Finite Group Databasebeta

← #103149

Subgroups — #103149

Order 512.

456 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 126 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#29218C212yesmaximal
3#9896C212yesmaximal
4#9637C211yesmaximal, characteristic
5#7015C211yesmaximal, characteristic
6#2868C2212yes—
7C4×C4⋊Q8C2211yescharacteristic
8#2100—24no—
9#1990—24no—
10#1990—22no—
11#1987—24no—
12#1842C2211yescharacteristic
13#1834—22no—
14#1834—22no—
15C4×C4⋊C8C2212yes—
16C42×C8C2211yescharacteristic
17C2×Q8⋊C8—22no—
18#1296—24no—
19C2×C4⋊Q8—22no—
20C2×C4⋊Q8—22no—
21C2×C4⋊Q8—22no—
22C2×C4⋊Q8D411yescharacteristic
23C2×C4×Q8—21no—
24C2×C4⋊C8—22no—
25C2×C4⋊C8—21no—
26C2×C4⋊C8D414yes—
27C2×C4×C8—22no—
28C2×C4×C8—22no—
29C2×C4×C8D412yes—
30#391—21no—
31#389—22no—
32#384—22no—
33#384—22no—
34#384—22no—
35#384D411yescharacteristic
36#384D414yes—
37C4×C4⋊C4—22no—
38C43C2311yescharacteristic
39#340—28no—
40#340—28no—
41#340—28no—
42#336—22no—
43Q8⋊C8—44no—
44C22×Q8—21no—
45C22×Q8—42no—
46C22×C8—22no—
47C22×C8—24no—
48C22×C8—41no—
49C4⋊Q8—21no—
50C4⋊Q8—22no—
51C4⋊Q8—48no—
52C4⋊Q8—44no—
53C4⋊Q8—44no—
54C4⋊Q8—84no—
55C4⋊Q8Q1612yes—
56C4×Q8—42no—
57C4×Q8—42no—
58C2×C4⋊C4—22no—
59C2×C4⋊C4—24no—
60C2×C4⋊C4—24no—
61C2×C4⋊C4—22no—
62C2×C4⋊C4—21no—
63C2×C4⋊C4—24no—
64C2×C4⋊C4—41no—
65C2×C4⋊C4—42no—
66C2×C4⋊C4—42no—
67C2×C4⋊C4—42no—
68C2×C42—41no—
69C2×C42C2×D412yes—
70C2×C42C2×D411yescharacteristic
71C2×C42C2×D411yescharacteristic
72C2×C42C2×D412yes—
73C2×C42#4111yescharacteristic
74C4⋊C8—24no—
75C4⋊C8—24no—
76C4⋊C8—42no—
77C4⋊C8—44no—
78C4×C8—22no—
79C4×C8—44no—
80C4×C8—42no—
81C4×C8—42no—
82C4×C8SD1614yes—
83#95—42no—
84C2×Q8—22no—
85C2×Q8—41no—
86C2×Q8—42no—
87C2×Q8—42no—
88C2×Q8—84no—
89C2×Q8—84no—
90C2×Q8—84no—
91C22×C4—41no—
92C22×C4—41no—
93C22×C4—44no—
94C22×C4#12011yescharacteristic
95C22×C4#12012yes—
96C22×C4#12112yes—
97C22×C4#12111yescharacteristic
98C22×C4#12711yescharacteristic
99C2×C8—24no—
100C2×C8—44no—
101C2×C8—44no—
102C2×C8—44no—
103C2×C8—44no—
104C2×C8—81no—
105C2×C8—82no—
106C4⋊C4—24no—
107C4⋊C4—48no—
108C4⋊C4—42no—
109C4⋊C4—48no—
110C4⋊C4—44no—
111C4⋊C4—42no—
112C4⋊C4—84no—
113C4⋊C4—82no—
114C4⋊C4—84no—
115C4⋊C4—84no—
116C4⋊C4—82no—
117C4⋊C4—82no—
118C42—24no—
119C42—22no—
120C42—81no—
121C42—81no—
122C42C2×SD1612yes—
123C42C2×Q1611yescharacteristic
124C42#13511yescharacteristic
125C42#13514yes—
126C42#13712yes—
127C42#13712yes—
128C42#13714yes—
129C23#39211yescharacteristic
130Q8—44no—
131Q8—82no—
132Q8—168no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—42no—
137C2×C4—81no—
138C2×C4—81no—
139C2×C4—84no—
140C2×C4—82no—
141C2×C4—81no—
142C2×C4—84no—
143C2×C4—84no—
144C2×C4#44812yes—
145C2×C4#45112yes—
146C2×C4#45214yes—
147C2×C4#45212yes—
148C2×C4#45414yes—
149C2×C4#46112yes—
150C2×C4#46414yes—
151C2×C4#46711yescharacteristic
152C2×C4#47011yescharacteristic
153C2×C4#47212yes—
154C2×C4#49211yescharacteristic
155C2×C4#49512yes—
156C2×C4#49712yes—
157C2×C4#49711yescharacteristic
158C8—44no—
159C8—84no—
160C8—161no—
161C22#200111yescharacteristic
162C22#200312yes—
163C22#201311yescharacteristic
164C22#201512yes—
165C22#201811yescharacteristic
166C4—22no—
167C4—24no—
168C4—82no—
169C4—161no—
170C4—164no—
171C4#163614yes—
172C4#163814yes—
173C4#167512yes—
174C4#169512yes—
175C4#170811yescharacteristic
176C4#171611yescharacteristic
177C4#171812yes—
178C2#1006112yes—
179C2#1014912yes—
180C2#1027811yescharacteristic
181C2#1028511yescharacteristic
182C2#1031711yescharacteristic
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
#292182
#98962
#96372
#70152