Finite Group Databasebeta

← #145227

Subgroups — #145227

Order 512.

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

normal subgroups only

This group has 258 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#19204C211yesmaximal, characteristic
2#12036C211yesmaximal, characteristic
3#11962C211yesmaximal, characteristic
4#11962C211yesmaximal, characteristic
5#11638C211yesmaximal, characteristic
6#8639C211yesmaximal, characteristic
7#7291C211yesmaximal, characteristic
8#3229—21no—
9C2×#494C2211yescharacteristic
10#2960C2211yescharacteristic
11#2162C2211yescharacteristic
12#2162C2211yescharacteristic
13#1690—22no—
14#1670—21no—
15#1670—21no—
16#1567C2211yescharacteristic
17#1567C2211yescharacteristic
18#1564C2211yescharacteristic
19#1561—21no—
20#1546—21no—
21#1372—21no—
22#1371—21no—
23#1362—22no—
24#1362—22no—
25Q8⋊C16—22no—
26#1309—21no—
27C22×Q16—21no—
28C22×Q16—21no—
29#533D411yescharacteristic
30C2×C4⋊Q8—21no—
31#498—41no—
32#494—21no—
33#494—21no—
34#494—21no—
35#494D412yes—
36#487—41no—
37#483—42no—
38#475—22no—
39#475—22no—
40#446—21no—
41#446—21no—
42C8×Q8—21no—
43C8×Q8—21no—
44#431—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#332—22no—
65#332—22no—
66#332—41no—
67#332—41no—
68C22×Q8—41no—
69C2×Q16—22no—
70C2×Q16—22no—
71C2×Q16—41no—
72C2×Q16—41no—
73C2×Q16—82no—
74C2×Q16—82no—
75C2×M16—21no—
76C2×M16—41no—
77C2×M16—41no—
78C22×C8#4111yescharacteristic
79C22×C8#4111yescharacteristic
80C4⋊Q8—22no—
81C4⋊Q8—41no—
82C4⋊Q8—41no—
83C4⋊Q8—41no—
84C4⋊Q8D811yescharacteristic
85C4⋊Q8D811yescharacteristic
86#125—21no—
87C22⋊Q8—21no—
88C22⋊Q8—21no—
89C4×Q8—21no—
90C4×Q8—21no—
91#117—21no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C42C2×D411yescharacteristic
95C2×C16—22no—
96C2×C16—41no—
97#106—42no—
98#106—42no—
99C4⋊C8—21no—
100C4⋊C8—21no—
101C4⋊C8—21no—
102C4⋊C8—21no—
103C4⋊C8—41no—
104C4⋊C8—41no—
105C4⋊C8—41no—
106C4⋊C8—41no—
107C4⋊C8—41no—
108C4⋊C8—41no—
109#103—42no—
110#103—42no—
111C22⋊C8—41no—
112#97—41no—
113C4×C8—41no—
114C4×C8—41no—
115C4×C8C2×D411yescharacteristic
116C4×C8C2×D411yescharacteristic
117C4×C8C2×D411yescharacteristic
118C4×C8#4111yescharacteristic
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—42no—
122C2×Q8—82no—
123C2×Q8—82no—
124C2×Q8—81no—
125C22×C4—81no—
126C22×C4#12311yescharacteristic
127C22×C4#13511yescharacteristic
128C22×C4AGL(1,ℤ/8)11yescharacteristic
129Q16—82no—
130Q16—82no—
131Q16—82no—
132Q16—82no—
133M16—81no—
134M16—161no—
135M16—161no—
136C2×C8—22no—
137C2×C8—41no—
138C2×C8—41no—
139C2×C8—41no—
140C2×C8—41no—
141C2×C8—81no—
142C2×C8—81no—
143C2×C8#12111yescharacteristic
144C2×C8#12111yescharacteristic
145C2×C8#12311yescharacteristic
146C2×C8#12411yescharacteristic
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—41no—
152C4⋊C4—41no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—81no—
156C4⋊C4—81no—
157C22⋊C4—41no—
158C42—41no—
159C42#12011yescharacteristic
160C42#12111yescharacteristic
161C42C2×D811yescharacteristic
162C42#13711yescharacteristic
163C16—42no—
164C16—81no—
165C23#48211yescharacteristic
166Q8—41no—
167Q8—41no—
168Q8—41no—
169Q8—41no—
170Q8—82no—
171Q8—82no—
172Q8—162no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—82no—
182C2×C4—162no—
183C2×C4#39411yescharacteristic
184C2×C4#44711yescharacteristic
185C2×C4#45211yescharacteristic
186C2×C4#46611yescharacteristic
187C2×C4#46811yescharacteristic
188C2×C4#48011yescharacteristic
189C8—21no—
190C8—21no—
191C8—21no—
192C8—81no—
193C8—81no—
194C8—81no—
195C8—161no—
196C8—161no—
197C8#47112yes—
198C22—21no—
199C22—21no—
200C22—21no—
201C22#203311yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—81no—
206C4—81no—
207C4—162no—
208C4#204611yescharacteristic
209C4#204811yescharacteristic
210C4#219311yescharacteristic
211C4#219511yescharacteristic
212C4#222211yescharacteristic
213C4#222311yescharacteristic
214C2—41no—
215C2#1044211yescharacteristic
216C2#1338811yescharacteristic
217C2#1339411yescharacteristic
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
#192042
#120362
#119622
#116382
#86392
#72912