Finite Group Databasebeta

← #145109

Subgroups — #145109

Order 512.

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

normal subgroups only

This group has 328 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#28531C211yesmaximal, characteristic
2#13290C211yesmaximal, characteristic
3#12819C211yesmaximal, characteristic
4#11941C211yesmaximal, characteristic
5#11594C211yesmaximal, characteristic
6#9627C211yesmaximal, characteristic
7#7169C211yesmaximal, characteristic
8C2×#500C2211yescharacteristic
9C2×#477—21no—
10C2×C4×Q16C2211yescharacteristic
11#2567—21no—
12#2150C2211yescharacteristic
13C2×#362—21no—
14C4×M32C2211yescharacteristic
15#2095—22no—
16#1969—21no—
17#1848C2211yescharacteristic
18#1845—21no—
19C8×C4⋊C4C2211yescharacteristic
20#1571—21no—
21#1564C2211yescharacteristic
22#1387—21no—
23#1387—22no—
24#1365—22no—
25#1332—22no—
26#1303—21no—
27C22×Q16D411yescharacteristic
28C2×C4⋊Q8—21no—
29C2×C4×Q8—21no—
30C2×M32—21no—
31C2×M32—21no—
32#500—21no—
33#500—21no—
34#500—21no—
35#500—21no—
36#477—42no—
37#477—42no—
38C4×Q16—21no—
39C4×Q16—21no—
40C4×Q16—21no—
41C4×Q16—21no—
42#431—21no—
43C2×#108—21no—
44C2×#108—21no—
45C2×#107—22no—
46C2×#107—21no—
47C2×#107D412yes—
48C2×#107D411yescharacteristic
49#423—21no—
50C2×C4⋊C8D411yescharacteristic
51C2×#103—22no—
52C2×#103—21no—
53C2×C4×C8—21no—
54C2×C4×C8C2311yescharacteristic
55#395—42no—
56#391—22no—
57#389—42no—
58#384—22no—
59C4×C4⋊C4D411yescharacteristic
60C4⋊C16—21no—
61C4⋊C16—21no—
62#362—42no—
63#346—21no—
64C4×C16—21no—
65#336—21no—
66#335—42no—
67#335D412yes—
68#334—21no—
69C22×Q8—21no—
70C22×Q8—41no—
71C2×Q16—21no—
72C2×Q16—21no—
73C2×Q16—21no—
74C2×Q16—21no—
75C2×Q16—21no—
76C2×Q16Q1612yes—
77C2×M16—41no—
78C22×C8—21no—
79C22×C8C2×D411yescharacteristic
80C22×C8C2×D411yescharacteristic
81C4⋊Q8—41no—
82C4⋊Q8—41no—
83C4⋊Q8—41no—
84C4⋊Q8—41no—
85C4×Q8—41no—
86C4×Q8—41no—
87C4×Q8—41no—
88C4×Q8—41no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—22no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—44no—
95C2×C42—21no—
96C2×C42—41no—
97C2×C42C2×D411yescharacteristic
98M32—22no—
99M32—41no—
100M32—41no—
101M32—41no—
102C2×C16—41no—
103C2×C16—41no—
104#108—42no—
105#108—41no—
106#108—41no—
107#107—21no—
108#107—22no—
109#107—21no—
110#107—22no—
111#107—44no—
112#107—41no—
113#107—41no—
114C4⋊C8—22no—
115C4⋊C8—21no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8D812yes—
119#103—44no—
120#103—41no—
121#103—41no—
122C22⋊C8—41no—
123C4×C8—41no—
124C4×C8—41no—
125C4×C8—41no—
126C4×C8C2×D411yescharacteristic
127C4×C8#4111yescharacteristic
128C4×C8#4111yescharacteristic
129C4×C8#4111yescharacteristic
130#95—44no—
131#95SD1612yes—
132C2×Q8—22no—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8—41no—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—81no—
139C2×Q8—81no—
140C2×Q8—162no—
141C22×C4—22no—
142C22×C4—41no—
143C22×C4—42no—
144C22×C4—41no—
145C22×C4#12011yescharacteristic
146C22×C4C2×SD1611yescharacteristic
147C22×C4AGL(1,ℤ/8)11yescharacteristic
148Q16—22no—
149Q16—22no—
150Q16—41no—
151Q16—41no—
152M16—81no—
153M16—81no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—22no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—42no—
160C2×C8—81no—
161C2×C8#12111yescharacteristic
162C2×C8#12111yescharacteristic
163C2×C8#12311yescharacteristic
164C2×C8#12311yescharacteristic
165C2×C8C2×Q1611yescharacteristic
166C2×C8#13511yescharacteristic
167C2×C8AGL(1,ℤ/8)11yescharacteristic
168C2×C8#13711yescharacteristic
169C4⋊C4—24no—
170C4⋊C4—41no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—41no—
174C4⋊C4—81no—
175C4⋊C4—81no—
176C4⋊C4—81no—
177C4⋊C4—81no—
178C4⋊C4—164no—
179C42—41no—
180C42—41no—
181C42—81no—
182C42—81no—
183C42#12111yescharacteristic
184C42#12411yescharacteristic
185C42C2×D811yescharacteristic
186C42AGL(1,ℤ/8)11yescharacteristic
187C16—42no—
188C16—81no—
189C23#45011yescharacteristic
190Q8—42no—
191Q8—42no—
192Q8—81no—
193Q8—81no—
194Q8—162no—
195Q8—162no—
196C2×C4—22no—
197C2×C4—24no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—82no—
205C2×C4—84no—
206C2×C4—81no—
207C2×C4—82no—
208C2×C4#39411yescharacteristic
209C2×C4#44711yescharacteristic
210C2×C4#44911yescharacteristic
211C2×C4#45111yescharacteristic
212C2×C4#45411yescharacteristic
213C2×C4#45611yescharacteristic
214C2×C4#45911yescharacteristic
215C2×C4#46011yescharacteristic
216C2×C4#48611yescharacteristic
217C2×C4#49011yescharacteristic
218C8—21no—
219C8—21no—
220C8—42no—
221C8—82no—
222C8—161no—
223C8#46711yescharacteristic
224C8#46811yescharacteristic
225C8#48411yescharacteristic
226C8#48511yescharacteristic
227C22—21no—
228C22—21no—
229C22#163711yescharacteristic
230C22#165411yescharacteristic
231C22#204111yescharacteristic
232C4—21no—
233C4—21no—
234C4—21no—
235C4—44no—
236C4—82no—
237C4—161no—
238C4—162no—
239C4#162511yescharacteristic
240C4#164911yescharacteristic
241C4#203611yescharacteristic
242C4#203811yescharacteristic
243C4#221412yes—
244C2—21no—
245C2—21no—
246C2#1042111yescharacteristic
247C2#1341511yescharacteristic
248C2#1341711yescharacteristic
subgroupG/H
center, socleC22#2041
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#450
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×C4⋊C4 ◁ 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
#285312
#132902
#128192
#119412
#115942
#96272
#71692