Finite Group Databasebeta

← #32843

Subgroups — #32843

Order 256.

289 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 289 conjugacy classes of subgroups — too many to draw. Only its 107 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#2100C211yesmaximal, characteristic
4#2099C211yesmaximal, characteristic
5#2096C211yesmaximal, characteristic
6#2095C211yesmaximal, characteristic
7#2085C212yesmaximal
8#2074C212yesmaximal
9#2059C212yesmaximal
10#2026C212yesmaximal
11#1839C211yesmaximal, characteristic
12C2×#125C2212yes—
13C2×#107C2212yes—
14C2×#106C2212yes—
15C2×#103C2212yes—
16C2×#103C2212yes—
17#391C2211yescharacteristic
18#391C2211yescharacteristic
19#391C2211yescharacteristic
20#389—21no—
21#389—21no—
22#389—21no—
23#389—21no—
24#389C2211yescharacteristic
25#389C2211yescharacteristic
26#389C2211yescharacteristic
27#387—21no—
28#387—21no—
29#387—21no—
30#384C2211yescharacteristic
31#384C2211yescharacteristic
32#383—21no—
33#382C2212yes—
34C43C2211yescharacteristic
35#340C2212yes—
36#340C2212yes—
37#340C2212yes—
38#340C2212yes—
39#336C2212yes—
40#336C2212yes—
41#336C2211yescharacteristic
42#336C2211yescharacteristic
43C22×Q8C2311yescharacteristic
44C22×C8C2312yes—
45C22×C8C2312yes—
46#125—42no—
47#125—42no—
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⋊C4—21no—
57C2×C4⋊C4C2312yes—
58C2×C4⋊C4C2312yes—
59C2×C4⋊C4C2311yescharacteristic
60C2×C4⋊C4C2311yescharacteristic
61C2×C4⋊C4C2311yescharacteristic
62C2×C42D411yescharacteristic
63C2×C42D411yescharacteristic
64C2×C42D411yescharacteristic
65C2×C42D411yescharacteristic
66C2×C42C2311yescharacteristic
67C2×C42C2311yescharacteristic
68C2×C42C2311yescharacteristic
69#107—42no—
70#106—42no—
71#103—42no—
72#103—42no—
73#95—22no—
74#95—22no—
75#95—21no—
76#95—21no—
77#95—21no—
78#95—21no—
79#95—21no—
80#95—21no—
81#95—21no—
82#95—21no—
83#95—21no—
84C2×Q8—22no—
85C2×Q8—22no—
86C2×Q8—21no—
87C2×Q8—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—22no—
93C22×C4—22no—
94C22×C4C2×D411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97C22×C4C2×D411yescharacteristic
98C22×C4C2×D411yescharacteristic
99C22×C4C2×D411yescharacteristic
100C22×C4C2411yescharacteristic
101C2×C8—22no—
102C2×C8—22no—
103C2×C8—22no—
104C2×C8—22no—
105C2×C8—22no—
106C2×C8—22no—
107C4⋊C4—22no—
108C4⋊C4—22no—
109C4⋊C4—22no—
110C4⋊C4—22no—
111C4⋊C4—22no—
112C4⋊C4—22no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—42no—
116C4⋊C4—42no—
117C4⋊C4—42no—
118C4⋊C4—42no—
119C4⋊C4—44no—
120C4⋊C4—44no—
121C4⋊C4—42no—
122C4⋊C4—42no—
123C4⋊C4—42no—
124C42—22no—
125C42—22no—
126C42—22no—
127C42—22no—
128C42—21no—
129C42—21no—
130C42—41no—
131C42—41no—
132C23C22×D411yescharacteristic
133Q8—42no—
134Q8—42no—
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—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4#13512yes—
170C2×C4#13712yes—
171C2×C4H(5,𝔽2)12yes—
172C2×C42−1+412yes—
173C2×C42−1+411yescharacteristic
174C2×C42−1+411yescharacteristic
175C8—42no—
176C8—42no—
177C22#53511yescharacteristic
178C22#53611yescharacteristic
179C22#53611yescharacteristic
180C22C2×#13511yescharacteristic
181C22C2×#13711yescharacteristic
182C22#57511yescharacteristic
183C22#57511yescharacteristic
184C4—22no—
185C4—22no—
186C4—41no—
187C4—41no—
188C4—41no—
189C4—41no—
190C4—81no—
191C4—82no—
192C4—82no—
193C4—81no—
194C4—81no—
195C4—81no—
196C4#56312yes—
197C4#56312yes—
198C2#282111yescharacteristic
199C2#321011yescharacteristic
200C2#321911yescharacteristic
201C2#323211yescharacteristic
202C2#323311yescharacteristic
203C2#323611yescharacteristic
204C2#323711yescharacteristic
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
#21002
#20992
#20962
#20952
#20852
#20742
#20592
#20262
#18392