Finite Group Databasebeta

← #11777094

Subgroups — #11777094

Order 1152.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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#10593731C211yesmaximal, characteristic
2#10593726C211yesmaximal, characteristic
3#10593725C211yesmaximal, characteristic
4#10590089C212yesmaximal, complemented
5#10590088C212yesmaximal, complemented
6C2×#3787—21no—
7C42×C3⋊D3C2211yescharacteristic
8#63779C412yes—
9#63779C2211yescharacteristic
10#63779C2212yes—
11#63779C2211yescharacteristic
12#63778—21no—
13#63778C412yes—
14#63777—21no—
15C4⋊#622—21no—
16C4×#622C2212yes—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3Q811yescharacteristic
20C2×#622—22no—
21C2×#622—21no—
22C2×#622—21no—
23C2×#622C2×C414yes—
24#3787—42no—
25C32×C42Q811yescharacteristic
26C4×C3⋊Dic3C2×C411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C4×C3⋊Dic3C2311yescharacteristic
29#1573—91nomaximal, Sylow
30C42×D3—121no—
31C22×C3⋊D3C4⋊C411yescharacteristic
32C2×C32×C4C4⋊C411yescharacteristic
33C2×C32×C4C4⋊C411yescharacteristic
34C2×C32×C4C2×Q811yescharacteristic
35C2×C3⋊Dic3C4⋊C411yescharacteristic
36C2×C3⋊Dic3C22×C411yescharacteristic
37C2×C3⋊Dic3C2×D411yescharacteristic
38C4×C3⋊D3—22no—
39C4×C3⋊D3—22no—
40C4×C3⋊D3—21no—
41C4×C3⋊D3—21no—
42#622—24no—
43#622—42no—
44#622—41no—
45#622—41no—
46#432—91no—
47#431—91no—
48C2×C4⋊C8—91no—
49#335—92no—
50#334—92no—
51C2×C4×D3—121no—
52C2×C4×D3—121no—
53C2×C4×D3—121no—
54C3×C42—41no—
55C4×Dic3—121no—
56C4×Dic3—121no—
57C4×Dic3—121no—
58C22×C32C2×C4⋊C411yescharacteristic
59C2×C3⋊D3—21no—
60C2×C3⋊D3—21no—
61C2×C3⋊D3#10812yes—
62C32×C4—21no—
63C32×C4—21no—
64C32×C4—21no—
65C3⋊Dic3—21no—
66C3⋊Dic3#13112yes—
67C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
68C3⋊Dic3#13711yescharacteristic
69C22×C8—181no—
70C2×C42—91no—
71C4⋊C8—92no—
72C4⋊C8—91no—
73C4⋊C8—92no—
74C4⋊C8—91no—
75C4⋊C8—181no—
76C22⋊C8—92no—
77C22⋊C8—181no—
78#97—181no—
79C4×C8—92no—
80C22×D3—121no—
81C2×C3×C4—41no—
82C2×C3×C4—41no—
83C2×C3×C4—41no—
84C2×Dic3—121no—
85C2×Dic3—121no—
86C2×Dic3—121no—
87C4×D3—122no—
88C4×D3—124no—
89C4×D3—122no—
90C4×D3—124no—
91C2×C32#42411yescharacteristic
92C2×C32#42811yescharacteristic
93C2×C32C2×#10811yescharacteristic
94C3⋊D3—22no—
95C22×C4—91no—
96C22×C4—91no—
97C22×C4—91no—
98C2×C8—94no—
99C2×C8—181no—
100C2×C8—181no—
101C2×C8—182no—
102C2×C8—362no—
103C42—91no—
104C42—91no—
105C42—91no—
106C42PSU(3,𝔽2)11yescharacteristic
107C22×C3—41no—
108C2×D3—122no—
109C2×D3—122no—
110C2×D3—122no—
111C3×C4—42no—
112C3×C4—42no—
113C3×C4—42no—
114Dic3—122no—
115Dic3—121no—
116Dic3—121no—
117Dic3—122no—
118C32#157311yescharacteristic, complemented, Sylow
119C23—91no—
120C2×C4—91no—
121C2×C4—91no—
122C2×C4—91no—
123C2×C4—181no—
124C2×C4—182no—
125C2×C4—181no—
126C2×C4—182no—
127C2×C4#377711yescharacteristic
128C2×C4#377711yescharacteristic
129C2×C4C2×PSU(3,𝔽2)11yescharacteristic
130C8—184no—
131C8—362no—
132C8—361no—
133C8—361no—
134C2×C3—41no—
135C2×C3—41no—
136C2×C3—41no—
137D3—124no—
138C22—92no—
139C22—181no—
140C22—181no—
141C22C2×#377711yescharacteristic
142C4—21no—
143C4—21no—
144C4—21no—
145C4—92no—
146C4—91no—
147C4—91no—
148C4—181no—
149C3—41no—
150C2—182no—
151C2#1059354011yescharacteristic
152C2#1059354411yescharacteristic
153C2#1059354611yescharacteristic
subgroupG/H
centerC22C2×#3777
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC32×C42Q8
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42PSU(3,𝔽2)
hypocenterC32#1573
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590089C2semidirect
5. #10590088C2semidirect
118. C32#1573semidirect

Maximal subgroups

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

subgroupindex
#105937312
#105937262
#105937252
#105900892
#105900882
#15739