Finite Group Databasebeta

← #121460

Subgroups — #121460

Order 512.

476 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21994C211yesmaximal, characteristic
2#17822C211yesmaximal, characteristic
3#17797C211yesmaximal, characteristic
4#7994C211yesmaximal, characteristic
5#7930C211yesmaximal, characteristic
6#7903C211yesmaximal, characteristic
7#7868C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1950—22no—
16#1855—22no—
17#1849—21no—
18#1838—21no—
19#1573—22no—
20#1571—21no—
21#1570—21no—
22#1569—21no—
23#1569—21no—
24#1569—22no—
25#1568—22no—
26#1565—21no—
27#1565—21no—
28#1291C412yescomplemented
29#1291C412yescomplemented
30#1282—22no—
31#1279—22no—
32#1276—22no—
33C22×M16—21no—
34C22×M16—21no—
35C2×#117Q812yes—
36C22×C42C2311yescharacteristic
37#432—21no—
38#432—21no—
39#432—21no—
40#432—21no—
41#432—21no—
42#432—21no—
43#432—21no—
44#432—21no—
45#432—21no—
46#432C2×C412yes—
47#432C2×C412yes—
48#432Q812yes—
49#431—21no—
50#431—21no—
51#431—21no—
52#431D412yes—
53C2×#108—24no—
54#423—21no—
55#423—21no—
56#423—21no—
57#423D411yescharacteristic
58#423D411yescharacteristic
59#423D412yes—
60#423Q812yes—
61C2×C4⋊C8—21no—
62C2×C4⋊C8—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8D411yescharacteristic
65C2×C4⋊C8D411yescharacteristic
66#407—21no—
67#407—21no—
68C2×C22⋊C8—21no—
69C2×C22⋊C8D412yes—
70C4×M16—21no—
71C4×M16—21no—
72C4×M16—21no—
73C4×M16—21no—
74C4×M16C2×C411yescharacteristic
75C4×M16C2×C411yescharacteristic
76C4×M16Q812yes—
77C2×#97—21no—
78C2×#97—21no—
79C2×#97—21no—
80C2×C4×C8D412yes—
81C4×C4⋊C4—21no—
82C4×C4⋊C4—21no—
83C4×C22⋊C4—21no—
84C4×C22⋊C4—21no—
85#376—21no—
86C43—21no—
87#341—24no—
88#335—22no—
89#335—22no—
90#335—24no—
91#334—22no—
92#334—22no—
93#334—24no—
94C23×C4C2×D411yescharacteristic
95C23×C4C2×Q811yescharacteristic
96C23×C4#4111yescharacteristic
97C2×M16—21no—
98C2×M16—21no—
99C2×M16—22no—
100C2×M16—22no—
101C2×M16—22no—
102C2×M16—21no—
103C2×M16—21no—
104C2×M16—44no—
105C2×M16—41no—
106C2×M16—82no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—21no—
110C22×C8—21no—
111C22×C8—41no—
112#117—44no—
113C2×C4⋊C4—22no—
114C2×C22⋊C4—22no—
115C2×C42—22no—
116C2×C42—41no—
117C2×C42—41no—
118C2×C42C22×C411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×Q811yescharacteristic
125C2×C42C2×Q811yescharacteristic
126C2×C42C2×Q811yescharacteristic
127C2×C42#4111yescharacteristic
128C2×C42#4111yescharacteristic
129C2×C42#4111yescharacteristic
130#108—84no—
131C4⋊C8—22no—
132C4⋊C8—21no—
133C4⋊C8—22no—
134C4⋊C8—21no—
135C4⋊C8—21no—
136C4⋊C8—21no—
137C4⋊C8—21no—
138C4⋊C8—21no—
139C4⋊C8—22no—
140C4⋊C8—21no—
141C4⋊C8—21no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C4⋊C8C4⋊C414yes—
147C22⋊C8—22no—
148C22⋊C8—22no—
149C22⋊C8—22no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C22⋊C8C4⋊C414yes—
155#97—21no—
156#97—21no—
157#97—22no—
158#97—22no—
159#97—22no—
160#97—22no—
161#97—41no—
162#97—41no—
163#97—41no—
164C4×C8—22no—
165C4×C8—22no—
166C4×C8—41no—
167C4×C8C4⋊C412yes—
168C4×C8C4⋊C412yes—
169#95—41no—
170#95—41no—
171C24C22⋊Q811yescharacteristic
172C22×C4—42no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4C2×C4⋊C411yescharacteristic
178C22×C4C4×D411yescharacteristic
179C22×C4C4×Q811yescharacteristic
180C22×C4#12011yescharacteristic
181C22×C4#12111yescharacteristic
182C22×C4C22⋊Q811yescharacteristic
183C22×C4C22⋊Q811yescharacteristic
184C22×C4C22⋊Q811yescharacteristic
185C22×C4C22⋊Q811yescharacteristic
186C22×C4#12311yescharacteristic
187C22×C4#12311yescharacteristic
188C22×C4#12311yescharacteristic
189C22×C4#12511yescharacteristic
190C22×C4#12711yescharacteristic
191C22×C4C4⋊Q811yescharacteristic
192C22×C4C4⋊Q811yescharacteristic
193C22×C4C4⋊Q811yescharacteristic
194C22×C4C4⋊Q811yescharacteristic
195M16—24no—
196M16—44no—
197M16—42no—
198M16—42no—
199M16—44no—
200M16—42no—
201M16—82no—
202M16—82no—
203C2×C8—22no—
204C2×C8—22no—
205C2×C8—24no—
206C2×C8—24no—
207C2×C8—44no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—42no—
215C2×C8—82no—
216C2×C8—81no—
217C2×C8—81no—
218C4⋊C4—24no—
219C4⋊C4—42no—
220C22⋊C4—24no—
221C22⋊C4—42no—
222C42—24no—
223C42—42no—
224C42—82no—
225C42—81no—
226C42—81no—
227C42C2×C4⋊C411yescharacteristic
228C42C2×C4⋊C411yescharacteristic
229C42C4×D411yescharacteristic
230C42C4×D411yescharacteristic
231C42#12011yescharacteristic
232C42#12011yescharacteristic
233C42#12111yescharacteristic
234C42#12111yescharacteristic
235C42C22⋊Q811yescharacteristic
236C42C22⋊Q811yescharacteristic
237C42C22⋊Q811yescharacteristic
238C42C22⋊Q811yescharacteristic
239C42#12511yescharacteristic
240C42#12511yescharacteristic
241C42C4⋊Q811yescharacteristic
242C42C4⋊Q811yescharacteristic
243C23—22no—
244C23—41no—
245C23—41no—
246C23#38911yescharacteristic
247C23#39511yescharacteristic
248C23#39911yescharacteristic
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—44no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4#38411yescharacteristic
274C2×C4#38511yescharacteristic
275C2×C4#38511yescharacteristic
276C2×C4#38511yescharacteristic
277C2×C4#38911yescharacteristic
278C2×C4#38911yescharacteristic
279C2×C4#39211yescharacteristic
280C2×C4#39511yescharacteristic
281C2×C4#39511yescharacteristic
282C2×C4#39811yescharacteristic
283C2×C4#39811yescharacteristic
284C2×C4#39811yescharacteristic
285C8—24no—
286C8—44no—
287C8—42no—
288C8—44no—
289C8—81no—
290C8—82no—
291C8—81no—
292C8—81no—
293C8—81no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—82no—
303C22#144411yescharacteristic
304C22#209112yes—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—84no—
316C4#186112yes—
317C4#200811yescharacteristic
318C4#200911yescharacteristic
319C2—22no—
320C2—41no—
321C2—41no—
322C2#1133311yescharacteristic
323C2#1133811yescharacteristic
324C2#1134111yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1444
prime radicalC24C22⋊Q8
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
28. #1291C4semidirect
29. #1291C4semidirect

Maximal subgroups

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

subgroupindex
#219942
#178222
#177972
#79942
#79302
#79032
#78682