Finite Group Databasebeta

← #104931

Subgroups — #104931

Order 512.

296 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 76 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#32850C211yesmaximal, characteristic
2#9902C212yesmaximal
3#9891C212yesmaximal
4#8786C211yesmaximal, characteristic
5#7049C211yesmaximal, characteristic
6#2859C2212yes—
7#2100—22no—
8#2087—22no—
9#2083—22no—
10#1842C2211yescharacteristic
11#1831C2211yescharacteristic
12#1767C2212yes—
13C4×#97C2211yescharacteristic
14#1296—22no—
15#1296—22no—
16#1295—22no—
17#1295—22no—
18#1277—22no—
19C2×#125—22no—
20C2×#107—22no—
21C2×C4⋊C8—22no—
22C2×C4⋊C8—22no—
23C2×C4⋊C8—21no—
24C2×C4⋊C8D412yes—
25C2×#97—22no—
26C2×#97—21no—
27C2×#97D411yescharacteristic
28C2×#97D411yescharacteristic
29C2×C4×C8—21no—
30#389—22no—
31#389—22no—
32#389—22no—
33#389—22no—
34#384D412yes—
35#384D412yes—
36#382—22no—
37C43C2311yescharacteristic
38#340—24no—
39#340—22no—
40#336—22no—
41#336—22no—
42C22×C8—21no—
43C22×C8—21no—
44C22×C8—22no—
45C22×C8—42no—
46C22×C8—41no—
47#125—84no—
48C2×C4⋊C4—22no—
49C2×C4⋊C4—22no—
50C2×C4⋊C4—22no—
51C2×C4⋊C4—22no—
52C2×C4⋊C4—22no—
53C2×C4⋊C4—22no—
54C2×C4⋊C4—42no—
55C2×C4⋊C4—42no—
56C2×C42C2×D412yes—
57C2×C42C2×D411yescharacteristic
58C2×C42C2×D411yescharacteristic
59C2×C42#4111yescharacteristic
60C2×C42#4112yes—
61#107—82no—
62C4⋊C8—24no—
63C4⋊C8—42no—
64C4⋊C8—42no—
65C4⋊C8—42no—
66C4⋊C8—44no—
67#97—21no—
68#97—22no—
69#97—42no—
70#97—42no—
71#97—42no—
72#97Q1612yes—
73C4×C8—41no—
74C4×C8—41no—
75#95—42no—
76#95—42no—
77C22×C4—42no—
78C22×C4—42no—
79C22×C4#12011yescharacteristic
80C22×C4#12112yes—
81C22×C4#12111yescharacteristic
82C22×C4#12312yes—
83C22×C4#12411yescharacteristic
84C2×C8—22no—
85C2×C8—22no—
86C2×C8—41no—
87C2×C8—41no—
88C2×C8—41no—
89C2×C8—41no—
90C2×C8—44no—
91C2×C8—42no—
92C2×C8—42no—
93C2×C8—42no—
94C2×C8—82no—
95C2×C8—82no—
96C2×C8—81no—
97C2×C8—82no—
98C4⋊C4—42no—
99C4⋊C4—42no—
100C4⋊C4—42no—
101C4⋊C4—42no—
102C4⋊C4—82no—
103C4⋊C4—82no—
104C4⋊C4—82no—
105C4⋊C4—82no—
106C4⋊C4—84no—
107C4⋊C4—84no—
108C42—21no—
109C42—22no—
110C42—21no—
111C42—22no—
112C42—41no—
113C42—42no—
114C42C2×Q1611yescharacteristic
115C42#13511yescharacteristic
116C42#13712yes—
117C23#39411yescharacteristic
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—22no—
121C2×C4—21no—
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—21no—
127C2×C4—82no—
128C2×C4—82no—
129C2×C4—82no—
130C2×C4—82no—
131C2×C4—82no—
132C2×C4—82no—
133C2×C4#45411yescharacteristic
134C2×C4#45412yes—
135C2×C4#45511yescharacteristic
136C2×C4#45612yes—
137C2×C4#46212yes—
138C2×C4#46412yes—
139C2×C4#46711yescharacteristic
140C2×C4#47011yescharacteristic
141C8—42no—
142C8—42no—
143C8—84no—
144C8—82no—
145C8—161no—
146C22#203812yes—
147C22#204011yescharacteristic
148C22#204812yes—
149C22#205011yescharacteristic
150C22#205611yescharacteristic
151C4—22no—
152C4—22no—
153C4—21no—
154C4—21no—
155C4—42no—
156C4—41no—
157C4—162no—
158C4—162no—
159C4#165811yescharacteristic
160C4#166311yescharacteristic
161C4#166412yes—
162C2#1042811yescharacteristic
163C2#1049712yes—
164C2#1050612yes—
165C2#1052311yescharacteristic
166C2#1052511yescharacteristic
subgroupG/H
center, socle, prime radicalC23#394
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
#328502
#99022
#98912
#87862
#70492