Finite Group Databasebeta

← #8763

Subgroups — #8763

Order 256.

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

normal subgroups only

This group has 236 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#2353C211yesmaximal, characteristic
2#1799C211yesmaximal, characteristic
3#1459C211yesmaximal, characteristic
4#1294C212yesmaximal, complemented
5#1289C212yesmaximal, complemented
6C2×C4×D4C2211yescharacteristic
7C2×#99—21no—
8C2×C22⋊C8C2212yes—
9#388—21no—
10#387—21no—
11#386—21no—
12#383C411yescharacteristic, complemented
13#381C411yescharacteristic, complemented
14#380C2212yes—
15#380C2211yescharacteristic
16C4×C22⋊C4—21no—
17C4×C22⋊C4C411yescharacteristic, complemented
18#376C411yescharacteristic, complemented
19C2×#95C2211yescharacteristic
20#342—21no—
21#324—21no—
22#323—21no—
23C22×D4D411yescharacteristic
24C23×C4—21no—
25C23×C4C2×C411yescharacteristic
26C23×C4C2311yescharacteristic
27C22×C8—22no—
28C4×D4—22no—
29C4×D4—22no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—22no—
32C2×C4⋊C4D411yescharacteristic
33C2×C22⋊C4—21no—
34C2×C22⋊C4—21no—
35C2×C22⋊C4—22no—
36C2×C22⋊C4—21no—
37C2×C22⋊C4D411yescharacteristic
38C2×C22⋊C4D411yescharacteristic
39C2×C42—21no—
40C2×C42—21no—
41C2×C42C2×C411yescharacteristic
42#99—42no—
43C22⋊C8—22no—
44C22⋊C8—22no—
45#95—21no—
46#95—21no—
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—21no—
60C2×D4—21no—
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—42no—
68C22×C4—42no—
69C22×C4—42no—
70C22×C4—81no—
71C22×C4—81no—
72C22×C4—81no—
73C22×C4C22⋊C411yescharacteristic
74C22×C4C22⋊C411yescharacteristic
75C22×C4C22⋊C411yescharacteristic
76C22×C4C22×C411yescharacteristic
77C22×C4C2×D411yescharacteristic
78C22×C4#4112yes—
79C22×C4#4112yes—
80C2×C8—42no—
81C2×C8—82no—
82C4⋊C4—22no—
83C4⋊C4—81no—
84C4⋊C4—82no—
85C22⋊C4—22no—
86C22⋊C4—22no—
87C22⋊C4—42no—
88C22⋊C4—41no—
89C22⋊C4—41no—
90C22⋊C4—42no—
91C22⋊C4—42no—
92C22⋊C4—81no—
93C42—21no—
94C42—21no—
95C42—42no—
96C42—81no—
97C23—21no—
98C23—21no—
99C23—21no—
100C23—41no—
101C23—41no—
102C23—41no—
103C23—41no—
104C23C2×C22⋊C411yescharacteristic
105C23#12312yes—
106C23#13512yes—
107C23AGL(1,ℤ/8)11yescharacteristic
108C23#13711yescharacteristic
109D4—42no—
110D4—42no—
111C2×C4—22no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—41no—
118C2×C4—42no—
119C2×C4—42no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—81no—
135C2×C4—81no—
136C2×C4—84no—
137C2×C4—82no—
138C2×C4—82no—
139C2×C4—82no—
140C2×C4#11711yescharacteristic
141C2×C4#11711yescharacteristic
142C2×C4#12312yes—
143C8—82no—
144C22—21no—
145C22—22no—
146C22—21no—
147C22—22no—
148C22—42no—
149C22—41no—
150C22—41no—
151C22—41no—
152C22—41no—
153C22—41no—
154C22—81no—
155C22—81no—
156C22#38111yescharacteristic
157C22#41611yescharacteristic
158C22#41711yescharacteristic
159C22#48212yes—
160C22#48512yes—
161C4—22no—
162C4—21no—
163C4—21no—
164C4—42no—
165C4—41no—
166C4—41no—
167C4—41no—
168C4—81no—
169C4—81no—
170C4—81no—
171C4—162no—
172C2—21no—
173C2—21no—
174C2—22no—
175C2—22no—
176C2—81no—
177C2#182511yescharacteristic
178C2#182711yescharacteristic
179C2#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. #1294C2semidirect
5. #1289C2semidirect
12. #383C4semidirect
13. #381C4semidirect
17. C4×C22⋊C4C4semidirect
18. #376C4semidirect

Maximal subgroups

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

subgroupindex
#23532
#17992
#14592
#12942
#12892