Finite Group Databasebeta

← #100120

Subgroups — #100120

Order 512.

374 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 88 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#23266C211yesmaximal, characteristic
2#21657C211yesmaximal, characteristic
3#7602C211yesmaximal, characteristic
4#7591C212yesmaximal
5#7030C212yesmaximal
6C2×#491C411yescharacteristic
7C4×C4⋊Q8C2211yescharacteristic
8C4×#125C2211yescharacteristic
9#1992C411yescharacteristic
10#1960C411yescharacteristic
11#1933—22no—
12#1917—22no—
13#1916—22no—
14#1836C411yescharacteristic
15#1831C2212yes—
16#1771—22no—
17#1763—22no—
18#1744C2212yes—
19C4×#97C2211yescharacteristic
20#1271—22no—
21#1271—22no—
22#1271—22no—
23C2×C4⋊Q8C2×C411yescharacteristic
24C2×#125C2×C411yescharacteristic
25C2×C4×Q8—21no—
26#491—22no—
27#491—22no—
28C2×C4⋊C8—22no—
29C2×C4⋊C8—22no—
30C2×#103—22no—
31C2×#103—22no—
32C2×#97—22no—
33C2×#97—21no—
34C2×#97C2×C411yescharacteristic
35C2×#97C2×C411yescharacteristic
36C2×C4×C8—22no—
37C2×C4×C8—21no—
38#391—21no—
39#389—22no—
40#389D412yes—
41#387—22no—
42#384C2×C411yescharacteristic
43#382C2×C411yescharacteristic
44C4×C4⋊C4—22no—
45C4×C4⋊C4—22no—
46C4×C4⋊C4D412yes—
47C43C2311yescharacteristic
48#340—22no—
49#340—22no—
50#336—22no—
51#336—22no—
52#336—22no—
53#336—22no—
54#336—22no—
55#336D412yes—
56#336D412yes—
57C22×Q8—21no—
58C22×C8—21no—
59C22×C8—21no—
60C22×C8—22no—
61C22×C8—22no—
62C22×C8—42no—
63C4⋊Q8—21no—
64C4⋊Q8—22no—
65C4⋊Q8M1612yes—
66#125—21no—
67#125—21no—
68#125—22no—
69C4×Q8—44no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—22no—
73C2×C4⋊C4—21no—
74C2×C4⋊C4—22no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4C22⋊C412yes—
77C2×C4⋊C4C22⋊C412yes—
78C2×C42—22no—
79C2×C42—41no—
80C2×C42C22×C411yescharacteristic
81C2×C42C2×D411yescharacteristic
82C2×C42C2×D411yescharacteristic
83C2×C42C2×D412yes—
84C2×C42#4112yes—
85C4⋊C8—44no—
86C4⋊C8—82no—
87#103—28no—
88#103—44no—
89#97—21no—
90#97—22no—
91#97—42no—
92#97—44no—
93#97M1612yes—
94C4×C8—44no—
95C4×C8—42no—
96#95—22no—
97#95—22no—
98#95—22no—
99#95—42no—
100C2×Q8—22no—
101C2×Q8—42no—
102C2×Q8—42no—
103C2×Q8—41no—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—41no—
107C22×C4—41no—
108C22×C4C2×C22⋊C411yescharacteristic
109C22×C4C4×D412yes—
110C22×C4#12011yescharacteristic
111C22×C4#12112yes—
112C22×C4#12311yescharacteristic
113C2×C8—24no—
114C2×C8—22no—
115C2×C8—22no—
116C2×C8—41no—
117C2×C8—41no—
118C2×C8—41no—
119C2×C8—42no—
120C2×C8—41no—
121C2×C8—42no—
122C2×C8—42no—
123C2×C8—42no—
124C2×C8—42no—
125C2×C8—82no—
126C2×C8—82no—
127C2×C8—82no—
128C4⋊C4—22no—
129C4⋊C4—22no—
130C4⋊C4—24no—
131C4⋊C4—42no—
132C4⋊C4—42no—
133C4⋊C4—42no—
134C4⋊C4—42no—
135C4⋊C4—42no—
136C4⋊C4—42no—
137C4⋊C4—42no—
138C4⋊C4—82no—
139C4⋊C4—82no—
140C42—22no—
141C42—22no—
142C42—22no—
143C42—41no—
144C42—42no—
145C42—42no—
146C42—42no—
147C42—82no—
148C42C2×M1611yescharacteristic
149C42C2×M1611yescharacteristic
150C42#13112yes—
151C23#38611yescharacteristic
152Q8—44no—
153Q8—82no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4—81no—
173C2×C4—82no—
174C2×C4#40711yescharacteristic
175C2×C4#40811yescharacteristic
176C2×C4#43512yes—
177C2×C4#43612yes—
178C2×C4#45412yes—
179C2×C4#47112yes—
180C2×C4#47312yes—
181C8—42no—
182C8—42no—
183C8—44no—
184C8—82no—
185C8—162no—
186C22#187011yescharacteristic
187C22#188411yescharacteristic
188C22#188811yescharacteristic
189C22#190612yes—
190C22#190812yes—
191C4—21no—
192C4—21no—
193C4—22no—
194C4—22no—
195C4—22no—
196C4—22no—
197C4—22no—
198C4—41no—
199C4—82no—
200C4—82no—
201C4—82no—
202C4—161no—
203C2#896411yescharacteristic
204C2#909812yes—
205C2#943112yes—
206C2#943611yescharacteristic
207C2#944211yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C22 ▷ 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
#232662
#216572
#76022
#75912
#70302