Finite Group Databasebeta

← #145079

Subgroups — #145079

Order 512.

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

normal subgroups only

This group has 270 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#28701C211yesmaximal, characteristic
2#13281C211yesmaximal, characteristic
3#13184C211yesmaximal, characteristic
4#11935C211yesmaximal, characteristic
5#11608C211yesmaximal, characteristic
6#8675C211yesmaximal, characteristic
7#7172C211yesmaximal, characteristic
8#3166—21no—
9C2×#499C2211yescharacteristic
10#2960C2211yescharacteristic
11C2×#365—21no—
12#2150C2211yescharacteristic
13C2×C4×C16C2211yescharacteristic
14#2089—21no—
15#2089—21no—
16#1998—21no—
17#1951—21no—
18#1951—21no—
19#1846C2211yescharacteristic
20C4×#108C2211yescharacteristic
21#1564C2211yescharacteristic
22#1518—21no—
23#1383—21no—
24#1380—21no—
25#1380—21no—
26#1363—22no—
27Q8⋊C16—22no—
28#1286—21no—
29#533D411yescharacteristic
30C2×#125—21no—
31C2×M32—21no—
32C22×C16—21no—
33#501—41no—
34#501—41no—
35#499—21no—
36#499—21no—
37#499—21no—
38#499—21no—
39#499—41no—
40#499—41no—
41#446—21no—
42#446—21no—
43C8×Q8—21no—
44C8×Q8—21no—
45#431—21no—
46C2×#108D411yescharacteristic
47C2×#108D411yescharacteristic
48#428—21no—
49#428—21no—
50#428—21no—
51#428—21no—
52C2×#107—21no—
53C2×#107D411yescharacteristic
54C2×#107D411yescharacteristic
55C2×#106—21no—
56C2×#106—21no—
57#424—21no—
58#423D411yescharacteristic
59#405—21no—
60C4×M16—21no—
61C2×C4×C8C2311yescharacteristic
62#382—21no—
63#365—42no—
64C4⋊C16—21no—
65C4⋊C16D412yes—
66C4×C16—21no—
67C4×C16—21no—
68#343—21no—
69#343—21no—
70#343—21no—
71#343—21no—
72#341—21no—
73#335—21no—
74#334—21no—
75#328—42no—
76C2×M16—21no—
77C2×M16—21no—
78C2×M16—21no—
79C22×C8C2×D411yescharacteristic
80C22×C8C2×D411yescharacteristic
81C4⋊Q8SD1611yescharacteristic
82C4⋊Q8SD1611yescharacteristic
83#125—21no—
84#125—41no—
85#125—41no—
86#125—41no—
87#125—41no—
88C22⋊Q8—21no—
89C22⋊Q8—21no—
90C4×Q8—21no—
91C4×Q8—21no—
92#117—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—41no—
98C2×C42C2×D411yescharacteristic
99M32—41no—
100M32—41no—
101C2×C16—22no—
102C2×C16—22no—
103C2×C16—41no—
104C2×C16—41no—
105#108—21no—
106#108—21no—
107#108SD1612yes—
108#108Q1612yes—
109#107—21no—
110#107—21no—
111#107—21no—
112#107—21no—
113#107—41no—
114#107—41no—
115#107—41no—
116#107—41no—
117#107—42no—
118#106—41no—
119#106—41no—
120#106—41no—
121#106—41no—
122#106—41no—
123#106—41no—
124#106—41no—
125#106—41no—
126C4⋊C8—21no—
127C4⋊C8—21no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C22⋊C8—41no—
132#97—41no—
133#97—41no—
134C4×C8—41no—
135C4×C8—41no—
136C4×C8—41no—
137C4×C8C2×D411yescharacteristic
138C4×C8#4111yescharacteristic
139C4×C8#4111yescharacteristic
140C4×C8#4111yescharacteristic
141#95—41no—
142#95—41no—
143C2×Q8—21no—
144C2×Q8—21no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—81no—
148C22×C4#12011yescharacteristic
149C22×C4#13511yescharacteristic
150C22×C4AGL(1,ℤ/8)11yescharacteristic
151M16—22no—
152M16—22no—
153M16—41no—
154M16—41no—
155M16—41no—
156M16—41no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—41no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—81no—
163C2×C8#12111yescharacteristic
164C2×C8#12111yescharacteristic
165C2×C8#12311yescharacteristic
166C2×C8#12411yescharacteristic
167C2×C8C2×SD1611yescharacteristic
168C2×C8C2×Q1611yescharacteristic
169C2×C8#13711yescharacteristic
170C2×C8#13711yescharacteristic
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—81no—
182C4⋊C4—81no—
183C4⋊C4—81no—
184C4⋊C4—81no—
185C4⋊C4—81no—
186C4⋊C4—81no—
187C22⋊C4—41no—
188C42—41no—
189C42#12111yescharacteristic
190C42#12311yescharacteristic
191C42C2×SD1611yescharacteristic
192C42AGL(1,ℤ/8)11yescharacteristic
193C16—42no—
194C16—42no—
195C23#44911yescharacteristic
196Q8—42no—
197Q8—81no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—161no—
205C2×C4—161no—
206C2×C4—161no—
207C2×C4—161no—
208C2×C4—161no—
209C2×C4#39411yescharacteristic
210C2×C4#44811yescharacteristic
211C2×C4#45011yescharacteristic
212C2×C4#45111yescharacteristic
213C2×C4#45411yescharacteristic
214C2×C4#45611yescharacteristic
215C2×C4#46511yescharacteristic
216C2×C4#46911yescharacteristic
217C2×C4#48111yescharacteristic
218C2×C4#48211yescharacteristic
219C8—21no—
220C8—21no—
221C8—42no—
222C8—42no—
223C8—81no—
224C8—161no—
225C8#46111yescharacteristic
226C8#46211yescharacteristic
227C8#48711yescharacteristic
228C8#49111yescharacteristic
229C22—21no—
230C22—21no—
231C22#162611yescharacteristic
232C22#164811yescharacteristic
233C22#203411yescharacteristic
234C4—21no—
235C4—21no—
236C4—21no—
237C4—21no—
238C4—81no—
239C4—81no—
240C4—161no—
241C4—161no—
242C4—321no—
243C4#163711yescharacteristic
244C4#165111yescharacteristic
245C4#203811yescharacteristic
246C4#204311yescharacteristic
247C2—21no—
248C2—21no—
249C2#1041811yescharacteristic
250C2#1340111yescharacteristic
251C2#1340611yescharacteristic
subgroupG/H
center, socleC22#2034
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#449
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
#287012
#132812
#131842
#119352
#116082
#86752
#71722