Finite Group Databasebeta

← #11800468

Subgroups — #11800468

Order 1152.

273 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 273 conjugacy classes of subgroups — too many to draw. Only its 94 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×C16×C3⋊D3C211yesmaximal, characteristic
2C3×#4499C212yesmaximal, complemented
3#10589069C212yesmaximal, complemented
4#10589067C212yesmaximal, complemented
5D3×M64—32nomaximal
6C2×C8×C3⋊D3C411yescharacteristic
7C2×C32×C16C2211yescharacteristic
8C2×C3⋊(C3⋊C16)C411yescharacteristic
9C16×C3⋊D3C411yescharacteristic
10C16×C3⋊D3C411yescharacteristic
11C16×C3⋊D3C2211yescharacteristic
12C16×C3⋊D3C2211yescharacteristic
13C3×C3⋊C32C2214yescomplemented
14C2×D3×C16—32no—
15C2×D3×C16—61no—
16C3×M64—32no—
17#4499D312yescomplemented
18#4447—34no—
19D3×C32—34no—
20C2×C4×C3⋊D3C811yescharacteristic
21C2×C32×C8C2×C411yescharacteristic
22C2×C3⋊(C3⋊C8)C811yescharacteristic
23C8×C3⋊D3C811yescharacteristic
24C8×C3⋊D3C811yescharacteristic
25C8×C3⋊D3C2×C411yescharacteristic
26C8×C3⋊D3C2×C411yescharacteristic
27C32×C16C2×C411yescharacteristic
28C32×C16C2311yescharacteristic
29C3⋊(C3⋊C16)C2×C411yescharacteristic
30C3⋊(C3⋊C16)C2×C411yescharacteristic
31C2×M64—91noSylow
32C2×D3×C8—32no—
33C2×D3×C8—61no—
34C2×C3×C16—21no—
35C2×C3×C16C2×D312yes—
36C2×C3⋊C16—32no—
37C2×C3⋊C16—61no—
38D3×C16—32no—
39D3×C16—32no—
40D3×C16—32no—
41D3×C16—32no—
42D3×C16—61no—
43D3×C16—61no—
44D3×C16—61no—
45D3×C16—61no—
46C3×C32—34no—
47C3⋊C32C2×D314yescomplemented
48C22×C3⋊D3C1611yescharacteristic
49C2×C32×C4C2×C811yescharacteristic
50C2×C3⋊Dic3C1611yescharacteristic
51C4×C3⋊D3C1611yescharacteristic
52C4×C3⋊D3C1611yescharacteristic
53C4×C3⋊D3C2×C811yescharacteristic
54C4×C3⋊D3C2×C811yescharacteristic
55C32×C8C2×C811yescharacteristic
56C32×C8C22×C411yescharacteristic
57C3⋊(C3⋊C8)C2×C811yescharacteristic
58C3⋊(C3⋊C8)C2×C811yescharacteristic
59C22×C16—91no—
60M64—32no—
61M64—92no—
62C2×C32—92no—
63C2×C4×D3—32no—
64C2×C4×D3—61no—
65C2×C3×C8—21no—
66C2×C3×C8C4×D312yes—
67C2×C3⋊C8—32no—
68C2×C3⋊C8—61no—
69D3×C8—32no—
70D3×C8—32no—
71D3×C8—32no—
72D3×C8—32no—
73D3×C8—61no—
74D3×C8—61no—
75D3×C8—61no—
76D3×C8—61no—
77C3×C16—21no—
78C3×C16—21no—
79C3×C16C4×D312yes—
80C3×C16C22×D312yes—
81C3⋊C16—32no—
82C3⋊C16—32no—
83C3⋊C16—61no—
84C3⋊C16—61no—
85C22×C32C2×C1611yescharacteristic
86C2×C3⋊D3—22no—
87C2×C3⋊D3C2×C1611yescharacteristic
88C2×C3⋊D3C2×C1611yescharacteristic
89C32×C4C2×C1611yescharacteristic
90C32×C4C22×C811yescharacteristic
91C3⋊Dic3C2×C1611yescharacteristic
92C3⋊Dic3C2×C1611yescharacteristic
93C22×C8—91no—
94C2×C16—91no—
95C2×C16—91no—
96C2×C16—91no—
97C2×C16—91no—
98C2×C16—91no—
99C2×C16D3211yescharacteristic
100C32—34no—
101C22×D3—32no—
102C22×D3—61no—
103C2×C3×C4—21no—
104C2×C3×C4D3×C812yes—
105C2×Dic3—32no—
106C2×Dic3—61no—
107C4×D3—32no—
108C4×D3—32no—
109C4×D3—32no—
110C4×D3—32no—
111C4×D3—61no—
112C4×D3—61no—
113C4×D3—61no—
114C4×D3—61no—
115C3×C8—21no—
116C3×C8—21no—
117C3×C8D3×C812yes—
118C3×C8C2×C4×D312yes—
119C3⋊C8—32no—
120C3⋊C8—32no—
121C3⋊C8—61no—
122C3⋊C8—61no—
123C2×C32—21no—
124C2×C32C22×C1611yescharacteristic
125C3⋊D3—21no—
126C3⋊D3M6412yescomplemented
127C22×C4—91no—
128C2×C8—91no—
129C2×C8—91no—
130C2×C8—91no—
131C2×C8—91no—
132C2×C8—91no—
133C2×C8#62411yescharacteristic
134C16—91no—
135C16—91no—
136C16#62411yescharacteristic
137C16C2×D3211yescharacteristic
138C22×C3—21no—
139C22×C3D3×C1612yes—
140C2×D3—32no—
141C2×D3—32no—
142C2×D3—61no—
143C2×D3—61no—
144C2×D3—64no—
145C2×D3—64no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4D3×C1612yes—
149C3×C4C2×D3×C812yes—
150Dic3—32no—
151Dic3—32no—
152Dic3—61no—
153Dic3—61no—
154C32C2×M6411yescharacteristic, complemented, Sylow
155C23—91no—
156C2×C4—91no—
157C2×C4—91no—
158C2×C4—91no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4#371011yescharacteristic
162C8—91no—
163C8—91no—
164C8#371011yescharacteristic
165C8C2×#62411yescharacteristic
166C2×C3—22no—
167C2×C3—22no—
168C2×C3—21no—
169C2×C3C2×D3×C1612yes—
170D3—34no—
171D3—62no—
172D3—62no—
173D3—62no—
174C22—91no—
175C22—91no—
176C22—182no—
177C22#6354211yescharacteristic
178C4—91no—
179C4—91no—
180C4#6354211yescharacteristic
181C4C2×#371011yescharacteristic
182C3—21no—
183C3D3×M6412yescomplemented
184C2—21no—
185C2—92no—
186C2—181no—
187C2C2×#6354211yescharacteristic
subgroupG/H
center, FrattiniC16C2×D32
commutator, socleC2×C32C22×C16
FittingC2×C32×C16C22
prime radicalC22×C3⋊D3C16
cosocleC32×C16C23
hypercenterC2×C16D32
hypocenterC32C2×M64
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C16 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. C3×#4499C2semidirect
3. #10589069C2semidirect
4. #10589067C2semidirect
13. C3×C3⋊C32C22semidirect
17. #4499D3semidirect
47. C3⋊C32C2×D3semidirect
126. C3⋊D3M64semidirect
154. C32C2×M64semidirect
183. C3D3×M64semidirect

Maximal subgroups

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

subgroupindex
C2×C16×C3⋊D32
C3×#44992
#105890692
#105890672
D3×M643