Finite Group Databasebeta

← #146189

Subgroups — #146189

Order 512.

197 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 197 conjugacy classes of subgroups — too many to draw. Only its 56 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#12034C211yesmaximal, characteristic
2#12031C211yesmaximal, characteristic
3#11668C211yesmaximal, characteristic
4#11662C211yesmaximal, characteristic
5#9671C211yesmaximal, characteristic
6#8798C211yesmaximal, characteristic
7#7147C211yesmaximal, characteristic
8C2×C4×Q16C2211yescharacteristic
9#2163C2211yescharacteristic
10#2162C2211yescharacteristic
11#1568C2211yescharacteristic
12#1568C2211yescharacteristic
13#1564C2211yescharacteristic
14#1479—21no—
15#1461—21no—
16#1452C2211yescharacteristic
17#1372—21no—
18#1371—21no—
19#1368—22no—
20#1334—22no—
21#1332—21no—
22#1332—21no—
23#1287—21no—
24#1287—21no—
25C22×Q16Q811yescharacteristic
26C2×C4×Q8—21no—
27C4×Q16—21no—
28C4×Q16—21no—
29C4×Q16—21no—
30C4×Q16—21no—
31#432—21no—
32#432—21no—
33#431—21no—
34#431D411yescharacteristic
35#431D411yescharacteristic
36C2×#107Q811yescharacteristic
37C2×#103—21no—
38C2×C4×C8C2311yescharacteristic
39C4⋊C16—21no—
40C4⋊C16—21no—
41C22⋊C16—21no—
42C22⋊C16—21no—
43#346D412yes—
44C4×C16D411yescharacteristic
45C4×C16D411yescharacteristic
46#335—21no—
47#335—21no—
48#335—21no—
49#334—21no—
50#334—21no—
51#334—21no—
52Q8⋊C8—42no—
53#324—42no—
54#322—21no—
55#322—21no—
56C22×Q8—21no—
57C2×Q16—21no—
58C2×Q16—21no—
59C2×Q16—42no—
60C22×C8C2×Q811yescharacteristic
61C22×C8#4111yescharacteristic
62C4×Q8—41no—
63C4×Q8—41no—
64C4×Q8—41no—
65C4×Q8—41no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4—41no—
68C2×C42—41no—
69C2×C42C2×D411yescharacteristic
70C2×C16—21no—
71C2×C16—21no—
72C2×C16—22no—
73#107—21no—
74#107—21no—
75C4⋊C8—21no—
76C4⋊C8—21no—
77C4⋊C8—41no—
78C4⋊C8—41no—
79C4⋊C8—41no—
80#103—41no—
81#103—41no—
82C22⋊C8—21no—
83C22⋊C8—21no—
84C22⋊C8—41no—
85C22⋊C8—41no—
86C22⋊C8—41no—
87#97—41no—
88#97—41no—
89C4×C8—21no—
90C4×C8—21no—
91C4×C8—41no—
92C4×C8C2×D411yescharacteristic
93C4×C8C2×D411yescharacteristic
94C4×C8#4111yescharacteristic
95C4×C8#4111yescharacteristic
96C2×Q8—22no—
97C2×Q8—41no—
98C2×Q8—41no—
99C2×Q8—41no—
100C2×Q8—41no—
101C2×Q8—41no—
102C22×C4—41no—
103C22×C4—41no—
104C22×C4C22⋊Q811yescharacteristic
105C22×C4#13511yescharacteristic
106C22×C4AGL(1,ℤ/8)11yescharacteristic
107Q16—22no—
108Q16—22no—
109Q16—41no—
110Q16—41no—
111C2×C8—41no—
112C2×C8—41no—
113C2×C8—41no—
114C2×C8—41no—
115C2×C8—81no—
116C2×C8—81no—
117C2×C8—81no—
118C2×C8C22⋊Q811yescharacteristic
119C2×C8C22⋊Q811yescharacteristic
120C2×C8#12311yescharacteristic
121C2×C8#12311yescharacteristic
122C4⋊C4—41no—
123C4⋊C4—41no—
124C4⋊C4—81no—
125C4⋊C4—81no—
126C42—81no—
127C42—81no—
128C42#12311yescharacteristic
129C42#12711yescharacteristic
130C42#13511yescharacteristic
131C42AGL(1,ℤ/8)11yescharacteristic
132C16—41no—
133C16—41no—
134C16—42no—
135C23#47811yescharacteristic
136Q8—42no—
137Q8—42no—
138Q8—81no—
139Q8—81no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—42no—
145C2×C4—81no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—161no—
149C2×C4#39911yescharacteristic
150C2×C4#47811yescharacteristic
151C2×C4#48211yescharacteristic
152C2×C4#48211yescharacteristic
153C2×C4#49511yescharacteristic
154C2×C4#49611yescharacteristic
155C8—21no—
156C8—21no—
157C8—21no—
158C8—21no—
159C8—81no—
160C8—81no—
161C8—161no—
162C8—161no—
163C8—161no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22#209211yescharacteristic
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—82no—
174C4—161no—
175C4#209111yescharacteristic
176C4#209811yescharacteristic
177C2—41no—
178C2#1065911yescharacteristic
179C2#1352411yescharacteristic
180C2#1352511yescharacteristic
subgroupG/H
center, socleC22#2092
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#478
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1452 ◁ 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
#120342
#120312
#116682
#116622
#96712
#87982
#71472