Finite Group Databasebeta

← #145263

Subgroups — #145263

Order 512.

234 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 60 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#19210C211yesmaximal, characteristic
2#12028C211yesmaximal, characteristic
3#11973C211yesmaximal, characteristic
4#11970C211yesmaximal, characteristic
5#11640C211yesmaximal, characteristic
6#8631C211yesmaximal, characteristic
7#7290C211yesmaximal, characteristic
8#3249—21no—
9#3160C2211yescharacteristic
10#2960C2211yescharacteristic
11#2163C2211yescharacteristic
12#2162C2211yescharacteristic
13#1696—21no—
14#1694—21no—
15#1672—22no—
16#1568C2211yescharacteristic
17#1568C2211yescharacteristic
18C2×#334C2211yescharacteristic
19#1550—21no—
20#1537—21no—
21#1368—22no—
22#1365—21no—
23#1364—21no—
24#1363—22no—
25Q8⋊C16—22no—
26#1307—21no—
27#533—21no—
28#533D411yescharacteristic
29#500D411yescharacteristic
30#500D411yescharacteristic
31#499—21no—
32#499—21no—
33#498—21no—
34#477—22no—
35#477—41no—
36#467—42no—
37#462—22no—
38#462—41no—
39#446—21no—
40#446—21no—
41C8×Q8—21no—
42C8×Q8—21no—
43#432—21no—
44#432—21no—
45#427—21no—
46#427—21no—
47#424—21no—
48#423D411yescharacteristic
49C2×C4⋊C8—21no—
50#405—21no—
51C2×C4×C8C2311yescharacteristic
52C4⋊C16—21no—
53C4⋊C16D412yes—
54C22⋊C16—21no—
55C22⋊C16—21no—
56#346—21no—
57C4×C16—21no—
58#335—21no—
59#335—21no—
60#334—21no—
61#334—21no—
62#334—21no—
63#334D412yes—
64#333—22no—
65#332—22no—
66#330—42no—
67C2×Q16—42no—
68C2×M16—21no—
69C22×C8—41no—
70C22×C8#4111yescharacteristic
71C22×C8#4111yescharacteristic
72C4⋊Q8—21no—
73C4⋊Q8—21no—
74C4⋊Q8SD1611yescharacteristic
75C4⋊Q8SD1611yescharacteristic
76#125—21no—
77#125—41no—
78C22⋊Q8—21no—
79C22⋊Q8—21no—
80C22⋊Q8—41no—
81C22⋊Q8—41no—
82C4×Q8—21no—
83C4×Q8—21no—
84C4×Q8—41no—
85C4×Q8—41no—
86#117—21no—
87#117—41no—
88C2×C42C2×D411yescharacteristic
89C2×C16—22no—
90C2×C16—41no—
91#107—21no—
92#107—21no—
93#107—21no—
94#107—21no—
95#107—42no—
96#106—41no—
97#106—41no—
98C4⋊C8—21no—
99C4⋊C8—22no—
100C4⋊C8—21no—
101C4⋊C8—41no—
102C4⋊C8—41no—
103C4⋊C8—41no—
104C4⋊C8—41no—
105C4⋊C8—41no—
106#103—42no—
107#103—42no—
108C22⋊C8—41no—
109C22⋊C8—41no—
110#97—41no—
111#97—41no—
112#97—41no—
113C4×C8—41no—
114C4×C8C2×D411yescharacteristic
115C4×C8C2×D411yescharacteristic
116C4×C8C2×D411yescharacteristic
117C4×C8#4111yescharacteristic
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—41no—
121C2×Q8—41no—
122C22×C4#12311yescharacteristic
123C22×C4#13511yescharacteristic
124C22×C4AGL(1,ℤ/8)11yescharacteristic
125Q16—162no—
126M16—81no—
127C2×C8—22no—
128C2×C8—41no—
129C2×C8—41no—
130C2×C8—42no—
131C2×C8—81no—
132C2×C8—81no—
133C2×C8—161no—
134C2×C8#12111yescharacteristic
135C2×C8#12111yescharacteristic
136C2×C8#12311yescharacteristic
137C2×C8#12411yescharacteristic
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—41no—
148C4⋊C4—81no—
149C4⋊C4—81no—
150C22⋊C4—41no—
151C22⋊C4—81no—
152C42—41no—
153C42—81no—
154C42#12011yescharacteristic
155C42#12111yescharacteristic
156C42C2×SD1611yescharacteristic
157C42AGL(1,ℤ/8)11yescharacteristic
158C16—42no—
159C16—81no—
160C23#48211yescharacteristic
161Q8—42no—
162Q8—42no—
163Q8—81no—
164Q8—81no—
165Q8—161no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—81no—
173C2×C4—81no—
174C2×C4#39411yescharacteristic
175C2×C4#44911yescharacteristic
176C2×C4#45011yescharacteristic
177C2×C4#46511yescharacteristic
178C2×C4#46911yescharacteristic
179C2×C4#48111yescharacteristic
180C8—21no—
181C8—21no—
182C8—21no—
183C8—82no—
184C8—81no—
185C8—161no—
186C8—161no—
187C8#47312yes—
188C22—21no—
189C22—21no—
190C22—21no—
191C22#203411yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—81no—
198C4—81no—
199C4—161no—
200C4—161no—
201C4#204711yescharacteristic
202C4#204911yescharacteristic
203C2—41no—
204C2#1044711yescharacteristic
205C2#1340011yescharacteristic
206C2#1340611yescharacteristic
subgroupG/H
center, socleC22#2034
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#482
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960 ◁ 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
#192102
#120282
#119732
#119702
#116402
#86312
#72902