Finite Group Databasebeta

← #11799768

Subgroups — #11799768

Order 1152.

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

normal subgroups only

This group has 450 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#10592856C211yesmaximal, characteristic
2C3⋊D3×#107C211yesmaximal, characteristic, complemented
3C32×#357C211yesmaximal, characteristic, complemented
4#10589428C211yesmaximal, characteristic, complemented
5#10589373C211yesmaximal, characteristic, complemented
6#10589370C211yesmaximal, characteristic, complemented
7#10589355C211yesmaximal, characteristic, complemented
8#69199—34nomaximal
9C2×C32×D8C2211yescharacteristic
10#64147—21no—
11C2×C8×C3⋊D3C2211yescharacteristic
12C4⋊C4×C3⋊D3—21no—
13C2×C32×C16C2211yescharacteristic
14C32×#107C2211yescharacteristic
15#63659—21no—
16#63645C2211yescharacteristic
17#63645C2211yescharacteristic
18C2×C3⋊(C3⋊C16)C2211yescharacteristic
19#63634—21no—
20#5157—34no—
21D3×#107—34no—
22C3×#357D314yescomplemented
23#4562—34no—
24(C2×D3)⋊C16—34no—
25#4504—34no—
26#4489—34no—
27C2×C32×D4—21no—
28C2×#638—41no—
29C2×C4×C3⋊D3—41no—
30C2×C4×C3⋊D3D411yescharacteristic
31C32×D8—21no—
32C32×D8—21no—
33C2×C32×C8C2311yescharacteristic
34C32×C4⋊C4—21no—
35#3757—41no—
36C4⋊(C3⋊Dic3)—21no—
37C4⋊(C3⋊Dic3)—21no—
38#3750—41no—
39C2×C3⋊(C3⋊C8)D411yescharacteristic
40C8×C3⋊D3—21no—
41C8×C3⋊D3—21no—
42C32×C16—21no—
43C3⋊(C3⋊C16)—21no—
44#2232—91noSylow
45C2×C3×D8C2×D314yes—
46#938—64no—
47C2×D3×C8—34no—
48D3×C4⋊C4—64no—
49C2×C3×C16C2×D314yes—
50C3×#107C2×D314yes—
51#832—64no—
52#818—34no—
53#818—34no—
54C2×C3⋊C16—34no—
55#807—64no—
56C23×C32—41no—
57C22×C3⋊D3D811yescharacteristic
58C32×D4—41no—
59C32×D4—41no—
60C2×C32×C4—41no—
61C2×C32×C4C2×D411yescharacteristic
62#638—82no—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3D811yescharacteristic
66C4×C3⋊D3—21no—
67C4×C3⋊D3—21no—
68C4×C3⋊D3—82no—
69C32×C8#4111yescharacteristic
70C32×C8#4111yescharacteristic
71C3⋊(C3⋊C8)—21no—
72#466—91no—
73C2×#107—91no—
74#366—91no—
75#366—91no—
76#357—91no—
77#357C3⋊D311yescharacteristic, complemented
78C22⋊C16—91no—
79C2×C3×D4—24no—
80C2×#67—124no—
81C2×C4×D3—34no—
82C2×C4×D3—124no—
83C3×D8—24no—
84C3×D8—24no—
85C2×C3×C8C22×D314yes—
86C3×C4⋊C4—24no—
87#217—124no—
88C4⋊Dic3—64no—
89C4⋊Dic3—64no—
90Dic3⋊C4—124no—
91C2×C3⋊C8—34no—
92D3×C8—64no—
93D3×C8—64no—
94C3×C16—24no—
95C3⋊C16—64no—
96C22×C32—81no—
97C22×C32—81no—
98C22×C32—81no—
99C22×C32C2×D811yescharacteristic
100C2×C3⋊D3—21no—
101C2×C3⋊D3—21no—
102C2×C3⋊D3D1612yes—
103C32×C4—81no—
104C32×C4#12311yescharacteristic
105C32×C4#13711yescharacteristic
106C3⋊Dic3—21no—
107C3⋊Dic3—81no—
108C3⋊Dic3—81no—
109C2×D8C2×C3⋊D311yescharacteristic
110C22×C8—91no—
111#121—181no—
112C2×C4⋊C4—181no—
113C2×C16—91no—
114C2×C16C2×C3⋊D311yescharacteristic
115#107—91no—
116#107—91no—
117#107—181no—
118#107C2×C3⋊D311yescharacteristic
119#102—181no—
120C23×C3—44no—
121C22×D3—34no—
122C3×D4—44no—
123C3×D4—44no—
124C2×C3×C4—44no—
125C2×C3×C4D3×D414yes—
126#67—248no—
127C2×Dic3—34no—
128C2×Dic3—124no—
129C2×Dic3—124no—
130C4×D3—64no—
131C4×D3—64no—
132C4×D3—248no—
133C3×C8#23514yes—
134C3×C8#23714yes—
135C3⋊C8—64no—
136C2×C32—161no—
137C2×C32#48011yescharacteristic
138C2×C32C2×D1611yescharacteristic
139C2×C32#51011yescharacteristic
140C3⋊D3—22no—
141C2×D4—21no—
142C2×D4—361no—
143C22×C4—91no—
144C22×C4—361no—
145D8—21no—
146D8—21no—
147C2×C8—91no—
148C2×C8—181no—
149C2×C8—181no—
150C2×C8C22×C3⋊D311yescharacteristic
151C4⋊C4—21no—
152C4⋊C4—181no—
153C4⋊C4—181no—
154C4⋊C4—361no—
155C22⋊C4—361no—
156C16—21no—
157C16—181no—
158C22×C3—84no—
159C22×C3—84no—
160C22×C3—84no—
161C22×C3D3×D814yes—
162C2×D3—38no—
163C2×D3—64no—
164C2×D3—64no—
165C3×C4—84no—
166C3×C4#88314yes—
167C3×C4#91514yes—
168Dic3—64no—
169Dic3—244no—
170Dic3—244no—
171C32#223211yescharacteristic, complemented, Sylow
172C23—41no—
173C23—91no—
174D4—41no—
175D4—41no—
176D4—722no—
177C2×C4—41no—
178C2×C4—91no—
179C2×C4—181no—
180C2×C4—181no—
181C2×C4—361no—
182C2×C4—361no—
183C2×C4—722no—
184C2×C4D4×C3⋊D311yescharacteristic
185C8—181no—
186C8#382811yescharacteristic
187C8#383011yescharacteristic
188C2×C3—164no—
189C2×C3#477414yes—
190C2×C3D3×D1614yes—
191C2×C3#491514yes—
192D3—68no—
193C22—81no—
194C22—81no—
195C22—81no—
196C22—92no—
197C22—181no—
198C22—181no—
199C22D8×C3⋊D311yescharacteristic
200C4—81no—
201C4—181no—
202C4—721no—
203C4—721no—
204C4#6409211yescharacteristic
205C4#6412411yescharacteristic
206C3#6919914yescomplemented
207C2—161no—
208C2—182no—
209C2#1059247311yescharacteristic
210C2C3⋊D3×D1611yescharacteristic
211C2#1059261411yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#357C2
socleC22×C32C2×D8
prime radical#10592856C2
hypercenter#357C3⋊D3
hypocenterC32#2232
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#107C2semidirect
3. C32×#357C2semidirect
4. #10589428C2semidirect
5. #10589373C2semidirect
6. #10589370C2semidirect
7. #10589355C2semidirect
22. C3×#357D3semidirect
77. #357C3⋊D3semidirect
171. C32#2232semidirect
206. C3#69199semidirect

Maximal subgroups

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

subgroupindex
#105928562
C3⋊D3×#1072
C32×#3572
#105894282
#105893732
#105893702
#105893552
#691993