Finite Group Databasebeta

← #11796978

Subgroups — #11796978

Order 1152.

417 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 417 conjugacy classes of subgroups — too many to draw. Only its 130 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
2C8×#624C211yesmaximal, characteristic
3C2×#63542C211yesmaximal, characteristic
4C3×Dic3⋊C16C212yesmaximal, complemented
5Dic3⋊(C3⋊C16)C212yesmaximal, complemented
6D3×C4⋊C16—32nomaximal
7C2×C8×C3⋊D3C2211yescharacteristic
8C4×#624C411yescharacteristic
9C2×#3710C411yescharacteristic
10C2×C32×C16C2211yescharacteristic
11C2×C3⋊(C3⋊C16)C2211yescharacteristic
12C16×C3⋊D3—22no—
13C3×C8×Dic3C2212yes—
14C2×C3×C3⋊C16C2212yes—
15Dic3×C3⋊C8C412yes—
16#63542—22no—
17C2×D3×C16—32no—
18C2×D3×C16—32no—
19C2×D3×C16—61no—
20C4×D3×C8—32no—
21C3×C4⋊C16—32no—
22Dic3⋊C16—32no—
23Dic3⋊C16D312yescomplemented
24C4⋊(C3⋊C16)—32no—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×#624C811yescharacteristic
27C2×#624C811yescharacteristic
28C2×C32×C8C2311yescharacteristic
29C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
30C8×C3⋊D3D412yes—
31C8×C3⋊D3Q812yes—
32C3×C4×Dic3C2×C412yes—
33C2×C3×C3⋊C8C2×C412yes—
34Dic32C812yes—
35#3710—22no—
36C32×C16—21no—
37C3⋊(C3⋊C16)—21no—
38C3×C3⋊C16—22no—
39C2×C4⋊C16—91noSylow
40C2×D3×C8—32no—
41C2×D3×C8—32no—
42C2×D3×C8—61no—
43C42×D3—32no—
44C2×C3×C16—21no—
45C2×C3×C16—32no—
46C2×C3×C16C2×D312yes—
47C3×C4×C8—32no—
48C8×Dic3—32no—
49C8×Dic3C2×D312yes—
50C2×C3⋊C16—32no—
51C2×C3⋊C16—61no—
52C2×C3⋊C16C2×D312yes—
53C4×C3⋊C8—32no—
54D3×C16—64no—
55D3×C16—64no—
56D3×C16—64no—
57C22×C3⋊D3C2×C811yescharacteristic
58C2×C32×C4C22×C411yescharacteristic
59C2×C3⋊Dic3C2×C811yescharacteristic
60C4×C3⋊D3C4⋊C412yes—
61C4×C3⋊D3M1612yes—
62C2×C3×Dic3C2×C812yes—
63C2×C3×Dic3C2×C812yes—
64#624—22no—
65#624C1614yescomplemented
66C32×C8C2×D411yescharacteristic
67C32×C8C2×Q811yescharacteristic
68C3⋊(C3⋊C8)C4⋊C412yes—
69C3×C3⋊C8—22no—
70C22×C16—91no—
71C22×C16—91no—
72C2×C4×C8—91no—
73C4⋊C16—32no—
74C4⋊C16—92no—
75C2×C4×D3—32no—
76C2×C4×D3—32no—
77C2×C4×D3—32no—
78C2×C4×D3—61no—
79C2×C3×C8—21no—
80C2×C3×C8—32no—
81C2×C3×C8C22×D312yes—
82C3×C42—32no—
83C4×Dic3—32no—
84C4×Dic3—32no—
85C4×Dic3C4×D312yes—
86C2×C3⋊C8—32no—
87C2×C3⋊C8—61no—
88C2×C3⋊C8C4×D312yes—
89D3×C8—34no—
90D3×C8—34no—
91D3×C8—62no—
92D3×C8—62no—
93D3×C8—64no—
94C3×C16—22no—
95C3×C16—22no—
96C3×C16—62no—
97C3⋊C16—22no—
98C3⋊C16—62no—
99C3⋊C16—62no—
100C22×C32C22×C811yescharacteristic
101C2×C3⋊D3C4⋊C812yes—
102C2×C3⋊D3C2×C1612yes—
103C2×C3⋊D3M3212yes—
104C32×C4C2×C4⋊C411yescharacteristic
105C32×C4C2×M1611yescharacteristic
106C3⋊Dic3C4⋊C812yes—
107C3×Dic3—22no—
108C3×Dic3C2×C1614yescomplemented
109C22×C8—91no—
110C22×C8—91no—
111C2×C42—91no—
112C2×C16—32no—
113C2×C16—91no—
114C2×C16—182no—
115C2×C16—182no—
116C2×C16D3211yescharacteristic
117C4×C8—32no—
118C4×C8—92no—
119C22×D3—32no—
120C22×D3—61no—
121C2×C3×C4—21no—
122C2×C3×C4—32no—
123C2×C3×C4—32no—
124C2×C3×C4C2×C4×D312yes—
125C2×Dic3—32no—
126C2×Dic3—61no—
127C2×Dic3D3×C812yes—
128C2×Dic3D3×C812yes—
129C4×D3—34no—
130C4×D3—34no—
131C4×D3—38no—
132C4×D3—62no—
133C4×D3—62no—
134C4×D3—64no—
135C3×C8—21no—
136C3×C8—21no—
137C3×C8—62no—
138C3×C8D3×D412yes—
139C3×C8D3×Q812yes—
140C3⋊C8—22no—
141C3⋊C8—34no—
142C3⋊C8—62no—
143C2×C32C2×C4⋊C811yescharacteristic
144C2×C32C22×C1611yescharacteristic
145C2×C32C2×M3211yescharacteristic
146C3⋊D3C4⋊C1614yescomplemented
147C22×C4—91no—
148C22×C4—91no—
149C22×C4—91no—
150C2×C8—32no—
151C2×C8—91no—
152C2×C8—92no—
153C2×C8—92no—
154C2×C8—182no—
155C2×C8C2×D3211yescharacteristic
156C42—32no—
157C42—92no—
158C16—21no—
159C16—62no—
160C16—181no—
161C22×C3—21no—
162C22×C3C2×D3×C812yes—
163C2×D3—34no—
164C2×D3—34no—
165C2×D3—34no—
166C2×D3—62no—
167C2×D3—62no—
168C2×D3—62no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—34no—
172C3×C4—62no—
173C3×C4D3×C4⋊C412yes—
174C3×C4D3×M1612yes—
175Dic3—22no—
176Dic3—34no—
177Dic3—62no—
178Dic3D3×C1614yescomplemented
179C32C2×C4⋊C1611yescharacteristic, complemented, Sylow
180C23—91no—
181C2×C4—32no—
182C2×C4—32no—
183C2×C4—94no—
184C2×C4—91no—
185C2×C4—92no—
186C2×C4—92no—
187C2×C4—182no—
188C2×C4C4×D3211yescharacteristic
189C8—62no—
190C8—92no—
191C8#379711yescharacteristic
192C8#381111yescharacteristic
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3D3×C4⋊C812yes—
197C2×C3C2×D3×C1612yes—
198C2×C3D3×M3212yes—
199D3—38no—
200D3—64no—
201C22—92no—
202C22—92no—
203C22—92no—
204C22D32×C811yescharacteristic
205C4—34no—
206C4—62no—
207C4—92no—
208C4#6379111yescharacteristic
209C4#6388311yescharacteristic
210C3—21no—
211C3D3×C4⋊C1612yescomplemented
212C2—94no—
213C2D32×C1611yescharacteristic
214C2#1059022611yescharacteristic
215C2#1059065811yescharacteristic
subgroupG/H
center, FrattiniC2×C8C2×D32
commutatorC2×C32C22×C16
FittingC2×C32×C16C22
socleC22×C32C22×C8
prime radicalC22×C3⋊D3C2×C8
cosocleC2×C32×C8C23
hypercenterC2×C16D32
hypocenterC32C2×C4⋊C16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
4. C3×Dic3⋊C16C2semidirect
5. Dic3⋊(C3⋊C16)C2semidirect
23. Dic3⋊C16D3semidirect
65. #624C16semidirect
108. C3×Dic3C2×C16semidirect
146. C3⋊D3C4⋊C16semidirect
178. Dic3D3×C16semidirect
179. C32C2×C4⋊C16semidirect
211. C3D3×C4⋊C16semidirect

Maximal subgroups

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

subgroupindex
C2×C16×C3⋊D32
C8×#6242
C2×#635422
C3×Dic3⋊C162
Dic3⋊(C3⋊C16)2
D3×C4⋊C163