Finite Group Databasebeta

← #11783409

Subgroups — #11783409

Order 1152.

1164 conjugacy classes of subgroups; only the 253 normal subgroups are shown.

normal subgroups only

This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 253 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×M16×C3⋊D3C212yesmaximal
2C2×#64101C211yesmaximal, characteristic
3C32×#343C211yesmaximal, characteristic, complemented
4#10589420C212yesmaximal, complemented
5#10589396C211yesmaximal, characteristic, complemented
6#68989—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—
14M16×C3⋊D3—24no—
15M16×C3⋊D3C418yescomplemented
16C2×#3743—22no—
17C2×C8×C3⋊D3—22no—
18#64101—22no—
19#64101—22no—
20C2×D3×M16—38no—
21C2×#892—34no—
22C3×#343D314yescomplemented
23#4554—38no—
24#4530—34no—
25C23×C3⋊D3C2×C411yescharacteristic
26C22×C32×C4C2×C412yes—
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3C2×C412yes—
29C22×C3⋊Dic3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2×C414yes—
31C2×C4×C3⋊D3D412yes—
32C2×C4×C3⋊D3D412yes—
33C2×C4×C3⋊D3D412yes—
34C2×C4×C3⋊D3Q812yes—
35C32×M16—22no—
36C32×M16C2×C414yes—
37C2×C32×C8—22no—
38C32×C4⋊C4—22no—
39#3752—24no—
40C4⋊(C3⋊Dic3)—22no—
41C4×C3⋊Dic3—22no—
42C4×C3⋊Dic3—22no—
43#3748—22no—
44#3748C2×C414yes—
45C2×C3⋊(C3⋊C8)—22no—
46#3743—28no—
47C8×C3⋊D3—28no—
48#1742—91noSylow
49C22×C4×D3—34no—
50C2×C3×M16C2×D318yes—
51C2×C3×C4⋊C4C2×D314yes—
52C2×(C2×D3)⋊C4—38no—
53C2×C4⋊Dic3—34no—
54C2×C4×Dic3—38no—
55C2×#208—38no—
56D3×M16—332no—
57D3×M16—616no—
58C2×ΓL(1,𝔽25)—68no—
59C2×D3×C8—68no—
60#892—68no—
61#892—68no—
62C23×C32C22×C411yescharacteristic
63C22×C3⋊D3—41no—
64C22×C3⋊D3—41no—
65C22×C3⋊D3C4212yes—
66C22×C3⋊D3C22⋊C412yes—
67C22×C3⋊D3C4⋊C412yes—
68C2×C32×C4—22no—
69C2×C32×C4—42no—
70C2×C32×C4C22×C412yes—
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4C2×D412yes—
73C2×C32×C4C2×Q811yescharacteristic
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—42no—
76C2×C3⋊Dic3C4212yes—
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C2×C3⋊Dic3C4⋊C412yes—
80C4×C3⋊D3C22⋊C414yes—
81C4×C3⋊D3C22⋊C414yes—
82C4×C3⋊D3C4⋊C414yes—
83C4×C3⋊D3C4⋊C414yes—
84C32×C8—24no—
85C3⋊(C3⋊C8)—24no—
86C22×M16—92no—
87C2×#117—91no—
88#343—92no—
89#343—91no—
90#343C3⋊D311yescharacteristic, complemented
91C23×D3—34no—
92C22×C3×C4C4×D318yes—
93C22×C3×C4C22×D314yes—
94C22×Dic3—34no—
95C22×Dic3—38no—
96C2×C4×D3—316no—
97C2×C4×D3—38no—
98C2×C4×D3—38no—
99C2×C4×D3—38no—
100C2×C4×D3—38no—
101C3×M16—28no—
102C3×M16C4×D3116yes—
103C2×C3×C8—28no—
104C3×C4⋊C4—28no—
105(C2×D3)⋊C4—616no—
106C4⋊Dic3—68no—
107C4×Dic3—68no—
108C4×Dic3—68no—
109#208—316no—
110#208—68no—
111C2×C3⋊C8—68no—
112ΓL(1,𝔽25)—632no—
113D3×C8—632no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32C2×C4211yescharacteristic
117C22×C32C2×C22⋊C411yescharacteristic
118C22×C32C2×C4⋊C411yescharacteristic
119C2×C3⋊D3—22no—
120C2×C3⋊D3—22no—
121C2×C3⋊D3—42no—
122C2×C3⋊D3—42no—
123C2×C3⋊D3#9514yes—
124C32×C4—42no—
125C32×C4C2×C22⋊C412yes—
126C32×C4C2×C4⋊C412yes—
127C3⋊Dic3—42no—
128C3⋊Dic3#9512yes—
129C3⋊Dic3#9512yes—
130C23×C4—91no—
131C2×M16—92no—
132C2×M16—98no—
133C2×M16—182no—
134C2×M16—184no—
135C2×M16C2×C3⋊D312yes—
136C22×C8—182no—
137#117—182no—
138#117—182no—
139C2×C4⋊C4—91no—
140C2×C4⋊C4C2×C3⋊D311yescharacteristic
141C2×C22⋊C4—92no—
142C2×C42—92no—
143C23×C3C2×C4×D314yes—
144C22×D3—38no—
145C22×D3—38no—
146C22×D3—38no—
147C22×D3—124no—
148C22×D3—124no—
149C2×C3×C4—28no—
150C2×C3×C4—48no—
151C2×C3×C4C2×C4×D318yes—
152C2×C3×C4D3×D414yes—
153C2×C3×C4D3×D418yes—
154C2×C3×C4D3×Q814yes—
155C2×Dic3—38no—
156C2×Dic3—34no—
157C2×Dic3—34no—
158C2×Dic3—38no—
159C2×Dic3—68no—
160C2×Dic3—128no—
161C4×D3—316no—
162C4×D3—316no—
163C4×D3—316no—
164C4×D3—316no—
165C3×C8—216no—
166C3⋊C8—616no—
167C2×C32—21no—
168C2×C32—21no—
169C2×C32C2×#9511yescharacteristic
170C2×C32#41311yescharacteristic
171C2×C32#41311yescharacteristic
172C3⋊D3—24no—
173C24—91no—
174C22×C4—91no—
175C22×C4—94no—
176C22×C4—92no—
177C22×C4—92no—
178C22×C4—92no—
179C22×C4—92no—
180C22×C4—92no—
181C22×C4C4×C3⋊D312yes—
182C22×C4C22×C3⋊D311yescharacteristic
183M16—22no—
184M16—94no—
185M16—188no—
186M16—182no—
187M16C4×C3⋊D314yes—
188C2×C8—22no—
189C2×C8—188no—
190C2×C8—182no—
191C4⋊C4—22no—
192C4⋊C4—182no—
193C22⋊C4—184no—
194C42—182no—
195C42—182no—
196C22×C3—24no—
197C22×C3—24no—
198C22×C3C42×D314yes—
199C22×C3D3×C22⋊C414yes—
200C22×C3D3×C4⋊C414yes—
201C2×D3—316no—
202C2×D3—68no—
203C2×D3—68no—
204C2×D3—128no—
205C2×D3—128no—
206C3×C4—48no—
207C3×C4D3×C22⋊C418yes—
208C3×C4D3×C4⋊C418yes—
209Dic3—38no—
210Dic3—38no—
211Dic3—128no—
212C32#174211yescharacteristic, complemented, Sylow
213C23—92no—
214C23—92no—
215C23—92no—
216C23—361no—
217C23—361no—
218C23C2×C4×C3⋊D311yescharacteristic
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—92no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—92no—
225C2×C4—94no—
226C2×C4—94no—
227C2×C4—94no—
228C2×C4—94no—
229C2×C4—182no—
230C2×C4—362no—
231C2×C4C2×C4×C3⋊D312yes—
232C2×C4D4×C3⋊D311yescharacteristic
233C2×C4D4×C3⋊D312yes—
234C2×C4Q8×C3⋊D311yescharacteristic
235C8—24no—
236C8—184no—
237C2×C3—24no—
238C2×C3—24no—
239C2×C3D3×#9514yes—
240C2×C3#474514yes—
241C2×C3#475114yes—
242D3—616no—
243C22—21no—
244C22—21no—
245C22—94no—
246C22—182no—
247C22—182no—
248C22—362no—
249C22—362no—
250C22C42×C3⋊D311yescharacteristic
251C22C22⋊C4×C3⋊D311yescharacteristic
252C22C4⋊C4×C3⋊D311yescharacteristic
253C4—42no—
254C4—92no—
255C4—92no—
256C4—362no—
257C4C22⋊C4×C3⋊D312yes—
258C4C4⋊C4×C3⋊D312yes—
259C3#6898914yescomplemented
260C2—21no—
261C2—21no—
262C2—184no—
263C2C3⋊D3×#9511yescharacteristic
264C2#1059244411yescharacteristic
265C2#1059245011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C2×C42
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenter#343C3⋊D3
hypocenterC32#1742
LCSG ▷ C22×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
15. M16×C3⋊D3C4semidirect
22. C3×#343D3semidirect
90. #343C3⋊D3semidirect
212. C32#1742semidirect
259. C3#68989semidirect

Maximal subgroups

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

subgroupindex
C2×M16×C3⋊D32
C2×#641012
C32×#3432
#105894202
#105893962
#689893