Finite Group Databasebeta

← #11771249

Subgroups — #11771249

Order 1152.

493 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 493 conjugacy classes of subgroups — too many to draw. Only its 104 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#10592910C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3#67686—32nomaximal
4C23×C32×C4C2211yescharacteristic
5C2×#3757C412yes—
6C2×C3×#208—22no—
7#63658—22no—
8C3×#830—22no—
9C3×#830C414yescomplemented
10C3×#407—32no—
11#5211—32no—
12#5211—61no—
13#5207D312yes—
14C24×C32C2×C411yescharacteristic
15C22×C32×C4—42no—
16C22×C32×C4C2×C412yes—
17C22×C32×C4D412yes—
18C22×C32×C4D411yescharacteristic
19C22×C32×C4Q811yescharacteristic
20C22×C3⋊Dic3—22no—
21#3757—42no—
22C3×#208—44no—
23C2×C3×C3⋊C8—24no—
24#1306—91noSylow
25C23×C3×C4—21no—
26C23×C3×C4C2×D312yes—
27C2×C3×M16—62no—
28C2×#217—34no—
29C2×#217—62no—
30C2×#208—22no—
31C3×C22⋊C8—34no—
32C3×C22⋊C8—62no—
33C3⋊#95—64no—
34C3⋊#95—62no—
35C3⋊#95—62no—
36#830—22no—
37#830Dic314yescomplemented
38C23×C32—22no—
39C23×C32—42no—
40C23×C32C4211yescharacteristic
41C23×C32C22⋊C411yescharacteristic
42C23×C32C4⋊C411yescharacteristic
43C2×C32×C4—24no—
44C2×C32×C4—42no—
45C2×C32×C4—41no—
46C2×C32×C4—41no—
47C2×C32×C4C22⋊C412yes—
48C2×C32×C4C4⋊C412yes—
49C2×C3⋊Dic3—44no—
50C2×C3⋊Dic3—42no—
51C3×C3⋊C8—44no—
52#407—32no—
53#381—91no—
54C24×C3—21no—
55C24×C3C4×D312yes—
56C22×C3×C4—22no—
57C22×C3×C4—21no—
58C22×C3×C4—22no—
59C22×C3×C4—21no—
60C22×C3×C4—44no—
61C22×C3×C4—44no—
62C22×C3×C4Dic612yes—
63C22×C3×C4C4×D312yes—
64C22×C3×C4D1212yes—
65C22×C3×C4C2×Dic312yes—
66C22×C3×C4#6712yes—
67C22×C3×C4#6712yes—
68C22×Dic3—64no—
69C22×Dic3—64no—
70C3×M16—124no—
71C2×C3×C8—64no—
72#217—124no—
73#217—124no—
74#208—44no—
75C2×C3⋊C8—24no—
76C22×C32—22no—
77C22×C32—21no—
78C22×C32—21no—
79C22×C32—22no—
80C22×C32—22no—
81C22×C32—44no—
82C22×C32#9511yescharacteristic
83C22×C32#9912yes—
84C32×C4—22no—
85C32×C4—22no—
86C3⋊Dic3—82no—
87C23×C4D3211yescharacteristic
88C2×M16—62no—
89C2×C22⋊C4—92no—
90C22⋊C8—34no—
91C22⋊C8—62no—
92#95—182no—
93C23×C3—24no—
94C23×C3—24no—
95C23×C3—21no—
96C23×C3—21no—
97C23×C3—21no—
98C23×C3—42no—
99C23×C3—42no—
100C23×C3—44no—
101C23×C3C4×Dic312yes—
102C23×C3Dic3⋊C412yes—
103C23×C3(C2×D3)⋊C412yes—
104C2×C3×C4—24no—
105C2×C3×C4—24no—
106C2×C3×C4—22no—
107C2×C3×C4—22no—
108C2×C3×C4—44no—
109C2×C3×C4—42no—
110C2×C3×C4—42no—
111C2×C3×C4—42no—
112C2×C3×C4—42no—
113C2×C3×C4—44no—
114C2×C3×C4—42no—
115C2×C3×C4—42no—
116C2×C3×C4Dic3⋊C412yes—
117C2×C3×C4C4⋊Dic312yes—
118C2×C3×C4(C2×D3)⋊C412yes—
119C2×C3×C4#21712yes—
120C2×Dic3—124no—
121C2×Dic3—128no—
122C2×Dic3—124no—
123C2×Dic3—124no—
124C2×Dic3—124no—
125C3×C8—124no—
126C3⋊C8—44no—
127C2×C32—22no—
128C2×C32—41no—
129C2×C32—41no—
130C2×C32#34211yescharacteristic
131C2×C32#34412yes—
132C24#62411yescharacteristic
133C22×C4—42no—
134C22×C4—182no—
135C22×C4D3×Dic312yes—
136C22×C4#62511yescharacteristic
137C22×C4#62612yes—
138C22×C4#62711yescharacteristic
139M16—124no—
140C2×C8—64no—
141C22⋊C4—362no—
142C22×C3—24no—
143C22×C3—22no—
144C22×C3—22no—
145C22×C3—22no—
146C22×C3—22no—
147C22×C3—22no—
148C22×C3—22no—
149C22×C3—22no—
150C22×C3—22no—
151C22×C3—22no—
152C22×C3—22no—
153C22×C3—21no—
154C22×C3—22no—
155C22×C3—42no—
156C22×C3—42no—
157C22×C3—48no—
158C22×C3—48no—
159C22×C3#80614yes—
160C22×C3C3⋊#9512yes—
161C3×C4—22no—
162C3×C4—22no—
163C3×C4—22no—
164C3×C4—22no—
165C3×C4—42no—
166C3×C4—42no—
167Dic3—244no—
168Dic3—244no—
169C32#130611yescharacteristic, complemented, Sylow
170C23—22no—
171C23—42no—
172C23Dic3211yescharacteristic
173C23#372211yescharacteristic
174C23#372411yescharacteristic
175C2×C4—24no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—364no—
180C2×C4—362no—
181C2×C4(C2×D3)⋊Dic312yes—
182C2×C4Dic3⋊Dic312yes—
183C8—124no—
184C2×C3—24no—
185C2×C3—24no—
186C2×C3—21no—
187C2×C3—22no—
188C2×C3—42no—
189C2×C3—42no—
190C2×C3—42no—
191C2×C3—42no—
192C2×C3#452712yes—
193C2×C3#455612yes—
194C2×C3#455912yes—
195C22—22no—
196C22—21no—
197C22—21no—
198C22—22no—
199C22—22no—
200C22—44no—
201C22#6357911yescharacteristic
202C22#6358112yes—
203C4—22no—
204C4—22no—
205C4—722no—
206C3—21no—
207C3#6768612yescomplemented
208C2—22no—
209C2—41no—
210C2—41no—
211C2#1058917112yes—
212C2#1058918711yescharacteristic
subgroupG/H
centerC22#63579
commutatorC23×C32C42
Frattini, hypercenterC23×C4D32
Fitting, cosocleC23×C32×C4C22
socleC22×C32#95
prime radicalC24×C32C2×C4
hypocenterC32#1306
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
9. C3×#830C4semidirect
37. #830Dic3semidirect
169. C32#1306semidirect
207. C3#67686semidirect

Maximal subgroups

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

subgroupindex
#105929102
C3×#52072
#676863