Finite Group Databasebeta

← #11799107

Subgroups — #11799107

Order 1152.

510 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 115 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#10592607C212yesmaximal, complemented
2#10592399C211yesmaximal, characteristic, complemented
3#10592394C211yesmaximal, characteristic, complemented
4C32×#364C211yesmaximal, characteristic, complemented
5#10589382C212yesmaximal, complemented
6#69305—34nomaximal
7#64113C2211yescharacteristic
8C2×#3745—21no—
9C2×#3745C2212yes—
10#64110—21no—
11#64083—21no—
12C32×M32C2212yes—
13C32×C4×C8C2211yescharacteristic
14#63646C2211yescharacteristic
15#63632—21no—
16#63627—22no—
17#63626—22no—
18#4908—38no—
19#4700—34no—
20#4695—34no—
21C3×#364D314yescomplemented
22#4516—38no—
23#3828—21no—
24C2×C4⋊(C3⋊D3)—22no—
25C2×C4⋊(C3⋊D3)—42no—
26C2×C32×C8D411yescharacteristic
27C2×C32×C8C2311yescharacteristic
28C32×C42D411yescharacteristic
29#3748—21no—
30#3746D411yescharacteristic, complemented
31#3745—22no—
32#3745—22no—
33#3745—41no—
34#3745—41no—
35#3745D411yescharacteristic, complemented
36#3744—21no—
37#3743—41no—
38C8×C3⋊D3—41no—
39C32×C16—22no—
40#2213—91noSylow
41#904—34no—
42C2×D24—38no—
43C2×D24—64no—
44#901—64no—
45#874—64no—
46C3×M32C2×D318yes—
47C3×C4×C8C2×D314yes—
48#819—34no—
49#805—64no—
50#800—68no—
51D48—68no—
52C22×C3⋊D3—42no—
53C2×C32×C4—21no—
54C2×C32×C4C2×D411yescharacteristic
55#638—41no—
56C4⋊(C3⋊D3)—21no—
57C4⋊(C3⋊D3)—42no—
58C4⋊(C3⋊D3)—42no—
59C4⋊(C3⋊D3)—84no—
60C4×C3⋊D3—41no—
61#634—21no—
62C32×C8D811yescharacteristic
63C32×C8D811yescharacteristic
64C32×C8C2×D411yescharacteristic
65C32×C8#4111yescharacteristic
66C3⋊(C3⋊C8)—41no—
67#509—92no—
68#493—91no—
69#443—91no—
70#364C3⋊D311yescharacteristic, complemented
71#361—92no—
72#235—64no—
73C2×D12—68no—
74C2×D12—128no—
75C2×C3×C8D1214yes—
76C2×C3×C8C22×D314yes—
77C3×C42D1214yes—
78#208—64no—
79Dic12—34no—
80D24—34no—
81D24—68no—
82D24—68no—
83D24—124no—
84D24—124no—
85#204—64no—
86ΓL(1,𝔽25)—124no—
87D3×C8—124no—
88C3×C16—28no—
89C22×C32AGL(1,ℤ/8)11yescharacteristic
90C2×C3⋊D3—41no—
91C2×C3⋊D3—84no—
92C2×C3⋊D3—82no—
93C32×C4—22no—
94C32×C4#12111yescharacteristic
95C32×C4C2×D811yescharacteristic
96C3⋊Dic3—41no—
97#135—91no—
98C2×D8—92no—
99C2×D8—181no—
100#131—181no—
101#127—181no—
102SD32—182no—
103D16—182no—
104M32C2×C3⋊D312yes—
105#108—91no—
106#104—181no—
107C4×C8C2×C3⋊D311yescharacteristic
108C22×D3—128no—
109C2×C3×C4—24no—
110C2×C3×C4C2×D1214yes—
111#67—124no—
112D12—64no—
113D12—128no—
114D12—128no—
115D12—2416no—
116C4×D3—124no—
117Dic6—64no—
118C3×C8D2414yes—
119C3×C8D2414yes—
120C3×C8D3×D414yes—
121C3×C8#23914yes—
122C3⋊C8—124no—
123C2×C32—21no—
124C2×C32#45911yescharacteristic
125C3⋊D3—81no—
126C3⋊D3—162no—
127#41—181no—
128C2×D4—182no—
129C2×D4—362no—
130Q16—91no—
131SD16—181no—
132D8—91no—
133D8—182no—
134D8—182no—
135D8—361no—
136D8—361no—
137M16—181no—
138M16—361no—
139C2×C8—361no—
140C2×C8C4⋊(C3⋊D3)11yescharacteristic
141C2×C8C22×C3⋊D311yescharacteristic
142C42C4⋊(C3⋊D3)11yescharacteristic
143C16—22no—
144C22×C3#90814yes—
145C2×D3—124no—
146C2×D3—2416no—
147C2×D3—248no—
148C3×C4—28no—
149C3×C4#89514yes—
150C3×C4C2×D2414yes—
151Dic3—124no—
152C32#221311yescharacteristic, complemented, Sylow
153C23—362no—
154Q8—181no—
155D4—181no—
156D4—361no—
157D4—362no—
158D4—362no—
159D4—724no—
160C2×C4—21no—
161C2×C4—361no—
162C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
163C8—361no—
164C8#374511yescharacteristic
165C8#374511yescharacteristic
166C8D4×C3⋊D311yescharacteristic
167C8#383211yescharacteristic
168C2×C3—24no—
169C2×C3#484314yes—
170D3—244no—
171D3—488no—
172C22—361no—
173C22—724no—
174C22—722no—
175C22#6411711yescharacteristic
176C4—22no—
177C4—361no—
178C4#6410411yescharacteristic
179C4C2×#374511yescharacteristic
180C3#6930514yescomplemented
181C2—21no—
182C2—721no—
183C2—1442no—
184C2#1059254211yescharacteristic
subgroupG/H
centerC2#10592542
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#364C2
socleC2×C32#459
hypercenter#364C3⋊D3
hypocenterC32#2213
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
1. #10592607C2semidirect
2. #10592399C2semidirect
3. #10592394C2semidirect
4. C32×#364C2semidirect
5. #10589382C2semidirect
21. C3×#364D3semidirect
30. #3746D4semidirect
35. #3745D4semidirect
70. #364C3⋊D3semidirect
152. C32#2213semidirect
180. C3#69305semidirect

Maximal subgroups

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

subgroupindex
#105926072
#105923992
#105923942
C32×#3642
#105893822
#693053