Finite Group Databasebeta

← #145084

Subgroups — #145084

Order 512.

307 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 307 conjugacy classes of subgroups — too many to draw. Only its 80 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#28683C211yesmaximal, characteristic
2#13290C211yesmaximal, characteristic
3#13185C211yesmaximal, characteristic
4#11941C211yesmaximal, characteristic
5#11611C211yesmaximal, characteristic
6#8663C211yesmaximal, characteristic
7#7174C211yesmaximal, characteristic
8C2×#500C2211yescharacteristic
9C2×#446C2211yescharacteristic
10#2546—21no—
11C2×#365—21no—
12#2150C2211yescharacteristic
13C4×M32C2211yescharacteristic
14#2087—22no—
15#1988—21no—
16#1944—21no—
17#1944—21no—
18#1848C2211yescharacteristic
19C4×#106C2211yescharacteristic
20#1564C2211yescharacteristic
21#1487—21no—
22#1387—22no—
23#1383—21no—
24#1365—22no—
25#1338—22no—
26#1301—21no—
27C2×C4⋊Q8—21no—
28C2×C4⋊Q8—41no—
29C2×C4×Q8D411yescharacteristic
30C2×M32—21no—
31C2×M32—21no—
32#500—21no—
33#500—21no—
34#500—21no—
35#500—21no—
36#446—21no—
37#446—21no—
38#446—21no—
39#446—21no—
40#431—21no—
41C2×#108—21no—
42C2×#108—21no—
43C2×#107—21no—
44C2×#107D412yes—
45C2×#106D411yescharacteristic
46C2×#106D411yescharacteristic
47#423—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8D411yescharacteristic
50C2×#97—21no—
51C2×C4×C8C2311yescharacteristic
52#398—42no—
53#391—41no—
54#389—22no—
55#389—22no—
56C4×C4⋊C4—21no—
57#365—42no—
58C4⋊C16—21no—
59C4⋊C16D412yes—
60#346—21no—
61C4×C16—21no—
62#340—22no—
63#340—22no—
64#340—21no—
65#335—21no—
66#334—21no—
67Q8⋊C8—42no—
68C22×Q8—41no—
69C22×Q8SD1611yescharacteristic
70C2×M16—41no—
71C22×C8—21no—
72C22×C8C2×D411yescharacteristic
73C22×C8C2×D411yescharacteristic
74C4⋊Q8—41no—
75C4⋊Q8—41no—
76C4⋊Q8—41no—
77C4⋊Q8—41no—
78C4⋊Q8—84no—
79C4×Q8—21no—
80C4×Q8—21no—
81C4×Q8—21no—
82C4×Q8—21no—
83C2×C4⋊C4—21no—
84C2×C4⋊C4—21no—
85C2×C4⋊C4—21no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—42no—
88C2×C4⋊C4—42no—
89C2×C4⋊C4—41no—
90C2×C4⋊C4SD1611yescharacteristic
91C2×C42—21no—
92C2×C42—41no—
93C2×C42C2×D411yescharacteristic
94M32—22no—
95M32—41no—
96M32—41no—
97M32—41no—
98C2×C16—22no—
99C2×C16—41no—
100#108—42no—
101#108—41no—
102#108—41no—
103#107—22no—
104#107—22no—
105#107—41no—
106#107—41no—
107#106—21no—
108#106—21no—
109#106SD1612yes—
110#106Q1612yes—
111C4⋊C8—21no—
112C4⋊C8—21no—
113C4⋊C8—41no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C22⋊C8—41no—
119#97—41no—
120#97—41no—
121C4×C8—41no—
122C4×C8C2×D411yescharacteristic
123C4×C8#4111yescharacteristic
124C4×C8#4111yescharacteristic
125C4×C8#4111yescharacteristic
126#95—42no—
127#95—42no—
128#95—41no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—42no—
132C2×Q8—82no—
133C2×Q8—82no—
134C2×Q8—81no—
135C2×Q8—81no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—41no—
139C22×C4—41no—
140C22×C4—42no—
141C22×C4#12011yescharacteristic
142C22×C4C2×SD1611yescharacteristic
143C22×C4AGL(1,ℤ/8)11yescharacteristic
144M16—81no—
145M16—81no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—41no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—81no—
152C2×C8—81no—
153C2×C8#12111yescharacteristic
154C2×C8#12111yescharacteristic
155C2×C8#12311yescharacteristic
156C2×C8#12411yescharacteristic
157C2×C8C2×SD1611yescharacteristic
158C2×C8C2×Q1611yescharacteristic
159C2×C8#13711yescharacteristic
160C2×C8#13711yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—84no—
172C4⋊C4—84no—
173C4⋊C4—81no—
174C4⋊C4—81no—
175C42—41no—
176C42—41no—
177C42—82no—
178C42#12111yescharacteristic
179C42#12311yescharacteristic
180C42#13511yescharacteristic
181C42AGL(1,ℤ/8)11yescharacteristic
182C16—42no—
183C16—42no—
184C23#45011yescharacteristic
185Q8—42no—
186Q8—81no—
187Q8—162no—
188Q8—162no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4—82no—
202C2×C4—82no—
203C2×C4—82no—
204C2×C4#39411yescharacteristic
205C2×C4#44811yescharacteristic
206C2×C4#44911yescharacteristic
207C2×C4#45111yescharacteristic
208C2×C4#45411yescharacteristic
209C2×C4#45611yescharacteristic
210C2×C4#46511yescharacteristic
211C2×C4#46911yescharacteristic
212C2×C4#48111yescharacteristic
213C2×C4#48211yescharacteristic
214C8—21no—
215C8—21no—
216C8—81no—
217C8—161no—
218C8—161no—
219C8#46111yescharacteristic
220C8#46211yescharacteristic
221C8#48711yescharacteristic
222C8#49111yescharacteristic
223C22—21no—
224C22—21no—
225C22#163711yescharacteristic
226C22#165111yescharacteristic
227C22#203411yescharacteristic
228C4—21no—
229C4—21no—
230C4—21no—
231C4—82no—
232C4—82no—
233C4—81no—
234C4—81no—
235C4—162no—
236C4#162611yescharacteristic
237C4#164811yescharacteristic
238C4#203811yescharacteristic
239C4#204311yescharacteristic
240C4#223812yes—
241C2—21no—
242C2—21no—
243C2#1041811yescharacteristic
244C2#1339711yescharacteristic
245C2#1339811yescharacteristic
subgroupG/H
center, socleC22#2034
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#450
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#446 ◁ 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
#286832
#132902
#131852
#119412
#116112
#86632
#71742