Finite Group Databasebeta

← #145230

Subgroups — #145230

Order 512.

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

normal subgroups only

This group has 251 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#19204C211yesmaximal, characteristic
2#12031C211yesmaximal, characteristic
3#11965C211yesmaximal, characteristic
4#11965C211yesmaximal, characteristic
5#11643C211yesmaximal, characteristic
6#8635C211yesmaximal, characteristic
7#7293C211yesmaximal, characteristic
8#3229—21no—
9C2×#494C2211yescharacteristic
10#2960C2211yescharacteristic
11#2163C2211yescharacteristic
12#2163C2211yescharacteristic
13#1690—22no—
14#1670—22no—
15#1568C2211yescharacteristic
16#1568C2211yescharacteristic
17#1564C2211yescharacteristic
18#1546—21no—
19#1537—21no—
20#1368—22no—
21#1362—22no—
22#1362—22no—
23#1338—22no—
24#1307—21no—
25C22×Q16—21no—
26C22×Q16—21no—
27#533D411yescharacteristic
28C2×C4⋊Q8—21no—
29#498—41no—
30#494—21no—
31#494—21no—
32#494—21no—
33#494D412yes—
34#487—41no—
35#483—42no—
36#475—24no—
37#446—21no—
38#446—21no—
39C8×Q8—21no—
40C8×Q8—21no—
41#432—21no—
42#432—21no—
43#431—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—22no—
64C2×Q16—22no—
65C2×Q16—41no—
66C2×Q16—41no—
67C2×Q16—82no—
68C2×Q16—82no—
69C2×M16—21no—
70C22×C8#4111yescharacteristic
71C22×C8#4111yescharacteristic
72C4⋊Q8—22no—
73C4⋊Q8—41no—
74C4⋊Q8—41no—
75C4⋊Q8—41no—
76C4⋊Q8SD1611yescharacteristic
77C4⋊Q8SD1611yescharacteristic
78#125—21no—
79C22⋊Q8—21no—
80C22⋊Q8—21no—
81C4×Q8—21no—
82C4×Q8—21no—
83#117—21no—
84C2×C4⋊C4—41no—
85C2×C4⋊C4—41no—
86C2×C42C2×D411yescharacteristic
87C2×C16—22no—
88C2×C16—41no—
89#106—44no—
90C4⋊C8—21no—
91C4⋊C8—22no—
92C4⋊C8—21no—
93C4⋊C8—41no—
94C4⋊C8—41no—
95C4⋊C8—41no—
96C4⋊C8—41no—
97#103—44no—
98C22⋊C8—41no—
99C22⋊C8—41no—
100C22⋊C8—41no—
101#97—41no—
102#97—41no—
103#97—41no—
104C4×C8—41no—
105C4×C8—41no—
106C4×C8C2×D411yescharacteristic
107C4×C8C2×D411yescharacteristic
108C4×C8C2×D411yescharacteristic
109C4×C8#4111yescharacteristic
110C2×Q8—21no—
111C2×Q8—21no—
112C2×Q8—42no—
113C2×Q8—82no—
114C2×Q8—82no—
115C2×Q8—81no—
116C22×C4—81no—
117C22×C4#12311yescharacteristic
118C22×C4#13511yescharacteristic
119C22×C4AGL(1,ℤ/8)11yescharacteristic
120Q16—82no—
121Q16—82no—
122Q16—82no—
123Q16—82no—
124M16—81no—
125C2×C8—22no—
126C2×C8—41no—
127C2×C8—41no—
128C2×C8—42no—
129C2×C8—81no—
130C2×C8—81no—
131C2×C8#12111yescharacteristic
132C2×C8#12111yescharacteristic
133C2×C8#12311yescharacteristic
134C2×C8#12411yescharacteristic
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C4⋊C4—42no—
142C4⋊C4—42no—
143C4⋊C4—81no—
144C4⋊C4—81no—
145C22⋊C4—41no—
146C42—41no—
147C42#12011yescharacteristic
148C42#12111yescharacteristic
149C42C2×SD1611yescharacteristic
150C42AGL(1,ℤ/8)11yescharacteristic
151C16—42no—
152C16—81no—
153C23#48211yescharacteristic
154Q8—42no—
155Q8—81no—
156Q8—82no—
157Q8—82no—
158Q8—162no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—82no—
166C2×C4—162no—
167C2×C4#39411yescharacteristic
168C2×C4#44911yescharacteristic
169C2×C4#45011yescharacteristic
170C2×C4#46511yescharacteristic
171C2×C4#46911yescharacteristic
172C2×C4#48111yescharacteristic
173C8—21no—
174C8—21no—
175C8—21no—
176C8—82no—
177C8—81no—
178C8—161no—
179C8—161no—
180C8#47112yes—
181C22—21no—
182C22—21no—
183C22—21no—
184C22#203411yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—21no—
189C4—21no—
190C4—81no—
191C4—81no—
192C4—162no—
193C4#204611yescharacteristic
194C4#204811yescharacteristic
195C2—41no—
196C2#1044311yescharacteristic
197C2#1339711yescharacteristic
198C2#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
#192042
#120312
#119652
#116432
#86352
#72932