Finite Group Databasebeta

← C139×#9159 #48003755

Subgroups — C139×#9159 #48003755

Order 35584.

452 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3116×C139C211yesmaximal, characteristic
2#2970×C139C211yesmaximal, characteristic
3#1759×C139C211yesmaximal, characteristic
4#1526×C139C211yesmaximal, characteristic, complemented
5#1506×C139C211yesmaximal, characteristic, complemented
6#1300×C139C211yesmaximal, characteristic, complemented
7#1291×C139C211yesmaximal, characteristic, complemented
8#533×C139C2211yescharacteristic
9C4×#41×C139C2211yescharacteristic
10#485×C139—21no—
11#477×C139C411yescharacteristic, complemented
12#476×C139C411yescharacteristic, complemented
13#462×C139C411yescharacteristic, complemented
14#461×C139C411yescharacteristic, complemented
15#452×C139—21no—
16#446×C139—21no—
17#441×C139—21no—
18#440×C139—21no—
19#435×C139—22no—
20C8×D4×C139—21no—
21#432×C139—21no—
22#432×C139C2211yescharacteristic
23#432×C139C2211yescharacteristic
24C2×#104×C139—21no—
25C4×M16×C139C2211yescharacteristic
26C4×M16×C139C2211yescharacteristic
27C2×#97×C139—21no—
28#376×C139C2211yescharacteristic
29#339×C139—21no—
30#330×C139—21no—
31#330×C139—21no—
32#328×C139—22no—
33C2×#41×C139D411yescharacteristic
34C2×Q16×C139—21no—
35C2×SD16×C139—21no—
36C2×M16×C139—21no—
37C2×M16×C139—21no—
38C22×C8×C139—22no—
39C4⋊Q8×C139C2×C411yescharacteristic
40C4⋊Q8×C139C2×C411yescharacteristic
41#125×C139—21no—
42C22⋊Q8×C139—21no—
43C22⋊Q8×C139—21no—
44C4×Q8×C139—21no—
45C4×Q8×C139—21no—
46C4×Q8×C139C2×C411yescharacteristic
47C4×Q8×C139D411yescharacteristic
48C4×D4×C139—21no—
49C4×D4×C139—21no—
50C4×D4×C139C2×C411yescharacteristic
51C4×D4×C139D411yescharacteristic
52#117×C139—21no—
53#117×C139—21no—
54#117×C139D411yescharacteristic
55C2×C42×C139—21no—
56C2×C42×C139—21no—
57C2×C42×C139C2311yescharacteristic
58#107×C139—21no—
59#106×C139—21no—
60C4⋊C8×C139—22no—
61C4⋊C8×C139—21no—
62C4⋊C8×C139C2×C411yescharacteristic
63C4⋊C8×C139C2×C411yescharacteristic
64#104×C139—24no—
65#103×C139—21no—
66#103×C139—21no—
67#103×C139—21no—
68#102×C139—21no—
69C22⋊C8×C139—22no—
70C22⋊C8×C139—21no—
71C22⋊C8×C139D412yes—
72#97×C139—22no—
73#97×C139—21no—
74#97×C139—21no—
75#97×C139—21no—
76#97×C139D411yescharacteristic
77#97×C139D411yescharacteristic
78C4×C8×C139—21no—
79C4×C8×C139—21no—
80#95×C139—21no—
81#95×C139—21no—
82#41×C139—22no—
83#41×C139—41no—
84C2×Q8×C139—21no—
85C2×Q8×C139—21no—
86C2×Q8×C139C22⋊C411yescharacteristic
87C2×D4×C139—21no—
88C2×D4×C139C22⋊C411yescharacteristic
89C22×C4×C139—21no—
90C22×C4×C139—21no—
91C22×C4×C139—21no—
92C22×C4×C139—41no—
93C22×C4×C139C2×D411yescharacteristic
94C22×C4×C139C2×D411yescharacteristic
95C22×C4×C139#4111yescharacteristic
96Q16×C139—42no—
97SD16×C139—42no—
98M16×C139—22no—
99M16×C139—42no—
100M16×C139—41no—
101C2×C8×C139—21no—
102C2×C8×C139—21no—
103C2×C8×C139—21no—
104C2×C8×C139—21no—
105C2×C8×C139—22no—
106C2×C8×C139—44no—
107C2×C8×C139—41no—
108C4⋊C4×C139—21no—
109C4⋊C4×C139—21no—
110C4⋊C4×C139—21no—
111C4⋊C4×C139—21no—
112C4⋊C4×C139—21no—
113C4⋊C4×C139—21no—
114C4⋊C4×C139—41no—
115C4⋊C4×C139—41no—
116C4⋊C4×C139C22⋊C411yescharacteristic
117C4⋊C4×C139C22⋊C411yescharacteristic
118C22⋊C4×C139—21no—
119C22⋊C4×C139—21no—
120C22⋊C4×C139—21no—
121C22⋊C4×C139—41no—
122C42×C139—21no—
123C42×C139—21no—
124C42×C139—21no—
125C42×C139—22no—
126C42×C139—41no—
127C42×C139—41no—
128C42×C139C22×C411yescharacteristic
129C42×C139C2×D411yescharacteristic
130C42×C139C2×D411yescharacteristic
131C42×C139#4111yescharacteristic
132C23×C139—21no—
133C23×C139#12111yescharacteristic
134Q8×C139—21no—
135Q8×C139—21no—
136Q8×C139—41no—
137Q8×C139—41no—
138Q8×C139—81no—
139D4×C139—21no—
140D4×C139—42no—
141D4×C139#10412yes—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—41no—
148C2×C4×C139—41no—
149C2×C4×C139—42no—
150C2×C4×C139—42no—
151C2×C4×C139—42no—
152C2×C4×C139—41no—
153C2×C4×C139—41no—
154C2×C4×C139—81no—
155C2×C4×C139—81no—
156C2×C4×C139—81no—
157C2×C4×C139C2×C22⋊C411yescharacteristic
158C2×C4×C139C4×D411yescharacteristic
159C2×C4×C139C4×D411yescharacteristic
160C2×C4×C139#12011yescharacteristic
161C2×C4×C139#12111yescharacteristic
162C2×C4×C139#12311yescharacteristic
163C8×C139—22no—
164C8×C139—42no—
165C8×C139—41no—
166C8×C139—42no—
167C8×C139—41no—
168C8×C139—41no—
169C22×C139—21no—
170C22×C139—22no—
171C22×C139—21no—
172C22×C139—21no—
173C22×C139—41no—
174C22×C139—41no—
175C22×C139#38611yescharacteristic
176C4×C139—21no—
177C4×C139—21no—
178C4×C139—21no—
179C4×C139—21no—
180C4×C139—21no—
181C4×C139—41no—
182C4×C139—41no—
183C4×C139—41no—
184C4×C139—82no—
185C4×C139—81no—
186C4×C139—81no—
187C4×C139C2×#10411yescharacteristic
188C4×C139#42111yescharacteristic
189C2×C139—41no—
190C2×C139—42no—
191C2×C139#187111yescharacteristic
192C2×C139#190211yescharacteristic
193C2×C139#190611yescharacteristic
194#9159C13911yesmaximal, characteristic, direct product factor, Sylow
195C139#915911yescharacteristic, direct product factor, Sylow
196#3116C2×C13911yescharacteristic
197#2970C2×C13911yescharacteristic
198#1759C2×C13911yescharacteristic
199#1526C2×C13911yescharacteristic, complemented
200#1506C2×C13911yescharacteristic, complemented
201#1300C2×C13911yescharacteristic, complemented
202#1291C2×C13911yescharacteristic, complemented
203#533C22×C13911yescharacteristic
204C4×#41C22×C13911yescharacteristic
205#485—21no—
206#477C4×C13911yescharacteristic, complemented
207#476C4×C13911yescharacteristic, complemented
208#462C4×C13911yescharacteristic, complemented
209#461C4×C13911yescharacteristic, complemented
210#452—21no—
211#446—21no—
212#441—21no—
213#440—21no—
214#435—22no—
215C8×D4—21no—
216#432—21no—
217#432C22×C13911yescharacteristic
218#432C22×C13911yescharacteristic
219C2×#104—21no—
220C4×M16C22×C13911yescharacteristic
221C4×M16C22×C13911yescharacteristic
222C2×#97—21no—
223#376C22×C13911yescharacteristic
224#339—21no—
225#330—21no—
226#330—21no—
227#328—22no—
228C2×#41D4×C13911yescharacteristic
229C2×Q16—21no—
230C2×SD16—21no—
231C2×M16—21no—
232C2×M16—21no—
233C22×C8—22no—
234C4⋊Q8C2×C4×C13911yescharacteristic
235C4⋊Q8C2×C4×C13911yescharacteristic
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8C2×C4×C13911yescharacteristic
242C4×Q8D4×C13911yescharacteristic
243C4×D4—21no—
244C4×D4—21no—
245C4×D4C2×C4×C13911yescharacteristic
246C4×D4D4×C13911yescharacteristic
247#117—21no—
248#117—21no—
249#117D4×C13911yescharacteristic
250C2×C42—21no—
251C2×C42—21no—
252C2×C42C23×C13911yescharacteristic
253#107—21no—
254#106—21no—
255C4⋊C8—22no—
256C4⋊C8—21no—
257C4⋊C8C2×C4×C13911yescharacteristic
258C4⋊C8C2×C4×C13911yescharacteristic
259#104—24no—
260#103—21no—
261#103—21no—
262#103—21no—
263#102—21no—
264C22⋊C8—22no—
265C22⋊C8—21no—
266C22⋊C8D4×C13912yes—
267#97—22no—
268#97—21no—
269#97—21no—
270#97—21no—
271#97D4×C13911yescharacteristic
272#97D4×C13911yescharacteristic
273C4×C8—21no—
274C4×C8—21no—
275#95—21no—
276#95—21no—
277#41—22no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8C22⋊C4×C13911yescharacteristic
282C2×D4—21no—
283C2×D4C22⋊C4×C13911yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4C2×D4×C13911yescharacteristic
289C22×C4C2×D4×C13911yescharacteristic
290C22×C4#41×C13911yescharacteristic
291Q16—42no—
292SD16—42no—
293M16—22no—
294M16—42no—
295M16—41no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—22no—
301C2×C8—44no—
302C2×C8—41no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4C22⋊C4×C13911yescharacteristic
312C4⋊C4C22⋊C4×C13911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—41no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—22no—
321C42—41no—
322C42—41no—
323C42C22×C4×C13911yescharacteristic
324C42C2×D4×C13911yescharacteristic
325C42C2×D4×C13911yescharacteristic
326C42#41×C13911yescharacteristic
327C23—21no—
328C23#121×C13911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—41no—
332Q8—41no—
333Q8—81no—
334D4—21no—
335D4—42no—
336D4#104×C13912yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4C2×C22⋊C4×C13911yescharacteristic
353C2×C4C4×D4×C13911yescharacteristic
354C2×C4C4×D4×C13911yescharacteristic
355C2×C4#120×C13911yescharacteristic
356C2×C4#121×C13911yescharacteristic
357C2×C4#123×C13911yescharacteristic
358C8—22no—
359C8—42no—
360C8—41no—
361C8—42no—
362C8—41no—
363C8—41no—
364C22—21no—
365C22—22no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22#386×C13911yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—82no—
380C4—81no—
381C4—81no—
382C4C2×#104×C13911yescharacteristic
383C4#421×C13911yescharacteristic
384C2—41no—
385C2—42no—
386C2#1871×C13911yescharacteristic
387C2#1902×C13911yescharacteristic
388C2#1906×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radicalC2×#41×C139D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1526×C139C2semidirect
5. #1506×C139C2semidirect
6. #1300×C139C2semidirect
7. #1291×C139C2semidirect
11. #477×C139C4semidirect
12. #476×C139C4semidirect
13. #462×C139C4semidirect
14. #461×C139C4semidirect
194. #9159C139direct (N × H)
195. C139#9159direct (N × H)
199. #1526C2×C139semidirect
200. #1506C2×C139semidirect
201. #1300C2×C139semidirect
202. #1291C2×C139semidirect
206. #477C4×C139semidirect
207. #476C4×C139semidirect
208. #462C4×C139semidirect
209. #461C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3116×C1392
#2970×C1392
#1759×C1392
#1526×C1392
#1506×C1392
#1300×C1392
#1291×C1392
#9159139