Finite Group Databasebeta

← #11785736

Subgroups — #11785736

Order 1152.

816 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 177 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×#64101C211yesmaximal, characteristic
2#10592825C212yesmaximal
3C32×#343C211yesmaximal, characteristic, complemented
4#10589420C212yesmaximal, complemented
5#10589396C211yesmaximal, characteristic, complemented
6#68991—34nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C32×M16C2212yes—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×#3752C412yes—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×C4×C3⋊Dic3C412yes—
13C2×#3748C2212yes—
14#64101—24no—
15#63647—24no—
16C2×#892—34no—
17#5126—38no—
18C3×#343D314yescomplemented
19#4554—38no—
20#4530—34no—
21C23×C3⋊D3C2×C411yescharacteristic
22C22×C32×C4C2×C412yes—
23C22×C32×C4C2311yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3C2×C412yes—
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3—21no—
28C2×C4×C3⋊D3—21no—
29C2×C4×C3⋊D3D414yes—
30C32×M16—22no—
31C32×M16—22no—
32C2×C32×C8—22no—
33C32×C4⋊C4—22no—
34#3752—24no—
35C4⋊(C3⋊Dic3)—22no—
36C4×C3⋊Dic3—24no—
37#3748—22no—
38#3748—22no—
39C2×C3⋊(C3⋊C8)—22no—
40#1822—91noSylow
41C22×C4×D3—34no—
42C2×C3×M16C2×D318yes—
43C2×C3×C4⋊C4C2×D314yes—
44C2×(C2×D3)⋊C4—38no—
45C2×C4⋊Dic3—34no—
46C2×C4×Dic3—38no—
47C2×#208—38no—
48#892—616no—
49(C2×D3)⋊C8—616no—
50C23×C32C22×C411yescharacteristic
51C22×C3⋊D3—21no—
52C22×C3⋊D3—21no—
53C22×C3⋊D3—41no—
54C22×C3⋊D3—41no—
55C22×C3⋊D3C22⋊C412yes—
56C2×C32×C4—22no—
57C2×C32×C4—42no—
58C2×C32×C4C2×D412yes—
59C2×C32×C4#4112yes—
60C2×C32×C4#4111yescharacteristic
61C2×C32×C4#4111yescharacteristic
62C2×C3⋊Dic3—21no—
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—42no—
66C2×C3⋊Dic3C22⋊C412yes—
67C4×C3⋊D3—24no—
68C4×C3⋊D3—24no—
69C32×C8—42no—
70C3⋊(C3⋊C8)—42no—
71C2×#117—91no—
72#407—92no—
73#343—92no—
74#343—91no—
75#343C3⋊D311yescharacteristic, complemented
76C23×D3—34no—
77C22×C3×C4C4×D318yes—
78C22×C3×C4C22×D314yes—
79C22×Dic3—34no—
80C22×Dic3—38no—
81C2×C4×D3—316no—
82C2×C4×D3—68no—
83C2×C4×D3—64no—
84C2×C4×D3—64no—
85C3×M16—28no—
86C3×M16—28no—
87C2×C3×C8—28no—
88C3×C4⋊C4—28no—
89(C2×D3)⋊C4—616no—
90C4⋊Dic3—68no—
91C4×Dic3—616no—
92#208—68no—
93#208—68no—
94C2×C3⋊C8—68no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32C2×C22⋊C411yescharacteristic
98C22×C32#11711yescharacteristic
99C22×C32#11711yescharacteristic
100C2×C3⋊D3—22no—
101C2×C3⋊D3—22no—
102C2×C3⋊D3—22no—
103C2×C3⋊D3—42no—
104C2×C3⋊D3—42no—
105C32×C4—42no—
106C32×C4#12312yes—
107C32×C4#12312yes—
108C3⋊Dic3—22no—
109C3⋊Dic3—42no—
110C23×C4—91no—
111C2×M16—92no—
112C2×M16C2×C3⋊D312yes—
113#117—184no—
114C2×C4⋊C4—91no—
115C2×C4⋊C4C2×C3⋊D311yescharacteristic
116C2×C22⋊C4—92no—
117C2×C42—92no—
118C22⋊C8—184no—
119C23×C3C2×C4×D314yes—
120C22×D3—38no—
121C22×D3—64no—
122C22×D3—64no—
123C22×D3—124no—
124C22×D3—124no—
125C2×C3×C4—28no—
126C2×C3×C4—48no—
127C2×C3×C4#23518yes—
128C2×C3×C4D3×D418yes—
129C2×C3×C4#23714yes—
130C2×C3×C4#23914yes—
131C2×Dic3—38no—
132C2×Dic3—64no—
133C2×Dic3—64no—
134C2×Dic3—68no—
135C2×Dic3—128no—
136C4×D3—616no—
137C4×D3—616no—
138C3×C8—48no—
139C3⋊C8—128no—
140C2×C32—21no—
141C2×C32—21no—
142C2×C32#38111yescharacteristic
143C2×C32#41311yescharacteristic
144C2×C32#41311yescharacteristic
145C3⋊D3—42no—
146C24—91no—
147C22×C4—91no—
148C22×C4—94no—
149C22×C4—92no—
150C22×C4—182no—
151C22×C4—181no—
152C22×C4—181no—
153C22×C4C4×C3⋊D312yes—
154C22×C4C22×C3⋊D311yescharacteristic
155M16—22no—
156M16—22no—
157M16—182no—
158M16—182no—
159C2×C8—22no—
160C2×C8—182no—
161C4⋊C4—22no—
162C4⋊C4—182no—
163C22⋊C4—184no—
164C42—184no—
165C22×C3—24no—
166C22×C3—24no—
167C22×C3#87214yes—
168C22×C3D3×C22⋊C414yes—
169C22×C3#89214yes—
170C2×D3—68no—
171C2×D3—68no—
172C2×D3—68no—
173C2×D3—128no—
174C2×D3—128no—
175C3×C4—48no—
176C3×C4#88318yes—
177C3×C4#89418yes—
178Dic3—68no—
179Dic3—128no—
180C32#182211yescharacteristic, complemented, Sylow
181C23—92no—
182C23—181no—
183C23—181no—
184C23—361no—
185C23—361no—
186C23C2×C4×C3⋊D311yescharacteristic
187C2×C4—22no—
188C2×C4—42no—
189C2×C4—92no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4—184no—
193C2×C4—184no—
194C2×C4—182no—
195C2×C4—362no—
196C2×C4#382812yes—
197C2×C4D4×C3⋊D312yes—
198C2×C4#383011yescharacteristic
199C2×C4#383211yescharacteristic
200C8—42no—
201C8—362no—
202C2×C3—24no—
203C2×C3—24no—
204C2×C3#466414yes—
205C2×C3#474514yes—
206C2×C3#475114yes—
207D3—128no—
208C22—21no—
209C22—21no—
210C22—182no—
211C22—182no—
212C22—182no—
213C22—362no—
214C22—362no—
215C22#6408111yescharacteristic
216C22C22⋊C4×C3⋊D311yescharacteristic
217C22#6410111yescharacteristic
218C4—42no—
219C4—182no—
220C4—362no—
221C4#6409212yes—
222C4#6410312yes—
223C3#6899114yescomplemented
224C2—21no—
225C2—21no—
226C2—362no—
227C2#1059236311yescharacteristic
228C2#1059244411yescharacteristic
229C2#1059245011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenter#343C3⋊D3
hypocenterC32#1822
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. C32×#343C2semidirect
4. #10589420C2semidirect
5. #10589396C2semidirect
18. C3×#343D3semidirect
75. #343C3⋊D3semidirect
180. C32#1822semidirect
223. C3#68991semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
#105928252
C32×#3432
#105894202
#105893962
#689913