Finite Group Databasebeta

← #145436

Subgroups — #145436

Order 512.

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

normal subgroups only

This group has 261 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#19209C211yesmaximal, characteristic
2#13283C211yesmaximal, characteristic
3#13267C211yesmaximal, characteristic
4#11999C211yesmaximal, characteristic
5#11940C211yesmaximal, characteristic
6#8677C211yesmaximal, characteristic
7#7279C211yesmaximal, characteristic
8#3230—21no—
9C2×#500C2211yescharacteristic
10#2960C2211yescharacteristic
11#2150C2211yescharacteristic
12C2×#346C2211yescharacteristic
13#1846C2211yescharacteristic
14#1696—22no—
15#1676—22no—
16#1564C2211yescharacteristic
17#1564C2211yescharacteristic
18#1548—21no—
19#1518—21no—
20#1380—21no—
21#1380—21no—
22#1379—21no—
23#1379—21no—
24#1368—22no—
25#1364—22no—
26#1286—21no—
27#533D411yescharacteristic
28C2×C4⋊Q8—21no—
29C2×M32—21no—
30C22×C16D411yescharacteristic
31C22×C16D411yescharacteristic
32#500—21no—
33#500—21no—
34#500—21no—
35#500—41no—
36#500D412yes—
37#487—41no—
38#484—42no—
39#477—24no—
40#446—21no—
41#446—21no—
42C8×Q8—21no—
43C8×Q8—21no—
44#431—21no—
45#431—21no—
46C2×#107—21no—
47C2×#107—21no—
48C2×#107—21no—
49C2×#106—21no—
50#424—21no—
51#423D411yescharacteristic
52#405—21no—
53C2×C4×C8C2311yescharacteristic
54#382—21no—
55C4⋊C16—21no—
56C4⋊C16—21no—
57#346—21no—
58#346—21no—
59#335—21no—
60#335—21no—
61#334—21no—
62#334D412yes—
63#333—24no—
64#328—42no—
65C22×Q8—41no—
66C2×M16—21no—
67C22×C8C2×D411yescharacteristic
68C22×C8#4111yescharacteristic
69C4⋊Q8—22no—
70C4⋊Q8—41no—
71C4⋊Q8—41no—
72C4⋊Q8—41no—
73C4⋊Q8SD1611yescharacteristic
74C4⋊Q8SD1611yescharacteristic
75#125—21no—
76C22⋊Q8—21no—
77C22⋊Q8—21no—
78C4×Q8—21no—
79C4×Q8—21no—
80#117—21no—
81C2×C4⋊C4—41no—
82C2×C4⋊C4—41no—
83C2×C4⋊C4—41no—
84C2×C42C2×D411yescharacteristic
85M32—41no—
86M32—41no—
87C2×C16—21no—
88C2×C16—21no—
89C2×C16—21no—
90C2×C16—21no—
91C2×C16—21no—
92C2×C16—41no—
93C2×C16Q1612yes—
94#107—22no—
95#107—22no—
96#107—44no—
97#107—41no—
98#107—41no—
99#107—41no—
100#107—41no—
101#106—81no—
102C4⋊C8—21no—
103C4⋊C8—22no—
104C4⋊C8—21no—
105C4⋊C8—41no—
106C4⋊C8—41no—
107C4⋊C8—41no—
108#103—44no—
109C22⋊C8—41no—
110C22⋊C8—41no—
111#97—41no—
112C4×C8—41no—
113C4×C8—41no—
114C4×C8—41no—
115C4×C8C2×D411yescharacteristic
116C4×C8C2×D411yescharacteristic
117C4×C8#4111yescharacteristic
118C4×C8#4111yescharacteristic
119#95—41no—
120#95—41no—
121C2×Q8—21no—
122C2×Q8—21no—
123C2×Q8—42no—
124C2×Q8—81no—
125C2×Q8—162no—
126C22×C4—81no—
127C22×C4—81no—
128C22×C4#12111yescharacteristic
129C22×C4AGL(1,ℤ/8)11yescharacteristic
130C22×C4AGL(1,ℤ/8)11yescharacteristic
131M16—41no—
132M16—41no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—41no—
136C2×C8—42no—
137C2×C8—81no—
138C2×C8#12111yescharacteristic
139C2×C8#12111yescharacteristic
140C2×C8#12311yescharacteristic
141C2×C8#12411yescharacteristic
142C2×C8C2×Q1611yescharacteristic
143C2×C8#13511yescharacteristic
144C2×C8#13711yescharacteristic
145C2×C8#13711yescharacteristic
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—41no—
151C4⋊C4—41no—
152C4⋊C4—42no—
153C4⋊C4—42no—
154C4⋊C4—81no—
155C4⋊C4—81no—
156C4⋊C4—81no—
157C4⋊C4—81no—
158C22⋊C4—41no—
159C42—41no—
160C42#12011yescharacteristic
161C42#12311yescharacteristic
162C42C2×SD1611yescharacteristic
163C42#13511yescharacteristic
164C16—22no—
165C16—41no—
166C16—81no—
167C23#46911yescharacteristic
168Q8—42no—
169Q8—81no—
170Q8—162no—
171Q8—162no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—82no—
177C2×C4—162no—
178C2×C4—161no—
179C2×C4—161no—
180C2×C4—161no—
181C2×C4#39411yescharacteristic
182C2×C4#44911yescharacteristic
183C2×C4#45011yescharacteristic
184C2×C4#46211yescharacteristic
185C2×C4#46411yescharacteristic
186C2×C4#46511yescharacteristic
187C2×C4#47111yescharacteristic
188C2×C4#47311yescharacteristic
189C2×C4#48111yescharacteristic
190C2×C4#48211yescharacteristic
191C8—21no—
192C8—21no—
193C8—82no—
194C8—81no—
195C8—161no—
196C8#46211yescharacteristic
197C8#46411yescharacteristic
198C8#46711yescharacteristic
199C8#47011yescharacteristic
200C22—21no—
201C22—21no—
202C22#169411yescharacteristic
203C22#170211yescharacteristic
204C22#203411yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—81no—
210C4—81no—
211C4—162no—
212C4—321no—
213C4#167211yescharacteristic
214C4#168011yescharacteristic
215C4#205211yescharacteristic
216C4#205611yescharacteristic
217C2—21no—
218C2—21no—
219C2#1047911yescharacteristic
220C2#1339711yescharacteristic
221C2#1340411yescharacteristic
subgroupG/H
center, socleC22#2034
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#469
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
#192092
#132832
#132672
#119992
#119402
#86772
#72792