Finite Group Databasebeta

← #11776968

Subgroups — #11776968

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#10593805C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic
3C4×#3792C211yesmaximal, characteristic
4#10590089C212yesmaximal, complemented
5#10590088C212yesmaximal, complemented
6C2×#3792—21no—
7C2×#3792C412yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C22⋊#622—21no—
10#63779C2211yescharacteristic
11#63779C2211yescharacteristic
12#63779C2212yes—
13#63777—21no—
14#63777C411yescharacteristic
15#63777C411yescharacteristic
16C4⋊#622—21no—
17C4×#622C2212yes—
18C22×C32×C4Q811yescharacteristic
19C22×C3⋊Dic3C2×C411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21#3792—24no—
22#3792—42no—
23C2×#622—22no—
24C2×#622—21no—
25C2×#622—21no—
26C2×#622C2×C412yes—
27C2×#622C2×C412yes—
28C4×C3⋊Dic3C2×C411yescharacteristic
29C4×C3⋊Dic3D411yescharacteristic
30C4×C3⋊Dic3Q811yescharacteristic
31C4×C3⋊Dic3C2311yescharacteristic
32#1569—91nomaximal, Sylow
33C2×C4×Dic3—121no—
34C23×C32C4⋊C411yescharacteristic
35C2×C32×C4—41no—
36C2×C32×C4C4⋊C411yescharacteristic
37C2×C32×C4C2×Q811yescharacteristic
38C2×C3⋊Dic3—22no—
39C2×C3⋊Dic3—21no—
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3C4⋊C411yescharacteristic
42C2×C3⋊Dic3C4⋊C411yescharacteristic
43C2×C3⋊Dic3C22×C411yescharacteristic
44C2×C3⋊Dic3C2×D411yescharacteristic
45#622—22no—
46#622—41no—
47#622—42no—
48#622—41no—
49#622M1614yescomplemented
50#432—91no—
51#423—91no—
52C4×M16—91no—
53#335—92no—
54#334—92no—
55C22×C3×C4—41no—
56C22×Dic3—121no—
57C22×Dic3—121no—
58C4×Dic3—121no—
59C4×Dic3—121no—
60C4×Dic3—121no—
61C4×Dic3—121no—
62C22×C32—21no—
63C22×C32—21no—
64C22×C32—21no—
65C22×C32C2×C4⋊C411yescharacteristic
66C32×C4—21no—
67C32×C4—21no—
68C3⋊Dic3—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—
85C23×C3—41no—
86C2×C3×C4—44no—
87C2×C3×C4—41no—
88C2×C3×C4—41no—
89C2×Dic3—121no—
90C2×Dic3—121no—
91C2×Dic3—121no—
92C2×Dic3—121no—
93C2×Dic3—124no—
94C2×Dic3—122no—
95C2×Dic3—122no—
96C2×C32—41no—
97C2×C32#42311yescharacteristic
98C2×C32#42811yescharacteristic
99C2×C32#43011yescharacteristic
100C22×C4—91no—
101C22×C4—91no—
102C22×C4PSU(3,𝔽2)11yescharacteristic
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—
113C42—91no—
114C22×C3—42no—
115C22×C3—42no—
116C22×C3—42no—
117C22×C3—41no—
118C3×C4—42no—
119C3×C4—42no—
120Dic3—122no—
121Dic3—121no—
122Dic3—121no—
123Dic3—122no—
124Dic3—122no—
125C32#156911yescharacteristic, complemented, Sylow
126C23#377711yescharacteristic
127C2×C4—41no—
128C2×C4—91no—
129C2×C4—91no—
130C2×C4—91no—
131C2×C4—91no—
132C2×C4—182no—
133C2×C4—181no—
134C2×C4—181no—
135C2×C4#377711yescharacteristic
136C2×C4C2×PSU(3,𝔽2)11yescharacteristic
137C8—94no—
138C8—182no—
139C8—362no—
140C8—361no—
141C8—361no—
142C2×C3—44no—
143C2×C3—41no—
144C2×C3—41no—
145C2×C3—41no—
146C22—21no—
147C22—21no—
148C22—21no—
149C22C2×#377711yescharacteristic
150C4—21no—
151C4—21no—
152C4—92no—
153C4—91no—
154C4—91no—
155C4—181no—
156C4—181no—
157C3—41no—
158C2—41no—
159C2#1059353911yescharacteristic
160C2#1059354411yescharacteristic
161C2#1059356511yescharacteristic
subgroupG/H
centerC22C2×#3777
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC22×C32×C4Q8
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4PSU(3,𝔽2)
hypocenterC32#1569
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

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
#105938052
#105938042
C4×#37922
#105900892
#105900882
#15699