Finite Group Databasebeta

← #11771111

Subgroups — #11771111

Order 1152.

475 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 475 conjugacy classes of subgroups — too many to draw. Only its 120 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#10592906C211yesmaximal, characteristic
2C2×C3×#830C212yesmaximal
3#67680—32nomaximal
4C23×C32×C4C2211yescharacteristic
5C2×#3748C412yes—
6C22×C3×C3⋊C8—22no—
7#63657—22no—
8C3×#830—22no—
9C3×#830C414yes—
10C2×C3×C22⋊C8—32no—
11#5207—32no—
12#5207—61no—
13C2×#830D312yes—
14C24×C32Q811yescharacteristic
15C22×C32×C4—42no—
16C22×C32×C4C2×C411yescharacteristic
17C22×C32×C4C2×C412yes—
18C22×C32×C4D412yes—
19C22×C32×C4D411yescharacteristic
20#3748—42no—
21C2×C3⋊(C3⋊C8)—22no—
22C2×C3×C3⋊C8—24no—
23C2×C3×C3⋊C8—44no—
24#1298—91noSylow
25C23×C3×C4—21no—
26C23×C3×C4C2×D312yes—
27C22×C3×C8—62no—
28C2×#208—34no—
29C2×#208—62no—
30C22×C3⋊C8—22no—
31C3×C22⋊C8—34no—
32C3×C22⋊C8—62no—
33#830—22no—
34#830—64no—
35#830—62no—
36#830—62no—
37#830Dic314yes—
38C23×C32—24no—
39C23×C32—41no—
40C23×C32C4⋊C411yescharacteristic
41C23×C32C4⋊C412yes—
42C2×C32×C4—22no—
43C2×C32×C4—24no—
44C2×C32×C4—42no—
45C2×C32×C4—41no—
46C2×C32×C4C4211yescharacteristic
47C2×C32×C4C22⋊C411yescharacteristic
48C2×C32×C4C22⋊C412yes—
49C3⋊(C3⋊C8)—42no—
50C3×C3⋊C8—44no—
51#407—91no—
52C2×C22⋊C8—32no—
53C24×C3—21no—
54C24×C3Dic612yes—
55C22×C3×C4—22no—
56C22×C3×C4—21no—
57C22×C3×C4—21no—
58C22×C3×C4—22no—
59C22×C3×C4—44no—
60C22×C3×C4—44no—
61C22×C3×C4C4×D312yes—
62C22×C3×C4C4×D312yes—
63C22×C3×C4D1212yes—
64C22×C3×C4C2×Dic312yes—
65C22×C3×C4#6712yes—
66C22×C3×C4#6712yes—
67C2×C3×C8—64no—
68C2×C3×C8—124no—
69#208—124no—
70#208—124no—
71C2×C3⋊C8—24no—
72C2×C3⋊C8—44no—
73C2×C3⋊C8—64no—
74C2×C3⋊C8—64no—
75C22×C32—21no—
76C22×C32—22no—
77C22×C32—22no—
78C22×C32—22no—
79C22×C32—44no—
80C22×C32#9511yescharacteristic
81C22×C32#10814yes—
82C32×C4—21no—
83C32×C4—22no—
84C32×C4#9912yes—
85C23×C4D3211yescharacteristic
86C2×M16—92no—
87C22×C8—62no—
88C22⋊C8—34no—
89C22⋊C8—62no—
90C22⋊C8—182no—
91C23×C3—24no—
92C23×C3—24no—
93C23×C3—22no—
94C23×C3—21no—
95C23×C3—44no—
96C23×C3—42no—
97C23×C3—42no—
98C23×C3Dic3⋊C412yes—
99C23×C3Dic3⋊C412yes—
100C23×C3C4⋊Dic312yes—
101C2×C3×C4—24no—
102C2×C3×C4—24no—
103C2×C3×C4—24no—
104C2×C3×C4—24no—
105C2×C3×C4—21no—
106C2×C3×C4—22no—
107C2×C3×C4—21no—
108C2×C3×C4—44no—
109C2×C3×C4—42no—
110C2×C3×C4—42no—
111C2×C3×C4—42no—
112C2×C3×C4—44no—
113C2×C3×C4—42no—
114C2×C3×C4C4×Dic312yes—
115C2×C3×C4(C2×D3)⋊C412yes—
116C2×C3×C4(C2×D3)⋊C412yes—
117C2×C3×C4#21712yes—
118C3×C8—124no—
119C3⋊C8—44no—
120C3⋊C8—124no—
121C3⋊C8—124no—
122C2×C32—24no—
123C2×C32—41no—
124C2×C32#34112yes—
125C2×C32#34211yescharacteristic
126C24#62711yescharacteristic
127C22×C4—42no—
128C22×C4D3×Dic312yes—
129C22×C4#62411yescharacteristic
130C22×C4#62511yescharacteristic
131C22×C4#62612yes—
132M16—362no—
133C2×C8—64no—
134C2×C8—124no—
135C2×C8—182no—
136C22×C3—22no—
137C22×C3—22no—
138C22×C3—22no—
139C22×C3—22no—
140C22×C3—22no—
141C22×C3—22no—
142C22×C3—22no—
143C22×C3—22no—
144C22×C3—24no—
145C22×C3—21no—
146C22×C3—42no—
147C22×C3—42no—
148C22×C3—42no—
149C22×C3—48no—
150C22×C3—48no—
151C22×C3#81914yes—
152C22×C3#82214yes—
153C22×C3C3⋊#9512yes—
154C3×C4—22no—
155C3×C4—22no—
156C3×C4—22no—
157C3×C4—22no—
158C3×C4—22no—
159C3×C4—42no—
160C3×C4#80614yes—
161C32#129811yescharacteristic, complemented, Sylow
162C23—24no—
163C23—41no—
164C23Dic3⋊Dic312yes—
165C23#372411yescharacteristic
166C2×C4—24no—
167C2×C4—22no—
168C2×C4—42no—
169C2×C4—41no—
170C2×C4Dic3211yescharacteristic
171C2×C4(C2×D3)⋊Dic312yes—
172C2×C4#372211yescharacteristic
173C8—124no—
174C8—362no—
175C2×C3—24no—
176C2×C3—24no—
177C2×C3—21no—
178C2×C3—22no—
179C2×C3—44no—
180C2×C3—42no—
181C2×C3—42no—
182C2×C3#452712yes—
183C2×C3#455212yes—
184C2×C3#455812yes—
185C22—22no—
186C22—22no—
187C22—21no—
188C22—22no—
189C22—44no—
190C22#6357714yes—
191C22#6357911yescharacteristic
192C4—22no—
193C4—21no—
194C4#6358112yes—
195C3—21no—
196C3#6768012yescomplemented
197C2—24no—
198C2—41no—
199C2#1058916612yes—
200C2#1058918711yescharacteristic
subgroupG/H
centerC2×C4#3722
commutatorC2×C32×C4C42
Frattini, hypercenterC23×C4D32
Fitting, cosocleC23×C32×C4C22
socleC22×C32#95
prime radicalC24×C32Q8
hypocenterC32#1298
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
161. C32#1298semidirect
196. C3#67680semidirect

Maximal subgroups

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

subgroupindex
#105929062
C2×C3×#8302
#676803