Finite Group Databasebeta

← #11796521

Subgroups — #11796521

Order 1152.

690 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 107 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#10596195C211yesmaximal, characteristic
2C3⋊D3×#101C212yesmaximal, complemented
3C32×#356C211yesmaximal, characteristic, complemented
4#10589414C211yesmaximal, characteristic, complemented
5#10589343C212yesmaximal, complemented
6#69171—34nomaximal
7C2×#3832C411yescharacteristic
8C2×Q8×C3⋊D3C2211yescharacteristic
9C32×C4⋊Q8C2211yescharacteristic
10#64156C2211yescharacteristic
11#64153C411yescharacteristic
12M16×C3⋊D3—22no—
13#64105—22no—
14#64103—22no—
15#64084C411yescharacteristic
16#64081C411yescharacteristic
17C32×#101C2212yes—
18#63663C2212yes—
19#63651—22no—
20#5724—34no—
21D3×#101—38no—
22C3×#356D314yescomplemented
23#4548—34no—
24#4477—38no—
25C2×C32×Q8C2×C411yescharacteristic
26C2×C32×Q8C2311yescharacteristic
27#3832—42no—
28Q8×C3⋊D3—42no—
29C2×C4⋊(C3⋊D3)—21no—
30C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3D412yes—
34C2×#634C2×C411yescharacteristic
35C2×#634D412yes—
36C32×M16—22no—
37C32×C4⋊C4—22no—
38C32×C42C2×C411yescharacteristic
39#3752—21no—
40#3752—22no—
41#3752—22no—
42#3750—21no—
43#3750—22no—
44C4×C3⋊Dic3C2×C411yescharacteristic
45#3748—22no—
46#3743—42no—
47C8×C3⋊D3—42no—
48#2133—91noSylow
49C2×#239—34no—
50C2×D3×Q8—34no—
51C3×C4⋊Q8C2×D314yes—
52#947—34no—
53#944—34no—
54D3×M16—68no—
55#896—68no—
56#894—68no—
57#875—34no—
58#872—34no—
59C3×#101C2×D318yes—
60#836—38no—
61#824—68no—
62C22×C3⋊D3—21no—
63C22×C3⋊D3C22⋊C411yescharacteristic
64C32×Q8—41no—
65C32×Q8—41no—
66C2×C32×C4—21no—
67C2×C32×C4—21no—
68C2×C32×C4C22×C411yescharacteristic
69C2×C32×C4C2×D412yes—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3C22⋊C412yes—
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C4⋊(C3⋊D3)—41no—
74C4⋊(C3⋊D3)—42no—
75C4×C3⋊D3—22no—
76C4×C3⋊D3—22no—
77C4×C3⋊D3—22no—
78C4×C3⋊D3—42no—
79#634—41no—
80#634—42no—
81C32×C8—42no—
82C3⋊(C3⋊C8)—42no—
83#536—91no—
84C2×#101—92no—
85#356—91no—
86#356C3⋊D311yescharacteristic, complemented
87#355—92no—
88C2×C3×Q8C4×D314yes—
89C2×C3×Q8C22×D314yes—
90#239—128no—
91D3×Q8—128no—
92C2×D12—34no—
93C2×D12—64no—
94C2×C4×D3—34no—
95C2×C4×D3—38no—
96C2×C4×D3—64no—
97C2×Dic6—34no—
98C2×Dic6—38no—
99C3×M16—28no—
100C3×C4⋊C4—28no—
101C3×C42C4×D314yes—
102(C2×D3)⋊C4—68no—
103(C2×D3)⋊C4—64no—
104(C2×D3)⋊C4—68no—
105Dic3⋊C4—64no—
106Dic3⋊C4—68no—
107C4×Dic3—34no—
108#208—68no—
109ΓL(1,𝔽25)—128no—
110D3×C8—128no—
111C22×C32C2×C22⋊C411yescharacteristic
112C2×C3⋊D3—41no—
113C2×C3⋊D3—42no—
114C2×C3⋊D3—41no—
115C2×C3⋊D3#9912yes—
116C32×C4—22no—
117C32×C4—21no—
118C32×C4—41no—
119C32×C4—41no—
120C3⋊Dic3—21no—
121C3⋊Dic3—22no—
122C3⋊Dic3—41no—
123C2×#41—91no—
124C22×Q8—91no—
125C2×M16—182no—
126C4⋊Q8—91no—
127C4⋊Q8C2×C3⋊D311yescharacteristic
128#124—91no—
129#124—91no—
130#123—182no—
131C22⋊Q8—182no—
132#117—91no—
133#101—92no—
134#101—182no—
135#101C2×C3⋊D312yes—
136C22×D3—34no—
137C22×D3—64no—
138C3×Q8—44no—
139C3×Q8—44no—
140C2×C3×C4—24no—
141C2×C3×C4—24no—
142C2×C3×C4C2×C4×D314yes—
143C2×C3×C4D3×D418yes—
144C2×Dic3—38no—
145C2×Dic3—34no—
146C2×Dic3—64no—
147D12—124no—
148D12—128no—
149C4×D3—68no—
150C4×D3—68no—
151C4×D3—68no—
152C4×D3—128no—
153Dic6—128no—
154Dic6—124no—
155C3×C8—48no—
156C3⋊C8—128no—
157C2×C32—21no—
158C2×C32C2×#9911yescharacteristic
159C3⋊D3—22no—
160C3⋊D3—81no—
161#41—362no—
162C2×Q8—91no—
163C2×Q8—92no—
164C2×Q8—362no—
165C2×Q8C4×C3⋊D311yescharacteristic
166C2×Q8C22×C3⋊D311yescharacteristic
167C2×D4—91no—
168C2×D4—181no—
169C22×C4—91no—
170C22×C4—92no—
171C22×C4—181no—
172M16—22no—
173M16—182no—
174M16—362no—
175C2×C8—362no—
176C4⋊C4—22no—
177C4⋊C4—181no—
178C4⋊C4—182no—
179C22⋊C4—182no—
180C22⋊C4—181no—
181C22⋊C4—182no—
182C42—91no—
183C42C4×C3⋊D311yescharacteristic
184C22×C3D3×C22⋊C414yes—
185C2×D3—38no—
186C2×D3—124no—
187C2×D3—128no—
188C2×D3—124no—
189C3×C4—28no—
190C3×C4—24no—
191C3×C4—44no—
192C3×C4—44no—
193Dic3—64no—
194Dic3—68no—
195Dic3—124no—
196C32#213311yescharacteristic, complemented, Sylow
197C23—91no—
198C23—181no—
199Q8—41no—
200Q8—41no—
201Q8—362no—
202Q8—361no—
203D4—361no—
204D4—362no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—92no—
208C2×C4—91no—
209C2×C4—182no—
210C2×C4—182no—
211C2×C4—182no—
212C2×C4—181no—
213C2×C4—362no—
214C2×C4C2×C4×C3⋊D311yescharacteristic
215C2×C4D4×C3⋊D312yes—
216C8—42no—
217C8—362no—
218C2×C3—24no—
219C2×C3D3×#9914yes—
220D3—68no—
221D3—244no—
222C22—92no—
223C22—361no—
224C22—362no—
225C22—361no—
226C22C22⋊C4×C3⋊D311yescharacteristic
227C4—22no—
228C4—21no—
229C4—41no—
230C4—41no—
231C4—181no—
232C4—182no—
233C4—361no—
234C3#6917114yescomplemented
235C2—21no—
236C2—182no—
237C2—721no—
238C2C3⋊D3×#9911yescharacteristic
subgroupG/H
centerC2C3⋊D3×#99
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C22×C3⋊D3
FittingC32×#356C2
socleC2×C32C2×#99
prime radicalC2×#3832C4
cosocleC2×C32×Q8C23
hypercenter#356C3⋊D3
hypocenterC32#2133
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#101C2semidirect
3. C32×#356C2semidirect
4. #10589414C2semidirect
5. #10589343C2semidirect
22. C3×#356D3semidirect
86. #356C3⋊D3semidirect
196. C32#2133semidirect
234. C3#69171semidirect

Maximal subgroups

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

subgroupindex
#105961952
C3⋊D3×#1012
C32×#3562
#105894142
#105893432
#691713