Finite Group Databasebeta

← C139×#8519 #48003115

Subgroups — C139×#8519 #48003115

Order 35584.

754 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#542×C139C211yesmaximal, characteristic
2#1822×C139C211yesmaximal, characteristic, complemented
3#1820×C139C211yesmaximal, characteristic, complemented
4#1511×C139C212yesmaximal, complemented
5#1510×C139C212yesmaximal
6#542×C139—24no—
7#542×C139—24no—
8C2×C4⋊Q8×C139C411yescharacteristic, complemented
9C2×#126×C139—21no—
10C2×#124×C139—21no—
11C2×#124×C139C411yescharacteristic, complemented
12C2×#123×C139—21no—
13C2×C22⋊Q8×C139—21no—
14C2×C22⋊Q8×C139C2211yescharacteristic
15C2×#121×C139C2211yescharacteristic
16C2×C4×Q8×C139C411yescharacteristic, complemented
17C2×C4×D4×C139C411yescharacteristic, complemented
18C2×#117×C139C2211yescharacteristic
19#407×C139C2212yes—
20#381×C139C2212yes—
21#343×C139—21no—
22#343×C139—21no—
23#342×C139—21no—
24#342×C139—21no—
25#328×C139—24no—
26#327×C139—24no—
27C22×Q8×C139—21no—
28C22×Q8×C139C2×C411yescharacteristic
29C22×D4×C139—21no—
30C22×D4×C139C2×C411yescharacteristic
31C23×C4×C139—21no—
32C23×C4×C139C2311yescharacteristic
33C2×M16×C139—22no—
34C4⋊Q8×C139—22no—
35C4⋊Q8×C139—22no—
36#126×C139—28no—
37#124×C139—28no—
38#124×C139—22no—
39#124×C139—22no—
40#123×C139—28no—
41C22⋊Q8×C139—28no—
42C22⋊Q8×C139—22no—
43C22⋊Q8×C139D414yes—
44#121×C139—22no—
45#121×C139D414yes—
46C4×Q8×C139—22no—
47C4×Q8×C139—22no—
48C4×D4×C139—22no—
49C4×D4×C139—22no—
50#117×C139—22no—
51#117×C139—22no—
52C2×C4⋊C4×C139—21no—
53C2×C4⋊C4×C139—21no—
54C2×C4⋊C4×C139—21no—
55C2×C4⋊C4×C139C2×C411yescharacteristic
56C2×C4⋊C4×C139C2×C411yescharacteristic
57C2×C4⋊C4×C139D411yescharacteristic
58C2×C4⋊C4×C139D411yescharacteristic
59C2×C22⋊C4×C139—21no—
60C2×C22⋊C4×C139—21no—
61C2×C22⋊C4×C139—21no—
62C2×C22⋊C4×C139—21no—
63C2×C22⋊C4×C139—21no—
64C2×C22⋊C4×C139—22no—
65C2×C22⋊C4×C139D411yescharacteristic
66C2×C22⋊C4×C139D411yescharacteristic
67C2×C42×C139—21no—
68C2×C42×C139C2×C411yescharacteristic
69C2×C42×C139C2×C411yescharacteristic
70C22⋊C8×C139—22no—
71C22⋊C8×C139—22no—
72#95×C139—22no—
73#95×C139—22no—
74C24×C139—21no—
75C24×C139C2×D411yescharacteristic
76C2×Q8×C139—24no—
77C2×Q8×C139—21no—
78C2×Q8×C139—42no—
79C2×Q8×C139—82no—
80C2×Q8×C139C22⋊C412yes—
81C2×D4×C139—24no—
82C2×D4×C139—21no—
83C2×D4×C139—42no—
84C2×D4×C139—82no—
85C2×D4×C139C22⋊C412yes—
86C22×C4×C139—21no—
87C22×C4×C139—21no—
88C22×C4×C139—21no—
89C22×C4×C139—24no—
90C22×C4×C139—42no—
91C22×C4×C139—42no—
92C22×C4×C139—82no—
93C22×C4×C139C22⋊C411yescharacteristic
94C22×C4×C139C22⋊C411yescharacteristic
95C22×C4×C139C22⋊C411yescharacteristic
96C22×C4×C139C22⋊C411yescharacteristic
97C22×C4×C139C22×C411yescharacteristic
98C22×C4×C139C2×D411yescharacteristic
99C22×C4×C139C2×D412yes—
100C22×C4×C139C2×D412yes—
101M16×C139—44no—
102C2×C8×C139—42no—
103C4⋊C4×C139—24no—
104C4⋊C4×C139—24no—
105C4⋊C4×C139—21no—
106C4⋊C4×C139—21no—
107C4⋊C4×C139—24no—
108C4⋊C4×C139—22no—
109C4⋊C4×C139—22no—
110C4⋊C4×C139C22⋊C412yes—
111C4⋊C4×C139C22⋊C412yes—
112C22⋊C4×C139—24no—
113C22⋊C4×C139—24no—
114C22⋊C4×C139—24no—
115C22⋊C4×C139—24no—
116C22⋊C4×C139—22no—
117C22⋊C4×C139—22no—
118C22⋊C4×C139—24no—
119C22⋊C4×C139—44no—
120C42×C139—24no—
121C42×C139—21no—
122C42×C139—21no—
123C42×C139—21no—
124C42×C139—21no—
125C23×C139—22no—
126C23×C139—22no—
127C23×C139—41no—
128C23×C139—41no—
129C23×C139—42no—
130C23×C139—42no—
131C23×C139—42no—
132C23×C139C2×C22⋊C411yescharacteristic
133C23×C139#12012yes—
134Q8×C139—42no—
135Q8×C139—42no—
136Q8×C139—84no—
137D4×C139—42no—
138D4×C139—42no—
139D4×C139—84no—
140C2×C4×C139—22no—
141C2×C4×C139—22no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—22no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—22no—
148C2×C4×C139—22no—
149C2×C4×C139—42no—
150C2×C4×C139—42no—
151C2×C4×C139—42no—
152C2×C4×C139—42no—
153C2×C4×C139—42no—
154C2×C4×C139—41no—
155C2×C4×C139—41no—
156C2×C4×C139—41no—
157C2×C4×C139—41no—
158C2×C4×C139—84no—
159C2×C4×C139—82no—
160C2×C4×C139—82no—
161C2×C4×C139—82no—
162C2×C4×C139C2×C22⋊C411yescharacteristic
163C2×C4×C139C2×C22⋊C411yescharacteristic
164C2×C4×C139#12012yes—
165C8×C139—82no—
166C22×C139—21no—
167C22×C139—21no—
168C22×C139—22no—
169C22×C139—22no—
170C22×C139—22no—
171C22×C139—42no—
172C22×C139—42no—
173C22×C139—42no—
174C22×C139—82no—
175C22×C139—84no—
176C22×C139#37911yescharacteristic
177C22×C139#41012yes—
178C4×C139—22no—
179C4×C139—21no—
180C4×C139—21no—
181C4×C139—42no—
182C4×C139—42no—
183C4×C139—41no—
184C4×C139—41no—
185C4×C139—41no—
186C4×C139—41no—
187C4×C139—42no—
188C4×C139—162no—
189C2×C139—22no—
190C2×C139—42no—
191C2×C139—82no—
192C2×C139#178211yescharacteristic
193C2×C139#179511yescharacteristic
194C2×C139#179611yescharacteristic
195#8519C13911yesmaximal, characteristic, direct product factor, Sylow
196C139#851911yescharacteristic, direct product factor, Sylow
197C2×#542C2×C13911yescharacteristic
198#1822C2×C13911yescharacteristic, complemented
199#1820C2×C13911yescharacteristic, complemented
200#1511C2×C13912yescomplemented
201#1510C2×C13912yes—
202#542—24no—
203#542—24no—
204C2×C4⋊Q8C4×C13911yescharacteristic, complemented
205C2×#126—21no—
206C2×#124—21no—
207C2×#124C4×C13911yescharacteristic, complemented
208C2×#123—21no—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8C22×C13911yescharacteristic
211C2×#121C22×C13911yescharacteristic
212C2×C4×Q8C4×C13911yescharacteristic, complemented
213C2×C4×D4C4×C13911yescharacteristic, complemented
214C2×#117C22×C13911yescharacteristic
215#407C22×C13912yes—
216#381C22×C13912yes—
217#343—21no—
218#343—21no—
219#342—21no—
220#342—21no—
221#328—24no—
222#327—24no—
223C22×Q8—21no—
224C22×Q8C2×C4×C13911yescharacteristic
225C22×D4—21no—
226C22×D4C2×C4×C13911yescharacteristic
227C23×C4—21no—
228C23×C4C23×C13911yescharacteristic
229C2×M16—22no—
230C4⋊Q8—22no—
231C4⋊Q8—22no—
232#126—28no—
233#124—28no—
234#124—22no—
235#124—22no—
236#123—28no—
237C22⋊Q8—28no—
238C22⋊Q8—22no—
239C22⋊Q8D4×C13914yes—
240#121—22no—
241#121D4×C13914yes—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×D4—22no—
245C4×D4—22no—
246#117—22no—
247#117—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C2×C4×C13911yescharacteristic
252C2×C4⋊C4C2×C4×C13911yescharacteristic
253C2×C4⋊C4D4×C13911yescharacteristic
254C2×C4⋊C4D4×C13911yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4D4×C13911yescharacteristic
262C2×C22⋊C4D4×C13911yescharacteristic
263C2×C42—21no—
264C2×C42C2×C4×C13911yescharacteristic
265C2×C42C2×C4×C13911yescharacteristic
266C22⋊C8—22no—
267C22⋊C8—22no—
268#95—22no—
269#95—22no—
270C24—21no—
271C24C2×D4×C13911yescharacteristic
272C2×Q8—24no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×Q8—82no—
276C2×Q8C22⋊C4×C13912yes—
277C2×D4—24no—
278C2×D4—21no—
279C2×D4—42no—
280C2×D4—82no—
281C2×D4C22⋊C4×C13912yes—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—24no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—82no—
289C22×C4C22⋊C4×C13911yescharacteristic
290C22×C4C22⋊C4×C13911yescharacteristic
291C22×C4C22⋊C4×C13911yescharacteristic
292C22×C4C22⋊C4×C13911yescharacteristic
293C22×C4C22×C4×C13911yescharacteristic
294C22×C4C2×D4×C13911yescharacteristic
295C22×C4C2×D4×C13912yes—
296C22×C4C2×D4×C13912yes—
297M16—44no—
298C2×C8—42no—
299C4⋊C4—24no—
300C4⋊C4—24no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—24no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4C22⋊C4×C13912yes—
307C4⋊C4C22⋊C4×C13912yes—
308C22⋊C4—24no—
309C22⋊C4—24no—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—24no—
315C22⋊C4—44no—
316C42—24no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—21no—
321C23—22no—
322C23—22no—
323C23—41no—
324C23—41no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23C2×C22⋊C4×C13911yescharacteristic
329C23#120×C13912yes—
330Q8—42no—
331Q8—42no—
332Q8—84no—
333D4—42no—
334D4—42no—
335D4—84no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—84no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4C2×C22⋊C4×C13911yescharacteristic
359C2×C4C2×C22⋊C4×C13911yescharacteristic
360C2×C4#120×C13912yes—
361C8—82no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—82no—
371C22—84no—
372C22#379×C13911yescharacteristic
373C22#410×C13912yes—
374C4—22no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—162no—
385C2—22no—
386C2—42no—
387C2—82no—
388C2#1782×C13911yescharacteristic
389C2#1795×C13911yescharacteristic
390C2#1796×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#379
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC2×#121×C139C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1822×C139C2semidirect
3. #1820×C139C2semidirect
4. #1511×C139C2semidirect
8. C2×C4⋊Q8×C139C4semidirect
11. C2×#124×C139C4semidirect
16. C2×C4×Q8×C139C4semidirect
17. C2×C4×D4×C139C4semidirect
195. #8519C139direct (N × H)
196. C139#8519direct (N × H)
198. #1822C2×C139semidirect
199. #1820C2×C139semidirect
200. #1511C2×C139semidirect
204. C2×C4⋊Q8C4×C139semidirect
207. C2×#124C4×C139semidirect
212. C2×C4×Q8C4×C139semidirect
213. C2×C4×D4C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#542×C1392
#1822×C1392
#1820×C1392
#1511×C1392
#1510×C1392
#8519139