Finite Group Databasebeta

← #136562

Subgroups — #136562

Order 512.

246 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 78 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#18086C211yesmaximal, characteristic
2#12036C211yesmaximal, characteristic
3#11950C211yesmaximal, characteristic
4#11672C211yesmaximal, characteristic
5#9634C211yesmaximal, characteristic
6#7163C211yesmaximal, characteristic
7#7155C211yesmaximal, characteristic
8#3170C2211yescharacteristic
9#2986—21no—
10#2162C2211yescharacteristic
11C2×C4×C16C2211yescharacteristic
12#1591—21no—
13#1587—22no—
14C8×Q16—21no—
15#1574—21no—
16#1567C2211yescharacteristic
17#1564C2211yescharacteristic
18#1564C2211yescharacteristic
19#1485—21no—
20C8×M16C2211yescharacteristic
21#1372—21no—
22#1371—21no—
23#1364C411yescharacteristic
24#1364C411yescharacteristic
25#1362C411yescharacteristic
26#1362C411yescharacteristic
27#1332—22no—
28#1299—21no—
29#533—21no—
30C22×C16—21no—
31#500C2×C411yescharacteristic
32#494C2×C411yescharacteristic
33#487—21no—
34#467—21no—
35#467Q812yes—
36#446—22no—
37#446—41no—
38C8×Q8—22no—
39C8×Q8—41no—
40C4×Q16—21no—
41C4×Q16D412yes—
42#433—42no—
43#431—21no—
44#431—21no—
45#431D411yescharacteristic
46#423—21no—
47C4×M16D411yescharacteristic
48C2×C4×C8C2311yescharacteristic
49C4⋊C16C2×C411yescharacteristic
50C4⋊C16C2×C411yescharacteristic
51C22⋊C16—21no—
52C4×C16—21no—
53C4×C16—21no—
54C4×C16—21no—
55#335—21no—
56#335—21no—
57#335—41no—
58#335C2×C411yescharacteristic
59#335C2×C411yescharacteristic
60#335D411yescharacteristic
61#335D411yescharacteristic
62#334—21no—
63#334—21no—
64#334—41no—
65Q8⋊C8—22no—
66Q8⋊C8—22no—
67#322—21no—
68C82—21no—
69C2×Q16—21no—
70C2×Q16C4⋊C412yes—
71C2×M16—21no—
72C2×M16—41no—
73C22×C8C2×Q811yescharacteristic
74C22×C8#4111yescharacteristic
75C4⋊Q8—21no—
76C4⋊Q8—21no—
77#125—41no—
78C22⋊Q8—22no—
79C22⋊Q8—41no—
80C4×Q8—22no—
81C4×Q8—41no—
82#117—41no—
83C2×C42C2×D411yescharacteristic
84C2×C16—22no—
85C2×C16—21no—
86C2×C16—21no—
87C2×C16—41no—
88C2×C16—41no—
89#107—21no—
90#107C4⋊C412yes—
91C4⋊C8—21no—
92C4⋊C8—21no—
93C4⋊C8—21no—
94C4⋊C8—21no—
95C4⋊C8—42no—
96C4⋊C8—42no—
97C4⋊C8—41no—
98C4⋊C8—41no—
99C4⋊C8D811yescharacteristic
100C4⋊C8D811yescharacteristic
101#103—22no—
102#103—22no—
103C22⋊C8—21no—
104C22⋊C8—41no—
105C22⋊C8—41no—
106#97—21no—
107#97—42no—
108C4×C8—21no—
109C4×C8—21no—
110C4×C8—42no—
111C4×C8—41no—
112C4×C8—41no—
113C4×C8C22×C411yescharacteristic
114C4×C8C2×D411yescharacteristic
115C4×C8C2×D411yescharacteristic
116C4×C8#4111yescharacteristic
117C2×Q8—22no—
118C2×Q8—41no—
119C22×C4C22⋊Q811yescharacteristic
120C22×C4#13511yescharacteristic
121C22×C4AGL(1,ℤ/8)11yescharacteristic
122Q16—42no—
123Q16—41no—
124Q16—41no—
125M16—22no—
126M16—41no—
127M16—161no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—41no—
133C2×C8—41no—
134C2×C8—41no—
135C2×C8—41no—
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—81no—
139C2×C8C2×C4⋊C411yescharacteristic
140C2×C8C4×D411yescharacteristic
141C2×C8C22⋊Q811yescharacteristic
142C2×C8#12311yescharacteristic
143C4⋊C4—22no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C22⋊C4—42no—
150C42—42no—
151C42C4×D411yescharacteristic
152C42#12011yescharacteristic
153C42C2×D811yescharacteristic
154C42#13711yescharacteristic
155C16—42no—
156C16—41no—
157C16—41no—
158C23#47811yescharacteristic
159Q8—42no—
160Q8—42no—
161Q8—81no—
162Q8—81no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4#38511yescharacteristic
172C2×C4C4×D811yescharacteristic
173C2×C4#44011yescharacteristic
174C2×C4#44711yescharacteristic
175C2×C4#45211yescharacteristic
176C2×C4#47411yescharacteristic
177C8—21no—
178C8—21no—
179C8—21no—
180C8—42no—
181C8—41no—
182C8—41no—
183C8—81no—
184C8—81no—
185C8—81no—
186C8—81no—
187C8—161no—
188C8#44311yescharacteristic
189C8#44411yescharacteristic
190C22—21no—
191C22—21no—
192C22—21no—
193C22#186211yescharacteristic
194C4—21no—
195C4—21no—
196C4—21no—
197C4—82no—
198C4—82no—
199C4#185811yescharacteristic
200C4#186611yescharacteristic
201C4#217811yescharacteristic
202C4#217911yescharacteristic
203C4#219311yescharacteristic
204C4#219511yescharacteristic
205C2—41no—
206C2#893011yescharacteristic
207C2#1293911yescharacteristic
208C2#1294111yescharacteristic
subgroupG/H
centerC2×C4#447
commutatorC4×C8C22×C4
Frattini, cosocleC2×C4×C8C23
socleC22#1862
prime radicalC23#478
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×M16 ◁ 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
#180862
#120362
#119502
#116722
#96342
#71632
#71552