Finite Group Databasebeta

← #11772493

Subgroups — #11772493

Order 1152.

266 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 52 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×#63770C211yesmaximal, characteristic
2C2×#63765C211yesmaximal, characteristic
3C3⋊D3×#107C211yesmaximal, characteristic
4C2×#3788—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6C4⋊C4×C3⋊D3—21no—
7C2×#3708—21no—
8#63770—21no—
9#63770C412yescomplemented
10#63765—21no—
11#63765C412yescomplemented
12C32×#107C411yescharacteristic
13#63645C411yescharacteristic
14#63634—21no—
15D3×#107—62no—
16C2×C4×C3⋊D3—41no—
17C2×C4×C3⋊D3D411yescharacteristic
18C2×#622—41no—
19#3788—22no—
20#3788—41no—
21C2×C32×C8C2×C411yescharacteristic
22C32×C4⋊C4—21no—
23C4⋊(C3⋊Dic3)—21no—
24#3750—41no—
25C2×C3⋊(C3⋊C8)D411yescharacteristic
26C8×C3⋊D3C2×C411yescharacteristic
27C8×C3⋊D3C2×C411yescharacteristic
28C8×C3⋊D3D411yescharacteristic
29C8×C3⋊D3Q811yescharacteristic
30#3708—22no—
31#1387—91nomaximal, Sylow
32C2×D3×C8—62no—
33D3×C4⋊C4—64no—
34C3×#107—22no—
35#818—62no—
36#807—64no—
37C22×C3⋊D3SD1611yescharacteristic
38C2×C32×C4—41no—
39C2×C32×C4C22⋊C411yescharacteristic
40C2×C3⋊Dic3—41no—
41C2×C3⋊Dic3D811yescharacteristic
42C4×C3⋊D3—82no—
43C4×C3⋊D3C22⋊C411yescharacteristic
44C4×C3⋊D3C4⋊C411yescharacteristic
45C4×C3⋊D3SD1611yescharacteristic
46C4×C3⋊D3Q1611yescharacteristic
47#622—42no—
48C32×C8C4211yescharacteristic
49C32×C8C4⋊C411yescharacteristic
50C3⋊(C3⋊C8)C22⋊C411yescharacteristic
51C3⋊(C3⋊C8)C4⋊C411yescharacteristic
52C2×M32—91no—
53C2×#108—91no—
54C2×#107—91no—
55C2×C4×D3—62no—
56C2×C4×D3—124no—
57C2×C3×C8—22no—
58C3×C4⋊C4—24no—
59C4⋊Dic3—64no—
60Dic3⋊C4—124no—
61C2×C3⋊C8—62no—
62D3×C8—62no—
63D3×C8—62no—
64D3×C8—62no—
65D3×C8—62no—
66C22×C32#10211yescharacteristic
67C2×C3⋊D3—21no—
68C2×C3⋊D3—21no—
69C2×C3⋊D3#10311yescharacteristic
70C2×C3⋊D3#10611yescharacteristic
71C32×C4—81no—
72C32×C4#9511yescharacteristic
73C32×C4#10311yescharacteristic
74C3⋊Dic3—81no—
75C3⋊Dic3#10211yescharacteristic
76C3⋊Dic3#10711yescharacteristic
77C2×M16—181no—
78C22×C8—91no—
79C2×C4⋊C4—181no—
80M32—92no—
81M32—181no—
82C2×C16—181no—
83#108—92no—
84#108—181no—
85#107—91no—
86#107—181no—
87#107#15711yescharacteristic
88C22×D3—62no—
89C2×C3×C4—22no—
90C2×C3×C4—44no—
91C2×Dic3—62no—
92C2×Dic3—124no—
93C4×D3—62no—
94C4×D3—62no—
95C4×D3—62no—
96C4×D3—62no—
97C4×D3—248no—
98C3×C8—22no—
99C3×C8—22no—
100C3⋊C8—62no—
101C3⋊C8—62no—
102C2×C32#34011yescharacteristic
103C2×C32#36111yescharacteristic
104C2×C32#36211yescharacteristic
105C3⋊D3—21no—
106C3⋊D3—21no—
107C22×C4—91no—
108C22×C4—361no—
109M16—182no—
110M16—361no—
111C2×C8—91no—
112C2×C8—91no—
113C2×C8—91no—
114C2×C8—91no—
115C2×C8—91no—
116C2×C8—361no—
117C2×C8C2×#15711yescharacteristic
118C4⋊C4—21no—
119C4⋊C4—181no—
120C4⋊C4—361no—
121C16—182no—
122C22×C3—22no—
123C2×D3—62no—
124C2×D3—62no—
125C2×D3—64no—
126C2×D3—64no—
127C3×C4—22no—
128C3×C4—22no—
129C3×C4—84no—
130Dic3—62no—
131Dic3—62no—
132Dic3—244no—
133C32#138711yescharacteristic, complemented, Sylow
134C23—91no—
135C2×C4—41no—
136C2×C4—91no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—91no—
141C2×C4—361no—
142C2×C4—722no—
143C2×C4C22⋊#15711yescharacteristic
144C8—91no—
145C8—91no—
146C8—362no—
147C8C4×#15711yescharacteristic
148C8C4⋊#15711yescharacteristic
149C2×C3—22no—
150C2×C3—22no—
151C2×C3—22no—
152D3—64no—
153D3—64no—
154C22—91no—
155C22—91no—
156C22—181no—
157C22—181no—
158C22#6378211yescharacteristic
159C4—81no—
160C4—91no—
161C4—91no—
162C4—721no—
163C4#6378111yescharacteristic
164C4#6378411yescharacteristic
165C3—22no—
166C2—181no—
167C2—181no—
168C2#1059016311yescharacteristic
169C2#1059019511yescharacteristic
170C2#1059019911yescharacteristic
subgroupG/H
centerC22#63782
commutatorC32×C8C42
FrattiniC2×C8C2×#157
FittingC32×#107C4
socleC22×C32#102
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypercenter#107#157
hypocenterC32#1387
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
9. #63770C4semidirect
11. #63765C4semidirect
133. C32#1387semidirect

Maximal subgroups

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

subgroupindex
C2×#637702
C2×#637652
C3⋊D3×#1072
#13879