Finite Group Databasebeta

← #103111

Subgroups — #103111

Order 512.

490 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 126 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#28717C211yesmaximal, characteristic
3#28687C211yesmaximal, characteristic
4#9898C211yesmaximal, characteristic
5#9870C211yesmaximal, characteristic
6#9694C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#498—21no—
9C2×#487—21no—
10#2868C2211yescharacteristic
11#2868C2211yescharacteristic
12C4×C4⋊Q8C2211yescharacteristic
13#2084—22no—
14#2072—22no—
15#1990—22no—
16#1990—22no—
17#1990—21no—
18#1990—21no—
19#1948—22no—
20#1842C2211yescharacteristic
21#1834—22no—
22#1803—22no—
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C42×C8C2211yescharacteristic
26C2×#332—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#487—42no—
40#487—42no—
41C2×#106—24no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8D412yes—
46C2×C4⋊C8D412yes—
47C2×#103—24no—
48C2×C4×C8—21no—
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52C2×C4×C8D412yes—
53#391—21no—
54#389—21no—
55#389—21no—
56#384—21no—
57#384—21no—
58#384—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384D411yescharacteristic
63#384D412yes—
64#384D412yes—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C43C2311yescharacteristic
68#340—24no—
69#340—24no—
70#340—28no—
71#336—21no—
72#336—21no—
73#332—44no—
74C22×Q8—21no—
75C22×Q8—41no—
76C22×Q8—41no—
77C22×C8—22no—
78C22×C8—22no—
79C22×C8—22no—
80C22×C8—41no—
81C4⋊Q8—21no—
82C4⋊Q8—21no—
83C4⋊Q8—21no—
84C4⋊Q8—44no—
85C4⋊Q8—41no—
86C4⋊Q8—41no—
87C4⋊Q8—42no—
88C4⋊Q8—41no—
89C4⋊Q8—41no—
90C4⋊Q8—42no—
91C4⋊Q8—41no—
92C4⋊Q8—41no—
93C4⋊Q8—41no—
94C4⋊Q8—41no—
95C4⋊Q8—42no—
96C4⋊Q8—42no—
97C4⋊Q8—82no—
98C4⋊Q8D812yes—
99C4×Q8—42no—
100C4×Q8—42no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—22no—
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—41no—
119C2×C42—41no—
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42#4111yescharacteristic
127#106—48no—
128C4⋊C8—22no—
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—42no—
132C4⋊C8—42no—
133C4⋊C8—42no—
134C4⋊C8SD1614yes—
135#103—48no—
136C4×C8—24no—
137C4×C8—22no—
138C4×C8—22no—
139C4×C8—42no—
140C4×C8—41no—
141C4×C8—41no—
142C4×C8—41no—
143C4×C8—41no—
144#95—41no—
145#95—41no—
146C2×Q8—22no—
147C2×Q8—41no—
148C2×Q8—42no—
149C2×Q8—42no—
150C2×Q8—81no—
151C2×Q8—82no—
152C2×Q8—81no—
153C2×Q8—82no—
154C2×Q8—82no—
155C2×Q8—81no—
156C2×Q8—81no—
157C2×Q8—82no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4#12011yescharacteristic
163C22×C4#12011yescharacteristic
164C22×C4#12011yescharacteristic
165C22×C4#12111yescharacteristic
166C22×C4#12111yescharacteristic
167C22×C4#12111yescharacteristic
168C22×C4#12711yescharacteristic
169C2×C8—24no—
170C2×C8—24no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—44no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—44no—
192C4⋊C4—42no—
193C4⋊C4—44no—
194C4⋊C4—42no—
195C4⋊C4—82no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—82no—
201C4⋊C4—81no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C42—22no—
208C42—22no—
209C42—22no—
210C42—81no—
211C42—81no—
212C42C2×D811yescharacteristic
213C42C2×SD1612yes—
214C42#13511yescharacteristic
215C42#13512yes—
216C42#13512yes—
217C42AGL(1,ℤ/8)11yescharacteristic
218C42AGL(1,ℤ/8)11yescharacteristic
219C42#13712yes—
220C42#13712yes—
221C42#13712yes—
222C23#39211yescharacteristic
223Q8—44no—
224Q8—82no—
225Q8—162no—
226Q8—162no—
227Q8—162no—
228Q8—162no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—82no—
241C2×C4—81no—
242C2×C4—82no—
243C2×C4—81no—
244C2×C4—82no—
245C2×C4—81no—
246C2×C4—82no—
247C2×C4#44711yescharacteristic
248C2×C4#44711yescharacteristic
249C2×C4#44812yes—
250C2×C4#44911yescharacteristic
251C2×C4#44911yescharacteristic
252C2×C4#45212yes—
253C2×C4#45212yes—
254C2×C4#45412yes—
255C2×C4#45612yes—
256C2×C4#46112yes—
257C2×C4#46412yes—
258C2×C4#46412yes—
259C2×C4#46611yescharacteristic
260C2×C4#46911yescharacteristic
261C2×C4#47112yes—
262C2×C4#49211yescharacteristic
263C2×C4#49511yescharacteristic
264C2×C4#49511yescharacteristic
265C2×C4#49711yescharacteristic
266C2×C4#49711yescharacteristic
267C2×C4#49711yescharacteristic
268C8—44no—
269C8—44no—
270C8—82no—
271C8—161no—
272C22#199911yescharacteristic
273C22#200311yescharacteristic
274C22#200511yescharacteristic
275C22#201311yescharacteristic
276C22#201511yescharacteristic
277C22#201511yescharacteristic
278C22#201911yescharacteristic
279C4—22no—
280C4—22no—
281C4—22no—
282C4—82no—
283C4—162no—
284C4—162no—
285C4—161no—
286C4#162612yes—
287C4#162712yes—
288C4#164712yes—
289C4#165012yes—
290C4#168212yes—
291C4#170212yes—
292C4#170811yescharacteristic
293C4#171611yescharacteristic
294C4#171811yescharacteristic
295C4#171811yescharacteristic
296C2#1005111yescharacteristic
297C2#1006611yescharacteristic
298C2#1015611yescharacteristic
299C2#1016711yescharacteristic
300C2#1026311yescharacteristic
301C2#1029611yescharacteristic
302C2#1031711yescharacteristic
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
#287172
#286872
#98982
#98702
#96942
#70152