Finite Group Databasebeta

← #103115

Subgroups — #103115

Order 512.

500 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 130 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#28687C211yesmaximal, characteristic
3#28511C211yesmaximal, characteristic
4#9898C211yesmaximal, characteristic
5#9896C211yesmaximal, characteristic
6#9870C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#498—21no—
9C2×#477—22no—
10#2868C2211yescharacteristic
11#2868C2211yescharacteristic
12C4×C4⋊Q8C2211yescharacteristic
13#2095—22no—
14#2084—22no—
15#1990—22no—
16#1990—22no—
17#1990—21no—
18#1956—21no—
19#1948—22no—
20#1845—21no—
21#1842C2211yescharacteristic
22#1834—22no—
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C42×C8C2211yescharacteristic
26#1296—22no—
27#1296—22no—
28#1279—22no—
29C2×C4⋊Q8—21no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8D411yescharacteristic
36C2×C4×Q8—21no—
37#498—42no—
38#498—42no—
39#477—44no—
40#477—44no—
41C2×#107—24no—
42C2×#106—24no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8D412yes—
47C2×C4⋊C8D412yes—
48C2×#103—24no—
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52C2×C4×C8—21no—
53C2×C4×C8D412yes—
54#391—21no—
55#389—21no—
56#389—21no—
57#384—21no—
58#384—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384—21no—
63#384D411yescharacteristic
64#384D412yes—
65#384D412yes—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C43C2311yescharacteristic
69#340—24no—
70#340—28no—
71#336—21no—
72#336—21no—
73C22×Q8—21no—
74C22×Q8—41no—
75C22×Q8—41no—
76C22×C8—22no—
77C22×C8—22no—
78C22×C8—22no—
79C22×C8—41no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8—21no—
83C4⋊Q8—44no—
84C4⋊Q8—42no—
85C4⋊Q8—41no—
86C4⋊Q8—41no—
87C4⋊Q8—42no—
88C4⋊Q8—42no—
89C4⋊Q8—41no—
90C4⋊Q8—41no—
91C4⋊Q8—42no—
92C4⋊Q8—82no—
93C4⋊Q8—82no—
94C4⋊Q8SD1612yes—
95C4×Q8—42no—
96C4×Q8—42no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C42—41no—
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42#4111yescharacteristic
123#107—48no—
124#106—48no—
125C4⋊C8—22no—
126C4⋊C8—22no—
127C4⋊C8—42no—
128C4⋊C8—42no—
129C4⋊C8—42no—
130C4⋊C8SD1614yes—
131C4⋊C8Q1614yes—
132#103—48no—
133C4×C8—24no—
134C4×C8—22no—
135C4×C8—22no—
136C4×C8—42no—
137C4×C8—41no—
138C4×C8—41no—
139C4×C8—41no—
140C4×C8—41no—
141#95—41no—
142#95—41no—
143C2×Q8—22no—
144C2×Q8—41no—
145C2×Q8—42no—
146C2×Q8—42no—
147C2×Q8—82no—
148C2×Q8—82no—
149C2×Q8—82no—
150C2×Q8—82no—
151C2×Q8—81no—
152C2×Q8—81no—
153C2×Q8—82no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—42no—
157C22×C4—42no—
158C22×C4#12011yescharacteristic
159C22×C4#12011yescharacteristic
160C22×C4#12011yescharacteristic
161C22×C4#12111yescharacteristic
162C22×C4#12111yescharacteristic
163C22×C4#12111yescharacteristic
164C22×C4#12711yescharacteristic
165C2×C8—24no—
166C2×C8—24no—
167C2×C8—24no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—81no—
175C2×C8—81no—
176C2×C8—81no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—44no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C4⋊C4—44no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—44no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—82no—
190C4⋊C4—82no—
191C4⋊C4—82no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—82no—
195C4⋊C4—82no—
196C4⋊C4—82no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C42—22no—
202C42—22no—
203C42—22no—
204C42—81no—
205C42—81no—
206C42C2×SD1611yescharacteristic
207C42C2×SD1612yes—
208C42C2×Q1612yes—
209C42#13511yescharacteristic
210C42#13512yes—
211C42AGL(1,ℤ/8)11yescharacteristic
212C42AGL(1,ℤ/8)12yes—
213C42#13711yescharacteristic
214C42#13712yes—
215C42#13712yes—
216C23#39211yescharacteristic
217Q8—44no—
218Q8—82no—
219Q8—164no—
220Q8—162no—
221Q8—162no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—82no—
232C2×C4—82no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—82no—
236C2×C4—82no—
237C2×C4—81no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4#44811yescharacteristic
241C2×C4#44911yescharacteristic
242C2×C4#45011yescharacteristic
243C2×C4#45012yes—
244C2×C4#45112yes—
245C2×C4#45212yes—
246C2×C4#45211yescharacteristic
247C2×C4#45412yes—
248C2×C4#45612yes—
249C2×C4#46012yes—
250C2×C4#46212yes—
251C2×C4#46412yes—
252C2×C4#46511yescharacteristic
253C2×C4#46811yescharacteristic
254C2×C4#47212yes—
255C2×C4#49211yescharacteristic
256C2×C4#49411yescharacteristic
257C2×C4#49511yescharacteristic
258C2×C4#49611yescharacteristic
259C2×C4#49711yescharacteristic
260C2×C4#49711yescharacteristic
261C8—44no—
262C8—44no—
263C8—44no—
264C8—161no—
265C22#200011yescharacteristic
266C22#200311yescharacteristic
267C22#200511yescharacteristic
268C22#201411yescharacteristic
269C22#201511yescharacteristic
270C22#201611yescharacteristic
271C22#201811yescharacteristic
272C4—22no—
273C4—22no—
274C4—22no—
275C4—82no—
276C4—162no—
277C4—161no—
278C4—162no—
279C4#163612yes—
280C4#163712yes—
281C4#165112yes—
282C4#165412yes—
283C4#167812yes—
284C4#169812yes—
285C4#170711yescharacteristic
286C4#171611yescharacteristic
287C4#172011yescharacteristic
288C4#172311yescharacteristic
289C2#1005911yescharacteristic
290C2#1006811yescharacteristic
291C2#1014811yescharacteristic
292C2#1016511yescharacteristic
293C2#1026911yescharacteristic
294C2#1029611yescharacteristic
295C2#1031811yescharacteristic
subgroupG/H
center, socle, prime radicalC23#392
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ 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
#286872
#285112
#98982
#98962
#98702
#70152