Finite Group Databasebeta

← #145570

Subgroups — #145570

Order 512.

285 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 285 conjugacy classes of subgroups — too many to draw. Only its 76 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#33705C211yesmaximal, characteristic
2#13163C211yesmaximal, characteristic
3#11942C211yesmaximal, characteristic
4#11932C211yesmaximal, characteristic
5#9749C211yesmaximal, characteristic
6#9733C211yesmaximal, characteristic
7#7159C211yesmaximal, characteristic
8#3160C2211yescharacteristic
9C2×#494C2211yescharacteristic
10#2245—22no—
11#2241—21no—
12#2241—21no—
13C2×#364—21no—
14#2150C2211yescharacteristic
15#2141—21no—
16#2141—21no—
17C4×M32C2211yescharacteristic
18#1988—21no—
19C8×C4⋊C4C2211yescharacteristic
20#1564C2211yescharacteristic
21C2×#335C2211yescharacteristic
22C2×#332—21no—
23#1503—21no—
24#1481—21no—
25#1376—21no—
26#1365—21no—
27#1364—21no—
28#1362—22no—
29C22×Q16—21no—
30C22×Q16—21no—
31#533—21no—
32C2×C4⋊Q8—21no—
33C2×M32—21no—
34C2×M32D411yescharacteristic
35C2×M32D411yescharacteristic
36#500D411yescharacteristic
37#500D411yescharacteristic
38#499—21no—
39#499—21no—
40#498—21no—
41#494—21no—
42#494—21no—
43#494—21no—
44#494D412yes—
45#431—21no—
46#427—21no—
47#427—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8D411yescharacteristic
50C2×C4×C8—21no—
51C2×C4×C8C2311yescharacteristic
52C4×C4⋊C4D411yescharacteristic
53#364—42no—
54C4⋊C16—21no—
55C4⋊C16—21no—
56#358—22no—
57#358—22no—
58#358—22no—
59#358—22no—
60#346—21no—
61C4×C16—21no—
62#340—42no—
63#336—21no—
64#335—21no—
65#335—21no—
66#335—21no—
67#334—21no—
68#332—42no—
69#328—42no—
70Q8⋊C8—42no—
71C22×Q8—41no—
72C2×Q16—22no—
73C2×Q16—22no—
74C2×Q16—41no—
75C2×Q16—41no—
76C2×Q16—41no—
77C2×Q16—41no—
78C2×Q16—41no—
79C2×Q16—41no—
80C2×Q16—81no—
81C2×Q16—81no—
82C22×C8—21no—
83C22×C8—41no—
84C22×C8C2×D411yescharacteristic
85C22×C8#4111yescharacteristic
86C4⋊Q8—22no—
87C4⋊Q8—21no—
88C4⋊Q8—21no—
89C4⋊Q8—41no—
90C4⋊Q8—41no—
91C4⋊Q8—41no—
92#125—41no—
93C22⋊Q8—41no—
94C22⋊Q8—41no—
95C4×Q8—41no—
96C4×Q8—41no—
97#117—41no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—41no—
101C2×C42—21no—
102C2×C42C2×D411yescharacteristic
103M32—21no—
104M32—21no—
105M32—21no—
106M32—21no—
107M32—41no—
108M32—41no—
109C2×C16—21no—
110C2×C16—21no—
111C2×C16—41no—
112#107—21no—
113#107—21no—
114#107—21no—
115#107—21no—
116#106—41no—
117#106—41no—
118C4⋊C8—21no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8D812yes—
123C22⋊C8—41no—
124C4×C8—41no—
125C4×C8—41no—
126C4×C8—41no—
127C4×C8C2×D411yescharacteristic
128C4×C8C2×D411yescharacteristic
129C4×C8#4111yescharacteristic
130C4×C8#4111yescharacteristic
131#95—21no—
132C2×Q8—42no—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8—81no—
136C2×Q8—81no—
137C2×Q8—81no—
138C2×Q8—81no—
139C2×Q8—81no—
140C22×C4—41no—
141C22×C4—81no—
142C22×C4#12111yescharacteristic
143C22×C4AGL(1,ℤ/8)11yescharacteristic
144C22×C4AGL(1,ℤ/8)11yescharacteristic
145Q16—42no—
146Q16—42no—
147Q16—82no—
148Q16—82no—
149Q16—81no—
150Q16—81no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—22no—
154C2×C8—41no—
155C2×C8—41no—
156C2×C8—82no—
157C2×C8—81no—
158C2×C8—81no—
159C2×C8#12011yescharacteristic
160C2×C8#12311yescharacteristic
161C2×C8#12311yescharacteristic
162C2×C8#12411yescharacteristic
163C2×C8#13511yescharacteristic
164C2×C8#13511yescharacteristic
165C2×C8AGL(1,ℤ/8)11yescharacteristic
166C2×C8#13711yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—42no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—41no—
175C4⋊C4—81no—
176C4⋊C4—81no—
177C4⋊C4—81no—
178C4⋊C4—81no—
179C22⋊C4—81no—
180C42—41no—
181C42—41no—
182C42—81no—
183C42#12111yescharacteristic
184C42#12111yescharacteristic
185C42C2×D811yescharacteristic
186C42#13511yescharacteristic
187C16—41no—
188C16—41no—
189C16—81no—
190C23#46911yescharacteristic
191Q8—81no—
192Q8—81no—
193Q8—82no—
194Q8—82no—
195Q8—161no—
196Q8—161no—
197Q8—161no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—81no—
205C2×C4—81no—
206C2×C4—82no—
207C2×C4—161no—
208C2×C4—161no—
209C2×C4#39411yescharacteristic
210C2×C4#45911yescharacteristic
211C2×C4#45911yescharacteristic
212C2×C4#46311yescharacteristic
213C2×C4#46311yescharacteristic
214C2×C4#46311yescharacteristic
215C2×C4#46411yescharacteristic
216C2×C4#46611yescharacteristic
217C2×C4#47111yescharacteristic
218C2×C4#47111yescharacteristic
219C8—21no—
220C8—21no—
221C8—42no—
222C8—161no—
223C8—161no—
224C8#44911yescharacteristic
225C8#45211yescharacteristic
226C8#48811yescharacteristic
227C8#48911yescharacteristic
228C22—21no—
229C22—21no—
230C22#170111yescharacteristic
231C22#170211yescharacteristic
232C22#205411yescharacteristic
233C4—21no—
234C4—21no—
235C4—21no—
236C4—82no—
237C4—162no—
238C4—161no—
239C4—161no—
240C4#168111yescharacteristic
241C4#168211yescharacteristic
242C4#204211yescharacteristic
243C4#204611yescharacteristic
244C4#221211yescharacteristic
245C4#221411yescharacteristic
246C2—21no—
247C2—21no—
248C2#1054011yescharacteristic
249C2#1344311yescharacteristic
250C2#1344611yescharacteristic
subgroupG/H
center, socleC22#2054
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#469
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ 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
#337052
#131632
#119422
#119322
#97492
#97332
#71592