Finite Group Databasebeta

← #32853

Subgroups — #32853

Order 256.

284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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#2864C211yesmaximal, characteristic
2#2859C211yesmaximal, characteristic
3#2101C212yesmaximal
4#2100C211yesmaximal, characteristic
5#2100C211yesmaximal, characteristic
6#2088C212yesmaximal
7#2086C212yesmaximal
8#2085C212yesmaximal
9#2084C211yesmaximal, characteristic
10#2083C211yesmaximal, characteristic
11#1831C211yesmaximal, characteristic
12C2×#125—21no—
13C2×#107C2212yes—
14C2×#106C2212yes—
15C2×C4⋊C8C2212yes—
16#389—21no—
17#389—21no—
18#389C2211yescharacteristic
19#389C2211yescharacteristic
20#389C2212yes—
21#389C2211yescharacteristic
22#389C2212yes—
23#389C2211yescharacteristic
24#387—21no—
25#387—21no—
26#387—21no—
27#387—21no—
28#384C2211yescharacteristic
29#384C2211yescharacteristic
30#382—21no—
31#382C2211yescharacteristic
32#382C2211yescharacteristic
33C43C2211yescharacteristic
34#340C2212yes—
35#340C2212yes—
36#340C2212yes—
37#340C2212yes—
38#340C2212yes—
39#340C2212yes—
40#336C2211yescharacteristic
41#336C2211yescharacteristic
42#336C2212yes—
43C22×C8C2312yes—
44C22×C8C2312yes—
45#125—44no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—22no—
49C2×C4⋊C4—22no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4C2311yescharacteristic
57C2×C4⋊C4C2311yescharacteristic
58C2×C4⋊C4C2312yes—
59C2×C4⋊C4C2311yescharacteristic
60C2×C4⋊C4C2311yescharacteristic
61C2×C4⋊C4C2312yes—
62C2×C42D411yescharacteristic
63C2×C42D411yescharacteristic
64C2×C42D411yescharacteristic
65C2×C42D411yescharacteristic
66C2×C42C2311yescharacteristic
67C2×C42C2311yescharacteristic
68C2×C42C2311yescharacteristic
69#107—42no—
70#106—42no—
71C4⋊C8—42no—
72#95—22no—
73#95—22no—
74#95—21no—
75#95—21no—
76#95—21no—
77#95—21no—
78#95—21no—
79#95—21no—
80#95—21no—
81#95—21no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—22no—
87C22×C4—22no—
88C22×C4C2×D411yescharacteristic
89C22×C4C2×D411yescharacteristic
90C22×C4C2×D411yescharacteristic
91C22×C4C2×D411yescharacteristic
92C22×C4C2×D411yescharacteristic
93C22×C4C2×D411yescharacteristic
94C22×C4C2411yescharacteristic
95C2×C8—22no—
96C2×C8—22no—
97C2×C8—22no—
98C2×C8—22no—
99C2×C8—22no—
100C2×C8—22no—
101C4⋊C4—21no—
102C4⋊C4—22no—
103C4⋊C4—21no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—24no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—22no—
110C4⋊C4—42no—
111C4⋊C4—42no—
112C4⋊C4—42no—
113C4⋊C4—42no—
114C4⋊C4—44no—
115C4⋊C4—42no—
116C4⋊C4—42no—
117C4⋊C4—42no—
118C4⋊C4—44no—
119C4⋊C4—42no—
120C42—22no—
121C42—22no—
122C42—22no—
123C42—21no—
124C42—22no—
125C42—21no—
126C42—22no—
127C42—41no—
128C23C22×D411yescharacteristic
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
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—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—42no—
146C2×C4—41no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—41no—
162C2×C4#13512yes—
163C2×C4AGL(1,ℤ/8)12yes—
164C2×C4#13712yes—
165C2×C4H(5,𝔽2)11yescharacteristic
166C2×C42−1+412yes—
167C2×C42−1+412yes—
168C2×C42−1+411yescharacteristic
169C8—42no—
170C8—42no—
171C22#53611yescharacteristic
172C22#53611yescharacteristic
173C22#53711yescharacteristic
174C22C2×#13511yescharacteristic
175C22C2×AGL(1,ℤ/8)11yescharacteristic
176C22C2×#13711yescharacteristic
177C22#57511yescharacteristic
178C4—22no—
179C4—22no—
180C4—22no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—82no—
186C4—81no—
187C4—82no—
188C4—81no—
189C4—81no—
190C4#56312yes—
191C4#56412yes—
192C2#282211yescharacteristic
193C2#323111yescharacteristic
194C2#323211yescharacteristic
195C2#323511yescharacteristic
196C2#323911yescharacteristic
197C2#324711yescharacteristic
198C2#325211yescharacteristic
subgroupG/H
center, socle, prime radicalC23C22×D4
commutator, Frattini, cosocleC22×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ 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
#28642
#28592
#21012
#21002
#20882
#20862
#20852
#20842
#20832
#18312