Finite Group Databasebeta

← C139×#9145 #48003741

Subgroups — C139×#9145 #48003741

Order 35584.

694 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2855×C139C211yesmaximal, characteristic
2C2×#376×C139C211yesmaximal, characteristic
3#1817×C139C211yesmaximal, characteristic
4C2×#328×C139C212yesmaximal
5#1294×C139C212yesmaximal
6C2×C22⋊Q8×C139C2211yescharacteristic
7C22×C42×C139—21no—
8C22×C42×C139C2211yescharacteristic
9C2×C22⋊C8×C139C2212yes—
10#391×C139C412yescomplemented
11#389×C139C412yescomplemented
12#387×C139—22no—
13#385×C139—21no—
14#381×C139—21no—
15#380×C139C2211yescharacteristic
16#376×C139—24no—
17C2×#95×C139—21no—
18C2×#95×C139C2212yes—
19#336×C139—22no—
20#328×C139—24no—
21C22×Q8×C139C2×C411yescharacteristic
22C23×C4×C139—22no—
23C23×C4×C139D411yescharacteristic
24C23×C4×C139D411yescharacteristic
25C23×C4×C139C2311yescharacteristic
26C22×C8×C139—22no—
27C22⋊Q8×C139—22no—
28C22⋊Q8×C139—22no—
29C2×C4⋊C4×C139—22no—
30C2×C4⋊C4×C139—21no—
31C2×C4⋊C4×C139C2×C411yescharacteristic
32C2×C4⋊C4×C139C2×C412yes—
33C2×C22⋊C4×C139—21no—
34C2×C22⋊C4×C139—21no—
35C2×C42×C139—28no—
36C2×C42×C139—24no—
37C2×C42×C139—22no—
38C2×C42×C139—22no—
39C2×C42×C139C2×C412yes—
40C2×C42×C139D412yes—
41C22⋊C8×C139—22no—
42C22⋊C8×C139—22no—
43#95×C139—24no—
44#95×C139—22no—
45#95×C139—22no—
46#95×C139—22no—
47#95×C139—22no—
48#95×C139—21no—
49#95×C139D414yes—
50C24×C139C2×D411yescharacteristic
51C2×Q8×C139—22no—
52C2×Q8×C139—42no—
53C22×C4×C139—21no—
54C22×C4×C139—21no—
55C22×C4×C139—24no—
56C22×C4×C139—28no—
57C22×C4×C139—21no—
58C22×C4×C139—24no—
59C22×C4×C139—21no—
60C22×C4×C139—22no—
61C22×C4×C139—22no—
62C22×C4×C139—22no—
63C22×C4×C139—21no—
64C22×C4×C139—21no—
65C22×C4×C139—42no—
66C22×C4×C139—44no—
67C22×C4×C139—42no—
68C22×C4×C139—42no—
69C22×C4×C139C22⋊C412yes—
70C22×C4×C139C22⋊C412yes—
71C22×C4×C139C22×C411yescharacteristic
72C22×C4×C139C2×D411yescharacteristic
73C22×C4×C139C2×D412yes—
74C22×C4×C139#4112yes—
75C2×C8×C139—44no—
76C2×C8×C139—42no—
77C4⋊C4×C139—22no—
78C4⋊C4×C139—42no—
79C4⋊C4×C139—44no—
80C4⋊C4×C139—42no—
81C22⋊C4×C139—41no—
82C22⋊C4×C139—41no—
83C22⋊C4×C139—42no—
84C42×C139—216no—
85C42×C139—24no—
86C42×C139—24no—
87C23×C139—22no—
88C23×C139—22no—
89C23×C139C2×C22⋊C411yescharacteristic
90C23×C139#12011yescharacteristic
91C23×C139#12311yescharacteristic
92C23×C139#13512yes—
93C23×C139#13712yes—
94Q8×C139—82no—
95C2×C4×C139—24no—
96C2×C4×C139—24no—
97C2×C4×C139—22no—
98C2×C4×C139—22no—
99C2×C4×C139—22no—
100C2×C4×C139—22no—
101C2×C4×C139—28no—
102C2×C4×C139—22no—
103C2×C4×C139—22no—
104C2×C4×C139—22no—
105C2×C4×C139—42no—
106C2×C4×C139—42no—
107C2×C4×C139—44no—
108C2×C4×C139—48no—
109C2×C4×C139—48no—
110C2×C4×C139—42no—
111C2×C4×C139—44no—
112C2×C4×C139—42no—
113C2×C4×C139—41no—
114C2×C4×C139—41no—
115C2×C4×C139—42no—
116C2×C4×C139—42no—
117C2×C4×C139—42no—
118C2×C4×C139—42no—
119C2×C4×C139—42no—
120C2×C4×C139#10414yes—
121C2×C4×C139C4×D412yes—
122C2×C4×C139#12112yes—
123C8×C139—82no—
124C22×C139—21no—
125C22×C139—21no—
126C22×C139—21no—
127C22×C139—21no—
128C22×C139—24no—
129C22×C139—24no—
130C22×C139#38611yescharacteristic
131C22×C139#41012yes—
132C22×C139#41611yescharacteristic
133C22×C139#41911yescharacteristic
134C22×C139C2×#10412yes—
135C22×C139#45212yes—
136C22×C139#48512yes—
137C4×C139—24no—
138C4×C139—22no—
139C4×C139—22no—
140C4×C139—48no—
141C4×C139—42no—
142C4×C139—81no—
143C4×C139—81no—
144C4×C139—82no—
145C2×C139—22no—
146C2×C139—22no—
147C2×C139#150012yes—
148C2×C139#150612yes—
149C2×C139#187311yescharacteristic
150C2×C139#189611yescharacteristic
151C2×C139#189911yescharacteristic
152#9145C13911yesmaximal, characteristic, direct product factor, Sylow
153C139#914511yescharacteristic, direct product factor, Sylow
154#2855C2×C13911yescharacteristic
155C2×#376C2×C13911yescharacteristic
156#1817C2×C13911yescharacteristic
157C2×#328C2×C13912yes—
158#1294C2×C13912yes—
159C2×C22⋊Q8C22×C13911yescharacteristic
160C22×C42—21no—
161C22×C42C22×C13911yescharacteristic
162C2×C22⋊C8C22×C13912yes—
163#391C4×C13912yescomplemented
164#389C4×C13912yescomplemented
165#387—22no—
166#385—21no—
167#381—21no—
168#380C22×C13911yescharacteristic
169#376—24no—
170C2×#95—21no—
171C2×#95C22×C13912yes—
172#336—22no—
173#328—24no—
174C22×Q8C2×C4×C13911yescharacteristic
175C23×C4—22no—
176C23×C4D4×C13911yescharacteristic
177C23×C4D4×C13911yescharacteristic
178C23×C4C23×C13911yescharacteristic
179C22×C8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4C2×C4×C13911yescharacteristic
185C2×C4⋊C4C2×C4×C13912yes—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C42—24no—
189C2×C42—28no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42C2×C4×C13912yes—
193C2×C42D4×C13912yes—
194C22⋊C8—22no—
195C22⋊C8—22no—
196#95—24no—
197#95—22no—
198#95—22no—
199#95—22no—
200#95—22no—
201#95—21no—
202#95D4×C13914yes—
203C24C2×D4×C13911yescharacteristic
204C2×Q8—22no—
205C2×Q8—42no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—24no—
209C22×C4—28no—
210C22×C4—21no—
211C22×C4—24no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—42no—
219C22×C4—44no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4C22⋊C4×C13912yes—
223C22×C4C22⋊C4×C13912yes—
224C22×C4C22×C4×C13911yescharacteristic
225C22×C4C2×D4×C13911yescharacteristic
226C22×C4C2×D4×C13912yes—
227C22×C4#41×C13912yes—
228C2×C8—44no—
229C2×C8—42no—
230C4⋊C4—22no—
231C4⋊C4—42no—
232C4⋊C4—44no—
233C4⋊C4—42no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—42no—
237C42—216no—
238C42—24no—
239C42—24no—
240C23—22no—
241C23—22no—
242C23C2×C22⋊C4×C13911yescharacteristic
243C23#120×C13911yescharacteristic
244C23#123×C13911yescharacteristic
245C23#135×C13912yes—
246C23#137×C13912yes—
247Q8—82no—
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—28no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—48no—
261C2×C4—48no—
262C2×C4—44no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4#104×C13914yes—
274C2×C4C4×D4×C13912yes—
275C2×C4#121×C13912yes—
276C8—82no—
277C22—24no—
278C22—24no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22#386×C13911yescharacteristic
284C22#410×C13912yes—
285C22#416×C13911yescharacteristic
286C22#419×C13911yescharacteristic
287C22C2×#104×C13912yes—
288C22#452×C13912yes—
289C22#485×C13912yes—
290C4—24no—
291C4—22no—
292C4—22no—
293C4—48no—
294C4—42no—
295C4—82no—
296C4—81no—
297C4—81no—
298C2—22no—
299C2—22no—
300C2#1500×C13912yes—
301C2#1506×C13912yes—
302C2#1873×C13911yescharacteristic
303C2#1896×C13911yescharacteristic
304C2#1899×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC24×C139C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
10. #391×C139C4semidirect
11. #389×C139C4semidirect
152. #9145C139direct (N × H)
153. C139#9145direct (N × H)
163. #391C4×C139semidirect
164. #389C4×C139semidirect

Maximal subgroups

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

subgroupindex
#2855×C1392
C2×#376×C1392
#1817×C1392
C2×#328×C1392
#1294×C1392
#9145139