Finite Group Databasebeta

← C139×#11648 #48006244

Subgroups — C139×#11648 #48006244

Order 35584.

320 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3168×C139C211yesmaximal, characteristic
2#2162×C139C211yesmaximal, characteristic, complemented
3C2×#335×C139C211yesmaximal, characteristic, complemented
4#1332×C139C212yesmaximal, complemented
5#1331×C139C212yesmaximal, complemented
6#529×C139—21no—
7#499×C139C411yescharacteristic
8#495×C139C411yescharacteristic
9#488×C139—21no—
10#467×C139C411yescharacteristic
11#466×C139C411yescharacteristic
12#465×C139—21no—
13C4×Q16×C139C2211yescharacteristic
14C4×SD16×C139—21no—
15C4×D8×C139C2211yescharacteristic
16C2×C4⋊C8×C139—21no—
17C2×C4×C8×C139C2211yescharacteristic
18C4⋊C16×C139—21no—
19C22⋊C16×C139—21no—
20C4×C16×C139C2212yes—
21#335×C139—21no—
22#335×C139C2212yes—
23C2×Q16×C139C2×C411yescharacteristic
24C2×SD16×C139—21no—
25C2×D8×C139C2×C411yescharacteristic
26C22×C8×C139—41no—
27C22×C8×C139C2×C411yescharacteristic
28C22×C8×C139D411yescharacteristic
29#126×C139—41no—
30#125×C139—21no—
31#124×C139—21no—
32#123×C139—41no—
33C22⋊Q8×C139—21no—
34#121×C139—21no—
35C4×Q8×C139—21no—
36C4×D4×C139—21no—
37C4×D4×C139—41no—
38#117×C139—41no—
39C2×C42×C139D411yescharacteristic
40C2×C16×C139—22no—
41#107×C139C2×C411yescharacteristic
42#107×C139C2×C411yescharacteristic
43#106×C139—21no—
44C4⋊C8×C139—22no—
45C4⋊C8×C139—41no—
46#103×C139—21no—
47#103×C139—21no—
48#102×C139—21no—
49#102×C139—21no—
50C4×C8×C139C2×C411yescharacteristic
51C4×C8×C139D411yescharacteristic
52C4×C8×C139D411yescharacteristic
53C4×C8×C139C2311yescharacteristic
54C2×Q8×C139—21no—
55C2×D4×C139—21no—
56C2×D4×C139—41no—
57C22×C4×C139—41no—
58C22×C4×C139C22⋊C411yescharacteristic
59C22×C4×C139D811yescharacteristic
60C22×C4×C139SD1611yescharacteristic
61Q16×C139—22no—
62SD16×C139—42no—
63D8×C139—22no—
64C2×C8×C139—22no—
65C2×C8×C139—41no—
66C2×C8×C139—42no—
67C2×C8×C139—82no—
68C2×C8×C139C22⋊C411yescharacteristic
69C2×C8×C139C22⋊C411yescharacteristic
70C2×C8×C139C22×C411yescharacteristic
71C2×C8×C139C2×D411yescharacteristic
72C4⋊C4×C139—21no—
73C4⋊C4×C139—21no—
74C4⋊C4×C139—41no—
75C4⋊C4×C139—41no—
76C4⋊C4×C139—41no—
77C4⋊C4×C139—41no—
78C22⋊C4×C139—41no—
79C22⋊C4×C139—41no—
80C22⋊C4×C139—41no—
81C22⋊C4×C139—41no—
82C22⋊C4×C139—41no—
83C42×C139—41no—
84C42×C139C22⋊C411yescharacteristic
85C42×C139D811yescharacteristic
86C42×C139SD1611yescharacteristic
87C42×C139C2×D411yescharacteristic
88C16×C139—42no—
89C23×C139—41no—
90C23×C139#10211yescharacteristic
91Q8×C139—41no—
92Q8×C139—41no—
93D4×C139—41no—
94D4×C139—41no—
95D4×C139—82no—
96C2×C4×C139—22no—
97C2×C4×C139—21no—
98C2×C4×C139—21no—
99C2×C4×C139—21no—
100C2×C4×C139—21no—
101C2×C4×C139—41no—
102C2×C4×C139—41no—
103C2×C4×C139—41no—
104C2×C4×C139—81no—
105C2×C4×C139—81no—
106C2×C4×C139#10211yescharacteristic
107C2×C4×C139#10211yescharacteristic
108C2×C4×C139#10211yescharacteristic
109C2×C4×C139C2×C22⋊C411yescharacteristic
110C2×C4×C139C2×D811yescharacteristic
111C2×C4×C139C2×SD1611yescharacteristic
112C8×C139—21no—
113C8×C139—21no—
114C8×C139—21no—
115C8×C139—82no—
116C8×C139#13112yes—
117C22×C139—21no—
118C22×C139—21no—
119C22×C139—81no—
120C22×C139—81no—
121C22×C139—81no—
122C22×C139#35912yes—
123C22×C139C2×#10211yescharacteristic
124C4×C139—21no—
125C4×C139—21no—
126C4×C139—21no—
127C4×C139—21no—
128C4×C139—81no—
129C4×C139—81no—
130C4×C139—81no—
131C4×C139#40811yescharacteristic
132C4×C139#42111yescharacteristic
133C4×C139#50911yescharacteristic
134C4×C139#51011yescharacteristic
135C2×C139—22no—
136C2×C139—161no—
137C2×C139#148011yescharacteristic
138C2×C139#213911yescharacteristic
139C2×C139C2×#35911yescharacteristic
140#11648C13911yesmaximal, characteristic, direct product factor, Sylow
141C139#1164811yescharacteristic, direct product factor, Sylow
142#3168C2×C13911yescharacteristic
143#2162C2×C13911yescharacteristic, complemented
144C2×#335C2×C13911yescharacteristic, complemented
145#1332C2×C13912yescomplemented
146#1331C2×C13912yescomplemented
147#529—21no—
148#499C4×C13911yescharacteristic
149#495C4×C13911yescharacteristic
150#488—21no—
151#467C4×C13911yescharacteristic
152#466C4×C13911yescharacteristic
153#465—21no—
154C4×Q16C22×C13911yescharacteristic
155C4×SD16—21no—
156C4×D8C22×C13911yescharacteristic
157C2×C4⋊C8—21no—
158C2×C4×C8C22×C13911yescharacteristic
159C4⋊C16—21no—
160C22⋊C16—21no—
161C4×C16C22×C13912yes—
162#335—21no—
163#335C22×C13912yes—
164C2×Q16C2×C4×C13911yescharacteristic
165C2×SD16—21no—
166C2×D8C2×C4×C13911yescharacteristic
167C22×C8—41no—
168C22×C8C2×C4×C13911yescharacteristic
169C22×C8D4×C13911yescharacteristic
170#126—41no—
171#125—21no—
172#124—21no—
173#123—41no—
174C22⋊Q8—21no—
175#121—21no—
176C4×Q8—21no—
177C4×D4—21no—
178C4×D4—41no—
179#117—41no—
180C2×C42D4×C13911yescharacteristic
181C2×C16—22no—
182#107C2×C4×C13911yescharacteristic
183#107C2×C4×C13911yescharacteristic
184#106—21no—
185C4⋊C8—22no—
186C4⋊C8—41no—
187#103—21no—
188#103—21no—
189#102—21no—
190#102—21no—
191C4×C8C2×C4×C13911yescharacteristic
192C4×C8D4×C13911yescharacteristic
193C4×C8D4×C13911yescharacteristic
194C4×C8C23×C13911yescharacteristic
195C2×Q8—21no—
196C2×D4—21no—
197C2×D4—41no—
198C22×C4—41no—
199C22×C4C22⋊C4×C13911yescharacteristic
200C22×C4D8×C13911yescharacteristic
201C22×C4SD16×C13911yescharacteristic
202Q16—22no—
203SD16—42no—
204D8—22no—
205C2×C8—22no—
206C2×C8—41no—
207C2×C8—42no—
208C2×C8—82no—
209C2×C8C22⋊C4×C13911yescharacteristic
210C2×C8C22⋊C4×C13911yescharacteristic
211C2×C8C22×C4×C13911yescharacteristic
212C2×C8C2×D4×C13911yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C42—41no—
225C42C22⋊C4×C13911yescharacteristic
226C42D8×C13911yescharacteristic
227C42SD16×C13911yescharacteristic
228C42C2×D4×C13911yescharacteristic
229C16—42no—
230C23—41no—
231C23#102×C13911yescharacteristic
232Q8—41no—
233Q8—41no—
234D4—41no—
235D4—41no—
236D4—82no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4#102×C13911yescharacteristic
248C2×C4#102×C13911yescharacteristic
249C2×C4#102×C13911yescharacteristic
250C2×C4C2×C22⋊C4×C13911yescharacteristic
251C2×C4C2×D8×C13911yescharacteristic
252C2×C4C2×SD16×C13911yescharacteristic
253C8—21no—
254C8—21no—
255C8—21no—
256C8—82no—
257C8#131×C13912yes—
258C22—21no—
259C22—21no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22#359×C13912yes—
264C22C2×#102×C13911yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—81no—
270C4—81no—
271C4—81no—
272C4#408×C13911yescharacteristic
273C4#421×C13911yescharacteristic
274C4#509×C13911yescharacteristic
275C4#510×C13911yescharacteristic
276C2—22no—
277C2—161no—
278C2#1480×C13911yescharacteristic
279C2#2139×C13911yescharacteristic
280C2C2×#359×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139C2×D8
commutatorC2×C8C22×C4×C139
Frattini, cosocleC4×C8C23×C139
socleC22×C139C2×#102
prime radical#466×C139C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C2×C42×C139 ◁ C2×C4×C8×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2162×C139C2semidirect
3. C2×#335×C139C2semidirect
4. #1332×C139C2semidirect
5. #1331×C139C2semidirect
140. #11648C139direct (N × H)
141. C139#11648direct (N × H)
143. #2162C2×C139semidirect
144. C2×#335C2×C139semidirect
145. #1332C2×C139semidirect
146. #1331C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3168×C1392
#2162×C1392
C2×#335×C1392
#1332×C1392
#1331×C1392
#11648139