Finite Group Databasebeta

← #352441

Subgroups — #352441

Order 512.

560 conjugacy classes of subgroups.

The subgroup lattice has 323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33256C211yesmaximal, characteristic
2#33073C212yesmaximal
3C4×#446C211yesmaximal, characteristic
4#9901C212yesmaximal
5#9622C212yesmaximal
6#9618C211yesmaximal, characteristic
7#9617C211yesmaximal, characteristic
8#8807C211yesmaximal, characteristic
9#8657C212yesmaximal
10#8651C211yesmaximal, characteristic
11#8651C211yesmaximal, characteristic
12C2×#446C2211yescharacteristic
13C2×#446C2211yescharacteristic
14#2859C2212yes—
15C42×Q8C2211yescharacteristic
16#1948C2212yes—
17#1947C2212yes—
18#1941—21no—
19#1941—21no—
20#1941—21no—
21#1941—21no—
22#1920—22no—
23#1918—22no—
24#1865—22no—
25#1863—22no—
26#1844C2211yescharacteristic
27#1844C2211yescharacteristic
28#1834C2212yes—
29#1831C2212yes—
30#1803C2212yes—
31#1803C2212yes—
32#1771—21no—
33#1771—21no—
34#1770C2211yescharacteristic
35#1770C2211yescharacteristic
36C4×C4⋊C8—21no—
37C4×C4⋊C8C2211yescharacteristic
38C4×#97—21no—
39C42×C8C2211yescharacteristic
40C2×#335C2211yescharacteristic
41C2×#335C2211yescharacteristic
42C2×#334C2212yes—
43#1296C2212yes—
44#1296C2212yes—
45#1296C2212yes—
46#1296C2212yes—
47C2×#125—22no—
48C2×C4×Q8D412yes—
49C2×C4×Q8C2311yescharacteristic
50#446—22no—
51#446—22no—
52#446Q814yes—
53#446Q814yes—
54C2×#107—22no—
55C2×#106—21no—
56C2×#106—21no—
57C2×#106—21no—
58C2×#106—21no—
59C2×#106—22no—
60C2×C4⋊C8—21no—
61C2×C4⋊C8—21no—
62C2×C4⋊C8C2312yes—
63C2×C4⋊C8C2312yes—
64C2×C4⋊C8C2311yescharacteristic
65C2×C4⋊C8C2311yescharacteristic
66C2×#103—22no—
67C2×#103—22no—
68C2×#97—21no—
69C2×#97—21no—
70C2×#97—21no—
71C2×#97—21no—
72C2×C4×C8—21no—
73C2×C4×C8D411yescharacteristic
74C2×C4×C8D411yescharacteristic
75C2×C4×C8D411yescharacteristic
76C2×C4×C8D411yescharacteristic
77C2×C4×C8C2311yescharacteristic
78C2×C4×C8C2311yescharacteristic
79#389—22no—
80#389—22no—
81#389—22no—
82#389—22no—
83#384C2312yes—
84#384C2312yes—
85#382—22no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—22no—
88C4×C4⋊C4D412yes—
89C4×C4⋊C4C2311yescharacteristic
90C43—21no—
91C43C2311yescharacteristic
92#340—22no—
93#340—22no—
94#340—22no—
95#340—22no—
96#340—22no—
97#340—22no—
98#336—21no—
99#336—21no—
100#336—22no—
101#336—22no—
102#336—21no—
103#335—22no—
104#335—22no—
105#334—24no—
106C22×Q8C2×D411yescharacteristic
107C22×C8—21no—
108C22×C8—21no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8C2×D411yescharacteristic
112C22×C8C2×D411yescharacteristic
113C22×C8C2×D411yescharacteristic
114C22×C8C2×D411yescharacteristic
115#125—84no—
116C4×Q8—21no—
117C4×Q8—21no—
118C4×Q8—42no—
119C4×Q8—42no—
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—22no—
136C2×C42—22no—
137C2×C42—21no—
138C2×C42C2×D412yes—
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42#4112yes—
142C2×C42C2411yescharacteristic
143#107—44no—
144#106—44no—
145#106—42no—
146#106—42no—
147#106—42no—
148#106—42no—
149C4⋊C8—24no—
150C4⋊C8—24no—
151C4⋊C8—21no—
152C4⋊C8—21no—
153C4⋊C8—22no—
154C4⋊C8—22no—
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8C2×Q812yes—
158C4⋊C8C2×Q812yes—
159#103—44no—
160#103—44no—
161#97—24no—
162#97—24no—
163#97—42no—
164#97—42no—
165C4×C8—22no—
166C4×C8—22no—
167C4×C8—41no—
168C4×C8—41no—
169C4×C8—42no—
170C4×C8C2×Q812yes—
171C4×C8C2×Q812yes—
172C4×C8#4112yes—
173C4×C8#4112yes—
174#95—22no—
175#95—21no—
176#95—42no—
177#95—42no—
178C2×Q8—21no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8C4⋊Q812yes—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4#12112yes—
188C22×C4#12112yes—
189C22×C4C22×D411yescharacteristic
190C22×C4C22×D411yescharacteristic
191C22×C4C2×#4111yescharacteristic
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—
214C2×C8#13512yes—
215C2×C8#13712yes—
216C4⋊C4—21no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—44no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C4⋊C4—82no—
231C4⋊C4—82no—
232C4⋊C4—84no—
233C4⋊C4—84no—
234C4⋊C4C4⋊Q812yes—
235C42—22no—
236C42—22no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—22no—
242C42—22no—
243C42—24no—
244C42—44no—
245C42—41no—
246C42—41no—
247C42—44no—
248C42C22×Q811yescharacteristic
249C42C22×Q811yescharacteristic
250C42C2×#4111yescharacteristic
251C42C2×#4111yescharacteristic
252C23C2×#12111yescharacteristic
253Q8—24no—
254Q8—41no—
255Q8—41no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4—82no—
274C2×C4—82no—
275C2×C4#47114yes—
276C2×C4C2×C22⋊Q811yescharacteristic
277C2×C4C2×C22⋊Q811yescharacteristic
278C2×C4C2×C4⋊Q811yescharacteristic
279C2×C4#53211yescharacteristic
280C2×C4#53311yescharacteristic
281C2×C4#53311yescharacteristic
282C2×C4C2×#13511yescharacteristic
283C2×C4C2×#13711yescharacteristic
284C2×C4#57511yescharacteristic
285C2×C4#57511yescharacteristic
286C2×C4#57512yes—
287C2×C4#57512yes—
288C8—22no—
289C8—22no—
290C8—22no—
291C8—42no—
292C8—42no—
293C8—82no—
294C8—82no—
295C8#47914yes—
296C22#285711yescharacteristic
297C22#303511yescharacteristic
298C22#303711yescharacteristic
299C22#305412yes—
300C22C2×#47112yes—
301C4—24no—
302C4—21no—
303C4—21no—
304C4—42no—
305C4—42no—
306C4—42no—
307C4—82no—
308C4—162no—
309C4—162no—
310C4C2×#47911yescharacteristic
311C4#307611yescharacteristic
312C4#307811yescharacteristic
313C4#308011yescharacteristic
314C4#316612yes—
315C4#318311yescharacteristic
316C4#318311yescharacteristic
317C2#1915912yes—
318C2#1928812yes—
319C2#3320011yescharacteristic
320C2#3321111yescharacteristic
321C2#3322011yescharacteristic
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
#332562
#330732
C4×#4462
#99012
#96222
#96182
#96172
#88072
#86572
#86512