Finite Group Databasebeta

← #11772495

Subgroups — #11772495

Order 1152.

242 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 50 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×#63769C211yesmaximal, characteristic
2#10593762C211yesmaximal, characteristic
3C3⋊D3×#108C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5M16×C3⋊D3—21no—
6C2×C8×C3⋊D3C2211yescharacteristic
7#63773—21no—
8#63769—21no—
9#63769C412yes—
10#63765C412yescomplemented
11#63764—21no—
12C32×#108C411yescharacteristic, complemented
13#63649—21no—
14#63646C411yescharacteristic, complemented
15D3×#108—62no—
16C22×#157—41no—
17C2×C4×C3⋊D3D411yescharacteristic
18C4⋊#157—22no—
19C4⋊#157—41no—
20C32×M16—21no—
21C2×C32×C8C2×C411yescharacteristic
22#3748—21no—
23C2×C3⋊(C3⋊C8)D411yescharacteristic
24#3743—41no—
25C8×C3⋊D3—41no—
26C8×C3⋊D3C2×C411yescharacteristic
27C8×C3⋊D3C2×C411yescharacteristic
28C8×C3⋊D3D411yescharacteristic
29C8×C3⋊D3Q811yescharacteristic
30#3708—22no—
31#1387—91nomaximal, Sylow
32D3×M16—64no—
33C2×D3×C8—62no—
34C3×#108—22no—
35#822—64no—
36#819—62no—
37C22×C3⋊D3SD1611yescharacteristic
38C2×#157—42no—
39C2×#157—82no—
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C3⋊Dic3Q1611yescharacteristic
42C4×C3⋊D3C22⋊C411yescharacteristic
43C4×C3⋊D3C4⋊C411yescharacteristic
44C4×C3⋊D3D811yescharacteristic
45C4×C3⋊D3SD1611yescharacteristic
46C32×C8—41no—
47C32×C8C4211yescharacteristic
48C32×C8C4⋊C411yescharacteristic
49C3⋊(C3⋊C8)—41no—
50C3⋊(C3⋊C8)C22⋊C411yescharacteristic
51C3⋊(C3⋊C8)C4⋊C411yescharacteristic
52C2×M32—91no—
53C2×#108—91no—
54C2×#107—91no—
55C2×C4×D3—62no—
56C3×M16—24no—
57C2×C3×C8—22no—
58#208—64no—
59C2×C3⋊C8—62no—
60ΓL(1,𝔽25)—124no—
61D3×C8—62no—
62D3×C8—62no—
63D3×C8—62no—
64D3×C8—62no—
65D3×C8—124no—
66C22×C32#10311yescharacteristic
67C2×C3⋊D3—21no—
68C2×C3⋊D3—21no—
69C2×C3⋊D3#10211yescharacteristic
70C2×C3⋊D3#10611yescharacteristic
71#157—82no—
72C32×C4#9511yescharacteristic
73C32×C4#10211yescharacteristic
74C3⋊Dic3#10311yescharacteristic
75C3⋊Dic3#10711yescharacteristic
76C2×M16—181no—
77C22×C8—91no—
78C2×C4⋊C4—181no—
79M32—92no—
80M32—181no—
81C2×C16—181no—
82#108—91no—
83#108—181no—
84#108#15711yescharacteristic, complemented
85#107—92no—
86#107—181no—
87C22×D3—62no—
88C2×C3×C4—22no—
89C2×Dic3—62no—
90C4×D3—62no—
91C4×D3—62no—
92C4×D3—62no—
93C4×D3—62no—
94C3×C8—22no—
95C3×C8—22no—
96C3×C8—44no—
97C3⋊C8—62no—
98C3⋊C8—62no—
99C3⋊C8—124no—
100C2×C32—21no—
101C2×C32#34011yescharacteristic
102C3⋊D3—21no—
103C3⋊D3#36111yescharacteristic
104C3⋊D3#36211yescharacteristic
105C22×C4—91no—
106C22×C4—361no—
107M16—21no—
108M16—181no—
109M16—361no—
110C2×C8—91no—
111C2×C8—91no—
112C2×C8—91no—
113C2×C8—91no—
114C2×C8—91no—
115C2×C8—361no—
116C2×C8C2×#15711yescharacteristic
117C4⋊C4—182no—
118C4⋊C4—361no—
119C16—182no—
120C22×C3—22no—
121C2×D3—62no—
122C2×D3—62no—
123C2×D3—122no—
124C2×D3—122no—
125C3×C4—22no—
126C3×C4—22no—
127Dic3—62no—
128Dic3—62no—
129C32#138711yescharacteristic, complemented, Sylow
130C23—91no—
131C2×C4—91no—
132C2×C4—91no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—91no—
136C2×C4—362no—
137C2×C4—722no—
138C2×C4C22⋊#15711yescharacteristic
139C8—41no—
140C8—91no—
141C8—91no—
142C8—361no—
143C8C4×#15711yescharacteristic
144C8C4⋊#15711yescharacteristic
145C2×C3—22no—
146C2×C3—42no—
147D3—62no—
148D3—62no—
149D3—122no—
150C22—91no—
151C22—91no—
152C22—181no—
153C22—181no—
154C22#6378411yescharacteristic
155C4—91no—
156C4—91no—
157C4—722no—
158C4#6378111yescharacteristic
159C4#6378211yescharacteristic
160C3—22no—
161C2—21no—
162C2—91no—
163C2—91no—
164C2—181no—
165C2#1059016311yescharacteristic
subgroupG/H
centerC2#10590163
commutatorC32×C8C42
FrattiniC2×C8C2×#157
FittingC32×#108C4
socleC2×C32#340
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypercenter#108#157
hypocenterC32#1387
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
10. #63765C4semidirect
12. C32×#108C4semidirect
14. #63646C4semidirect
84. #108#157semidirect
129. C32#1387semidirect

Maximal subgroups

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

subgroupindex
C2×#637692
#105937622
C3⋊D3×#1082
#13879