Finite Group Databasebeta

← #30385

Subgroups — #30385

Order 256.

306 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 113 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#2863C211yesmaximal, characteristic
2#2859C211yesmaximal, characteristic
3#2099C211yesmaximal, characteristic
4#2096C211yesmaximal, characteristic
5#2088C212yesmaximal
6#2083C211yesmaximal, characteristic
7#2072C211yesmaximal, characteristic
8#2068C212yesmaximal
9#1944C212yesmaximal
10#1935C212yesmaximal
11#1767C211yesmaximal, characteristic
12C2×#125—21no—
13C2×#107C2212yes—
14C2×#106C2212yes—
15C2×C4⋊C8C2212yes—
16C2×#103C2212yes—
17C2×#103C2212yes—
18C2×#97C2212yes—
19#391C2211yescharacteristic
20#391C2211yescharacteristic
21#391C2211yescharacteristic
22#389—21no—
23#389—21no—
24#389C2212yes—
25#389C2211yescharacteristic
26#389C2211yescharacteristic
27#389C2212yes—
28#389C2211yescharacteristic
29#387—21no—
30#387—21no—
31#387—21no—
32#384C2211yescharacteristic
33#384C2211yescharacteristic
34#383—21no—
35#382—21no—
36C43C2211yescharacteristic
37#340C2212yes—
38#340C2212yes—
39#340C2212yes—
40#340C2212yes—
41#336C2211yescharacteristic
42#336C2211yescharacteristic
43C22×Q8C2311yescharacteristic
44C22×C8C2312yes—
45C22×C8C2312yes—
46#125—44no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—22no—
50C2×C4⋊C4—22no—
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⋊C4C2312yes—
58C2×C4⋊C4C2312yes—
59C2×C4⋊C4C2311yescharacteristic
60C2×C4⋊C4C2311yescharacteristic
61C2×C42D411yescharacteristic
62C2×C42D411yescharacteristic
63C2×C42D411yescharacteristic
64C2×C42D411yescharacteristic
65C2×C42C2311yescharacteristic
66C2×C42C2311yescharacteristic
67C2×C42C2311yescharacteristic
68#107—42no—
69#106—24no—
70C4⋊C8—24no—
71#103—24no—
72#103—42no—
73#97—42no—
74#95—22no—
75#95—22no—
76#95—21no—
77#95—21no—
78#95—21no—
79#95—21no—
80#95—21no—
81#95—21no—
82#95—21no—
83#95—21no—
84#95—21no—
85C2×Q8—22no—
86C2×Q8—21no—
87C2×Q8—22no—
88C2×Q8—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—22no—
94C22×C4—22no—
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97C22×C4C2×D411yescharacteristic
98C22×C4C2×D411yescharacteristic
99C22×C4C2×D411yescharacteristic
100C22×C4C2×D411yescharacteristic
101C22×C4C2411yescharacteristic
102C2×C8—22no—
103C2×C8—22no—
104C2×C8—22no—
105C2×C8—22no—
106C2×C8—22no—
107C2×C8#4114yes—
108C4⋊C4—22no—
109C4⋊C4—22no—
110C4⋊C4—22no—
111C4⋊C4—22no—
112C4⋊C4—21no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C4⋊C4—21no—
116C4⋊C4—42no—
117C4⋊C4—42no—
118C4⋊C4—44no—
119C4⋊C4—44no—
120C4⋊C4—42no—
121C4⋊C4—42no—
122C4⋊C4—42no—
123C4⋊C4—42no—
124C4⋊C4—42no—
125C42—22no—
126C42—22no—
127C42—22no—
128C42—22no—
129C42—21no—
130C42—22no—
131C42—21no—
132C42—41no—
133C23C22×D411yescharacteristic
134Q8—42no—
135Q8—42no—
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—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4AGL(1,ℤ/8)12yes—
170C2×C4#13712yes—
171C2×C4#13712yes—
172C2×C4C2×#4112yes—
173C2×C4H(5,𝔽2)11yescharacteristic
174C2×C42−1+412yes—
175C2×C42−1+411yescharacteristic
176C8—24no—
177C8—42no—
178C22#53211yescharacteristic
179C22#53611yescharacteristic
180C22#53711yescharacteristic
181C22C2×AGL(1,ℤ/8)11yescharacteristic
182C22C2×#13711yescharacteristic
183C22C2×#13711yescharacteristic
184C22#57511yescharacteristic
185C4—22no—
186C4—22no—
187C4—22no—
188C4—41no—
189C4—41no—
190C4—41no—
191C4—81no—
192C4—81no—
193C4—82no—
194C4—81no—
195C4—82no—
196C4—81no—
197C4#53912yes—
198C4#54112yes—
199C2#266411yescharacteristic
200C2#318111yescharacteristic
201C2#318211yescharacteristic
202C2#323611yescharacteristic
203C2#323811yescharacteristic
204C2#325111yescharacteristic
205C2#325511yescharacteristic
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
#28632
#28592
#20992
#20962
#20882
#20832
#20722
#20682
#19442
#19352
#17672