Finite Group Databasebeta

← #11771005

Subgroups — #11771005

Order 1152.

280 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 42 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#10593731C211yesmaximal, characteristic
3C4×#3743C211yesmaximal, characteristic
4C2×#3743—21no—
5C42×C3⋊D3C2211yescharacteristic
6#63779—21no—
7#63779C412yes—
8#63778—21no—
9#63778C412yes—
10#63777—21no—
11#63777—21no—
12C32×C4×C8C411yescharacteristic
13#63642—21no—
14C4×C3⋊(C3⋊C8)C411yescharacteristic
15C4×ΓL(1,𝔽25)—62no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C4×C3⋊D3Q811yescharacteristic
19C2×#622—22no—
20C2×#622—22no—
21C2×C32×C8—21no—
22C32×C42C2×C411yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3D411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C2×C3⋊(C3⋊C8)—21no—
27#3743—24no—
28#1291—91nomaximal, Sylow
29C2×ΓL(1,𝔽25)—64no—
30C42×D3—62no—
31C3×C4×C8—22no—
32#815—64no—
33C4×C3⋊C8—62no—
34C22×C3⋊D3C4⋊C411yescharacteristic
35C2×C32×C4C4211yescharacteristic
36C2×C32×C4C22⋊C411yescharacteristic
37C2×C32×C4C4⋊C411yescharacteristic
38C2×C3⋊Dic3C22⋊C411yescharacteristic
39C2×C3⋊Dic3C22⋊C411yescharacteristic
40C2×C3⋊Dic3C4⋊C411yescharacteristic
41C4×C3⋊D3—22no—
42C4×C3⋊D3—41no—
43C4×C3⋊D3—41no—
44#622—42no—
45#622—42no—
46C32×C8—22no—
47C3⋊(C3⋊C8)—22no—
48#432—91no—
49#432—91no—
50C4×M16—91no—
51C2×C4×D3—62no—
52C2×C4×D3—62no—
53C2×C4×D3—62no—
54C2×C3×C8—24no—
55C3×C42—22no—
56C4×Dic3—62no—
57C4×Dic3—62no—
58C4×Dic3—62no—
59C2×C3⋊C8—64no—
60ΓL(1,𝔽25)—616no—
61C22×C32#9511yescharacteristic
62C2×C3⋊D3—21no—
63C2×C3⋊D3—21no—
64C2×C3⋊D3—21no—
65C32×C4—21no—
66C32×C4—21no—
67C32×C4—21no—
68C3⋊Dic3—21no—
69C3⋊Dic3—21no—
70C3⋊Dic3#10412yes—
71C2×M16—181no—
72C2×C42—91no—
73C4⋊C8—92no—
74C4⋊C8—181no—
75C22⋊C8—92no—
76C22⋊C8—181no—
77#97—181no—
78#97—181no—
79#97—181no—
80C4×C8—91no—
81C4×C8#15711yescharacteristic
82C22×D3—62no—
83C2×C3×C4—22no—
84C2×C3×C4—22no—
85C2×C3×C4—22no—
86C2×Dic3—62no—
87C2×Dic3—62no—
88C2×Dic3—62no—
89C4×D3—68no—
90C4×D3—124no—
91C4×D3—124no—
92C3×C8—28no—
93C3⋊C8—68no—
94C2×C32#33811yescharacteristic
95C2×C32#33911yescharacteristic
96C2×C32#34411yescharacteristic
97C3⋊D3—41no—
98C22×C4—91no—
99C22×C4—91no—
100C22×C4—91no—
101M16—184no—
102C2×C8—21no—
103C2×C8—181no—
104C2×C8—182no—
105C2×C8—182no—
106C42—91no—
107C42—91no—
108C42—91no—
109C42C2×#15711yescharacteristic
110C22×C3—22no—
111C2×D3—64no—
112C2×D3—122no—
113C2×D3—122no—
114C3×C4—24no—
115C3×C4—24no—
116C3×C4—24no—
117Dic3—64no—
118Dic3—122no—
119Dic3—122no—
120C32#129111yescharacteristic, complemented, Sylow
121C23—91no—
122C2×C4—91no—
123C2×C4—91no—
124C2×C4—91no—
125C2×C4—182no—
126C2×C4—361no—
127C2×C4—361no—
128C2×C4C4×#15711yescharacteristic
129C2×C4C4⋊#15711yescharacteristic
130C2×C4C22⋊#15711yescharacteristic
131C8—22no—
132C8—182no—
133C8—362no—
134C8—362no—
135C2×C3—22no—
136C2×C3—22no—
137C2×C3—22no—
138D3—124no—
139C22—181no—
140C22—181no—
141C22—181no—
142C22#6378111yescharacteristic
143C4—21no—
144C4—21no—
145C4—21no—
146C4—92no—
147C4—181no—
148C4—181no—
149C3—22no—
150C2—361no—
151C2#1059015111yescharacteristic
152C2#1059018311yescharacteristic
153C2#1059018611yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC42C2×#157
FittingC32×C4×C8C4
socleC22×C32#95
prime radicalC22×C3⋊D3C4⋊C4
cosocleC42×C3⋊D3C22
hypercenterC4×C8#157
hypocenterC32#1291
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
120. C32#1291semidirect

Maximal subgroups

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

subgroupindex
#105937312
C4×#37432
#12919