Finite Group Databasebeta

← #11776969

Subgroups — #11776969

Order 1152.

220 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 59 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#10593729C211yesmaximal, characteristic
3C4×#3788C211yesmaximal, characteristic
4#10590089C212yesmaximal, complemented
5#10590088C212yesmaximal, complemented
6C2×#3788—21no—
7C2×#3788C412yes—
8C42×C3⋊D3C2211yescharacteristic
9#63779—21no—
10#63779C2211yescharacteristic
11#63779C2212yes—
12#63779C2211yescharacteristic
13#63778—21no—
14#63777—21no—
15#63777C411yescharacteristic
16#63777C411yescharacteristic
17C4×#622C2212yes—
18C2×C4×C3⋊D3C2×C411yescharacteristic
19C2×C4×C3⋊D3D411yescharacteristic
20C2×C4×C3⋊D3Q811yescharacteristic
21C2×#622—22no—
22C2×#622—21no—
23C2×#622—21no—
24C2×#622C2×C412yes—
25C2×#622C2×C412yes—
26#3788—24no—
27#3788—42no—
28C32×C42Q811yescharacteristic
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3D411yescharacteristic
31C4×C3⋊Dic3C2311yescharacteristic
32#1569—91nomaximal, Sylow
33C42×D3—121no—
34C22×C3⋊D3C4⋊C411yescharacteristic
35C2×C32×C4C4⋊C411yescharacteristic
36C2×C32×C4C4⋊C411yescharacteristic
37C2×C32×C4C2×Q811yescharacteristic
38C2×C3⋊Dic3C4⋊C411yescharacteristic
39C2×C3⋊Dic3C22×C411yescharacteristic
40C2×C3⋊Dic3C2×D411yescharacteristic
41C4×C3⋊D3—22no—
42C4×C3⋊D3—21no—
43C4×C3⋊D3—21no—
44C4×C3⋊D3—41no—
45#622—22no—
46#622—42no—
47#622—41no—
48#622—41no—
49#622M1614yescomplemented
50#432—91no—
51#423—91no—
52C4×M16—91no—
53#335—92no—
54#334—92no—
55C2×C4×D3—121no—
56C2×C4×D3—121no—
57C2×C4×D3—121no—
58C3×C42—41no—
59C4×Dic3—121no—
60C4×Dic3—121no—
61C4×Dic3—121no—
62C22×C32C2×C4⋊C411yescharacteristic
63C2×C3⋊D3—21no—
64C2×C3⋊D3—21no—
65C2×C3⋊D3—21no—
66C32×C4—21no—
67C32×C4—21no—
68C32×C4—21no—
69C3⋊Dic3—21no—
70C3⋊Dic3C2×M1612yes—
71C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
72C3⋊Dic3#13711yescharacteristic
73C2×M16—92no—
74C2×M16—181no—
75C2×C42—91no—
76C4⋊C8—91no—
77C4⋊C8—92no—
78C4⋊C8—91no—
79C4⋊C8—181no—
80C22⋊C8—181no—
81#97—91no—
82#97—91no—
83#97—181no—
84C4×C8—92no—
85C22×D3—121no—
86C2×C3×C4—41no—
87C2×C3×C4—41no—
88C2×C3×C4—41no—
89C2×Dic3—121no—
90C2×Dic3—121no—
91C2×Dic3—121no—
92C4×D3—124no—
93C4×D3—122no—
94C4×D3—122no—
95C4×D3—124no—
96C2×C32#42311yescharacteristic
97C2×C32#42811yescharacteristic
98C2×C32#43011yescharacteristic
99C3⋊D3—41no—
100C22×C4—91no—
101C22×C4—91no—
102C22×C4—91no—
103M16—184no—
104M16—362no—
105C2×C8—92no—
106C2×C8—92no—
107C2×C8—181no—
108C2×C8—181no—
109C2×C8—182no—
110C42—91no—
111C42—91no—
112C42—91no—
113C42PSU(3,𝔽2)11yescharacteristic
114C22×C3—41no—
115C2×D3—122no—
116C2×D3—122no—
117C2×D3—122no—
118C3×C4—42no—
119C3×C4—42no—
120C3×C4—42no—
121Dic3—122no—
122Dic3—121no—
123Dic3—121no—
124Dic3—122no—
125C32#156911yescharacteristic, complemented, Sylow
126C23—91no—
127C2×C4—91no—
128C2×C4—91no—
129C2×C4—91no—
130C2×C4—182no—
131C2×C4—181no—
132C2×C4—181no—
133C2×C4—361no—
134C2×C4#377711yescharacteristic
135C2×C4#377711yescharacteristic
136C2×C4C2×PSU(3,𝔽2)11yescharacteristic
137C8—94no—
138C8—182no—
139C8—362no—
140C8—361no—
141C8—361no—
142C2×C3—41no—
143C2×C3—41no—
144C2×C3—41no—
145D3—124no—
146C22—181no—
147C22—181no—
148C22—181no—
149C22C2×#377711yescharacteristic
150C4—21no—
151C4—21no—
152C4—21no—
153C4—92no—
154C4—91no—
155C4—91no—
156C4—181no—
157C3—41no—
158C2—361no—
159C2#1059353911yescharacteristic
160C2#1059354411yescharacteristic
161C2#1059354711yescharacteristic
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#1569
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
49. #622M16semidirect
125. C32#1569semidirect

Maximal subgroups

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

subgroupindex
#105937312
#105937292
C4×#37882
#105900892
#105900882
#15699