Finite Group Databasebeta

← #11770959

Subgroups — #11770959

Order 1152.

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

normal subgroups only

This group has 294 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#10593737C211yesmaximal, characteristic
2#10593731C211yesmaximal, characteristic
3C4×#3743C211yesmaximal, characteristic
4C2×#3743—21no—
5C42×C3⋊D3C2211yescharacteristic
6#63781—21no—
7#63781—21no—
8#63781C412yes—
9#63779—21no—
10#63778—21no—
11#63777C412yescomplemented
12C32×C4×C8C411yescharacteristic, complemented
13#63642—21no—
14C4×C3⋊(C3⋊C8)C411yescharacteristic, complemented
15C4×ΓL(1,𝔽25)—62no—
16C22×#157—22no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3D411yescharacteristic
20C2×#622—22no—
21C2×C32×C8—21no—
22C32×C42C2×C411yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3D411yescharacteristic
25C4×C3⋊Dic3Q811yescharacteristic
26C2×C3⋊(C3⋊C8)—21no—
27#3743—24no—
28#1288—91nomaximal, Sylow
29C2×ΓL(1,𝔽25)—64no—
30C42×D3—62no—
31C3×C4×C8—22no—
32#815—64no—
33C4×C3⋊C8—62no—
34C22×C3⋊D3C22⋊C411yescharacteristic
35C2×#157—42no—
36C2×#157—42no—
37C2×#157—42no—
38C2×C32×C4C4211yescharacteristic
39C2×C32×C4C22⋊C411yescharacteristic
40C2×C32×C4C4⋊C411yescharacteristic
41C2×C3⋊Dic3C22⋊C411yescharacteristic
42C2×C3⋊Dic3C4⋊C411yescharacteristic
43C2×C3⋊Dic3C4⋊C411yescharacteristic
44C4×C3⋊D3—22no—
45C4×C3⋊D3—41no—
46C4×C3⋊D3—41no—
47#622—42no—
48C32×C8—22no—
49C3⋊(C3⋊C8)—22no—
50#432—91no—
51C4×M16—91no—
52#383—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—
62ΓL(1,𝔽25)—616no—
63C22×C32#9511yescharacteristic
64C2×C3⋊D3—21no—
65C2×C3⋊D3—21no—
66C2×C3⋊D3#10412yes—
67#157—82no—
68C32×C4—21no—
69C32×C4—21no—
70C32×C4—21no—
71C3⋊Dic3—21no—
72C3⋊Dic3—21no—
73C3⋊Dic3—21no—
74C2×M16—181no—
75C2×C42—91no—
76C4⋊C8—181no—
77C22⋊C8—181no—
78#97—92no—
79#97—181no—
80C4×C8—91no—
81C4×C8#15711yescharacteristic, complemented
82#95—92no—
83#95—181no—
84#95—181no—
85C22×D3—62no—
86C2×C3×C4—22no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×Dic3—62no—
90C2×Dic3—62no—
91C2×Dic3—62no—
92C4×D3—68no—
93C4×D3—124no—
94C4×D3—124no—
95C3×C8—28no—
96C3⋊C8—68no—
97C2×C32H(3,ℤ/4)11yescharacteristic
98C2×C32#33911yescharacteristic
99C2×C32#34411yescharacteristic
100C3⋊D3—22no—
101C22×C4—91no—
102C22×C4—91no—
103C22×C4—91no—
104C22×C4—182no—
105M16—184no—
106C2×C8—21no—
107C2×C8—181no—
108C2×C8—182no—
109C42—91no—
110C42—91no—
111C42—91no—
112C42C2×#15711yescharacteristic
113C22×C3—22no—
114C2×D3—64no—
115C2×D3—122no—
116C2×D3—122no—
117C3×C4—24no—
118C3×C4—24no—
119C3×C4—24no—
120Dic3—64no—
121Dic3—122no—
122Dic3—122no—
123C32#128811yescharacteristic, complemented, Sylow
124C23—91no—
125C2×C4—91no—
126C2×C4—91no—
127C2×C4—91no—
128C2×C4—182no—
129C2×C4—361no—
130C2×C4—361no—
131C2×C4—362no—
132C2×C4—362no—
133C2×C4—362no—
134C2×C4C4×#15711yescharacteristic
135C2×C4C4⋊#15711yescharacteristic
136C2×C4C22⋊#15711yescharacteristic
137C8—22no—
138C8—182no—
139C8—362no—
140C2×C3—22no—
141C2×C3—22no—
142C2×C3—22no—
143D3—124no—
144C22—92no—
145C22—181no—
146C22—181no—
147C22#6378111yescharacteristic
148C4—21no—
149C4—21no—
150C4—21no—
151C4—181no—
152C4—181no—
153C4—181no—
154C4—722no—
155C3—22no—
156C2—182no—
157C2#1059015111yescharacteristic
158C2#1059018311yescharacteristic
159C2#1059018411yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC42C2×#157
FittingC32×C4×C8C4
socleC22×C32#95
prime radicalC22×C3⋊D3C22⋊C4
cosocleC42×C3⋊D3C22
hypercenterC4×C8#157
hypocenterC32#1288
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
11. #63777C4semidirect
12. C32×C4×C8C4semidirect
14. C4×C3⋊(C3⋊C8)C4semidirect
81. C4×C8#157semidirect
123. C32#1288semidirect

Maximal subgroups

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

subgroupindex
#105937372
#105937312
C4×#37432
#12889