Finite Group Databasebeta

← #145082

Subgroups — #145082

Order 512.

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

normal subgroups only

This group has 295 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#28678C211yesmaximal, characteristic
2#13289C211yesmaximal, characteristic
3#13185C211yesmaximal, characteristic
4#11935C211yesmaximal, characteristic
5#11607C211yesmaximal, characteristic
6#8659C211yesmaximal, characteristic
7#7175C211yesmaximal, characteristic
8C2×#499C2211yescharacteristic
9C2×C8×Q8C2211yescharacteristic
10#2584—21no—
11C2×#365—21no—
12#2150C2211yescharacteristic
13C4×M32C2211yescharacteristic
14#2087—21no—
15#2086—21no—
16#1989—21no—
17#1941—21no—
18#1941—21no—
19#1848C2211yescharacteristic
20C4×#106C2211yescharacteristic
21#1564C2211yescharacteristic
22#1487—21no—
23#1387—21no—
24#1387—21no—
25#1383—21no—
26#1363—22no—
27Q8⋊C16—22no—
28#1301—21no—
29C2×#125—21no—
30C2×C4×Q8D411yescharacteristic
31C2×M32—21no—
32C2×M32—21no—
33#499—21no—
34#499—21no—
35#499—21no—
36#499—21no—
37C8×Q8—21no—
38C8×Q8—21no—
39C8×Q8—21no—
40C8×Q8—21no—
41#431—21no—
42C2×#108—21no—
43C2×#108—21no—
44C2×#107D411yescharacteristic
45C2×#107D411yescharacteristic
46C2×#106—21no—
47C2×#106D411yescharacteristic
48C2×#106D411yescharacteristic
49#423—21no—
50C2×C4⋊C8—21no—
51C2×C4⋊C8D411yescharacteristic
52C2×C4×C8—21no—
53C2×C4×C8C2311yescharacteristic
54#398—41no—
55#395—41no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—41no—
61#389—41no—
62C4×C4⋊C4—21no—
63#365—42no—
64C4⋊C16—21no—
65C4⋊C16D412yes—
66#346—21no—
67C4×C16—21no—
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#340—21no—
73#335—21no—
74#334—21no—
75Q8⋊C8—42no—
76C22×Q8SD1611yescharacteristic
77C2×M16—41no—
78C22×C8—21no—
79C22×C8C2×D411yescharacteristic
80C22×C8C2×D411yescharacteristic
81#125—41no—
82#125—41no—
83#125—41no—
84#125—41no—
85C4×Q8—21no—
86C4×Q8—21no—
87C4×Q8—21no—
88C4×Q8—21no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—41no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4SD1611yescharacteristic
101C2×C42—21no—
102C2×C42—41no—
103C2×C42C2×D411yescharacteristic
104M32—22no—
105M32—41no—
106M32—41no—
107M32—41no—
108C2×C16—22no—
109C2×C16—41no—
110#108—42no—
111#108—41no—
112#108—41no—
113#107—21no—
114#107—21no—
115#107—21no—
116#107—21no—
117#106—21no—
118#106—21no—
119#106—41no—
120#106—41no—
121#106SD1612yes—
122#106Q1612yes—
123C4⋊C8—21no—
124C4⋊C8—21no—
125C4⋊C8—41no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C22⋊C8—41no—
131C4×C8—41no—
132C4×C8—41no—
133C4×C8—41no—
134C4×C8C2×D411yescharacteristic
135C4×C8#4111yescharacteristic
136C4×C8#4111yescharacteristic
137C4×C8#4111yescharacteristic
138#95—41no—
139#95—41no—
140#95—41no—
141#95—41no—
142#95—41no—
143C2×Q8—21no—
144C2×Q8—21no—
145C2×Q8—42no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4#12011yescharacteristic
153C22×C4C2×SD1611yescharacteristic
154C22×C4AGL(1,ℤ/8)11yescharacteristic
155M16—81no—
156M16—81no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—41no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—81no—
163C2×C8—81no—
164C2×C8#12111yescharacteristic
165C2×C8#12111yescharacteristic
166C2×C8#12311yescharacteristic
167C2×C8#12411yescharacteristic
168C2×C8C2×SD1611yescharacteristic
169C2×C8C2×Q1611yescharacteristic
170C2×C8#13711yescharacteristic
171C2×C8#13711yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—82no—
185C4⋊C4—82no—
186C4⋊C4—81no—
187C4⋊C4—81no—
188C4⋊C4—81no—
189C4⋊C4—81no—
190C4⋊C4—161no—
191C4⋊C4—161no—
192C42—41no—
193C42—41no—
194C42—161no—
195C42#12111yescharacteristic
196C42#12311yescharacteristic
197C42#13511yescharacteristic
198C42AGL(1,ℤ/8)11yescharacteristic
199C16—42no—
200C16—42no—
201C23#45011yescharacteristic
202Q8—22no—
203Q8—22no—
204Q8—41no—
205Q8—41no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4#39411yescharacteristic
227C2×C4#44811yescharacteristic
228C2×C4#44911yescharacteristic
229C2×C4#45111yescharacteristic
230C2×C4#45411yescharacteristic
231C2×C4#45611yescharacteristic
232C2×C4#46511yescharacteristic
233C2×C4#46911yescharacteristic
234C2×C4#48111yescharacteristic
235C2×C4#48211yescharacteristic
236C8—21no—
237C8—21no—
238C8—81no—
239C8—161no—
240C8—161no—
241C8#46111yescharacteristic
242C8#46211yescharacteristic
243C8#48711yescharacteristic
244C8#49111yescharacteristic
245C22—21no—
246C22—21no—
247C22#163711yescharacteristic
248C22#165111yescharacteristic
249C22#203411yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—42no—
255C4—82no—
256C4—82no—
257C4—81no—
258C4—161no—
259C4—161no—
260C4#162611yescharacteristic
261C4#164811yescharacteristic
262C4#203811yescharacteristic
263C4#204311yescharacteristic
264C2—21no—
265C2—21no—
266C2#1041811yescharacteristic
267C2#1339511yescharacteristic
268C2#1340011yescharacteristic
subgroupG/H
center, socleC22#2034
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#450
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C8×Q8 ◁ 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
#286782
#132892
#131852
#119352
#116072
#86592
#71752