Finite Group Databasebeta

← #13295

Subgroups — #13295

Order 256.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#2487C211yesmaximal, characteristic
2#1800C211yesmaximal, characteristic
3C4×#99C211yesmaximal, characteristic
4#1390C214yesmaximal
5C2×C4×D4C2211yescharacteristic
6C22×C4⋊C4C411yescharacteristic, complemented
7#423—21no—
8C2×#100C2212yes—
9C2×#99C2212yes—
10#400—21no—
11#399—21no—
12#389—21no—
13#386C2212yes—
14#385C412yescomplemented
15#380—21no—
16#380C411yescharacteristic, complemented
17C4×C22⋊C4—21no—
18#343—21no—
19#342—21no—
20C22×D4C2311yescharacteristic
21C23×C4C2×C411yescharacteristic
22C23×C4C2×C412yes—
23C23×C4D411yescharacteristic
24C2×M16—22no—
25C4×D4—41no—
26C4×D4—41no—
27C2×C4⋊C4—21no—
28C2×C4⋊C4—21no—
29C2×C4⋊C4—21no—
30C2×C4⋊C4—22no—
31C2×C4⋊C4—41no—
32C2×C4⋊C4—41no—
33C2×C4⋊C4D411yescharacteristic
34C2×C22⋊C4—22no—
35C2×C22⋊C4—22no—
36C2×C22⋊C4C2×C412yes—
37C2×C22⋊C4C2×C411yescharacteristic
38C2×C22⋊C4D411yescharacteristic
39C2×C42—41no—
40C2×C42D411yescharacteristic
41C4⋊C8—41no—
42C4⋊C8—41no—
43#100—24no—
44#99—22no—
45#99Q814yes—
46#95—22no—
47#95—21no—
48#95—22no—
49#95—41no—
50C24C22×C411yescharacteristic
51C24C2×D411yescharacteristic
52C2×D4—41no—
53C2×D4—41no—
54C2×D4C2×Q812yes—
55C2×D4#4112yes—
56C22×C4—21no—
57C22×C4—21no—
58C22×C4—21no—
59C22×C4—21no—
60C22×C4—22no—
61C22×C4—22no—
62C22×C4—42no—
63C22×C4—42no—
64C22×C4—42no—
65C22×C4—42no—
66C22×C4—82no—
67C22×C4C22⋊C411yescharacteristic
68C22×C4C22⋊C411yescharacteristic
69C22×C4C22⋊C411yescharacteristic
70C22×C4C22⋊C411yescharacteristic
71C22×C4C2×D411yescharacteristic
72M16—42no—
73M16—42no—
74C2×C8—42no—
75C4⋊C4—41no—
76C4⋊C4—42no—
77C4⋊C4—42no—
78C4⋊C4—41no—
79C4⋊C4—41no—
80C4⋊C4—82no—
81C22⋊C4—24no—
82C22⋊C4—41no—
83C22⋊C4—41no—
84C22⋊C4—42no—
85C22⋊C4—42no—
86C22⋊C4—82no—
87C42—21no—
88C42—21no—
89C42—82no—
90C23—21no—
91C23—21no—
92C23—21no—
93C23—21no—
94C23—41no—
95C23—41no—
96C23—41no—
97C23—41no—
98C23C2×C22⋊C411yescharacteristic
99C23C4×Q812yes—
100C23C22⋊Q812yes—
101D4—42no—
102D4—42no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—22no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—42no—
110C2×C4—42no—
111C2×C4—42no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—44no—
116C2×C4—42no—
117C2×C4—42no—
118C2×C4—42no—
119C2×C4—42no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—81no—
123C2×C4—82no—
124C2×C4—82no—
125C2×C4—84no—
126C2×C4#9911yescharacteristic
127C2×C4#9911yescharacteristic
128C2×C4#12411yescharacteristic
129C2×C4C4⋊Q811yescharacteristic
130C8—82no—
131C22—21no—
132C22—21no—
133C22—22no—
134C22—22no—
135C22—42no—
136C22—42no—
137C22—42no—
138C22—41no—
139C22—41no—
140C22—41no—
141C22—41no—
142C22—81no—
143C22#39111yescharacteristic
144C22C2×#9911yescharacteristic
145C22#41011yescharacteristic
146C4—21no—
147C4—21no—
148C4—21no—
149C4—41no—
150C4—41no—
151C4—41no—
152C4—82no—
153C4—84no—
154C4—82no—
155C4#35212yes—
156C2—21no—
157C2—21no—
158C2—42no—
159C2—42no—
160C2#199611yescharacteristic
161C2C2×#35211yescharacteristic
162C2#212211yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC24C22×C4
Frattini, prime radical, cosocleC22×D4C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ G
LECSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
6. C22×C4⋊C4C4semidirect
14. #385C4semidirect
16. #380C4semidirect

Maximal subgroups

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

subgroupindex
#24872
#18002
C4×#992
#13902