Finite Group Databasebeta

← #102280

Subgroups — #102280

Order 512.

410 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 134 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#33289C211yesmaximal, characteristic
2#9898C211yesmaximal, characteristic
3#9694C211yesmaximal, characteristic
4#9692C211yesmaximal, characteristic
5#9692C211yesmaximal, characteristic
6#8784C211yesmaximal, characteristic
7#8260C211yesmaximal, characteristic
8#2868C2211yescharacteristic
9#2868C2211yescharacteristic
10#1990—21no—
11#1990—21no—
12#1990—22no—
13#1842C2211yescharacteristic
14#1842C2211yescharacteristic
15#1834C414yes—
16C4×C4⋊C8C2211yescharacteristic
17C4×C4⋊C8C2211yescharacteristic
18C42×C8C2211yescharacteristic
19C2×#332—22no—
20C2×#332—22no—
21C2×#332—22no—
22C2×#322—21no—
23#1296—22no—
24#1277—22no—
25#1273—21no—
26C2×C4⋊Q8—21no—
27C2×C4⋊Q8—21no—
28C2×C4⋊Q8—21no—
29C2×C4⋊Q8—21no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊C8—21no—
33C2×C4⋊C8—21no—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—21no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8D412yes—
39C2×C4⋊C8D412yes—
40C2×C4×C8—21no—
41C2×C4×C8—21no—
42C2×C4×C8C2×C412yes—
43C2×C4×C8D411yescharacteristic
44C2×C4×C8D411yescharacteristic
45C2×C4×C8D412yes—
46#384—21no—
47#384—21no—
48#384—21no—
49#384—21no—
50#384—21no—
51#384—21no—
52#384C2×C412yes—
53#384C2×C412yes—
54C43C2311yescharacteristic
55#340—24no—
56#340—24no—
57#336—21no—
58#336—21no—
59#332—44no—
60#332—44no—
61#332—44no—
62#322—42no—
63C22×Q8—41no—
64C22×Q8—41no—
65C22×C8—22no—
66C22×C8—22no—
67C22×C8—41no—
68C22×C8—41no—
69C22×C8C22⋊C412yes—
70C22×C8C22⋊C412yes—
71C4⋊Q8—41no—
72C4⋊Q8—41no—
73C4⋊Q8—42no—
74C4⋊Q8—42no—
75C4⋊Q8—41no—
76C4⋊Q8—42no—
77C4⋊Q8—42no—
78C4⋊Q8—42no—
79C4⋊Q8—42no—
80C4⋊Q8—42no—
81C4⋊Q8—41no—
82C4⋊Q8—42no—
83C4⋊Q8—82no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4—22no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—41no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C42C22×C411yescharacteristic
97C2×C42C2×D411yescharacteristic
98C2×C42C2×D411yescharacteristic
99C2×C42C2×D411yescharacteristic
100C2×C42C2×D411yescharacteristic
101C2×C42#4111yescharacteristic
102C2×C42#4111yescharacteristic
103C4⋊C8—22no—
104C4⋊C8—22no—
105C4⋊C8—22no—
106C4⋊C8—22no—
107C4⋊C8—42no—
108C4⋊C8—42no—
109C4⋊C8—42no—
110C4⋊C8—42no—
111C4⋊C8—42no—
112C4⋊C8—42no—
113C4×C8—24no—
114C4×C8—21no—
115C4×C8—21no—
116C4×C8—22no—
117C4×C8—22no—
118C4×C8—21no—
119C4×C8—21no—
120C4×C8—41no—
121C4×C8—41no—
122C4×C8—41no—
123C4×C8—41no—
124C2×Q8—81no—
125C2×Q8—81no—
126C2×Q8—82no—
127C2×Q8—82no—
128C2×Q8—81no—
129C2×Q8—81no—
130C2×Q8—81no—
131C2×Q8—81no—
132C2×Q8—81no—
133C2×Q8—81no—
134C22×C4—42no—
135C22×C4—42no—
136C22×C4C2×C22⋊C411yescharacteristic
137C22×C4C4×D411yescharacteristic
138C22×C4C4×D411yescharacteristic
139C22×C4#12111yescharacteristic
140C22×C4#12111yescharacteristic
141C22×C4#12411yescharacteristic
142C22×C4#12711yescharacteristic
143C2×C8—22no—
144C2×C8—22no—
145C2×C8—22no—
146C2×C8—22no—
147C2×C8—22no—
148C2×C8—42no—
149C2×C8—42no—
150C2×C8—42no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—42no—
154C2×C8—81no—
155C2×C8—81no—
156C2×C8—81no—
157C2×C8—81no—
158C2×C8—81no—
159C2×C8—81no—
160C2×C8#10114yes—
161C4⋊C4—44no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—44no—
165C4⋊C4—44no—
166C4⋊C4—44no—
167C4⋊C4—82no—
168C4⋊C4—82no—
169C4⋊C4—81no—
170C4⋊C4—81no—
171C4⋊C4—82no—
172C4⋊C4—82no—
173C4⋊C4—82no—
174C4⋊C4—81no—
175C4⋊C4—81no—
176C42—22no—
177C42—22no—
178C42—22no—
179C42#13511yescharacteristic
180C42#13511yescharacteristic
181C42#13512yes—
182C42#13512yes—
183C42AGL(1,ℤ/8)11yescharacteristic
184C42AGL(1,ℤ/8)12yes—
185C42AGL(1,ℤ/8)12yes—
186C42AGL(1,ℤ/8)12yes—
187C42#13711yescharacteristic
188C42#13712yes—
189C23#39011yescharacteristic
190Q8—162no—
191Q8—162no—
192Q8—161no—
193Q8—161no—
194Q8—161no—
195Q8—161no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—82no—
203C2×C4—82no—
204C2×C4—82no—
205C2×C4—82no—
206C2×C4—82no—
207C2×C4—82no—
208C2×C4C2×#10112yes—
209C2×C4#41611yescharacteristic
210C2×C4#41612yes—
211C2×C4#41711yescharacteristic
212C2×C4#44012yes—
213C2×C4#44212yes—
214C2×C4#46311yescharacteristic
215C2×C4#46311yescharacteristic
216C2×C4#46411yescharacteristic
217C2×C4#46411yescharacteristic
218C2×C4#46812yes—
219C2×C4#46912yes—
220C2×C4#47112yes—
221C2×C4#47312yes—
222C2×C4#48812yes—
223C2×C4#49511yescharacteristic
224C2×C4#49511yescharacteristic
225C2×C4#49611yescharacteristic
226C2×C4#49611yescharacteristic
227C2×C4#49611yescharacteristic
228C2×C4#49711yescharacteristic
229C8—24no—
230C8—42no—
231C8—82no—
232C8—82no—
233C8—161no—
234C8—161no—
235C22#195811yescharacteristic
236C22#196611yescharacteristic
237C22#197211yescharacteristic
238C22#197311yescharacteristic
239C22#197711yescharacteristic
240C22#197911yescharacteristic
241C22#198311yescharacteristic
242C4—22no—
243C4—22no—
244C4—22no—
245C4—162no—
246C4—162no—
247C4#154412yes—
248C4#155212yes—
249C4#169912yes—
250C4#170012yes—
251C4#170112yes—
252C4#170212yes—
253C4#171711yescharacteristic
254C4#171711yescharacteristic
255C4#171911yescharacteristic
256C4#172011yescharacteristic
257C2#970011yescharacteristic
258C2#974611yescharacteristic
259C2#974811yescharacteristic
260C2#977011yescharacteristic
261C2#980611yescharacteristic
262C2#980811yescharacteristic
263C2#983811yescharacteristic
subgroupG/H
center, socle, prime radicalC23#390
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#332892
#98982
#96942
#96922
#87842
#82602