Finite Group Databasebeta

← #145259

Subgroups — #145259

Order 512.

241 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 241 conjugacy classes of subgroups — too many to draw. Only its 60 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#19208C211yesmaximal, characteristic
2#12031C211yesmaximal, characteristic
3#11975C211yesmaximal, characteristic
4#11974C211yesmaximal, characteristic
5#11643C211yesmaximal, characteristic
6#8635C211yesmaximal, characteristic
7#7293C211yesmaximal, characteristic
8#3209—21no—
9C2×#500C2211yescharacteristic
10#2960C2211yescharacteristic
11#2163C2211yescharacteristic
12#2163C2211yescharacteristic
13#1694—22no—
14#1674—22no—
15#1568C2211yescharacteristic
16#1568C2211yescharacteristic
17#1564C2211yescharacteristic
18#1549—21no—
19#1537—21no—
20#1368—22no—
21#1365—22no—
22#1364—22no—
23#1338—22no—
24#1307—21no—
25#533D411yescharacteristic
26C2×C4⋊Q8—21no—
27#500—21no—
28#500—21no—
29#500—21no—
30#500D412yes—
31#494—41no—
32#487—41no—
33#462—24no—
34#451—42no—
35#446—21no—
36#446—21no—
37C8×Q8—21no—
38C8×Q8—21no—
39#432—21no—
40#432—21no—
41#431—21no—
42C2×#107—21no—
43C2×#107—21no—
44#424—21no—
45#423D411yescharacteristic
46#405—21no—
47C2×C4×C8C2311yescharacteristic
48C4⋊C16—21no—
49C4⋊C16D412yes—
50C22⋊C16—21no—
51C22⋊C16—21no—
52#346—21no—
53#346—21no—
54#335—21no—
55#335—21no—
56#335—21no—
57#334—21no—
58#334—21no—
59#334D412yes—
60#332—24no—
61#330—42no—
62C22×Q8—41no—
63C2×Q16—44no—
64C2×M16—21no—
65C22×C8#4111yescharacteristic
66C22×C8#4111yescharacteristic
67C4⋊Q8—22no—
68C4⋊Q8—41no—
69C4⋊Q8—41no—
70C4⋊Q8—41no—
71C4⋊Q8SD1611yescharacteristic
72C4⋊Q8SD1611yescharacteristic
73#125—21no—
74C22⋊Q8—21no—
75C22⋊Q8—21no—
76C4×Q8—21no—
77C4×Q8—21no—
78#117—21no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—41no—
81C2×C42C2×D411yescharacteristic
82C2×C16—22no—
83C2×C16—41no—
84#107—22no—
85#107—22no—
86#107—41no—
87#107—41no—
88C4⋊C8—21no—
89C4⋊C8—22no—
90C4⋊C8—21no—
91C4⋊C8—41no—
92C4⋊C8—41no—
93C4⋊C8—41no—
94C4⋊C8—41no—
95#103—44no—
96C22⋊C8—41no—
97C22⋊C8—41no—
98C22⋊C8—41no—
99#97—41no—
100#97—41no—
101#97—41no—
102C4×C8—41no—
103C4×C8—41no—
104C4×C8C2×D411yescharacteristic
105C4×C8C2×D411yescharacteristic
106C4×C8C2×D411yescharacteristic
107C4×C8#4111yescharacteristic
108C2×Q8—21no—
109C2×Q8—21no—
110C2×Q8—42no—
111C2×Q8—81no—
112C2×Q8—162no—
113C22×C4—81no—
114C22×C4#12311yescharacteristic
115C22×C4#13511yescharacteristic
116C22×C4AGL(1,ℤ/8)11yescharacteristic
117Q16—164no—
118M16—81no—
119C2×C8—22no—
120C2×C8—41no—
121C2×C8—41no—
122C2×C8—42no—
123C2×C8—81no—
124C2×C8—81no—
125C2×C8#12111yescharacteristic
126C2×C8#12111yescharacteristic
127C2×C8#12311yescharacteristic
128C2×C8#12411yescharacteristic
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—42no—
136C4⋊C4—42no—
137C4⋊C4—81no—
138C4⋊C4—81no—
139C22⋊C4—41no—
140C42—41no—
141C42#12011yescharacteristic
142C42#12111yescharacteristic
143C42C2×SD1611yescharacteristic
144C42AGL(1,ℤ/8)11yescharacteristic
145C16—42no—
146C16—81no—
147C23#48211yescharacteristic
148Q8—42no—
149Q8—81no—
150Q8—84no—
151Q8—162no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—82no—
159C2×C4—162no—
160C2×C4#39411yescharacteristic
161C2×C4#44911yescharacteristic
162C2×C4#45011yescharacteristic
163C2×C4#46511yescharacteristic
164C2×C4#46911yescharacteristic
165C2×C4#48111yescharacteristic
166C8—21no—
167C8—21no—
168C8—21no—
169C8—82no—
170C8—81no—
171C8—161no—
172C8—161no—
173C8#47312yes—
174C22—21no—
175C22—21no—
176C22—21no—
177C22#203411yescharacteristic
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—81no—
184C4—81no—
185C4—162no—
186C4#204711yescharacteristic
187C4#204911yescharacteristic
188C2—41no—
189C2#1044711yescharacteristic
190C2#1339611yescharacteristic
191C2#1340311yescharacteristic
subgroupG/H
center, socleC22#2034
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#482
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
#192082
#120312
#119752
#119742
#116432
#86352
#72932