Finite Group Databasebeta

← #11785746

Subgroups — #11785746

Order 1152.

709 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 709 conjugacy classes of subgroups — too many to draw. Only its 148 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
1C2×#64135C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3#10589168C214yesmaximal, complemented
4#69974—32nomaximal
5C23×C32×C4C2211yescharacteristic
6C2×#3757C412yes—
7#64135—24no—
8C2×C4⋊(C3⋊Dic3)C2212yes—
9C2×C4×C3⋊Dic3C412yes—
10C2×C3×#208C2214yes—
11C3×#830—24no—
12C2×#926—32no—
13C2×#926—61no—
14C3×#407—32no—
15#5207D312yes—
16#4554—38no—
17C24×C32C2×C411yescharacteristic
18C22×C32×C4—24no—
19C22×C32×C4C2×C411yescharacteristic
20C22×C32×C4D414yes—
21C22×C32×C4C2311yescharacteristic
22C22×C3⋊Dic3C2×C414yes—
23#3757—24no—
24C4⋊(C3⋊Dic3)—24no—
25C4×C3⋊Dic3—24no—
26C3×#208—28no—
27C2×C3×C3⋊C8—24no—
28#1822—91noSylow
29C23×C3×C4—21no—
30C23×C3×C4C2×D312yes—
31C2×C3×M16—34no—
32C2×#217—34no—
33C2×#217—62no—
34#926—68no—
35#926—64no—
36#926—64no—
37C2×C4⋊Dic3—34no—
38C2×C4⋊Dic3—62no—
39C2×C4×Dic3—34no—
40C2×C4×Dic3—62no—
41C2×#208C2×D314yes—
42C3×C22⋊C8—64no—
43#830—24no—
44C23×C32—22no—
45C23×C32—42no—
46C23×C32C22⋊C412yes—
47C23×C32C22×C411yescharacteristic
48C2×C32×C4—22no—
49C2×C32×C4—28no—
50C2×C32×C4C22⋊C412yes—
51C2×C32×C4C2×D412yes—
52C2×C32×C4#4114yes—
53C2×C3⋊Dic3—24no—
54C2×C3⋊Dic3—44no—
55C3×C3⋊C8—44no—
56C2×#117—91no—
57#407—32no—
58#343—94no—
59C24×C3—21no—
60C24×C3C4×D312yes—
61C22×C3×C4—28no—
62C22×C3×C4—28no—
63C22×C3×C4—21no—
64C22×C3×C4—24no—
65C22×C3×C4—21no—
66C22×C3×C4C4×D312yes—
67C22×C3×C4D1214yes—
68C22×C3×C4#6714yes—
69C22×C3×C4C22×D312yes—
70C22×Dic3—38no—
71C22×Dic3—64no—
72C3×M16—68no—
73C2×C3×C8—64no—
74#217—68no—
75#217—68no—
76C4⋊Dic3—68no—
77C4⋊Dic3—64no—
78C4⋊Dic3—64no—
79C4×Dic3—68no—
80C4×Dic3—68no—
81#208—28no—
82C2×C3⋊C8—24no—
83C22×C32—22no—
84C22×C32—22no—
85C22×C32—24no—
86C22×C32—44no—
87C22×C32C2×C22⋊C411yescharacteristic
88C22×C32#11712yes—
89C32×C4—22no—
90C32×C4#12314yes—
91C3⋊Dic3—44no—
92C23×C4D3211yescharacteristic
93C2×M16—34no—
94#117—184no—
95C2×C4⋊C4—92no—
96C2×C22⋊C4—92no—
97C2×C42—92no—
98C22⋊C8—64no—
99C23×C3—24no—
100C23×C3—24no—
101C23×C3—22no—
102C23×C3—21no—
103C23×C3—44no—
104C23×C3—44no—
105C23×C3(C2×D3)⋊C414yes—
106C23×C3C2×C4×D312yes—
107C2×C3×C4—24no—
108C2×C3×C4—216no—
109C2×C3×C4—24no—
110C2×C3×C4—28no—
111C2×C3×C4—28no—
112C2×C3×C4—22no—
113C2×C3×C4—24no—
114C2×C3×C4—22no—
115C2×C3×C4(C2×D3)⋊C414yes—
116C2×C3×C4C2×D1212yes—
117C2×C3×C4#23718yes—
118C2×C3×C4C2×#6712yes—
119C2×Dic3—68no—
120C2×Dic3—68no—
121C2×Dic3—128no—
122C2×Dic3—128no—
123C3×C8—124no—
124C3⋊C8—44no—
125C2×C32—22no—
126C2×C32—42no—
127C2×C32#38111yescharacteristic
128C2×C32#41312yes—
129C24#62411yescharacteristic
130C22×C4—24no—
131C22×C4—94no—
132C22×C4#62411yescharacteristic
133C22×C4#62614yes—
134C22×C4C2×D3211yescharacteristic
135M16—68no—
136C2×C8—64no—
137C4⋊C4—184no—
138C22⋊C4—184no—
139C42—184no—
140C22×C3—24no—
141C22×C3—24no—
142C22×C3—24no—
143C22×C3—28no—
144C22×C3—24no—
145C22×C3—22no—
146C22×C3—21no—
147C22×C3—44no—
148C22×C3—48no—
149C22×C3—48no—
150C22×C3#87714yes—
151C22×C3C2×(C2×D3)⋊C412yes—
152C3×C4—24no—
153C3×C4—24no—
154C3×C4—24no—
155C3×C4#88614yes—
156C3×C4#93514yes—
157Dic3—128no—
158Dic3—128no—
159C32#182211yescharacteristic, complemented, Sylow
160C23—22no—
161C23—42no—
162C23#372212yes—
163C23C2×#62411yescharacteristic
164C2×C4—22no—
165C2×C4—28no—
166C2×C4—184no—
167C2×C4—364no—
168C2×C4#372212yes—
169C2×C4#380514yes—
170C2×C4C2×#62612yes—
171C8—124no—
172C2×C3—24no—
173C2×C3—24no—
174C2×C3—22no—
175C2×C3—21no—
176C2×C3—44no—
177C2×C3—44no—
178C2×C3#494312yes—
179C2×C3#513214yes—
180C22—22no—
181C22—24no—
182C22—22no—
183C22—44no—
184C22#6395712yes—
185C22C2×#372211yescharacteristic
186C4—22no—
187C4—364no—
188C4#6396214yes—
189C3—21no—
190C3#6997412yescomplemented
191C2—22no—
192C2—42no—
193C2#1059107812yes—
194C2#1059169711yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1822
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10589168C2semidirect
159. C32#1822semidirect
190. C3#69974semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C3×#52072
#105891682
#699743