Finite Group Databasebeta

← #102637

Subgroups — #102637

Order 512.

475 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 475 conjugacy classes of subgroups — too many to draw. Only its 84 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#30199C211yesmaximal, characteristic
2#27960C211yesmaximal, characteristic
3#27948C211yesmaximal, characteristic
4#11354C211yesmaximal, characteristic
5#7687C211yesmaximal, characteristic
6#7685C211yesmaximal, characteristic
7#7026C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9#2857C2211yescharacteristic
10C2×#384C2211yescharacteristic
11#2099—21no—
12#2099—22no—
13#2084—22no—
14#2072—21no—
15#2043—21no—
16#2024—21no—
17#1990—21no—
18#1990—21no—
19#1894—22no—
20#1853—22no—
21#1844—21no—
22#1834—21no—
23#1823—22no—
24C4×C22⋊C8C2211yescharacteristic
25C4×C22⋊C8C2211yescharacteristic
26C2×#343—22no—
27#1728C2211yescharacteristic
28#1728C2211yescharacteristic
29#1272—22no—
30#1271—22no—
31C22×M16—21no—
32C22×M16D412yes—
33C2×C4⋊Q8D411yescharacteristic
34C2×C4⋊Q8D411yescharacteristic
35C2×C22⋊Q8—21no—
36C2×C22⋊Q8—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4—21no—
39C22×C4⋊C4D412yes—
40C22×C42C2311yescharacteristic
41C2×#106—24no—
42C2×#103—22no—
43C2×#103—22no—
44C2×C22⋊C8—21no—
45C2×C22⋊C8—21no—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48#391—21no—
49#391—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#384—21no—
55#384—21no—
56#384—21no—
57#384—21no—
58#384D411yescharacteristic
59#384D411yescharacteristic
60#380—21no—
61#380—21no—
62#380—21no—
63#380—21no—
64#343—44no—
65#340—22no—
66#340—24no—
67#340—24no—
68#340—24no—
69#340—22no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336D412yes—
75#336D412yes—
76C22×Q8—21no—
77C22×Q8—21no—
78C23×C4—22no—
79C23×C4C2×D411yescharacteristic
80C23×C4C2×D411yescharacteristic
81C23×C4#4111yescharacteristic
82C2×M16—22no—
83C2×M16—22no—
84C2×M16—22no—
85C2×M16—41no—
86C2×M16—42no—
87C2×M16—42no—
88C2×M16—42no—
89C2×M16—42no—
90C22×C8—22no—
91C22×C8—22no—
92C22×C8—22no—
93C22×C8—41no—
94C4⋊Q8—42no—
95C4⋊Q8—42no—
96C22⋊Q8—42no—
97C22⋊Q8—42no—
98C22⋊Q8—82no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—44no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—82no—
121C2×C22⋊C4—41no—
122C2×C22⋊C4—41no—
123C2×C42—42no—
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128#106—84no—
129#103—82no—
130#103—82no—
131C22⋊C8—24no—
132C22⋊C8—42no—
133C4×C8—42no—
134C4×C8—42no—
135#95—41no—
136#95—41no—
137#95—41no—
138#95—41no—
139C24#12111yescharacteristic
140C2×Q8—42no—
141C2×Q8—41no—
142C2×Q8—41no—
143C2×Q8—42no—
144C2×Q8—42no—
145C2×Q8—81no—
146C2×Q8—81no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—42no—
161C22×C4—44no—
162C22×C4—82no—
163C22×C4—82no—
164C22×C4#12011yescharacteristic
165C22×C4#12011yescharacteristic
166C22×C4#12011yescharacteristic
167C22×C4#12111yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12711yescharacteristic
170C22×C4#13512yes—
171C22×C4AGL(1,ℤ/8)12yes—
172M16—44no—
173M16—44no—
174M16—82no—
175M16—82no—
176C2×C8—24no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—81no—
187C2×C8—81no—
188C4⋊C4—44no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—44no—
195C4⋊C4—42no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—82no—
202C4⋊C4—82no—
203C4⋊C4—82no—
204C4⋊C4—82no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—81no—
209C22⋊C4—82no—
210C22⋊C4—82no—
211C42—22no—
212C42—22no—
213C42—41no—
214C42—41no—
215C23—21no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23#39211yescharacteristic
222C23#46312yes—
223Q8—82no—
224Q8—82no—
225Q8—162no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—44no—
241C2×C4—44no—
242C2×C4—82no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—82no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—82no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—164no—
258C2×C4#44912yes—
259C2×C4#45512yes—
260C2×C4#45511yescharacteristic
261C2×C4#45612yes—
262C2×C4#45611yescharacteristic
263C2×C4#45812yes—
264C2×C4#47112yes—
265C2×C4#47112yes—
266C2×C4#49511yescharacteristic
267C2×C4#49611yescharacteristic
268C8—44no—
269C8—82no—
270C8—82no—
271C8—82no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22#200411yescharacteristic
280C22#200511yescharacteristic
281C22#200711yescharacteristic
282C22#201211yescharacteristic
283C22#201911yescharacteristic
284C22#201911yescharacteristic
285C22#202211yescharacteristic
286C4—22no—
287C4—22no—
288C4—22no—
289C4—22no—
290C4—21no—
291C4—21no—
292C4—161no—
293C4—161no—
294C4—161no—
295C4—162no—
296C4—161no—
297C4#160912yes—
298C4#161212yes—
299C2—42no—
300C2#997111yescharacteristic
301C2#999311yescharacteristic
302C2#1011411yescharacteristic
303C2#1011911yescharacteristic
304C2#1016611yescharacteristic
305C2#1016911yescharacteristic
306C2#1033511yescharacteristic
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
#301992
#279602
#279482
#113542
#76872
#76852
#70262