Finite Group Databasebeta

← #102784

Subgroups — #102784

Order 512.

405 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 405 conjugacy classes of subgroups — too many to draw. Only its 74 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#32848C211yesmaximal, characteristic
2#29319C212yesmaximal
3#9891C212yesmaximal
4#9647C211yesmaximal, characteristic
5#7042C211yesmaximal, characteristic
6#2859C2212yes—
7C4×C4⋊Q8C2211yescharacteristic
8#2099—22no—
9#2086—22no—
10#2084—22no—
11#2083—22no—
12#2057—22no—
13#1948—22no—
14#1947—22no—
15#1943—24no—
16#1831C2211yescharacteristic
17#1767C2212yes—
18C4×#97C2211yescharacteristic
19C2×Q8⋊C8—22no—
20#1295—24no—
21C2×C4⋊Q8D411yescharacteristic
22C2×#125—22no—
23C2×C4×Q8—21no—
24C2×#107—24no—
25C2×#107—22no—
26C2×#106—24no—
27C2×C4⋊C8—22no—
28C2×C4⋊C8D412yes—
29C2×#97—22no—
30C2×#97D414yes—
31C2×C4×C8—21no—
32#391—21no—
33#389—22no—
34#389—22no—
35#389—22no—
36#389—22no—
37#389—22no—
38#384D411yescharacteristic
39#384D412yes—
40#384D412yes—
41#382—22no—
42C4×C4⋊C4—22no—
43C43C2311yescharacteristic
44#340—24no—
45#340—24no—
46#340—24no—
47#340—22no—
48#336—22no—
49#336—22no—
50Q8⋊C8—44no—
51C22×Q8—21no—
52C22×C8—24no—
53C22×C8—22no—
54C22×C8—41no—
55C4⋊Q8—42no—
56#125—84no—
57C4×Q8—42no—
58C4×Q8—42no—
59C2×C4⋊C4—22no—
60C2×C4⋊C4—22no—
61C2×C4⋊C4—22no—
62C2×C4⋊C4—22no—
63C2×C4⋊C4—22no—
64C2×C4⋊C4—22no—
65C2×C4⋊C4—21no—
66C2×C4⋊C4—22no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—42no—
69C2×C4⋊C4—42no—
70C2×C4⋊C4—41no—
71C2×C42—41no—
72C2×C42C2×D412yes—
73C2×C42C2×D411yescharacteristic
74C2×C42C2×D412yes—
75C2×C42C2×D411yescharacteristic
76C2×C42#4111yescharacteristic
77#107—48no—
78#107—82no—
79#106—84no—
80C4⋊C8—28no—
81C4⋊C8—42no—
82#97—24no—
83#97—44no—
84#97—42no—
85C4×C8—22no—
86C4×C8—41no—
87#95—42no—
88#95—42no—
89#95—42no—
90C2×Q8—22no—
91C2×Q8—41no—
92C2×Q8—42no—
93C2×Q8—42no—
94C22×C4—41no—
95C22×C4—41no—
96C22×C4—42no—
97C22×C4—42no—
98C22×C4#12012yes—
99C22×C4#12011yescharacteristic
100C22×C4#12112yes—
101C22×C4#12111yescharacteristic
102C22×C4#12711yescharacteristic
103C2×C8—28no—
104C2×C8—42no—
105C2×C8—44no—
106C2×C8—44no—
107C2×C8—44no—
108C2×C8—42no—
109C2×C8—44no—
110C4⋊C4—24no—
111C4⋊C4—42no—
112C4⋊C4—44no—
113C4⋊C4—42no—
114C4⋊C4—42no—
115C4⋊C4—42no—
116C4⋊C4—42no—
117C4⋊C4—42no—
118C4⋊C4—44no—
119C4⋊C4—42no—
120C4⋊C4—42no—
121C4⋊C4—82no—
122C4⋊C4—82no—
123C4⋊C4—82no—
124C4⋊C4—84no—
125C4⋊C4—84no—
126C42—21no—
127C42—21no—
128C42—22no—
129C42—22no—
130C42—24no—
131C42—22no—
132C42—41no—
133C42—81no—
134C42—81no—
135C23#39211yescharacteristic
136Q8—44no—
137Q8—82no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—21no—
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—42no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4—82no—
151C2×C4—81no—
152C2×C4—82no—
153C2×C4—82no—
154C2×C4—82no—
155C2×C4—82no—
156C2×C4—82no—
157C2×C4—82no—
158C2×C4#45311yescharacteristic
159C2×C4#45411yescharacteristic
160C2×C4#45512yes—
161C2×C4#45612yes—
162C2×C4#45614yes—
163C2×C4#47212yes—
164C8—48no—
165C8—44no—
166C8—82no—
167C22#200512yes—
168C22#200611yescharacteristic
169C22#200712yes—
170C22#201011yescharacteristic
171C22#201811yescharacteristic
172C4—22no—
173C4—22no—
174C4—22no—
175C4—41no—
176C4—42no—
177C4—82no—
178C4—162no—
179C4—161no—
180C4—162no—
181C4#166012yes—
182C4#166312yes—
183C2#1001112yes—
184C2#1002611yescharacteristic
185C2#1008711yescharacteristic
186C2#1011812yes—
187C2#1030211yescharacteristic
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
#328482
#293192
#98912
#96472
#70422