Finite Group Databasebeta

← #244462

Subgroups — #244462

Order 512.

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

normal subgroups only

This group has 443 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#21735C211yesmaximal, characteristic
2#21717C211yesmaximal, characteristic
3#10687C211yesmaximal, characteristic
4#10687C211yesmaximal, characteristic
5#10628C212yesmaximal
6#10548C211yesmaximal, characteristic
7#10548C211yesmaximal, characteristic
8#10371C212yesmaximal
9#8258C212yesmaximal
10#8254C212yesmaximal
11#8139C211yesmaximal, characteristic
12#3162C2211yescharacteristic
13#2960C2212yes—
14C2×#446—21no—
15#2399C2211yescharacteristic
16#1995C2212yes—
17#1984—21no—
18#1946—21no—
19#1946—21no—
20#1940C2211yescharacteristic
21#1940C2211yescharacteristic
22#1939—21no—
23#1849C2211yescharacteristic
24#1843C2211yescharacteristic
25#1772—21no—
26#1772—21no—
27#1771—21no—
28#1770C2211yescharacteristic
29C8×C4⋊C4C2211yescharacteristic
30#1726C2211yescharacteristic
31#1542C2212yes—
32#1542C2212yes—
33#1503C2212yes—
34#1503C2212yes—
35#1452C2212yes—
36#1303C2212yes—
37#1303C2212yes—
38#1301C2212yes—
39#1301C2212yes—
40#1275C2211yescharacteristic
41#1275C2211yescharacteristic
42#1274C2212yes—
43#533C2312yes—
44C2×C4×Q8—21no—
45#501—22no—
46#501—22no—
47#446—22no—
48#446—22no—
49#446—44no—
50C8×Q8—22no—
51C8×Q8—22no—
52#431C2312yes—
53#431C2312yes—
54C2×#108—21no—
55C2×#108—21no—
56#427—21no—
57#427—21no—
58#424—22no—
59#423C2312yes—
60C2×C4⋊C8—21no—
61C2×C4⋊C8—21no—
62C2×C4⋊C8—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8C2311yescharacteristic
65C2×C4⋊C8C2311yescharacteristic
66#405—22no—
67C2×#97—21no—
68C2×#97D411yescharacteristic
69C2×#97D411yescharacteristic
70C2×#97C2311yescharacteristic
71C2×C4×C8—21no—
72C2×C4×C8D411yescharacteristic
73C2×C4×C8D411yescharacteristic
74C2×C4×C8C2311yescharacteristic
75#398—21no—
76#398—21no—
77#395—21no—
78#395—21no—
79C4×C4⋊C4—21no—
80C4×C4⋊C4C2311yescharacteristic
81C4×C4⋊C4C2311yescharacteristic
82#376C2311yescharacteristic
83#339—22no—
84#339—22no—
85#336—21no—
86#336—21no—
87#336—21no—
88#336—21no—
89#333—22no—
90#333—22no—
91#332—22no—
92#332—22no—
93#328—22no—
94#328—22no—
95#328—22no—
96#328—22no—
97#322—22no—
98#322—22no—
99C22×Q8—21no—
100C2×M16—22no—
101C22×C8—21no—
102C22×C8—21no—
103C22×C8C2×D411yescharacteristic
104C22×C8C2×D411yescharacteristic
105C22×C8C2×D411yescharacteristic
106C22×C8C2×D411yescharacteristic
107C4⋊Q8#4112yes—
108C4⋊Q8#4112yes—
109#125—22no—
110C22⋊Q8—22no—
111C22⋊Q8—22no—
112C4×Q8—22no—
113C4×Q8—22no—
114C4×Q8—42no—
115C4×Q8—42no—
116#117—22no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2411yescharacteristic
129#108—42no—
130#108—42no—
131#107—21no—
132#107—21no—
133#107—21no—
134#107—21no—
135#106—22no—
136#106—22no—
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8—22no—
140C4⋊C8—22no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—42no—
144C4⋊C8—42no—
145C4⋊C8—42no—
146C4⋊C8—42no—
147C4⋊C8—42no—
148C4⋊C8—42no—
149C22⋊C8—22no—
150C22⋊C8—22no—
151#97—22no—
152#97—22no—
153#97—22no—
154#97—42no—
155#97—42no—
156C4×C8—22no—
157C4×C8—22no—
158C4×C8—22no—
159C4×C8—22no—
160C4×C8—42no—
161C4×C8—42no—
162C4×C8#4112yes—
163C4×C8#4112yes—
164#95—21no—
165#95—21no—
166#95—21no—
167#95—21no—
168#95#4111yescharacteristic
169#95#4111yescharacteristic
170#95#4111yescharacteristic
171#95#4111yescharacteristic
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—42no—
176C2×Q8—81no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4C22×D411yescharacteristic
184C22×C4C2×#4111yescharacteristic
185C22×C4C2×#4111yescharacteristic
186M16—42no—
187M16—42no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—42no—
199C2×C8—42no—
200C2×C8—42no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8#12411yescharacteristic
206C2×C8#12411yescharacteristic
207C2×C8#12412yes—
208C2×C8AGL(1,ℤ/8)12yes—
209C2×C8#13712yes—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—81no—
222C4⋊C4—81no—
223C22⋊C4—42no—
224C42—21no—
225C42—21no—
226C42—42no—
227C42—41no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42#13712yes—
232C42#13712yes—
233C42C2×#4112yes—
234C42C2×#4112yes—
235C23#52511yescharacteristic
236Q8—82no—
237Q8—82no—
238Q8—84no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4#52511yescharacteristic
262C2×C4C2×#12411yescharacteristic
263C2×C4#52912yes—
264C2×C4#52912yes—
265C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
266C2×C4C2×#13711yescharacteristic
267C2×C4C2×#13711yescharacteristic
268C2×C4C2×#13711yescharacteristic
269C8—22no—
270C8—22no—
271C8—21no—
272C8—21no—
273C8—22no—
274C8—82no—
275C8—82no—
276C8—81no—
277C8—81no—
278C8—82no—
279C22—21no—
280C22—21no—
281C22#239811yescharacteristic
282C22#311011yescharacteristic
283C22#311311yescharacteristic
284C4—22no—
285C4—22no—
286C4—42no—
287C4—42no—
288C4—42no—
289C4—81no—
290C4—81no—
291C4—81no—
292C4—82no—
293C4—82no—
294C4#311211yescharacteristic
295C4#311311yescharacteristic
296C4#313911yescharacteristic
297C4#314111yescharacteristic
298C2—21no—
299C2—21no—
300C2#2382311yescharacteristic
301C2#2383311yescharacteristic
302C2#2383411yescharacteristic
subgroupG/H
centerC2×C4C2×#124
commutator, Frattini, cosocleC2×C42C24
socleC22#2398
prime radicalC23#525
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#217352
#217172
#106872
#106282
#105482
#103712
#82582
#82542
#81392