Finite Group Databasebeta

← C139×#13144 #48007740

Subgroups — C139×#13144 #48007740

Order 35584.

334 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#361×C139C211yesmaximal, characteristic
2C2×#357×C139C211yesmaximal, characteristic
3#2108×C139C211yesmaximal, characteristic, complemented
4#1978×C139C211yesmaximal, characteristic
5#1952×C139C211yesmaximal, characteristic, complemented
6#1387×C139C211yesmaximal, characteristic, complemented
7#1381×C139C211yesmaximal, characteristic, complemented
8C22×D8×C139C2211yescharacteristic
9C2×M32×C139C2211yescharacteristic
10C22×C16×C139C2211yescharacteristic
11C2×#108×C139C2211yescharacteristic
12C2×#108×C139C2211yescharacteristic
13#428×C139—21no—
14C2×#107×C139C2211yescharacteristic
15#418×C139—21no—
16C2×#100×C139—21no—
17#405×C139C2211yescharacteristic
18#361×C139C414yescomplemented
19#357×C139—21no—
20#357×C139—21no—
21#346×C139—21no—
22C4×C16×C139—21no—
23#343×C139—21no—
24C22×D4×C139—21no—
25C2×D8×C139—21no—
26C2×D8×C139—21no—
27C2×D8×C139—21no—
28C2×D8×C139—21no—
29C2×D8×C139—21no—
30C2×D8×C139C2×C412yes—
31C2×M16×C139—21no—
32C2×M16×C139—21no—
33C2×M16×C139D411yescharacteristic
34C22×C8×C139C2311yescharacteristic
35#117×C139D411yescharacteristic
36C2×C4⋊C4×C139—21no—
37M32×C139—21no—
38M32×C139C2×C412yes—
39C2×C16×C139—21no—
40C2×C16×C139—21no—
41C2×C16×C139—21no—
42C2×C16×C139D411yescharacteristic
43C2×C16×C139D411yescharacteristic
44#108×C139—21no—
45#108×C139—21no—
46#108×C139—21no—
47#108×C139C2×C412yes—
48#107×C139—21no—
49#107×C139—21no—
50#107×C139—41no—
51#106×C139—41no—
52#102×C139—41no—
53#102×C139—41no—
54#100×C139—42no—
55#97×C139—21no—
56C4×C8×C139—21no—
57C24×C139—41no—
58C2×D4×C139—22no—
59C2×D4×C139—41no—
60C2×D4×C139—41no—
61C2×D4×C139—41no—
62C2×D4×C139—41no—
63C2×D4×C139—41no—
64C22×C4×C139—41no—
65C22×C4×C139C2×D411yescharacteristic
66D8×C139—22no—
67D8×C139—22no—
68D8×C139—41no—
69D8×C139—41no—
70M16×C139—21no—
71M16×C139—22no—
72M16×C139—41no—
73M16×C139—41no—
74M16×C139—41no—
75M16×C139SD1612yes—
76C2×C8×C139—21no—
77C2×C8×C139—41no—
78C2×C8×C139—41no—
79C2×C8×C139C22×C411yescharacteristic
80C2×C8×C139C2×D411yescharacteristic
81C2×C8×C139#4111yescharacteristic
82C2×C8×C139#4111yescharacteristic
83C2×C8×C139#4111yescharacteristic
84C2×C8×C139#4111yescharacteristic
85C4⋊C4×C139—41no—
86C4⋊C4×C139—41no—
87C4⋊C4×C139D811yescharacteristic
88C4⋊C4×C139D811yescharacteristic
89C22⋊C4×C139—21no—
90C42×C139—21no—
91C16×C139—22no—
92C16×C139—21no—
93C16×C139—21no—
94C23×C139—42no—
95C23×C139—81no—
96C23×C139—81no—
97C23×C139—161no—
98C23×C139—161no—
99C23×C139#13511yescharacteristic
100D4×C139—42no—
101D4×C139—42no—
102D4×C139—81no—
103D4×C139—81no—
104C2×C4×C139—21no—
105C2×C4×C139—21no—
106C2×C4×C139—81no—
107C2×C4×C139—161no—
108C2×C4×C139C4×D411yescharacteristic
109C2×C4×C139#12111yescharacteristic
110C2×C4×C139#12411yescharacteristic
111C2×C4×C139C2×D811yescharacteristic
112C2×C4×C139C2×SD1611yescharacteristic
113C2×C4×C139#13511yescharacteristic
114C8×C139—22no—
115C8×C139—42no—
116C8×C139—81no—
117C8×C139#11711yescharacteristic
118C8×C139C4×D411yescharacteristic
119C8×C139#12311yescharacteristic
120C8×C139#12611yescharacteristic
121C22×C139—21no—
122C22×C139—21no—
123C22×C139—82no—
124C22×C139—162no—
125C22×C139—162no—
126C22×C139—161no—
127C22×C139—161no—
128C22×C139C4×SD1611yescharacteristic
129C22×C139#46611yescharacteristic
130C22×C139#48811yescharacteristic
131C4×C139—41no—
132C4×C139—41no—
133C4×C139—161no—
134C4×C139#38811yescharacteristic
135C4×C139C4×D811yescharacteristic
136C4×C139#46511yescharacteristic
137C4×C139#48611yescharacteristic
138C2×C139—21no—
139C2×C139—21no—
140C2×C139—162no—
141C2×C139#193411yescharacteristic
142C2×C139#222111yescharacteristic
143C2×C139#222311yescharacteristic
144#13144C13911yesmaximal, characteristic, direct product factor, Sylow
145C139#1314411yescharacteristic, direct product factor, Sylow
146C2×#361C2×C13911yescharacteristic
147C2×#357C2×C13911yescharacteristic
148#2108C2×C13911yescharacteristic, complemented
149#1978C2×C13911yescharacteristic
150#1952C2×C13911yescharacteristic, complemented
151#1387C2×C13911yescharacteristic, complemented
152#1381C2×C13911yescharacteristic, complemented
153C22×D8C22×C13911yescharacteristic
154C2×M32C22×C13911yescharacteristic
155C22×C16C22×C13911yescharacteristic
156C2×#108C22×C13911yescharacteristic
157C2×#108C22×C13911yescharacteristic
158#428—21no—
159C2×#107C22×C13911yescharacteristic
160#418—21no—
161C2×#100—21no—
162#405C22×C13911yescharacteristic
163#361C4×C13914yescomplemented
164#357—21no—
165#357—21no—
166#346—21no—
167C4×C16—21no—
168#343—21no—
169C22×D4—21no—
170C2×D8—21no—
171C2×D8—21no—
172C2×D8—21no—
173C2×D8—21no—
174C2×D8—21no—
175C2×D8C2×C4×C13912yes—
176C2×M16—21no—
177C2×M16—21no—
178C2×M16D4×C13911yescharacteristic
179C22×C8C23×C13911yescharacteristic
180#117D4×C13911yescharacteristic
181C2×C4⋊C4—21no—
182M32—21no—
183M32C2×C4×C13912yes—
184C2×C16—21no—
185C2×C16—21no—
186C2×C16—21no—
187C2×C16D4×C13911yescharacteristic
188C2×C16D4×C13911yescharacteristic
189#108—21no—
190#108—21no—
191#108—21no—
192#108C2×C4×C13912yes—
193#107—21no—
194#107—21no—
195#107—41no—
196#106—41no—
197#102—41no—
198#102—41no—
199#100—42no—
200#97—21no—
201C4×C8—21no—
202C24—41no—
203C2×D4—22no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—41no—
209C22×C4—41no—
210C22×C4C2×D4×C13911yescharacteristic
211D8—22no—
212D8—22no—
213D8—41no—
214D8—41no—
215M16—21no—
216M16—22no—
217M16—41no—
218M16—41no—
219M16—41no—
220M16SD16×C13912yes—
221C2×C8—21no—
222C2×C8—41no—
223C2×C8—41no—
224C2×C8C22×C4×C13911yescharacteristic
225C2×C8C2×D4×C13911yescharacteristic
226C2×C8#41×C13911yescharacteristic
227C2×C8#41×C13911yescharacteristic
228C2×C8#41×C13911yescharacteristic
229C2×C8#41×C13911yescharacteristic
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4D8×C13911yescharacteristic
233C4⋊C4D8×C13911yescharacteristic
234C22⋊C4—21no—
235C42—21no—
236C16—22no—
237C16—21no—
238C16—21no—
239C23—42no—
240C23—81no—
241C23—81no—
242C23—161no—
243C23—161no—
244C23#135×C13911yescharacteristic
245D4—42no—
246D4—42no—
247D4—81no—
248D4—81no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—81no—
252C2×C4—161no—
253C2×C4C4×D4×C13911yescharacteristic
254C2×C4#121×C13911yescharacteristic
255C2×C4#124×C13911yescharacteristic
256C2×C4C2×D8×C13911yescharacteristic
257C2×C4C2×SD16×C13911yescharacteristic
258C2×C4#135×C13911yescharacteristic
259C8—22no—
260C8—42no—
261C8—81no—
262C8#117×C13911yescharacteristic
263C8C4×D4×C13911yescharacteristic
264C8#123×C13911yescharacteristic
265C8#126×C13911yescharacteristic
266C22—21no—
267C22—21no—
268C22—82no—
269C22—162no—
270C22—162no—
271C22—161no—
272C22—161no—
273C22C4×SD16×C13911yescharacteristic
274C22#466×C13911yescharacteristic
275C22#488×C13911yescharacteristic
276C4—41no—
277C4—41no—
278C4—161no—
279C4#388×C13911yescharacteristic
280C4C4×D8×C13911yescharacteristic
281C4#465×C13911yescharacteristic
282C4#486×C13911yescharacteristic
283C2—21no—
284C2—21no—
285C2—162no—
286C2#1934×C13911yescharacteristic
287C2#2221×C13911yescharacteristic
288C2#2223×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#466
commutatorC2×C8C22×C4×C139
Frattini, cosocleC22×C8C23×C139
prime radicalC22×D8×C139C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C22×C4×C139 ◁ #405×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2108×C139C2semidirect
5. #1952×C139C2semidirect
6. #1387×C139C2semidirect
7. #1381×C139C2semidirect
18. #361×C139C4semidirect
144. #13144C139direct (N × H)
145. C139#13144direct (N × H)
148. #2108C2×C139semidirect
150. #1952C2×C139semidirect
151. #1387C2×C139semidirect
152. #1381C2×C139semidirect
163. #361C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#361×C1392
C2×#357×C1392
#2108×C1392
#1978×C1392
#1952×C1392
#1387×C1392
#1381×C1392
#13144139