Finite Group Databasebeta

← #141945

Subgroups — #141945

Order 512.

382 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 114 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#21143C211yesmaximal, characteristic
2#12783C211yesmaximal, characteristic
3#12599C211yesmaximal, characteristic
4#7186C214yesmaximal
5C2×#424C412yes—
6C2×#423C411yescharacteristic
7C22×C4×C8C2211yescharacteristic
8#2285C411yescharacteristic
9C2×C4⋊C16—21no—
10C2×C22⋊C16C2212yes—
11C2×C22⋊C16C2212yes—
12C2×#346—21no—
13#1939—21no—
14#1939—21no—
15#1939—21no—
16#1939—21no—
17#1729C2212yes—
18#1374—21no—
19#1374—21no—
20C22×M16C2×C412yes—
21C23×C8C2×C411yescharacteristic
22C23×C8C2311yescharacteristic
23C2×#117C2×C412yes—
24C22×C42C2×C411yescharacteristic
25C22×C16—22no—
26C22×C16—22no—
27#424—44no—
28#423—42no—
29C2×C4⋊C8—22no—
30C2×C4⋊C8—22no—
31C2×C4⋊C8—21no—
32C2×C4⋊C8—21no—
33C2×C4×C8—42no—
34C2×C4×C8D411yescharacteristic
35C2×C4×C8D411yescharacteristic
36C2×C4×C8D411yescharacteristic
37C2×C4×C8D411yescharacteristic
38#384C811yescharacteristic
39#384C811yescharacteristic
40#382C812yes—
41#380—21no—
42#380—21no—
43C4×C4⋊C4—21no—
44C4×C4⋊C4—21no—
45C4⋊C16—42no—
46C22⋊C16—22no—
47C22⋊C16—24no—
48C22⋊C16Q814yes—
49#346—42no—
50#336—22no—
51#336—22no—
52C23×C4M1611yescharacteristic
53C23×C4M1611yescharacteristic
54C23×C4C22×C411yescharacteristic
55C2×M16—24no—
56C2×M16—42no—
57C2×M16—42no—
58C22×C8—22no—
59C22×C8—22no—
60C22×C8—22no—
61C22×C8—41no—
62C22×C8—41no—
63C22×C8—41no—
64C22×C8C22⋊C411yescharacteristic
65C22×C8C22⋊C411yescharacteristic
66C22×C8C2×D411yescharacteristic
67C22×C8C2×D411yescharacteristic
68C22×C8C2×Q812yes—
69C22×C8#4112yes—
70#117—42no—
71#117—42no—
72C2×C4⋊C4—21no—
73C2×C4⋊C4—21no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4—21no—
76C2×C4⋊C4C2×C812yes—
77C2×C4⋊C4C2×C812yes—
78C2×C22⋊C4—22no—
79C2×C42—22no—
80C2×C42—22no—
81C2×C42—22no—
82C2×C42C22⋊C411yescharacteristic
83C2×C42C22⋊C411yescharacteristic
84C2×C42C2×C811yescharacteristic
85C2×C42C2×C811yescharacteristic
86C2×C16—24no—
87C2×C16—42no—
88C2×C16—42no—
89C2×C16—42no—
90C2×C16—42no—
91C2×C16—42no—
92C4⋊C8—42no—
93C4⋊C8—44no—
94C4⋊C8—44no—
95C4⋊C8—42no—
96C4×C8—22no—
97C4×C8—22no—
98C4×C8—41no—
99C4×C8—41no—
100#95—22no—
101#95—22no—
102C24C2×M1611yescharacteristic
103C22×C4—21no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—22no—
108C22×C4—22no—
109C22×C4—22no—
110C22×C4—22no—
111C22×C4—22no—
112C22×C4—41no—
113C22×C4—41no—
114C22×C4—41no—
115C22×C4C22⋊C811yescharacteristic
116C22×C4C22⋊C811yescharacteristic
117C22×C4C22⋊C811yescharacteristic
118C22×C4C22⋊C811yescharacteristic
119C22×C4C2×C22⋊C411yescharacteristic
120C22×C4C4×Q812yes—
121C22×C4C22×C811yescharacteristic
122C22×C4#13112yes—
123M16—84no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—42no—
134C2×C8—42no—
135C2×C8—44no—
136C2×C8—42no—
137C2×C8—42no—
138C2×C8—42no—
139C2×C8#10012yes—
140C2×C8C22⋊Q812yes—
141C2×C8#12411yescharacteristic
142C2×C8C4⋊Q811yescharacteristic
143C4⋊C4—42no—
144C4⋊C4—42no—
145C4⋊C4—42no—
146C4⋊C4—42no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C22⋊C4—44no—
150C42—22no—
151C42—22no—
152C42—21no—
153C42—21no—
154C42—42no—
155C42—42no—
156C42#9912yes—
157C42#10112yes—
158C16—44no—
159C16—82no—
160C23—21no—
161C23—21no—
162C23—21no—
163C23—21no—
164C23—21no—
165C23—21no—
166C23C2×C22⋊C811yescharacteristic
167C23#44612yes—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—44no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4#32412yes—
192C2×C4#32412yes—
193C2×C4#35012yes—
194C2×C4#39111yescharacteristic
195C2×C4#40811yescharacteristic
196C2×C4C2×#9911yescharacteristic
197C2×C4#41011yescharacteristic
198C2×C4C2×#10011yescharacteristic
199C2×C4C2×#10111yescharacteristic
200C2×C4C8×Q812yes—
201C8—22no—
202C8—22no—
203C8—21no—
204C8—21no—
205C8—41no—
206C8—82no—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—41no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22C2×#32411yescharacteristic
215C22#146011yescharacteristic
216C22#198411yescharacteristic
217C22C2×#35011yescharacteristic
218C22#211711yescharacteristic
219C22#211711yescharacteristic
220C22#211711yescharacteristic
221C4—22no—
222C4—22no—
223C4—22no—
224C4—22no—
225C4—41no—
226C4—82no—
227C4—82no—
228C4#147011yescharacteristic
229C4#147111yescharacteristic
230C4#199611yescharacteristic
231C4#199711yescharacteristic
232C2—42no—
233C2#987911yescharacteristic
234C2#1144311yescharacteristic
235C2#1144411yescharacteristic
236C2#1149111yescharacteristic
237C2#1149211yescharacteristic
238C2#1326511yescharacteristic
239C2#1326711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊C4
commutatorC22×C4C22×C8
Frattini, cosocleC23×C8C23
socleC23C2×C22⋊C8
prime radicalC24C2×M16
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C4×C8 ◁ G
LECSG ▷ C23×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
#211432
#127832
#125992
#71862