Finite Group Databasebeta

← #103138

Subgroups — #103138

Order 512.

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

normal subgroups only

This group has 508 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#33312C211yesmaximal, characteristic
2#29218C211yesmaximal, characteristic
3#29206C211yesmaximal, characteristic
4#9896C211yesmaximal, characteristic
5#9691C211yesmaximal, characteristic
6#9637C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#500—22no—
9#2868C2211yescharacteristic
10#2868C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2100—22no—
13#2058—22no—
14#1990—21no—
15#1990—21no—
16#1987—22no—
17#1948—22no—
18#1845—22no—
19#1845—22no—
20#1844—21no—
21#1842C2211yescharacteristic
22#1834—21no—
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C42×C8C2211yescharacteristic
26C2×#333—22no—
27C2×Q8⋊C8—22no—
28#1296—22no—
29C2×C4⋊Q8—21no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D412yes—
36C2×C4×Q8—21no—
37#500—48no—
38C2×#107—28no—
39C2×#106—24no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8D412yes—
44C2×C4⋊C8D412yes—
45C2×C4×C8—21no—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48C2×C4×C8—21no—
49C2×C4×C8D412yes—
50#391—21no—
51#389—21no—
52#389—21no—
53#384—21no—
54#384—21no—
55#384—21no—
56#384—21no—
57#384—21no—
58#384—21no—
59#384—21no—
60#384D411yescharacteristic
61#384D412yes—
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C43C2311yescharacteristic
65#340—24no—
66#340—24no—
67#340—24no—
68#336—21no—
69#336—21no—
70#333—44no—
71Q8⋊C8—44no—
72C22×Q8—21no—
73C22×Q8—22no—
74C22×Q8—41no—
75C22×C8—22no—
76C22×C8—22no—
77C22×C8—22no—
78C22×C8—41no—
79C4⋊Q8—21no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8—44no—
83C4⋊Q8—44no—
84C4⋊Q8—42no—
85C4⋊Q8—42no—
86C4⋊Q8—42no—
87C4⋊Q8—42no—
88C4⋊Q8—82no—
89C4⋊Q8—82no—
90C4⋊Q8Q1612yes—
91C4×Q8—42no—
92C4×Q8—42no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C42—41no—
112C2×C42C2×D411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42C2×D411yescharacteristic
115C2×C42C2×D411yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42#4111yescharacteristic
119#107—416no—
120#106—84no—
121C4⋊C8—22no—
122C4⋊C8—22no—
123C4⋊C8—22no—
124C4⋊C8—42no—
125C4⋊C8—42no—
126C4⋊C8—42no—
127C4⋊C8Q1614yes—
128C4×C8—24no—
129C4×C8—24no—
130C4×C8—22no—
131C4×C8—41no—
132C4×C8—41no—
133C4×C8—41no—
134C4×C8—41no—
135C4×C8SD1614yes—
136#95—41no—
137#95—41no—
138C2×Q8—22no—
139C2×Q8—41no—
140C2×Q8—42no—
141C2×Q8—44no—
142C2×Q8—42no—
143C2×Q8—82no—
144C2×Q8—82no—
145C2×Q8—82no—
146C2×Q8—82no—
147C2×Q8—82no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4#12011yescharacteristic
153C22×C4#12011yescharacteristic
154C22×C4#12011yescharacteristic
155C22×C4#12111yescharacteristic
156C22×C4#12111yescharacteristic
157C22×C4#12111yescharacteristic
158C22×C4#12711yescharacteristic
159C2×C8—24no—
160C2×C8—24no—
161C2×C8—24no—
162C2×C8—24no—
163C2×C8—42no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—81no—
169C2×C8—81no—
170C2×C8—81no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—44no—
174C4⋊C4—44no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—44no—
178C4⋊C4—42no—
179C4⋊C4—44no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—82no—
183C4⋊C4—82no—
184C4⋊C4—82no—
185C4⋊C4—82no—
186C4⋊C4—82no—
187C4⋊C4—82no—
188C4⋊C4—82no—
189C4⋊C4—81no—
190C4⋊C4—81no—
191C4⋊C4—81no—
192C4⋊C4—81no—
193C42—22no—
194C42—22no—
195C42—22no—
196C42—81no—
197C42—81no—
198C42C2×SD1612yes—
199C42C2×Q1611yescharacteristic
200C42C2×Q1612yes—
201C42#13512yes—
202C42#13511yescharacteristic
203C42AGL(1,ℤ/8)12yes—
204C42#13712yes—
205C42#13711yescharacteristic
206C42#13711yescharacteristic
207C42#13712yes—
208C23#39211yescharacteristic
209Q8—44no—
210Q8—82no—
211Q8—164no—
212Q8—164no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4—82no—
223C2×C4—82no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—82no—
227C2×C4—82no—
228C2×C4—81no—
229C2×C4—82no—
230C2×C4—82no—
231C2×C4#44812yes—
232C2×C4#44912yes—
233C2×C4#45112yes—
234C2×C4#45111yescharacteristic
235C2×C4#45111yescharacteristic
236C2×C4#45211yescharacteristic
237C2×C4#45211yescharacteristic
238C2×C4#45312yes—
239C2×C4#45612yes—
240C2×C4#46112yes—
241C2×C4#46212yes—
242C2×C4#46312yes—
243C2×C4#46711yescharacteristic
244C2×C4#47011yescharacteristic
245C2×C4#47212yes—
246C2×C4#49211yescharacteristic
247C2×C4#49411yescharacteristic
248C2×C4#49511yescharacteristic
249C2×C4#49611yescharacteristic
250C2×C4#49711yescharacteristic
251C2×C4#49711yescharacteristic
252C8—28no—
253C8—44no—
254C8—82no—
255C8—161no—
256C22#200111yescharacteristic
257C22#200211yescharacteristic
258C22#200511yescharacteristic
259C22#201211yescharacteristic
260C22#201311yescharacteristic
261C22#201611yescharacteristic
262C22#201811yescharacteristic
263C4—22no—
264C4—22no—
265C4—22no—
266C4—82no—
267C4—161no—
268C4—162no—
269C4—162no—
270C4#163212yes—
271C4#163312yes—
272C4#164812yes—
273C4#165012yes—
274C4#167512yes—
275C4#169512yes—
276C4#170711yescharacteristic
277C4#171411yescharacteristic
278C4#171811yescharacteristic
279C4#172311yescharacteristic
280C2#1005711yescharacteristic
281C2#1007711yescharacteristic
282C2#1014511yescharacteristic
283C2#1016511yescharacteristic
284C2#1027811yescharacteristic
285C2#1028311yescharacteristic
286C2#1031411yescharacteristic
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
#333122
#292182
#292062
#98962
#96912
#96372
#70152