Finite Group Databasebeta

← #33259

Subgroups — #33259

Order 256.

329 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 329 conjugacy classes of subgroups — too many to draw. Only its 147 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#1944C212yesmaximal
4#1943C212yesmaximal
5#1942C212yesmaximal
6#1941C212yesmaximal
7#1847C211yesmaximal, characteristic
8#1847C211yesmaximal, characteristic
9#1836C211yesmaximal, characteristic
10#1836C211yesmaximal, characteristic
11C4×#97C211yesmaximal, characteristic
12C2×#125—21no—
13C2×#107C2212yes—
14C2×#107C2212yes—
15C2×#106C2212yes—
16C2×#106C2212yes—
17C2×#97C2212yes—
18C2×#97C2211yescharacteristic
19C2×#97C2211yescharacteristic
20C2×C4×C8C2212yes—
21#389—21no—
22#389—21no—
23#389C2212yes—
24#389C2212yes—
25#389C2211yescharacteristic
26#389C2211yescharacteristic
27#389C2211yescharacteristic
28#389C2211yescharacteristic
29#387—21no—
30#387—21no—
31#387—21no—
32#387—21no—
33#384C2211yescharacteristic
34#384C2211yescharacteristic
35#382—21no—
36#382C2211yescharacteristic
37#382C2211yescharacteristic
38C43C2211yescharacteristic
39#340C2212yes—
40#340C2212yes—
41#340C2212yes—
42#340C2212yes—
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⋊C4C2311yescharacteristic
59C2×C4⋊C4C2311yescharacteristic
60C2×C4⋊C4C2312yes—
61C2×C4⋊C4C2312yes—
62C2×C42D411yescharacteristic
63C2×C42D411yescharacteristic
64C2×C42D411yescharacteristic
65C2×C42D411yescharacteristic
66C2×C42C2311yescharacteristic
67C2×C42C2311yescharacteristic
68C2×C42C2311yescharacteristic
69#107—24no—
70#107—24no—
71#106—24no—
72#106—24no—
73#97—24no—
74#97Q814yes—
75#97Q814yes—
76C4×C8—24no—
77#95—22no—
78#95—22no—
79#95—21no—
80#95—21no—
81#95—21no—
82#95—21no—
83#95—21no—
84#95—21no—
85#95—21no—
86#95—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—22no—
92C22×C4—22no—
93C22×C4C2×D411yescharacteristic
94C22×C4C2×D411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97C22×C4C2×D411yescharacteristic
98C22×C4C2×D411yescharacteristic
99C22×C4C2411yescharacteristic
100C2×C8—22no—
101C2×C8—22no—
102C2×C8C2×Q814yes—
103C2×C8C2×Q814yes—
104C2×C8#4114yes—
105C2×C8#4114yes—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—22no—
109C4⋊C4—22no—
110C4⋊C4—22no—
111C4⋊C4—22no—
112C4⋊C4—22no—
113C4⋊C4—22no—
114C4⋊C4—42no—
115C4⋊C4—42no—
116C4⋊C4—42no—
117C4⋊C4—42no—
118C4⋊C4—42no—
119C4⋊C4—42no—
120C4⋊C4—44no—
121C4⋊C4—42no—
122C4⋊C4—44no—
123C4⋊C4—42no—
124C42—22no—
125C42—22no—
126C42—22no—
127C42—22no—
128C42—41no—
129C42—41no—
130C42C2×Q812yes—
131C42C2×Q812yes—
132C23C22×D411yescharacteristic
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—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—42no—
151C2×C4—41no—
152C2×C4—41no—
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—41no—
163C2×C4—42no—
164C2×C4—41no—
165C2×C4C4⋊Q812yes—
166C2×C4C4⋊Q812yes—
167C2×C4AGL(1,ℤ/8)12yes—
168C2×C4#13712yes—
169C2×C4C22×Q811yescharacteristic
170C2×C4C22×Q811yescharacteristic
171C2×C4C2×#4112yes—
172C2×C4C2×#4112yes—
173C8—24no—
174C8#12518yescomplemented
175C22C2×C4⋊Q811yescharacteristic
176C22#53211yescharacteristic
177C22#53211yescharacteristic
178C22C2×AGL(1,ℤ/8)11yescharacteristic
179C22C2×#13711yescharacteristic
180C22#57511yescharacteristic
181C22#57511yescharacteristic
182C4—22no—
183C4—22no—
184C4—22no—
185C4—22no—
186C4—41no—
187C4—41no—
188C4—82no—
189C4—81no—
190C4—81no—
191C4—82no—
192C4—81no—
193C4—81no—
194C4C2×#12512yes—
195C4#53312yes—
196C2#285911yescharacteristic
197C2#316511yescharacteristic
198C2#316611yescharacteristic
199C2#317111yescharacteristic
200C2#317211yescharacteristic
201C2#318011yescharacteristic
202C2#318111yescharacteristic
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

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
174. C8#125semidirect

Maximal subgroups

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

subgroupindex
#28642
#28592
#19442
#19432
#19422
#19412
#18472
#18362
C4×#972