Finite Group Databasebeta

← #145080

Subgroups — #145080

Order 512.

275 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 275 conjugacy classes of subgroups — too many to draw. Only its 78 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#28699C211yesmaximal, characteristic
2#13283C211yesmaximal, characteristic
3#13184C211yesmaximal, characteristic
4#11941C211yesmaximal, characteristic
5#11612C211yesmaximal, characteristic
6#8675C211yesmaximal, characteristic
7#7177C211yesmaximal, characteristic
8#3165—21no—
9C2×#500C2211yescharacteristic
10#2960C2211yescharacteristic
11C2×#365—21no—
12#2150C2211yescharacteristic
13C2×#346C2211yescharacteristic
14#2089—22no—
15#1997—21no—
16#1952—21no—
17#1952—21no—
18#1846C2211yescharacteristic
19C4×#108C2211yescharacteristic
20#1564C2211yescharacteristic
21#1518—21no—
22#1383—21no—
23#1380—22no—
24#1365—22no—
25#1338—22no—
26#1286—21no—
27#533D411yescharacteristic
28C2×C4⋊Q8—21no—
29C2×M32—21no—
30C22×C16—21no—
31#501—42no—
32#500—21no—
33#500—21no—
34#500—21no—
35#500—21no—
36#500—41no—
37#498—41no—
38#446—21no—
39#446—21no—
40C8×Q8—21no—
41C8×Q8—21no—
42#431—21no—
43C2×#108D411yescharacteristic
44C2×#108D411yescharacteristic
45#428—22no—
46#428—22no—
47C2×#107—21no—
48C2×#107—21no—
49C2×#107D412yes—
50C2×#106—21no—
51#424—21no—
52#423D411yescharacteristic
53#405—21no—
54C4×M16—21no—
55C2×C4×C8C2311yescharacteristic
56#382—21no—
57#365—42no—
58C4⋊C16—21no—
59C4⋊C16D412yes—
60#346—21no—
61#346—21no—
62#343—22no—
63#343—22no—
64#341—21no—
65#335—21no—
66#334—21no—
67#328—42no—
68C22×Q8—41no—
69C2×M16—21no—
70C2×M16—21no—
71C2×M16—21no—
72C22×C8C2×D411yescharacteristic
73C22×C8C2×D411yescharacteristic
74C4⋊Q8—41no—
75C4⋊Q8—41no—
76C4⋊Q8—41no—
77C4⋊Q8—41no—
78C4⋊Q8SD1611yescharacteristic
79C4⋊Q8SD1611yescharacteristic
80#125—21no—
81C22⋊Q8—21no—
82C22⋊Q8—21no—
83C4×Q8—21no—
84C4×Q8—21no—
85#117—21no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—41no—
89C2×C42C2×D411yescharacteristic
90M32—41no—
91M32—41no—
92C2×C16—22no—
93C2×C16—22no—
94C2×C16—41no—
95C2×C16—41no—
96#108—21no—
97#108—21no—
98#108SD1612yes—
99#108Q1612yes—
100#107—22no—
101#107—22no—
102#107—42no—
103#107—42no—
104#107—41no—
105#107—41no—
106#107—42no—
107#106—42no—
108#106—42no—
109#106—41no—
110#106—41no—
111C4⋊C8—21no—
112C4⋊C8—21no—
113C4⋊C8—41no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116C22⋊C8—41no—
117#97—41no—
118#97—41no—
119C4×C8—41no—
120C4×C8—41no—
121C4×C8—41no—
122C4×C8C2×D411yescharacteristic
123C4×C8#4111yescharacteristic
124C4×C8#4111yescharacteristic
125C4×C8#4111yescharacteristic
126#95—41no—
127#95—41no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—81no—
131C2×Q8—81no—
132C2×Q8—162no—
133C22×C4—42no—
134C22×C4—81no—
135C22×C4#12011yescharacteristic
136C22×C4#13511yescharacteristic
137C22×C4AGL(1,ℤ/8)11yescharacteristic
138M16—22no—
139M16—22no—
140M16—41no—
141M16—41no—
142M16—41no—
143M16—41no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—41no—
147C2×C8—41no—
148C2×C8—41no—
149C2×C8—81no—
150C2×C8#12111yescharacteristic
151C2×C8#12111yescharacteristic
152C2×C8#12311yescharacteristic
153C2×C8#12411yescharacteristic
154C2×C8C2×SD1611yescharacteristic
155C2×C8C2×Q1611yescharacteristic
156C2×C8#13711yescharacteristic
157C2×C8#13711yescharacteristic
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—81no—
167C4⋊C4—81no—
168C4⋊C4—81no—
169C4⋊C4—81no—
170C22⋊C4—41no—
171C42—41no—
172C42#12111yescharacteristic
173C42#12311yescharacteristic
174C42C2×SD1611yescharacteristic
175C42AGL(1,ℤ/8)11yescharacteristic
176C16—42no—
177C16—42no—
178C23#44911yescharacteristic
179Q8—81no—
180Q8—81no—
181Q8—162no—
182Q8—162no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—82no—
188C2×C4—162no—
189C2×C4—161no—
190C2×C4—161no—
191C2×C4—161no—
192C2×C4#39411yescharacteristic
193C2×C4#44811yescharacteristic
194C2×C4#45011yescharacteristic
195C2×C4#45111yescharacteristic
196C2×C4#45411yescharacteristic
197C2×C4#45611yescharacteristic
198C2×C4#46511yescharacteristic
199C2×C4#46911yescharacteristic
200C2×C4#48111yescharacteristic
201C2×C4#48211yescharacteristic
202C8—21no—
203C8—21no—
204C8—42no—
205C8—42no—
206C8—81no—
207C8—161no—
208C8#46111yescharacteristic
209C8#46211yescharacteristic
210C8#48711yescharacteristic
211C8#49111yescharacteristic
212C22—21no—
213C22—21no—
214C22#162611yescharacteristic
215C22#164811yescharacteristic
216C22#203411yescharacteristic
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—81no—
222C4—81no—
223C4—162no—
224C4—321no—
225C4#163711yescharacteristic
226C4#165111yescharacteristic
227C4#203811yescharacteristic
228C4#204311yescharacteristic
229C2—21no—
230C2—21no—
231C2#1041811yescharacteristic
232C2#1340211yescharacteristic
233C2#1340511yescharacteristic
subgroupG/H
center, socleC22#2034
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#449
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960 ◁ 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
#286992
#132832
#131842
#119412
#116122
#86752
#71772