Finite Group Databasebeta

← C139×#20524 #48015120

Subgroups — C139×#20524 #48015120

Order 35584.

1314 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#407×C139C212yesmaximal
2C2×C4×C22⋊C4×C139C211yesmaximal, characteristic
3#1753×C139C218yesmaximal, complemented
4#1749×C139C212yesmaximal, complemented
5C4×C22⋊C8×C139C212yesmaximal, complemented
6C24×C4×C139C2211yescharacteristic
7C22×M16×C139C2214yes—
8C22×C22⋊C4×C139C412yes—
9C22×C42×C139C2211yescharacteristic
10C22×C42×C139C2211yescharacteristic
11#407×C139C4116yescomplemented
12C2×C22⋊C8×C139C2214yes—
13C2×C22⋊C8×C139C2214yes—
14C2×#97×C139C2214yescomplemented
15C2×C4×C8×C139C2214yescomplemented
16C4×C22⋊C4×C139C414yes—
17C4×C22⋊C4×C139C2214yes—
18C2×#95×C139C412yes—
19#336×C139C2214yescomplemented
20#336×C139C2214yescomplemented
21C25×C139C2×C411yescharacteristic
22C23×C4×C139—42no—
23C23×C4×C139—42no—
24C23×C4×C139C2×C412yes—
25C23×C4×C139C2×C411yescharacteristic
26C23×C4×C139C2×C412yes—
27C23×C4×C139C2×C418yes—
28C23×C4×C139C2×C412yes—
29C23×C4×C139C2311yescharacteristic
30C23×C4×C139C2312yes—
31C2×M16×C139—44no—
32C2×M16×C139—44no—
33C2×M16×C139C2×C4116yescomplemented
34C22×C8×C139C2318yes—
35C2×C22⋊C4×C139—28no—
36C2×C22⋊C4×C139C2×C418yes—
37C2×C42×C139—42no—
38C2×C42×C139—42no—
39C2×C42×C139C2×C412yes—
40C2×C42×C139C2×C412yes—
41C2×C42×C139C2312yes—
42C2×C42×C139C2312yes—
43C22⋊C8×C139C2×C4116yes—
44C22⋊C8×C139C2×C4116yescomplemented
45#97×C139—44no—
46C4×C8×C139—44no—
47#95×C139C2×C418yes—
48C24×C139—24no—
49C24×C139—41no—
50C24×C139—41no—
51C24×C139—42no—
52C24×C139C4214yes—
53C24×C139C22×C412yes—
54C24×C139C22×C411yescharacteristic
55C22×C4×C139—22no—
56C22×C4×C139—22no—
57C22×C4×C139—24no—
58C22×C4×C139—24no—
59C22×C4×C139—24no—
60C22×C4×C139—416no—
61C22×C4×C139—42no—
62C22×C4×C139—42no—
63C22×C4×C139—42no—
64C22×C4×C139—42no—
65C22×C4×C139—41no—
66C22×C4×C139—41no—
67C22×C4×C139—42no—
68C22×C4×C139—42no—
69C22×C4×C139C4218yes—
70C22×C4×C139C4214yes—
71C22×C4×C139M1618yescomplemented
72C22×C4×C139C22×C414yes—
73C22×C4×C139C22×C412yes—
74C22×C4×C139C22×C411yescharacteristic
75C22×C4×C139C22×C414yes—
76C22×C4×C139C22×C414yes—
77C22×C4×C139C22×C414yes—
78C22×C4×C139C22×C414yes—
79C22×C4×C139C2411yescharacteristic
80M16×C139—416no—
81C2×C8×C139—28no—
82C2×C8×C139—28no—
83C2×C8×C139C22×C4116yes—
84C22⋊C4×C139—216no—
85C42×C139—24no—
86C42×C139—24no—
87C42×C139—42no—
88C42×C139—42no—
89C23×C139—21no—
90C23×C139—21no—
91C23×C139—22no—
92C23×C139—22no—
93C23×C139—22no—
94C23×C139—24no—
95C23×C139—24no—
96C23×C139—28no—
97C23×C139—44no—
98C23×C139—44no—
99C23×C139—48no—
100C23×C139—48no—
101C23×C139C2×C4214yes—
102C23×C139C2×C4212yes—
103C23×C139C2×M1614yes—
104C23×C139C23×C411yescharacteristic
105C2×C4×C139—24no—
106C2×C4×C139—21no—
107C2×C4×C139—21no—
108C2×C4×C139—22no—
109C2×C4×C139—22no—
110C2×C4×C139—24no—
111C2×C4×C139—28no—
112C2×C4×C139—28no—
113C2×C4×C139—28no—
114C2×C4×C139—24no—
115C2×C4×C139—24no—
116C2×C4×C139—24no—
117C2×C4×C139—44no—
118C2×C4×C139—48no—
119C2×C4×C139—48no—
120C2×C4×C139—48no—
121C2×C4×C139C2×C4214yes—
122C2×C4×C139C2×C4212yes—
123C2×C4×C139C2×M1618yes—
124C2×C4×C139C23×C412yes—
125C2×C4×C139H(5,𝔽2)12yes—
126C2×C4×C139H(5,𝔽2)12yes—
127C8×C139—216no—
128C22×C139—22no—
129C22×C139—24no—
130C22×C139—24no—
131C22×C139—22no—
132C22×C139—24no—
133C22×C139—24no—
134C22×C139—24no—
135C22×C139—416no—
136C22×C139—44no—
137C22×C139—44no—
138C22×C139C4×M1614yes—
139C22×C139C22×C4211yescharacteristic
140C22×C139#51811yescharacteristic
141C22×C139#51811yescharacteristic
142C22×C139C22×M1612yes—
143C22×C139#56812yes—
144C4×C139—28no—
145C4×C139—22no—
146C4×C139—24no—
147C4×C139—44no—
148C4×C139#51814yes—
149C2×C139—24no—
150C2×C139—44no—
151C2×C139#227311yescharacteristic
152C2×C139C2×C4×M1611yescharacteristic
153C2×C139#287311yescharacteristic
154C2×C139#297312yes—
155C2×C139#297512yes—
156#20524C13911yesmaximal, characteristic, direct product factor, Sylow
157C139#2052411yescharacteristic, direct product factor, Sylow
158C2×#407C2×C13912yes—
159C2×C4×C22⋊C4C2×C13911yescharacteristic
160#1753C2×C13918yescomplemented
161#1749C2×C13912yescomplemented
162C4×C22⋊C8C2×C13912yescomplemented
163C24×C4C22×C13911yescharacteristic
164C22×M16C22×C13914yes—
165C22×C22⋊C4C4×C13912yes—
166C22×C42C22×C13911yescharacteristic
167C22×C42C22×C13911yescharacteristic
168#407C4×C139116yescomplemented
169C2×C22⋊C8C22×C13914yes—
170C2×C22⋊C8C22×C13914yes—
171C2×#97C22×C13914yescomplemented
172C2×C4×C8C22×C13914yescomplemented
173C4×C22⋊C4C4×C13914yes—
174C4×C22⋊C4C22×C13914yes—
175C2×#95C4×C13912yes—
176#336C22×C13914yescomplemented
177#336C22×C13914yescomplemented
178C25C2×C4×C13911yescharacteristic
179C23×C4—42no—
180C23×C4—42no—
181C23×C4C2×C4×C13912yes—
182C23×C4C2×C4×C13911yescharacteristic
183C23×C4C2×C4×C13912yes—
184C23×C4C2×C4×C13918yes—
185C23×C4C2×C4×C13912yes—
186C23×C4C23×C13912yes—
187C23×C4C23×C13911yescharacteristic
188C2×M16—44no—
189C2×M16—44no—
190C2×M16C2×C4×C139116yescomplemented
191C22×C8C23×C13918yes—
192C2×C22⋊C4—28no—
193C2×C22⋊C4C2×C4×C13918yes—
194C2×C42—42no—
195C2×C42—42no—
196C2×C42C2×C4×C13912yes—
197C2×C42C2×C4×C13912yes—
198C2×C42C23×C13912yes—
199C2×C42C23×C13912yes—
200C22⋊C8C2×C4×C139116yes—
201C22⋊C8C2×C4×C139116yescomplemented
202#97—44no—
203C4×C8—44no—
204#95C2×C4×C13918yes—
205C24—24no—
206C24—41no—
207C24—41no—
208C24—42no—
209C24C42×C13914yes—
210C24C22×C4×C13912yes—
211C24C22×C4×C13911yescharacteristic
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—416no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4C42×C13918yes—
227C22×C4C42×C13914yes—
228C22×C4M16×C13918yescomplemented
229C22×C4C22×C4×C13914yes—
230C22×C4C22×C4×C13912yes—
231C22×C4C22×C4×C13911yescharacteristic
232C22×C4C22×C4×C13914yes—
233C22×C4C22×C4×C13914yes—
234C22×C4C22×C4×C13914yes—
235C22×C4C22×C4×C13914yes—
236C22×C4C24×C13911yescharacteristic
237M16—416no—
238C2×C8—28no—
239C2×C8—28no—
240C2×C8C22×C4×C139116yes—
241C22⋊C4—216no—
242C42—24no—
243C42—24no—
244C42—42no—
245C42—42no—
246C23—21no—
247C23—21no—
248C23—22no—
249C23—28no—
250C23—22no—
251C23—22no—
252C23—24no—
253C23—24no—
254C23—44no—
255C23—44no—
256C23—48no—
257C23—48no—
258C23C2×C42×C13914yes—
259C23C2×C42×C13912yes—
260C23C2×M16×C13914yes—
261C23C23×C4×C13911yescharacteristic
262C2×C4—24no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—28no—
269C2×C4—28no—
270C2×C4—28no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—44no—
275C2×C4—48no—
276C2×C4—48no—
277C2×C4—48no—
278C2×C4C2×C42×C13914yes—
279C2×C4C2×C42×C13912yes—
280C2×C4C2×M16×C13918yes—
281C2×C4C23×C4×C13912yes—
282C2×C4H(5,𝔽2)×C13912yes—
283C2×C4H(5,𝔽2)×C13912yes—
284C8—216no—
285C22—22no—
286C22—22no—
287C22—24no—
288C22—24no—
289C22—24no—
290C22—24no—
291C22—24no—
292C22—416no—
293C22—44no—
294C22—44no—
295C22C4×M16×C13914yes—
296C22C22×C42×C13911yescharacteristic
297C22#518×C13911yescharacteristic
298C22#518×C13911yescharacteristic
299C22C22×M16×C13912yes—
300C22#568×C13912yes—
301C4—22no—
302C4—24no—
303C4—28no—
304C4—44no—
305C4#518×C13914yes—
306C2—24no—
307C2—44no—
308C2#2273×C13911yescharacteristic
309C2C2×C4×M16×C13911yescharacteristic
310C2#2873×C13911yescharacteristic
311C2#2973×C13912yes—
312C2#2975×C13912yes—
subgroupG/H
centerC22×C4×C139C24
commutatorC22C22×C42×C139
Frattini, cosocleC22×C4C24×C139
socleC23×C139C23×C4
prime radicalC25×C139C2×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1753×C139C2semidirect
4. #1749×C139C2semidirect
5. C4×C22⋊C8×C139C2semidirect
11. #407×C139C4semidirect
14. C2×#97×C139C22semidirect
15. C2×C4×C8×C139C22semidirect
19. #336×C139C22semidirect
20. #336×C139C22semidirect
33. C2×M16×C139C2×C4semidirect
44. C22⋊C8×C139C2×C4semidirect
71. C22×C4×C139M16semidirect
156. #20524C139direct (N × H)
157. C139#20524direct (N × H)
160. #1753C2×C139semidirect
161. #1749C2×C139semidirect
162. C4×C22⋊C8C2×C139semidirect
168. #407C4×C139semidirect
171. C2×#97C22×C139semidirect
172. C2×C4×C8C22×C139semidirect
176. #336C22×C139semidirect
177. #336C22×C139semidirect
190. C2×M16C2×C4×C139semidirect
201. C22⋊C8C2×C4×C139semidirect
228. C22×C4M16×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#407×C1392
C2×C4×C22⋊C4×C1392
#1753×C1392
#1749×C1392
C4×C22⋊C8×C1392
#20524139