Finite Group Databasebeta

← #11800094

Subgroups — #11800094

Order 1152.

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

normal subgroups only

This group has 414 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#10592890C211yesmaximal, characteristic
2#10592577C211yesmaximal, characteristic, complemented
3C32×#358C211yesmaximal, characteristic, complemented
4#10589430C211yesmaximal, characteristic, complemented
5#10589375C211yesmaximal, characteristic
6C16×C3⋊Dic3C211yesmaximal, characteristic, complemented
7#10589357C211yesmaximal, characteristic
8#69216—34nomaximal
9C2×C32×Q16C2211yescharacteristic
10#64156—21no—
11C2×#3755—21no—
12C2×#3745C2211yescharacteristic
13#64099—21no—
14C2×C32×C16C2211yescharacteristic
15C32×#107C2211yescharacteristic
16#63645C2211yescharacteristic
17C8×C3⋊Dic3C2211yescharacteristic
18C2×C3⋊(C3⋊C16)C2211yescharacteristic
19#63635—21no—
20#5191—34no—
21#4878—34no—
22C3×#358D314yescomplemented
23#4564—34no—
24#4509—34no—
25Dic3×C16—34no—
26#4491—34no—
27C2×C32×Q8—21no—
28C2×C4⋊(C3⋊D3)—21no—
29C32×Q16—21no—
30C32×Q16—21no—
31C2×C32×C8C2311yescharacteristic
32C32×C4⋊C4—21no—
33#3755—42no—
34#3752—41no—
35#3752—41no—
36C4⋊(C3⋊Dic3)—21no—
37C4⋊(C3⋊Dic3)—41no—
38#3750—41no—
39C4×C3⋊Dic3D411yescharacteristic
40C2×C3⋊(C3⋊C8)D411yescharacteristic
41#3745—21no—
42#3745—21no—
43C32×C16—21no—
44C3⋊(C3⋊C16)—21no—
45#2242—91noSylow
46C2×C3×Q16C2×D314yes—
47#947—64no—
48C2×#215—64no—
49C2×D24—34no—
50#890—64no—
51C2×C3×C16C2×D314yes—
52C3×#107C2×D314yes—
53#818—34no—
54C8×Dic3—34no—
55C2×C3⋊C16—34no—
56#808—64no—
57C22×C3⋊D3—41no—
58C32×Q8—41no—
59C32×Q8—41no—
60C2×C32×C4—41no—
61C2×C32×C4—41no—
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3D811yescharacteristic
65C2×C3⋊Dic3D811yescharacteristic
66C4⋊(C3⋊D3)—41no—
67C4⋊(C3⋊D3)—41no—
68C32×C8#4111yescharacteristic
69C32×C8#4111yescharacteristic
70C3⋊(C3⋊C8)SD1612yes—
71#499—91no—
72#495—91no—
73#358—91no—
74#358C3⋊D311yescharacteristic, complemented
75#357—91no—
76#357—91no—
77C4×C16—91no—
78C2×C3×Q8—24no—
79C2×D12—64no—
80C3×Q16—24no—
81C3×Q16—24no—
82C2×C3×C8C22×D314yes—
83C3×C4⋊C4—24no—
84#215—128no—
85(C2×D3)⋊C4—124no—
86(C2×D3)⋊C4—124no—
87C4⋊Dic3—64no—
88C4⋊Dic3—124no—
89Dic3⋊C4—124no—
90C4×Dic3—34no—
91C2×C3⋊C8—34no—
92D24—64no—
93D24—64no—
94C3×C16—24no—
95C3⋊C16—64no—
96C22×C32C2×D811yescharacteristic
97C2×C3⋊D3—81no—
98C2×C3⋊D3—81no—
99C2×C3⋊D3—81no—
100C32×C4—81no—
101C32×C4—81no—
102C32×C4#12411yescharacteristic
103C32×C4C2×SD1611yescharacteristic
104C3⋊Dic3—21no—
105C3⋊Dic3—21no—
106C3⋊Dic3—81no—
107C2×Q16C2×C3⋊D311yescharacteristic
108C2×SD16—181no—
109C2×D8—91no—
110#125—181no—
111#124—181no—
112C2×C16—91no—
113C2×C16C2×C3⋊D311yescharacteristic
114#107—91no—
115#107C2×C3⋊D311yescharacteristic
116#106—181no—
117C4×C8—91no—
118C22×D3—124no—
119C3×Q8—44no—
120C3×Q8—44no—
121C2×C3×C4—44no—
122C2×C3×C4—44no—
123C2×C3×C4D3×D414yes—
124C2×Dic3—34no—
125C2×Dic3—34no—
126C2×Dic3—124no—
127D12—124no—
128D12—124no—
129C3×C8#23514yes—
130C3×C8#23714yes—
131C3⋊C8—38no—
132C2×C32#48611yescharacteristic
133C2×C32#50811yescharacteristic
134C2×C32#50811yescharacteristic
135C3⋊D3—161no—
136C2×Q8—21no—
137C2×D4—181no—
138Q16—21no—
139Q16—21no—
140SD16—362no—
141D8—181no—
142D8—181no—
143C2×C8—91no—
144C2×C8C22×C3⋊D311yescharacteristic
145C4⋊C4—21no—
146C4⋊C4—181no—
147C4⋊C4—361no—
148C4⋊C4—361no—
149C22⋊C4—361no—
150C22⋊C4—361no—
151C42—91no—
152C16—21no—
153C16—181no—
154C22×C3D3×D814yes—
155C2×D3—244no—
156C2×D3—244no—
157C2×D3—244no—
158C3×C4—84no—
159C3×C4—84no—
160C3×C4#88514yes—
161C3×C4D3×SD1614yes—
162Dic3—64no—
163Dic3—64no—
164Dic3—244no—
165C32#224211yescharacteristic, complemented, Sylow
166C23—361no—
167Q8—41no—
168Q8—41no—
169D4—361no—
170D4—361no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—361no—
176C2×C4D4×C3⋊D311yescharacteristic
177C8—92no—
178C8#382811yescharacteristic
179C8#383011yescharacteristic
180C2×C3#476014yes—
181C2×C3#491614yes—
182C2×C3#491914yes—
183D3—484no—
184C22—721no—
185C22—721no—
186C22—721no—
187C22D8×C3⋊D311yescharacteristic
188C4—81no—
189C4—81no—
190C4—181no—
191C4—181no—
192C4—721no—
193C4#6409411yescharacteristic
194C4SD16×C3⋊D311yescharacteristic
195C3#6921614yescomplemented
196C2—1441no—
197C2#1059245911yescharacteristic
198C2#1059261511yescharacteristic
199C2#1059261811yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#358C2
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenter#358C3⋊D3
hypocenterC32#2242
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
2. #10592577C2semidirect
3. C32×#358C2semidirect
4. #10589430C2semidirect
6. C16×C3⋊Dic3C2semidirect
22. C3×#358D3semidirect
74. #358C3⋊D3semidirect
165. C32#2242semidirect
195. C3#69216semidirect

Maximal subgroups

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

subgroupindex
#105928902
#105925772
C32×#3582
#105894302
#105893752
C16×C3⋊Dic32
#105893572
#692163