Finite Group Databasebeta

← #125461

Subgroups — #125461

Order 512.

246 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 64 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#33276C211yesmaximal, characteristic
2#12881C211yesmaximal, characteristic
3#8140C211yesmaximal, characteristic
4#7127C211yesmaximal, characteristic
5#7126C211yesmaximal, characteristic
6#7111C211yesmaximal, characteristic
7#7111C211yesmaximal, characteristic
8#2645—21no—
9C2×#364—21no—
10#1971C411yescharacteristic
11#1971C2211yescharacteristic
12#1969C411yescharacteristic
13#1944C2211yescharacteristic
14#1943C411yescharacteristic
15#1941C411yescharacteristic
16#1935—21no—
17#1933—21no—
18#1933—21no—
19#1726C2211yescharacteristic
20#1452—21no—
21#1377C2211yescharacteristic
22#1377C2211yescharacteristic
23#1375—21no—
24#1275C2211yescharacteristic
25#1275C2211yescharacteristic
26#1274—21no—
27C22×Q16C2×C411yescharacteristic
28C2×M32—21no—
29C2×M32—21no—
30#431—21no—
31#431—21no—
32C2×#107C2×C411yescharacteristic
33C2×#106C2×C411yescharacteristic
34C2×#106C2×C411yescharacteristic
35C2×#103—21no—
36C2×#103—21no—
37C2×#103—21no—
38C2×#97C2×C411yescharacteristic
39C2×#97D411yescharacteristic
40C2×#97C2311yescharacteristic
41C2×C4×C8C2×C411yescharacteristic
42C2×C4×C8D411yescharacteristic
43C2×C4×C8D411yescharacteristic
44#401—41no—
45#400—41no—
46#400—41no—
47#400—41no—
48#391—21no—
49#391—21no—
50#391—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#376D411yescharacteristic
55#364—42no—
56#340—21no—
57#340—21no—
58#340—21no—
59#322—24no—
60C22×Q8—21no—
61C2×Q16—22no—
62C2×Q16—41no—
63C2×Q16—41no—
64C22×C8C22⋊C411yescharacteristic
65C22×C8C22⋊C411yescharacteristic
66C22×C8C22×C411yescharacteristic
67C22×C8C2×D411yescharacteristic
68C2×C4⋊C4—21no—
69C2×C4⋊C4—21no—
70C2×C4⋊C4—21no—
71C2×C4⋊C4—41no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4—41no—
74C2×C42C22⋊C411yescharacteristic
75C2×C42C22⋊C411yescharacteristic
76C2×C42C2×D411yescharacteristic
77M32—41no—
78M32—41no—
79M32—41no—
80M32—41no—
81C2×C16—41no—
82C2×C16—41no—
83#107—41no—
84#106—22no—
85#106—41no—
86C4⋊C8—41no—
87C4⋊C8—41no—
88#103—42no—
89#103—42no—
90#103—41no—
91#103—41no—
92C22⋊C8—41no—
93C22⋊C8—41no—
94#97—41no—
95#97—41no—
96#97—41no—
97C4×C8—22no—
98C4×C8—22no—
99C4×C8—21no—
100C4×C8—21no—
101C4×C8—22no—
102C4×C8—22no—
103#95—21no—
104#95—21no—
105#95—41no—
106#95—41no—
107#95—41no—
108#95—41no—
109#95—41no—
110#95—41no—
111#95—41no—
112#95—41no—
113#95—41no—
114C2×Q8—41no—
115C2×Q8—41no—
116C2×Q8—41no—
117C2×Q8—41no—
118C2×Q8—41no—
119C2×Q8—41no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—41no—
123C22×C4—41no—
124C22×C4—41no—
125C22×C4—41no—
126C22×C4C2×C22⋊C411yescharacteristic
127C22×C4AGL(1,ℤ/8)11yescharacteristic
128C22×C4AGL(1,ℤ/8)11yescharacteristic
129Q16—82no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—42no—
140C2×C8—42no—
141C2×C8#10412yes—
142C2×C8#13112yes—
143C2×C8AGL(1,ℤ/8)11yescharacteristic
144C2×C8#13711yescharacteristic
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—161no—
152C4⋊C4—161no—
153C4⋊C4—161no—
154C42—21no—
155C42—21no—
156C42—21no—
157C42—21no—
158C42—21no—
159C42—21no—
160C16—81no—
161C16—81no—
162C23#41811yescharacteristic
163Q8—81no—
164Q8—81no—
165Q8—81no—
166Q8—81no—
167C2×C4—21no—
168C2×C4—21no—
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—81no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—81no—
183C2×C4—81no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4#40811yescharacteristic
190C2×C4#41011yescharacteristic
191C2×C4#41311yescharacteristic
192C2×C4#41711yescharacteristic
193C2×C4C2×#10411yescharacteristic
194C2×C4#42111yescharacteristic
195C8—22no—
196C8—22no—
197C8—21no—
198C8—21no—
199C8—41no—
200C8—82no—
201C8—82no—
202C22—21no—
203C22—21no—
204C22#149611yescharacteristic
205C22#150511yescharacteristic
206C22#155711yescharacteristic
207C4—41no—
208C4—41no—
209C4—81no—
210C4—81no—
211C4—161no—
212C4—161no—
213C4—161no—
214C4—161no—
215C4#147311yescharacteristic
216C4#148311yescharacteristic
217C4#151211yescharacteristic
218C4#152911yescharacteristic
219C2—21no—
220C2—21no—
221C2#770611yescharacteristic
222C2#1176911yescharacteristic
223C2#1177111yescharacteristic
subgroupG/H
center, socleC22#1505
commutatorC22×C8C22×C4
Frattini, cosocleC2×#97C23
prime radicalC23#418
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ #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
#332762
#128812
#81402
#71272
#71262
#71112