Finite Group Databasebeta

← C139×#12944 #48007540

Subgroups — C139×#12944 #48007540

Order 35584.

388 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#444×C139C211yesmaximal, characteristic
2#2161×C139C211yesmaximal, characteristic, complemented
3#2145×C139C211yesmaximal, characteristic
4#2143×C139C211yesmaximal, characteristic
5#1946×C139C211yesmaximal, characteristic, complemented
6#1389×C139C211yesmaximal, characteristic, complemented
7#1377×C139C211yesmaximal, characteristic, complemented
8C2×#135×C139C2211yescharacteristic
9C2×#131×C139—21no—
10C2×M32×C139C2211yescharacteristic
11C2×M32×C139C2211yescharacteristic
12#444×C139—22no—
13#444×C139—22no—
14C2×#108×C139C2211yescharacteristic
15C2×#108×C139C2211yescharacteristic
16#427×C139C2211yescharacteristic
17#424×C139—21no—
18C2×#104×C139—21no—
19C2×#97×C139C2211yescharacteristic
20#368×C139—22no—
21#360×C139C414yescomplemented
22#359×C139—22no—
23#339×C139—21no—
24C2×#41×C139—21no—
25#135×C139—21no—
26#135×C139—21no—
27#135×C139C2×C412yes—
28#135×C139D412yes—
29C2×Q16×C139Q811yescharacteristic
30C2×SD16×C139—21no—
31C2×D8×C139Q811yescharacteristic
32#131×C139—24no—
33#131×C139—42no—
34C2×M16×C139—21no—
35C2×M16×C139—21no—
36C2×M16×C139—41no—
37C22×C8×C139—41no—
38C22×C8×C139D411yescharacteristic
39C22×C8×C139C2311yescharacteristic
40#117×C139—21no—
41C2×C42×C139D411yescharacteristic
42M32×C139—21no—
43M32×C139—21no—
44M32×C139—21no—
45M32×C139C2×C412yes—
46C2×C16×C139—21no—
47C2×C16×C139—21no—
48#108×C139—21no—
49#108×C139—21no—
50#108×C139—21no—
51#108×C139D412yes—
52#107×C139—21no—
53#106×C139C2×C412yes—
54C4⋊C8×C139—42no—
55#104×C139—24no—
56#97×C139—21no—
57#97×C139—21no—
58#41×C139—22no—
59#41×C139—22no—
60#41×C139—41no—
61#41×C139—41no—
62C2×Q8×C139—21no—
63C2×D4×C139—21no—
64C2×D4×C139—41no—
65C22×C4×C139—21no—
66C22×C4×C139—41no—
67C22×C4×C139C2×D411yescharacteristic
68Q16×C139—21no—
69Q16×C139C4⋊C412yes—
70SD16×C139—22no—
71SD16×C139—22no—
72D8×C139—21no—
73D8×C139C4⋊C412yes—
74M16×C139—22no—
75M16×C139—44no—
76M16×C139—41no—
77M16×C139—41no—
78M16×C139—41no—
79C2×C8×C139—21no—
80C2×C8×C139—21no—
81C2×C8×C139—44no—
82C2×C8×C139—41no—
83C2×C8×C139—41no—
84C2×C8×C139D812yes—
85C2×C8×C139C22×C411yescharacteristic
86C2×C8×C139C2×D411yescharacteristic
87C2×C8×C139C2×D411yescharacteristic
88C2×C8×C139C2×Q811yescharacteristic
89C2×C8×C139#4111yescharacteristic
90C2×C8×C139#4111yescharacteristic
91C4⋊C4×C139—22no—
92C22⋊C4×C139—41no—
93C42×C139—21no—
94C42×C139—21no—
95C42×C139—41no—
96C16×C139—22no—
97C16×C139—41no—
98C23×C139—41no—
99C23×C139#13511yescharacteristic
100Q8×C139—22no—
101Q8×C139—41no—
102D4×C139—22no—
103D4×C139—42no—
104D4×C139—42no—
105D4×C139—41no—
106C2×C4×C139—41no—
107C2×C4×C139—42no—
108C2×C4×C139—42no—
109C2×C4×C139—42no—
110C2×C4×C139—41no—
111C2×C4×C139—81no—
112C2×C4×C139C4×D411yescharacteristic
113C2×C4×C139#12011yescharacteristic
114C2×C4×C139C22⋊Q811yescharacteristic
115C2×C4×C139C2×D811yescharacteristic
116C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C139#13711yescharacteristic
118C8×C139—22no—
119C8×C139—42no—
120C8×C139—81no—
121C8×C139C2×C4⋊C411yescharacteristic
122C8×C139C4×D411yescharacteristic
123C8×C139C22⋊Q811yescharacteristic
124C8×C139#12311yescharacteristic
125C22×C139—41no—
126C22×C139—42no—
127C22×C139—82no—
128C22×C139C4×D811yescharacteristic
129C22×C139#45211yescharacteristic
130C22×C139#47811yescharacteristic
131C4×C139—42no—
132C4×C139—82no—
133C4×C139—81no—
134C4×C139#38511yescharacteristic
135C4×C139#44011yescharacteristic
136C4×C139#44711yescharacteristic
137C4×C139#47411yescharacteristic
138C2×C139—21no—
139C2×C139—21no—
140C2×C139—21no—
141C2×C139—82no—
142C2×C139#186211yescharacteristic
143#12944C13911yesmaximal, characteristic, direct product factor, Sylow
144C139#1294411yescharacteristic, direct product factor, Sylow
145C2×#444C2×C13911yescharacteristic
146#2161C2×C13911yescharacteristic, complemented
147#2145C2×C13911yescharacteristic
148#2143C2×C13911yescharacteristic
149#1946C2×C13911yescharacteristic, complemented
150#1389C2×C13911yescharacteristic, complemented
151#1377C2×C13911yescharacteristic, complemented
152C2×#135C22×C13911yescharacteristic
153C2×#131—21no—
154C2×M32C22×C13911yescharacteristic
155C2×M32C22×C13911yescharacteristic
156#444—22no—
157#444—22no—
158C2×#108C22×C13911yescharacteristic
159C2×#108C22×C13911yescharacteristic
160#427C22×C13911yescharacteristic
161#424—21no—
162C2×#104—21no—
163C2×#97C22×C13911yescharacteristic
164#368—22no—
165#360C4×C13914yescomplemented
166#359—22no—
167#339—21no—
168C2×#41—21no—
169#135—21no—
170#135—21no—
171#135C2×C4×C13912yes—
172#135D4×C13912yes—
173C2×Q16Q8×C13911yescharacteristic
174C2×SD16—21no—
175C2×D8Q8×C13911yescharacteristic
176#131—24no—
177#131—42no—
178C2×M16—21no—
179C2×M16—21no—
180C2×M16—41no—
181C22×C8—41no—
182C22×C8D4×C13911yescharacteristic
183C22×C8C23×C13911yescharacteristic
184#117—21no—
185C2×C42D4×C13911yescharacteristic
186M32—21no—
187M32—21no—
188M32—21no—
189M32C2×C4×C13912yes—
190C2×C16—21no—
191C2×C16—21no—
192#108—21no—
193#108—21no—
194#108—21no—
195#108D4×C13912yes—
196#107—21no—
197#106C2×C4×C13912yes—
198C4⋊C8—42no—
199#104—24no—
200#97—21no—
201#97—21no—
202#41—22no—
203#41—22no—
204#41—41no—
205#41—41no—
206C2×Q8—21no—
207C2×D4—21no—
208C2×D4—41no—
209C22×C4—21no—
210C22×C4—41no—
211C22×C4C2×D4×C13911yescharacteristic
212Q16—21no—
213Q16C4⋊C4×C13912yes—
214SD16—22no—
215SD16—22no—
216D8—21no—
217D8C4⋊C4×C13912yes—
218M16—22no—
219M16—44no—
220M16—41no—
221M16—41no—
222M16—41no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—44no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8D8×C13912yes—
229C2×C8C22×C4×C13911yescharacteristic
230C2×C8C2×D4×C13911yescharacteristic
231C2×C8C2×D4×C13911yescharacteristic
232C2×C8C2×Q8×C13911yescharacteristic
233C2×C8#41×C13911yescharacteristic
234C2×C8#41×C13911yescharacteristic
235C4⋊C4—22no—
236C22⋊C4—41no—
237C42—21no—
238C42—21no—
239C42—41no—
240C16—22no—
241C16—41no—
242C23—41no—
243C23#135×C13911yescharacteristic
244Q8—22no—
245Q8—41no—
246D4—22no—
247D4—42no—
248D4—42no—
249D4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—81no—
256C2×C4C4×D4×C13911yescharacteristic
257C2×C4#120×C13911yescharacteristic
258C2×C4C22⋊Q8×C13911yescharacteristic
259C2×C4C2×D8×C13911yescharacteristic
260C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
261C2×C4#137×C13911yescharacteristic
262C8—22no—
263C8—42no—
264C8—81no—
265C8C2×C4⋊C4×C13911yescharacteristic
266C8C4×D4×C13911yescharacteristic
267C8C22⋊Q8×C13911yescharacteristic
268C8#123×C13911yescharacteristic
269C22—41no—
270C22—42no—
271C22—82no—
272C22C4×D8×C13911yescharacteristic
273C22#452×C13911yescharacteristic
274C22#478×C13911yescharacteristic
275C4—42no—
276C4—81no—
277C4—82no—
278C4#385×C13911yescharacteristic
279C4#440×C13911yescharacteristic
280C4#447×C13911yescharacteristic
281C4#474×C13911yescharacteristic
282C2—21no—
283C2—21no—
284C2—21no—
285C2—82no—
286C2#1862×C13911yescharacteristic
subgroupG/H
centerC4×C139#447
commutatorC2×C8C22×C4×C139
Frattini, cosocleC22×C8C23×C139
socleC2×C139#1862
prime radicalC2×#135×C139C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C139 ◁ C22×C4×C139 ◁ C2×#97×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2161×C139C2semidirect
5. #1946×C139C2semidirect
6. #1389×C139C2semidirect
7. #1377×C139C2semidirect
21. #360×C139C4semidirect
143. #12944C139direct (N × H)
144. C139#12944direct (N × H)
146. #2161C2×C139semidirect
149. #1946C2×C139semidirect
150. #1389C2×C139semidirect
151. #1377C2×C139semidirect
165. #360C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#444×C1392
#2161×C1392
#2145×C1392
#2143×C1392
#1946×C1392
#1389×C1392
#1377×C1392
#12944139