Finite Group Databasebeta

← #145299

Subgroups — #145299

Order 512.

238 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 60 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#19342C211yesmaximal, characteristic
2#12021C211yesmaximal, characteristic
3#11984C211yesmaximal, characteristic
4#11676C211yesmaximal, characteristic
5#11606C211yesmaximal, characteristic
6#8633C211yesmaximal, characteristic
7#7242C211yesmaximal, characteristic
8#3237—21no—
9#3170C2211yescharacteristic
10#2960C2211yescharacteristic
11C2×C4⋊C16C2211yescharacteristic
12C4×M32C2211yescharacteristic
13#1704—22no—
14#1676—21no—
15#1670—21no—
16#1568C2211yescharacteristic
17#1568C2211yescharacteristic
18#1568C2211yescharacteristic
19#1559—21no—
20#1537—21no—
21#1368—22no—
22#1364—21no—
23#1362—21no—
24Q8⋊C16—21no—
25Q8⋊C16—21no—
26#1332—21no—
27#1332—21no—
28#1307—21no—
29#533—21no—
30#533D411yescharacteristic
31C2×M32—21no—
32C22×C16—21no—
33#501—41no—
34#500D411yescharacteristic
35#494D411yescharacteristic
36#491—41no—
37#487—21no—
38#485—42no—
39#477—22no—
40#475—22no—
41#467—21no—
42#467—21no—
43#446—21no—
44#446—21no—
45C8×Q8—21no—
46C8×Q8—21no—
47C4×Q16—21no—
48C4×Q16—21no—
49#432—21no—
50#432—21no—
51#432—21no—
52#424—21no—
53#423D411yescharacteristic
54#405—21no—
55C2×C4×C8C2311yescharacteristic
56C4⋊C16—21no—
57C4⋊C16—21no—
58#346—21no—
59C4×C16D411yescharacteristic
60C4×C16D411yescharacteristic
61#335—21no—
62#335—21no—
63#335—21no—
64#334—21no—
65#334—21no—
66#334D412yes—
67#333—22no—
68#332—22no—
69#330—42no—
70C2×Q16—21no—
71C2×Q16—21no—
72C2×M16—21no—
73C22×C8#4111yescharacteristic
74C22×C8#4111yescharacteristic
75C4⋊Q8—21no—
76C4⋊Q8—21no—
77C4⋊Q8SD1611yescharacteristic
78C4⋊Q8SD1611yescharacteristic
79#125—21no—
80#125—41no—
81C22⋊Q8—21no—
82C22⋊Q8—21no—
83C22⋊Q8—41no—
84C22⋊Q8—41no—
85C4×Q8—21no—
86C4×Q8—21no—
87C4×Q8—41no—
88C4×Q8—41no—
89#117—21no—
90#117—41no—
91C2×C42C2×D411yescharacteristic
92M32—42no—
93C2×C16—21no—
94C2×C16—21no—
95C2×C16—41no—
96C2×C16—81no—
97#107—21no—
98#107—21no—
99#107—42no—
100#106—42no—
101C4⋊C8—21no—
102C4⋊C8—22no—
103C4⋊C8—21no—
104C4⋊C8—41no—
105C4⋊C8—41no—
106C4⋊C8—41no—
107C4⋊C8—41no—
108#103—42no—
109#103—42no—
110#103—41no—
111#103—41no—
112C22⋊C8—41no—
113C22⋊C8—41no—
114C22⋊C8—41no—
115#97—41no—
116#97—41no—
117#97—41no—
118#97—41no—
119C4×C8—41no—
120C4×C8C2×D411yescharacteristic
121C4×C8C2×D411yescharacteristic
122C4×C8C2×D411yescharacteristic
123C4×C8#4111yescharacteristic
124C2×Q8—21no—
125C2×Q8—21no—
126C2×Q8—41no—
127C2×Q8—41no—
128C22×C4#12311yescharacteristic
129C22×C4#13511yescharacteristic
130C22×C4AGL(1,ℤ/8)11yescharacteristic
131Q16—41no—
132Q16—41no—
133Q16—81no—
134M16—81no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—41no—
138C2×C8—41no—
139C2×C8—42no—
140C2×C8—81no—
141C2×C8—81no—
142C2×C8#12111yescharacteristic
143C2×C8#12111yescharacteristic
144C2×C8#12311yescharacteristic
145C2×C8#12411yescharacteristic
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—41no—
151C4⋊C4—41no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—81no—
157C4⋊C4—81no—
158C22⋊C4—41no—
159C22⋊C4—81no—
160C42—41no—
161C42—81no—
162C42#12011yescharacteristic
163C42#12111yescharacteristic
164C42C2×SD1611yescharacteristic
165C42AGL(1,ℤ/8)11yescharacteristic
166C16—22no—
167C16—41no—
168C16—81no—
169C23#48211yescharacteristic
170Q8—42no—
171Q8—42no—
172Q8—81no—
173Q8—81no—
174Q8—161no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—81no—
182C2×C4—81no—
183C2×C4#39411yescharacteristic
184C2×C4#44911yescharacteristic
185C2×C4#45011yescharacteristic
186C2×C4#46511yescharacteristic
187C2×C4#46911yescharacteristic
188C2×C4#48111yescharacteristic
189C8—21no—
190C8—21no—
191C8—21no—
192C8—82no—
193C8—81no—
194C8—161no—
195C8—161no—
196C8#47111yescharacteristic
197C8#47311yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22#203411yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—81no—
208C4—81no—
209C4—161no—
210C4—161no—
211C4#205011yescharacteristic
212C4#205211yescharacteristic
213C2—41no—
214C2#1045911yescharacteristic
215C2#1339711yescharacteristic
216C2#1340611yescharacteristic
subgroupG/H
center, socleC22#2034
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
#193422
#120212
#119842
#116762
#116062
#86332
#72422