Finite Group Databasebeta

← #145892

Subgroups — #145892

Order 512.

295 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 295 conjugacy classes of subgroups — too many to draw. Only its 100 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#28827C211yesmaximal, characteristic
2#13177C211yesmaximal, characteristic
3#12888C211yesmaximal, characteristic
4#9614C211yesmaximal, characteristic
5#7274C211yesmaximal, characteristic
6#7171C211yesmaximal, characteristic
7#7167C211yesmaximal, characteristic
8#2552—21no—
9C2×#367—21no—
10C2×C4⋊C16C2211yescharacteristic
11C2×C4×C16C2211yescharacteristic
12#2083—22no—
13#1947—21no—
14#1947—21no—
15#1942—21no—
16#1845—21no—
17#1845C2211yescharacteristic
18#1845C2211yescharacteristic
19C4×#107C2211yescharacteristic
20C8×C4⋊C4C2211yescharacteristic
21C2×#335C2211yescharacteristic
22#1380—22no—
23#1380—21no—
24#1296—21no—
25C2×#125—41no—
26C22×C16—21no—
27C22×C16—21no—
28C2×#107—21no—
29C2×#107—21no—
30C2×#107—21no—
31C2×#107—22no—
32C2×#107—41no—
33C2×#107D411yescharacteristic
34C2×#107D411yescharacteristic
35C2×#107D412yes—
36C2×C4⋊C8—21no—
37C2×C4⋊C8D411yescharacteristic
38C2×C4×C8—21no—
39C2×C4×C8C2311yescharacteristic
40#398—42no—
41#389—22no—
42#389—41no—
43#384—22no—
44#384—21no—
45#384—21no—
46C4×C4⋊C4—21no—
47C4×C4⋊C4D411yescharacteristic
48#367—42no—
49C4⋊C16—21no—
50C4⋊C16Q812yes—
51C4×C16—21no—
52C4×C16Q812yes—
53#340—22no—
54#340—21no—
55#340—41no—
56#336—21no—
57#335—21no—
58#335Q812yes—
59C22×C8—21no—
60C22×C8—41no—
61C22×C8C2×D411yescharacteristic
62C22×C8C2×D411yescharacteristic
63#125—82no—
64#125—82no—
65C2×C4⋊C4—21no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—42no—
69C2×C4⋊C4—42no—
70C2×C4⋊C4—41no—
71C2×C4⋊C4—41no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4—42no—
74C2×C4⋊C4—41no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4D811yescharacteristic
77C2×C4⋊C4D811yescharacteristic
78C2×C42—21no—
79C2×C42—41no—
80C2×C42C2×D411yescharacteristic
81C2×C16—22no—
82C2×C16—22no—
83C2×C16—41no—
84C2×C16—41no—
85C2×C16—41no—
86C2×C16—41no—
87#107—21no—
88#107—21no—
89#107—21no—
90#107—21no—
91#107—41no—
92#107—41no—
93#107—42no—
94#107—42no—
95#107—41no—
96#107—41no—
97#107—82no—
98#107—82no—
99C4⋊C8—22no—
100C4⋊C8—21no—
101C4⋊C8—41no—
102C4⋊C8Q1612yes—
103C4×C8—41no—
104C4×C8—41no—
105C4×C8C2×Q811yescharacteristic
106C4×C8C2×Q811yescharacteristic
107C4×C8C2×Q811yescharacteristic
108C4×C8#4111yescharacteristic
109#95—21no—
110#95—42no—
111#95—41no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—41no—
115C22×C4—41no—
116C22×C4—42no—
117C22×C4—81no—
118C22×C4#12011yescharacteristic
119C22×C4C2×D811yescharacteristic
120C22×C4AGL(1,ℤ/8)11yescharacteristic
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—22no—
124C2×C8—41no—
125C2×C8—41no—
126C2×C8—42no—
127C2×C8—81no—
128C2×C8—81no—
129C2×C8C22⋊Q811yescharacteristic
130C2×C8C22⋊Q811yescharacteristic
131C2×C8C4⋊Q811yescharacteristic
132C2×C8C4⋊Q811yescharacteristic
133C2×C8#13511yescharacteristic
134C2×C8#13511yescharacteristic
135C2×C8AGL(1,ℤ/8)11yescharacteristic
136C2×C8#13711yescharacteristic
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C4⋊C4—42no—
142C4⋊C4—41no—
143C4⋊C4—42no—
144C4⋊C4—41no—
145C4⋊C4—84no—
146C4⋊C4—84no—
147C4⋊C4—81no—
148C4⋊C4—81no—
149C4⋊C4—81no—
150C4⋊C4—81no—
151C4⋊C4—81no—
152C4⋊C4—81no—
153C4⋊C4—161no—
154C4⋊C4—161no—
155C4⋊C4—162no—
156C4⋊C4SD3212yes—
157C4⋊C4SD3212yes—
158C42—41no—
159C42—41no—
160C42—81no—
161C42—81no—
162C42C22⋊Q811yescharacteristic
163C42C4⋊Q811yescharacteristic
164C42C2×Q1611yescharacteristic
165C42#13711yescharacteristic
166C16—42no—
167C16—42no—
168C23#44711yescharacteristic
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—81no—
178C2×C4—81no—
179C2×C4—82no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—82no—
183C2×C4—82no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4—161no—
187C2×C4—161no—
188C2×C4—161no—
189C2×C4#39511yescharacteristic
190C2×C4#44911yescharacteristic
191C2×C4#45111yescharacteristic
192C2×C4#45211yescharacteristic
193C2×C4#45411yescharacteristic
194C2×C4#45511yescharacteristic
195C2×C4#47411yescharacteristic
196C2×C4#47711yescharacteristic
197C2×C4#50011yescharacteristic
198C2×C4#50111yescharacteristic
199C2×C4C2×SD3211yescharacteristic
200C2×C4C2×SD3211yescharacteristic
201C2×C4#50911yescharacteristic
202C2×C4#51011yescharacteristic
203C8—21no—
204C8—21no—
205C8—42no—
206C8—82no—
207C8#47811yescharacteristic
208C8#47911yescharacteristic
209C8#49911yescharacteristic
210C8#50111yescharacteristic
211C22#162511yescharacteristic
212C22#164111yescharacteristic
213C22#205711yescharacteristic
214C22#218511yescharacteristic
215C22#218711yescharacteristic
216C22#219211yescharacteristic
217C22#219511yescharacteristic
218C4—21no—
219C4—21no—
220C4—42no—
221C4—42no—
222C4—161no—
223C4—161no—
224C4—162no—
225C4—321no—
226C4#163611yescharacteristic
227C4#164411yescharacteristic
228C4#205911yescharacteristic
229C4#206111yescharacteristic
230C4#222511yescharacteristic
231C4#222611yescharacteristic
232C4#225411yescharacteristic
233C4#225511yescharacteristic
234C2#1058111yescharacteristic
235C2#1234211yescharacteristic
236C2#1234411yescharacteristic
237C2#1238211yescharacteristic
238C2#1238411yescharacteristic
239C2#1345211yescharacteristic
240C2#1345511yescharacteristic
subgroupG/H
center, socle, prime radicalC23#447
commutator, Frattini, cosocleC2×C4×C8C23
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ C8×C4⋊C4 ◁ 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
#288272
#131772
#128882
#96142
#72742
#71712
#71672