharacteristic
106C22×C4—21no—
107C22×C4—62no—
108SD16—124no—
109SD16—122no—
110D8—42no—
111C2×C8—21no—
112C2×C8—61no—
113C2×C8—61no—
114C4⋊C4—31no—
115C4⋊C4—62no—
116C4⋊C4—62no—
117C4⋊C4—61no—
118C4⋊C4—61no—
119C4⋊C4—61no—
120C4⋊C4#6711yescharacteristic
121C22⋊C4—21no—
122C22⋊C4—62no—
123C42—61no—
124C42C22×D311yescharacteristic
125C22×C3—22no—
126C22×C3—41no—
127C22×C3—41no—
128C22×C3—81no—
129C22×C3—81no—
130C22×C3—81no—
131C22×C3#12011yescharacteristic
132C3×C4—21no—
133C3×C4—41no—
134C3×C4C2×SD1611yescharacteristic
135C3×C4#13511yescharacteristic
136C3×C4AGL(1,ℤ/8)11yescharacteristic
137C3×C4#13711yescharacteristic
138Dic3—41no—
139Dic3—42no—
140Dic3—41no—
141C23—21no—
142C23—41no—
143Q8—61no—
144Q8—61no—
145Q8—122no—
146D4—21no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4#21412yescomplemented
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—61no—
157C2×C4—61no—
158C2×C4—62no—
159C2×C4—242no—
160C2×C4D3×D411yescharacteristic
161C2×C4D3×D411yescharacteristic
162C2×C4C2×#6711yescharacteristic
163C8—41no—
164C8—62no—
165C8—121no—
166C2×C3—42no—
167C2×C3—161no—
168C2×C3#44811yescharacteristic
169C2×C3#44911yescharacteristic
170C2×C3#45311yescharacteristic
171C22—22no—
172C22—41no—
173C22—41no—
174C22—81no—
175C22—81no—
176C22—81no—
177C22#93711yescharacteristic
178C4—21no—
179C4—41no—
180C4—121no—
181C4—121no—
182C4—122no—
183C4#91111yescharacteristic
184C4#91211yescharacteristic
185C4C2×#21411yescharacteristic
186C4#95111yescharacteristic
187C3#162211yescharacteristic, complemented, Sylow
188C2—42no—
189C2—161no—
190C2#504011yescharacteristic
191C2#515811yescharacteristic
192C2#519811yescharacteristic
subgroupG/H
centerC22#937
commutator, cosocleC3×C42C23
FrattiniC42C22×D3
Fitting, prime radicalC3×#459C2
socleC22×C3#120
hypercenter#459D3
hypocenterC3#1622
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #5543C2semidirect
3. #5076C2semidirect
4. #5075C2semidirect
5. D4⋊(C3⋊C8)C2semidirect
6. #4484C2semidirect
7. #4481C2semidirect
83. C3×D4SD16semidirect
152. D4#214semidirect
187. C3#1622semidirect

Maximal subgroups

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

subgroupindex
#55432
C3×#4592
#50762
#50752
D4⋊(C3⋊C8)2
#44842
#44812
#16223