Finite Group Databasebeta

← C139×#8249 #48002845

Subgroups — C139×#8249 #48002845

Order 35584.

436 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2966×C139C211yesmaximal, characteristic
2#1726×C139C211yesmaximal, characteristic, complemented
3#1524×C139C211yesmaximal, characteristic
4#1500×C139C211yesmaximal, characteristic
5#1451×C139C211yesmaximal, characteristic, complemented
6#1302×C139C211yesmaximal, characteristic, complemented
7#1300×C139C211yesmaximal, characteristic, complemented
8#529×C139C2211yescharacteristic
9#446×C139C411yescharacteristic, complemented
10C8×Q8×C139C411yescharacteristic, complemented
11#436×C139C411yescharacteristic, complemented
12#435×C139—21no—
13C8×D4×C139—21no—
14C8×D4×C139C411yescharacteristic, complemented
15#433×C139—21no—
16#432×C139C2211yescharacteristic
17#431×C139C2211yescharacteristic
18#405×C139—21no—
19C4×M16×C139C2211yescharacteristic
20C2×#97×C139—21no—
21C2×#97×C139C2211yescharacteristic
22C2×C4×C8×C139—21no—
23C2×C4×C8×C139C2211yescharacteristic
24#376×C139C2211yescharacteristic
25#330×C139C412yescomplemented
26#329×C139C412yescomplemented
27#328×C139C412yes—
28#327×C139C412yes—
29#322×C139—21no—
30#322×C139—21no—
31C2×M16×C139—21no—
32C2×M16×C139—21no—
33C22×C8×C139—21no—
34C22×C8×C139—21no—
35C22×C8×C139D411yescharacteristic
36C22×C8×C139D411yescharacteristic
37#126×C139—21no—
38#125×C139C2×C411yescharacteristic
39#124×C139C2×C411yescharacteristic
40#123×C139—21no—
41C22⋊Q8×C139C2×C411yescharacteristic
42#121×C139C2×C411yescharacteristic
43C4×Q8×C139C2×C411yescharacteristic
44C4×D4×C139—21no—
45C4×D4×C139C2×C411yescharacteristic
46#117×C139—21no—
47C2×C42×C139—21no—
48C2×C42×C139C2311yescharacteristic
49C4⋊C8×C139—21no—
50C4⋊C8×C139—21no—
51C4⋊C8×C139—21no—
52C4⋊C8×C139C2×C411yescharacteristic
53C4⋊C8×C139C2×C411yescharacteristic
54C22⋊C8×C139—21no—
55C22⋊C8×C139—21no—
56C22⋊C8×C139—21no—
57C22⋊C8×C139C2×C412yes—
58#97×C139—24no—
59#97×C139—21no—
60#97×C139—21no—
61#97×C139—21no—
62#97×C139C2×C412yes—
63#97×C139C2×C412yes—
64C4×C8×C139—24no—
65C4×C8×C139—21no—
66C4×C8×C139—21no—
67C4×C8×C139—21no—
68C4×C8×C139C2×C411yescharacteristic
69C4×C8×C139C2×C411yescharacteristic
70C4×C8×C139D411yescharacteristic
71C4×C8×C139D411yescharacteristic
72#95×C139—21no—
73#95×C139C2×C412yes—
74C2×Q8×C139C4211yescharacteristic
75C2×D4×C139—21no—
76C2×D4×C139C4211yescharacteristic
77C22×C4×C139—22no—
78C22×C4×C139—21no—
79C22×C4×C139C22×C411yescharacteristic
80C22×C4×C139C2×D411yescharacteristic
81C22×C4×C139#4111yescharacteristic
82M16×C139—42no—
83M16×C139—42no—
84C2×C8×C139—22no—
85C2×C8×C139—22no—
86C2×C8×C139—22no—
87C2×C8×C139—22no—
88C2×C8×C139—22no—
89C2×C8×C139—21no—
90C2×C8×C139—21no—
91C2×C8×C139—22no—
92C2×C8×C139—22no—
93C2×C8×C139—42no—
94C2×C8×C139C22⋊C411yescharacteristic
95C2×C8×C139C22⋊C411yescharacteristic
96C2×C8×C139C22⋊C411yescharacteristic
97C2×C8×C139C22⋊C411yescharacteristic
98C4⋊C4×C139—21no—
99C4⋊C4×C139—21no—
100C4⋊C4×C139—21no—
101C4⋊C4×C139—21no—
102C4⋊C4×C139C4211yescharacteristic
103C4⋊C4×C139C4211yescharacteristic
104C22⋊C4×C139—21no—
105C22⋊C4×C139—21no—
106C22⋊C4×C139—21no—
107C22⋊C4×C139—21no—
108C22⋊C4×C139—21no—
109C42×C139—22no—
110C42×C139—22no—
111C42×C139—21no—
112C42×C139C22×C411yescharacteristic
113C42×C139C22×C411yescharacteristic
114C42×C139C2×D411yescharacteristic
115C42×C139#4111yescharacteristic
116C23×C139—21no—
117C23×C139C4×D411yescharacteristic
118Q8×C139—41no—
119D4×C139—41no—
120D4×C139—42no—
121C2×C4×C139—22no—
122C2×C4×C139—21no—
123C2×C4×C139—21no—
124C2×C4×C139—24no—
125C2×C4×C139—21no—
126C2×C4×C139—21no—
127C2×C4×C139—21no—
128C2×C4×C139—41no—
129C2×C4×C139—42no—
130C2×C4×C139—42no—
131C2×C4×C139—41no—
132C2×C4×C139—41no—
133C2×C4×C139C2×C4211yescharacteristic
134C2×C4×C139C2×C22⋊C411yescharacteristic
135C2×C4×C139#11711yescharacteristic
136C2×C4×C139C4×D411yescharacteristic
137C2×C4×C139C4×D411yescharacteristic
138C2×C4×C139C4×D411yescharacteristic
139C8×C139—24no—
140C8×C139—21no—
141C8×C139—21no—
142C8×C139—42no—
143C8×C139—42no—
144C8×C139—41no—
145C8×C139—41no—
146C8×C139#10412yes—
147C8×C139#10412yes—
148C22×C139—21no—
149C22×C139—21no—
150C22×C139—41no—
151C22×C139—41no—
152C22×C139—41no—
153C22×C139C4×C22⋊C411yescharacteristic
154C22×C139#44412yes—
155C4×C139—21no—
156C4×C139—21no—
157C4×C139—21no—
158C4×C139—21no—
159C4×C139—21no—
160C4×C139—44no—
161C4×C139—41no—
162C4×C139—41no—
163C4×C139—41no—
164C4×C139C2×#10411yescharacteristic
165C4×C139C2×#10411yescharacteristic
166C2×C139—22no—
167C2×C139—81no—
168C2×C139#175711yescharacteristic
169C2×C139C4×#10411yescharacteristic
170C2×C139#176511yescharacteristic
171#8249C13911yesmaximal, characteristic, direct product factor, Sylow
172C139#824911yescharacteristic, direct product factor, Sylow
173#2966C2×C13911yescharacteristic
174#1726C2×C13911yescharacteristic, complemented
175#1524C2×C13911yescharacteristic
176#1500C2×C13911yescharacteristic
177#1451C2×C13911yescharacteristic, complemented
178#1302C2×C13911yescharacteristic, complemented
179#1300C2×C13911yescharacteristic, complemented
180#529C22×C13911yescharacteristic
181#446C4×C13911yescharacteristic, complemented
182C8×Q8C4×C13911yescharacteristic, complemented
183#436C4×C13911yescharacteristic, complemented
184#435—21no—
185C8×D4—21no—
186C8×D4C4×C13911yescharacteristic, complemented
187#433—21no—
188#432C22×C13911yescharacteristic
189#431C22×C13911yescharacteristic
190#405—21no—
191C4×M16C22×C13911yescharacteristic
192C2×#97—21no—
193C2×#97C22×C13911yescharacteristic
194C2×C4×C8—21no—
195C2×C4×C8C22×C13911yescharacteristic
196#376C22×C13911yescharacteristic
197#330C4×C13912yescomplemented
198#329C4×C13912yescomplemented
199#328C4×C13912yes—
200#327C4×C13912yes—
201#322—21no—
202#322—21no—
203C2×M16—21no—
204C2×M16—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8D4×C13911yescharacteristic
208C22×C8D4×C13911yescharacteristic
209#126—21no—
210#125C2×C4×C13911yescharacteristic
211#124C2×C4×C13911yescharacteristic
212#123—21no—
213C22⋊Q8C2×C4×C13911yescharacteristic
214#121C2×C4×C13911yescharacteristic
215C4×Q8C2×C4×C13911yescharacteristic
216C4×D4—21no—
217C4×D4C2×C4×C13911yescharacteristic
218#117—21no—
219C2×C42—21no—
220C2×C42C23×C13911yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8C2×C4×C13911yescharacteristic
225C4⋊C8C2×C4×C13911yescharacteristic
226C22⋊C8—21no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229C22⋊C8C2×C4×C13912yes—
230#97—24no—
231#97—21no—
232#97—21no—
233#97—21no—
234#97C2×C4×C13912yes—
235#97C2×C4×C13912yes—
236C4×C8—24no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8—21no—
240C4×C8C2×C4×C13911yescharacteristic
241C4×C8C2×C4×C13911yescharacteristic
242C4×C8D4×C13911yescharacteristic
243C4×C8D4×C13911yescharacteristic
244#95—21no—
245#95C2×C4×C13912yes—
246C2×Q8C42×C13911yescharacteristic
247C2×D4—21no—
248C2×D4C42×C13911yescharacteristic
249C22×C4—22no—
250C22×C4—21no—
251C22×C4C22×C4×C13911yescharacteristic
252C22×C4C2×D4×C13911yescharacteristic
253C22×C4#41×C13911yescharacteristic
254M16—42no—
255M16—42no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—42no—
266C2×C8C22⋊C4×C13911yescharacteristic
267C2×C8C22⋊C4×C13911yescharacteristic
268C2×C8C22⋊C4×C13911yescharacteristic
269C2×C8C22⋊C4×C13911yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4C42×C13911yescharacteristic
275C4⋊C4C42×C13911yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C42—22no—
282C42—22no—
283C42—21no—
284C42C22×C4×C13911yescharacteristic
285C42C22×C4×C13911yescharacteristic
286C42C2×D4×C13911yescharacteristic
287C42#41×C13911yescharacteristic
288C23—21no—
289C23C4×D4×C13911yescharacteristic
290Q8—41no—
291D4—41no—
292D4—42no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4C2×C42×C13911yescharacteristic
306C2×C4C2×C22⋊C4×C13911yescharacteristic
307C2×C4#117×C13911yescharacteristic
308C2×C4C4×D4×C13911yescharacteristic
309C2×C4C4×D4×C13911yescharacteristic
310C2×C4C4×D4×C13911yescharacteristic
311C8—24no—
312C8—21no—
313C8—21no—
314C8—42no—
315C8—42no—
316C8—41no—
317C8—41no—
318C8#104×C13912yes—
319C8#104×C13912yes—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22C4×C22⋊C4×C13911yescharacteristic
326C22#444×C13912yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—44no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4C2×#104×C13911yescharacteristic
337C4C2×#104×C13911yescharacteristic
338C2—22no—
339C2—81no—
340C2#1757×C13911yescharacteristic
341C2C4×#104×C13911yescharacteristic
342C2#1765×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139C2×C22⋊C4
commutatorC2×C4C2×C42×C139
Frattini, cosocleC2×C42C23×C139
socleC22×C139C4×C22⋊C4
prime radical#121×C139C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C2×C4×C8×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1726×C139C2semidirect
5. #1451×C139C2semidirect
6. #1302×C139C2semidirect
7. #1300×C139C2semidirect
9. #446×C139C4semidirect
10. C8×Q8×C139C4semidirect
11. #436×C139C4semidirect
14. C8×D4×C139C4semidirect
25. #330×C139C4semidirect
26. #329×C139C4semidirect
171. #8249C139direct (N × H)
172. C139#8249direct (N × H)
174. #1726C2×C139semidirect
177. #1451C2×C139semidirect
178. #1302C2×C139semidirect
179. #1300C2×C139semidirect
181. #446C4×C139semidirect
182. C8×Q8C4×C139semidirect
183. #436C4×C139semidirect
186. C8×D4C4×C139semidirect
197. #330C4×C139semidirect
198. #329C4×C139semidirect

Maximal subgroups

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

subgroupindex
#2966×C1392
#1726×C1392
#1524×C1392
#1500×C1392
#1451×C1392
#1302×C1392
#1300×C1392
#8249139