Finite Group Databasebeta

← #145586

Subgroups — #145586

Order 512.

292 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 74 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#19618C211yesmaximal, characteristic
2#11949C212yesmaximal
3#11743C212yesmaximal
4#9598C211yesmaximal, characteristic
5#7145C211yesmaximal, characteristic
6#3170—21no—
7#3170C2212yes—
8#3160—21no—
9#2162C2212yes—
10#1939—21no—
11C4×#107C2211yescharacteristic
12#1723—22no—
13#1723—22no—
14C2×#335C2211yescharacteristic
15C2×#322C2211yescharacteristic
16#1365—22no—
17#1362—22no—
18#1348—22no—
19#1348—22no—
20#1279—21no—
21#533—22no—
22#500—21no—
23#500—21no—
24#500—21no—
25#500D412yes—
26#499—41no—
27#499—41no—
28#498—22no—
29#494—21no—
30#494D412yes—
31#487—22no—
32#487—22no—
33#467—22no—
34#467—22no—
35#467—42no—
36C4×Q16—22no—
37C4×Q16—22no—
38C4×Q16—42no—
39#427—41no—
40#427—41no—
41C2×#107—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—41no—
44C2×C4×C8D411yescharacteristic
45C2×C4×C8D411yescharacteristic
46C2×C4×C8C2311yescharacteristic
47C4×C4⋊C4—21no—
48C4⋊C16—22no—
49C22⋊C16—22no—
50C4×C16—22no—
51#340D411yescharacteristic
52#340D411yescharacteristic
53#336—41no—
54#335—22no—
55#322—22no—
56C2×Q16—22no—
57C2×Q16—22no—
58C2×Q16—42no—
59C22×C8—21no—
60C22×C8—41no—
61C22×C8D811yescharacteristic
62C22×C8D811yescharacteristic
63C22×C8C2×D411yescharacteristic
64C22×C8#4111yescharacteristic
65C4⋊Q8—22no—
66C4⋊Q8—22no—
67#125—42no—
68C22⋊Q8—42no—
69C22⋊Q8—42no—
70C4×Q8—42no—
71C4×Q8—42no—
72#117—42no—
73C2×C4⋊C4—21no—
74C2×C4⋊C4—21no—
75C2×C42—41no—
76C2×C42C2×D411yescharacteristic
77C2×C16—42no—
78#107—22no—
79#107—22no—
80#107—42no—
81#107—41no—
82#107—41no—
83#107—41no—
84#107—41no—
85#107—42no—
86#106—42no—
87#106—42no—
88C4⋊C8—41no—
89C4⋊C8—41no—
90C4⋊C8—82no—
91#103—44no—
92#103—42no—
93#103—42no—
94C4×C8—21no—
95C4×C8—21no—
96C4×C8—21no—
97C4×C8SD1612yes—
98C4×C8C2×D412yes—
99C4×C8#4112yes—
100#95—41no—
101C2×Q8—42no—
102C2×Q8—42no—
103C22×C4—41no—
104C22×C4—41no—
105C22×C4#12111yescharacteristic
106C22×C4C2×D811yescharacteristic
107C22×C4AGL(1,ℤ/8)11yescharacteristic
108Q16—82no—
109Q16—82no—
110Q16—84no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—21no—
114C2×C8—21no—
115C2×C8—22no—
116C2×C8—41no—
117C2×C8—41no—
118C2×C8—81no—
119C2×C8—81no—
120C2×C8—81no—
121C2×C8—81no—
122C2×C8SD3212yes—
123C2×C8Q3212yes—
124C2×C8#12112yes—
125C2×C8#12312yes—
126C4⋊C4—22no—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—41no—
130C4⋊C4—42no—
131C4⋊C4—42no—
132C4⋊C4—42no—
133C4⋊C4—42no—
134C4⋊C4—82no—
135C4⋊C4—82no—
136C22⋊C4—82no—
137C42—82no—
138C42—81no—
139C42—81no—
140C42#12011yescharacteristic
141C42#12411yescharacteristic
142C42C2×SD1611yescharacteristic
143C42AGL(1,ℤ/8)11yescharacteristic
144C16—82no—
145C23#45911yescharacteristic
146Q8—84no—
147Q8—82no—
148Q8—82no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—81no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—82no—
159C2×C4—82no—
160C2×C4#39411yescharacteristic
161C2×C4#44711yescharacteristic
162C2×C4#45011yescharacteristic
163C2×C4#46011yescharacteristic
164C2×C4#48611yescharacteristic
165C2×C4#49011yescharacteristic
166C2×C4C2×SD3211yescharacteristic
167C2×C4C2×Q3211yescharacteristic
168C2×C4#51011yescharacteristic
169C2×C4#51011yescharacteristic
170C8—22no—
171C8—22no—
172C8—22no—
173C8—22no—
174C8—42no—
175C8—161no—
176C22—21no—
177C22—21no—
178C22#204111yescharacteristic
179C22#220811yescharacteristic
180C22#220911yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—82no—
185C4—161no—
186C4—162no—
187C4—162no—
188C4#205011yescharacteristic
189C4#205311yescharacteristic
190C4#218511yescharacteristic
191C4#218811yescharacteristic
192C4#224111yescharacteristic
193C4#224511yescharacteristic
194C2—21no—
195C2—21no—
196C2#1054611yescharacteristic
197C2#1340911yescharacteristic
198C2#1341611yescharacteristic
subgroupG/H
centerC2×C4#486
commutator, Frattini, cosocleC2×C4×C8C23
socleC22#2041
prime radicalC23#459
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#322 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#196182
#119492
#117432
#95982
#71452