Finite Group Databasebeta

← #103159

Subgroups — #103159

Order 512.

488 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 134 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#33289C211yesmaximal, characteristic
2#29206C212yesmaximal
3#9691C212yesmaximal
4#9637C211yesmaximal, characteristic
5#7015C211yesmaximal, characteristic
6#2868C2212yes—
7C4×C4⋊Q8C2211yescharacteristic
8#2058—24no—
9#1990—24no—
10#1990—22no—
11#1948—24no—
12#1844—22no—
13#1842C2211yescharacteristic
14#1834—22no—
15C4×C4⋊C8C2212yes—
16C42×C8C2211yescharacteristic
17C2×#333—24no—
18C2×Q8⋊C8—22no—
19C2×C4⋊Q8—22no—
20C2×C4⋊Q8—22no—
21C2×C4⋊Q8D411yescharacteristic
22C2×C4⋊Q8D414yes—
23C2×C4×Q8—21no—
24C2×#106—28no—
25C2×C4⋊C8—22no—
26C2×C4⋊C8—21no—
27C2×C4⋊C8D414yes—
28C2×C4×C8—22no—
29C2×C4×C8—22no—
30C2×C4×C8D412yes—
31#391—21no—
32#389—22no—
33#384—22no—
34#384—22no—
35#384—22no—
36#384—22no—
37#384D411yescharacteristic
38C4×C4⋊C4—22no—
39C43C2311yescharacteristic
40#340—28no—
41#340—28no—
42#336—22no—
43#333—48no—
44Q8⋊C8—44no—
45C22×Q8—21no—
46C22×Q8—24no—
47C22×C8—24no—
48C22×C8—22no—
49C22×C8—41no—
50C4⋊Q8—21no—
51C4⋊Q8—22no—
52C4⋊Q8—48no—
53C4⋊Q8—44no—
54C4⋊Q8—44no—
55C4⋊Q8—84no—
56C4⋊Q8Q1612yes—
57C4×Q8—42no—
58C4×Q8—42no—
59C2×C4⋊C4—22no—
60C2×C4⋊C4—24no—
61C2×C4⋊C4—24no—
62C2×C4⋊C4—22no—
63C2×C4⋊C4—21no—
64C2×C4⋊C4—41no—
65C2×C4⋊C4—42no—
66C2×C4⋊C4—42no—
67C2×C4⋊C4—42no—
68C2×C4⋊C4—42no—
69C2×C42—41no—
70C2×C42C2×D412yes—
71C2×C42C2×D411yescharacteristic
72C2×C42C2×D412yes—
73C2×C42C2×D411yescharacteristic
74C2×C42#4111yescharacteristic
75#106—88no—
76C4⋊C8—24no—
77C4⋊C8—42no—
78C4⋊C8—44no—
79C4⋊C8SD1618yes—
80C4×C8—22no—
81C4×C8—44no—
82C4×C8—42no—
83C4×C8—42no—
84C4×C8SD1614yes—
85#95—42no—
86C2×Q8—22no—
87C2×Q8—41no—
88C2×Q8—42no—
89C2×Q8—48no—
90C2×Q8—42no—
91C2×Q8—84no—
92C2×Q8—84no—
93C22×C4—41no—
94C22×C4—41no—
95C22×C4—44no—
96C22×C4#12011yescharacteristic
97C22×C4#12012yes—
98C22×C4#12112yes—
99C22×C4#12111yescharacteristic
100C22×C4#12711yescharacteristic
101C2×C8—24no—
102C2×C8—28no—
103C2×C8—44no—
104C2×C8—44no—
105C2×C8—44no—
106C2×C8—81no—
107C2×C8—82no—
108C4⋊C4—24no—
109C4⋊C4—48no—
110C4⋊C4—42no—
111C4⋊C4—44no—
112C4⋊C4—48no—
113C4⋊C4—42no—
114C4⋊C4—84no—
115C4⋊C4—82no—
116C4⋊C4—84no—
117C4⋊C4—84no—
118C4⋊C4—82no—
119C4⋊C4—82no—
120C42—24no—
121C42—22no—
122C42—81no—
123C42—81no—
124C42C2×SD1612yes—
125C42C2×SD1614yes—
126C42C2×Q1611yescharacteristic
127C42#13511yescharacteristic
128C42#13712yes—
129C42#13714yes—
130C42#13712yes—
131C23#39211yescharacteristic
132Q8—44no—
133Q8—82no—
134Q8—168no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—81no—
140C2×C4—81no—
141C2×C4—84no—
142C2×C4—82no—
143C2×C4—81no—
144C2×C4—84no—
145C2×C4—84no—
146C2×C4#44812yes—
147C2×C4#44814yes—
148C2×C4#45112yes—
149C2×C4#45212yes—
150C2×C4#45514yes—
151C2×C4#46114yes—
152C2×C4#46112yes—
153C2×C4#46711yescharacteristic
154C2×C4#47011yescharacteristic
155C2×C4#47212yes—
156C2×C4#49211yescharacteristic
157C2×C4#49212yes—
158C2×C4#49711yescharacteristic
159C2×C4#49712yes—
160C8—44no—
161C8—48no—
162C8—161no—
163C22#200111yescharacteristic
164C22#200412yes—
165C22#201311yescharacteristic
166C22#201312yes—
167C22#201811yescharacteristic
168C4—22no—
169C4—24no—
170C4—82no—
171C4—161no—
172C4—164no—
173C4#164314yes—
174C4#164514yes—
175C4#167512yes—
176C4#169512yes—
177C4#170511yescharacteristic
178C4#171611yescharacteristic
179C4#171612yes—
180C2#1007312yes—
181C2#1016112yes—
182C2#1027811yescharacteristic
183C2#1028711yescharacteristic
184C2#1031611yescharacteristic
subgroupG/H
center, socle, prime radicalC23#392
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#332892
#292062
#96912
#96372
#70152