Finite Group Databasebeta

← #508623

Subgroups — #508623

Order 512.

464 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33258C211yesmaximal, characteristic
2#21276C211yesmaximal, characteristic
3#13516C212yesmaximal
4#13514C212yesmaximal
5#13477C212yesmaximal
6#13475C212yesmaximal
7#13177C211yesmaximal, characteristic
8#13176C211yesmaximal, characteristic
9#12898C211yesmaximal, characteristic
10#12812C211yesmaximal, characteristic
11#12812C211yesmaximal, characteristic
12C2×C4×Q16C2211yescharacteristic
13#2859—21no—
14#2295—21no—
15C2×#367C2212yes—
16C2×#366C2212yes—
17C2×C4⋊C16C2211yescharacteristic
18C2×C4⋊C16C2211yescharacteristic
19C2×C4⋊C16C2212yes—
20C2×C4⋊C16C2212yes—
21C2×#358C2212yes—
22C2×#358C2212yes—
23#1969C2211yescharacteristic
24#1969C2211yescharacteristic
25#1942—21no—
26#1942—21no—
27#1942C2211yescharacteristic
28#1942C2211yescharacteristic
29#1942C2212yes—
30#1942C2212yes—
31#1933—21no—
32#1933—21no—
33#1845C2211yescharacteristic
34#1845C2211yescharacteristic
35#1834—21no—
36C4×#107C2211yescharacteristic
37C4×#103—21no—
38C42×C8C2211yescharacteristic
39#1380C2212yes—
40#1380C2212yes—
41#1380C2212yes—
42#1380C2212yes—
43C22×Q16C2311yescharacteristic
44C2×#125—41no—
45C2×C4×Q8—21no—
46C22×C16C2312yes—
47C22×C16C2312yes—
48C4×Q16—22no—
49C4×Q16Q814yes—
50C2×#107—21no—
51C2×#107—21no—
52C2×#107C2312yes—
53C2×#107C2312yes—
54C2×#107C2311yescharacteristic
55C2×#107C2311yescharacteristic
56C2×#107C2311yescharacteristic
57C2×#103—21no—
58C2×#103—21no—
59C2×#103—21no—
60C2×C4×C8D411yescharacteristic
61C2×C4×C8D411yescharacteristic
62C2×C4×C8D411yescharacteristic
63C2×C4×C8C2311yescharacteristic
64C2×C4×C8C2311yescharacteristic
65C2×C4×C8C2311yescharacteristic
66#391—21no—
67#391—21no—
68#389—22no—
69#389—22no—
70#389—21no—
71#389—21no—
72#389—41no—
73#389—41no—
74#387—41no—
75#387—41no—
76#384—21no—
77#384—21no—
78#382—41no—
79C4×C4⋊C4—21no—
80C4×C4⋊C4—41no—
81#376—41no—
82C43D411yescharacteristic
83#367—42no—
84#366—42no—
85C4⋊C16—22no—
86C4⋊C16—22no—
87C4⋊C16—42no—
88C4⋊C16—42no—
89#358—42no—
90#358—42no—
91#340—22no—
92#340—22no—
93#340—21no—
94#340—21no—
95#340—21no—
96C22×Q8—21no—
97C2×Q16—21no—
98C2×Q16—21no—
99C2×Q16—21no—
100C2×Q16—21no—
101C2×Q16—21no—
102C2×Q16C2×Q812yes—
103C22×C8C2×D411yescharacteristic
104C22×C8C2×D411yescharacteristic
105C22×C8C2×D411yescharacteristic
106C22×C8C2411yescharacteristic
107#125—84no—
108C4×Q8—24no—
109C4×Q8—42no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C42—41no—
125C2×C42—41no—
126C2×C42D811yescharacteristic
127C2×C42D811yescharacteristic
128C2×C42D811yescharacteristic
129C2×C42D811yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C16—22no—
134C2×C16—22no—
135C2×C16—22no—
136C2×C16—22no—
137C2×C16—22no—
138C2×C16—22no—
139#107—21no—
140#107—22no—
141#107—22no—
142#107—21no—
143#107—21no—
144#107—22no—
145#107—22no—
146#107—21no—
147#107—21no—
148#107—42no—
149#107—42no—
150#107C2×Q812yes—
151#103—24no—
152#103—42no—
153#103—42no—
154C4×C8—21no—
155C4×C8—21no—
156C4×C8—21no—
157C4×C8—21no—
158C4×C8—22no—
159C4×C8—41no—
160C4×C8—41no—
161C4×C8C2×Q812yes—
162C4×C8#4112yes—
163#95—41no—
164#95—41no—
165#95—41no—
166#95—41no—
167#95—41no—
168#95—41no—
169#95—41no—
170#95—42no—
171#95—42no—
172C2×Q8—22no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4C2×D811yescharacteristic
185C22×C4C2×D811yescharacteristic
186C22×C4C2×D811yescharacteristic
187C22×C4C2×D811yescharacteristic
188C22×C4C2×D811yescharacteristic
189C22×C4C2×D811yescharacteristic
190C22×C4C22×D411yescharacteristic
191Q16—22no—
192Q16—22no—
193Q16—41no—
194Q16—41no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—21no—
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—21no—
203C2×C8C22⋊Q812yes—
204C2×C8C22×Q811yescharacteristic
205C2×C8C2×#4111yescharacteristic
206C2×C8H(5,𝔽2)11yescharacteristic
207C2×C8H(5,𝔽2)11yescharacteristic
208C2×C82−1+411yescharacteristic
209C2×C82−1+411yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—41no—
212C4⋊C4—44no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—82no—
222C4⋊C4—82no—
223C4⋊C4—84no—
224C4⋊C4—82no—
225C4⋊C4—82no—
226C4⋊C4—84no—
227C4⋊C4—82no—
228C4⋊C4—82no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—22no—
234C42—22no—
235C42—22no—
236C42—22no—
237C42—44no—
238C42—82no—
239C42C22⋊Q812yes—
240C42#13712yes—
241C16—42no—
242C16—42no—
243C23C22×D811yescharacteristic
244Q8—42no—
245Q8—42no—
246Q8—81no—
247Q8—81no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—82no—
274C2×C4—81no—
275C2×C4—82no—
276C2×C4—81no—
277C2×C4—82no—
278C2×C4#47412yes—
279C2×C4#47412yes—
280C2×C4#50812yes—
281C2×C4#50912yes—
282C2×C4#51012yes—
283C2×C4#51012yes—
284C2×C4C2×C22⋊Q811yescharacteristic
285C2×C4#53711yescharacteristic
286C2×C4#53711yescharacteristic
287C2×C4C2×#13711yescharacteristic
288C2×C4#57511yescharacteristic
289C2×C4#57511yescharacteristic
290C8—22no—
291C8—41no—
292C8—41no—
293C8#54011yescharacteristic
294C8#54111yescharacteristic
295C8#54411yescharacteristic
296C8#54411yescharacteristic
297C22C2×#47411yescharacteristic
298C22#324511yescharacteristic
299C22#324511yescharacteristic
300C22C2×#50811yescharacteristic
301C22C2×#50911yescharacteristic
302C22C2×#51011yescharacteristic
303C22C2×#51011yescharacteristic
304C4—22no—
305C4—22no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—82no—
310C4—82no—
311C4—161no—
312C4—162no—
313C4—161no—
314C4—162no—
315C4#222914yes—
316C4#262911yescharacteristic
317C4#308011yescharacteristic
318C4#325211yescharacteristic
319C4#325211yescharacteristic
320C2#2999411yescharacteristic
321C2C2×#222911yescharacteristic
322C2#3362911yescharacteristic
323C2#3381311yescharacteristic
324C2#3381411yescharacteristic
325C2#3382011yescharacteristic
326C2#3382111yescharacteristic
subgroupG/H
center, socle, prime radicalC23C22×D8
commutator, Frattini, cosocleC22×C8C24
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ C42×C8 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#332582
#212762
#135162
#135142
#134772
#134752
#131772
#131762
#128982
#128122