Finite Group Databasebeta

← C139×#36053 #48030649

Subgroups — C139×#36053 #48030649

Order 35584.

1756 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2645×C139C211yesmaximal, characteristic, complemented
2#2643×C139C212yesmaximal, complemented
3#2514×C139C213yesmaximal, complemented
4#2510×C139C216yesmaximal, complemented
5#2494×C139C213yesmaximal, complemented
6#2493×C139C216yesmaximal, complemented
7#2401×C139C211yesmaximal, characteristic, complemented
8C2×#401×C139C212yesmaximal, complemented
9#2349×C139C213yesmaximal, complemented
10#2339×C139C213yesmaximal
11#2275×C139C211yesmaximal, characteristic, complemented
12C22×#41×C139C2211yescharacteristic
13C2×C4×D4×C139C2213yes—
14C2×C4×D4×C139C2213yes—
15#401×C139C2216yes—
16#401×C139C2212yes—
17#401×C139C2211yescharacteristic
18#401×C139C2216yes—
19#400×C139C2216yes—
20#400×C139C2216yes—
21#400×C139C2213yes—
22#397×C139C2213yes—
23#397×C139C2216yes—
24#396×C139C2211yescharacteristic
25#391×C139C2213yes—
26#391×C139C2213yes—
27#389×C139C2213yes—
28#389×C139C2213yes—
29#388×C139C2216yes—
30#387×C139C2216yes—
31#387×C139C2216yes—
32#386×C139C2216yes—
33#386×C139C2216yes—
34#385×C139C2216yes—
35#385×C139C2216yes—
36#383×C139C2216yes—
37#382×C139C2213yes—
38#381×C139C2216yes—
39#380×C139C2216yes—
40#380×C139C2213yes—
41C4×C4⋊C4×C139C2213yes—
42C4×C4⋊C4×C139C2213yes—
43C4×C22⋊C4×C139C2216yes—
44C4×C22⋊C4×C139C2213yes—
45#376×C139C2211yescharacteristic
46C2×#95×C139C2216yes—
47C2×#95×C139C2212yes—
48C2×#95×C139C2216yes—
49C2×#41×C139—212no—
50C22×Q8×C139C2311yescharacteristic
51C22×D4×C139C2312yes—
52C22×D4×C139C2311yescharacteristic
53C23×C4×C139C2312yes—
54C23×C4×C139C2311yescharacteristic
55C23×C4×C139C2316yes—
56C23×C4×C139C2316yes—
57C4×D4×C139—212no—
58C4×D4×C139—212no—
59C2×C4⋊C4×C139C2313yes—
60C2×C4⋊C4×C139C2313yes—
61C2×C4⋊C4×C139C2313yes—
62C2×C4⋊C4×C139C2313yes—
63C2×C4⋊C4×C139C2316yes—
64C2×C4⋊C4×C139C2316yes—
65C2×C22⋊C4×C139C2316yes—
66C2×C22⋊C4×C139C2316yes—
67C2×C22⋊C4×C139C2313yes—
68C2×C22⋊C4×C139C2313yes—
69C2×C22⋊C4×C139C2316yes—
70C2×C42×C139C2313yes—
71C2×C42×C139C2313yes—
72C2×C42×C139C2316yes—
73#95×C139C2311yescharacteristic
74#95×C139C2313yes—
75#95×C139C2316yes—
76#95×C139C2316yes—
77#95×C139C2313yes—
78#95×C139C2316yes—
79#95×C139C2313yes—
80#95×C139C2316yes—
81#95×C139C2313yes—
82#95×C139C2316yes—
83#95×C139C2316yes—
84#95×C139C2313yes—
85#95×C139C2316yes—
86#95×C139C2316yes—
87#95×C139C2316yes—
88#95×C139C2316yes—
89C24×C139C2411yescharacteristic
90C24×C139C2412yes—
91#41×C139—416no—
92C2×Q8×C139—26no—
93C2×D4×C139—212no—
94C2×D4×C139#41112yes—
95C22×C4×C139—212no—
96C22×C4×C139—212no—
97C22×C4×C139—212no—
98C22×C4×C139—26no—
99C22×C4×C139—46no—
100C22×C4×C139—46no—
101C22×C4×C139—46no—
102C22×C4×C139—46no—
103C22×C4×C139C2411yescharacteristic
104C22×C4×C139C2412yes—
105C22×C4×C139C2413yes—
106C22×C4×C139C2413yes—
107C22×C4×C139C2416yes—
108C22×C4×C139C2416yes—
109C22×C4×C139C2413yes—
110C22×C4×C139C2413yes—
111C22×C4×C139C2411yescharacteristic
112C4⋊C4×C139—26no—
113C4⋊C4×C139—26no—
114C4⋊C4×C139—43no—
115C4⋊C4×C139—46no—
116C4⋊C4×C139—43no—
117C4⋊C4×C139—46no—
118C22⋊C4×C139—212no—
119C22⋊C4×C139—212no—
120C22⋊C4×C139—46no—
121C22⋊C4×C139—43no—
122C22⋊C4×C139—43no—
123C42×C139—26no—
124C42×C139—26no—
125C42×C139—46no—
126C23×C139—26no—
127C23×C139—22no—
128C23×C139—23no—
129C23×C139—23no—
130C23×C139—21no—
131C23×C139C2×#41112yes—
132C23×C139C2511yescharacteristic
133Q8×C139—44no—
134D4×C139—48no—
135D4×C139#126116yes—
136C2×C4×C139—23no—
137C2×C4×C139—23no—
138C2×C4×C139—23no—
139C2×C4×C139—23no—
140C2×C4×C139—26no—
141C2×C4×C139—26no—
142C2×C4×C139—23no—
143C2×C4×C139—26no—
144C2×C4×C139—23no—
145C2×C4×C139—26no—
146C2×C4×C139—26no—
147C2×C4×C139—23no—
148C2×C4×C139—23no—
149C2×C4×C139—26no—
150C2×C4×C139—23no—
151C2×C4×C139—23no—
152C2×C4×C139—23no—
153C2×C4×C139—26no—
154C2×C4×C139—23no—
155C2×C4×C139—23no—
156C2×C4×C139—48no—
157C2×C4×C139—44no—
158C2×C4×C139—812no—
159C2×C4×C139—812no—
160C2×C4×C139C2×#4116yes—
161C22×C139—212no—
162C22×C139—212no—
163C22×C139—41no—
164C22×C139—43no—
165C22×C139—43no—
166C22×C139C2×#12618yes—
167C22×C139C22×#4113yes—
168C22×C139#58513yes—
169C22×C139#58511yescharacteristic
170C4×C139—41no—
171C4×C139—42no—
172C4×C139—43no—
173C4×C139—43no—
174C4×C139—46no—
175C4×C139—46no—
176C4×C139—43no—
177C4×C139—43no—
178C4×C139C2×#12614yes—
179C2×C139—28no—
180C2×C139—81no—
181C2×C139C22×#12611yescharacteristic
182C2×C139#352113yes—
183C2×C139#352113yes—
184#36053C13911yesmaximal, characteristic, direct product factor, Sylow
185C139#3605311yescharacteristic, direct product factor, Sylow
186#2645C2×C13911yescharacteristic, complemented
187#2643C2×C13912yescomplemented
188#2514C2×C13913yescomplemented
189#2510C2×C13916yescomplemented
190#2494C2×C13913yescomplemented
191#2493C2×C13916yescomplemented
192#2401C2×C13911yescharacteristic, complemented
193C2×#401C2×C13912yescomplemented
194#2349C2×C13913yescomplemented
195#2339C2×C13913yes—
196#2275C2×C13911yescharacteristic, complemented
197C22×#41C22×C13911yescharacteristic
198C2×C4×D4C22×C13913yes—
199C2×C4×D4C22×C13913yes—
200#401C22×C13912yes—
201#401C22×C13911yescharacteristic
202#401C22×C13916yes—
203#401C22×C13916yes—
204#400C22×C13916yes—
205#400C22×C13916yes—
206#400C22×C13913yes—
207#397C22×C13916yes—
208#397C22×C13913yes—
209#396C22×C13911yescharacteristic
210#391C22×C13913yes—
211#391C22×C13913yes—
212#389C22×C13913yes—
213#389C22×C13913yes—
214#388C22×C13916yes—
215#387C22×C13916yes—
216#387C22×C13916yes—
217#386C22×C13916yes—
218#386C22×C13916yes—
219#385C22×C13916yes—
220#385C22×C13916yes—
221#383C22×C13916yes—
222#382C22×C13913yes—
223#381C22×C13916yes—
224#380C22×C13913yes—
225#380C22×C13916yes—
226C4×C4⋊C4C22×C13913yes—
227C4×C4⋊C4C22×C13913yes—
228C4×C22⋊C4C22×C13913yes—
229C4×C22⋊C4C22×C13916yes—
230#376C22×C13911yescharacteristic
231C2×#95C22×C13916yes—
232C2×#95C22×C13916yes—
233C2×#95C22×C13912yes—
234C2×#41—212no—
235C22×Q8C23×C13911yescharacteristic
236C22×D4C23×C13912yes—
237C22×D4C23×C13911yescharacteristic
238C23×C4C23×C13912yes—
239C23×C4C23×C13911yescharacteristic
240C23×C4C23×C13916yes—
241C23×C4C23×C13916yes—
242C4×D4—212no—
243C4×D4—212no—
244C2×C4⋊C4C23×C13913yes—
245C2×C4⋊C4C23×C13913yes—
246C2×C4⋊C4C23×C13913yes—
247C2×C4⋊C4C23×C13913yes—
248C2×C4⋊C4C23×C13916yes—
249C2×C4⋊C4C23×C13916yes—
250C2×C22⋊C4C23×C13916yes—
251C2×C22⋊C4C23×C13916yes—
252C2×C22⋊C4C23×C13913yes—
253C2×C22⋊C4C23×C13913yes—
254C2×C22⋊C4C23×C13916yes—
255C2×C42C23×C13913yes—
256C2×C42C23×C13913yes—
257C2×C42C23×C13916yes—
258#95C23×C13911yescharacteristic
259#95C23×C13913yes—
260#95C23×C13913yes—
261#95C23×C13916yes—
262#95C23×C13916yes—
263#95C23×C13916yes—
264#95C23×C13916yes—
265#95C23×C13916yes—
266#95C23×C13916yes—
267#95C23×C13916yes—
268#95C23×C13913yes—
269#95C23×C13913yes—
270#95C23×C13913yes—
271#95C23×C13916yes—
272#95C23×C13916yes—
273#95C23×C13916yes—
274C24C24×C13911yescharacteristic
275C24C24×C13912yes—
276#41—416no—
277C2×Q8—26no—
278C2×D4—212no—
279C2×D4#41×C139112yes—
280C22×C4—212no—
281C22×C4—212no—
282C22×C4—212no—
283C22×C4—26no—
284C22×C4—46no—
285C22×C4—46no—
286C22×C4—46no—
287C22×C4—46no—
288C22×C4C24×C13911yescharacteristic
289C22×C4C24×C13912yes—
290C22×C4C24×C13913yes—
291C22×C4C24×C13913yes—
292C22×C4C24×C13916yes—
293C22×C4C24×C13916yes—
294C22×C4C24×C13913yes—
295C22×C4C24×C13913yes—
296C22×C4C24×C13911yescharacteristic
297C4⋊C4—26no—
298C4⋊C4—26no—
299C4⋊C4—43no—
300C4⋊C4—46no—
301C4⋊C4—43no—
302C4⋊C4—46no—
303C22⋊C4—212no—
304C22⋊C4—212no—
305C22⋊C4—46no—
306C22⋊C4—43no—
307C22⋊C4—43no—
308C42—26no—
309C42—26no—
310C42—46no—
311C23—26no—
312C23—22no—
313C23—23no—
314C23—23no—
315C23—21no—
316C23C2×#41×C139112yes—
317C23C25×C13911yescharacteristic
318Q8—44no—
319D4—48no—
320D4#126×C139116yes—
321C2×C4—23no—
322C2×C4—23no—
323C2×C4—23no—
324C2×C4—23no—
325C2×C4—26no—
326C2×C4—26no—
327C2×C4—23no—
328C2×C4—26no—
329C2×C4—23no—
330C2×C4—26no—
331C2×C4—26no—
332C2×C4—23no—
333C2×C4—23no—
334C2×C4—26no—
335C2×C4—23no—
336C2×C4—23no—
337C2×C4—23no—
338C2×C4—26no—
339C2×C4—23no—
340C2×C4—23no—
341C2×C4—48no—
342C2×C4—44no—
343C2×C4—812no—
344C2×C4—812no—
345C2×C4C2×#41×C13916yes—
346C22—212no—
347C22—212no—
348C22—41no—
349C22—43no—
350C22—43no—
351C22C2×#126×C13918yes—
352C22C22×#41×C13913yes—
353C22#585×C13913yes—
354C22#585×C13911yescharacteristic
355C4—41no—
356C4—42no—
357C4—43no—
358C4—43no—
359C4—46no—
360C4—46no—
361C4—43no—
362C4—43no—
363C4C2×#126×C13914yes—
364C2—28no—
365C2—81no—
366C2C22×#126×C13911yescharacteristic
367C2#3521×C13913yes—
368C2#3521×C13913yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC22×#41×C139C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2645×C139C2semidirect
2. #2643×C139C2semidirect
3. #2514×C139C2semidirect
4. #2510×C139C2semidirect
5. #2494×C139C2semidirect
6. #2493×C139C2semidirect
7. #2401×C139C2semidirect
8. C2×#401×C139C2semidirect
9. #2349×C139C2semidirect
11. #2275×C139C2semidirect
184. #36053C139direct (N × H)
185. C139#36053direct (N × H)
186. #2645C2×C139semidirect
187. #2643C2×C139semidirect
188. #2514C2×C139semidirect
189. #2510C2×C139semidirect
190. #2494C2×C139semidirect
191. #2493C2×C139semidirect
192. #2401C2×C139semidirect
193. C2×#401C2×C139semidirect
194. #2349C2×C139semidirect
196. #2275C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2645×C1392
#2643×C1392
#2514×C1392
#2510×C1392
#2494×C1392
#2493×C1392
#2401×C1392
C2×#401×C1392
#2349×C1392
#2339×C1392
#2275×C1392
#36053139