Finite Group Databasebeta

← #9449

Subgroups — #9449

Order 256.

245 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 245 conjugacy classes of subgroups — too many to draw. Only its 61 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
2#2566C211yesmaximal, characteristic
3#1534C212yesmaximal, complemented
4#1466C211yesmaximal, characteristic
5#1285C212yesmaximal, complemented
6C2×#125C2211yescharacteristic
7C2×C4×D4C2211yescharacteristic
8#435—24no—
9#432C2212yes—
10#432C2212yes—
11#407—21no—
12C2×C22⋊C8—21no—
13#396—21no—
14#396—21no—
15#390C411yescharacteristic
16#390C411yescharacteristic
17#385—21no—
18#385—21no—
19#384C411yescharacteristic
20#382C411yescharacteristic
21C4×C4⋊C4C2211yescharacteristic
22#330—24no—
23#323—21no—
24#323—21no—
25C22×D4C2×C411yescharacteristic
26C23×C4D411yescharacteristic
27C23×C4D411yescharacteristic
28C2×M16—22no—
29C22×C8—22no—
30#125—22no—
31#125—22no—
32C4×D4—22no—
33C4×D4—22no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4—21no—
38C2×C4⋊C4—21no—
39C2×C4⋊C4C2×C411yescharacteristic
40C2×C4⋊C4C2×C411yescharacteristic
41C2×C4⋊C4C2×C411yescharacteristic
42C2×C22⋊C4—21no—
43C2×C22⋊C4—21no—
44C2×C22⋊C4—21no—
45C2×C22⋊C4—21no—
46C2×C22⋊C4D411yescharacteristic
47C2×C22⋊C4D411yescharacteristic
48C2×C42C2×C411yescharacteristic
49C2×C42C2×C411yescharacteristic
50C2×C42C2311yescharacteristic
51C4⋊C8—22no—
52C4⋊C8—22no—
53C22⋊C8—22no—
54C22⋊C8—22no—
55C22⋊C8—22no—
56C22⋊C8—22no—
57#97—22no—
58#97D414yes—
59#95—21no—
60#95—21no—
61#95—21no—
62C24C22⋊C411yescharacteristic
63C24C22⋊C411yescharacteristic
64C2×D4—22no—
65C2×D4—22no—
66C2×D4—41no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—81no—
76C22×C4—81no—
77C22×C4C22⋊C411yescharacteristic
78C22×C4C22⋊C411yescharacteristic
79C22×C4C22×C411yescharacteristic
80C22×C4C2×D411yescharacteristic
81C22×C4C2×D411yescharacteristic
82M16—82no—
83C2×C8—24no—
84C2×C8—42no—
85C2×C8—82no—
86C4⋊C4—22no—
87C4⋊C4—22no—
88C4⋊C4—22no—
89C4⋊C4—42no—
90C4⋊C4—41no—
91C4⋊C4—42no—
92C4⋊C4—41no—
93C4⋊C4—81no—
94C4⋊C4—81no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C22⋊C4—42no—
98C22⋊C4—42no—
99C22⋊C4—81no—
100C22⋊C4—81no—
101C42—41no—
102C42—41no—
103C42C2×D412yes—
104C42#4112yes—
105C23—21no—
106C23—21no—
107C23—21no—
108C23—21no—
109C23—21no—
110C23—41no—
111C23—41no—
112C23—41no—
113C23—41no—
114C23#10112yes—
115C23C2×C22⋊C411yescharacteristic
116D4—44no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—22no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—42no—
125C2×C4—42no—
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—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—81no—
140C2×C4—81no—
141C2×C4C4×D412yes—
142C2×C4#12011yescharacteristic
143C2×C4#12112yes—
144C2×C4#12311yescharacteristic
145C8—44no—
146C8—82no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—42no—
152C22—41no—
153C22—41no—
154C22—41no—
155C22—41no—
156C22—41no—
157C22—81no—
158C22—81no—
159C22#38611yescharacteristic
160C22C2×#10111yescharacteristic
161C22#41311yescharacteristic
162C4—22no—
163C4—22no—
164C4—21no—
165C4—21no—
166C4—42no—
167C4—41no—
168C4—41no—
169C4—81no—
170C4—81no—
171C4—81no—
172C2—21no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2#188411yescharacteristic
177C2#190111yescharacteristic
178C2#191111yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC22×D4C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #1534C2semidirect
5. #1285C2semidirect

Maximal subgroups

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

subgroupindex
#29732
#25662
#15342
#14662
#12852