Finite Group Databasebeta

← C139×#9181 #48003777

Subgroups — C139×#9181 #48003777

Order 35584.

548 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3036×C139C211yesmaximal, characteristic
2#2357×C139C211yesmaximal, characteristic, complemented
3#1517×C139C211yesmaximal, characteristic, complemented
4#1502×C139C211yesmaximal, characteristic, complemented
5#1478×C139C211yesmaximal, characteristic, complemented
6#1303×C139C211yesmaximal, characteristic, complemented
7#1286×C139C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C139—21no—
9#532×C139C2211yescharacteristic
10C2×C4×D4×C139C2211yescharacteristic
11#463×C139—22no—
12#461×C139C412yescomplemented
13#459×C139C412yescomplemented
14#431×C139C2211yescharacteristic
15#431×C139C2211yescharacteristic
16#423×C139C2211yescharacteristic
17#417×C139—21no—
18#390×C139—21no—
19#388×C139—22no—
20#382×C139C2211yescharacteristic
21#381×C139—21no—
22C4×C4⋊C4×C139—21no—
23C4×C4⋊C4×C139C2211yescharacteristic
24C4×C22⋊C4×C139—21no—
25#327×C139—21no—
26#327×C139—21no—
27#327×C139—22no—
28D4⋊C8×C139—22no—
29C2×#41×C139—21no—
30C22×D4×C139D411yescharacteristic
31C23×C4×C139—21no—
32AGL(1,ℤ/8)×C139—42no—
33AGL(1,ℤ/8)×C139—42no—
34C2×SD16×C139—22no—
35C2×D8×C139—22no—
36C2×M16×C139—21no—
37C4⋊Q8×C139C2×C411yescharacteristic
38#127×C139C2×C411yescharacteristic
39#124×C139—21no—
40#121×C139—21no—
41#121×C139—21no—
42C4×D4×C139—21no—
43C4×D4×C139—21no—
44C4×D4×C139—21no—
45C4×D4×C139—21no—
46C4×D4×C139C2×C412yes—
47C4×D4×C139D412yes—
48C2×C4⋊C4×C139—21no—
49C2×C4⋊C4×C139—21no—
50C2×C4⋊C4×C139D411yescharacteristic
51C2×C22⋊C4×C139—21no—
52C2×C22⋊C4×C139—22no—
53C2×C22⋊C4×C139—22no—
54C2×C42×C139—21no—
55C2×C42×C139—22no—
56C2×C42×C139C2311yescharacteristic
57C4⋊C8×C139—21no—
58C4⋊C8×C139—21no—
59C4⋊C8×C139—21no—
60C4⋊C8×C139C2×C412yes—
61#103×C139—22no—
62#102×C139—22no—
63C22⋊C8×C139—21no—
64C22⋊C8×C139—21no—
65C4×C8×C139—21no—
66C4×C8×C139—21no—
67#95×C139—22no—
68#95×C139—21no—
69#95×C139D411yescharacteristic
70#95×C139D411yescharacteristic
71#95×C139D412yes—
72C24×C139—21no—
73#41×C139—41no—
74#41×C139—41no—
75#41×C139—41no—
76#41×C139—41no—
77C2×Q8×C139—21no—
78C2×D4×C139—21no—
79C2×D4×C139—21no—
80C2×D4×C139—21no—
81C2×D4×C139—21no—
82C2×D4×C139—21no—
83C2×D4×C139—21no—
84C2×D4×C139—21no—
85C2×D4×C139—21no—
86C2×D4×C139—41no—
87C2×D4×C139C22⋊C412yes—
88C22×C4×C139—21no—
89C22×C4×C139—21no—
90C22×C4×C139—22no—
91C22×C4×C139—22no—
92C22×C4×C139—22no—
93C22×C4×C139—21no—
94C22×C4×C139—41no—
95C22×C4×C139—82no—
96C22×C4×C139C2×D411yescharacteristic
97C22×C4×C139C2×D411yescharacteristic
98C22×C4×C139C2×D411yescharacteristic
99SD16×C139—44no—
100D8×C139—44no—
101M16×C139—41no—
102M16×C139—41no—
103C2×C8×C139—22no—
104C2×C8×C139—41no—
105C2×C8×C139—41no—
106C4⋊C4×C139—21no—
107C4⋊C4×C139—21no—
108C4⋊C4×C139—21no—
109C4⋊C4×C139—42no—
110C4⋊C4×C139—41no—
111C4⋊C4×C139—41no—
112C4⋊C4×C139C22⋊C412yes—
113C22⋊C4×C139—22no—
114C22⋊C4×C139—22no—
115C22⋊C4×C139—44no—
116C22⋊C4×C139—41no—
117C22⋊C4×C139—41no—
118C22⋊C4×C139—82no—
119C42×C139—41no—
120C42×C139—41no—
121C42×C139—82no—
122C42×C139C22×C411yescharacteristic
123C42×C139C2×D411yescharacteristic
124C42×C139#4111yescharacteristic
125C42×C139#4111yescharacteristic
126C23×C139—22no—
127C23×C139—42no—
128C23×C139—42no—
129C23×C139—41no—
130C23×C139—41no—
131C23×C139—41no—
132C23×C139#12011yescharacteristic
133Q8×C139—41no—
134Q8×C139—41no—
135D4×C139—22no—
136D4×C139—22no—
137D4×C139—41no—
138D4×C139—41no—
139D4×C139—41no—
140D4×C139—41no—
141D4×C139—81no—
142D4×C139—81no—
143D4×C139—81no—
144D4×C139—81no—
145C2×C4×C139—22no—
146C2×C4×C139—22no—
147C2×C4×C139—41no—
148C2×C4×C139—41no—
149C2×C4×C139—41no—
150C2×C4×C139—42no—
151C2×C4×C139—41no—
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—42no—
159C2×C4×C139—82no—
160C2×C4×C139—82no—
161C2×C4×C139—81no—
162C2×C4×C139—81no—
163C2×C4×C139C2×C22⋊C411yescharacteristic
164C2×C4×C139C4×D411yescharacteristic
165C2×C4×C139C4×D411yescharacteristic
166C2×C4×C139#12111yescharacteristic
167C2×C4×C139#12111yescharacteristic
168C2×C4×C139#12311yescharacteristic
169C2×C4×C139#13511yescharacteristic
170C2×C4×C139#13511yescharacteristic
171C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
173C8×C139—42no—
174C8×C139—81no—
175C8×C139—81no—
176C22×C139—21no—
177C22×C139—21no—
178C22×C139—42no—
179C22×C139—42no—
180C22×C139—42no—
181C22×C139—82no—
182C22×C139—82no—
183C22×C139—81no—
184C22×C139—81no—
185C22×C139—81no—
186C22×C139#38611yescharacteristic
187C22×C139#44911yescharacteristic
188C22×C139#44911yescharacteristic
189C4×C139—21no—
190C4×C139—21no—
191C4×C139—21no—
192C4×C139—21no—
193C4×C139—42no—
194C4×C139—42no—
195C4×C139—81no—
196C4×C139—82no—
197C4×C139—81no—
198C4×C139#41611yescharacteristic
199C4×C139#41811yescharacteristic
200C4×C139#48211yescharacteristic
201C4×C139#48211yescharacteristic
202C2×C139—21no—
203C2×C139—21no—
204C2×C139—82no—
205C2×C139—161no—
206C2×C139#187511yescharacteristic
207C2×C139#190411yescharacteristic
208C2×C139#190611yescharacteristic
209#9181C13911yesmaximal, characteristic, direct product factor, Sylow
210C139#918111yescharacteristic, direct product factor, Sylow
211#3036C2×C13911yescharacteristic
212#2357C2×C13911yescharacteristic, complemented
213#1517C2×C13911yescharacteristic, complemented
214#1502C2×C13911yescharacteristic, complemented
215#1478C2×C13911yescharacteristic, complemented
216#1303C2×C13911yescharacteristic, complemented
217#1286C2×C13911yescharacteristic, complemented
218C2×AGL(1,ℤ/8)—21no—
219#532C22×C13911yescharacteristic
220C2×C4×D4C22×C13911yescharacteristic
221#463—22no—
222#461C4×C13912yescomplemented
223#459C4×C13912yescomplemented
224#431C22×C13911yescharacteristic
225#431C22×C13911yescharacteristic
226#423C22×C13911yescharacteristic
227#417—21no—
228#390—21no—
229#388—22no—
230#382C22×C13911yescharacteristic
231#381—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4C22×C13911yescharacteristic
234C4×C22⋊C4—21no—
235#327—21no—
236#327—21no—
237#327—22no—
238D4⋊C8—22no—
239C2×#41—21no—
240C22×D4D4×C13911yescharacteristic
241C23×C4—21no—
242AGL(1,ℤ/8)—42no—
243AGL(1,ℤ/8)—42no—
244C2×SD16—22no—
245C2×D8—22no—
246C2×M16—21no—
247C4⋊Q8C2×C4×C13911yescharacteristic
248#127C2×C4×C13911yescharacteristic
249#124—21no—
250#121—21no—
251#121—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4C2×C4×C13912yes—
257C4×D4D4×C13912yes—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4D4×C13911yescharacteristic
261C2×C22⋊C4—21no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C42—21no—
265C2×C42—22no—
266C2×C42C23×C13911yescharacteristic
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8C2×C4×C13912yes—
271#103—22no—
272#102—22no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C4×C8—21no—
276C4×C8—21no—
277#95—22no—
278#95—21no—
279#95D4×C13911yescharacteristic
280#95D4×C13911yescharacteristic
281#95D4×C13912yes—
282C24—21no—
283#41—41no—
284#41—41no—
285#41—41no—
286#41—41no—
287C2×Q8—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4C22⋊C4×C13912yes—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—82no—
306C22×C4C2×D4×C13911yescharacteristic
307C22×C4C2×D4×C13911yescharacteristic
308C22×C4C2×D4×C13911yescharacteristic
309SD16—44no—
310D8—44no—
311M16—41no—
312M16—41no—
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4C22⋊C4×C13912yes—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—44no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—82no—
329C42—41no—
330C42—41no—
331C42—82no—
332C42C22×C4×C13911yescharacteristic
333C42C2×D4×C13911yescharacteristic
334C42#41×C13911yescharacteristic
335C42#41×C13911yescharacteristic
336C23—22no—
337C23—42no—
338C23—42no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23#120×C13911yescharacteristic
343Q8—41no—
344Q8—41no—
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—41no—
351D4—81no—
352D4—81no—
353D4—81no—
354D4—81no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4C2×C22⋊C4×C13911yescharacteristic
374C2×C4C4×D4×C13911yescharacteristic
375C2×C4C4×D4×C13911yescharacteristic
376C2×C4#121×C13911yescharacteristic
377C2×C4#121×C13911yescharacteristic
378C2×C4#123×C13911yescharacteristic
379C2×C4#135×C13911yescharacteristic
380C2×C4#135×C13911yescharacteristic
381C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
382C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
383C8—42no—
384C8—81no—
385C8—81no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—82no—
392C22—82no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22#386×C13911yescharacteristic
397C22#449×C13911yescharacteristic
398C22#449×C13911yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C4—81no—
406C4—82no—
407C4—81no—
408C4#416×C13911yescharacteristic
409C4#418×C13911yescharacteristic
410C4#482×C13911yescharacteristic
411C4#482×C13911yescharacteristic
412C2—21no—
413C2—21no—
414C2—82no—
415C2—161no—
416C2#1875×C13911yescharacteristic
417C2#1904×C13911yescharacteristic
418C2#1906×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radical#3036×C139C2
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
2. #2357×C139C2semidirect
3. #1517×C139C2semidirect
4. #1502×C139C2semidirect
5. #1478×C139C2semidirect
6. #1303×C139C2semidirect
7. #1286×C139C2semidirect
12. #461×C139C4semidirect
13. #459×C139C4semidirect
209. #9181C139direct (N × H)
210. C139#9181direct (N × H)
212. #2357C2×C139semidirect
213. #1517C2×C139semidirect
214. #1502C2×C139semidirect
215. #1478C2×C139semidirect
216. #1303C2×C139semidirect
217. #1286C2×C139semidirect
222. #461C4×C139semidirect
223. #459C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3036×C1392
#2357×C1392
#1517×C1392
#1502×C1392
#1478×C1392
#1303×C1392
#1286×C1392
#9181139