Finite Group Databasebeta

← #145897

Subgroups — #145897

Order 512.

275 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 275 conjugacy classes of subgroups — too many to draw. Only its 82 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#28829C211yesmaximal, characteristic
2#13185C211yesmaximal, characteristic
3#12886C211yesmaximal, characteristic
4#9628C211yesmaximal, characteristic
5#7278C211yesmaximal, characteristic
6#7175C211yesmaximal, characteristic
7#7169C211yesmaximal, characteristic
8#2552—21no—
9C2×#365—21no—
10#2150C2211yescharacteristic
11C4×M32C2211yescharacteristic
12#2084—22no—
13#1948—21no—
14#1941—21no—
15#1848C2211yescharacteristic
16#1844—21no—
17#1844C2211yescharacteristic
18C4×#106C2211yescharacteristic
19C8×C4⋊C4C2211yescharacteristic
20#1570—21no—
21#1564C2211yescharacteristic
22#1383—22no—
23#1383—21no—
24#1303—21no—
25C2×#125—41no—
26C2×M32—21no—
27C2×M32—21no—
28#431—21no—
29C2×#108—21no—
30C2×#108—21no—
31C2×#106—21no—
32C2×#106—22no—
33C2×#106D411yescharacteristic
34C2×#106D411yescharacteristic
35C2×#106D412yes—
36#423—21no—
37C2×C4⋊C8D411yescharacteristic
38C2×C4×C8—21no—
39C2×C4×C8C2311yescharacteristic
40#398—42no—
41#389—22no—
42#389—41no—
43#384—22no—
44#384—21no—
45C4×C4⋊C4—21no—
46C4×C4⋊C4D411yescharacteristic
47#365—42no—
48C4⋊C16—21no—
49C4⋊C16Q812yes—
50#346Q812yes—
51C4×C16—21no—
52#340—22no—
53#340—21no—
54#336—21no—
55#335Q812yes—
56#334—21no—
57#334—42no—
58C2×M16—41no—
59C22×C8—21no—
60C22×C8C2×D411yescharacteristic
61C22×C8C2×D411yescharacteristic
62#125—84no—
63C2×C4⋊C4—21no—
64C2×C4⋊C4—21no—
65C2×C4⋊C4—21no—
66C2×C4⋊C4—22no—
67C2×C4⋊C4—42no—
68C2×C4⋊C4—42no—
69C2×C4⋊C4—41no—
70C2×C4⋊C4—42no—
71C2×C4⋊C4—41no—
72C2×C42—21no—
73C2×C42—41no—
74C2×C42C2×D411yescharacteristic
75M32—41no—
76M32—41no—
77M32—41no—
78M32—41no—
79C2×C16—22no—
80C2×C16—22no—
81#108—42no—
82#108—41no—
83#108—41no—
84#106—21no—
85#106—21no—
86#106—21no—
87#106—21no—
88#106—41no—
89#106—41no—
90#106—42no—
91#106—82no—
92C4⋊C8—22no—
93C4⋊C8—21no—
94C4⋊C8—41no—
95C4⋊C8—41no—
96C4⋊C8SD1612yes—
97C22⋊C8—41no—
98C4×C8—41no—
99C4×C8—41no—
100C4×C8—41no—
101C4×C8C2×Q811yescharacteristic
102C4×C8C2×Q811yescharacteristic
103C4×C8C2×Q811yescharacteristic
104C4×C8#4111yescharacteristic
105#95—42no—
106#95—41no—
107#95SD1612yes—
108C22×C4—22no—
109C22×C4—41no—
110C22×C4—41no—
111C22×C4—42no—
112C22×C4#12011yescharacteristic
113C22×C4C2×SD1611yescharacteristic
114C22×C4AGL(1,ℤ/8)11yescharacteristic
115M16—81no—
116M16—81no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—22no—
120C2×C8—41no—
121C2×C8—41no—
122C2×C8—42no—
123C2×C8—81no—
124C2×C8C22⋊Q811yescharacteristic
125C2×C8C22⋊Q811yescharacteristic
126C2×C8C4⋊Q811yescharacteristic
127C2×C8C4⋊Q811yescharacteristic
128C2×C8#13511yescharacteristic
129C2×C8#13511yescharacteristic
130C2×C8AGL(1,ℤ/8)11yescharacteristic
131C2×C8#13711yescharacteristic
132C4⋊C4—24no—
133C4⋊C4—41no—
134C4⋊C4—42no—
135C4⋊C4—41no—
136C4⋊C4—41no—
137C4⋊C4—42no—
138C4⋊C4—41no—
139C4⋊C4—82no—
140C4⋊C4—84no—
141C4⋊C4—84no—
142C4⋊C4—161no—
143C4⋊C4—162no—
144C42—41no—
145C42—41no—
146C42—82no—
147C42C22⋊Q811yescharacteristic
148C42C4⋊Q811yescharacteristic
149C42C2×SD1611yescharacteristic
150C42#13711yescharacteristic
151C16—42no—
152C16—42no—
153C23#45011yescharacteristic
154C2×C4—22no—
155C2×C4—24no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—82no—
162C2×C4—81no—
163C2×C4—82no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—82no—
168C2×C4#39511yescharacteristic
169C2×C4#44811yescharacteristic
170C2×C4#44911yescharacteristic
171C2×C4#45211yescharacteristic
172C2×C4#45411yescharacteristic
173C2×C4#45511yescharacteristic
174C2×C4#47511yescharacteristic
175C2×C4#47611yescharacteristic
176C2×C4#49811yescharacteristic
177C2×C4#50111yescharacteristic
178C8—21no—
179C8—21no—
180C8—42no—
181C8—82no—
182C8—161no—
183C8#47811yescharacteristic
184C8#47911yescharacteristic
185C8#49911yescharacteristic
186C8#50111yescharacteristic
187C22—21no—
188C22—21no—
189C22#163511yescharacteristic
190C22#164211yescharacteristic
191C22#205811yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—44no—
196C4—161no—
197C4—161no—
198C4—162no—
199C4#162611yescharacteristic
200C4#164311yescharacteristic
201C4#205911yescharacteristic
202C4#206111yescharacteristic
203C4#223012yes—
204C2—21no—
205C2—21no—
206C2#1058211yescharacteristic
207C2#1345711yescharacteristic
208C2#1346011yescharacteristic
subgroupG/H
center, socleC22#2058
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#450
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×C4⋊C4 ◁ 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
#288292
#131852
#128862
#96282
#72782
#71752
#71692