Finite Group Databasebeta

← #124805

Subgroups — #124805

Order 512.

277 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 277 conjugacy classes of subgroups — too many to draw. Only its 78 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#21717C211yesmaximal, characteristic
2#12897C211yesmaximal, characteristic
3#12660C211yesmaximal, characteristic
4#7124C212yesmaximal
5#7124C212yesmaximal
6C2×#446—21no—
7#2399C411yescharacteristic
8C2×#364—21no—
9C2×#347—21no—
10#1984—21no—
11#1940C2211yescharacteristic
12#1940C2211yescharacteristic
13#1939—21no—
14#1843C411yescharacteristic
15#1771—21no—
16#1770C411yescharacteristic
17C8×C4⋊C4C411yescharacteristic
18#1726C2211yescharacteristic
19#1377C2212yes—
20#1377C2212yes—
21#1376—21no—
22#1375—21no—
23C2×C4×Q8—21no—
24C2×M32—22no—
25C2×M32—22no—
26#446—44no—
27C2×C4⋊C8—21no—
28C2×C4⋊C8—21no—
29C2×C4⋊C8—21no—
30C2×C4⋊C8—21no—
31C2×C4⋊C8C2×C411yescharacteristic
32C2×C4⋊C8C2×C411yescharacteristic
33C2×#97—21no—
34C2×#97D411yescharacteristic
35C2×#97D411yescharacteristic
36C2×#97C2311yescharacteristic
37C2×C4×C8—21no—
38C2×C4×C8C2×C411yescharacteristic
39C2×C4×C8D411yescharacteristic
40C2×C4×C8D411yescharacteristic
41#398—21no—
42#398—21no—
43#395—21no—
44#395—21no—
45C4×C4⋊C4—21no—
46C4×C4⋊C4C2×C411yescharacteristic
47C4×C4⋊C4C2×C411yescharacteristic
48#376C2×C411yescharacteristic
49#364—24no—
50#347—42no—
51#336—21no—
52#336—21no—
53#336—21no—
54#336—21no—
55C22×Q8—21no—
56C22×C8—21no—
57C22×C8—21no—
58C22×C8C22⋊C411yescharacteristic
59C22×C8C22⋊C411yescharacteristic
60C22×C8C2×D411yescharacteristic
61C22×C8C2×D411yescharacteristic
62C4×Q8—42no—
63C4×Q8—42no—
64C2×C4⋊C4—21no—
65C2×C4⋊C4—21no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4—21no—
68C2×C4⋊C4—21no—
69C2×C4⋊C4—21no—
70C2×C4⋊C4—21no—
71C2×C42—21no—
72C2×C42—21no—
73C2×C42C22⋊C411yescharacteristic
74C2×C42C22⋊C411yescharacteristic
75C2×C42C22×C411yescharacteristic
76M32—24no—
77M32—42no—
78M32—42no—
79M32—42no—
80C2×C16—42no—
81C2×C16—42no—
82C4⋊C8—41no—
83C4⋊C8—41no—
84C4⋊C8—42no—
85C4⋊C8—42no—
86C4⋊C8—42no—
87C4⋊C8—42no—
88#97—22no—
89#97—41no—
90#97—42no—
91#97SD1612yes—
92#97Q1612yes—
93C4×C8—22no—
94C4×C8—22no—
95C4×C8—41no—
96C4×C8—42no—
97#95—21no—
98#95—21no—
99#95—21no—
100#95—21no—
101#95M1611yescharacteristic
102#95M1611yescharacteristic
103#95M1611yescharacteristic
104#95M1611yescharacteristic
105C2×Q8—42no—
106C2×Q8—42no—
107C2×Q8—81no—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4C2×C22⋊C411yescharacteristic
115C22×C4C2×M1611yescharacteristic
116C22×C4C2×M1611yescharacteristic
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—41no—
126C2×C8—41no—
127C2×C8—41no—
128C2×C8—41no—
129C2×C8—41no—
130C2×C8—41no—
131C2×C8#10112yes—
132C2×C8#10312yes—
133C2×C8C2×SD1611yescharacteristic
134C2×C8C2×Q1611yescharacteristic
135C2×C8AGL(1,ℤ/8)12yes—
136C4⋊C4—42no—
137C4⋊C4—42no—
138C4⋊C4—42no—
139C4⋊C4—42no—
140C4⋊C4—42no—
141C4⋊C4—81no—
142C4⋊C4—81no—
143C42—21no—
144C42—21no—
145C42—21no—
146C42—21no—
147C42—41no—
148C42—41no—
149C42—41no—
150C42—41no—
151C42#10312yes—
152C42#10412yes—
153C16—44no—
154C16—82no—
155C23#40711yescharacteristic
156Q8—84no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4#41011yescharacteristic
180C2×C4C2×#10111yescharacteristic
181C2×C4C2×#10311yescharacteristic
182C2×C4#41811yescharacteristic
183C2×C4C2×#10411yescharacteristic
184C2×C4#42111yescharacteristic
185C8—22no—
186C8—21no—
187C8—21no—
188C8—22no—
189C8—22no—
190C8—81no—
191C8—81no—
192C22—21no—
193C22—21no—
194C22#146711yescharacteristic
195C22#148711yescharacteristic
196C22#149011yescharacteristic
197C4—42no—
198C4—42no—
199C4—42no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—81no—
204C4—81no—
205C4#150311yescharacteristic
206C4#151411yescharacteristic
207C4#153111yescharacteristic
208C4#154911yescharacteristic
209C2—21no—
210C2—21no—
211C2#762211yescharacteristic
212C2#1153911yescharacteristic
213C2#1154011yescharacteristic
subgroupG/H
centerC2×C4#410
commutatorC2×C42C22×C4
Frattini, cosocleC2×#97C23
socleC22#1467
prime radicalC23#407
LCSG ▷ C2×C42 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1726 ◁ G
LECSG ▷ C2×#97 ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#217172
#128972
#126602
#71242