Finite Group Databasebeta

← #2430×C163 #35211188

Subgroups — #2430×C163 #35211188

Order 20864.

914 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×C163C211yesmaximal, characteristic, complemented
2C2×#123×C163C211yesmaximal, characteristic, complemented
3C2×#121×C163C212yesmaximal, complemented
4#395×C163C211yesmaximal, characteristic, complemented
5#394×C163C211yesmaximal, characteristic, complemented
6#393×C163C211yesmaximal, characteristic, complemented
7#392×C163C211yesmaximal, characteristic, complemented
8#386×C163C212yesmaximal, complemented
9#386×C163C212yesmaximal, complemented
10#385×C163C212yesmaximal, complemented
11C2×#95×C163C211yesmaximal, characteristic, complemented
12C2×#41×C163—28no—
13C2×#41×C163—24no—
14C22×Q8×C163C2211yescharacteristic
15C22×D4×C163C2211yescharacteristic
16C22×D4×C163C2211yescharacteristic
17C22×D4×C163C2212yes—
18C22×D4×C163C2212yes—
19C23×C4×C163C2212yes—
20C23×C4×C163C2212yes—
21C23×C4×C163C2211yescharacteristic
22#123×C163—24no—
23#121×C163—28no—
24C2×C4⋊C4×C163C2211yescharacteristic
25C2×C4⋊C4×C163C2212yes—
26C2×C4⋊C4×C163C2211yescharacteristic
27C2×C22⋊C4×C163C2212yes—
28C2×C22⋊C4×C163C2212yes—
29C2×C22⋊C4×C163C2211yescharacteristic
30C2×C22⋊C4×C163C2211yescharacteristic
31C2×C22⋊C4×C163C2212yes—
32C2×C22⋊C4×C163C2211yescharacteristic
33C2×C22⋊C4×C163C2212yes—
34#95×C163C2212yes—
35#95×C163C2211yescharacteristic
36#95×C163C2211yescharacteristic
37#95×C163C2212yes—
38#95×C163C2212yes—
39C24×C163C2311yescharacteristic
40C24×C163C2312yes—
41C24×C163C2311yescharacteristic
42#41×C163—232no—
43C2×Q8×C163—24no—
44C2×Q8×C163—22no—
45C2×D4×C163—24no—
46C2×D4×C163—24no—
47C2×D4×C163—24no—
48C2×D4×C163—24no—
49C2×D4×C163—24no—
50C2×D4×C163—22no—
51C2×D4×C163—22no—
52C2×D4×C163—24no—
53C2×D4×C163—42no—
54C2×D4×C163D418yescomplemented
55C22×C4×C163—24no—
56C22×C4×C163—24no—
57C22×C4×C163—24no—
58C22×C4×C163—24no—
59C22×C4×C163—24no—
60C22×C4×C163—24no—
61C22×C4×C163—42no—
62C22×C4×C163D414yescomplemented
63C22×C4×C163C2312yes—
64C22×C4×C163C2311yescharacteristic
65C22×C4×C163C2311yescharacteristic
66C22×C4×C163C2311yescharacteristic
67C22×C4×C163C2311yescharacteristic
68C22×C4×C163C2312yes—
69C22×C4×C163C2311yescharacteristic
70C22×C4×C163C2312yes—
71C4⋊C4×C163—24no—
72C4⋊C4×C163—22no—
73C4⋊C4×C163—22no—
74C22⋊C4×C163—24no—
75C22⋊C4×C163—22no—
76C22⋊C4×C163—24no—
77C22⋊C4×C163—22no—
78C22⋊C4×C163—22no—
79C22⋊C4×C163—24no—
80C22⋊C4×C163—42no—
81C23×C163—22no—
82C23×C163—21no—
83C23×C163—21no—
84C23×C163—22no—
85C23×C163—22no—
86C23×C163—22no—
87C23×C163—22no—
88C23×C163—22no—
89C23×C163—22no—
90C23×C163—21no—
91C23×C163—22no—
92C23×C163—22no—
93C23×C163—21no—
94C23×C163—21no—
95C23×C163C2×D414yes—
96C23×C163C2×D412yes—
97C23×C163C2×D414yes—
98C23×C163C2411yescharacteristic
99Q8×C163—28no—
100D4×C163—28no—
101D4×C163—216no—
102D4×C163—48no—
103D4×C163—44no—
104C2×C4×C163—216no—
105C2×C4×C163—28no—
106C2×C4×C163—22no—
107C2×C4×C163—22no—
108C2×C4×C163—22no—
109C2×C4×C163—22no—
110C2×C4×C163—22no—
111C2×C4×C163—22no—
112C2×C4×C163—21no—
113C2×C4×C163—21no—
114C2×C4×C163—22no—
115C2×C4×C163—22no—
116C2×C4×C163—21no—
117C2×C4×C163—22no—
118C2×C4×C163—22no—
119C2×C4×C163—21no—
120C2×C4×C163—22no—
121C2×C4×C163—21no—
122C2×C4×C163—48no—
123C2×C4×C163C2×D412yes—
124C2×C4×C163C2×D414yes—
125C2×C4×C163C2×D412yes—
126C2×C4×C163#4114yescomplemented
127C22×C163—22no—
128C22×C163—22no—
129C22×C163—24no—
130C22×C163—24no—
131C22×C163—24no—
132C22×C163—24no—
133C22×C163—24no—
134C22×C163—42no—
135C22×C163—42no—
136C22×C163—42no—
137C22×C163—42no—
138C22×C163—41no—
139C22×C163—41no—
140C22×C163—41no—
141C22×C163—42no—
142C22×C163—42no—
143C22×C163#12014yes—
144C22×C163C22×D411yescharacteristic
145C22×C163C22×D412yes—
146C22×C163C2×#4112yes—
147C22×C163H(5,𝔽2)11yescharacteristic
148C22×C1632−1+411yescharacteristic
149C4×C163—22no—
150C4×C163—24no—
151C4×C163—22no—
152C4×C163—24no—
153C4×C163—41no—
154C4×C163—41no—
155C4×C163—41no—
156C4×C163—42no—
157C2×C163—24no—
158C2×C163—44no—
159C2×C163—81no—
160C2×C163C2×#12011yescharacteristic
161C2×C163#53211yescharacteristic
162C2×C163#53711yescharacteristic
163C2×C163#54612yes—
164C2×C163#54712yes—
165C163#243011yescharacteristic, direct product factor, Sylow
166#2430C16311yesmaximal, characteristic, direct product factor, Sylow
167C22×#41C2×C16311yescharacteristic, complemented
168C2×#123C2×C16311yescharacteristic, complemented
169C2×#121C2×C16312yescomplemented
170#395C2×C16311yescharacteristic, complemented
171#394C2×C16311yescharacteristic, complemented
172#393C2×C16311yescharacteristic, complemented
173#392C2×C16311yescharacteristic, complemented
174#386C2×C16312yescomplemented
175#386C2×C16312yescomplemented
176#385C2×C16312yescomplemented
177C2×#95C2×C16311yescharacteristic, complemented
178C2×#41—28no—
179C2×#41—24no—
180C22×Q8C22×C16311yescharacteristic
181C22×D4C22×C16311yescharacteristic
182C22×D4C22×C16311yescharacteristic
183C22×D4C22×C16312yes—
184C22×D4C22×C16312yes—
185C23×C4C22×C16312yes—
186C23×C4C22×C16312yes—
187C23×C4C22×C16311yescharacteristic
188#123—24no—
189#121—28no—
190C2×C4⋊C4C22×C16312yes—
191C2×C4⋊C4C22×C16311yescharacteristic
192C2×C4⋊C4C22×C16311yescharacteristic
193C2×C22⋊C4C22×C16312yes—
194C2×C22⋊C4C22×C16312yes—
195C2×C22⋊C4C22×C16311yescharacteristic
196C2×C22⋊C4C22×C16311yescharacteristic
197C2×C22⋊C4C22×C16311yescharacteristic
198C2×C22⋊C4C22×C16312yes—
199C2×C22⋊C4C22×C16312yes—
200#95C22×C16312yes—
201#95C22×C16311yescharacteristic
202#95C22×C16311yescharacteristic
203#95C22×C16312yes—
204#95C22×C16312yes—
205C24C23×C16311yescharacteristic
206C24C23×C16312yes—
207C24C23×C16311yescharacteristic
208#41—232no—
209C2×Q8—24no—
210C2×Q8—22no—
211C2×D4—24no—
212C2×D4—24no—
213C2×D4—24no—
214C2×D4—24no—
215C2×D4—24no—
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—24no—
219C2×D4—42no—
220C2×D4D4×C16318yescomplemented
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—42no—
228C22×C4D4×C16314yescomplemented
229C22×C4C23×C16312yes—
230C22×C4C23×C16311yescharacteristic
231C22×C4C23×C16311yescharacteristic
232C22×C4C23×C16311yescharacteristic
233C22×C4C23×C16311yescharacteristic
234C22×C4C23×C16312yes—
235C22×C4C23×C16311yescharacteristic
236C22×C4C23×C16312yes—
237C4⋊C4—24no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C22⋊C4—24no—
241C22⋊C4—22no—
242C22⋊C4—24no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—24no—
246C22⋊C4—42no—
247C23—22no—
248C23—21no—
249C23—21no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—21no—
257C23—22no—
258C23—22no—
259C23—21no—
260C23—21no—
261C23C2×D4×C16314yes—
262C23C2×D4×C16312yes—
263C23C2×D4×C16314yes—
264C23C24×C16311yescharacteristic
265Q8—28no—
266D4—28no—
267D4—216no—
268D4—48no—
269D4—44no—
270C2×C4—216no—
271C2×C4—28no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—48no—
289C2×C4C2×D4×C16312yes—
290C2×C4C2×D4×C16314yes—
291C2×C4C2×D4×C16312yes—
292C2×C4#41×C16314yescomplemented
293C22—22no—
294C22—22no—
295C22—24no—
296C22—24no—
297C22—24no—
298C22—24no—
299C22—24no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—42no—
308C22—42no—
309C22#120×C16314yes—
310C22C22×D4×C16311yescharacteristic
311C22C22×D4×C16312yes—
312C22C2×#41×C16312yes—
313C22H(5,𝔽2)×C16311yescharacteristic
314C222−1+4×C16311yescharacteristic
315C4—22no—
316C4—24no—
317C4—22no—
318C4—24no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—42no—
323C2—24no—
324C2—44no—
325C2—81no—
326C2C2×#120×C16311yescharacteristic
327C2#532×C16311yescharacteristic
328C2#537×C16311yescharacteristic
329C2#546×C16312yes—
330C2#547×C16312yes—
subgroupG/H
center, socleC23×C163C24
commutator, Frattini, cosocleC23C24×C163
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C163 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#41×C163C2semidirect
2. C2×#123×C163C2semidirect
3. C2×#121×C163C2semidirect
4. #395×C163C2semidirect
5. #394×C163C2semidirect
6. #393×C163C2semidirect
7. #392×C163C2semidirect
8. #386×C163C2semidirect
9. #386×C163C2semidirect
10. #385×C163C2semidirect
11. C2×#95×C163C2semidirect
54. C2×D4×C163D4semidirect
62. C22×C4×C163D4semidirect
126. C2×C4×C163#41semidirect
165. C163#2430direct (N × H)
166. #2430C163direct (N × H)
167. C22×#41C2×C163semidirect
168. C2×#123C2×C163semidirect
169. C2×#121C2×C163semidirect
170. #395C2×C163semidirect
171. #394C2×C163semidirect
172. #393C2×C163semidirect
173. #392C2×C163semidirect
174. #386C2×C163semidirect
175. #386C2×C163semidirect
176. #385C2×C163semidirect
177. C2×#95C2×C163semidirect
220. C2×D4D4×C163semidirect
228. C22×C4D4×C163semidirect
292. C2×C4#41×C163semidirect

Maximal subgroups

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

subgroupindex
C22×#41×C1632
C2×#123×C1632
C2×#121×C1632
#395×C1632
#394×C1632
#393×C1632
#392×C1632
#386×C1632
#385×C1632
C2×#95×C1632
#2430163