Finite Group Databasebeta

← #11799779

Subgroups — #11799779

Order 1152.

367 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 367 conjugacy classes of subgroups — too many to draw. Only its 74 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#10592856C211yesmaximal, characteristic
2#10590687C211yesmaximal, characteristic, complemented
3C3×#4562C212yesmaximal, complemented
4#10589139C212yesmaximal, complemented
5#10589108C211yesmaximal, characteristic, complemented
6#69199—32nomaximal
7C2×C32×D8C2211yescharacteristic
8#64147—21no—
9C2×C8×C3⋊D3C2211yescharacteristic
10#63900—21no—
11#63659—21no—
12#63645C2211yescharacteristic
13C3×#818C2212yes—
14C2×C3×C3⋊C16C2212yes—
15#63576—21no—
16#5157—32no—
17#5157—61no—
18D3×#107—32no—
19C3×#357—32no—
20#4562D312yescomplemented
21(C2×D3)⋊C16—32no—
22#4504—32no—
23#4489—32no—
24C2×C32×D4—21no—
25C2×#638—41no—
26C2×C4×C3⋊D3D411yescharacteristic
27C2×#624—41no—
28C32×D8—22no—
29C2×C32×C8C2311yescharacteristic
30#3757—41no—
31C4⋊(C3⋊Dic3)—21no—
32C2×C3⋊(C3⋊C8)D411yescharacteristic
33C8×C3⋊D3—22no—
34C3×C4⋊Dic3—22no—
35#3724—41no—
36C3×C3⋊C16—22no—
37#2232—91noSylow
38C2×C3×D8—21no—
39C2×C3×D8C2×D312yes—
40#938—62no—
41#938—62no—
42C2×D3×C8—32no—
43C2×D3×C8—61no—
44D3×C4⋊C4—62no—
45C2×C3×C16—32no—
46C3×#107—32no—
47#832—62no—
48#832—62no—
49#818—32no—
50#818—61no—
51#818C2×D312yes—
52C2×C3⋊C16C2×D312yes—
53#807—62no—
54C23×C32—41no—
55C22×C3⋊D3D811yescharacteristic
56C32×D4—41no—
57C32×D4—41no—
58C2×C32×C4C2×D411yescharacteristic
59#638—82no—
60C2×C3⋊Dic3—41no—
61C2×C3⋊Dic3D811yescharacteristic
62C4×C3⋊D3—21no—
63C4×C3⋊D3—21no—
64C2×C3×Dic3—42no—
65#624—82no—
66C32×C8#4112yes—
67C3⋊(C3⋊C8)—21no—
68#466—91no—
69C2×#107—91no—
70#366—92no—
71#357—32no—
72C22⋊C16—91no—
73C2×C3×D4—22no—
74C2×C3×D4—22no—
75C2×#67—122no—
76C2×#67—122no—
77C2×C4×D3—32no—
78C2×C4×D3—61no—
79C2×C4×D3—122no—
80C3×D8—22no—
81C3×D8—22no—
82C3×D8—42no—
83C2×C3×C8—21no—
84C2×C3×C8C22×D312yes—
85C3×C4⋊C4—62no—
86#217—122no—
87#217—122no—
88C4⋊Dic3—22no—
89C4⋊Dic3—62no—
90C4⋊Dic3—62no—
91Dic3⋊C4—122no—
92C2×C3⋊C8—32no—
93C2×C3⋊C8—61no—
94D3×C8—62no—
95D3×C8—62no—
96D3×C8—122no—
97C3×C16—62no—
98C3⋊C16—22no—
99C22×C32—81no—
100C22×C32—81no—
101C22×C32—81no—
102C22×C32C2×D811yescharacteristic
103C2×C3⋊D3—21no—
104C2×C3⋊D3—21no—
105C2×C3⋊D3D1612yes—
106C32×C4#12311yescharacteristic
107C32×C4#13711yescharacteristic
108C3⋊Dic3—21no—
109C3⋊Dic3—81no—
110C3×Dic3—82no—
111C2×D8D3211yescharacteristic
112C22×C8—91no—
113#121—181no—
114C2×C4⋊C4—181no—
115C2×C16—32no—
116#107—32no—
117#107—91no—
118#107—181no—
119#102—181no—
120C23×C3—42no—
121C23×C3—42no—
122C22×D3—32no—
123C22×D3—61no—
124C3×D4—42no—
125C3×D4—42no—
126C3×D4—42no—
127C3×D4—42no—
128C2×C3×C4—21no—
129C2×C3×C4—122no—
130C2×C3×C4D3×D412yes—
131#67—244no—
132#67—244no—
133C2×Dic3—32no—
134C2×Dic3—42no—
135C2×Dic3—61no—
136C2×Dic3—122no—
137C2×Dic3—122no—
138C4×D3—62no—
139C4×D3—62no—
140C4×D3—121no—
141C4×D3—121no—
142C4×D3—244no—
143C3×C8—22no—
144C3×C8#23512yes—
145C3×C8#23712yes—
146C3⋊C8—62no—
147C3⋊C8—121no—
148C2×C32—161no—
149C2×C32#48011yescharacteristic
150C2×C32C2×D1611yescharacteristic
151C2×C32#51011yescharacteristic
152C3⋊D3—22no—
153C2×D4—21no—
154C2×D4—361no—
155C22×C4—91no—
156C22×C4—361no—
157D8—22no—
158C2×C8—91no—
159C2×C8—182no—
160C2×C8C2×D3211yescharacteristic
161C4⋊C4—62no—
162C4⋊C4—181no—
163C4⋊C4—361no—
164C22⋊C4—361no—
165C16—62no—
166C22×C3—21no—
167C22×C3—82no—
168C22×C3—82no—
169C22×C3—82no—
170C22×C3—82no—
171C22×C3—82no—
172C22×C3—82no—
173C22×C3D3×D812yes—
174C2×D3—34no—
175C2×D3—62no—
176C2×D3—62no—
177C2×D3—62no—
178C2×D3—121no—
179C2×D3—121no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—242no—
183C3×C4#88312yes—
184C3×C4#91512yes—
185Dic3—62no—
186Dic3—82no—
187Dic3—121no—
188Dic3—242no—
189Dic3—242no—
190C32#223211yescharacteristic, complemented, Sylow
191C23—41no—
192C23—91no—
193D4—41no—
194D4—41no—
195D4—722no—
196C2×C4—91no—
197C2×C4—122no—
198C2×C4—181no—
199C2×C4—181no—
200C2×C4—361no—
201C2×C4—722no—
202C2×C4#381111yescharacteristic
203C8—181no—
204C8#380412yes—
205C2×C3—21no—
206C2×C3—21no—
207C2×C3—21no—
208C2×C3—162no—
209C2×C3—162no—
210C2×C3#477412yes—
211C2×C3D3×D1612yes—
212C2×C3#491512yes—
213D3—64no—
214D3—122no—
215C22—81no—
216C22—81no—
217C22—81no—
218C22—92no—
219C22—181no—
220C22—181no—
221C22#6392611yescharacteristic
222C4—181no—
223C4—242no—
224C4—721no—
225C4#6393111yescharacteristic
226C4#6397511yescharacteristic
227C3—21no—
228C3#6919912yescomplemented
229C2—161no—
230C2—182no—
231C2#1059102511yescharacteristic
232C2#1059103011yescharacteristic
233C2#1059141711yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC22×C32C2×D8
prime radical#10592856C2
hypercenterC2×D8D32
hypocenterC32#2232
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10590687C2semidirect
3. C3×#4562C2semidirect
4. #10589139C2semidirect
5. #10589108C2semidirect
20. #4562D3semidirect
190. C32#2232semidirect
228. C3#69199semidirect

Maximal subgroups

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

subgroupindex
#105928562
#105906872
C3×#45622
#105891392
#105891082
#691993