Finite Group Databasebeta

← C139×#13137 #48007733

Subgroups — C139×#13137 #48007733

Order 35584.

316 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2161×C139C211yesmaximal, characteristic, complemented
2#2148×C139C211yesmaximal, characteristic
3#2143×C139C211yesmaximal, characteristic
4#1974×C139C211yesmaximal, characteristic
5C4×#108×C139C211yesmaximal, characteristic, complemented
6#1388×C139C211yesmaximal, characteristic, complemented
7#1376×C139C211yesmaximal, characteristic, complemented
8C2×#135×C139C2211yescharacteristic
9C2×M32×C139C2211yescharacteristic
10C2×M32×C139C2211yescharacteristic
11C2×#108×C139C2211yescharacteristic
12C2×#108×C139C2211yescharacteristic
13C2×#108×C139C2211yescharacteristic
14C2×#104×C139—21no—
15#408×C139—21no—
16C4×M16×C139—21no—
17C2×C4×C8×C139C2211yescharacteristic
18#368×C139—22no—
19#362×C139C412yescomplemented
20#361×C139C412yescomplemented
21#359×C139—22no—
22#341×C139—21no—
23C2×#41×C139—21no—
24#135×C139—21no—
25#135×C139—21no—
26#135×C139—21no—
27#135×C139—21no—
28C2×Q16×C139C2×C411yescharacteristic
29C2×SD16×C139—21no—
30C2×D8×C139C2×C411yescharacteristic
31C2×M16×C139—21no—
32C2×M16×C139—21no—
33C2×M16×C139—21no—
34C22×C8×C139D411yescharacteristic
35C22×C8×C139C2311yescharacteristic
36C2×C42×C139D411yescharacteristic
37M32×C139—21no—
38M32×C139—21no—
39M32×C139—21no—
40M32×C139C2×C412yes—
41C2×C16×C139—21no—
42C2×C16×C139—21no—
43#108×C139—21no—
44#108×C139—21no—
45#108×C139—21no—
46#108×C139—21no—
47#108×C139C2×C412yes—
48#108×C139D412yes—
49#104×C139—41no—
50#104×C139—41no—
51C22⋊C8×C139—42no—
52#97×C139—41no—
53C4×C8×C139—21no—
54C4×C8×C139—21no—
55C4×C8×C139—41no—
56#41×C139—41no—
57#41×C139—41no—
58#41×C139—41no—
59#41×C139—41no—
60C2×Q8×C139—21no—
61C2×D4×C139—21no—
62C2×D4×C139—41no—
63C22×C4×C139—21no—
64C22×C4×C139—41no—
65C22×C4×C139C2×D411yescharacteristic
66Q16×C139—21no—
67Q16×C139—21no—
68SD16×C139—41no—
69SD16×C139—41no—
70D8×C139—21no—
71D8×C139—21no—
72M16×C139—22no—
73M16×C139—22no—
74M16×C139—41no—
75M16×C139—41no—
76M16×C139—41no—
77M16×C139—41no—
78C2×C8×C139—21no—
79C2×C8×C139—21no—
80C2×C8×C139—21no—
81C2×C8×C139—41no—
82C2×C8×C139—41no—
83C2×C8×C139—41no—
84C2×C8×C139C22×C411yescharacteristic
85C2×C8×C139C2×D411yescharacteristic
86C2×C8×C139#4111yescharacteristic
87C2×C8×C139#4111yescharacteristic
88C2×C8×C139#4111yescharacteristic
89C2×C8×C139#4111yescharacteristic
90C42×C139—21no—
91C42×C139D811yescharacteristic
92C42×C139D811yescharacteristic
93C16×C139—22no—
94C16×C139—41no—
95C23×C139—41no—
96C23×C139#13711yescharacteristic
97Q8×C139—41no—
98Q8×C139—41no—
99D4×C139—41no—
100D4×C139—41no—
101D4×C139—81no—
102D4×C139—81no—
103C2×C4×C139—21no—
104C2×C4×C139—21no—
105C2×C4×C139—42no—
106C2×C4×C139—41no—
107C2×C4×C139—81no—
108C2×C4×C139—81no—
109C2×C4×C139C4×D411yescharacteristic
110C2×C4×C139#12111yescharacteristic
111C2×C4×C139#12311yescharacteristic
112C2×C4×C139C2×D811yescharacteristic
113C2×C4×C139#13511yescharacteristic
114C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
115C8×C139—42no—
116C8×C139—42no—
117C8×C139—41no—
118C8×C139—81no—
119C8×C139#11711yescharacteristic
120C8×C139C4×D411yescharacteristic
121C8×C139#12411yescharacteristic
122C8×C139#12611yescharacteristic
123C22×C139—41no—
124C22×C139—82no—
125C22×C139—81no—
126C22×C139#44011yescharacteristic
127C22×C139#46411yescharacteristic
128C22×C139#48011yescharacteristic
129C4×C139—22no—
130C4×C139—41no—
131C4×C139—81no—
132C4×C139#38811yescharacteristic
133C4×C139C4×D811yescharacteristic
134C4×C139#45911yescharacteristic
135C4×C139#48211yescharacteristic
136C2×C139—21no—
137C2×C139—21no—
138C2×C139—21no—
139C2×C139—161no—
140C2×C139#192511yescharacteristic
141#13137C13911yesmaximal, characteristic, direct product factor, Sylow
142C139#1313711yescharacteristic, direct product factor, Sylow
143#2161C2×C13911yescharacteristic, complemented
144#2148C2×C13911yescharacteristic
145#2143C2×C13911yescharacteristic
146#1974C2×C13911yescharacteristic
147C4×#108C2×C13911yescharacteristic, complemented
148#1388C2×C13911yescharacteristic, complemented
149#1376C2×C13911yescharacteristic, complemented
150C2×#135C22×C13911yescharacteristic
151C2×M32C22×C13911yescharacteristic
152C2×M32C22×C13911yescharacteristic
153C2×#108C22×C13911yescharacteristic
154C2×#108C22×C13911yescharacteristic
155C2×#108C22×C13911yescharacteristic
156C2×#104—21no—
157#408—21no—
158C4×M16—21no—
159C2×C4×C8C22×C13911yescharacteristic
160#368—22no—
161#362C4×C13912yescomplemented
162#361C4×C13912yescomplemented
163#359—22no—
164#341—21no—
165C2×#41—21no—
166#135—21no—
167#135—21no—
168#135—21no—
169#135—21no—
170C2×Q16C2×C4×C13911yescharacteristic
171C2×SD16—21no—
172C2×D8C2×C4×C13911yescharacteristic
173C2×M16—21no—
174C2×M16—21no—
175C2×M16—21no—
176C22×C8D4×C13911yescharacteristic
177C22×C8C23×C13911yescharacteristic
178C2×C42D4×C13911yescharacteristic
179M32—21no—
180M32—21no—
181M32—21no—
182M32C2×C4×C13912yes—
183C2×C16—21no—
184C2×C16—21no—
185#108—21no—
186#108—21no—
187#108—21no—
188#108—21no—
189#108C2×C4×C13912yes—
190#108D4×C13912yes—
191#104—41no—
192#104—41no—
193C22⋊C8—42no—
194#97—41no—
195C4×C8—21no—
196C4×C8—21no—
197C4×C8—41no—
198#41—41no—
199#41—41no—
200#41—41no—
201#41—41no—
202C2×Q8—21no—
203C2×D4—21no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—41no—
207C22×C4C2×D4×C13911yescharacteristic
208Q16—21no—
209Q16—21no—
210SD16—41no—
211SD16—41no—
212D8—21no—
213D8—21no—
214M16—22no—
215M16—22no—
216M16—41no—
217M16—41no—
218M16—41no—
219M16—41no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8C22×C4×C13911yescharacteristic
227C2×C8C2×D4×C13911yescharacteristic
228C2×C8#41×C13911yescharacteristic
229C2×C8#41×C13911yescharacteristic
230C2×C8#41×C13911yescharacteristic
231C2×C8#41×C13911yescharacteristic
232C42—21no—
233C42D8×C13911yescharacteristic
234C42D8×C13911yescharacteristic
235C16—22no—
236C16—41no—
237C23—41no—
238C23#137×C13911yescharacteristic
239Q8—41no—
240Q8—41no—
241D4—41no—
242D4—41no—
243D4—81no—
244D4—81no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4C4×D4×C13911yescharacteristic
252C2×C4#121×C13911yescharacteristic
253C2×C4#123×C13911yescharacteristic
254C2×C4C2×D8×C13911yescharacteristic
255C2×C4#135×C13911yescharacteristic
256C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
257C8—42no—
258C8—42no—
259C8—41no—
260C8—81no—
261C8#117×C13911yescharacteristic
262C8C4×D4×C13911yescharacteristic
263C8#124×C13911yescharacteristic
264C8#126×C13911yescharacteristic
265C22—41no—
266C22—82no—
267C22—81no—
268C22#440×C13911yescharacteristic
269C22#464×C13911yescharacteristic
270C22#480×C13911yescharacteristic
271C4—22no—
272C4—41no—
273C4—81no—
274C4#388×C13911yescharacteristic
275C4C4×D8×C13911yescharacteristic
276C4#459×C13911yescharacteristic
277C4#482×C13911yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—161no—
282C2#1925×C13911yescharacteristic
subgroupG/H
centerC4×C139#459
commutatorC2×C8C22×C4×C139
Frattini, cosocleC22×C8C23×C139
socleC2×C139#1925
prime radicalC2×#135×C139C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C139 ◁ C22×C4×C139 ◁ C2×C4×C8×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2161×C139C2semidirect
5. C4×#108×C139C2semidirect
6. #1388×C139C2semidirect
7. #1376×C139C2semidirect
19. #362×C139C4semidirect
20. #361×C139C4semidirect
141. #13137C139direct (N × H)
142. C139#13137direct (N × H)
143. #2161C2×C139semidirect
147. C4×#108C2×C139semidirect
148. #1388C2×C139semidirect
149. #1376C2×C139semidirect
161. #362C4×C139semidirect
162. #361C4×C139semidirect

Maximal subgroups

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

subgroupindex
#2161×C1392
#2148×C1392
#2143×C1392
#1974×C1392
C4×#108×C1392
#1388×C1392
#1376×C1392
#13137139