Finite Group Databasebeta

← #146003

Subgroups — #146003

Order 512.

198 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 62 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#12028C211yesmaximal, characteristic
2#12016C211yesmaximal, characteristic
3#11969C211yesmaximal, characteristic
4C2×#1363C211yesmaximal, characteristic
5#9788C211yesmaximal, characteristic
6#9623C211yesmaximal, characteristic
7#7243C211yesmaximal, characteristic
8C2×#499C2211yescharacteristic
9#2163C2211yescharacteristic
10C2×C4⋊C16C2211yescharacteristic
11#1950—21no—
12#1568C2211yescharacteristic
13#1566C2211yescharacteristic
14C2×#334C2211yescharacteristic
15#1528—21no—
16#1470—21no—
17C8×M16C2211yescharacteristic
18#1370—21no—
19#1368—22no—
20#1367—21no—
21#1363—21no—
22#1363—21no—
23#1363—22no—
24#1301—21no—
25C2×#125—21no—
26C22×C16—21no—
27#499—21no—
28#499—21no—
29#499—21no—
30#499—21no—
31#432—21no—
32#431D411yescharacteristic
33C2×#108—41no—
34C2×#107Q811yescharacteristic
35C2×#107Q811yescharacteristic
36C2×#106—21no—
37#423—21no—
38C2×C4⋊C8—21no—
39C4×M16D411yescharacteristic
40C2×C4×C8C2311yescharacteristic
41C4⋊C16—21no—
42C4⋊C16—21no—
43C4⋊C16D411yescharacteristic
44C4⋊C16D411yescharacteristic
45C22⋊C16—21no—
46#346—21no—
47#341—41no—
48#335—21no—
49#334—21no—
50#334—21no—
51#334—21no—
52#334—21no—
53#334D412yes—
54#330—42no—
55#324—42no—
56#322—21no—
57C82—21no—
58C2×M16—21no—
59C2×M16—41no—
60C22×C8—41no—
61C22×C8C2×Q811yescharacteristic
62C22×C8#4111yescharacteristic
63#125—41no—
64#125—41no—
65#125—41no—
66#125—41no—
67C2×C4⋊C4—21no—
68C2×C4⋊C4—21no—
69C2×C4⋊C4—41no—
70C2×C4⋊C4—41no—
71C2×C42C2×D411yescharacteristic
72C2×C16—21no—
73C2×C16—21no—
74C2×C16—41no—
75C2×C16—81no—
76#108—82no—
77#107—21no—
78#107—21no—
79#107—21no—
80#107—21no—
81#106—41no—
82#106—41no—
83C4⋊C8—22no—
84C4⋊C8—21no—
85C4⋊C8—41no—
86C4⋊C8—41no—
87C4⋊C8—41no—
88C4⋊C8—41no—
89C22⋊C8—41no—
90C22⋊C8SD1612yes—
91#97—21no—
92#97—41no—
93C4×C8—21no—
94C4×C8—21no—
95C4×C8C2×D411yescharacteristic
96C4×C8C2×D411yescharacteristic
97C4×C8#4111yescharacteristic
98C4×C8#4111yescharacteristic
99C22×C4—41no—
100C22×C4—41no—
101C22×C4C22⋊Q811yescharacteristic
102C22×C4C2×SD1611yescharacteristic
103C22×C4AGL(1,ℤ/8)11yescharacteristic
104M16—22no—
105M16—41no—
106M16—81no—
107M16—81no—
108C2×C8—21no—
109C2×C8—21no—
110C2×C8—22no—
111C2×C8—41no—
112C2×C8—41no—
113C2×C8—42no—
114C2×C8—81no—
115C2×C8—81no—
116C2×C8—81no—
117C2×C8—81no—
118C2×C8#12111yescharacteristic
119C2×C8C22⋊Q811yescharacteristic
120C2×C8C22⋊Q811yescharacteristic
121C2×C8#12611yescharacteristic
122C4⋊C4—41no—
123C4⋊C4—41no—
124C4⋊C4—41no—
125C4⋊C4—41no—
126C4⋊C4—81no—
127C4⋊C4—81no—
128C4⋊C4—81no—
129C4⋊C4—81no—
130C42#12111yescharacteristic
131C42#12111yescharacteristic
132C42#13511yescharacteristic
133C42AGL(1,ℤ/8)11yescharacteristic
134C16—41no—
135C16—41no—
136C16—81no—
137C23#47611yescharacteristic
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—81no—
144C2×C4—81no—
145C2×C4—81no—
146C2×C4—81no—
147C2×C4—161no—
148C2×C4#39611yescharacteristic
149C2×C4#46011yescharacteristic
150C2×C4#46311yescharacteristic
151C2×C4#46511yescharacteristic
152C2×C4#46911yescharacteristic
153C2×C4#47811yescharacteristic
154C8—21no—
155C8—21no—
156C8—21no—
157C8—42no—
158C8—42no—
159C8—82no—
160C8—161no—
161C8—161no—
162C8#47111yescharacteristic
163C8#47311yescharacteristic
164C22—21no—
165C22—21no—
166C22#206511yescharacteristic
167C22#223011yescharacteristic
168C22#223111yescharacteristic
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—161no—
175C4—161no—
176C4#206411yescharacteristic
177C4#207011yescharacteristic
178C2—21no—
179C2—21no—
180C2#1060811yescharacteristic
181C2#1346711yescharacteristic
182C2#1346811yescharacteristic
subgroupG/H
center, socleC22#2065
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#476
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×M16 ◁ 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
#120282
#120162
#119692
C2×#13632
#97882
#96232
#72432