Finite Group Databasebeta

← #145875

Subgroups — #145875

Order 512.

285 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 285 conjugacy classes of subgroups — too many to draw. Only its 86 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#28811C211yesmaximal, characteristic
2#13185C211yesmaximal, characteristic
3#12886C211yesmaximal, characteristic
4#9627C211yesmaximal, characteristic
5#7278C211yesmaximal, characteristic
6#7175C211yesmaximal, characteristic
7#7169C211yesmaximal, characteristic
8C2×#499—21no—
9#2552—21no—
10C2×#365—21no—
11#2150C2211yescharacteristic
12C4×M32C2211yescharacteristic
13#2059—22no—
14#1947—21no—
15#1941—21no—
16#1848C2211yescharacteristic
17#1844C2211yescharacteristic
18C4×#106C2211yescharacteristic
19C8×C4⋊C4C2211yescharacteristic
20#1571—21no—
21#1564C2211yescharacteristic
22#1383—22no—
23#1383—21no—
24#1303—21no—
25C2×#125—22no—
26C2×M32—21no—
27C2×M32—21no—
28#499—42no—
29#499—42no—
30#431—21no—
31C2×#108—21no—
32C2×#108—21no—
33C2×#107—22no—
34C2×#106—21no—
35C2×#106D411yescharacteristic
36C2×#106D411yescharacteristic
37C2×#106D412yes—
38#423—21no—
39C2×C4⋊C8D411yescharacteristic
40C2×C4×C8—21no—
41C2×C4×C8C2311yescharacteristic
42#398—42no—
43#389—22no—
44#389—41no—
45#384—21no—
46#384—41no—
47C4×C4⋊C4—21no—
48C4×C4⋊C4D411yescharacteristic
49#365—42no—
50C4⋊C16—21no—
51C4⋊C16Q812yes—
52#346Q812yes—
53C4×C16—21no—
54#340—22no—
55#340—21no—
56#336—21no—
57#335—42no—
58#335Q812yes—
59#334—21no—
60C2×M16—41no—
61C22×C8—21no—
62C22×C8C2×D411yescharacteristic
63C22×C8C2×D411yescharacteristic
64#125—44no—
65#125—82no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4—21no—
68C2×C4⋊C4—21no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—42no—
71C2×C4⋊C4—42no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4—42no—
74C2×C4⋊C4—41no—
75C2×C42—21no—
76C2×C42—41no—
77C2×C42C2×D411yescharacteristic
78M32—41no—
79M32—41no—
80M32—41no—
81M32—41no—
82C2×C16—22no—
83C2×C16—22no—
84#108—42no—
85#108—41no—
86#108—41no—
87#107—44no—
88#106—21no—
89#106—21no—
90#106—41no—
91#106—41no—
92#106—42no—
93#106D812yes—
94#106Q1612yes—
95C4⋊C8—22no—
96C4⋊C8—21no—
97C4⋊C8—41no—
98C4⋊C8—41no—
99C4⋊C8SD1612yes—
100C22⋊C8—41no—
101C4×C8—41no—
102C4×C8—41no—
103C4×C8—41no—
104C4×C8C2×Q811yescharacteristic
105C4×C8C2×Q811yescharacteristic
106C4×C8C2×Q811yescharacteristic
107C4×C8#4111yescharacteristic
108#95—42no—
109#95—41no—
110#95SD1612yes—
111C22×C4—22no—
112C22×C4—41no—
113C22×C4—41no—
114C22×C4—42no—
115C22×C4#12011yescharacteristic
116C22×C4C2×SD1611yescharacteristic
117C22×C4AGL(1,ℤ/8)11yescharacteristic
118M16—81no—
119M16—81no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—22no—
123C2×C8—41no—
124C2×C8—41no—
125C2×C8—42no—
126C2×C8—81no—
127C2×C8C22⋊Q811yescharacteristic
128C2×C8C22⋊Q811yescharacteristic
129C2×C8C4⋊Q811yescharacteristic
130C2×C8C4⋊Q811yescharacteristic
131C2×C8C2×D811yescharacteristic
132C2×C8C2×Q1611yescharacteristic
133C2×C8AGL(1,ℤ/8)11yescharacteristic
134C2×C8#13711yescharacteristic
135C4⋊C4—22no—
136C4⋊C4—22no—
137C4⋊C4—42no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—42no—
141C4⋊C4—42no—
142C4⋊C4—82no—
143C4⋊C4—84no—
144C4⋊C4—84no—
145C4⋊C4—161no—
146C4⋊C4—162no—
147C42—41no—
148C42—41no—
149C42—82no—
150C42C22⋊Q811yescharacteristic
151C42C4⋊Q811yescharacteristic
152C42C2×SD1611yescharacteristic
153C42#13711yescharacteristic
154C16—42no—
155C16—42no—
156C23#45011yescharacteristic
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4—82no—
169C2×C4—82no—
170C2×C4—82no—
171C2×C4#39511yescharacteristic
172C2×C4#44711yescharacteristic
173C2×C4#44811yescharacteristic
174C2×C4#45111yescharacteristic
175C2×C4#45411yescharacteristic
176C2×C4#45511yescharacteristic
177C2×C4#47511yescharacteristic
178C2×C4#47611yescharacteristic
179C2×C4#49811yescharacteristic
180C2×C4#50111yescharacteristic
181C8—21no—
182C8—21no—
183C8—42no—
184C8—82no—
185C8—161no—
186C8#47411yescharacteristic
187C8#47711yescharacteristic
188C8#50011yescharacteristic
189C8#50111yescharacteristic
190C22—21no—
191C22—21no—
192C22#163711yescharacteristic
193C22#163911yescharacteristic
194C22#205811yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—82no—
199C4—82no—
200C4—82no—
201C4—162no—
202C4#162711yescharacteristic
203C4#164511yescharacteristic
204C4#205711yescharacteristic
205C4#206111yescharacteristic
206C4#223112yes—
207C2—21no—
208C2—21no—
209C2#1057511yescharacteristic
210C2#1345811yescharacteristic
211C2#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
#288112
#131852
#128862
#96272
#72782
#71752
#71692