Finite Group Databasebeta

← C139×#8504 #48003100

Subgroups — C139×#8504 #48003100

Order 35584.

728 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3529×C139C211yesmaximal, characteristic
2#1963×C139C211yesmaximal, characteristic, complemented
3#1543×C139C211yesmaximal, characteristic, complemented
4#1500×C139C212yesmaximal, complemented
5#1495×C139C212yesmaximal, complemented
6#563×C139—21no—
7#563×C139C411yescharacteristic, complemented
8#562×C139—22no—
9#562×C139C412yescomplemented
10H(3,𝔽4)×C139C411yescharacteristic, complemented
11#560×C139—21no—
12#560×C139—22no—
13#532×C139—21no—
14#532×C139C2211yescharacteristic
15#529×C139—22no—
16#529×C139C2212yes—
17#525×C139—21no—
18#525×C139—22no—
19#431×C139C2212yescomplemented
20#423×C139C2211yescharacteristic, complemented
21C2×#104×C139—21no—
22C2×#104×C139—21no—
23#376×C139C2211yescharacteristic, complemented
24#333×C139—21no—
25#331×C139—21no—
26#328×C139—22no—
27#327×C139—22no—
28Q8⋊C8×C139—22no—
29D4⋊C8×C139—22no—
30C2×#41×C139—21no—
31C2×#41×C139D411yescharacteristic
32C2×#41×C139D411yescharacteristic
33C23×C4×C139—21no—
34C2×M16×C139—21no—
35C4⋊Q8×C139—21no—
36C4⋊Q8×C139D411yescharacteristic
37#127×C139—21no—
38#127×C139D411yescharacteristic
39#126×C139—22no—
40#126×C139—22no—
41#126×C139—22no—
42#125×C139—22no—
43#125×C139C2×C412yes—
44#124×C139—21no—
45#124×C139—22no—
46#124×C139—21no—
47#124×C139C2×C412yes—
48#124×C139C2×C411yescharacteristic
49#124×C139C2×C411yescharacteristic
50#123×C139—22no—
51#123×C139—21no—
52#123×C139—22no—
53#123×C139—21no—
54#123×C139—22no—
55#123×C139—22no—
56#123×C139—22no—
57C22⋊Q8×C139—22no—
58C22⋊Q8×C139—22no—
59C22⋊Q8×C139—22no—
60C22⋊Q8×C139—22no—
61C22⋊Q8×C139D412yes—
62#121×C139—22no—
63#121×C139—22no—
64#121×C139—22no—
65#121×C139—22no—
66#121×C139—22no—
67#121×C139—22no—
68#121×C139—22no—
69#121×C139D412yes—
70#120×C139—21no—
71#120×C139—22no—
72#120×C139—21no—
73#120×C139—22no—
74C4×Q8×C139D412yes—
75C4×D4×C139—22no—
76C4×D4×C139—22no—
77C4×D4×C139—22no—
78C4×D4×C139—22no—
79C4×D4×C139D412yes—
80#117×C139—21no—
81#117×C139—22no—
82C2×C42×C139—21no—
83C2×C42×C139—21no—
84C2×C42×C139C2311yescharacteristic
85C4⋊C8×C139—22no—
86C4⋊C8×C139—22no—
87#104×C139—42no—
88#104×C139—42no—
89C22⋊C8×C139—22no—
90C4×C8×C139—22no—
91#95×C139—22no—
92C24×C139—21no—
93#41×C139—41no—
94#41×C139—41no—
95#41×C139—41no—
96#41×C139—41no—
97#41×C139—81no—
98#41×C139—81no—
99C2×Q8×C139—21no—
100C2×Q8×C139C22⋊C412yes—
101C2×Q8×C139C22⋊C411yescharacteristic
102C2×Q8×C139C22⋊C411yescharacteristic
103C2×D4×C139—22no—
104C2×D4×C139—22no—
105C2×D4×C139—21no—
106C2×D4×C139—22no—
107C2×D4×C139—22no—
108C2×D4×C139—21no—
109C2×D4×C139—21no—
110C2×D4×C139—22no—
111C2×D4×C139C22⋊C412yes—
112C2×D4×C139C22⋊C411yescharacteristic
113C2×D4×C139C22⋊C411yescharacteristic
114C22×C4×C139—22no—
115C22×C4×C139—22no—
116C22×C4×C139—21no—
117C22×C4×C139—21no—
118C22×C4×C139—21no—
119C22×C4×C139—22no—
120C22×C4×C139—41no—
121C22×C4×C139—81no—
122C22×C4×C139—81no—
123C22×C4×C139C2×D411yescharacteristic
124C22×C4×C139C2×D412yes—
125M16×C139—41no—
126M16×C139—41no—
127C2×C8×C139—42no—
128C2×C8×C139—41no—
129C4⋊C4×C139—22no—
130C4⋊C4×C139—22no—
131C4⋊C4×C139—22no—
132C4⋊C4×C139—22no—
133C4⋊C4×C139—22no—
134C4⋊C4×C139—22no—
135C4⋊C4×C139—22no—
136C4⋊C4×C139—22no—
137C4⋊C4×C139C22⋊C412yes—
138C4⋊C4×C139C22⋊C412yes—
139C22⋊C4×C139—21no—
140C22⋊C4×C139—21no—
141C22⋊C4×C139—22no—
142C22⋊C4×C139—22no—
143C22⋊C4×C139—22no—
144C22⋊C4×C139—22no—
145C22⋊C4×C139—22no—
146C22⋊C4×C139—22no—
147C22⋊C4×C139—22no—
148C22⋊C4×C139—22no—
149C22⋊C4×C139—22no—
150C22⋊C4×C139—22no—
151C22⋊C4×C139—22no—
152C42×C139—21no—
153C42×C139—21no—
154C42×C139—22no—
155C42×C139—22no—
156C42×C139—41no—
157C42×C139C22×C411yescharacteristic
158C42×C139C2×D411yescharacteristic
159C42×C139C2×D412yes—
160C23×C139—21no—
161C23×C139—22no—
162C23×C139—21no—
163C23×C139—81no—
164C23×C139—82no—
165C23×C139#12011yescharacteristic
166Q8×C139—42no—
167Q8×C139—41no—
168Q8×C139—41no—
169Q8×C139—81no—
170D4×C139—42no—
171D4×C139—41no—
172D4×C139—41no—
173D4×C139—82no—
174D4×C139—82no—
175D4×C139—81no—
176D4×C139—81no—
177D4×C139—82no—
178D4×C139—82no—
179D4×C139—82no—
180D4×C139—81no—
181C2×C4×C139—21no—
182C2×C4×C139—21no—
183C2×C4×C139—22no—
184C2×C4×C139—22no—
185C2×C4×C139—21no—
186C2×C4×C139—21no—
187C2×C4×C139—22no—
188C2×C4×C139—42no—
189C2×C4×C139—41no—
190C2×C4×C139—42no—
191C2×C4×C139—41no—
192C2×C4×C139—41no—
193C2×C4×C139—42no—
194C2×C4×C139—41no—
195C2×C4×C139—42no—
196C2×C4×C139—82no—
197C2×C4×C139—82no—
198C2×C4×C139—81no—
199C2×C4×C139—82no—
200C2×C4×C139C2×C22⋊C412yes—
201C2×C4×C139C2×C22⋊C411yescharacteristic
202C2×C4×C139#12012yes—
203C2×C4×C139#12011yescharacteristic
204C8×C139—82no—
205C8×C139—81no—
206C22×C139—21no—
207C22×C139—22no—
208C22×C139—41no—
209C22×C139—42no—
210C22×C139—41no—
211C22×C139—42no—
212C22×C139—42no—
213C22×C139—42no—
214C22×C139—42no—
215C22×C139—84no—
216C22×C139#37911yescharacteristic
217C4×C139—21no—
218C4×C139—22no—
219C4×C139—22no—
220C4×C139—41no—
221C4×C139—42no—
222C4×C139—41no—
223C4×C139—42no—
224C4×C139—42no—
225C4×C139—82no—
226C4×C139#45311yescharacteristic
227C4×C139#45511yescharacteristic
228C2×C139—41no—
229C2×C139—81no—
230C2×C139—81no—
231C2×C139—82no—
232C2×C139#179211yescharacteristic
233C2×C139#179412yes—
234#8504C13911yesmaximal, characteristic, direct product factor, Sylow
235C139#850411yescharacteristic, direct product factor, Sylow
236#3529C2×C13911yescharacteristic
237#1963C2×C13911yescharacteristic, complemented
238#1543C2×C13911yescharacteristic, complemented
239#1500C2×C13912yescomplemented
240#1495C2×C13912yescomplemented
241#563—21no—
242#563C4×C13911yescharacteristic, complemented
243#562—22no—
244#562C4×C13912yescomplemented
245H(3,𝔽4)C4×C13911yescharacteristic, complemented
246#560—21no—
247#560—22no—
248#532—21no—
249#532C22×C13911yescharacteristic
250#529—22no—
251#529C22×C13912yes—
252#525—21no—
253#525—22no—
254#431C22×C13912yescomplemented
255#423C22×C13911yescharacteristic, complemented
256C2×#104—21no—
257C2×#104—21no—
258#376C22×C13911yescharacteristic, complemented
259#333—21no—
260#331—21no—
261#328—22no—
262#327—22no—
263Q8⋊C8—22no—
264D4⋊C8—22no—
265C2×#41—21no—
266C2×#41D4×C13911yescharacteristic
267C2×#41D4×C13911yescharacteristic
268C23×C4—21no—
269C2×M16—21no—
270C4⋊Q8—21no—
271C4⋊Q8D4×C13911yescharacteristic
272#127—21no—
273#127D4×C13911yescharacteristic
274#126—22no—
275#126—22no—
276#126—22no—
277#125—22no—
278#125C2×C4×C13912yes—
279#124—21no—
280#124—22no—
281#124—21no—
282#124C2×C4×C13912yes—
283#124C2×C4×C13911yescharacteristic
284#124C2×C4×C13911yescharacteristic
285#123—22no—
286#123—21no—
287#123—22no—
288#123—21no—
289#123—22no—
290#123—22no—
291#123—22no—
292C22⋊Q8—22no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8—22no—
296C22⋊Q8D4×C13912yes—
297#121—22no—
298#121—22no—
299#121—22no—
300#121—22no—
301#121—22no—
302#121—22no—
303#121—22no—
304#121D4×C13912yes—
305#120—21no—
306#120—22no—
307#120—21no—
308#120—22no—
309C4×Q8D4×C13912yes—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4D4×C13912yes—
315#117—21no—
316#117—22no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42C23×C13911yescharacteristic
320C4⋊C8—22no—
321C4⋊C8—22no—
322#104—42no—
323#104—42no—
324C22⋊C8—22no—
325C4×C8—22no—
326#95—22no—
327C24—21no—
328#41—41no—
329#41—41no—
330#41—41no—
331#41—41no—
332#41—81no—
333#41—81no—
334C2×Q8—21no—
335C2×Q8C22⋊C4×C13912yes—
336C2×Q8C22⋊C4×C13911yescharacteristic
337C2×Q8C22⋊C4×C13911yescharacteristic
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—21no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4C22⋊C4×C13912yes—
347C2×D4C22⋊C4×C13911yescharacteristic
348C2×D4C22⋊C4×C13911yescharacteristic
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—41no—
356C22×C4—81no—
357C22×C4—81no—
358C22×C4C2×D4×C13911yescharacteristic
359C22×C4C2×D4×C13912yes—
360M16—41no—
361M16—41no—
362C2×C8—42no—
363C2×C8—41no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4C22⋊C4×C13912yes—
373C4⋊C4C22⋊C4×C13912yes—
374C22⋊C4—21no—
375C22⋊C4—21no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C42—21no—
388C42—21no—
389C42—22no—
390C42—22no—
391C42—41no—
392C42C22×C4×C13911yescharacteristic
393C42C2×D4×C13912yes—
394C42C2×D4×C13911yescharacteristic
395C23—21no—
396C23—22no—
397C23—21no—
398C23—81no—
399C23—82no—
400C23#120×C13911yescharacteristic
401Q8—41no—
402Q8—41no—
403Q8—42no—
404Q8—81no—
405D4—41no—
406D4—41no—
407D4—42no—
408D4—82no—
409D4—81no—
410D4—81no—
411D4—82no—
412D4—82no—
413D4—81no—
414D4—82no—
415D4—82no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—82no—
432C2×C4—81no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4C2×C22⋊C4×C13912yes—
436C2×C4C2×C22⋊C4×C13911yescharacteristic
437C2×C4#120×C13912yes—
438C2×C4#120×C13911yescharacteristic
439C8—82no—
440C8—81no—
441C22—21no—
442C22—22no—
443C22—41no—
444C22—42no—
445C22—41no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—84no—
451C22#379×C13911yescharacteristic
452C4—21no—
453C4—22no—
454C4—22no—
455C4—41no—
456C4—42no—
457C4—41no—
458C4—42no—
459C4—42no—
460C4—82no—
461C4#453×C13911yescharacteristic
462C4#455×C13911yescharacteristic
463C2—41no—
464C2—81no—
465C2—82no—
466C2—81no—
467C2#1792×C13911yescharacteristic
468C2#1794×C13912yes—
subgroupG/H
centerC2×C4×C139#120
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
socleC22×C139#379
prime radical#3529×C139C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1963×C139C2semidirect
3. #1543×C139C2semidirect
4. #1500×C139C2semidirect
5. #1495×C139C2semidirect
7. #563×C139C4semidirect
9. #562×C139C4semidirect
10. H(3,𝔽4)×C139C4semidirect
19. #431×C139C22semidirect
20. #423×C139C22semidirect
23. #376×C139C22semidirect
234. #8504C139direct (N × H)
235. C139#8504direct (N × H)
237. #1963C2×C139semidirect
238. #1543C2×C139semidirect
239. #1500C2×C139semidirect
240. #1495C2×C139semidirect
242. #563C4×C139semidirect
244. #562C4×C139semidirect
245. H(3,𝔽4)C4×C139semidirect
254. #431C22×C139semidirect
255. #423C22×C139semidirect
258. #376C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3529×C1392
#1963×C1392
#1543×C1392
#1500×C1392
#1495×C1392
#8504139