Finite Group Databasebeta

← #9031

Subgroups — #9031

Order 256.

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

normal subgroups only

This group has 335 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#2973C211yesmaximal, characteristic, complemented
2#2397C211yesmaximal, characteristic
3C4×#100C211yesmaximal, characteristic, complemented
4#1490C212yesmaximal, complemented
5#1300C212yesmaximal, complemented
6C2×C4×D4—21no—
7C2×C4×D4—21no—
8C2×C4×D4C2211yescharacteristic
9C2×C4×D4C2211yescharacteristic
10#435—24no—
11#432C2212yes—
12C2×#100—21no—
13#407—21no—
14C2×C22⋊C8—21no—
15C4×M16C2212yes—
16#399—21no—
17#399C411yescharacteristic
18#399C411yescharacteristic
19#392—21no—
20#392C411yescharacteristic
21#392C411yescharacteristic
22#376C2211yescharacteristic
23#343—21no—
24D4⋊C8—24no—
25C22×D4—21no—
26C22×D4—21no—
27C22×D4C2×C411yescharacteristic
28C22×D4D411yescharacteristic
29C23×C4—21no—
30C23×C4D411yescharacteristic
31C23×C4D411yescharacteristic
32C2×M16—22no—
33C2×M16—22no—
34C22×C8—22no—
35C4×D4—22no—
36C4×D4—22no—
37C4×D4—22no—
38C4×D4—22no—
39C4×D4—44no—
40C4×D4—44no—
41C2×C4⋊C4—21no—
42C2×C4⋊C4—21no—
43C2×C4⋊C4C2×C411yescharacteristic
44C2×C4⋊C4D411yescharacteristic
45C2×C22⋊C4—21no—
46C2×C22⋊C4—21no—
47C2×C22⋊C4—21no—
48C2×C22⋊C4—21no—
49C2×C22⋊C4—21no—
50C2×C22⋊C4C2×C411yescharacteristic
51C2×C22⋊C4C2×C411yescharacteristic
52C2×C42—21no—
53C2×C42C2311yescharacteristic
54C4⋊C8D414yescomplemented
55#100—24no—
56C22⋊C8—22no—
57C22⋊C8—22no—
58C22⋊C8—22no—
59#97—22no—
60#97—22no—
61C4×C8—22no—
62#95—21no—
63#95C2×C411yescharacteristic
64#95C2×C411yescharacteristic
65C24—21no—
66C24C22⋊C411yescharacteristic
67C24C22⋊C411yescharacteristic
68C2×D4—22no—
69C2×D4—22no—
70C2×D4—22no—
71C2×D4—41no—
72C2×D4—42no—
73C2×D4—42no—
74C2×D4—42no—
75C2×D4—42no—
76C2×D4—42no—
77C2×D4—42no—
78C2×D4—42no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—42no—
87C22×C4—42no—
88C22×C4—42no—
89C22×C4—42no—
90C22×C4—41no—
91C22×C4—41no—
92C22×C4C22⋊C411yescharacteristic
93C22×C4C22⋊C411yescharacteristic
94C22×C4C22×C411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97M16—24no—
98M16—42no—
99M16—82no—
100C2×C8—24no—
101C2×C8—42no—
102C2×C8—82no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—42no—
106C4⋊C4—42no—
107C22⋊C4—22no—
108C22⋊C4—22no—
109C22⋊C4—42no—
110C22⋊C4—42no—
111C22⋊C4—42no—
112C22⋊C4—42no—
113C22⋊C4—42no—
114C42—24no—
115C42C2×D412yes—
116C42#4112yes—
117C23—21no—
118C23—21no—
119C23—22no—
120C23—21no—
121C23—21no—
122C23—21no—
123C23—41no—
124C23—41no—
125C23—41no—
126C23—41no—
127C23—41no—
128C23—41no—
129C23—41no—
130C23—41no—
131C23—41no—
132C23—41no—
133C23#10412yes—
134C23C2×C22⋊C411yescharacteristic
135D4—24no—
136D4—44no—
137D4—42no—
138D4—48no—
139D4—48no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—82no—
162C2×C4—82no—
163C2×C4C4×D412yes—
164C2×C4#12011yescharacteristic
165C2×C4#12112yes—
166C2×C4#12311yescharacteristic
167C8—44no—
168C8—44no—
169C22—21no—
170C22—21no—
171C22—22no—
172C22—42no—
173C22—42no—
174C22—42no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—42no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22#38611yescharacteristic
189C22C2×#10411yescharacteristic
190C22#42111yescharacteristic
191C4—22no—
192C4—21no—
193C4—22no—
194C4—42no—
195C4—42no—
196C4—41no—
197C4—41no—
198C4—81no—
199C4#45312yes—
200C2—21no—
201C2—21no—
202C2—42no—
203C2—81no—
204C2—82no—
205C2#187111yescharacteristic
206C2#188711yescharacteristic
207C2#189111yescharacteristic
subgroupG/H
centerC2×C4#120
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
socleC22#386
prime radical#2397C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #2973C2semidirect
3. C4×#100C2semidirect
4. #1490C2semidirect
5. #1300C2semidirect
54. C4⋊C8D4semidirect

Maximal subgroups

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

subgroupindex
#29732
#23972
C4×#1002
#14902
#13002