Finite Group Databasebeta

← #102440

Subgroups — #102440

Order 512.

532 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 98 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#33108C212yesmaximal
2#30291C211yesmaximal, characteristic
3#11346C211yesmaximal, characteristic
4#7665C212yesmaximal
5#7020C211yesmaximal, characteristic
6C2×#483—22no—
7#2857C2212yes—
8C2×C4×C4⋊C4C2211yescharacteristic
9#2083—22no—
10#2057—22no—
11#1981—22no—
12#1948—22no—
13#1927—24no—
14#1872—22no—
15#1808—22no—
16#1797C2212yes—
17C2×#336—22no—
18C2×#336C2211yescharacteristic
19C2×#336C2211yescharacteristic
20#1271—24no—
21C23×C8—21no—
22C23×C8D412yes—
23C2×C4⋊Q8D412yes—
24C2×C22⋊Q8—22no—
25C22×C4⋊C4D411yescharacteristic
26C22×C4⋊C4D411yescharacteristic
27C22×C42—21no—
28C22×C42C2311yescharacteristic
29#483—44no—
30#483—44no—
31C2×#107—22no—
32C2×#107—22no—
33C2×#106—24no—
34C2×C4⋊C8—22no—
35C2×#103—24no—
36C2×#103—24no—
37C2×C22⋊C8—22no—
38#391—22no—
39#389—22no—
40#389—22no—
41#384D412yes—
42#380—22no—
43#380—22no—
44C4×C4⋊C4—22no—
45C4×C4⋊C4—22no—
46C2×#95—21no—
47#340—24no—
48#340—24no—
49#336—22no—
50#336—22no—
51#336—44no—
52#336D414yes—
53C22×Q8—22no—
54C23×C4—21no—
55C23×C4—21no—
56C23×C4C2×D411yescharacteristic
57C23×C4C2×D411yescharacteristic
58C23×C4#4111yescharacteristic
59C22×C8—22no—
60C22×C8—22no—
61C22×C8—22no—
62C22×C8—24no—
63C22×C8—42no—
64C22×C8—42no—
65C22×C8—41no—
66C22×C8—42no—
67C22×C8—41no—
68C22×C8—42no—
69C22×C8SD1614yes—
70C4⋊Q8—44no—
71C22⋊Q8—42no—
72C22⋊Q8—42no—
73C22⋊Q8—42no—
74C22⋊Q8—42no—
75C2×C4⋊C4—22no—
76C2×C4⋊C4—22no—
77C2×C4⋊C4—22no—
78C2×C4⋊C4—21no—
79C2×C4⋊C4—22no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—42no—
85C2×C4⋊C4—42no—
86C2×C4⋊C4D812yes—
87C2×C22⋊C4—42no—
88C2×C42—42no—
89C2×C42—41no—
90C2×C42—41no—
91C2×C42—42no—
92C2×C42—42no—
93C2×C42C2×D412yes—
94C2×C42C2×D412yes—
95#107—82no—
96#107—82no—
97#106—48no—
98C4⋊C8—44no—
99#103—48no—
100#103—48no—
101C22⋊C8—42no—
102C22⋊C8—42no—
103#95—42no—
104#95—42no—
105#95—42no—
106C24#12111yescharacteristic
107C2×Q8—44no—
108C2×Q8—44no—
109C2×Q8—42no—
110C2×Q8—42no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—22no—
114C22×C4—22no—
115C22×C4—22no—
116C22×C4—22no—
117C22×C4—41no—
118C22×C4—41no—
119C22×C4—41no—
120C22×C4—41no—
121C22×C4—41no—
122C22×C4—42no—
123C22×C4—41no—
124C22×C4—41no—
125C22×C4—42no—
126C22×C4—42no—
127C22×C4—41no—
128C22×C4—42no—
129C22×C4—42no—
130C22×C4—42no—
131C22×C4#12012yes—
132C22×C4#12011yescharacteristic
133C22×C4#12112yes—
134C22×C4#12711yescharacteristic
135C22×C4C2×D811yescharacteristic
136C22×C4C2×SD1612yes—
137C22×C4#13511yescharacteristic
138C22×C4AGL(1,ℤ/8)12yes—
139C22×C4#13712yes—
140C2×C8—24no—
141C2×C8—42no—
142C2×C8—42no—
143C2×C8—44no—
144C2×C8—44no—
145C2×C8—44no—
146C2×C8—42no—
147C2×C8—44no—
148C2×C8—44no—
149C2×C8—82no—
150C2×C8—81no—
151C2×C8—82no—
152C2×C8—81no—
153C4⋊C4—24no—
154C4⋊C4—24no—
155C4⋊C4—42no—
156C4⋊C4—44no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—44no—
163C4⋊C4—82no—
164C4⋊C4—82no—
165C4⋊C4—82no—
166C22⋊C4—82no—
167C22⋊C4—82no—
168C42—24no—
169C42—42no—
170C42—82no—
171C42—81no—
172C42—81no—
173C23—21no—
174C23—21no—
175C23—21no—
176C23—21no—
177C23#39211yescharacteristic
178C23#46112yes—
179C23#46611yescharacteristic
180C23#46911yescharacteristic
181C23#47312yes—
182Q8—84no—
183Q8—84no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—44no—
199C2×C4—44no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—82no—
203C2×C4—82no—
204C2×C4—82no—
205C2×C4—81no—
206C2×C4—81no—
207C2×C4—81no—
208C2×C4—81no—
209C2×C4—82no—
210C2×C4—82no—
211C2×C4—82no—
212C2×C4—82no—
213C2×C4—82no—
214C2×C4—82no—
215C2×C4#44712yes—
216C2×C4#44812yes—
217C2×C4#44912yes—
218C2×C4#45511yescharacteristic
219C2×C4#45611yescharacteristic
220C2×C4#45812yes—
221C2×C4#49211yescharacteristic
222C2×C4#49711yescharacteristic
223C8—44no—
224C8—84no—
225C8—82no—
226C22—21no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—22no—
233C22—22no—
234C22#167312yes—
235C22#169312yes—
236C22#199911yescharacteristic
237C22#200711yescharacteristic
238C22#201011yescharacteristic
239C22#201311yescharacteristic
240C22#201711yescharacteristic
241C22#202011yescharacteristic
242C22#202211yescharacteristic
243C4—22no—
244C4—22no—
245C4—21no—
246C4—21no—
247C4—42no—
248C4—82no—
249C4—82no—
250C4—162no—
251C4—162no—
252C4#160812yes—
253C4#161112yes—
254C2—22no—
255C2—22no—
256C2#997311yescharacteristic
257C2#997911yescharacteristic
258C2#1003111yescharacteristic
259C2#1003611yescharacteristic
260C2#1025511yescharacteristic
261C2#1026411yescharacteristic
262C2#1032111yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C22×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#331082
#302912
#113462
#76652
#70202