Finite Group Databasebeta

← #145257

Subgroups — #145257

Order 512.

242 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 64 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#19209C211yesmaximal, characteristic
2#12036C211yesmaximal, characteristic
3#11972C211yesmaximal, characteristic
4#11971C211yesmaximal, characteristic
5#11638C211yesmaximal, characteristic
6#8639C211yesmaximal, characteristic
7#7291C211yesmaximal, characteristic
8#3230—21no—
9C2×#500C2211yescharacteristic
10#2960C2211yescharacteristic
11#2162C2211yescharacteristic
12#2162C2211yescharacteristic
13#1696—22no—
14#1676—21no—
15#1676—21no—
16#1567C2211yescharacteristic
17#1567C2211yescharacteristic
18#1564C2211yescharacteristic
19#1561—21no—
20#1548—21no—
21#1372—21no—
22#1371—21no—
23#1365—22no—
24#1364—22no—
25Q8⋊C16—22no—
26#1309—21no—
27#533D411yescharacteristic
28C2×C4⋊Q8—21no—
29#500—21no—
30#500—21no—
31#500—21no—
32#500—41no—
33#500D412yes—
34#487—41no—
35#484—42no—
36#477—22no—
37#477—22no—
38#446—21no—
39#446—21no—
40C8×Q8—21no—
41C8×Q8—21no—
42#431—21no—
43C2×#107—21no—
44C2×#107—21no—
45#424—21no—
46#423—21no—
47#423—21no—
48#423D411yescharacteristic
49#405—21no—
50C2×C4×C8C2311yescharacteristic
51C4⋊C16—21no—
52C4⋊C16D412yes—
53C22⋊C16—21no—
54C22⋊C16—21no—
55C4×C16—21no—
56C4×C16—21no—
57#335—21no—
58#335—21no—
59#335—21no—
60#335—21no—
61#335D411yescharacteristic
62#335D411yescharacteristic
63#334—21no—
64#333—22no—
65#333—22no—
66#332—41no—
67#332—41no—
68C22×Q8—41no—
69C2×M16—21no—
70C2×M16—41no—
71C2×M16—41no—
72C22×C8#4111yescharacteristic
73C22×C8#4111yescharacteristic
74C4⋊Q8—22no—
75C4⋊Q8—41no—
76C4⋊Q8—41no—
77C4⋊Q8—41no—
78C4⋊Q8D811yescharacteristic
79C4⋊Q8D811yescharacteristic
80#125—21no—
81C22⋊Q8—21no—
82C22⋊Q8—21no—
83C4×Q8—21no—
84C4×Q8—21no—
85#117—21no—
86C2×C4⋊C4—41no—
87C2×C4⋊C4—41no—
88C2×C42C2×D411yescharacteristic
89C2×C16—22no—
90C2×C16—41no—
91#107—22no—
92#107—22no—
93#107—42no—
94#107—42no—
95#107—41no—
96#107—41no—
97C4⋊C8—21no—
98C4⋊C8—21no—
99C4⋊C8—21no—
100C4⋊C8—21no—
101C4⋊C8—41no—
102C4⋊C8—41no—
103C4⋊C8—41no—
104C4⋊C8—41no—
105C4⋊C8—41no—
106C4⋊C8—41no—
107#103—42no—
108#103—42no—
109C22⋊C8—41no—
110#97—41no—
111C4×C8—41no—
112C4×C8—41no—
113C4×C8C2×D411yescharacteristic
114C4×C8C2×D411yescharacteristic
115C4×C8C2×D411yescharacteristic
116C4×C8#4111yescharacteristic
117C2×Q8—21no—
118C2×Q8—21no—
119C2×Q8—42no—
120C2×Q8—81no—
121C2×Q8—161no—
122C2×Q8—161no—
123C22×C4—81no—
124C22×C4#12311yescharacteristic
125C22×C4#13511yescharacteristic
126C22×C4AGL(1,ℤ/8)11yescharacteristic
127M16—81no—
128M16—161no—
129M16—161no—
130C2×C8—22no—
131C2×C8—41no—
132C2×C8—41no—
133C2×C8—41no—
134C2×C8—41no—
135C2×C8—81no—
136C2×C8—81no—
137C2×C8#12111yescharacteristic
138C2×C8#12111yescharacteristic
139C2×C8#12311yescharacteristic
140C2×C8#12411yescharacteristic
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C4⋊C4—81no—
150C4⋊C4—81no—
151C22⋊C4—41no—
152C42—41no—
153C42#12011yescharacteristic
154C42#12111yescharacteristic
155C42C2×D811yescharacteristic
156C42#13711yescharacteristic
157C16—42no—
158C16—81no—
159C23#48211yescharacteristic
160Q8—41no—
161Q8—41no—
162Q8—41no—
163Q8—41no—
164Q8—162no—
165Q8—161no—
166Q8—161no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—82no—
176C2×C4—162no—
177C2×C4#39411yescharacteristic
178C2×C4#44711yescharacteristic
179C2×C4#45211yescharacteristic
180C2×C4#46611yescharacteristic
181C2×C4#46811yescharacteristic
182C2×C4#48011yescharacteristic
183C8—21no—
184C8—21no—
185C8—21no—
186C8—81no—
187C8—81no—
188C8—81no—
189C8—161no—
190C8—161no—
191C8#47312yes—
192C22—21no—
193C22—21no—
194C22—21no—
195C22#203311yescharacteristic
196C4—21no—
197C4—21no—
198C4—21no—
199C4—81no—
200C4—81no—
201C4—162no—
202C4#204711yescharacteristic
203C4#204911yescharacteristic
204C4#219311yescharacteristic
205C4#219511yescharacteristic
206C4#222111yescharacteristic
207C4#222311yescharacteristic
208C2—41no—
209C2#1044611yescharacteristic
210C2#1338811yescharacteristic
211C2#1339311yescharacteristic
subgroupG/H
center, socleC22#2033
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
#192092
#120362
#119722
#119712
#116382
#86392
#72912