Finite Group Databasebeta

← #11771004

Subgroups — #11771004

Order 1152.

248 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 44 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#10593730C211yesmaximal, characteristic
2C4×#3788C211yesmaximal, characteristic
3#10592534C211yesmaximal, characteristic
4C2×#3788—21no—
5C42×C3⋊D3C2211yescharacteristic
6#63778C412yes—
7#63777—21no—
8#63777—21no—
9C4⋊#622—21no—
10C4×#622C412yes—
11C32×C4⋊C8C411yescharacteristic
12#63647—21no—
13#63642—21no—
14C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
15#4835—62no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C4×C3⋊D3Q811yescharacteristic
19C2×#622—22no—
20C2×#622—22no—
21#3788—22no—
22#3788—22no—
23C2×C32×C8—21no—
24C32×C42C2×C411yescharacteristic
25C4×C3⋊Dic3C2×C411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C2×C3⋊(C3⋊C8)—21no—
29#1291—91nomaximal, Sylow
30C42×D3—62no—
31C3×C4⋊C8—22no—
32(C2×D3)⋊C8—64no—
33#815—64no—
34C4⋊(C3⋊C8)—62no—
35C22×C3⋊D3C4⋊C411yescharacteristic
36C2×C32×C4C4211yescharacteristic
37C2×C32×C4C22⋊C411yescharacteristic
38C2×C32×C4C4⋊C411yescharacteristic
39C2×C3⋊Dic3C22⋊C411yescharacteristic
40C2×C3⋊Dic3C22⋊C411yescharacteristic
41C2×C3⋊Dic3C4⋊C411yescharacteristic
42C4×C3⋊D3—21no—
43C4×C3⋊D3—21no—
44C4×C3⋊D3—41no—
45C4×C3⋊D3—41no—
46#622—24no—
47#622—42no—
48C32×C8—41no—
49C3⋊(C3⋊C8)—41no—
50#432—91no—
51#432—91no—
52C4×M16—91no—
53C2×C4×D3—62no—
54C2×C4×D3—62no—
55C2×C4×D3—62no—
56C2×C3×C8—24no—
57C3×C42—22no—
58C4×Dic3—62no—
59C4×Dic3—62no—
60C4×Dic3—62no—
61C2×C3⋊C8—64no—
62C22×C32#9511yescharacteristic
63C2×C3⋊D3—21no—
64C2×C3⋊D3—21no—
65C2×C3⋊D3—21no—
66C32×C4—21no—
67C32×C4—21no—
68C32×C4#10411yescharacteristic
69C32×C4#10411yescharacteristic
70C3⋊Dic3—21no—
71C3⋊Dic3—21no—
72C3⋊Dic3—21no—
73C2×M16—181no—
74C2×C42—91no—
75C4⋊C8—91no—
76C4⋊C8—181no—
77C4⋊C8#15711yescharacteristic
78C22⋊C8—92no—
79C22⋊C8—181no—
80#97—181no—
81#97—181no—
82#97—181no—
83C4×C8—92no—
84C22×D3—62no—
85C2×C3×C4—22no—
86C2×C3×C4—22no—
87C2×C3×C4—22no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90C2×Dic3—62no—
91C4×D3—122no—
92C4×D3—122no—
93C4×D3—124no—
94C4×D3—124no—
95C3×C8—44no—
96C3⋊C8—124no—
97C2×C32#33811yescharacteristic
98C2×C32#33911yescharacteristic
99C2×C32#34411yescharacteristic
100C3⋊D3—41no—
101C22×C4—91no—
102C22×C4—91no—
103C22×C4—91no—
104M16—182no—
105M16—182no—
106C2×C8—21no—
107C2×C8—182no—
108C2×C8—182no—
109C2×C8—181no—
110C42—91no—
111C42—91no—
112C42—91no—
113C42C2×#15711yescharacteristic
114C22×C3—22no—
115C2×D3—64no—
116C2×D3—122no—
117C2×D3—122no—
118C3×C4—24no—
119C3×C4—22no—
120C3×C4—22no—
121C3×C4—42no—
122Dic3—122no—
123Dic3—122no—
124Dic3—122no—
125C32#129111yescharacteristic, complemented, Sylow
126C23—91no—
127C2×C4—91no—
128C2×C4—91no—
129C2×C4—91no—
130C2×C4—181no—
131C2×C4—181no—
132C2×C4—361no—
133C2×C4—361no—
134C2×C4C4×#15711yescharacteristic
135C2×C4C4⋊#15711yescharacteristic
136C2×C4C22⋊#15711yescharacteristic
137C8—41no—
138C8—184no—
139C8—362no—
140C8—361no—
141C2×C3—22no—
142C2×C3—22no—
143C2×C3—22no—
144D3—124no—
145C22—181no—
146C22—181no—
147C22—181no—
148C22#6378111yescharacteristic
149C4—21no—
150C4—21no—
151C4—181no—
152C4—181no—
153C4—181no—
154C4#6378311yescharacteristic
155C4#6378511yescharacteristic
156C3—22no—
157C2—361no—
158C2#1059016411yescharacteristic
159C2#1059018611yescharacteristic
160C2#1059019111yescharacteristic
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
125. C32#1291semidirect

Maximal subgroups

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

subgroupindex
#105937302
C4×#37882
#105925342
#12919