Finite Group Databasebeta

← #101877

Subgroups — #101877

Order 512.

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

normal subgroups only

This group has 366 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#27975C211yesmaximal, characteristic
2#21918C211yesmaximal, characteristic
3#8722C211yesmaximal, characteristic
4#7708C212yesmaximal
5#7021C212yesmaximal
6#2857C2211yescharacteristic
7#2285C2211yescharacteristic
8#2074—22no—
9#1956C412yes—
10#1917—22no—
11#1916—22no—
12#1873—21no—
13#1873—21no—
14#1834C412yes—
15#1817C2212yes—
16#1798—21no—
17#1750—21no—
18#1749C2212yes—
19C4×C22⋊C8C2211yescharacteristic
20#1295—22no—
21#1271—22no—
22#1271—22no—
23C2×C4⋊Q8C2×C411yescharacteristic
24C2×C22⋊Q8—21no—
25C2×#117D411yescharacteristic
26C2×#117D411yescharacteristic
27C22×C42C2311yescharacteristic
28C2×C4⋊C8—22no—
29C2×#103—22no—
30C2×#103—22no—
31C2×C22⋊C8—22no—
32C2×C22⋊C8—22no—
33C2×C22⋊C8—21no—
34C2×#97—22no—
35C2×#97—21no—
36C2×C4×C8—21no—
37C2×C4×C8C2×C412yes—
38#391—21no—
39#389—22no—
40#384C2×C411yescharacteristic
41#384C2×C412yes—
42#382D412yes—
43#380—22no—
44#380—22no—
45C4×C4⋊C4—22no—
46#340—22no—
47#340—22no—
48#336—21no—
49#336—21no—
50#336—22no—
51#336—22no—
52#336—21no—
53#336—22no—
54#336D412yes—
55#336D412yes—
56C22×Q8—21no—
57C23×C4C2×D411yescharacteristic
58C23×C4#4112yes—
59C22×C8—22no—
60C22×C8—22no—
61C22×C8—22no—
62C22×C8—42no—
63C4⋊Q8—42no—
64C22⋊Q8—44no—
65#117—81no—
66#117—81no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—21no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4C22⋊C412yes—
74C2×C4⋊C4C22⋊C412yes—
75C2×C22⋊C4—21no—
76C2×C22⋊C4—21no—
77C2×C22⋊C4—41no—
78C2×C42—21no—
79C2×C42—21no—
80C2×C42—42no—
81C2×C42C22×C411yescharacteristic
82C2×C42C2×D411yescharacteristic
83C2×C42C2×D412yes—
84C4⋊C8—82no—
85#103—82no—
86#103—82no—
87C22⋊C8—24no—
88C22⋊C8—42no—
89C22⋊C8—44no—
90C22⋊C8—42no—
91#97—44no—
92#97—81no—
93C4×C8—42no—
94C4×C8—81no—
95#95—24no—
96#95—42no—
97C24#12311yescharacteristic
98C2×Q8—42no—
99C2×Q8—42no—
100C2×Q8—42no—
101C22×C4—22no—
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—22no—
107C22×C4—41no—
108C22×C4—42no—
109C22×C4—42no—
110C22×C4—41no—
111C22×C4—41no—
112C22×C4C2×C22⋊C411yescharacteristic
113C22×C4C4×D412yes—
114C22×C4#12011yescharacteristic
115C22×C4#12112yes—
116C2×C8—42no—
117C2×C8—42no—
118C2×C8—44no—
119C2×C8—42no—
120C2×C8—42no—
121C2×C8—42no—
122C2×C8—42no—
123C2×C8—42no—
124C2×C8—42no—
125C2×C8—42no—
126C2×C8—82no—
127C2×C8—82no—
128C4⋊C4—42no—
129C4⋊C4—42no—
130C4⋊C4—42no—
131C4⋊C4—42no—
132C4⋊C4—42no—
133C4⋊C4—42no—
134C4⋊C4—42no—
135C4⋊C4—82no—
136C4⋊C4—82no—
137C4⋊C4—82no—
138C22⋊C4—81no—
139C22⋊C4—81no—
140C22⋊C4—82no—
141C42—22no—
142C42—22no—
143C42—42no—
144C42—41no—
145C42—41no—
146C42—42no—
147C23—22no—
148C23—21no—
149C23—21no—
150C23—22no—
151C23—21no—
152C23#38611yescharacteristic
153Q8—84no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—44no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—82no—
171C2×C4—82no—
172C2×C4—82no—
173C2×C4—81no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4—81no—
177C2×C4#41012yes—
178C2×C4#44312yes—
179C2×C4#44412yes—
180C2×C4#45412yes—
181C8—82no—
182C8—82no—
183C8—82no—
184C8—84no—
185C22—42no—
186C22—42no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22#187612yes—
191C22#188811yescharacteristic
192C22#189911yescharacteristic
193C22#190212yes—
194C22#191111yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—22no—
199C4—42no—
200C4—82no—
201C4—82no—
202C4—161no—
203C4—161no—
204C2—81no—
205C2#907011yescharacteristic
206C2#924012yes—
207C2#928512yes—
208C2#942211yescharacteristic
209C2#946511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#279752
#219182
#87222
#77082
#70212