Finite Group Databasebeta

← #103899

Subgroups — #103899

Order 512.

466 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 94 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#30280C211yesmaximal, characteristic
2#29211C211yesmaximal, characteristic
3#28717C211yesmaximal, characteristic
4#9705C211yesmaximal, characteristic
5#7662C211yesmaximal, characteristic
6#7591C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8C2×#498—21no—
9C2×#487—21no—
10C2×#487—21no—
11#2868C2211yescharacteristic
12#2862C2211yescharacteristic
13C4×C4⋊Q8C2211yescharacteristic
14#2096—22no—
15#2096—22no—
16#2072—22no—
17#2058—21no—
18#2057—21no—
19#1993—21no—
20#1990—21no—
21#1949—22no—
22#1847—21no—
23#1831C2211yescharacteristic
24#1803—22no—
25#1767C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27#1744C2211yescharacteristic
28C2×#332—22no—
29#1272—22no—
30#1271—22no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×C4×Q8—21no—
38#498—44no—
39#487—44no—
40#487—42no—
41#487—42no—
42C2×#107—22no—
43C2×#106—24no—
44C2×#106—22no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8D412yes—
48C2×#103—24no—
49C2×#103—24no—
50C2×#97—21no—
51C2×C4×C8—21no—
52C2×C4×C8—21no—
53#391—21no—
54#391—21no—
55#391—21no—
56#391—21no—
57#391—21no—
58#389—21no—
59#389—21no—
60#384—21no—
61#384—21no—
62#384—21no—
63#384D411yescharacteristic
64#384D412yes—
65#382—21no—
66#382—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C43C2311yescharacteristic
70#340—22no—
71#340—22no—
72#340—24no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336D412yes—
78#336D412yes—
79#332—44no—
80C22×Q8—21no—
81C22×Q8—21no—
82C22×Q8—21no—
83C22×Q8—41no—
84C22×C8—22no—
85C22×C8—22no—
86C22×C8—22no—
87C22×C8—41no—
88C4⋊Q8—21no—
89C4⋊Q8—21no—
90C4⋊Q8—21no—
91C4⋊Q8—42no—
92C4⋊Q8—42no—
93C4⋊Q8—42no—
94C4⋊Q8—42no—
95C4⋊Q8—42no—
96C4⋊Q8—41no—
97C4⋊Q8—41no—
98C4⋊Q8—41no—
99C4⋊Q8—41no—
100C4⋊Q8—42no—
101C4⋊Q8SD1612yes—
102C4×Q8—44no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
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#107—82no—
128#106—48no—
129#106—82no—
130C4⋊C8—22no—
131C4⋊C8—42no—
132C4⋊C8—42no—
133C4⋊C8SD1614yes—
134#103—48no—
135#103—48no—
136#97—41no—
137#97—41no—
138C4×C8—24no—
139C4×C8—41no—
140C4×C8—41no—
141#95—41no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—41no—
147C2×Q8—22no—
148C2×Q8—42no—
149C2×Q8—42no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—41no—
153C2×Q8—42no—
154C2×Q8—42no—
155C2×Q8—81no—
156C2×Q8—81no—
157C2×Q8—81no—
158C2×Q8—82no—
159C2×Q8—81no—
160C2×Q8—82no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—42no—
166C22×C4#12011yescharacteristic
167C22×C4#12011yescharacteristic
168C22×C4#12011yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4#12111yescharacteristic
171C22×C4#12111yescharacteristic
172C22×C4#12711yescharacteristic
173C2×C8—24no—
174C2×C8—24no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—81no—
183C2×C8—81no—
184C2×C8—81no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—44no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—82no—
202C4⋊C4—82no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C42—22no—
208C42—22no—
209C42—22no—
210C42—41no—
211C42—41no—
212C42—82no—
213C42C2×SD1611yescharacteristic
214C42C2×SD1612yes—
215C42#13511yescharacteristic
216C42AGL(1,ℤ/8)11yescharacteristic
217C42#13711yescharacteristic
218C42#13712yes—
219C23#39211yescharacteristic
220Q8—44no—
221Q8—82no—
222Q8—84no—
223Q8—162no—
224Q8—162no—
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—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—82no—
242C2×C4—81no—
243C2×C4—82no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—82no—
252C2×C4—81no—
253C2×C4#44812yes—
254C2×C4#44811yescharacteristic
255C2×C4#44911yescharacteristic
256C2×C4#45011yescharacteristic
257C2×C4#45211yescharacteristic
258C2×C4#45312yes—
259C2×C4#45412yes—
260C2×C4#46112yes—
261C2×C4#46511yescharacteristic
262C2×C4#46811yescharacteristic
263C2×C4#47312yes—
264C2×C4#49211yescharacteristic
265C2×C4#49711yescharacteristic
266C8—44no—
267C8—44no—
268C8—82no—
269C8—161no—
270C22#200011yescharacteristic
271C22#200211yescharacteristic
272C22#200311yescharacteristic
273C22#200911yescharacteristic
274C22#200911yescharacteristic
275C22#201311yescharacteristic
276C22#202011yescharacteristic
277C4—21no—
278C4—21no—
279C4—22no—
280C4—22no—
281C4—22no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—82no—
287C4—162no—
288C4—161no—
289C4—161no—
290C4—161no—
291C4#162212yes—
292C4#162312yes—
293C2#1004911yescharacteristic
294C2#1009411yescharacteristic
295C2#1013311yescharacteristic
296C2#1015911yescharacteristic
297C2#1018711yescharacteristic
298C2#1022711yescharacteristic
299C2#1024711yescharacteristic
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
#302802
#292112
#287172
#97052
#76622
#75912
#70272