Finite Group Databasebeta

← #26512

Subgroups — #26512

Order 256.

329 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 329 conjugacy classes of subgroups — too many to draw. Only its 139 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#2552C211yesmaximal, characteristic
2#2369C211yesmaximal, characteristic
3#2100C212yesmaximal
4#2087C212yesmaximal
5#1990C211yesmaximal, characteristic
6#1987C211yesmaximal, characteristic
7#1947C211yesmaximal, characteristic
8#1947C212yesmaximal
9#1939C211yesmaximal, characteristic
10#1921C212yesmaximal
11C4×#107C211yesmaximal, characteristic
12C2×C4⋊Q8C2211yescharacteristic
13C2×#125—21no—
14C2×#107C2211yescharacteristic
15C2×#107C2212yes—
16C2×#107C2211yescharacteristic
17C2×C4⋊C8C2212yes—
18C2×C4⋊C8C2211yescharacteristic
19C2×C4×C8C2211yescharacteristic
20#398—22no—
21#391—22no—
22#389—21no—
23#389—21no—
24#389C2212yes—
25#389C2212yes—
26#384C2212yes—
27#384C2211yescharacteristic
28C4×C4⋊C4—21no—
29C4×C4⋊C4C2212yes—
30C4×C4⋊C4C2211yescharacteristic
31C4×C4⋊C4C2211yescharacteristic
32C4×C4⋊C4C2211yescharacteristic
33#340C2212yes—
34#340C2212yes—
35#340C2212yes—
36#340C2211yescharacteristic
37#340C2212yes—
38#340C2212yes—
39#340C2211yescharacteristic
40#336C2212yes—
41C22×Q8—21no—
42C22×C8C2311yescharacteristic
43C22×C8C2312yes—
44C22×C8C2311yescharacteristic
45C4⋊Q8—22no—
46C4⋊Q8Q814yes—
47#125—44no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—22no—
51C2×C4⋊C4—22no—
52C2×C4⋊C4—22no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—22no—
55C2×C4⋊C4D411yescharacteristic
56C2×C4⋊C4D411yescharacteristic
57C2×C4⋊C4C2311yescharacteristic
58C2×C4⋊C4C2311yescharacteristic
59C2×C4⋊C4C2311yescharacteristic
60C2×C4⋊C4C2312yes—
61C2×C4⋊C4C2312yes—
62C2×C4⋊C4C2311yescharacteristic
63C2×C42—21no—
64C2×C42—21no—
65C2×C42—22no—
66C2×C42C2312yes—
67C2×C42C2311yescharacteristic
68#107—22no—
69#107—22no—
70#107—24no—
71C4⋊C8—24no—
72C4⋊C8—22no—
73C4×C8—22no—
74#95—22no—
75#95—22no—
76#95—21no—
77#95—21no—
78#95—22no—
79#95D412yes—
80C2×Q8—24no—
81C2×Q8—81no—
82C2×Q8—81no—
83C22×C4—21no—
84C22×C4—22no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—22no—
89C22×C4C2×D412yes—
90C22×C4C2×D411yescharacteristic
91C22×C4C2×D412yes—
92C22×C4C2×D411yescharacteristic
93C22×C4C2411yescharacteristic
94C2×C8—21no—
95C2×C8—21no—
96C2×C8—21no—
97C2×C8—22no—
98C2×C8—22no—
99C2×C8—22no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8#4112yes—
103C4⋊C4—24no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—22no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—22no—
115C4⋊C4—44no—
116C4⋊C4—44no—
117C4⋊C4—42no—
118C4⋊C4—82no—
119C4⋊C4—81no—
120C4⋊C4—82no—
121C4⋊C4Q1614yes—
122C4⋊C4C2×Q814yes—
123C4⋊C4#4112yes—
124C42—22no—
125C42—22no—
126C42—42no—
127C42—42no—
128C42—82no—
129C42C2×Q812yes—
130C42#4112yes—
131C23C22×D411yescharacteristic
132Q8—84no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—24no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4C22⋊Q812yes—
159C2×C4C22⋊Q812yes—
160C2×C4C2×Q1614yes—
161C2×C4C2×Q1612yes—
162C2×C4AGL(1,ℤ/8)12yes—
163C2×C4C22×Q811yescharacteristic
164C2×C4C2×#4111yescharacteristic
165C2×C4C2×#4111yescharacteristic
166C2×C4C2×#4111yescharacteristic
167C2×C42−1+411yescharacteristic
168C2×C42−1+411yescharacteristic
169C8—22no—
170C8—42no—
171C8—41no—
172C22C2×C22⋊Q811yescharacteristic
173C22#54711yescharacteristic
174C22#54811yescharacteristic
175C22C22×Q1611yescharacteristic
176C22C2×AGL(1,ℤ/8)11yescharacteristic
177C22#57611yescharacteristic
178C22#57711yescharacteristic
179C4—22no—
180C4—24no—
181C4—44no—
182C4—42no—
183C4—42no—
184C4—81no—
185C4—81no—
186C4—81no—
187C4—82no—
188C4#47714yes—
189C4#52911yescharacteristic
190C4#54111yescharacteristic
191C4#55711yescharacteristic
192C4#55711yescharacteristic
193C2#245311yescharacteristic
194C2C2×#47711yescharacteristic
195C2#308111yescharacteristic
196C2#333811yescharacteristic
197C2#335411yescharacteristic
198C2#336311yescharacteristic
199C2#336611yescharacteristic
subgroupG/H
center, socle, prime radicalC23C22×D4
commutator, Frattini, cosocleC22×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#25522
#23692
#21002
#20872
#19902
#19872
#19472
#19392
#19212
C4×#1072