Finite Group Databasebeta

← #126373

Subgroups — #126373

Order 512.

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

normal subgroups only

This group has 260 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#32686C211yesmaximal, characteristic
2#13537C211yesmaximal, characteristic
3#13505C211yesmaximal, characteristic
4#10617C211yesmaximal, characteristic
5#7128C211yesmaximal, characteristic
6#7121C211yesmaximal, characteristic
7#7120C211yesmaximal, characteristic
8#2584—21no—
9C2×#366—21no—
10#2088—21no—
11#2059—21no—
12#2059—21no—
13#1984C2211yescharacteristic
14#1942C2211yescharacteristic
15#1942C2211yescharacteristic
16#1921—21no—
17#1918—21no—
18#1845C2211yescharacteristic
19#1803—21no—
20#1380—21no—
21#1380—21no—
22#1380—21no—
23#1374C2211yescharacteristic
24#1374C2211yescharacteristic
25#1296—21no—
26#1277C2211yescharacteristic
27C2×#125—21no—
28C2×C4×Q8D411yescharacteristic
29C22×C16—21no—
30C22×C16—21no—
31C2×#107—21no—
32C2×#107—21no—
33C2×#107D411yescharacteristic
34C2×#107D411yescharacteristic
35C2×#107D411yescharacteristic
36C2×#107D411yescharacteristic
37C2×#106—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8D411yescharacteristic
40C2×#103—41no—
41C2×C4×C8C2311yescharacteristic
42#398—41no—
43#395—41no—
44#389—21no—
45#389—21no—
46#389—21no—
47#389—21no—
48#389—41no—
49#389—41no—
50#384—21no—
51C4×C4⋊C4—21no—
52#366—42no—
53#340—21no—
54#340—21no—
55#340—21no—
56#340—21no—
57#340—21no—
58#340—41no—
59#336—21no—
60#336—21no—
61C22×Q8D811yescharacteristic
62C22×C8—21no—
63C22×C8—41no—
64C22×C8C2×D411yescharacteristic
65C22×C8C2×D411yescharacteristic
66#125—81no—
67#125—81no—
68C4×Q8—41no—
69C4×Q8—41no—
70C2×C4⋊C4—21no—
71C2×C4⋊C4—21no—
72C2×C4⋊C4—21no—
73C2×C4⋊C4—21no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4—41no—
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×C42—21no—
86C2×C42—41no—
87C2×C42C2×D411yescharacteristic
88C2×C16—22no—
89C2×C16—41no—
90C2×C16—41no—
91C2×C16—41no—
92C2×C16—41no—
93C2×C16—41no—
94#107—21no—
95#107—21no—
96#107—41no—
97#107—41no—
98#107—42no—
99#107—41no—
100#107—41no—
101#107SD1612yes—
102#107Q1612yes—
103#106—81no—
104C4⋊C8—41no—
105C4⋊C8—41no—
106C4⋊C8—41no—
107#103—82no—
108C4×C8—41no—
109#95—41no—
110#95—41no—
111#95—41no—
112#95—41no—
113#95—41no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—41no—
117C2×Q8—41no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—41no—
121C22×C4—41no—
122C22×C4—41no—
123C22×C4—41no—
124C22×C4—81no—
125C22×C4#12011yescharacteristic
126C22×C4C2×D811yescharacteristic
127C22×C4AGL(1,ℤ/8)11yescharacteristic
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—41no—
133C2×C8—41no—
134C2×C8—41no—
135C2×C8—81no—
136C2×C8—81no—
137C2×C8—81no—
138C2×C8C2×SD1611yescharacteristic
139C2×C8C2×Q1611yescharacteristic
140C2×C8#13711yescharacteristic
141C2×C8#13711yescharacteristic
142C4⋊C4—22no—
143C4⋊C4—22no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—81no—
152C4⋊C4—82no—
153C4⋊C4—82no—
154C4⋊C4—82no—
155C4⋊C4—81no—
156C4⋊C4—81no—
157C4⋊C4—81no—
158C4⋊C4—81no—
159C4⋊C4—81no—
160C4⋊C4—81no—
161C4⋊C4—161no—
162C4⋊C4—161no—
163C4⋊C4—161no—
164C42—21no—
165C42—21no—
166C42—41no—
167C42—41no—
168C42—161no—
169C16—42no—
170C16—81no—
171C23#44711yescharacteristic
172Q8—42no—
173Q8—81no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—161no—
198C2×C4—161no—
199C2×C4—161no—
200C2×C4#44811yescharacteristic
201C2×C4#45111yescharacteristic
202C2×C4#45411yescharacteristic
203C2×C4#45511yescharacteristic
204C2×C4#45611yescharacteristic
205C2×C4#45811yescharacteristic
206C2×C4#50811yescharacteristic
207C2×C4#50911yescharacteristic
208C8—21no—
209C8—21no—
210C8—21no—
211C8—21no—
212C8—81no—
213C8—161no—
214C22#160711yescharacteristic
215C22#162711yescharacteristic
216C22#164911yescharacteristic
217C22#218611yescharacteristic
218C22#219111yescharacteristic
219C22#219211yescharacteristic
220C22#219511yescharacteristic
221C4—21no—
222C4—21no—
223C4—41no—
224C4—82no—
225C4—82no—
226C4—81no—
227C4—81no—
228C4—161no—
229C4—161no—
230C4—321no—
231C4#161111yescharacteristic
232C4#161711yescharacteristic
233C4#164511yescharacteristic
234C4#166411yescharacteristic
235C2#779411yescharacteristic
236C2#1228011yescharacteristic
237C2#1228711yescharacteristic
238C2#1235511yescharacteristic
239C2#1236311yescharacteristic
240C2#1240511yescharacteristic
241C2#1241211yescharacteristic
subgroupG/H
center, socle, prime radicalC23#447
commutator, Frattini, cosocleC2×C4×C8C23
LCSG ▷ C2×C4×C8 ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984 ◁ G
LECSG ▷ C2×C4×C8 ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#326862
#135372
#135052
#106172
#71282
#71212
#71202