Finite Group Databasebeta

← C139×#8422 #48003018

Subgroups — C139×#8422 #48003018

Order 35584.

756 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3511×C139C211yesmaximal, characteristic
2#1987×C139C211yesmaximal, characteristic, complemented
3#1806×C139C211yesmaximal, characteristic, complemented
4#1549×C139C211yesmaximal, characteristic, complemented
5#1547×C139C211yesmaximal, characteristic, complemented
6#1502×C139C211yesmaximal, characteristic, complemented
7#1477×C139C211yesmaximal, characteristic, complemented
8#556×C139C412yescomplemented
9#555×C139—21no—
10#554×C139—21no—
11#553×C139—22no—
12#548×C139—22no—
13#547×C139C412yescomplemented
14#542×C139—22no—
15#537×C139—21no—
16#533×C139—21no—
17#532×C139—21no—
18#532×C139C2211yescharacteristic
19C2×C4⋊Q8×C139C2211yescharacteristic
20#520×C139—21no—
21C4×#41×C139C2211yescharacteristic
22#431×C139C2211yescharacteristic
23#423×C139C2211yescharacteristic
24C2×C4⋊C8×C139C2211yescharacteristic
25C2×#104×C139—21no—
26C4×C4⋊C4×C139C2211yescharacteristic
27#340×C139—22no—
28#339×C139—21no—
29#332×C139—21no—
30#332×C139—22no—
31#331×C139—21no—
32#327×C139—22no—
33Q8⋊C8×C139—21no—
34D4⋊C8×C139—21no—
35C2×#41×C139—22no—
36C2×#41×C139—21no—
37C2×#41×C139D411yescharacteristic
38C22×Q8×C139—21no—
39C2×M16×C139—21no—
40C22×C8×C139—21no—
41C4⋊Q8×C139—21no—
42C4⋊Q8×C139—21no—
43C4⋊Q8×C139C2×C412yes—
44C4⋊Q8×C139D412yes—
45C4⋊Q8×C139D411yescharacteristic
46#127×C139D411yescharacteristic
47#126×C139—24no—
48#125×C139—22no—
49#124×C139—24no—
50#124×C139—22no—
51#124×C139—21no—
52#123×C139—24no—
53C22⋊Q8×C139—22no—
54C22⋊Q8×C139—24no—
55C22⋊Q8×C139—22no—
56C22⋊Q8×C139—22no—
57#121×C139—22no—
58#121×C139—22no—
59#121×C139—24no—
60#121×C139—22no—
61#121×C139—21no—
62#121×C139D412yes—
63C4×Q8×C139—22no—
64C4×Q8×C139—22no—
65C4×Q8×C139C2×C411yescharacteristic
66C4×Q8×C139D411yescharacteristic
67C4×D4×C139—22no—
68C4×D4×C139—24no—
69C4×D4×C139—22no—
70C4×D4×C139—21no—
71C4×D4×C139—21no—
72C4×D4×C139—21no—
73C4×D4×C139C2×C411yescharacteristic
74C4×D4×C139C2×C412yes—
75C4×D4×C139D411yescharacteristic
76#117×C139—22no—
77#117×C139—22no—
78#117×C139—21no—
79#117×C139D411yescharacteristic
80C2×C4⋊C4×C139—21no—
81C2×C4⋊C4×C139—22no—
82C2×C4⋊C4×C139—21no—
83C2×C4⋊C4×C139D412yes—
84C2×C42×C139—21no—
85C2×C42×C139—21no—
86C2×C42×C139C2311yescharacteristic
87C4⋊C8×C139—21no—
88C4⋊C8×C139—21no—
89C4⋊C8×C139—21no—
90C4⋊C8×C139—21no—
91C4⋊C8×C139—21no—
92#104×C139—42no—
93C22⋊C8×C139—21no—
94C4×C8×C139—21no—
95#95×C139—21no—
96#41×C139—21no—
97#41×C139—21no—
98#41×C139—21no—
99#41×C139—21no—
100#41×C139—41no—
101#41×C139—41no—
102#41×C139—41no—
103#41×C139—41no—
104#41×C139—84no—
105C2×Q8×C139—22no—
106C2×Q8×C139—21no—
107C2×Q8×C139—22no—
108C2×Q8×C139—82no—
109C2×Q8×C139C22⋊C411yescharacteristic
110C2×D4×C139—21no—
111C2×D4×C139—22no—
112C2×D4×C139—24no—
113C2×D4×C139—21no—
114C2×D4×C139—21no—
115C2×D4×C139C22⋊C411yescharacteristic
116C2×D4×C139C22⋊C412yes—
117C22×C4×C139—24no—
118C22×C4×C139—22no—
119C22×C4×C139—21no—
120C22×C4×C139—22no—
121C22×C4×C139—21no—
122C22×C4×C139—21no—
123C22×C4×C139—41no—
124C22×C4×C139C2×D411yescharacteristic
125C22×C4×C139C2×D411yescharacteristic
126C22×C4×C139C2×D411yescharacteristic
127M16×C139—41no—
128M16×C139—41no—
129C2×C8×C139—42no—
130C2×C8×C139—41no—
131C2×C8×C139—41no—
132C2×C8×C139—41no—
133C4⋊C4×C139—24no—
134C4⋊C4×C139—24no—
135C4⋊C4×C139—22no—
136C4⋊C4×C139—21no—
137C4⋊C4×C139—22no—
138C4⋊C4×C139—22no—
139C4⋊C4×C139—21no—
140C4⋊C4×C139—21no—
141C4⋊C4×C139—22no—
142C4⋊C4×C139—41no—
143C4⋊C4×C139C22⋊C411yescharacteristic
144C4⋊C4×C139C22⋊C414yes—
145C4⋊C4×C139C22⋊C411yescharacteristic
146C4⋊C4×C139C22⋊C412yes—
147C22⋊C4×C139—24no—
148C22⋊C4×C139—24no—
149C22⋊C4×C139—24no—
150C22⋊C4×C139—21no—
151C22⋊C4×C139—21no—
152C22⋊C4×C139—22no—
153C22⋊C4×C139—21no—
154C22⋊C4×C139—22no—
155C42×C139—24no—
156C42×C139—21no—
157C42×C139—21no—
158C42×C139—21no—
159C42×C139—41no—
160C42×C139—41no—
161C42×C139C22×C411yescharacteristic
162C42×C139C2×D411yescharacteristic
163C42×C139C2×D411yescharacteristic
164C42×C139C2×D411yescharacteristic
165C23×C139—21no—
166C23×C139—22no—
167C23×C139#12011yescharacteristic
168Q8×C139—21no—
169Q8×C139—21no—
170Q8×C139—44no—
171Q8×C139—41no—
172Q8×C139—41no—
173Q8×C139—82no—
174D4×C139—21no—
175D4×C139—21no—
176D4×C139—42no—
177D4×C139—41no—
178D4×C139—42no—
179D4×C139—41no—
180D4×C139—42no—
181D4×C139—41no—
182D4×C139—41no—
183D4×C139—41no—
184D4×C139—41no—
185D4×C139—84no—
186C2×C4×C139—21no—
187C2×C4×C139—21no—
188C2×C4×C139—21no—
189C2×C4×C139—21no—
190C2×C4×C139—22no—
191C2×C4×C139—21no—
192C2×C4×C139—24no—
193C2×C4×C139—41no—
194C2×C4×C139—42no—
195C2×C4×C139—42no—
196C2×C4×C139—42no—
197C2×C4×C139—41no—
198C2×C4×C139—41no—
199C2×C4×C139—41no—
200C2×C4×C139—41no—
201C2×C4×C139—42no—
202C2×C4×C139—82no—
203C2×C4×C139—84no—
204C2×C4×C139—81no—
205C2×C4×C139—81no—
206C2×C4×C139C2×C22⋊C411yescharacteristic
207C2×C4×C139C2×C22⋊C411yescharacteristic
208C2×C4×C139C2×C22⋊C411yescharacteristic
209C2×C4×C139#12011yescharacteristic
210C2×C4×C139#12011yescharacteristic
211C2×C4×C139#12011yescharacteristic
212C2×C4×C139#13511yescharacteristic
213C2×C4×C139#13511yescharacteristic
214C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
215C2×C4×C139#13711yescharacteristic
216C8×C139—81no—
217C8×C139—81no—
218C8×C139—81no—
219C22×C139—21no—
220C22×C139—21no—
221C22×C139—41no—
222C22×C139—42no—
223C22×C139—41no—
224C22×C139—42no—
225C22×C139—41no—
226C22×C139—42no—
227C22×C139#37911yescharacteristic
228C22×C139#44911yescharacteristic
229C22×C139#45211yescharacteristic
230C4×C139—21no—
231C4×C139—21no—
232C4×C139—21no—
233C4×C139—41no—
234C4×C139—41no—
235C4×C139—44no—
236C4×C139—41no—
237C4×C139—42no—
238C4×C139—82no—
239C4×C139#41611yescharacteristic
240C4×C139#41711yescharacteristic
241C4×C139#44911yescharacteristic
242C4×C139#45211yescharacteristic
243C4×C139#45411yescharacteristic
244C4×C139#45611yescharacteristic
245C2×C139—21no—
246C2×C139—21no—
247C2×C139—81no—
248C2×C139—82no—
249C2×C139#178811yescharacteristic
250C2×C139#179311yescharacteristic
251C2×C139#179511yescharacteristic
252#8422C13911yesmaximal, characteristic, direct product factor, Sylow
253C139#842211yescharacteristic, direct product factor, Sylow
254#3511C2×C13911yescharacteristic
255#1987C2×C13911yescharacteristic, complemented
256#1806C2×C13911yescharacteristic, complemented
257#1549C2×C13911yescharacteristic, complemented
258#1547C2×C13911yescharacteristic, complemented
259#1502C2×C13911yescharacteristic, complemented
260#1477C2×C13911yescharacteristic, complemented
261#556C4×C13912yescomplemented
262#555—21no—
263#554—21no—
264#553—22no—
265#548—22no—
266#547C4×C13912yescomplemented
267#542—22no—
268#537—21no—
269#533—21no—
270#532—21no—
271#532C22×C13911yescharacteristic
272C2×C4⋊Q8C22×C13911yescharacteristic
273#520—21no—
274C4×#41C22×C13911yescharacteristic
275#431C22×C13911yescharacteristic
276#423C22×C13911yescharacteristic
277C2×C4⋊C8C22×C13911yescharacteristic
278C2×#104—21no—
279C4×C4⋊C4C22×C13911yescharacteristic
280#340—22no—
281#339—21no—
282#332—21no—
283#332—22no—
284#331—21no—
285#327—22no—
286Q8⋊C8—21no—
287D4⋊C8—21no—
288C2×#41—22no—
289C2×#41—21no—
290C2×#41D4×C13911yescharacteristic
291C22×Q8—21no—
292C2×M16—21no—
293C22×C8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8C2×C4×C13912yes—
297C4⋊Q8D4×C13912yes—
298C4⋊Q8D4×C13911yescharacteristic
299#127D4×C13911yescharacteristic
300#126—24no—
301#125—22no—
302#124—24no—
303#124—22no—
304#124—21no—
305#123—24no—
306C22⋊Q8—22no—
307C22⋊Q8—24no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310#121—22no—
311#121—22no—
312#121—24no—
313#121—22no—
314#121—21no—
315#121D4×C13912yes—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8C2×C4×C13911yescharacteristic
319C4×Q8D4×C13911yescharacteristic
320C4×D4—22no—
321C4×D4—24no—
322C4×D4—22no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4C2×C4×C13911yescharacteristic
327C4×D4C2×C4×C13912yes—
328C4×D4D4×C13911yescharacteristic
329#117—22no—
330#117—22no—
331#117—21no—
332#117D4×C13911yescharacteristic
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4D4×C13912yes—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42C23×C13911yescharacteristic
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8—21no—
345#104—42no—
346C22⋊C8—21no—
347C4×C8—21no—
348#95—21no—
349#41—21no—
350#41—21no—
351#41—21no—
352#41—21no—
353#41—41no—
354#41—41no—
355#41—41no—
356#41—41no—
357#41—84no—
358C2×Q8—22no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—82no—
362C2×Q8C22⋊C4×C13911yescharacteristic
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—24no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4C22⋊C4×C13911yescharacteristic
369C2×D4C22⋊C4×C13912yes—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—41no—
377C22×C4C2×D4×C13911yescharacteristic
378C22×C4C2×D4×C13911yescharacteristic
379C22×C4C2×D4×C13911yescharacteristic
380M16—41no—
381M16—41no—
382C2×C8—42no—
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—41no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4C22⋊C4×C13911yescharacteristic
397C4⋊C4C22⋊C4×C13914yes—
398C4⋊C4C22⋊C4×C13911yescharacteristic
399C4⋊C4C22⋊C4×C13912yes—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—24no—
403C22⋊C4—21no—
404C22⋊C4—21no—
405C22⋊C4—22no—
406C22⋊C4—21no—
407C22⋊C4—22no—
408C42—24no—
409C42—21no—
410C42—21no—
411C42—21no—
412C42—41no—
413C42—41no—
414C42C22×C4×C13911yescharacteristic
415C42C2×D4×C13911yescharacteristic
416C42C2×D4×C13911yescharacteristic
417C42C2×D4×C13911yescharacteristic
418C23—21no—
419C23—22no—
420C23#120×C13911yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—44no—
424Q8—41no—
425Q8—41no—
426Q8—82no—
427D4—21no—
428D4—21no—
429D4—42no—
430D4—41no—
431D4—42no—
432D4—41no—
433D4—42no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—84no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—82no—
456C2×C4—84no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4C2×C22⋊C4×C13911yescharacteristic
460C2×C4C2×C22⋊C4×C13911yescharacteristic
461C2×C4C2×C22⋊C4×C13911yescharacteristic
462C2×C4#120×C13911yescharacteristic
463C2×C4#120×C13911yescharacteristic
464C2×C4#120×C13911yescharacteristic
465C2×C4#135×C13911yescharacteristic
466C2×C4#135×C13911yescharacteristic
467C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
468C2×C4#137×C13911yescharacteristic
469C8—81no—
470C8—81no—
471C8—81no—
472C22—21no—
473C22—21no—
474C22—41no—
475C22—42no—
476C22—41no—
477C22—42no—
478C22—41no—
479C22—42no—
480C22#379×C13911yescharacteristic
481C22#449×C13911yescharacteristic
482C22#452×C13911yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—41no—
487C4—42no—
488C4—41no—
489C4—41no—
490C4—44no—
491C4—82no—
492C4#416×C13911yescharacteristic
493C4#417×C13911yescharacteristic
494C4#449×C13911yescharacteristic
495C4#452×C13911yescharacteristic
496C4#454×C13911yescharacteristic
497C4#456×C13911yescharacteristic
498C2—21no—
499C2—21no—
500C2—81no—
501C2—82no—
502C2#1788×C13911yescharacteristic
503C2#1793×C13911yescharacteristic
504C2#1795×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#379
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radical#3511×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. #1987×C139C2semidirect
3. #1806×C139C2semidirect
4. #1549×C139C2semidirect
5. #1547×C139C2semidirect
6. #1502×C139C2semidirect
7. #1477×C139C2semidirect
8. #556×C139C4semidirect
13. #547×C139C4semidirect
252. #8422C139direct (N × H)
253. C139#8422direct (N × H)
255. #1987C2×C139semidirect
256. #1806C2×C139semidirect
257. #1549C2×C139semidirect
258. #1547C2×C139semidirect
259. #1502C2×C139semidirect
260. #1477C2×C139semidirect
261. #556C4×C139semidirect
266. #547C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3511×C1392
#1987×C1392
#1806×C1392
#1549×C1392
#1547×C1392
#1502×C1392
#1477×C1392
#8422139