Finite Group Databasebeta

← #145944

Subgroups — #145944

Order 512.

262 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 94 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#13282C211yesmaximal, characteristic
2#13159C211yesmaximal, characteristic
3C2×#1371C211yesmaximal, characteristic
4C2×#1364C211yesmaximal, characteristic
5#9731C211yesmaximal, characteristic
6#9614C211yesmaximal, characteristic
7#7274C211yesmaximal, characteristic
8C2×#500C2211yescharacteristic
9C2×C4⋊C16—21no—
10C2×C4⋊C16C2211yescharacteristic
11C2×C4×C16C2211yescharacteristic
12#1981—21no—
13#1947—21no—
14#1845C2211yescharacteristic
15C8×C4⋊C4C2211yescharacteristic
16C2×#335C2211yescharacteristic
17C2×#335C2211yescharacteristic
18C2×#332—21no—
19#1380—21no—
20#1380—21no—
21#1374—21no—
22#1371—22no—
23#1364—22no—
24#1296—21no—
25C2×C4⋊Q8—21no—
26C22×C16—21no—
27C22×C16D411yescharacteristic
28C22×C16D411yescharacteristic
29#500—21no—
30#500—21no—
31#500—21no—
32#500Q812yes—
33C2×#107—21no—
34C2×#107—21no—
35C2×#107—21no—
36C2×#107—21no—
37C2×#107—41no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8D411yescharacteristic
41C2×#103—41no—
42C2×#103—41no—
43C2×C4×C8—21no—
44C2×C4×C8C2311yescharacteristic
45#384—21no—
46C4×C4⋊C4D411yescharacteristic
47C4⋊C16—21no—
48C4⋊C16—21no—
49C4⋊C16—42no—
50C4×C16—21no—
51C4×C16—21no—
52#340—41no—
53#336—21no—
54#335—21no—
55#335—21no—
56#335—21no—
57#335D412yes—
58#332—42no—
59C22×Q8—41no—
60C22×C8—21no—
61C22×C8—41no—
62C22×C8—41no—
63C22×C8C2×D411yescharacteristic
64C22×C8#4111yescharacteristic
65C4⋊Q8—22no—
66C4⋊Q8—41no—
67C4⋊Q8—41no—
68C4⋊Q8—41no—
69C2×C4⋊C4—41no—
70C2×C4⋊C4—41no—
71C2×C4⋊C4—41no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4—41no—
74C2×C4⋊C4D811yescharacteristic
75C2×C4⋊C4D811yescharacteristic
76C2×C42—21no—
77C2×C42C2×D411yescharacteristic
78C2×C16—21no—
79C2×C16—21no—
80C2×C16—21no—
81C2×C16—21no—
82C2×C16—21no—
83C2×C16—41no—
84C2×C16—41no—
85C2×C16—41no—
86C2×C16Q1612yes—
87#107—22no—
88#107—22no—
89#107—41no—
90#107—41no—
91#107—41no—
92#107—41no—
93#107—82no—
94#107—81no—
95C4⋊C8—22no—
96C4⋊C8—21no—
97C4⋊C8—21no—
98C4⋊C8—41no—
99C4⋊C8—41no—
100C4⋊C8—41no—
101#103—82no—
102#103—82no—
103C4×C8—41no—
104C4×C8—41no—
105C4×C8C2×D411yescharacteristic
106C4×C8C2×Q811yescharacteristic
107C4×C8#4111yescharacteristic
108C4×C8#4111yescharacteristic
109#95—21no—
110C2×Q8—42no—
111C2×Q8—81no—
112C2×Q8—81no—
113C2×Q8—81no—
114C2×Q8—81no—
115C2×Q8—81no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—81no—
119C22×C4—81no—
120C22×C4#12111yescharacteristic
121C22×C4C2×D811yescharacteristic
122C22×C4#13511yescharacteristic
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—42no—
126C2×C8—41no—
127C2×C8—41no—
128C2×C8—41no—
129C2×C8—81no—
130C2×C8—81no—
131C2×C8—81no—
132C2×C8—81no—
133C2×C8—81no—
134C2×C8#12111yescharacteristic
135C2×C8C22⋊Q811yescharacteristic
136C2×C8C22⋊Q811yescharacteristic
137C2×C8#12611yescharacteristic
138C2×C8C2×Q1611yescharacteristic
139C2×C8#13511yescharacteristic
140C2×C8AGL(1,ℤ/8)11yescharacteristic
141C2×C8#13711yescharacteristic
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—42no—
146C4⋊C4—42no—
147C4⋊C4—81no—
148C4⋊C4—81no—
149C4⋊C4—81no—
150C4⋊C4—81no—
151C4⋊C4—81no—
152C4⋊C4—81no—
153C4⋊C4—161no—
154C4⋊C4D1612yes—
155C42—41no—
156C42—41no—
157C42#12111yescharacteristic
158C42C22⋊Q811yescharacteristic
159C42AGL(1,ℤ/8)11yescharacteristic
160C42#13711yescharacteristic
161C16—22no—
162C16—41no—
163C16—81no—
164C23#46611yescharacteristic
165Q8—82no—
166Q8—82no—
167Q8—161no—
168Q8—161no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—82no—
178C2×C4—161no—
179C2×C4—161no—
180C2×C4—161no—
181C2×C4—161no—
182C2×C4—161no—
183C2×C4#39611yescharacteristic
184C2×C4#45911yescharacteristic
185C2×C4#46211yescharacteristic
186C2×C4#46311yescharacteristic
187C2×C4#46411yescharacteristic
188C2×C4#46811yescharacteristic
189C2×C4#47111yescharacteristic
190C2×C4#47311yescharacteristic
191C2×C4#47411yescharacteristic
192C2×C4#47811yescharacteristic
193C2×C4C2×D1611yescharacteristic
194C2×C4#50811yescharacteristic
195C2×C4#50911yescharacteristic
196C2×C4#51011yescharacteristic
197C8—21no—
198C8—21no—
199C8—82no—
200C8—81no—
201C8—161no—
202C8#46711yescharacteristic
203C8#46811yescharacteristic
204C8#47711yescharacteristic
205C8#47911yescharacteristic
206C22#167411yescharacteristic
207C22#168111yescharacteristic
208C22#206711yescharacteristic
209C22#221511yescharacteristic
210C22#222011yescharacteristic
211C22#222211yescharacteristic
212C22#222311yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—81no—
217C4—162no—
218C4—321no—
219C4#169211yescharacteristic
220C4#169911yescharacteristic
221C4#206411yescharacteristic
222C4#206811yescharacteristic
223C4#220611yescharacteristic
224C4#221111yescharacteristic
225C4#222411yescharacteristic
226C4#222811yescharacteristic
227C2#1059411yescharacteristic
228C2#1245711yescharacteristic
229C2#1246211yescharacteristic
230C2#1246711yescharacteristic
231C2#1247411yescharacteristic
232C2#1347111yescharacteristic
233C2#1347411yescharacteristic
subgroupG/H
center, socle, prime radicalC23#466
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
#132822
#131592
C2×#13712
C2×#13642
#97312
#96142
#72742