Finite Group Databasebeta

← #8779

Subgroups — #8779

Order 256.

233 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 233 conjugacy classes of subgroups — too many to draw. Only its 57 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#2357C211yesmaximal, characteristic
2C4×#99C211yesmaximal, characteristic
3#1465C211yesmaximal, characteristic
4#1297C212yesmaximal, complemented
5#1284C212yesmaximal, complemented
6C2×C4×D4C2211yescharacteristic
7C2×#99—21no—
8#407C2212yes—
9#390—21no—
10#388—21no—
11#388—21no—
12#382C411yescharacteristic, complemented
13#381C411yescharacteristic, complemented
14#381C2211yescharacteristic
15C4×C4⋊C4—21no—
16C4×C4⋊C4C411yescharacteristic, complemented
17C4×C22⋊C4C411yescharacteristic, complemented
18C4×C22⋊C4C2212yes—
19C4×C22⋊C4C2211yescharacteristic
20#342—21no—
21#324—21no—
22#323—21no—
23C22×D4D411yescharacteristic
24C23×C4C2×C411yescharacteristic
25C23×C4C2311yescharacteristic
26C2×M16—22no—
27C4×D4—22no—
28C4×D4—22no—
29C2×C4⋊C4—21no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4D411yescharacteristic
32C2×C22⋊C4—22no—
33C2×C22⋊C4—21no—
34C2×C22⋊C4—21no—
35C2×C22⋊C4—21no—
36C2×C22⋊C4—21no—
37C2×C22⋊C4D411yescharacteristic
38C2×C22⋊C4D411yescharacteristic
39C2×C42—21no—
40C2×C42—21no—
41C2×C42—21no—
42C2×C42—22no—
43C2×C42C2×C411yescharacteristic
44#99—24no—
45C22⋊C8—22no—
46C22⋊C8—22no—
47#95—21no—
48#95—21no—
49#95—21no—
50#95—22no—
51#95C2×C411yescharacteristic
52#95C2×C411yescharacteristic
53#95C2×C411yescharacteristic
54#95C2×C411yescharacteristic
55C24C22⋊C411yescharacteristic
56C24C2×D411yescharacteristic
57C2×D4—22no—
58C2×D4—22no—
59C2×D4—41no—
60C22×C4—21no—
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—21no—
66C22×C4—42no—
67C22×C4—81no—
68C22×C4—81no—
69C22×C4C22⋊C411yescharacteristic
70C22×C4C22⋊C411yescharacteristic
71C22×C4C22⋊C411yescharacteristic
72C22×C4C22×C411yescharacteristic
73C22×C4C2×D411yescharacteristic
74C22×C4#4112yes—
75C22×C4#4112yes—
76M16—82no—
77C2×C8—42no—
78C4⋊C4—22no—
79C4⋊C4—42no—
80C4⋊C4—42no—
81C22⋊C4—22no—
82C22⋊C4—22no—
83C22⋊C4—24no—
84C22⋊C4—42no—
85C22⋊C4—42no—
86C22⋊C4—42no—
87C22⋊C4—81no—
88C22⋊C4—81no—
89C42—21no—
90C42—21no—
91C42—42no—
92C42—81no—
93C42—81no—
94C42—82no—
95C23—21no—
96C23—21no—
97C23—21no—
98C23—21no—
99C23—21no—
100C23—41no—
101C23—41no—
102C23—41no—
103C23—41no—
104C23C2×C22⋊C411yescharacteristic
105C23#12312yes—
106D4—44no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—22no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—41no—
113C2×C4—42no—
114C2×C4—42no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—44no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—81no—
131C2×C4—81no—
132C2×C4—82no—
133C2×C4—82no—
134C2×C4#10412yes—
135C2×C4#11711yescharacteristic
136C2×C4#11711yescharacteristic
137C2×C4#12312yes—
138C8—82no—
139C22—21no—
140C22—21no—
141C22—22no—
142C22—22no—
143C22—22no—
144C22—41no—
145C22—41no—
146C22—41no—
147C22—81no—
148C22—81no—
149C22—81no—
150C22—81no—
151C22#38111yescharacteristic
152C22C2×#10411yescharacteristic
153C22#42111yescharacteristic
154C4—22no—
155C4—22no—
156C4—21no—
157C4—21no—
158C4—42no—
159C4—41no—
160C4—41no—
161C4—81no—
162C4—81no—
163C4—81no—
164C4—84no—
165C2—21no—
166C2—21no—
167C2—42no—
168C2—81no—
169C2#182611yescharacteristic
170C2#182711yescharacteristic
171C2#182811yescharacteristic
subgroupG/H
center, socleC22#381
commutatorC22×C4C22×C4
Frattini, cosocleC23×C4C23
prime radicalC22×D4D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1297C2semidirect
5. #1284C2semidirect
12. #382C4semidirect
13. #381C4semidirect
16. C4×C4⋊C4C4semidirect
17. C4×C22⋊C4C4semidirect

Maximal subgroups

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

subgroupindex
#23572
C4×#992
#14652
#12972
#12842