Finite Group Databasebeta

← #145975

Subgroups — #145975

Order 512.

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

normal subgroups only

This group has 218 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#13274C211yesmaximal, characteristic
2#13184C211yesmaximal, characteristic
3#12005C211yesmaximal, characteristic
4#11936C211yesmaximal, characteristic
5#9755C211yesmaximal, characteristic
6#9607C211yesmaximal, characteristic
7#7275C211yesmaximal, characteristic
8#3160C2211yescharacteristic
9C2×#365—21no—
10#2150C2211yescharacteristic
11C2×C4⋊C16C2211yescharacteristic
12#1846C2211yescharacteristic
13C4×#108C2211yescharacteristic
14#1565—21no—
15C2×#334C2211yescharacteristic
16#1518—21no—
17#1518—21no—
18#1450C2211yescharacteristic
19#1383—21no—
20#1382—21no—
21#1382—21no—
22#1370—22no—
23#1363—22no—
24#1283—21no—
25#533—21no—
26C2×M32—21no—
27C22×C16—21no—
28#500Q811yescharacteristic
29#500Q811yescharacteristic
30#499—21no—
31#499—21no—
32#498—21no—
33#431D411yescharacteristic
34#431D411yescharacteristic
35C2×#108D411yescharacteristic
36C2×#108D411yescharacteristic
37#427—21no—
38#427—21no—
39C2×#107—21no—
40C2×#106—21no—
41C2×C4⋊C8—21no—
42C4×M16—21no—
43C2×C4×C8C2311yescharacteristic
44#382—21no—
45#365—42no—
46C4⋊C16—21no—
47C4⋊C16—21no—
48C4⋊C16—21no—
49C4⋊C16D412yes—
50#341—21no—
51#335—41no—
52#334—21no—
53#334—21no—
54#334—41no—
55#328—42no—
56#328—42no—
57#322—21no—
58C82—21no—
59C2×M16—21no—
60C2×M16—21no—
61C22×C8—41no—
62C22×C8C2×D411yescharacteristic
63C22×C8#4111yescharacteristic
64C4⋊Q8—21no—
65C4⋊Q8—21no—
66#125—41no—
67C22⋊Q8—41no—
68C22⋊Q8—41no—
69C4×Q8—41no—
70C4×Q8—41no—
71#117—41no—
72C2×C4⋊C4—41no—
73C2×C42C2×D411yescharacteristic
74M32—41no—
75M32—41no—
76C2×C16—22no—
77C2×C16—41no—
78C2×C16—41no—
79C2×C16—41no—
80#108—21no—
81#108—21no—
82#108—21no—
83#108Q1612yes—
84#107—21no—
85#107—21no—
86#107—21no—
87#107—21no—
88#107—81no—
89#106—41no—
90#106—41no—
91#106—41no—
92#106—41no—
93C4⋊C8—21no—
94C4⋊C8—21no—
95C4⋊C8—41no—
96C4⋊C8—41no—
97C22⋊C8—21no—
98C22⋊C8SD1612yes—
99#97—41no—
100C4×C8—21no—
101C4×C8—21no—
102C4×C8—41no—
103C4×C8C2×D411yescharacteristic
104C4×C8C2×Q811yescharacteristic
105C4×C8#4111yescharacteristic
106C4×C8#4111yescharacteristic
107#95—41no—
108#95—41no—
109C2×Q8—41no—
110C2×Q8—41no—
111C22×C4—81no—
112C22×C4#12111yescharacteristic
113C22×C4C2×SD1611yescharacteristic
114C22×C4AGL(1,ℤ/8)11yescharacteristic
115M16—22no—
116M16—41no—
117M16—41no—
118M16—41no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—22no—
122C2×C8—41no—
123C2×C8—41no—
124C2×C8—41no—
125C2×C8—81no—
126C2×C8—161no—
127C2×C8#12111yescharacteristic
128C2×C8C22⋊Q811yescharacteristic
129C2×C8C22⋊Q811yescharacteristic
130C2×C8#12611yescharacteristic
131C2×C8C2×Q1611yescharacteristic
132C2×C8#13511yescharacteristic
133C2×C8AGL(1,ℤ/8)11yescharacteristic
134C2×C8#13711yescharacteristic
135C4⋊C4—41no—
136C4⋊C4—41no—
137C4⋊C4—41no—
138C4⋊C4—41no—
139C4⋊C4—81no—
140C4⋊C4—81no—
141C4⋊C4—81no—
142C4⋊C4—81no—
143C22⋊C4—81no—
144C42—81no—
145C42#12111yescharacteristic
146C42C22⋊Q811yescharacteristic
147C42#13511yescharacteristic
148C42AGL(1,ℤ/8)11yescharacteristic
149C16—42no—
150C16—81no—
151C23#46011yescharacteristic
152Q8—161no—
153Q8—161no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—161no—
159C2×C4—161no—
160C2×C4—161no—
161C2×C4#39611yescharacteristic
162C2×C4#46311yescharacteristic
163C2×C4#46511yescharacteristic
164C2×C4#46711yescharacteristic
165C2×C4#46811yescharacteristic
166C2×C4#46911yescharacteristic
167C2×C4#47111yescharacteristic
168C2×C4#47311yescharacteristic
169C2×C4#47611yescharacteristic
170C2×C4#47811yescharacteristic
171C8—21no—
172C8—21no—
173C8—42no—
174C8—42no—
175C8—81no—
176C8—81no—
177C8—161no—
178C8#46211yescharacteristic
179C8#46311yescharacteristic
180C8#47711yescharacteristic
181C8#47911yescharacteristic
182C22—21no—
183C22—21no—
184C22#167011yescharacteristic
185C22#168611yescharacteristic
186C22#206511yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—21no—
191C4—161no—
192C4—161no—
193C4—321no—
194C4#168311yescharacteristic
195C4#169911yescharacteristic
196C4#206411yescharacteristic
197C4#206811yescharacteristic
198C2—21no—
199C2—21no—
200C2#1060011yescharacteristic
201C2#1346811yescharacteristic
202C2#1346911yescharacteristic
subgroupG/H
center, socleC22#2065
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#460
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
#132742
#131842
#120052
#119362
#97552
#96072
#72752