Finite Group Databasebeta

← #145467

Subgroups — #145467

Order 512.

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

normal subgroups only

This group has 271 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#33628C211yesmaximal, characteristic
2#12814C211yesmaximal, characteristic
3#12005C211yesmaximal, characteristic
4#11939C211yesmaximal, characteristic
5#9755C211yesmaximal, characteristic
6#9669C211yesmaximal, characteristic
7#7279C211yesmaximal, characteristic
8#3160C2211yescharacteristic
9C2×C4×Q16C2211yescharacteristic
10#2229—22no—
11#2227—21no—
12#2225—21no—
13#2159—21no—
14#2150C2211yescharacteristic
15C2×C4⋊C16C2211yescharacteristic
16#2141—21no—
17C2×#358—21no—
18#1846C2211yescharacteristic
19#1564C2211yescharacteristic
20#1518—21no—
21#1518—21no—
22#1479—21no—
23#1461—21no—
24#1450C2211yescharacteristic
25#1380—21no—
26#1370—22no—
27#1365—21no—
28#1364—21no—
29C22×Q16D411yescharacteristic
30#533—21no—
31C2×C4×Q8—21no—
32C2×M32—21no—
33C22×C16—21no—
34#500D411yescharacteristic
35#500D411yescharacteristic
36#499—21no—
37#499—21no—
38#498—21no—
39C4×Q16—21no—
40C4×Q16—21no—
41C4×Q16—21no—
42C4×Q16—21no—
43#431—21no—
44#431D411yescharacteristic
45#431D411yescharacteristic
46#427—21no—
47#427—21no—
48C2×#107—21no—
49C2×#107D411yescharacteristic
50C2×#106—21no—
51C2×#103—21no—
52C2×C4×C8C2311yescharacteristic
53#382—21no—
54#367—22no—
55#366—22no—
56C4⋊C16—21no—
57C4⋊C16—21no—
58C4⋊C16—21no—
59C4⋊C16D412yes—
60#358—22no—
61#358—22no—
62#358—42no—
63#335—21no—
64#334—21no—
65#328—42no—
66#328—42no—
67Q8⋊C8—42no—
68#324—42no—
69#322—21no—
70C82—21no—
71C22×Q8—21no—
72C2×Q16—21no—
73C2×Q16—21no—
74C2×Q16—21no—
75C2×Q16—21no—
76C2×Q16—21no—
77C2×Q16Q1612yes—
78C22×C8C2×D411yescharacteristic
79C22×C8#4111yescharacteristic
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82#125—41no—
83C22⋊Q8—41no—
84C22⋊Q8—41no—
85C4×Q8—41no—
86C4×Q8—41no—
87C4×Q8—41no—
88C4×Q8—41no—
89C4×Q8—41no—
90C4×Q8—41no—
91#117—41no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C42—41no—
96C2×C42C2×D411yescharacteristic
97M32—41no—
98M32—41no—
99C2×C16—22no—
100C2×C16—41no—
101C2×C16—41no—
102C2×C16—41no—
103#107—21no—
104#107—21no—
105#107—21no—
106#107—21no—
107#107—21no—
108#107—21no—
109#107—41no—
110#107—41no—
111#106—41no—
112#106—41no—
113#106—81no—
114C4⋊C8—21no—
115C4⋊C8—21no—
116C4⋊C8—41no—
117#103—41no—
118#103—41no—
119C22⋊C8—21no—
120C22⋊C8—41no—
121C22⋊C8D812yes—
122C4×C8—21no—
123C4×C8—21no—
124C4×C8—41no—
125C4×C8C2×D411yescharacteristic
126C4×C8C2×D411yescharacteristic
127C4×C8#4111yescharacteristic
128C4×C8#4111yescharacteristic
129#95—41no—
130#95—41no—
131C2×Q8—22no—
132C2×Q8—41no—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8—41no—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—41no—
139C22×C4—41no—
140C22×C4—41no—
141C22×C4—81no—
142C22×C4#12111yescharacteristic
143C22×C4C2×D811yescharacteristic
144C22×C4AGL(1,ℤ/8)11yescharacteristic
145Q16—22no—
146Q16—22no—
147Q16—41no—
148Q16—41no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—22no—
152C2×C8—41no—
153C2×C8—81no—
154C2×C8#12011yescharacteristic
155C2×C8#12311yescharacteristic
156C2×C8#12311yescharacteristic
157C2×C8#12411yescharacteristic
158C2×C8C2×Q1611yescharacteristic
159C2×C8#13511yescharacteristic
160C2×C8AGL(1,ℤ/8)11yescharacteristic
161C2×C8#13711yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—81no—
169C4⋊C4—81no—
170C4⋊C4—81no—
171C4⋊C4—81no—
172C4⋊C4—81no—
173C4⋊C4—81no—
174C22⋊C4—81no—
175C42—81no—
176C42—81no—
177C42—81no—
178C42#12111yescharacteristic
179C42#12111yescharacteristic
180C42#13511yescharacteristic
181C42AGL(1,ℤ/8)11yescharacteristic
182C16—42no—
183C16—81no—
184C23#45911yescharacteristic
185Q8—42no—
186Q8—42no—
187Q8—81no—
188Q8—81no—
189Q8—161no—
190Q8—161no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—161no—
200C2×C4—161no—
201C2×C4—161no—
202C2×C4—161no—
203C2×C4#39411yescharacteristic
204C2×C4#45911yescharacteristic
205C2×C4#46311yescharacteristic
206C2×C4#46311yescharacteristic
207C2×C4#46611yescharacteristic
208C2×C4#46711yescharacteristic
209C2×C4#46811yescharacteristic
210C2×C4#46911yescharacteristic
211C2×C4#47111yescharacteristic
212C2×C4#47311yescharacteristic
213C8—21no—
214C8—21no—
215C8—42no—
216C8—81no—
217C8—161no—
218C8#44911yescharacteristic
219C8#45111yescharacteristic
220C8#48411yescharacteristic
221C8#48511yescharacteristic
222C22—21no—
223C22—21no—
224C22#166911yescharacteristic
225C22#168511yescharacteristic
226C22#205411yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—82no—
232C4—161no—
233C4—161no—
234C4—161no—
235C4—321no—
236C4#168311yescharacteristic
237C4#169911yescharacteristic
238C4#203611yescharacteristic
239C4#205211yescharacteristic
240C2—21no—
241C2—21no—
242C2#1048511yescharacteristic
243C2#1344311yescharacteristic
244C2#1344711yescharacteristic
subgroupG/H
center, socleC22#2054
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#459
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1450 ◁ G
LECSG ▷ C2×C4×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
#336282
#128142
#120052
#119392
#97552
#96692
#72792