Finite Group Databasebeta

← C139×#12949 #48007545

Subgroups — C139×#12949 #48007545

Order 35584.

394 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2952×C139C211yesmaximal, characteristic
2C2×#365×C139C211yesmaximal, characteristic, complemented
3#2148×C139C211yesmaximal, characteristic
4#2143×C139C211yesmaximal, characteristic
5#1953×C139C211yesmaximal, characteristic, complemented
6#1383×C139C211yesmaximal, characteristic, complemented
7#1378×C139C211yesmaximal, characteristic, complemented
8C2×#135×C139C2211yescharacteristic
9#520×C139—21no—
10C2×M32×C139C2211yescharacteristic
11C2×M32×C139C2211yescharacteristic
12#442×C139—21no—
13#441×C139—21no—
14C4×SD16×C139—22no—
15#430×C139—21no—
16C2×#108×C139C2211yescharacteristic
17C2×#108×C139C2211yescharacteristic
18C2×#106×C139C2211yescharacteristic
19#417×C139—21no—
20#405×C139C2211yescharacteristic
21#365×C139—22no—
22#362×C139—21no—
23#361×C139—21no—
24#359×C139C414yescomplemented
25#344×C139—21no—
26C2×#41×C139—21no—
27#135×C139—21no—
28#135×C139—21no—
29#135×C139C2×C412yes—
30#135×C139Q812yes—
31C2×Q16×C139D411yescharacteristic
32C2×SD16×C139—21no—
33C2×D8×C139D411yescharacteristic
34C2×M16×C139—21no—
35C2×M16×C139—21no—
36C2×M16×C139D411yescharacteristic
37C22×C8×C139C2311yescharacteristic
38C4×Q8×C139—22no—
39C4×D4×C139—22no—
40C4×D4×C139—42no—
41#117×C139—41no—
42#117×C139D411yescharacteristic
43C2×C4⋊C4×C139—21no—
44C2×C4⋊C4×C139—41no—
45M32×C139—21no—
46M32×C139—21no—
47M32×C139—21no—
48M32×C139—21no—
49C2×C16×C139—21no—
50C2×C16×C139C2×C412yescomplemented
51#108×C139—21no—
52#108×C139—21no—
53#108×C139—21no—
54#108×C139—42no—
55#108×C139C2×C412yescomplemented
56#106×C139—21no—
57#106×C139D412yes—
58#103×C139—22no—
59#102×C139—22no—
60#97×C139—21no—
61C4×C8×C139—21no—
62#41×C139—22no—
63#41×C139—22no—
64#41×C139—41no—
65#41×C139—41no—
66C2×Q8×C139—21no—
67C2×D4×C139—21no—
68C2×D4×C139—41no—
69C22×C4×C139—42no—
70C22×C4×C139—41no—
71C22×C4×C139—41no—
72C22×C4×C139C2×D411yescharacteristic
73Q16×C139—21no—
74Q16×C139C4⋊C412yes—
75SD16×C139—22no—
76SD16×C139—22no—
77D8×C139—21no—
78D8×C139C4⋊C412yes—
79M16×C139—22no—
80M16×C139—21no—
81M16×C139—21no—
82M16×C139—41no—
83M16×C139—41no—
84M16×C139—41no—
85C2×C8×C139—21no—
86C2×C8×C139—41no—
87C2×C8×C139—41no—
88C2×C8×C139C22×C411yescharacteristic
89C2×C8×C139C2×D411yescharacteristic
90C2×C8×C139C2×D411yescharacteristic
91C2×C8×C139C2×Q811yescharacteristic
92C2×C8×C139#4111yescharacteristic
93C2×C8×C139#4111yescharacteristic
94C4⋊C4×C139—21no—
95C4⋊C4×C139—22no—
96C4⋊C4×C139—42no—
97C4⋊C4×C139—41no—
98C22⋊C4×C139—42no—
99C22⋊C4×C139SD1612yes—
100C42×C139—21no—
101C42×C139—42no—
102C16×C139—22no—
103C16×C139—41no—
104C23×C139—41no—
105C23×C139C2×SD1611yescharacteristic
106Q8×C139—22no—
107Q8×C139—41no—
108D4×C139—22no—
109D4×C139—42no—
110D4×C139—42no—
111D4×C139—41no—
112C2×C4×C139—22no—
113C2×C4×C139—41no—
114C2×C4×C139—42no—
115C2×C4×C139—42no—
116C2×C4×C139—42no—
117C2×C4×C139—162no—
118C2×C4×C139—161no—
119C2×C4×C139C4×D411yescharacteristic
120C2×C4×C139#12011yescharacteristic
121C2×C4×C139C22⋊Q811yescharacteristic
122C2×C4×C139#13511yescharacteristic
123C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
125C8×C139—42no—
126C8×C139—41no—
127C8×C139—81no—
128C8×C139C2×C4⋊C411yescharacteristic
129C8×C139C4×D411yescharacteristic
130C8×C139C22⋊Q811yescharacteristic
131C8×C139#12311yescharacteristic
132C22×C139—41no—
133C22×C139—42no—
134C22×C139—81no—
135C22×C139—81no—
136C22×C139C4×SD1611yescharacteristic
137C22×C139#45011yescharacteristic
138C22×C139#47611yescharacteristic
139C4×C139—42no—
140C4×C139—42no—
141C4×C139—82no—
142C4×C139#38511yescharacteristic
143C4×C139#44211yescharacteristic
144C4×C139#44911yescharacteristic
145C4×C139#47811yescharacteristic
146C2×C139—21no—
147C2×C139—21no—
148C2×C139—21no—
149C2×C139—82no—
150C2×C139#186411yescharacteristic
151#12949C13911yesmaximal, characteristic, direct product factor, Sylow
152C139#1294911yescharacteristic, direct product factor, Sylow
153#2952C2×C13911yescharacteristic
154C2×#365C2×C13911yescharacteristic, complemented
155#2148C2×C13911yescharacteristic
156#2143C2×C13911yescharacteristic
157#1953C2×C13911yescharacteristic, complemented
158#1383C2×C13911yescharacteristic, complemented
159#1378C2×C13911yescharacteristic, complemented
160C2×#135C22×C13911yescharacteristic
161#520—21no—
162C2×M32C22×C13911yescharacteristic
163C2×M32C22×C13911yescharacteristic
164#442—21no—
165#441—21no—
166C4×SD16—22no—
167#430—21no—
168C2×#108C22×C13911yescharacteristic
169C2×#108C22×C13911yescharacteristic
170C2×#106C22×C13911yescharacteristic
171#417—21no—
172#405C22×C13911yescharacteristic
173#365—22no—
174#362—21no—
175#361—21no—
176#359C4×C13914yescomplemented
177#344—21no—
178C2×#41—21no—
179#135—21no—
180#135—21no—
181#135C2×C4×C13912yes—
182#135Q8×C13912yes—
183C2×Q16D4×C13911yescharacteristic
184C2×SD16—21no—
185C2×D8D4×C13911yescharacteristic
186C2×M16—21no—
187C2×M16—21no—
188C2×M16D4×C13911yescharacteristic
189C22×C8C23×C13911yescharacteristic
190C4×Q8—22no—
191C4×D4—22no—
192C4×D4—42no—
193#117—41no—
194#117D4×C13911yescharacteristic
195C2×C4⋊C4—21no—
196C2×C4⋊C4—41no—
197M32—21no—
198M32—21no—
199M32—21no—
200M32—21no—
201C2×C16—21no—
202C2×C16C2×C4×C13912yescomplemented
203#108—21no—
204#108—21no—
205#108—21no—
206#108—42no—
207#108C2×C4×C13912yescomplemented
208#106—21no—
209#106D4×C13912yes—
210#103—22no—
211#102—22no—
212#97—21no—
213C4×C8—21no—
214#41—22no—
215#41—22no—
216#41—41no—
217#41—41no—
218C2×Q8—21no—
219C2×D4—21no—
220C2×D4—41no—
221C22×C4—42no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4C2×D4×C13911yescharacteristic
225Q16—21no—
226Q16C4⋊C4×C13912yes—
227SD16—22no—
228SD16—22no—
229D8—21no—
230D8C4⋊C4×C13912yes—
231M16—22no—
232M16—21no—
233M16—21no—
234M16—41no—
235M16—41no—
236M16—41no—
237C2×C8—21no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8C22×C4×C13911yescharacteristic
241C2×C8C2×D4×C13911yescharacteristic
242C2×C8C2×D4×C13911yescharacteristic
243C2×C8C2×Q8×C13911yescharacteristic
244C2×C8#41×C13911yescharacteristic
245C2×C8#41×C13911yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4SD16×C13912yes—
252C42—21no—
253C42—42no—
254C16—22no—
255C16—41no—
256C23—41no—
257C23C2×SD16×C13911yescharacteristic
258Q8—22no—
259Q8—41no—
260D4—22no—
261D4—42no—
262D4—42no—
263D4—41no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—162no—
270C2×C4—161no—
271C2×C4C4×D4×C13911yescharacteristic
272C2×C4#120×C13911yescharacteristic
273C2×C4C22⋊Q8×C13911yescharacteristic
274C2×C4#135×C13911yescharacteristic
275C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
276C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
277C8—42no—
278C8—41no—
279C8—81no—
280C8C2×C4⋊C4×C13911yescharacteristic
281C8C4×D4×C13911yescharacteristic
282C8C22⋊Q8×C13911yescharacteristic
283C8#123×C13911yescharacteristic
284C22—41no—
285C22—42no—
286C22—81no—
287C22—81no—
288C22C4×SD16×C13911yescharacteristic
289C22#450×C13911yescharacteristic
290C22#476×C13911yescharacteristic
291C4—42no—
292C4—42no—
293C4—82no—
294C4#385×C13911yescharacteristic
295C4#442×C13911yescharacteristic
296C4#449×C13911yescharacteristic
297C4#478×C13911yescharacteristic
298C2—21no—
299C2—21no—
300C2—21no—
301C2—82no—
302C2#1864×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#1864
commutatorC2×C8C22×C4×C139
Frattini, cosocleC22×C8C23×C139
prime radicalC2×#135×C139C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C22×C4×C139 ◁ #405×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#365×C139C2semidirect
5. #1953×C139C2semidirect
6. #1383×C139C2semidirect
7. #1378×C139C2semidirect
24. #359×C139C4semidirect
50. C2×C16×C139C2×C4semidirect
55. #108×C139C2×C4semidirect
151. #12949C139direct (N × H)
152. C139#12949direct (N × H)
154. C2×#365C2×C139semidirect
157. #1953C2×C139semidirect
158. #1383C2×C139semidirect
159. #1378C2×C139semidirect
176. #359C4×C139semidirect
202. C2×C16C2×C4×C139semidirect
207. #108C2×C4×C139semidirect

Maximal subgroups

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

subgroupindex
#2952×C1392
C2×#365×C1392
#2148×C1392
#2143×C1392
#1953×C1392
#1383×C1392
#1378×C1392
#12949139