Finite Group Databasebeta

← #11698

Subgroups — #11698

Order 256.

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

normal subgroups only

This group has 257 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#2618C211yesmaximal, characteristic
2C2×#343C211yesmaximal, characteristic, complemented
3C2×#324C211yesmaximal, characteristic, complemented
4#1346C212yesmaximal, complemented
5#1345C212yesmaximal, complemented
6C22×M16—21no—
7C2×#123—21no—
8C2×#121C411yescharacteristic
9C22×C4⋊C4C2211yescharacteristic
10C2×C22⋊C8—21no—
11#398C411yescharacteristic
12#398C2211yescharacteristic
13#396—21no—
14#396—21no—
15#394C411yescharacteristic
16#394C2211yescharacteristic
17#386—21no—
18#380C411yescharacteristic
19#343—21no—
20#343C2212yes—
21#324—21no—
22#324C2212yes—
23C22×D4—21no—
24C22×D4C2×C411yescharacteristic
25C23×C4C2×C411yescharacteristic
26C23×C4D411yescharacteristic
27C23×C4D411yescharacteristic
28C2×M16—24no—
29C2×M16—22no—
30C2×M16—41no—
31C2×M16—42no—
32C22×C8—41no—
33C22×C8—41no—
34#123—42no—
35#123—42no—
36#121—41no—
37#121—41no—
38C2×C4⋊C4—21no—
39C2×C4⋊C4—21no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4—41no—
42C2×C4⋊C4—41no—
43C2×C4⋊C4C2×C411yescharacteristic
44C2×C4⋊C4C2×C411yescharacteristic
45C2×C4⋊C4D411yescharacteristic
46C2×C4⋊C4D411yescharacteristic
47C2×C4⋊C4C2311yescharacteristic
48C2×C22⋊C4—21no—
49C2×C22⋊C4—21no—
50C2×C22⋊C4—21no—
51C2×C22⋊C4—21no—
52C2×C22⋊C4—21no—
53C2×C22⋊C4—21no—
54C22⋊C8—22no—
55C22⋊C8—41no—
56#95—21no—
57#95—21no—
58#95C2×C411yescharacteristic
59#95C2×C411yescharacteristic
60C24—21no—
61C24C22⋊C411yescharacteristic
62C2×D4—41no—
63C2×D4—41no—
64C2×D4—41no—
65C2×D4—42no—
66C2×D4—42no—
67C2×D4—81no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—22no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—81no—
79C22×C4—81no—
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22⋊C411yescharacteristic
82C22×C4C22⋊C411yescharacteristic
83C22×C4D812yes—
84C22×C4SD1612yes—
85C22×C4C22×C411yescharacteristic
86C22×C4C2×D411yescharacteristic
87C22×C4C2×D411yescharacteristic
88M16—24no—
89M16—44no—
90M16—42no—
91C2×C8—44no—
92C2×C8—42no—
93C2×C8—42no—
94C2×C8—82no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C4⋊C4—41no—
100C4⋊C4—42no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—81no—
104C22⋊C4—42no—
105C22⋊C4—42no—
106C22⋊C4—42no—
107C22⋊C4—41no—
108C22⋊C4—41no—
109C22⋊C4—81no—
110C22⋊C4—81no—
111C23—41no—
112C23—41no—
113C23—41no—
114C23—41no—
115C23—41no—
116C23—41no—
117C23—41no—
118C23—41no—
119C23—41no—
120C23#9911yescharacteristic
121C23#9911yescharacteristic
122C23#10212yes—
123C23#10412yes—
124C23C2×C22⋊C411yescharacteristic
125D4—82no—
126D4—82no—
127D4—82no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—42no—
141C2×C4—41no—
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—41no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4—81no—
157C2×C4#10212yes—
158C2×C4C2×D811yescharacteristic
159C2×C4C2×SD1611yescharacteristic
160C8—44no—
161C8—82no—
162C22—21no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—42no—
169C22—42no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22—81no—
177C22#32712yes—
178C22#32712yes—
179C22C2×#9911yescharacteristic
180C22C2×#10211yescharacteristic
181C22C2×#10411yescharacteristic
182C4—21no—
183C4—22no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—41no—
188C4—41no—
189C4—81no—
190C4—81no—
191C4—81no—
192C2—21no—
193C2—21no—
194C2—22no—
195C2—22no—
196C2—161no—
197C2C2×#32711yescharacteristic
198C2#212111yescharacteristic
199C2#213311yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radicalC2×#121C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#343C2semidirect
3. C2×#324C2semidirect
4. #1346C2semidirect
5. #1345C2semidirect

Maximal subgroups

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

subgroupindex
#26182
C2×#3432
C2×#3242
#13462
#13452