Finite Group Databasebeta

← #11543

Subgroups — #11543

Order 256.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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#2483C211yesmaximal, characteristic
2#1462C211yesmaximal, characteristic
3C2×#323C211yesmaximal, characteristic
4#1326C212yesmaximal, complemented
5#1317C212yesmaximal, complemented
6C22×C22⋊C4C411yescharacteristic
7C22×C22⋊C4C2211yescharacteristic
8#407—21no—
9C2×C22⋊C8—21no—
10#397—21no—
11#397—21no—
12#385—21no—
13#385C411yescharacteristic
14#385C2211yescharacteristic
15#381—21no—
16#381C411yescharacteristic
17#381C2211yescharacteristic
18#379C411yescharacteristic
19#323—21no—
20#323—21no—
21#323C2212yes—
22#323C2212yes—
23C25C2×C411yescharacteristic
24C23×C4C2×C411yescharacteristic
25C23×C4C2×C411yescharacteristic
26C23×C4D411yescharacteristic
27C23×C4D411yescharacteristic
28C2×M16—41no—
29C22×C8—41no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—21no—
32C2×C22⋊C4—21no—
33C2×C22⋊C4—21no—
34C2×C22⋊C4—21no—
35C2×C22⋊C4—21no—
36C2×C22⋊C4—41no—
37C2×C22⋊C4—41no—
38C2×C22⋊C4—41no—
39C2×C22⋊C4—41no—
40C2×C22⋊C4C2×C411yescharacteristic
41C2×C22⋊C4C2×C411yescharacteristic
42C2×C22⋊C4C2×C411yescharacteristic
43C2×C22⋊C4D411yescharacteristic
44C2×C22⋊C4D411yescharacteristic
45C2×C22⋊C4C2311yescharacteristic
46C22⋊C8—22no—
47C22⋊C8—22no—
48C22⋊C8—41no—
49C22⋊C8—41no—
50#95—21no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95—21no—
56C24—21no—
57C24—21no—
58C24—22no—
59C24—41no—
60C24—42no—
61C24—81no—
62C24C22⋊C411yescharacteristic
63C24C22⋊C411yescharacteristic
64C24C22×C411yescharacteristic
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—22no—
74C22×C4—42no—
75C22×C4—41no—
76C22×C4—41no—
77C22×C4—41no—
78C22×C4—81no—
79C22×C4—81no—
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22⋊C411yescharacteristic
82C22×C4C2×D411yescharacteristic
83C22×C4C2×D411yescharacteristic
84M16—82no—
85C2×C8—42no—
86C2×C8—42no—
87C2×C8—82no—
88C4⋊C4—81no—
89C4⋊C4—81no—
90C22⋊C4—22no—
91C22⋊C4—41no—
92C22⋊C4—41no—
93C22⋊C4—41no—
94C22⋊C4—41no—
95C22⋊C4—42no—
96C22⋊C4—42no—
97C22⋊C4—41no—
98C22⋊C4—41no—
99C22⋊C4—41no—
100C22⋊C4—81no—
101C23—22no—
102C23—21no—
103C23—21no—
104C23—21no—
105C23—21no—
106C23—21no—
107C23—21no—
108C23—21no—
109C23—41no—
110C23—42no—
111C23—42no—
112C23—41no—
113C23—41no—
114C23—42no—
115C23—41no—
116C23—41no—
117C23—42no—
118C23—81no—
119C23—81no—
120C23—84no—
121C23—84no—
122C23#9911yescharacteristic
123C23#9911yescharacteristic
124C23C2×C22⋊C411yescharacteristic
125C23#13112yes—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—42no—
131C2×C4—42no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
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—82no—
151C2×C4—82no—
152C8—82no—
153C8—82no—
154C22—21no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—21no—
160C22—22no—
161C22—21no—
162C22—42no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22—84no—
172C22—81no—
173C22—81no—
174C22—84no—
175C22#35212yes—
176C22#40811yescharacteristic
177C22C2×#9911yescharacteristic
178C22#41311yescharacteristic
179C4—41no—
180C4—41no—
181C4—41no—
182C4—41no—
183C4—81no—
184C4—81no—
185C4—81no—
186C4—81no—
187C2—21no—
188C2—21no—
189C2—22no—
190C2—41no—
191C2—42no—
192C2—81no—
193C2#146811yescharacteristic
194C2C2×#35211yescharacteristic
195C2#212111yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC24C22×C4
Frattini, cosocleC2×C22⋊C4C23
prime radicalC25C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1326C2semidirect
5. #1317C2semidirect

Maximal subgroups

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

subgroupindex
#24832
#14622
C2×#3232
#13262
#13172