Finite Group Databasebeta

← #352479

Subgroups — #352479

Order 512.

536 conjugacy classes of subgroups.

The subgroup lattice has 319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33291C211yesmaximal, characteristic
2#29999C211yesmaximal, characteristic
3#29996C211yesmaximal, characteristic
4#20516C211yesmaximal, characteristic
5#9904C211yesmaximal, characteristic
6#9902C211yesmaximal, characteristic
7#9622C212yesmaximal
8#9613C212yesmaximal
9#8805C211yesmaximal, characteristic
10#8657C212yesmaximal
11#8647C212yesmaximal
12C2×#446C2211yescharacteristic
13C2×C8×Q8C2211yescharacteristic
14#2859C2211yescharacteristic
15#2859C2211yescharacteristic
16#2295C2211yescharacteristic
17#2088—22no—
18#2087—22no—
19#2068—22no—
20#2066—22no—
21#1991—21no—
22#1991—21no—
23#1991—21no—
24#1991—21no—
25#1948C2212yes—
26#1947C2212yes—
27#1842C2211yescharacteristic
28#1842C2211yescharacteristic
29#1834C2212yes—
30#1834C2212yes—
31#1803C2212yes—
32#1803C2212yes—
33#1771—21no—
34#1770C2211yescharacteristic
35C8×C4⋊C4—21no—
36C8×C4⋊C4C2211yescharacteristic
37#1768—21no—
38#1767C2211yescharacteristic
39#1726—21no—
40C42×C8C2211yescharacteristic
41C2×#334C2212yes—
42C2×#334C2212yes—
43#1296C2212yes—
44#1296C2212yes—
45#1296C2212yes—
46#1296C2212yes—
47C2×#125—21no—
48C2×#125—21no—
49C2×C4×Q8C2311yescharacteristic
50#446—22no—
51#446Q814yes—
52C8×Q8—22no—
53C8×Q8Q814yes—
54C2×#107—22no—
55C2×#106—22no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—22no—
59C2×C4⋊C8—22no—
60C2×C4⋊C8C2312yes—
61C2×C4⋊C8C2312yes—
62C2×C4⋊C8C2311yescharacteristic
63C2×C4⋊C8C2311yescharacteristic
64C2×#103—22no—
65C2×#103—22no—
66C2×#97—21no—
67C2×#97—21no—
68C2×#97—21no—
69C2×C4×C8—21no—
70C2×C4×C8—21no—
71C2×C4×C8D411yescharacteristic
72C2×C4×C8D411yescharacteristic
73C2×C4×C8D411yescharacteristic
74C2×C4×C8D411yescharacteristic
75C2×C4×C8C2311yescharacteristic
76C2×C4×C8C2311yescharacteristic
77#391D412yes—
78#389—22no—
79#389—22no—
80#389—22no—
81#389—22no—
82#389D412yes—
83#387—22no—
84#384C2312yes—
85#384C2312yes—
86#382—21no—
87#382—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4C2311yescharacteristic
90#376—21no—
91C43C2311yescharacteristic
92#340—22no—
93#340—22no—
94#340—22no—
95#340—22no—
96#340—22no—
97#340—22no—
98#340—22no—
99#340—22no—
100#336—21no—
101#336—21no—
102#336—21no—
103#334—24no—
104#334—24no—
105C22×Q8C2×D411yescharacteristic
106C22×C8—21no—
107C22×C8—21no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8C2×D411yescharacteristic
111C22×C8C2×D411yescharacteristic
112C22×C8C2×D411yescharacteristic
113C22×C8C2×D411yescharacteristic
114#125—42no—
115#125—42no—
116#125—42no—
117#125—42no—
118C4×Q8—21no—
119C4×Q8—21no—
120C4×Q8C2×Q812yes—
121C4×Q8C2×Q812yes—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—42no—
131C2×C4⋊C4—42no—
132C2×C4⋊C4C2×D412yes—
133C2×C4⋊C4C2×D411yescharacteristic
134C2×C42—21no—
135C2×C42—21no—
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D412yes—
138C2×C42C2×D411yescharacteristic
139C2×C42#4112yes—
140C2×C42C2411yescharacteristic
141#107—82no—
142#106—82no—
143C4⋊C8—24no—
144C4⋊C8—24no—
145C4⋊C8—21no—
146C4⋊C8—21no—
147C4⋊C8—22no—
148C4⋊C8—22no—
149C4⋊C8—22no—
150C4⋊C8—22no—
151C4⋊C8—82no—
152C4⋊C8—82no—
153C4⋊C8C2×Q812yes—
154C4⋊C8C2×Q812yes—
155#103—82no—
156#103—82no—
157#97—24no—
158#97—42no—
159#97—42no—
160C4×C8—24no—
161C4×C8—22no—
162C4×C8—22no—
163C4×C8—41no—
164C4×C8—41no—
165C4×C8—42no—
166C4×C8C2×Q812yes—
167C4×C8C2×Q812yes—
168C4×C8#4112yes—
169C4×C8#4112yes—
170#95—22no—
171#95—22no—
172#95—22no—
173#95—21no—
174#95—42no—
175#95—42no—
176C2×Q8—21no—
177C2×Q8—22no—
178C2×Q8—22no—
179C2×Q8C4⋊Q812yes—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4#12112yes—
186C22×C4#12112yes—
187C22×C4C22×D411yescharacteristic
188C22×C4C22×D411yescharacteristic
189C22×C4C2×#4111yescharacteristic
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—22no—
199C2×C8—22no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8C22⋊Q812yes—
211C2×C8C22⋊Q812yes—
212C2×C8C22⋊Q812yes—
213C2×C8C22⋊Q812yes—
214C4⋊C4—21no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—44no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—82no—
229C4⋊C4—82no—
230C4⋊C4—84no—
231C4⋊C4—84no—
232C4⋊C4C4⋊Q812yes—
233C42—22no—
234C42—22no—
235C42—21no—
236C42—21no—
237C42—22no—
238C42—22no—
239C42—42no—
240C42—41no—
241C42—41no—
242C42#13512yes—
243C42#13712yes—
244C42C22×Q811yescharacteristic
245C42C22×Q811yescharacteristic
246C42C2×#4111yescharacteristic
247C42C2×#4111yescharacteristic
248C23C2×#12111yescharacteristic
249Q8—24no—
250Q8—41no—
251Q8—41no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4#46414yes—
272C2×C4C2×C22⋊Q811yescharacteristic
273C2×C4C2×C22⋊Q811yescharacteristic
274C2×C4C2×C4⋊Q811yescharacteristic
275C2×C4#53211yescharacteristic
276C2×C4#53311yescharacteristic
277C2×C4#53311yescharacteristic
278C2×C4C2×#13511yescharacteristic
279C2×C4C2×#13711yescharacteristic
280C2×C4#57511yescharacteristic
281C2×C4#57511yescharacteristic
282C2×C4#57712yes—
283C2×C4#57712yes—
284C8—22no—
285C8—22no—
286C8—22no—
287C8—22no—
288C8—42no—
289C8—42no—
290C8—82no—
291C8—82no—
292C22#285711yescharacteristic
293C22C2×#46411yescharacteristic
294C22#304011yescharacteristic
295C22#306012yes—
296C22#306712yes—
297C4—24no—
298C4—21no—
299C4—21no—
300C4—42no—
301C4—42no—
302C4—42no—
303C4—82no—
304C4—162no—
305C4—162no—
306C4#307611yescharacteristic
307C4#307611yescharacteristic
308C4#307811yescharacteristic
309C4#307811yescharacteristic
310C4#316312yes—
311C4#317411yescharacteristic
312C4#317411yescharacteristic
313C2#1921612yes—
314C2#1936612yes—
315C2#3320211yescharacteristic
316C2#3321411yescharacteristic
317C2#3322111yescharacteristic
subgroupG/H
center, socle, prime radicalC23C2×#121
commutator, Frattini, cosocleC2×C42C24
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ 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
#332912
#299992
#299962
#205162
#99042
#99022
#96222
#96132
#88052
#86572
#86472