Finite Group Databasebeta

← #26511

Subgroups — #26511

Order 256.

311 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 311 conjugacy classes of subgroups — too many to draw. Only its 131 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#2571C211yesmaximal, characteristic
2#2369C211yesmaximal, characteristic
3#2101C212yesmaximal
4#2088C212yesmaximal
5#1990C211yesmaximal, characteristic
6#1987C211yesmaximal, characteristic
7#1949C212yesmaximal
8#1947C211yesmaximal, characteristic
9#1939C211yesmaximal, characteristic
10#1918C212yesmaximal
11C4×#106C211yesmaximal, characteristic
12C2×C4⋊Q8C2211yescharacteristic
13C2×#107C2212yes—
14C2×#106C2211yescharacteristic
15C2×#106C2211yescharacteristic
16C2×C4⋊C8C2212yes—
17C2×C4⋊C8C2211yescharacteristic
18C2×C4×C8C2211yescharacteristic
19#400—22no—
20#391—22no—
21#389—21no—
22#389—21no—
23#389C2212yes—
24#389C2212yes—
25#384C2211yescharacteristic
26#382—21no—
27#382C2212yes—
28C4×C4⋊C4—21no—
29C4×C4⋊C4C2211yescharacteristic
30C4×C4⋊C4C2212yes—
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—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—22no—
51C2×C4⋊C4—22no—
52C2×C4⋊C4D411yescharacteristic
53C2×C4⋊C4D411yescharacteristic
54C2×C4⋊C4C2311yescharacteristic
55C2×C4⋊C4C2311yescharacteristic
56C2×C4⋊C4C2311yescharacteristic
57C2×C4⋊C4C2312yes—
58C2×C4⋊C4C2312yes—
59C2×C4⋊C4C2311yescharacteristic
60C2×C42—21no—
61C2×C42—21no—
62C2×C42—22no—
63C2×C42C2312yes—
64C2×C42C2311yescharacteristic
65#107—24no—
66#106—22no—
67#106—22no—
68C4⋊C8—24no—
69C4⋊C8—22no—
70C4×C8—22no—
71#95—22no—
72#95—22no—
73#95—21no—
74#95—21no—
75#95—22no—
76#95—22no—
77#95—22no—
78#95D412yes—
79C2×Q8—24no—
80C2×Q8—81no—
81C2×Q8—81no—
82C22×C4—21no—
83C22×C4—22no—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—22no—
88C22×C4C2×D412yes—
89C22×C4C2×D412yes—
90C22×C4C2×D411yescharacteristic
91C22×C4C2×D411yescharacteristic
92C22×C4C2411yescharacteristic
93C2×C8—21no—
94C2×C8—21no—
95C2×C8—21no—
96C2×C8—22no—
97C2×C8—22no—
98C2×C8—22no—
99C2×C8—21no—
100C2×C8—21no—
101C2×C8#4112yes—
102C4⋊C4—24no—
103C4⋊C4—22no—
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—42no—
116C4⋊C4—81no—
117C4⋊C4—82no—
118C4⋊C4—82no—
119C4⋊C4C2×Q814yes—
120C4⋊C4#4112yes—
121C42—22no—
122C42—22no—
123C42—42no—
124C42—42no—
125C42—82no—
126C42C2×Q812yes—
127C42#4112yes—
128C23C22×D411yescharacteristic
129Q8—84no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—24no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—42no—
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—41no—
156C2×C4C22⋊Q812yes—
157C2×C4C22⋊Q812yes—
158C2×C4#13512yes—
159C2×C4#13712yes—
160C2×C4C22×Q811yescharacteristic
161C2×C4C2×#4111yescharacteristic
162C2×C4C2×#4111yescharacteristic
163C2×C4C2×#4111yescharacteristic
164C2×C42−1+411yescharacteristic
165C2×C42−1+411yescharacteristic
166C8—22no—
167C8—42no—
168C8—41no—
169C22C2×C22⋊Q811yescharacteristic
170C22#54711yescharacteristic
171C22#54811yescharacteristic
172C22C2×#13511yescharacteristic
173C22C2×#13711yescharacteristic
174C22#57611yescharacteristic
175C22#57711yescharacteristic
176C4—22no—
177C4—44no—
178C4—42no—
179C4—42no—
180C4—42no—
181C4—81no—
182C4—81no—
183C4—82no—
184C4—81no—
185C4#47914yes—
186C4#52911yescharacteristic
187C4#54111yescharacteristic
188C4#55711yescharacteristic
189C4#55711yescharacteristic
190C2#245311yescharacteristic
191C2C2×#47911yescharacteristic
192C2#308111yescharacteristic
193C2#334011yescharacteristic
194C2#335711yescharacteristic
195C2#336111yescharacteristic
196C2#336911yescharacteristic
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
#25712
#23692
#21012
#20882
#19902
#19872
#19492
#19472
#19392
#19182
C4×#1062