Finite Group Databasebeta

← #11771260

Subgroups — #11771260

Order 1152.

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

normal subgroups only

This group has 240 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#10593805C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic
3#10592418C211yesmaximal, characteristic
4C2×#3792C412yes—
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C22⋊#622C412yes—
7#63779—21no—
8#63779—21no—
9#63777—21no—
10C4⋊#622—21no—
11C32×C22⋊C8C411yescharacteristic
12#63657C411yescharacteristic
13#63642—21no—
14#63641—21no—
15#4719—62no—
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3C2×C411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19#3792—42no—
20C2×#622—22no—
21C2×#622—22no—
22C2×C32×C8—21no—
23C4×C3⋊Dic3D411yescharacteristic
24C4×C3⋊Dic3D411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C4×C3⋊Dic3Q811yescharacteristic
27C2×C3⋊(C3⋊C8)—21no—
28#1307—91nomaximal, Sylow
29C2×C4×Dic3—62no—
30C3×C22⋊C8—22no—
31#830—62no—
32#815—64no—
33Dic3⋊C8—64no—
34C23×C32C4211yescharacteristic
35C2×C32×C4—41no—
36C2×C32×C4C22⋊C411yescharacteristic
37C2×C32×C4C4⋊C411yescharacteristic
38C2×C3⋊Dic3—21no—
39C2×C3⋊Dic3—21no—
40C2×C3⋊Dic3—41no—
41C2×C3⋊Dic3C22⋊C411yescharacteristic
42C2×C3⋊Dic3C22⋊C411yescharacteristic
43C2×C3⋊Dic3C4⋊C411yescharacteristic
44C2×C3⋊Dic3C4⋊C411yescharacteristic
45#622—42no—
46#622—42no—
47C32×C8—41no—
48C3⋊(C3⋊C8)—41no—
49#432—91no—
50#432—91no—
51#423—91no—
52C22×C3×C4—22no—
53C22×Dic3—62no—
54C22×Dic3—62no—
55C2×C3×C8—24no—
56C4×Dic3—62no—
57C4×Dic3—62no—
58C4×Dic3—62no—
59C4×Dic3—62no—
60C2×C3⋊C8—64no—
61C22×C32—21no—
62C22×C32—21no—
63C22×C32—21no—
64C22×C32#9511yescharacteristic
65C32×C4—21no—
66C32×C4—21no—
67C3⋊Dic3—21no—
68C3⋊Dic3—21no—
69C3⋊Dic3—21no—
70C3⋊Dic3#10011yescharacteristic
71C3⋊Dic3#10111yescharacteristic
72C2×M16—92no—
73C2×C42—91no—
74C4⋊C8—181no—
75C4⋊C8—181no—
76C4⋊C8—181no—
77C4⋊C8—181no—
78C22⋊C8—92no—
79C22⋊C8—91no—
80C22⋊C8#15711yescharacteristic
81#97—181no—
82#97—181no—
83C23×C3—22no—
84C2×C3×C4—22no—
85C2×C3×C4—22no—
86C2×C3×C4—44no—
87C2×Dic3—62no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90C2×Dic3—62no—
91C2×Dic3—122no—
92C2×Dic3—122no—
93C2×Dic3—124no—
94C3×C8—44no—
95C3⋊C8—124no—
96C2×C32—41no—
97C2×C32#34311yescharacteristic
98C2×C32#34411yescharacteristic
99C2×C32#34411yescharacteristic
100C22×C4—91no—
101C22×C4—91no—
102C22×C4C2×#15711yescharacteristic
103M16—362no—
104C2×C8—21no—
105C2×C8—182no—
106C2×C8—182no—
107C2×C8—181no—
108C42—91no—
109C42—91no—
110C42—91no—
111C42—91no—
112C22×C3—24no—
113C22×C3—22no—
114C22×C3—42no—
115C22×C3—42no—
116C3×C4—24no—
117C3×C4—42no—
118Dic3—62no—
119Dic3—62no—
120Dic3—122no—
121Dic3—122no—
122Dic3—122no—
123C32#130711yescharacteristic, complemented, Sylow
124C23C4×#15711yescharacteristic
125C2×C4—41no—
126C2×C4—91no—
127C2×C4—91no—
128C2×C4—91no—
129C2×C4—91no—
130C2×C4—181no—
131C2×C4—181no—
132C2×C4—361no—
133C2×C4C4⋊#15711yescharacteristic
134C2×C4C22⋊#15711yescharacteristic
135C8—41no—
136C8—361no—
137C8—362no—
138C8—362no—
139C2×C3—22no—
140C2×C3—22no—
141C2×C3—22no—
142C2×C3—44no—
143C22—21no—
144C22—21no—
145C22—21no—
146C22#6378111yescharacteristic
147C4—21no—
148C4—21no—
149C4—91no—
150C4—91no—
151C4—181no—
152C4—181no—
153C4—181no—
154C3—22no—
155C2—41no—
156C2#1059015611yescharacteristic
157C2#1059018311yescharacteristic
158C2#1059018811yescharacteristic
subgroupG/H
centerC22#63781
commutator, prime radicalC23×C32C42
FrattiniC22×C4C2×#157
FittingC32×C22⋊C8C4
socleC22×C32#95
cosocleC2×C4×C3⋊Dic3C22
hypercenterC22⋊C8#157
hypocenterC32#1307
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
123. C32#1307semidirect

Maximal subgroups

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

subgroupindex
#105938052
#105938042
#105924182
#13079