Finite Group Databasebeta

← #11799881

Subgroups — #11799881

Order 1152.

420 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 107 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#10592586C211yesmaximal, characteristic
2C3⋊D3×#107C211yesmaximal, characteristic
3C32×#367C211yesmaximal, characteristic, complemented
4#10589373C211yesmaximal, characteristic
5#10589369C211yesmaximal, characteristic, complemented
6#10589358C211yesmaximal, characteristic, complemented
7#10589356C211yesmaximal, characteristic, complemented
8#69352—34nomaximal
9C2×#3746C2211yescharacteristic
10C2×C8×C3⋊D3C2211yescharacteristic
11#64106—21no—
12C4⋊C4×C3⋊D3—21no—
13C2×C32×C16C2211yescharacteristic
14C32×#107C2211yescharacteristic
15C32×#107C2211yescharacteristic
16#63645C2211yescharacteristic
17C2×C3⋊(C3⋊C16)C2211yescharacteristic
18#63637—21no—
19#63634—21no—
20#4887—34no—
21D3×#107—34no—
22C3×#367D314yescomplemented
23(C2×D3)⋊C16—34no—
24#4503—34no—
25#4492—34no—
26#4490—34no—
27C2×C4×C3⋊D3—41no—
28C2×C4×C3⋊D3D411yescharacteristic
29C2×#634—21no—
30C2×C32×C8C2311yescharacteristic
31C32×C4⋊C4—21no—
32C32×C4⋊C4—21no—
33#3752—41no—
34C4⋊(C3⋊Dic3)—21no—
35C4⋊(C3⋊Dic3)—41no—
36#3750—41no—
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38#3746—21no—
39#3746—21no—
40C8×C3⋊D3—21no—
41C8×C3⋊D3—21no—
42C32×C16—21no—
43C3⋊(C3⋊C16)—21no—
44#2235—91noSylow
45C2×Dic12—34no—
46C2×D3×C8—34no—
47#897—64no—
48D3×C4⋊C4—64no—
49C2×C3×C16C2×D314yes—
50C3×#107C2×D314yes—
51C3×#107C2×D314yes—
52#818—34no—
53C2×C3⋊C16—34no—
54#810—64no—
55#807—64no—
56C22×C3⋊D3D811yescharacteristic
57C2×C32×C4—41no—
58C2×C32×C4—41no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3—41no—
61C2×C3⋊Dic3—41no—
62C2×C3⋊Dic3D811yescharacteristic
63C4×C3⋊D3—21no—
64C4×C3⋊D3—21no—
65C4×C3⋊D3—82no—
66#634—41no—
67#634—41no—
68C32×C8#4111yescharacteristic
69C32×C8#4111yescharacteristic
70C3⋊(C3⋊C8)—21no—
71#467—91no—
72C2×#107—91no—
73#367—91no—
74#367C3⋊D311yescharacteristic, complemented
75#358—91no—
76#358—91no—
77C22⋊C16—91no—
78C2×C4×D3—34no—
79C2×C4×D3—124no—
80C2×Dic6—64no—
81C2×C3×C8C22×D314yes—
82C3×C4⋊C4—24no—
83C3×C4⋊C4—24no—
84(C2×D3)⋊C4—124no—
85C4⋊Dic3—64no—
86C4⋊Dic3—124no—
87Dic3⋊C4—124no—
88C2×C3⋊C8—34no—
89Dic12—64no—
90Dic12—64no—
91D3×C8—64no—
92D3×C8—64no—
93C3×C16—24no—
94C3⋊C16—64no—
95C22×C32C2×D811yescharacteristic
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C2×C3⋊D3SD3212yes—
99C32×C4—81no—
100C32×C4—81no—
101C32×C4#12311yescharacteristic
102C32×C4#13711yescharacteristic
103C3⋊Dic3—21no—
104C3⋊Dic3—81no—
105C3⋊Dic3—81no—
106C2×Q16—91no—
107C22×C8—91no—
108C22⋊Q8—181no—
109C2×C4⋊C4—181no—
110C2×C16—91no—
111C2×C16C2×C3⋊D311yescharacteristic
112#107—91no—
113#107—181no—
114#107C2×C3⋊D311yescharacteristic
115#107C2×C3⋊D311yescharacteristic
116#103—181no—
117C22×D3—34no—
118C2×C3×C4—44no—
119C2×C3×C4—44no—
120C2×C3×C4D3×D414yes—
121C2×Dic3—34no—
122C2×Dic3—124no—
123C2×Dic3—124no—
124C4×D3—64no—
125C4×D3—64no—
126C4×D3—248no—
127Dic6—124no—
128Dic6—124no—
129C3×C8#23514yes—
130C3×C8#23914yes—
131C3⋊C8—64no—
132C2×C32#48011yescharacteristic
133C2×C32C2×SD3211yescharacteristic
134C2×C32#51011yescharacteristic
135C3⋊D3—22no—
136C2×Q8—181no—
137C22×C4—91no—
138C22×C4—361no—
139Q16—181no—
140Q16—181no—
141C2×C8—91no—
142C2×C8—181no—
143C2×C8—181no—
144C2×C8C22×C3⋊D311yescharacteristic
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—181no—
148C4⋊C4—361no—
149C4⋊C4—361no—
150C22⋊C4—361no—
151C16—21no—
152C16—181no—
153C22×C3D3×D814yes—
154C2×D3—38no—
155C2×D3—64no—
156C2×D3—64no—
157C3×C4—84no—
158C3×C4—84no—
159C3×C4#89414yes—
160C3×C4#91814yes—
161Dic3—64no—
162Dic3—244no—
163Dic3—244no—
164C32#223511yescharacteristic, complemented, Sylow
165C23—91no—
166Q8—361no—
167Q8—361no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—91no—
171C2×C4—181no—
172C2×C4—181no—
173C2×C4—361no—
174C2×C4—361no—
175C2×C4—722no—
176C2×C4D4×C3⋊D311yescharacteristic
177C8—181no—
178C8#382811yescharacteristic
179C8#383211yescharacteristic
180C2×C3#488214yes—
181C2×C3D3×SD3214yes—
182C2×C3#491514yes—
183D3—68no—
184C22—92no—
185C22—181no—
186C22—181no—
187C22D8×C3⋊D311yescharacteristic
188C4—81no—
189C4—81no—
190C4—181no—
191C4—721no—
192C4—721no—
193C4#6410311yescharacteristic
194C4#6412711yescharacteristic
195C3#6935214yescomplemented
196C2—182no—
197C2#1059258111yescharacteristic
198C2C3⋊D3×SD3211yescharacteristic
199C2#1059261411yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#367C2
socleC22×C32C2×D8
prime radicalC22×C3⋊D3D8
hypercenter#367C3⋊D3
hypocenterC32#2235
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

Complements

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

NH ≅ G/Ntype
3. C32×#367C2semidirect
5. #10589369C2semidirect
6. #10589358C2semidirect
7. #10589356C2semidirect
22. C3×#367D3semidirect
74. #367C3⋊D3semidirect
164. C32#2235semidirect
195. C3#69352semidirect

Maximal subgroups

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

subgroupindex
#105925862
C3⋊D3×#1072
C32×#3672
#105893732
#105893692
#105893582
#105893562
#693523