Finite Group Databasebeta

← #11776166

Subgroups — #11776166

Order 1152.

657 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 657 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2#10590331C212yesmaximal
3C3×#4546C212yesmaximal, complemented
4#10589096C212yesmaximal, complemented
5D3×#333—32nomaximal
6C2×Q8×C3⋊D3C412yes—
7C32×C4⋊Q8C2211yescharacteristic
8#64153C412yes—
9C4⋊C4×C3⋊D3—22no—
10#64097—22no—
11C42×C3⋊D3C2211yescharacteristic
12#64078C2211yescharacteristic
13C2×#3710—22no—
14C3×C4⋊(C3⋊C8)C2214yes—
15#63572—22no—
16D3×C4⋊Q8—32no—
17D3×C4⋊Q8—61no—
18D3×C4⋊C8—34no—
19C3×#333—32no—
20#4546D312yescomplemented
21#4481—34no—
22C2×C32×Q8C2×C412yes—
23Q8×C3⋊D3—44no—
24C2×C4×C3⋊D3—22no—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3D412yes—
27C2×#634—22no—
28C2×#634C2×C412yes—
29C32×C4⋊C4—22no—
30C32×C42C2311yescharacteristic
31C4⋊(C3⋊Dic3)—22no—
32#3750—24no—
33C4×C3⋊Dic3C2×C411yescharacteristic
34C4×C3⋊Dic3D412yes—
35C2×C3×C3⋊C8—24no—
36#3710—44no—
37C2×#333—91noSylow
38C2×D3×Q8—34no—
39C2×D3×Q8—62no—
40C3×C4⋊Q8—21no—
41C3×C4⋊Q8C2×D312yes—
42#944—34no—
43#944—62no—
44C2×D3×C8—64no—
45D3×C4⋊C4—64no—
46D3×C4⋊C4—64no—
47#888—64no—
48#888—64no—
49C42×D3—32no—
50C42×D3—61no—
51#869—32no—
52#869—61no—
53C3×C4⋊C8—34no—
54Dic3⋊C8—64no—
55C4⋊(C3⋊C8)C2×D314yes—
56C22×C3⋊D3C22⋊C411yescharacteristic
57C32×Q8—42no—
58C2×C32×C4—22no—
59C2×C32×C4C22×C411yescharacteristic
60C2×C32×C4C2×D412yes—
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3C22⋊C411yescharacteristic
63C2×C3⋊Dic3C22⋊C412yes—
64C4×C3⋊D3—22no—
65C4×C3⋊D3—44no—
66C4×C3⋊D3SD1614yes—
67C4×C3⋊D3Q1614yes—
68#634—44no—
69#634—42no—
70C3×C3⋊C8—44no—
71C2×C4⋊Q8—91no—
72C2×C4⋊C8—92no—
73#333—32no—
74#333—92no—
75C2×C3×Q8—22no—
76C2×C3×Q8C4×D314yes—
77D3×Q8—128no—
78D3×Q8—128no—
79C2×C4×D3—34no—
80C2×C4×D3—32no—
81C2×C4×D3—62no—
82C2×C4×D3—61no—
83C2×C4×D3—64no—
84C2×C4×D3—64no—
85C2×Dic6—34no—
86C2×Dic6—62no—
87C2×Dic6—64no—
88C2×Dic6—64no—
89C2×C3×C8—64no—
90C3×C4⋊C4—24no—
91C3×C4⋊C4—24no—
92C3×C42—21no—
93C3×C42C22×D312yes—
94C4⋊Dic3—64no—
95C4⋊Dic3—64no—
96Dic3⋊C4—68no—
97Dic3⋊C4—68no—
98C4×Dic3—32no—
99C4×Dic3—34no—
100C4×Dic3—62no—
101C4×Dic3—61no—
102C2×C3⋊C8—24no—
103D3×C8—128no—
104C22×C32C2×C22⋊C411yescharacteristic
105C2×C3⋊D3#10012yes—
106C2×C3⋊D3#10314yes—
107C32×C4—21no—
108C32×C4—42no—
109C32×C4C2×SD1612yes—
110C32×C4C2×Q1612yes—
111C3⋊Dic3—21no—
112C3⋊Dic3—42no—
113C3⋊Dic3#10314yes—
114C22×Q8—92no—
115C22×C8—182no—
116C4⋊Q8—92no—
117C4⋊Q8—91no—
118C4⋊Q8—182no—
119C4⋊Q8D3211yescharacteristic
120C2×C4⋊C4—182no—
121C2×C42—91no—
122C4⋊C8—34no—
123C4⋊C8—182no—
124C22×D3—32no—
125C22×D3—61no—
126C3×Q8—44no—
127C3×Q8—44no—
128C2×C3×C4—24no—
129C2×C3×C4—24no—
130C2×C3×C4—21no—
131C2×C3×C4—22no—
132C2×C3×C4C2×C4×D312yes—
133C2×C3×C4D3×D414yes—
134C2×Dic3—34no—
135C2×Dic3—32no—
136C2×Dic3—62no—
137C2×Dic3—61no—
138C2×Dic3—64no—
139C2×Dic3—64no—
140C4×D3—38no—
141C4×D3—38no—
142C4×D3—64no—
143C4×D3—64no—
144C4×D3—64no—
145C4×D3—64no—
146C4×D3—128no—
147C4×D3—128no—
148Dic6—128no—
149Dic6—128no—
150Dic6—124no—
151Dic6—124no—
152C3×C8—124no—
153C3⋊C8—44no—
154C2×C32C2×#10011yescharacteristic
155C2×C32C2×#10312yes—
156C3⋊D3#33314yescomplemented
157C2×Q8—92no—
158C2×Q8—182no—
159C2×Q8—364no—
160C2×Q8#62412yes—
161C22×C4—92no—
162C22×C4—91no—
163C22×C4—182no—
164C2×C8—64no—
165C2×C8—364no—
166C4⋊C4—22no—
167C4⋊C4—184no—
168C4⋊C4—182no—
169C42—91no—
170C42—92no—
171C42C2×D3211yescharacteristic
172C22×C3—21no—
173C22×C3D3×C22⋊C412yes—
174C2×D3—34no—
175C2×D3—38no—
176C2×D3—62no—
177C2×D3—64no—
178C3×C4—22no—
179C3×C4—22no—
180C3×C4—22no—
181C3×C4—22no—
182C3×C4—44no—
183C3×C4—44no—
184C3×C4D3×SD1614yes—
185C3×C4D3×Q1614yes—
186Dic3—38no—
187Dic3—64no—
188Dic3—62no—
189Dic3—62no—
190Dic3—124no—
191Dic3—124no—
192C32C2×#33311yescharacteristic, complemented, Sylow
193C23—91no—
194Q8—42no—
195Q8—362no—
196Q8—364no—
197C2×C4—22no—
198C2×C4—92no—
199C2×C4—94no—
200C2×C4—94no—
201C2×C4—91no—
202C2×C4—182no—
203C2×C4—182no—
204C2×C4—364no—
205C2×C4C2×#62411yescharacteristic
206C2×C4#381112yes—
207C8—124no—
208C2×C3—21no—
209C2×C3—22no—
210C2×C3D3×#10012yes—
211C2×C3D3×#10314yes—
212D3—38no—
213D3—64no—
214C22—92no—
215C22—94no—
216C22#6397411yescharacteristic
217C4—21no—
218C4—42no—
219C4—94no—
220C4—181no—
221C4—362no—
222C4#6394012yes—
223C4#6394412yes—
224C3—21no—
225C3D3×#33312yescomplemented
226C2—94no—
227C2#1059150311yescharacteristic
228C2#1059155212yes—
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊Q8D32
hypocenterC32C2×#333
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#4546C2semidirect
4. #10589096C2semidirect
20. #4546D3semidirect
156. C3⋊D3#333semidirect
192. C32C2×#333semidirect
225. C3D3×#333semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105903312
C3×#45462
#105890962
D3×#3333