Finite Group Databasebeta

← C139×#21942 #48016538

Subgroups — C139×#21942 #48016538

Order 35584.

1234 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#407×C139C211yesmaximal, characteristic
2C2×#380×C139C212yesmaximal
3#1853×C139C214yesmaximal, complemented
4#1852×C139C214yesmaximal, complemented
5#1809×C139C214yesmaximal, complemented
6C24×C4×C139C2211yescharacteristic
7C22×M16×C139C2212yes—
8C22×C4⋊C4×C139C2212yes—
9C22×C4⋊C4×C139C2212yes—
10C22×C22⋊C4×C139—22no—
11C2×#107×C139C2214yescomplemented
12C2×#106×C139C2214yescomplemented
13#407×C139C418yescomplemented
14C2×C22⋊C8×C139C2214yes—
15#380×C139—22no—
16#380×C139—22no—
17#380×C139C2214yes—
18#380×C139C2214yes—
19C2×#95×C139—22no—
20#340×C139C2218yescomplemented
21C25×C139D411yescharacteristic
22C23×C4×C139—22no—
23C23×C4×C139—22no—
24C23×C4×C139—42no—
25C23×C4×C139—42no—
26C23×C4×C139C2×C414yes—
27C23×C4×C139D412yes—
28C23×C4×C139D411yescharacteristic
29C23×C4×C139Q814yes—
30C23×C4×C139C2312yes—
31C23×C4×C139C2311yescharacteristic
32C2×M16×C139—42no—
33C2×M16×C139—42no—
34C2×M16×C139C2×C418yescomplemented
35C22×C8×C139C2314yes—
36C2×C4⋊C4×C139—22no—
37C2×C4⋊C4×C139—22no—
38C2×C4⋊C4×C139—44no—
39C2×C4⋊C4×C139—44no—
40C2×C4⋊C4×C139C2314yes—
41C2×C4⋊C4×C139C2314yes—
42C2×C22⋊C4×C139—24no—
43C2×C22⋊C4×C139—24no—
44C2×C22⋊C4×C139—48no—
45#107×C139—44no—
46#106×C139—44no—
47C22⋊C8×C139C2×C4116yescomplemented
48#95×C139—24no—
49#95×C139—24no—
50C24×C139—24no—
51C24×C139—24no—
52C24×C139—41no—
53C24×C139—41no—
54C24×C139C4⋊C414yes—
55C24×C139C2×D411yescharacteristic
56C24×C139C2×D412yes—
57C22×C4×C139—24no—
58C22×C4×C139—24no—
59C22×C4×C139—22no—
60C22×C4×C139—22no—
61C22×C4×C139—24no—
62C22×C4×C139—24no—
63C22×C4×C139—48no—
64C22×C4×C139—48no—
65C22×C4×C139—41no—
66C22×C4×C139—41no—
67C22×C4×C139—42no—
68C22×C4×C139—42no—
69C22×C4×C139—44no—
70C22×C4×C139—44no—
71C22×C4×C139—44no—
72C22×C4×C139—44no—
73C22×C4×C139—44no—
74C22×C4×C139—44no—
75C22×C4×C139C4⋊C414yes—
76C22×C4×C139C4⋊C418yes—
77C22×C4×C139C22×C414yes—
78C22×C4×C139C22×C412yes—
79C22×C4×C139C2×D411yescharacteristic
80C22×C4×C139C2×D412yes—
81C22×C4×C139C2×Q812yes—
82C22×C4×C139C2×Q814yes—
83C22×C4×C139C2411yescharacteristic
84M16×C139—48no—
85C2×C8×C139—24no—
86C2×C8×C139—24no—
87C2×C8×C139C22×C418yes—
88C4⋊C4×C139—28no—
89C4⋊C4×C139—28no—
90C4⋊C4×C139—44no—
91C4⋊C4×C139—44no—
92C22⋊C4×C139—48no—
93C22⋊C4×C139—48no—
94C23×C139—22no—
95C23×C139—22no—
96C23×C139—22no—
97C23×C139—22no—
98C23×C139—21no—
99C23×C139—21no—
100C23×C139—22no—
101C23×C139—22no—
102C23×C139—216no—
103C23×C139—44no—
104C23×C139—44no—
105C23×C139—48no—
106C23×C139—44no—
107C23×C139C2×C4⋊C412yes—
108C23×C139C2×C4⋊C414yes—
109C23×C139AGL(1,ℤ/8)14yes—
110C23×C139#13714yes—
111C23×C139C22×D411yescharacteristic
112C2×C4×C139—22no—
113C2×C4×C139—22no—
114C2×C4×C139—21no—
115C2×C4×C139—21no—
116C2×C4×C139—24no—
117C2×C4×C139—28no—
118C2×C4×C139—28no—
119C2×C4×C139—24no—
120C2×C4×C139—48no—
121C2×C4×C139—44no—
122C2×C4×C139—44no—
123C2×C4×C139—44no—
124C2×C4×C139—44no—
125C2×C4×C139—44no—
126C2×C4×C139—44no—
127C2×C4×C139—44no—
128C2×C4×C139—88no—
129C2×C4×C139—88no—
130C2×C4×C139C2×C4⋊C414yes—
131C2×C4×C139C2×C4⋊C412yes—
132C2×C4×C139C23×C411yescharacteristic
133C2×C4×C139C22×Q811yescharacteristic
134C2×C4×C139H(5,𝔽2)12yes—
135C2×C4×C139H(5,𝔽2)12yes—
136C8×C139—28no—
137C22×C139—24no—
138C22×C139—24no—
139C22×C139—24no—
140C22×C139—24no—
141C22×C139—24no—
142C22×C139—24no—
143C22×C139—22no—
144C22×C139—24no—
145C22×C139—416no—
146C22×C139—41no—
147C22×C139—42no—
148C22×C139—41no—
149C22×C139#42818yes—
150C22×C139C22×C4⋊C411yescharacteristic
151C22×C139#53411yescharacteristic
152C22×C139#53411yescharacteristic
153C22×C139C2×AGL(1,ℤ/8)12yes—
154C22×C139C2×#13712yes—
155C4×C139—24no—
156C4×C139—22no—
157C4×C139—84no—
158C4×C139—84no—
159C4×C139#51812yes—
160C4×C139#54312yes—
161C2×C139—28no—
162C2×C139—42no—
163C2×C139#231511yescharacteristic
164C2×C139C2×#42812yes—
165C2×C139#319211yescharacteristic
166C2×C139#319312yes—
167C2×C139#319511yescharacteristic
168#21942C13911yesmaximal, characteristic, direct product factor, Sylow
169C139#2194211yescharacteristic, direct product factor, Sylow
170C2×#407C2×C13911yescharacteristic
171C2×#380C2×C13912yes—
172#1853C2×C13914yescomplemented
173#1852C2×C13914yescomplemented
174#1809C2×C13914yescomplemented
175C24×C4C22×C13911yescharacteristic
176C22×M16C22×C13912yes—
177C22×C4⋊C4C22×C13912yes—
178C22×C4⋊C4C22×C13912yes—
179C22×C22⋊C4—22no—
180C2×#107C22×C13914yescomplemented
181C2×#106C22×C13914yescomplemented
182#407C4×C13918yescomplemented
183C2×C22⋊C8C22×C13914yes—
184#380—22no—
185#380—22no—
186#380C22×C13914yes—
187#380C22×C13914yes—
188C2×#95—22no—
189#340C22×C13918yescomplemented
190C25D4×C13911yescharacteristic
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—42no—
194C23×C4—42no—
195C23×C4C2×C4×C13914yes—
196C23×C4D4×C13912yes—
197C23×C4D4×C13911yescharacteristic
198C23×C4Q8×C13914yes—
199C23×C4C23×C13912yes—
200C23×C4C23×C13911yescharacteristic
201C2×M16—42no—
202C2×M16—42no—
203C2×M16C2×C4×C13918yescomplemented
204C22×C8C23×C13914yes—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—44no—
208C2×C4⋊C4—44no—
209C2×C4⋊C4C23×C13914yes—
210C2×C4⋊C4C23×C13914yes—
211C2×C22⋊C4—24no—
212C2×C22⋊C4—24no—
213C2×C22⋊C4—48no—
214#107—44no—
215#106—44no—
216C22⋊C8C2×C4×C139116yescomplemented
217#95—24no—
218#95—24no—
219C24—24no—
220C24—24no—
221C24—41no—
222C24—41no—
223C24C4⋊C4×C13914yes—
224C24C2×D4×C13911yescharacteristic
225C24C2×D4×C13912yes—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—48no—
233C22×C4—48no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—44no—
239C22×C4—44no—
240C22×C4—44no—
241C22×C4—44no—
242C22×C4—44no—
243C22×C4—44no—
244C22×C4C4⋊C4×C13914yes—
245C22×C4C4⋊C4×C13918yes—
246C22×C4C22×C4×C13914yes—
247C22×C4C22×C4×C13912yes—
248C22×C4C2×D4×C13911yescharacteristic
249C22×C4C2×D4×C13912yes—
250C22×C4C2×Q8×C13912yes—
251C22×C4C2×Q8×C13914yes—
252C22×C4C24×C13911yescharacteristic
253M16—48no—
254C2×C8—24no—
255C2×C8—24no—
256C2×C8C22×C4×C13918yes—
257C4⋊C4—28no—
258C4⋊C4—28no—
259C4⋊C4—44no—
260C4⋊C4—44no—
261C22⋊C4—48no—
262C22⋊C4—48no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—216no—
268C23—21no—
269C23—21no—
270C23—22no—
271C23—22no—
272C23—44no—
273C23—44no—
274C23—48no—
275C23—44no—
276C23C2×C4⋊C4×C13912yes—
277C23C2×C4⋊C4×C13914yes—
278C23AGL(1,ℤ/8)×C13914yes—
279C23#137×C13914yes—
280C23C22×D4×C13911yescharacteristic
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—24no—
286C2×C4—28no—
287C2×C4—28no—
288C2×C4—24no—
289C2×C4—48no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—88no—
298C2×C4—88no—
299C2×C4C2×C4⋊C4×C13914yes—
300C2×C4C2×C4⋊C4×C13912yes—
301C2×C4C23×C4×C13911yescharacteristic
302C2×C4C22×Q8×C13911yescharacteristic
303C2×C4H(5,𝔽2)×C13912yes—
304C2×C4H(5,𝔽2)×C13912yes—
305C8—28no—
306C22—24no—
307C22—24no—
308C22—24no—
309C22—24no—
310C22—24no—
311C22—24no—
312C22—22no—
313C22—24no—
314C22—416no—
315C22—41no—
316C22—42no—
317C22—41no—
318C22#428×C13918yes—
319C22C22×C4⋊C4×C13911yescharacteristic
320C22#534×C13911yescharacteristic
321C22#534×C13911yescharacteristic
322C22C2×AGL(1,ℤ/8)×C13912yes—
323C22C2×#137×C13912yes—
324C4—24no—
325C4—22no—
326C4—84no—
327C4—84no—
328C4#518×C13912yes—
329C4#543×C13912yes—
330C2—28no—
331C2—42no—
332C2#2315×C13911yescharacteristic
333C2C2×#428×C13912yes—
334C2#3192×C13911yescharacteristic
335C2#3193×C13912yes—
336C2#3195×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC25×C139D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C24×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1853×C139C2semidirect
4. #1852×C139C2semidirect
5. #1809×C139C2semidirect
11. C2×#107×C139C22semidirect
12. C2×#106×C139C22semidirect
13. #407×C139C4semidirect
20. #340×C139C22semidirect
34. C2×M16×C139C2×C4semidirect
47. C22⋊C8×C139C2×C4semidirect
168. #21942C139direct (N × H)
169. C139#21942direct (N × H)
172. #1853C2×C139semidirect
173. #1852C2×C139semidirect
174. #1809C2×C139semidirect
180. C2×#107C22×C139semidirect
181. C2×#106C22×C139semidirect
182. #407C4×C139semidirect
189. #340C22×C139semidirect
203. C2×M16C2×C4×C139semidirect
216. C22⋊C8C2×C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#407×C1392
C2×#380×C1392
#1853×C1392
#1852×C1392
#1809×C1392
#21942139