Finite Group Databasebeta

← #11777863

Subgroups — #11777863

Order 1152.

246 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 53 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
1C4×#3776C211yesmaximal, characteristic
2#10590788C212yesmaximal
3C8×#622C211yesmaximal, characteristic
4#10590042C211yesmaximal, characteristic
5#10590032C212yesmaximal
6C2×#3776C411yescharacteristic
7C4×#627C2212yes—
8C4×#622C2211yescharacteristic
9C4×#622C2211yescharacteristic
10#63743C411yescharacteristic
11#63740C412yes—
12C8×C3⋊Dic3C2211yescharacteristic
13C3×Dic3⋊C8—22no—
14#63572C2212yes—
15#63554—22no—
16#4828—62no—
17C2×#627C2×C412yes—
18C2×#622—21no—
19C2×#622C2×C411yescharacteristic
20C2×#622C2×C411yescharacteristic
21#3776—22no—
22C2×C32×C8D411yescharacteristic
23C4×C3⋊Dic3C2311yescharacteristic
24C2×C3⋊(C3⋊C8)D411yescharacteristic
25C3×C4×Dic3—22no—
26C2×C3×C3⋊C8—22no—
27#3724C2×C412yes—
28Dic3⋊Dic3—22no—
29#1591—91nomaximal, Sylow
30C4×Dic6—62no—
31C3×C4⋊C8—62no—
32#815—62no—
33Dic3⋊C8—22no—
34Dic3⋊C8—62no—
35C8×Dic3—62no—
36#803—62no—
37C2×C32×C4C2×D411yescharacteristic
38C2×C3⋊Dic3C22×C411yescharacteristic
39C2×C3⋊Dic3#4111yescharacteristic
40C2×C3×Dic3—22no—
41C2×C3×Dic3—22no—
42#627—22no—
43#627—22no—
44#622—22no—
45#622—21no—
46#622M1612yes—
47C32×C8—21no—
48C3⋊(C3⋊C8)Q1612yescomplemented
49C3×C3⋊C8—42no—
50#446—92no—
51C4×Q16—91no—
52#335—91no—
53Q8⋊C8—92no—
54C82—91no—
55C2×Dic6—62no—
56C2×C3×C8—22no—
57C2×C3×C8—62no—
58C3×C42—62no—
59C4⋊Dic3—62no—
60Dic3⋊C4—62no—
61Dic3⋊C4—62no—
62C4×Dic3—22no—
63C4×Dic3—62no—
64C2×C3⋊C8—22no—
65C2×C3⋊C8—62no—
66C22×C32C4×D411yescharacteristic
67C32×C4C2×Q1611yescharacteristic
68C32×C4#13511yescharacteristic
69C3⋊Dic3—21no—
70C3⋊Dic3C2×M1611yescharacteristic
71C3⋊Dic3#13111yescharacteristic
72C3×Dic3—42no—
73C3×Dic3—42no—
74C2×Q16—91no—
75C4×Q8—92no—
76#107—91no—
77C4⋊C8—62no—
78C4⋊C8—92no—
79#103—92no—
80#97—182no—
81C4×C8—91no—
82C4×C8—91no—
83C4×C8—91no—
84C2×C3×C4—22no—
85C2×C3×C4—62no—
86C2×C3×C4—62no—
87C2×Dic3—22no—
88C2×Dic3—22no—
89C2×Dic3—62no—
90C2×Dic3—62no—
91Dic6—122no—
92Dic6—122no—
93C3×C8—42no—
94C3×C8—122no—
95C3⋊C8—42no—
96C3⋊C8—64no—
97C2×C32#43611yescharacteristic
98C2×C32C4×Q1611yescharacteristic
99C2×C32#44311yescharacteristic
100C2×Q8—92no—
101Q16—182no—
102C2×C8—62no—
103C2×C8—91no—
104C2×C8—91no—
105C2×C8—91no—
106C2×C8—181no—
107C2×C8GO+(4,𝔽2)11yescharacteristic
108C4⋊C4—92no—
109C4⋊C4—182no—
110C42—62no—
111C42—91no—
112C22×C3—22no—
113C3×C4—22no—
114C3×C4—22no—
115C3×C4—122no—
116C3×C4—122no—
117Dic3—42no—
118Dic3—42no—
119Dic3—62no—
120Dic3—62no—
121Dic3—122no—
122C32#159111yescharacteristic, complemented, Sylow
123Q8—182no—
124Q8—182no—
125C2×C4—62no—
126C2×C4—62no—
127C2×C4—91no—
128C2×C4—91no—
129C2×C4C2×GO+(4,𝔽2)11yescharacteristic
130C8—21no—
131C8—92no—
132C8—92no—
133C8—122no—
134C8—181no—
135C8—182no—
136C2×C3—22no—
137C2×C3—22no—
138C2×C3—22no—
139C22C4×GO+(4,𝔽2)11yescharacteristic
140C4—91no—
141C4—91no—
142C4—122no—
143C4—122no—
144C4—181no—
145C4#6422811yescharacteristic
146C4#6423711yescharacteristic
147C3—22no—
148C2#1059328311yescharacteristic
149C2#1059329711yescharacteristic
150C2#1059344511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC2×C32×C8D4
socle, prime radicalC22×C32C4×D4
cosocleC4×C3⋊Dic3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1591
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
48. C3⋊(C3⋊C8)Q16semidirect
122. C32#1591semidirect

Maximal subgroups

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

subgroupindex
C4×#37762
#105907882
C8×#6222
#105900422
#105900322
#15919