Finite Group Databasebeta

← #145887

Subgroups — #145887

Order 512.

279 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 279 conjugacy classes of subgroups — too many to draw. Only its 88 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#28833C211yesmaximal, characteristic
2#13177C211yesmaximal, characteristic
3#12908C211yesmaximal, characteristic
4#9621C211yesmaximal, characteristic
5#7275C211yesmaximal, characteristic
6#7178C211yesmaximal, characteristic
7#7170C211yesmaximal, characteristic
8#2570—21no—
9C2×#367—21no—
10C2×#367—21no—
11C2×#366—21no—
12C2×C4⋊C16C2211yescharacteristic
13C2×#346C2211yescharacteristic
14#2085—21no—
15#2083—21no—
16#1949—21no—
17#1948—21no—
18#1944—21no—
19#1847—21no—
20#1846C2211yescharacteristic
21#1845C2211yescharacteristic
22C4×#107C2211yescharacteristic
23#1770C2211yescharacteristic
24C2×#334C2211yescharacteristic
25#1380—21no—
26#1296—21no—
27C22×C16—21no—
28C22×C16—21no—
29C2×#107—21no—
30C2×#107—21no—
31C2×#107—21no—
32C2×#107D411yescharacteristic
33C2×#107D411yescharacteristic
34C2×#107D411yescharacteristic
35C2×#107D411yescharacteristic
36C2×#106—21no—
37C2×#106—21no—
38C2×#106—41no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8D411yescharacteristic
41C2×#97—21no—
42C2×C4×C8C2311yescharacteristic
43#400—41no—
44#398—41no—
45#389—21no—
46#389—21no—
47#387—41no—
48#387—41no—
49#384—21no—
50#384—21no—
51#382—21no—
52#382—21no—
53C4×C4⋊C4—21no—
54C4×C4⋊C4D411yescharacteristic
55#367—42no—
56#367—42no—
57#366—42no—
58C4⋊C16—21no—
59C4⋊C16Q812yes—
60#346—21no—
61#346Q812yes—
62#340—21no—
63#340—21no—
64#340—21no—
65#340—41no—
66#336—21no—
67#334—21no—
68#334Q812yes—
69C22×C8—21no—
70C22×C8—41no—
71C22×C8C2×D411yescharacteristic
72C22×C8C2×D411yescharacteristic
73C2×C4⋊C4—21no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4—21no—
76C2×C4⋊C4—21no—
77C2×C4⋊C4—41no—
78C2×C4⋊C4—41no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—41no—
81C2×C4⋊C4—41no—
82C2×C4⋊C4—41no—
83C2×C4⋊C4—41no—
84C2×C4⋊C4D811yescharacteristic
85C2×C4⋊C4D811yescharacteristic
86C2×C42—21no—
87C2×C42—41no—
88C2×C42C2×D411yescharacteristic
89C2×C16—22no—
90C2×C16—22no—
91C2×C16—22no—
92C2×C16—22no—
93C2×C16—41no—
94C2×C16—41no—
95#107—21no—
96#107—21no—
97#107—21no—
98#107—21no—
99#107—41no—
100#107—41no—
101#107—41no—
102#107—41no—
103#107—41no—
104#107—41no—
105#107—81no—
106#106—41no—
107#106—41no—
108#106—81no—
109#106—82no—
110C4⋊C8—22no—
111C4⋊C8—21no—
112C4⋊C8—41no—
113C4⋊C8Q1612yes—
114#97—41no—
115#97—41no—
116C4×C8C2×Q811yescharacteristic
117C4×C8C2×Q811yescharacteristic
118C4×C8C2×Q811yescharacteristic
119C4×C8#4111yescharacteristic
120#95—21no—
121#95—41no—
122#95—41no—
123#95—41no—
124#95—41no—
125#95—41no—
126#95—41no—
127#95—41no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—41no—
131C22×C4—41no—
132C22×C4—41no—
133C22×C4—41no—
134C22×C4—81no—
135C22×C4#12011yescharacteristic
136C22×C4C2×D811yescharacteristic
137C22×C4AGL(1,ℤ/8)11yescharacteristic
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—22no—
141C2×C8—41no—
142C2×C8—41no—
143C2×C8—42no—
144C2×C8—81no—
145C2×C8—81no—
146C2×C8C22⋊Q811yescharacteristic
147C2×C8C22⋊Q811yescharacteristic
148C2×C8C4⋊Q811yescharacteristic
149C2×C8C4⋊Q811yescharacteristic
150C2×C8#13511yescharacteristic
151C2×C8#13511yescharacteristic
152C2×C8AGL(1,ℤ/8)11yescharacteristic
153C2×C8#13711yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—81no—
165C4⋊C4—81no—
166C4⋊C4—82no—
167C4⋊C4—82no—
168C4⋊C4—81no—
169C4⋊C4—81no—
170C4⋊C4—161no—
171C4⋊C4—161no—
172C4⋊C4—161no—
173C42—41no—
174C42—41no—
175C42—161no—
176C42C22⋊Q811yescharacteristic
177C42C4⋊Q811yescharacteristic
178C42C2×Q1611yescharacteristic
179C42#13711yescharacteristic
180C16—24no—
181C16—42no—
182C23#44711yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—81no—
205C2×C4—161no—
206C2×C4—161no—
207C2×C4—161no—
208C2×C4#39511yescharacteristic
209C2×C4#44911yescharacteristic
210C2×C4#45111yescharacteristic
211C2×C4#45211yescharacteristic
212C2×C4#45311yescharacteristic
213C2×C4#45611yescharacteristic
214C2×C4#47411yescharacteristic
215C2×C4#47711yescharacteristic
216C2×C4#50011yescharacteristic
217C2×C4#50111yescharacteristic
218C8—21no—
219C8—21no—
220C8—42no—
221C8—82no—
222C8#47811yescharacteristic
223C8#47911yescharacteristic
224C8#49911yescharacteristic
225C8#50111yescharacteristic
226C22#162111yescharacteristic
227C22#164711yescharacteristic
228C22#205711yescharacteristic
229C22#219011yescharacteristic
230C22#219111yescharacteristic
231C22#219311yescharacteristic
232C22#219411yescharacteristic
233C4—21no—
234C4—21no—
235C4—21no—
236C4—21no—
237C4—81no—
238C4—81no—
239C4—161no—
240C4—161no—
241C4—161no—
242C4—161no—
243C4—321no—
244C4#163211yescharacteristic
245C4#164811yescharacteristic
246C4#205911yescharacteristic
247C4#206011yescharacteristic
248C2#1057911yescharacteristic
249C2#1233711yescharacteristic
250C2#1233811yescharacteristic
251C2#1240111yescharacteristic
252C2#1240211yescharacteristic
253C2#1345411yescharacteristic
254C2#1345611yescharacteristic
subgroupG/H
center, socle, prime radicalC23#447
commutator, Frattini, cosocleC2×C4×C8C23
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1770 ◁ 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
#288332
#131772
#129082
#96212
#72752
#71782
#71702