Finite Group Databasebeta

← C139×#9713 #48004309

Subgroups — C139×#9713 #48004309

Order 35584.

742 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2850×C139C211yesmaximal, characteristic
2#1797×C139C211yesmaximal, characteristic, complemented
3C2×#328×C139C212yesmaximal, complemented
4C2×#327×C139C212yesmaximal
5C4×#95×C139C211yesmaximal, characteristic, complemented
6C2×#124×C139C411yescharacteristic, complemented
7C2×C22⋊Q8×C139C2211yescharacteristic
8C2×#121×C139C2211yescharacteristic
9C22×C42×C139—21no—
10C22×C42×C139C2211yescharacteristic
11C2×C4⋊C8×C139—21no—
12C2×C22⋊C8×C139C2212yes—
13#391×C139C411yescharacteristic, complemented
14#390×C139C411yescharacteristic, complemented
15#388×C139—21no—
16#388×C139—21no—
17#386×C139—21no—
18#386×C139—21no—
19#382×C139C411yescharacteristic, complemented
20C2×#95×C139—21no—
21C2×#95×C139C2212yes—
22#336×C139—21no—
23#328×C139—24no—
24#327×C139—24no—
25C22×Q8×C139C2×C411yescharacteristic
26C22×D4×C139—21no—
27C22×D4×C139C2×C411yescharacteristic
28C23×C4×C139—22no—
29C23×C4×C139D411yescharacteristic
30C23×C4×C139D411yescharacteristic
31C23×C4×C139C2311yescharacteristic
32C22×C8×C139—22no—
33#124×C139—42no—
34C22⋊Q8×C139—22no—
35C22⋊Q8×C139—22no—
36#121×C139—22no—
37#121×C139—22no—
38C2×C4⋊C4×C139—21no—
39C2×C4⋊C4×C139C2×C411yescharacteristic
40C2×C4⋊C4×C139C2×C411yescharacteristic
41C2×C22⋊C4×C139—21no—
42C2×C22⋊C4×C139—21no—
43C2×C22⋊C4×C139—21no—
44C2×C22⋊C4×C139—21no—
45C2×C22⋊C4×C139—21no—
46C2×C22⋊C4×C139—21no—
47C2×C42×C139—24no—
48C2×C42×C139—42no—
49C2×C42×C139—42no—
50C2×C42×C139—42no—
51C2×C42×C139C2×C411yescharacteristic
52C2×C42×C139C2×C411yescharacteristic
53C2×C42×C139D411yescharacteristic
54C2×C42×C139D411yescharacteristic
55C4⋊C8×C139—42no—
56C22⋊C8×C139—22no—
57C22⋊C8×C139—22no—
58#95×C139—24no—
59#95×C139—21no—
60#95×C139—21no—
61#95×C139—21no—
62#95×C139—21no—
63#95×C139—22no—
64#95×C139D414yes—
65C24×C139—21no—
66C24×C139C2×D411yescharacteristic
67C2×Q8×C139—22no—
68C2×Q8×C139—41no—
69C2×Q8×C139—41no—
70C2×D4×C139—22no—
71C2×D4×C139—41no—
72C2×D4×C139—41no—
73C2×D4×C139—42no—
74C2×D4×C139—42no—
75C2×D4×C139—41no—
76C2×D4×C139—41no—
77C22×C4×C139—21no—
78C22×C4×C139—21no—
79C22×C4×C139—22no—
80C22×C4×C139—22no—
81C22×C4×C139—24no—
82C22×C4×C139—24no—
83C22×C4×C139—24no—
84C22×C4×C139—22no—
85C22×C4×C139—22no—
86C22×C4×C139—21no—
87C22×C4×C139—21no—
88C22×C4×C139—21no—
89C22×C4×C139—41no—
90C22×C4×C139—41no—
91C22×C4×C139—41no—
92C22×C4×C139—42no—
93C22×C4×C139—42no—
94C22×C4×C139—42no—
95C22×C4×C139—42no—
96C22×C4×C139C22⋊C411yescharacteristic
97C22×C4×C139C22⋊C411yescharacteristic
98C22×C4×C139C22⋊C411yescharacteristic
99C22×C4×C139C22⋊C411yescharacteristic
100C22×C4×C139C22×C411yescharacteristic
101C22×C4×C139C2×D411yescharacteristic
102C22×C4×C139C2×D412yes—
103C22×C4×C139#4112yes—
104C2×C8×C139—42no—
105C2×C8×C139—42no—
106C2×C8×C139—42no—
107C4⋊C4×C139—22no—
108C4⋊C4×C139—22no—
109C4⋊C4×C139—41no—
110C4⋊C4×C139—41no—
111C22⋊C4×C139—42no—
112C22⋊C4×C139—42no—
113C22⋊C4×C139—42no—
114C22⋊C4×C139—42no—
115C22⋊C4×C139—42no—
116C22⋊C4×C139—41no—
117C22⋊C4×C139—41no—
118C42×C139—22no—
119C42×C139—22no—
120C42×C139—41no—
121C42×C139—41no—
122C42×C139—48no—
123C23×C139—21no—
124C23×C139—21no—
125C23×C139—21no—
126C23×C139—21no—
127C23×C139—41no—
128C23×C139—41no—
129C23×C139—41no—
130C23×C139—41no—
131C23×C139—41no—
132C23×C139—41no—
133C23×C139—41no—
134C23×C139C2×C22⋊C411yescharacteristic
135C23×C139#12112yes—
136C23×C139#13512yes—
137C23×C139AGL(1,ℤ/8)11yescharacteristic
138C23×C139#13711yescharacteristic
139Q8×C139—82no—
140D4×C139—82no—
141D4×C139—82no—
142D4×C139—82no—
143C2×C4×C139—24no—
144C2×C4×C139—24no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C2×C4×C139—21no—
149C2×C4×C139—21no—
150C2×C4×C139—21no—
151C2×C4×C139—21no—
152C2×C4×C139—21no—
153C2×C4×C139—21no—
154C2×C4×C139—21no—
155C2×C4×C139—28no—
156C2×C4×C139—21no—
157C2×C4×C139—21no—
158C2×C4×C139—21no—
159C2×C4×C139—42no—
160C2×C4×C139—42no—
161C2×C4×C139—44no—
162C2×C4×C139—44no—
163C2×C4×C139—44no—
164C2×C4×C139—44no—
165C2×C4×C139—44no—
166C2×C4×C139—44no—
167C2×C4×C139—44no—
168C2×C4×C139—41no—
169C2×C4×C139—41no—
170C2×C4×C139—41no—
171C2×C4×C139—41no—
172C2×C4×C139—41no—
173C2×C4×C139—41no—
174C2×C4×C139—41no—
175C2×C4×C139—41no—
176C2×C4×C139—41no—
177C2×C4×C139#9912yes—
178C2×C4×C139#10412yes—
179C2×C4×C139#10412yes—
180C2×C4×C139C4×D412yes—
181C2×C4×C139#12411yescharacteristic
182C2×C4×C139#12711yescharacteristic
183C8×C139—82no—
184C22×C139—22no—
185C22×C139—22no—
186C22×C139—22no—
187C22×C139—22no—
188C22×C139—21no—
189C22×C139—21no—
190C22×C139—21no—
191C22×C139—21no—
192C22×C139—81no—
193C22×C139—81no—
194C22×C139—81no—
195C22×C139—81no—
196C22×C139—81no—
197C22×C139—81no—
198C22×C139—81no—
199C22×C139#39011yescharacteristic
200C22×C139C2×#9911yescharacteristic
201C22×C139#41011yescharacteristic
202C22×C139#41611yescharacteristic
203C22×C139#41711yescharacteristic
204C22×C139C2×#10411yescharacteristic
205C22×C139C2×#10411yescharacteristic
206C22×C139#46312yes—
207C22×C139#46412yes—
208C4×C139—21no—
209C4×C139—22no—
210C4×C139—21no—
211C4×C139—22no—
212C4×C139—22no—
213C4×C139—22no—
214C4×C139—48no—
215C4×C139—41no—
216C4×C139—81no—
217C4×C139—81no—
218C4×C139—81no—
219C2×C139—22no—
220C2×C139—22no—
221C2×C139—161no—
222C2×C139#150011yescharacteristic
223C2×C139#150111yescharacteristic
224C2×C139#150411yescharacteristic
225C2×C139#150911yescharacteristic
226C2×C139#196211yescharacteristic
227C2×C139#196411yescharacteristic
228C2×C139#198311yescharacteristic
229#9713C13911yesmaximal, characteristic, direct product factor, Sylow
230C139#971311yescharacteristic, direct product factor, Sylow
231#2850C2×C13911yescharacteristic
232#1797C2×C13911yescharacteristic, complemented
233C2×#328C2×C13912yescomplemented
234C2×#327C2×C13912yes—
235C4×#95C2×C13911yescharacteristic, complemented
236C2×#124C4×C13911yescharacteristic, complemented
237C2×C22⋊Q8C22×C13911yescharacteristic
238C2×#121C22×C13911yescharacteristic
239C22×C42—21no—
240C22×C42C22×C13911yescharacteristic
241C2×C4⋊C8—21no—
242C2×C22⋊C8C22×C13912yes—
243#391C4×C13911yescharacteristic, complemented
244#390C4×C13911yescharacteristic, complemented
245#388—21no—
246#388—21no—
247#386—21no—
248#386—21no—
249#382C4×C13911yescharacteristic, complemented
250C2×#95—21no—
251C2×#95C22×C13912yes—
252#336—21no—
253#328—24no—
254#327—24no—
255C22×Q8C2×C4×C13911yescharacteristic
256C22×D4—21no—
257C22×D4C2×C4×C13911yescharacteristic
258C23×C4—22no—
259C23×C4D4×C13911yescharacteristic
260C23×C4D4×C13911yescharacteristic
261C23×C4C23×C13911yescharacteristic
262C22×C8—22no—
263#124—42no—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266#121—22no—
267#121—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4C2×C4×C13911yescharacteristic
270C2×C4⋊C4C2×C4×C13911yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C42—24no—
278C2×C42—42no—
279C2×C42—42no—
280C2×C42—42no—
281C2×C42C2×C4×C13911yescharacteristic
282C2×C42C2×C4×C13911yescharacteristic
283C2×C42D4×C13911yescharacteristic
284C2×C42D4×C13911yescharacteristic
285C4⋊C8—42no—
286C22⋊C8—22no—
287C22⋊C8—22no—
288#95—24no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—22no—
294#95D4×C13914yes—
295C24—21no—
296C24C2×D4×C13911yescharacteristic
297C2×Q8—22no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×D4—22no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C2×D4—42no—
305C2×D4—41no—
306C2×D4—41no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4C22⋊C4×C13911yescharacteristic
327C22×C4C22⋊C4×C13911yescharacteristic
328C22×C4C22⋊C4×C13911yescharacteristic
329C22×C4C22⋊C4×C13911yescharacteristic
330C22×C4C22×C4×C13911yescharacteristic
331C22×C4C2×D4×C13911yescharacteristic
332C22×C4C2×D4×C13912yes—
333C22×C4#41×C13912yes—
334C2×C8—42no—
335C2×C8—42no—
336C2×C8—42no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C42—22no—
349C42—22no—
350C42—41no—
351C42—41no—
352C42—48no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23C2×C22⋊C4×C13911yescharacteristic
365C23#121×C13912yes—
366C23#135×C13912yes—
367C23AGL(1,ℤ/8)×C13911yescharacteristic
368C23#137×C13911yescharacteristic
369Q8—82no—
370D4—82no—
371D4—82no—
372D4—82no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—28no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4#99×C13912yes—
408C2×C4#104×C13912yes—
409C2×C4#104×C13912yes—
410C2×C4C4×D4×C13912yes—
411C2×C4#124×C13911yescharacteristic
412C2×C4#127×C13911yescharacteristic
413C8—82no—
414C22—22no—
415C22—22no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—22no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22#390×C13911yescharacteristic
430C22C2×#99×C13911yescharacteristic
431C22#410×C13911yescharacteristic
432C22#416×C13911yescharacteristic
433C22#417×C13911yescharacteristic
434C22C2×#104×C13911yescharacteristic
435C22C2×#104×C13911yescharacteristic
436C22#463×C13912yes—
437C22#464×C13912yes—
438C4—22no—
439C4—22no—
440C4—22no—
441C4—21no—
442C4—22no—
443C4—21no—
444C4—48no—
445C4—41no—
446C4—81no—
447C4—81no—
448C4—81no—
449C2—22no—
450C2—22no—
451C2—161no—
452C2#1500×C13911yescharacteristic
453C2#1501×C13911yescharacteristic
454C2#1504×C13911yescharacteristic
455C2#1509×C13911yescharacteristic
456C2#1962×C13911yescharacteristic
457C2#1964×C13911yescharacteristic
458C2#1983×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC2×#121×C139C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1797×C139C2semidirect
3. C2×#328×C139C2semidirect
5. C4×#95×C139C2semidirect
6. C2×#124×C139C4semidirect
13. #391×C139C4semidirect
14. #390×C139C4semidirect
19. #382×C139C4semidirect
229. #9713C139direct (N × H)
230. C139#9713direct (N × H)
232. #1797C2×C139semidirect
233. C2×#328C2×C139semidirect
235. C4×#95C2×C139semidirect
236. C2×#124C4×C139semidirect
243. #391C4×C139semidirect
244. #390C4×C139semidirect
249. #382C4×C139semidirect

Maximal subgroups

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

subgroupindex
#2850×C1392
#1797×C1392
C2×#328×C1392
C2×#327×C1392
C4×#95×C1392
#9713139