Finite Group Databasebeta

← #139079

Subgroups — #139079

Order 512.

279 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 279 conjugacy classes of subgroups — too many to draw. Only its 74 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#33796C211yesmaximal, characteristic
2#17991C211yesmaximal, characteristic
3#11975C211yesmaximal, characteristic
4#11865C211yesmaximal, characteristic
5#9778C211yesmaximal, characteristic
6#7220C211yesmaximal, characteristic
7#7147C211yesmaximal, characteristic
8#3170C2211yescharacteristic
9C2×#500C2211yescharacteristic
10#2985—21no—
11#2252C412yes—
12#2241C412yes—
13#2236—22no—
14#2227—22no—
15#2163C2211yescharacteristic
16#2162C2211yescharacteristic
17#1837C2211yescharacteristic
18#1587—22no—
19#1584—22no—
20#1568C2211yescharacteristic
21#1549—21no—
22#1548—21no—
23#1497—21no—
24#1452C2211yescharacteristic
25#1365—22no—
26#1350—22no—
27#533—21no—
28C2×C4⋊Q8—21no—
29#500—21no—
30#500—21no—
31#500—21no—
32#500C2×C412yes—
33#500C2×C411yescharacteristic
34#494C2×C411yescharacteristic
35#487—21no—
36#467—21no—
37#467D412yes—
38#446—22no—
39#446—42no—
40C8×Q8—22no—
41C4×Q16—21no—
42C4×Q16D412yes—
43#433—42no—
44#432—21no—
45#431D411yescharacteristic
46#431D411yescharacteristic
47C2×#107—21no—
48C2×#107—21no—
49#423—21no—
50C2×C4×C8C2311yescharacteristic
51#366—24no—
52C4⋊C16—21no—
53C4⋊C16—21no—
54#358—24no—
55C22⋊C16—21no—
56C22⋊C16—21no—
57#346—21no—
58C4×C16C2×C412yes—
59#341—21no—
60#341—21no—
61#335D412yes—
62#334—21no—
63#333—42no—
64#332—42no—
65Q8⋊C8—24no—
66#322—21no—
67#322—21no—
68C22×Q8—41no—
69C2×Q16—21no—
70C2×Q16C22⋊C412yes—
71C2×M16—41no—
72C22×C8C2×D411yescharacteristic
73C22×C8#4111yescharacteristic
74C4⋊Q8—21no—
75C4⋊Q8—21no—
76C4⋊Q8—22no—
77C4⋊Q8—41no—
78C4⋊Q8—41no—
79C4⋊Q8—41no—
80#125—41no—
81C22⋊Q8—22no—
82C22⋊Q8—41no—
83C4×Q8—22no—
84C4×Q8—41no—
85#117—41no—
86C2×C4⋊C4—41no—
87C2×C4⋊C4—41no—
88C2×C42C2×D411yescharacteristic
89C2×C16—22no—
90C2×C16—41no—
91#107—21no—
92#107—22no—
93#107—22no—
94#107—41no—
95#107—41no—
96#107C22⋊C412yes—
97C4⋊C8—22no—
98C4⋊C8—21no—
99C4⋊C8—42no—
100C4⋊C8—42no—
101C4⋊C8—41no—
102C4⋊C8—41no—
103C4⋊C8D812yes—
104#103—22no—
105#103—22no—
106C22⋊C8—21no—
107C22⋊C8—21no—
108C22⋊C8—41no—
109#97—42no—
110#97—41no—
111C4×C8—21no—
112C4×C8—21no—
113C4×C8—42no—
114C4×C8C22×C411yescharacteristic
115C4×C8C2×D411yescharacteristic
116C4×C8C2×D411yescharacteristic
117C4×C8#4111yescharacteristic
118C2×Q8—22no—
119C2×Q8—41no—
120C2×Q8—42no—
121C2×Q8—81no—
122C2×Q8—162no—
123C22×C4—81no—
124C22×C4#12111yescharacteristic
125C22×C4#13511yescharacteristic
126C22×C4AGL(1,ℤ/8)11yescharacteristic
127Q16—42no—
128Q16—81no—
129M16—81no—
130M16—81no—
131C2×C8—22no—
132C2×C8—41no—
133C2×C8—41no—
134C2×C8—42no—
135C2×C8—41no—
136C2×C8—81no—
137C2×C8C2×C22⋊C411yescharacteristic
138C2×C8C4×D411yescharacteristic
139C2×C8#12111yescharacteristic
140C2×C8#12311yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—41no—
145C4⋊C4—42no—
146C4⋊C4—42no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C4⋊C4—81no—
150C4⋊C4—81no—
151C22⋊C4—42no—
152C42—42no—
153C42C4×D411yescharacteristic
154C42#12011yescharacteristic
155C42C2×D811yescharacteristic
156C42AGL(1,ℤ/8)11yescharacteristic
157C16—42no—
158C16—81no—
159C23#46311yescharacteristic
160Q8—42no—
161Q8—42no—
162Q8—161no—
163Q8—162no—
164Q8—162no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—82no—
172C2×C4—162no—
173C2×C4#38611yescharacteristic
174C2×C4C4×D811yescharacteristic
175C2×C4#44211yescharacteristic
176C2×C4#44711yescharacteristic
177C2×C4#44911yescharacteristic
178C2×C4#45911yescharacteristic
179C8—21no—
180C8—21no—
181C8—21no—
182C8—21no—
183C8—42no—
184C8—81no—
185C8—82no—
186C8—161no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22#187911yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—82no—
196C4—82no—
197C4—162no—
198C4#190211yescharacteristic
199C4#190911yescharacteristic
200C4#219512yes—
201C2—41no—
202C2#929111yescharacteristic
203C2#1302011yescharacteristic
204C2#1303611yescharacteristic
subgroupG/H
center, socleC22#1879
commutatorC4×C8C22×C4
Frattini, cosocleC2×C4×C8C23
prime radicalC23#463
LCSG ▷ 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
#337962
#179912
#119752
#118652
#97782
#72202
#71472