Finite Group Databasebeta

← #145434

Subgroups — #145434

Order 512.

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

normal subgroups only

This group has 268 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#19118C211yesmaximal, characteristic
2#13286C211yesmaximal, characteristic
3#13264C211yesmaximal, characteristic
4#11999C211yesmaximal, characteristic
5#11939C211yesmaximal, characteristic
6#8659C211yesmaximal, characteristic
7#7276C211yesmaximal, characteristic
8#3160C2211yescharacteristic
9#3104—21no—
10C2×C8×Q8C2211yescharacteristic
11C2×C4⋊C16C2211yescharacteristic
12C2×#346C2211yescharacteristic
13#1848C2211yescharacteristic
14#1676—21no—
15#1674—21no—
16#1672—22no—
17#1564C2211yescharacteristic
18#1564C2211yescharacteristic
19#1542—21no—
20#1487—21no—
21#1382—21no—
22#1382—21no—
23#1374—21no—
24#1374—21no—
25#1368—22no—
26#1365—21no—
27#1364—21no—
28#1301—21no—
29#533—21no—
30C2×C4×Q8D411yescharacteristic
31C22×C16—21no—
32C22×C16D411yescharacteristic
33C22×C16D411yescharacteristic
34#500D411yescharacteristic
35#500D411yescharacteristic
36#499—21no—
37#499—21no—
38#498—21no—
39#484—41no—
40#477—22no—
41#462—22no—
42#451—41no—
43C8×Q8—21no—
44C8×Q8—21no—
45C8×Q8—21no—
46C8×Q8—21no—
47C4×Q16—42no—
48#431—21no—
49#431—21no—
50C2×#108—21no—
51C2×#108—21no—
52#427—21no—
53#427—21no—
54#423—21no—
55C2×C4⋊C8—21no—
56C2×C4⋊C8D411yescharacteristic
57C2×C4×C8—21no—
58C2×C4×C8C2311yescharacteristic
59C4⋊C16—21no—
60C4⋊C16—21no—
61#346—21no—
62#346—21no—
63#335—21no—
64#335—21no—
65#334—21no—
66#334D412yes—
67#333—22no—
68#332—22no—
69Q8⋊C8—42no—
70C22×Q8SD1611yescharacteristic
71C2×Q16—42no—
72C2×M16—41no—
73C22×C8—21no—
74C22×C8C2×D411yescharacteristic
75C22×C8#4111yescharacteristic
76C4⋊Q8—21no—
77C4⋊Q8—21no—
78#125—41no—
79C22⋊Q8—41no—
80C22⋊Q8—41no—
81C4×Q8—21no—
82C4×Q8—21no—
83C4×Q8—21no—
84C4×Q8—21no—
85C4×Q8—41no—
86C4×Q8—41no—
87#117—41no—
88C2×C4⋊C4—21no—
89C2×C4⋊C4SD1611yescharacteristic
90C2×C42—21no—
91C2×C42C2×D411yescharacteristic
92C2×C16—21no—
93C2×C16—21no—
94C2×C16—21no—
95C2×C16—21no—
96C2×C16—21no—
97C2×C16—41no—
98C2×C16—41no—
99C2×C16—41no—
100C2×C16Q1612yescomplemented
101#108—41no—
102#108—41no—
103#108—81no—
104#107—21no—
105#107—21no—
106#107—21no—
107#107—21no—
108#107—42no—
109#106—41no—
110#106—41no—
111C4⋊C8—21no—
112C4⋊C8—22no—
113C4⋊C8—21no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119#103—42no—
120#103—42no—
121C22⋊C8—41no—
122C22⋊C8—41no—
123C4×C8—41no—
124C4×C8—41no—
125C4×C8—41no—
126C4×C8—41no—
127C4×C8C2×D411yescharacteristic
128C4×C8C2×D411yescharacteristic
129C4×C8#4111yescharacteristic
130C4×C8#4111yescharacteristic
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—42no—
134C2×Q8—41no—
135C2×Q8—41no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4#12111yescharacteristic
139C22×C4C2×SD1611yescharacteristic
140C22×C4#13511yescharacteristic
141Q16—84no—
142M16—81no—
143M16—81no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—41no—
147C2×C8—42no—
148C2×C8—41no—
149C2×C8—41no—
150C2×C8—81no—
151C2×C8—81no—
152C2×C8#12111yescharacteristic
153C2×C8#12111yescharacteristic
154C2×C8#12311yescharacteristic
155C2×C8#12411yescharacteristic
156C2×C8C2×Q1611yescharacteristic
157C2×C8#13511yescharacteristic
158C2×C8#13711yescharacteristic
159C2×C8#13711yescharacteristic
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—81no—
169C4⋊C4—81no—
170C22⋊C4—81no—
171C42—41no—
172C42—41no—
173C42—81no—
174C42#12011yescharacteristic
175C42#12311yescharacteristic
176C42AGL(1,ℤ/8)11yescharacteristic
177C42AGL(1,ℤ/8)11yescharacteristic
178C16—22no—
179C16—41no—
180C16—81no—
181C23#46511yescharacteristic
182Q8—22no—
183Q8—22no—
184Q8—41no—
185Q8—41no—
186Q8—82no—
187Q8—161no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—41no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4#39411yescharacteristic
198C2×C4#44911yescharacteristic
199C2×C4#45011yescharacteristic
200C2×C4#46211yescharacteristic
201C2×C4#46411yescharacteristic
202C2×C4#46911yescharacteristic
203C2×C4#47111yescharacteristic
204C2×C4#47311yescharacteristic
205C2×C4#48111yescharacteristic
206C2×C4#48211yescharacteristic
207C8—21no—
208C8—21no—
209C8—82no—
210C8—81no—
211C8—161no—
212C8—161no—
213C8#46211yescharacteristic
214C8#46411yescharacteristic
215C8#46711yescharacteristic
216C8#47011yescharacteristic
217C22—21no—
218C22—21no—
219C22#167211yescharacteristic
220C22#168011yescharacteristic
221C22#203411yescharacteristic
222C4—21no—
223C4—21no—
224C4—21no—
225C4—21no—
226C4—42no—
227C4—81no—
228C4—161no—
229C4—161no—
230C4#169411yescharacteristic
231C4#170211yescharacteristic
232C4#205211yescharacteristic
233C4#205611yescharacteristic
234C2—21no—
235C2—21no—
236C2#1047911yescharacteristic
237C2#1339511yescharacteristic
238C2#1340611yescharacteristic
subgroupG/H
centerC2×C4#469
commutator, Frattini, cosocleC2×C4×C8C23
socleC22#2034
prime radicalC23#465
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C8×Q8 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
100. C2×C16Q16semidirect

Maximal subgroups

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

subgroupindex
#191182
#132862
#132642
#119992
#119392
#86592
#72762