Finite Group Databasebeta

← C139×#36090 #48030686

Subgroups — C139×#36090 #48030686

Order 35584.

1516 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2634×C139C213yesmaximal
2#2605×C139C213yesmaximal
3#2565×C139C213yesmaximal
4#2524×C139C216yesmaximal
5#2520×C139C216yesmaximal
6#2399×C139C213yesmaximal
7#2371×C139C213yesmaximal
8#2356×C139C213yesmaximal
9#2276×C139C211yesmaximal, characteristic
10C2×#125×C139C2213yes—
11C2×C4×Q8×C139C2213yes—
12C2×C4×Q8×C139C2213yes—
13#400×C139C2216yes—
14#400×C139C2216yes—
15#398×C139C2213yes—
16#398×C139C2216yes—
17#398×C139C2213yes—
18#398×C139C2216yes—
19#395×C139C2216yes—
20#395×C139C2213yes—
21#395×C139C2211yescharacteristic
22#391×C139C2213yes—
23#391×C139C2216yes—
24#391×C139C2213yes—
25#387×C139C2216yes—
26#387×C139C2216yes—
27#387×C139C2216yes—
28#387×C139C2216yes—
29#387×C139C2216yes—
30#387×C139C2216yes—
31#387×C139C2216yes—
32#387×C139C2216yes—
33#384×C139C2211yescharacteristic
34#383×C139C2212yes—
35#383×C139C2213yes—
36#383×C139C2213yes—
37#382×C139C2213yes—
38#382×C139C2213yes—
39C4×C4⋊C4×C139C2216yes—
40C4×C4⋊C4×C139C2216yes—
41C4×C4⋊C4×C139C2216yes—
42C4×C4⋊C4×C139C2213yes—
43C4×C4⋊C4×C139C2213yes—
44#376×C139C2213yes—
45#376×C139C2213yes—
46#376×C139C2211yescharacteristic
47C22×Q8×C139C2311yescharacteristic
48C22×Q8×C139C2313yes—
49#125×C139—212no—
50C4×Q8×C139—212no—
51C4×Q8×C139—212no—
52C2×C4⋊C4×C139C2313yes—
53C2×C4⋊C4×C139C2313yes—
54C2×C4⋊C4×C139C2316yes—
55C2×C4⋊C4×C139C2316yes—
56C2×C4⋊C4×C139C2316yes—
57C2×C4⋊C4×C139C2313yes—
58C2×C4⋊C4×C139C2313yes—
59C2×C4⋊C4×C139C2313yes—
60C2×C4⋊C4×C139C2313yes—
61C2×C4⋊C4×C139C2316yes—
62C2×C4⋊C4×C139C2316yes—
63C2×C42×C139C2316yes—
64C2×C42×C139C2313yes—
65C2×C42×C139C2313yes—
66C2×C42×C139C2316yes—
67C2×C42×C139C2313yes—
68C2×C42×C139C2312yes—
69C2×C42×C139C2311yescharacteristic
70C2×C42×C139C2313yes—
71#95×C139C2313yes—
72#95×C139C2316yes—
73#95×C139C2313yes—
74#95×C139C2316yes—
75#95×C139C2316yes—
76#95×C139C2316yes—
77#95×C139C2316yes—
78#95×C139C2316yes—
79#95×C139C2316yes—
80#95×C139C2316yes—
81#95×C139C2316yes—
82#95×C139C2311yescharacteristic
83#95×C139C2313yes—
84#95×C139C2316yes—
85#95×C139C2313yes—
86#95×C139C2313yes—
87C2×Q8×C139—26no—
88C2×Q8×C139—26no—
89C2×Q8×C139—26no—
90C2×Q8×C139—43no—
91C22×C4×C139C2416yes—
92C22×C4×C139C2413yes—
93C22×C4×C139C2416yes—
94C22×C4×C139C2411yescharacteristic
95C22×C4×C139C2413yes—
96C22×C4×C139C2413yes—
97C22×C4×C139C2413yes—
98C22×C4×C139C2413yes—
99C22×C4×C139C2413yes—
100C4⋊C4×C139—26no—
101C4⋊C4×C139—212no—
102C4⋊C4×C139—26no—
103C4⋊C4×C139—26no—
104C4⋊C4×C139—26no—
105C4⋊C4×C139—212no—
106C4⋊C4×C139—212no—
107C4⋊C4×C139—26no—
108C4⋊C4×C139—26no—
109C4⋊C4×C139—212no—
110C4⋊C4×C139—46no—
111C42×C139—212no—
112C42×C139—26no—
113C42×C139—26no—
114C42×C139—212no—
115C42×C139—41no—
116C42×C139—43no—
117C42×C139—42no—
118C42×C139#41112yes—
119C23×C139C2511yescharacteristic
120Q8×C139—28no—
121Q8×C139—412no—
122C2×C4×C139—26no—
123C2×C4×C139—23no—
124C2×C4×C139—26no—
125C2×C4×C139—23no—
126C2×C4×C139—23no—
127C2×C4×C139—23no—
128C2×C4×C139—23no—
129C2×C4×C139—23no—
130C2×C4×C139—26no—
131C2×C4×C139—23no—
132C2×C4×C139—26no—
133C2×C4×C139—26no—
134C2×C4×C139—26no—
135C2×C4×C139—26no—
136C2×C4×C139—26no—
137C2×C4×C139—23no—
138C2×C4×C139—26no—
139C2×C4×C139—23no—
140C2×C4×C139C2×#4116yes—
141C2×C4×C139C2×#4116yes—
142C2×C4×C139C2×#4116yes—
143C2×C4×C1392−1+416yes—
144C22×C139C22×#4113yes—
145C22×C139C2×2−1+413yes—
146C22×C139#58511yescharacteristic
147C4×C139—26no—
148C4×C139—26no—
149C4×C139—26no—
150C4×C139—26no—
151C4×C139—41no—
152C4×C139—43no—
153C4×C139—46no—
154C4×C139—43no—
155C4×C139—46no—
156C2×C139#344411yescharacteristic
157C2×C139#349513yes—
158C2×C139#350913yes—
159#36090C13911yesmaximal, characteristic, direct product factor, Sylow
160C139#3609011yescharacteristic, direct product factor, Sylow
161#2634C2×C13913yes—
162#2605C2×C13913yes—
163#2565C2×C13913yes—
164#2524C2×C13916yes—
165#2520C2×C13916yes—
166#2399C2×C13913yes—
167#2371C2×C13913yes—
168#2356C2×C13913yes—
169#2276C2×C13911yescharacteristic
170C2×#125C22×C13913yes—
171C2×C4×Q8C22×C13913yes—
172C2×C4×Q8C22×C13913yes—
173#400C22×C13916yes—
174#400C22×C13916yes—
175#398C22×C13916yes—
176#398C22×C13916yes—
177#398C22×C13913yes—
178#398C22×C13913yes—
179#395C22×C13916yes—
180#395C22×C13913yes—
181#395C22×C13911yescharacteristic
182#391C22×C13913yes—
183#391C22×C13913yes—
184#391C22×C13916yes—
185#387C22×C13916yes—
186#387C22×C13916yes—
187#387C22×C13916yes—
188#387C22×C13916yes—
189#387C22×C13916yes—
190#387C22×C13916yes—
191#387C22×C13916yes—
192#387C22×C13916yes—
193#384C22×C13911yescharacteristic
194#383C22×C13913yes—
195#383C22×C13913yes—
196#383C22×C13912yes—
197#382C22×C13913yes—
198#382C22×C13913yes—
199C4×C4⋊C4C22×C13913yes—
200C4×C4⋊C4C22×C13913yes—
201C4×C4⋊C4C22×C13916yes—
202C4×C4⋊C4C22×C13916yes—
203C4×C4⋊C4C22×C13916yes—
204#376C22×C13913yes—
205#376C22×C13911yescharacteristic
206#376C22×C13913yes—
207C22×Q8C23×C13911yescharacteristic
208C22×Q8C23×C13913yes—
209#125—212no—
210C4×Q8—212no—
211C4×Q8—212no—
212C2×C4⋊C4C23×C13913yes—
213C2×C4⋊C4C23×C13916yes—
214C2×C4⋊C4C23×C13913yes—
215C2×C4⋊C4C23×C13913yes—
216C2×C4⋊C4C23×C13913yes—
217C2×C4⋊C4C23×C13916yes—
218C2×C4⋊C4C23×C13916yes—
219C2×C4⋊C4C23×C13913yes—
220C2×C4⋊C4C23×C13913yes—
221C2×C4⋊C4C23×C13916yes—
222C2×C4⋊C4C23×C13916yes—
223C2×C42C23×C13916yes—
224C2×C42C23×C13913yes—
225C2×C42C23×C13913yes—
226C2×C42C23×C13916yes—
227C2×C42C23×C13913yes—
228C2×C42C23×C13912yes—
229C2×C42C23×C13911yescharacteristic
230C2×C42C23×C13913yes—
231#95C23×C13911yescharacteristic
232#95C23×C13913yes—
233#95C23×C13916yes—
234#95C23×C13913yes—
235#95C23×C13913yes—
236#95C23×C13916yes—
237#95C23×C13913yes—
238#95C23×C13916yes—
239#95C23×C13913yes—
240#95C23×C13916yes—
241#95C23×C13916yes—
242#95C23×C13916yes—
243#95C23×C13916yes—
244#95C23×C13916yes—
245#95C23×C13916yes—
246#95C23×C13916yes—
247C2×Q8—26no—
248C2×Q8—26no—
249C2×Q8—26no—
250C2×Q8—43no—
251C22×C4C24×C13916yes—
252C22×C4C24×C13913yes—
253C22×C4C24×C13916yes—
254C22×C4C24×C13911yescharacteristic
255C22×C4C24×C13913yes—
256C22×C4C24×C13913yes—
257C22×C4C24×C13913yes—
258C22×C4C24×C13913yes—
259C22×C4C24×C13913yes—
260C4⋊C4—26no—
261C4⋊C4—212no—
262C4⋊C4—26no—
263C4⋊C4—26no—
264C4⋊C4—26no—
265C4⋊C4—212no—
266C4⋊C4—212no—
267C4⋊C4—26no—
268C4⋊C4—26no—
269C4⋊C4—212no—
270C4⋊C4—46no—
271C42—212no—
272C42—26no—
273C42—26no—
274C42—212no—
275C42—41no—
276C42—43no—
277C42—42no—
278C42#41×C139112yes—
279C23C25×C13911yescharacteristic
280Q8—28no—
281Q8—412no—
282C2×C4—26no—
283C2×C4—23no—
284C2×C4—26no—
285C2×C4—23no—
286C2×C4—23no—
287C2×C4—23no—
288C2×C4—23no—
289C2×C4—23no—
290C2×C4—26no—
291C2×C4—23no—
292C2×C4—26no—
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—23no—
298C2×C4—26no—
299C2×C4—23no—
300C2×C4C2×#41×C13916yes—
301C2×C4C2×#41×C13916yes—
302C2×C4C2×#41×C13916yes—
303C2×C42−1+4×C13916yes—
304C22C22×#41×C13913yes—
305C22C2×2−1+4×C13913yes—
306C22#585×C13911yescharacteristic
307C4—26no—
308C4—26no—
309C4—26no—
310C4—26no—
311C4—41no—
312C4—43no—
313C4—43no—
314C4—46no—
315C4—46no—
316C2#3444×C13911yescharacteristic
317C2#3495×C13913yes—
318C2#3509×C13913yes—
subgroupG/H
center, socle, prime radicalC23×C139C25
commutator, Frattini, cosocleC23C25×C139
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
159. #36090C139direct (N × H)
160. C139#36090direct (N × H)

Maximal subgroups

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

subgroupindex
#2634×C1392
#2605×C1392
#2565×C1392
#2524×C1392
#2520×C1392
#2399×C1392
#2371×C1392
#2356×C1392
#2276×C1392
#36090139