Finite Group Databasebeta

← #145613

Subgroups — #145613

Order 512.

268 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 66 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#19636C211yesmaximal, characteristic
2#11988C211yesmaximal, characteristic
3#11972C211yesmaximal, characteristic
4#11940C211yesmaximal, characteristic
5#11650C211yesmaximal, characteristic
6#9634C211yesmaximal, characteristic
7#7212C211yesmaximal, characteristic
8#3229—21no—
9#3170C2211yescharacteristic
10C2×#500C2211yescharacteristic
11#3139—21no—
12#2162C2211yescharacteristic
13#2150C2211yescharacteristic
14#1718—22no—
15#1710—21no—
16#1707—21no—
17#1574—21no—
18#1567C2211yescharacteristic
19#1564C2211yescharacteristic
20C8×M16C2211yescharacteristic
21#1365—22no—
22#1364—21no—
23#1364—22no—
24#1362—21no—
25#1332—22no—
26#1299—21no—
27#533—21no—
28C2×C4⋊Q8—21no—
29C2×M32—21no—
30#500—21no—
31#500—21no—
32#500—21no—
33#500D411yescharacteristic
34#500D412yes—
35#498—22no—
36#494D411yescharacteristic
37#491—42no—
38#487—22no—
39#487—22no—
40#487—22no—
41#487—21no—
42#483—42no—
43#475—41no—
44#475—41no—
45#467—21no—
46#467—21no—
47C4×Q16—21no—
48C4×Q16—21no—
49#431—21no—
50#431D411yescharacteristic
51C2×#107—21no—
52C2×#107—21no—
53#423—21no—
54#419—42no—
55C4×M16D411yescharacteristic
56C2×C4×C8C2311yescharacteristic
57C4⋊C16—21no—
58C4⋊C16—21no—
59C4⋊C16—21no—
60C22⋊C16—21no—
61C4×C16—21no—
62#335—21no—
63#335—21no—
64#335—41no—
65#335D412yes—
66#334—21no—
67#334—41no—
68#322—21no—
69C82—21no—
70C22×Q8—41no—
71C2×Q16—21no—
72C2×Q16—21no—
73C2×M16—21no—
74C2×M16—41no—
75C22×C8#4111yescharacteristic
76C22×C8#4111yescharacteristic
77C4⋊Q8—22no—
78C4⋊Q8—21no—
79C4⋊Q8—21no—
80C4⋊Q8—41no—
81C4⋊Q8—41no—
82C4⋊Q8—41no—
83#125—41no—
84C22⋊Q8—41no—
85C22⋊Q8—41no—
86C4×Q8—41no—
87C4×Q8—41no—
88#117—41no—
89C2×C4⋊C4—41no—
90C2×C4⋊C4—41no—
91C2×C42C2×D411yescharacteristic
92M32—81no—
93C2×C16—41no—
94C2×C16—41no—
95#107—22no—
96#107—21no—
97#107—22no—
98#107—21no—
99#107—41no—
100#107—41no—
101#106—42no—
102#106—42no—
103C4⋊C8—22no—
104C4⋊C8—41no—
105C4⋊C8—41no—
106C4⋊C8D811yescharacteristic
107C4⋊C8D811yescharacteristic
108#103—44no—
109#103—44no—
110#103—42no—
111#103—42no—
112#103—41no—
113#103—41no—
114C22⋊C8—21no—
115C22⋊C8—41no—
116#97SD1612yes—
117C4×C8—21no—
118C4×C8—21no—
119C4×C8—41no—
120C4×C8C2×D411yescharacteristic
121C4×C8C2×D411yescharacteristic
122C4×C8C2×D411yescharacteristic
123C4×C8#4111yescharacteristic
124C2×Q8—41no—
125C2×Q8—41no—
126C2×Q8—42no—
127C2×Q8—84no—
128C2×Q8—81no—
129C22×C4—81no—
130C22×C4#12411yescharacteristic
131C22×C4AGL(1,ℤ/8)11yescharacteristic
132C22×C4AGL(1,ℤ/8)11yescharacteristic
133Q16—41no—
134Q16—41no—
135Q16—81no—
136M16—42no—
137M16—161no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—22no—
143C2×C8—41no—
144C2×C8—42no—
145C2×C8—81no—
146C2×C8#12111yescharacteristic
147C2×C8#12111yescharacteristic
148C2×C8#12311yescharacteristic
149C2×C8#12311yescharacteristic
150C4⋊C4—41no—
151C4⋊C4—42no—
152C4⋊C4—42no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—81no—
157C4⋊C4—81no—
158C4⋊C4—81no—
159C4⋊C4—81no—
160C22⋊C4—81no—
161C42—81no—
162C42#12011yescharacteristic
163C42#12111yescharacteristic
164C42C2×D811yescharacteristic
165C42C2×SD1611yescharacteristic
166C16—81no—
167C16—81no—
168C23#49011yescharacteristic
169Q8—84no—
170Q8—81no—
171Q8—81no—
172Q8—81no—
173Q8—81no—
174Q8—162no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—82no—
183C2×C4—162no—
184C2×C4#39411yescharacteristic
185C2×C4#44711yescharacteristic
186C2×C4#45011yescharacteristic
187C2×C4#45911yescharacteristic
188C2×C4#46011yescharacteristic
189C2×C4#48611yescharacteristic
190C8—21no—
191C8—21no—
192C8—21no—
193C8—42no—
194C8—41no—
195C8—41no—
196C8—82no—
197C8—161no—
198C8#47111yescharacteristic
199C8#47311yescharacteristic
200C22—21no—
201C22—21no—
202C22—21no—
203C22#204111yescharacteristic
204C4—21no—
205C4—21no—
206C4—21no—
207C4—161no—
208C4—161no—
209C4—162no—
210C4#204911yescharacteristic
211C4#205211yescharacteristic
212C4#219311yescharacteristic
213C4#219511yescharacteristic
214C4#221212yes—
215C2—41no—
216C2#1055011yescharacteristic
217C2#1341211yescharacteristic
218C2#1341411yescharacteristic
subgroupG/H
center, socleC22#2041
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#490
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ 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
#196362
#119882
#119722
#119402
#116502
#96342
#72122