Finite Group Databasebeta

← #11832

Subgroups — #11832

Order 256.

225 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 225 conjugacy classes of subgroups — too many to draw. Only its 49 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#2635C211yesmaximal, characteristic
2#1800C211yesmaximal, characteristic, complemented
3#1465C211yesmaximal, characteristic, complemented
4#1353C212yesmaximal, complemented
5#1345C212yesmaximal, complemented
6C2×#121C411yescharacteristic
7C2×C4×D4C2211yescharacteristic
8#423—21no—
9C2×#100—21no—
10#407—21no—
11#400C2211yescharacteristic
12#399C411yescharacteristic
13#394—21no—
14#394C2211yescharacteristic
15#392—21no—
16#392C411yescharacteristic
17#388—21no—
18#386—21no—
19#381C411yescharacteristic
20#343C2212yes—
21#324C2212yes—
22#323—21no—
23C22×D4—21no—
24C22×D4—21no—
25C22×D4C2×C411yescharacteristic
26C22×D4D411yescharacteristic
27C23×C4C2×C411yescharacteristic
28C23×C4D411yescharacteristic
29C2×M16—22no—
30C2×M16—41no—
31#121—41no—
32#121—41no—
33C4×D4—41no—
34C4×D4—41no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C4⋊C4C2311yescharacteristic
38C2×C22⋊C4—21no—
39C2×C22⋊C4—21no—
40C2×C22⋊C4—21no—
41C2×C22⋊C4—21no—
42C2×C22⋊C4—21no—
43C2×C22⋊C4—21no—
44C2×C22⋊C4C2×C411yescharacteristic
45C2×C22⋊C4D411yescharacteristic
46C2×C42D411yescharacteristic
47C4⋊C8—41no—
48C4⋊C8—41no—
49#100—42no—
50C22⋊C8—22no—
51C22⋊C8—41no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95C2×C411yescharacteristic
56#95C2×C411yescharacteristic
57C24—21no—
58C24C22⋊C411yescharacteristic
59C24C22⋊C411yescharacteristic
60C2×D4—21no—
61C2×D4—21no—
62C2×D4—41no—
63C2×D4—41no—
64C2×D4—41no—
65C2×D4—42no—
66C2×D4—42no—
67C2×D4—81no—
68C2×D4—81no—
69C2×D4—81no—
70C2×D4—81no—
71C2×D4—81no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—81no—
80C22×C4—81no—
81C22×C4C22⋊C411yescharacteristic
82C22×C4C22⋊C411yescharacteristic
83C22×C4C22×C411yescharacteristic
84C22×C4C2×D411yescharacteristic
85C22×C4C2×D411yescharacteristic
86M16—42no—
87M16—42no—
88M16—82no—
89C2×C8—42no—
90C2×C8—42no—
91C4⋊C4—41no—
92C4⋊C4—41no—
93C4⋊C4—81no—
94C22⋊C4—41no—
95C22⋊C4—41no—
96C22⋊C4—41no—
97C22⋊C4—41no—
98C22⋊C4—41no—
99C22⋊C4—41no—
100C22⋊C4—81no—
101C22⋊C4—81no—
102C22⋊C4—81no—
103C22⋊C4—81no—
104C42—21no—
105C42—21no—
106C23—21no—
107C23—21no—
108C23—21no—
109C23—21no—
110C23—21no—
111C23—21no—
112C23—41no—
113C23—41no—
114C23—41no—
115C23—41no—
116C23—41no—
117C23—41no—
118C23—41no—
119C23—41no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23C2×C22⋊C411yescharacteristic
124D4—42no—
125D4—42no—
126D4—82no—
127D4—84no—
128D4—84no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—42no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4—81no—
151C2×C4#9911yescharacteristic
152C2×C4#9911yescharacteristic
153C2×C4AGL(1,ℤ/8)11yescharacteristic
154C2×C4#13711yescharacteristic
155C8—82no—
156C8—82no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—41no—
161C22—41no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22—81no—
167C22—81no—
168C22—81no—
169C22—81no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22C2×#9911yescharacteristic
177C22#41711yescharacteristic
178C22#42111yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—41no—
185C4—41no—
186C4—81no—
187C4—81no—
188C4—81no—
189C2—21no—
190C2—21no—
191C2—81no—
192C2—81no—
193C2—161no—
194C2#151311yescharacteristic
195C2#212111yescharacteristic
196C2#213411yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radical#2635C2
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. #1465C2semidirect
4. #1353C2semidirect
5. #1345C2semidirect

Maximal subgroups

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

subgroupindex
#26352
#18002
#14652
#13532
#13452