Finite Group Databasebeta

← #11884

Subgroups — #11884

Order 256.

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

normal subgroups only

This group has 255 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#2543C211yesmaximal, characteristic
2#1800C211yesmaximal, characteristic, complemented
3#1459C211yesmaximal, characteristic, complemented
4#1346C212yesmaximal, complemented
5#1345C212yesmaximal, complemented
6C2×#121—21no—
7C2×#121C411yescharacteristic
8C2×C4×D4C2211yescharacteristic
9#423—21no—
10C2×#100—21no—
11C2×C22⋊C8—21no—
12#398C2211yescharacteristic
13#397C411yescharacteristic
14#394C2211yescharacteristic
15#392C411yescharacteristic
16#388—21no—
17#386—21no—
18#386—21no—
19C2×#95C411yescharacteristic
20#343C2212yes—
21#324C2212yes—
22#323—21no—
23C22×D4—21no—
24C22×D4—21no—
25C22×D4C2×C411yescharacteristic
26C22×D4D411yescharacteristic
27C23×C4—21no—
28C23×C4C2×C411yescharacteristic
29C23×C4D411yescharacteristic
30C2×M16—22no—
31C22×C8—41no—
32#121—42no—
33#121—42no—
34#121—41no—
35#121—41no—
36C4×D4—41no—
37C4×D4—41no—
38C2×C4⋊C4—21no—
39C2×C4⋊C4C2×C411yescharacteristic
40C2×C4⋊C4C2311yescharacteristic
41C2×C22⋊C4—21no—
42C2×C22⋊C4—21no—
43C2×C22⋊C4—21no—
44C2×C22⋊C4—21no—
45C2×C22⋊C4—21no—
46C2×C22⋊C4C2×C411yescharacteristic
47C2×C22⋊C4D411yescharacteristic
48C2×C42D411yescharacteristic
49C4⋊C8—41no—
50C4⋊C8—41no—
51#100—42no—
52C22⋊C8—22no—
53C22⋊C8—41no—
54#95—21no—
55#95—21no—
56#95—21no—
57#95C2×C411yescharacteristic
58#95C2×C411yescharacteristic
59C24—21no—
60C24C22⋊C411yescharacteristic
61C24C22⋊C411yescharacteristic
62C2×D4—41no—
63C2×D4—41no—
64C2×D4—41no—
65C2×D4—42no—
66C2×D4—42no—
67C2×D4—42no—
68C2×D4—42no—
69C2×D4—42no—
70C2×D4—81no—
71C2×D4—81no—
72C2×D4D812yes—
73C2×D4SD1612yes—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—42no—
82C22×C4—42no—
83C22×C4—81no—
84C22×C4—81no—
85C22×C4—81no—
86C22×C4C22⋊C411yescharacteristic
87C22×C4C22⋊C411yescharacteristic
88C22×C4C22×C411yescharacteristic
89C22×C4C2×D411yescharacteristic
90C22×C4C2×D411yescharacteristic
91M16—42no—
92M16—42no—
93C2×C8—42no—
94C2×C8—42no—
95C2×C8—82no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C4⋊C4—41no—
100C22⋊C4—41no—
101C22⋊C4—41no—
102C22⋊C4—42no—
103C22⋊C4—42no—
104C22⋊C4—41no—
105C22⋊C4—41no—
106C22⋊C4—41no—
107C22⋊C4—41no—
108C22⋊C4—81no—
109C42—21no—
110C42—21no—
111C23—21no—
112C23—21no—
113C23—21no—
114C23—21no—
115C23—41no—
116C23—41no—
117C23—41no—
118C23—41no—
119C23—41no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23—41no—
124C23—41no—
125C23—41no—
126C23#10212yes—
127C23#10212yes—
128C23C2×C22⋊C411yescharacteristic
129D4—42no—
130D4—42no—
131D4—84no—
132D4—82no—
133D4—84no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—81no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4—84no—
157C2×C4#9911yescharacteristic
158C2×C4#9911yescharacteristic
159C2×C4C2×D811yescharacteristic
160C2×C4C2×SD1611yescharacteristic
161C8—82no—
162C8—82no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—22no—
167C22—42no—
168C22—42no—
169C22—42no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—81no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22C2×#9911yescharacteristic
183C22C2×#10211yescharacteristic
184C22#42111yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—21no—
189C4—42no—
190C4—41no—
191C4—41no—
192C4—41no—
193C4—81no—
194C4—81no—
195C2—21no—
196C2—21no—
197C2—42no—
198C2—42no—
199C2—161no—
200C2#151911yescharacteristic
201C2#212111yescharacteristic
202C2#213211yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radical#2543C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #1800C2semidirect
3. #1459C2semidirect
4. #1346C2semidirect
5. #1345C2semidirect

Maximal subgroups

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

subgroupindex
#25432
#18002
#14592
#13462
#13452