Finite Group Databasebeta

← C139×#18692 #48013288

Subgroups — C139×#18692 #48013288

Order 35584.

924 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3548×C139C211yesmaximal, characteristic
2#3255×C139C211yesmaximal, characteristic, complemented
3#3254×C139C211yesmaximal, characteristic, complemented
4#3131×C139C211yesmaximal, characteristic, complemented
5#1644×C139C212yesmaximal, complemented
6#1643×C139C212yesmaximal, complemented
7#1642×C139C212yesmaximal, complemented
8#1641×C139C212yesmaximal, complemented
9#1560×C139C211yesmaximal, characteristic, complemented
10#1493×C139C211yesmaximal, characteristic, complemented
11#1492×C139C211yesmaximal, characteristic, complemented
12#562×C139—22no—
13#554×C139—21no—
14#554×C139C2212yes—
15#550×C139—21no—
16#550×C139C2212yes—
17#547×C139—21no—
18#547×C139—21no—
19#540×C139—22no—
20#537×C139—22no—
21#537×C139—22no—
22#533×C139C2211yescharacteristic
23#533×C139C2211yescharacteristic
24#532×C139C2211yescharacteristic
25#532×C139C2211yescharacteristic
26#488×C139—22no—
27#487×C139C2211yescharacteristic
28#487×C139C2211yescharacteristic
29#486×C139C2211yescharacteristic
30#486×C139C2211yescharacteristic
31#477×C139—21no—
32#475×C139—21no—
33#475×C139C2212yes—
34#474×C139C2212yes—
35#470×C139—22no—
36#468×C139—22no—
37#462×C139—21no—
38#462×C139C2212yes—
39#461×C139C2212yes—
40#460×C139—21no—
41#423×C139C2211yescharacteristic
42#423×C139C2211yescharacteristic
43#416×C139—22no—
44C2×C4×C8×C139C2211yescharacteristic
45#333×C139C2212yes—
46#331×C139C2212yes—
47Q8⋊C8×C139C2212yes—
48Q8⋊C8×C139C2212yes—
49D4⋊C8×C139C2212yes—
50D4⋊C8×C139C2212yes—
51C2×#41×C139—22no—
52C2×#41×C139—22no—
53C2×#41×C139—21no—
54C2×#41×C139D412yes—
55C2×Q16×C139—22no—
56C2×SD16×C139—22no—
57C2×M16×C139—21no—
58C2×M16×C139—21no—
59C22×C8×C139—21no—
60C4⋊Q8×C139D411yescharacteristic
61C4⋊Q8×C139D411yescharacteristic
62C4⋊Q8×C139D411yescharacteristic
63C4⋊Q8×C139C2311yescharacteristic
64C4⋊Q8×C139C2311yescharacteristic
65C4⋊Q8×C139C2311yescharacteristic
66#127×C139—22no—
67#127×C139D411yescharacteristic
68#127×C139C2311yescharacteristic
69#125×C139—22no—
70#125×C139—21no—
71#125×C139—21no—
72#124×C139—21no—
73#124×C139D412yes—
74#123×C139—24no—
75#123×C139—24no—
76C22⋊Q8×C139—22no—
77C22⋊Q8×C139—24no—
78C22⋊Q8×C139—22no—
79C22⋊Q8×C139—24no—
80C22⋊Q8×C139—21no—
81C22⋊Q8×C139—21no—
82C22⋊Q8×C139—21no—
83C22⋊Q8×C139D412yes—
84#121×C139—24no—
85#121×C139—24no—
86#121×C139—22no—
87#121×C139—24no—
88#121×C139—24no—
89#121×C139—21no—
90#121×C139—21no—
91#121×C139—21no—
92#121×C139—22no—
93#121×C139D412yes—
94C4×Q8×C139—21no—
95C4×Q8×C139—21no—
96C4×Q8×C139—21no—
97C4×Q8×C139C2312yes—
98C4×D4×C139—22no—
99C4×D4×C139—22no—
100C4×D4×C139—21no—
101C4×D4×C139—21no—
102C4×D4×C139—21no—
103C4×D4×C139C2312yes—
104#117×C139—21no—
105#117×C139—21no—
106C2×C4⋊C4×C139—22no—
107C2×C4⋊C4×C139—22no—
108C2×C42×C139C2311yescharacteristic
109#107×C139—22no—
110#106×C139—22no—
111C4⋊C8×C139—21no—
112C4⋊C8×C139—21no—
113C4⋊C8×C139C2312yes—
114C4⋊C8×C139C2312yes—
115#103×C139—22no—
116#103×C139—22no—
117#103×C139—22no—
118#103×C139—22no—
119#103×C139—22no—
120#102×C139—22no—
121#102×C139—22no—
122#102×C139—22no—
123C4×C8×C139—21no—
124C4×C8×C139C2311yescharacteristic
125C4×C8×C139C2311yescharacteristic
126#41×C139—44no—
127#41×C139—81no—
128#41×C139—81no—
129#41×C139—82no—
130#41×C139—82no—
131#41×C139—84no—
132C2×Q8×C139—21no—
133C2×Q8×C139—21no—
134C2×Q8×C139—21no—
135C2×Q8×C139—21no—
136C2×Q8×C139C2×D412yes—
137C2×Q8×C139C2×D412yes—
138C2×D4×C139—24no—
139C2×D4×C139—24no—
140C2×D4×C139—22no—
141C2×D4×C139—22no—
142C2×D4×C139—21no—
143C2×D4×C139—21no—
144C2×D4×C139—21no—
145C2×D4×C139—21no—
146C2×D4×C139C2×D412yes—
147C2×D4×C139C2×D412yes—
148C22×C4×C139—24no—
149C22×C4×C139—24no—
150C22×C4×C139—22no—
151C22×C4×C139—22no—
152C22×C4×C139C2×D411yescharacteristic
153C22×C4×C139C2×D411yescharacteristic
154C22×C4×C139C2×D411yescharacteristic
155Q16×C139—82no—
156SD16×C139—82no—
157M16×C139—81no—
158M16×C139—81no—
159C2×C8×C139—21no—
160C2×C8×C139—21no—
161C2×C8×C139—22no—
162C2×C8×C139—22no—
163C2×C8×C139—42no—
164C4⋊C4×C139—24no—
165C4⋊C4×C139—24no—
166C4⋊C4×C139—21no—
167C4⋊C4×C139—21no—
168C4⋊C4×C139—21no—
169C4⋊C4×C139—21no—
170C4⋊C4×C139—22no—
171C4⋊C4×C139—21no—
172C4⋊C4×C139—21no—
173C4⋊C4×C139—22no—
174C4⋊C4×C139—21no—
175C4⋊C4×C139—21no—
176C4⋊C4×C139—21no—
177C4⋊C4×C139—21no—
178C4⋊C4×C139—41no—
179C4⋊C4×C139—41no—
180C4⋊C4×C139C2×D412yes—
181C4⋊C4×C139C2×D412yes—
182C22⋊C4×C139—24no—
183C22⋊C4×C139—24no—
184C22⋊C4×C139—22no—
185C22⋊C4×C139—22no—
186C22⋊C4×C139—22no—
187C22⋊C4×C139—22no—
188C22⋊C4×C139—22no—
189C22⋊C4×C139—41no—
190C42×C139—22no—
191C42×C139—41no—
192C42×C139C2×D411yescharacteristic
193C42×C139C2×D411yescharacteristic
194C42×C139C2×D411yescharacteristic
195C42×C139C2411yescharacteristic
196C23×C139—22no—
197C23×C139—22no—
198C23×C139#12011yescharacteristic
199Q8×C139—22no—
200Q8×C139—22no—
201Q8×C139—42no—
202Q8×C139—42no—
203Q8×C139—41no—
204Q8×C139—41no—
205Q8×C139—41no—
206Q8×C139—41no—
207Q8×C139—81no—
208D4×C139—22no—
209D4×C139—22no—
210D4×C139—42no—
211D4×C139—41no—
212D4×C139—41no—
213D4×C139—41no—
214D4×C139—41no—
215D4×C139—42no—
216D4×C139—81no—
217D4×C139—82no—
218D4×C139—82no—
219D4×C139—84no—
220D4×C139—84no—
221C2×C4×C139—21no—
222C2×C4×C139—21no—
223C2×C4×C139—21no—
224C2×C4×C139—21no—
225C2×C4×C139—22no—
226C2×C4×C139—22no—
227C2×C4×C139—22no—
228C2×C4×C139—22no—
229C2×C4×C139—22no—
230C2×C4×C139—42no—
231C2×C4×C139—42no—
232C2×C4×C139—44no—
233C2×C4×C139—41no—
234C2×C4×C139—41no—
235C2×C4×C139—84no—
236C2×C4×C139—84no—
237C2×C4×C139#12011yescharacteristic
238C2×C4×C139#12011yescharacteristic
239C2×C4×C139#12011yescharacteristic
240C2×C4×C139C22×D411yescharacteristic
241C2×C4×C139C22×D411yescharacteristic
242C2×C4×C139C22×D411yescharacteristic
243C8×C139—41no—
244C8×C139—41no—
245C8×C139—42no—
246C8×C139—42no—
247C22×C139—21no—
248C22×C139—21no—
249C22×C139—21no—
250C22×C139—42no—
251C22×C139—42no—
252C22×C139—42no—
253C22×C139—42no—
254C22×C139—42no—
255C22×C139—42no—
256C22×C139C2×#12011yescharacteristic
257C4×C139—21no—
258C4×C139—21no—
259C4×C139—21no—
260C4×C139—42no—
261C4×C139—42no—
262C4×C139—42no—
263C4×C139—42no—
264C4×C139—81no—
265C4×C139—81no—
266C4×C139#45512yes—
267C4×C139#57611yescharacteristic
268C4×C139#57711yescharacteristic
269C4×C139#57711yescharacteristic
270C4×C139#57811yescharacteristic
271C2×C139—41no—
272C2×C139—82no—
273C2×C139—82no—
274C2×C139#301211yescharacteristic
275C2×C139#301311yescharacteristic
276C2×C139C2×#45511yescharacteristic
277#18692C13911yesmaximal, characteristic, direct product factor, Sylow
278C139#1869211yescharacteristic, direct product factor, Sylow
279#3548C2×C13911yescharacteristic
280#3255C2×C13911yescharacteristic, complemented
281#3254C2×C13911yescharacteristic, complemented
282#3131C2×C13911yescharacteristic, complemented
283#1644C2×C13912yescomplemented
284#1643C2×C13912yescomplemented
285#1642C2×C13912yescomplemented
286#1641C2×C13912yescomplemented
287#1560C2×C13911yescharacteristic, complemented
288#1493C2×C13911yescharacteristic, complemented
289#1492C2×C13911yescharacteristic, complemented
290#562—22no—
291#554—21no—
292#554C22×C13912yes—
293#550—21no—
294#550C22×C13912yes—
295#547—21no—
296#547—21no—
297#540—22no—
298#537—22no—
299#537—22no—
300#533C22×C13911yescharacteristic
301#533C22×C13911yescharacteristic
302#532C22×C13911yescharacteristic
303#532C22×C13911yescharacteristic
304#488—22no—
305#487C22×C13911yescharacteristic
306#487C22×C13911yescharacteristic
307#486C22×C13911yescharacteristic
308#486C22×C13911yescharacteristic
309#477—21no—
310#475—21no—
311#475C22×C13912yes—
312#474C22×C13912yes—
313#470—22no—
314#468—22no—
315#462—21no—
316#462C22×C13912yes—
317#461C22×C13912yes—
318#460—21no—
319#423C22×C13911yescharacteristic
320#423C22×C13911yescharacteristic
321#416—22no—
322C2×C4×C8C22×C13911yescharacteristic
323#333C22×C13912yes—
324#331C22×C13912yes—
325Q8⋊C8C22×C13912yes—
326Q8⋊C8C22×C13912yes—
327D4⋊C8C22×C13912yes—
328D4⋊C8C22×C13912yes—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—21no—
332C2×#41D4×C13912yes—
333C2×Q16—22no—
334C2×SD16—22no—
335C2×M16—21no—
336C2×M16—21no—
337C22×C8—21no—
338C4⋊Q8D4×C13911yescharacteristic
339C4⋊Q8D4×C13911yescharacteristic
340C4⋊Q8D4×C13911yescharacteristic
341C4⋊Q8C23×C13911yescharacteristic
342C4⋊Q8C23×C13911yescharacteristic
343C4⋊Q8C23×C13911yescharacteristic
344#127—22no—
345#127D4×C13911yescharacteristic
346#127C23×C13911yescharacteristic
347#125—22no—
348#125—21no—
349#125—21no—
350#124—21no—
351#124D4×C13912yes—
352#123—24no—
353#123—24no—
354C22⋊Q8—22no—
355C22⋊Q8—24no—
356C22⋊Q8—22no—
357C22⋊Q8—24no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8D4×C13912yes—
362#121—24no—
363#121—24no—
364#121—22no—
365#121—24no—
366#121—24no—
367#121—21no—
368#121—21no—
369#121—21no—
370#121—22no—
371#121D4×C13912yes—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C13912yes—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4C23×C13912yes—
382#117—21no—
383#117—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C42C23×C13911yescharacteristic
387#107—22no—
388#106—22no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8C23×C13912yes—
392C4⋊C8C23×C13912yes—
393#103—22no—
394#103—22no—
395#103—22no—
396#103—22no—
397#103—22no—
398#102—22no—
399#102—22no—
400#102—22no—
401C4×C8—21no—
402C4×C8C23×C13911yescharacteristic
403C4×C8C23×C13911yescharacteristic
404#41—44no—
405#41—81no—
406#41—81no—
407#41—82no—
408#41—82no—
409#41—84no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8C2×D4×C13912yes—
415C2×Q8C2×D4×C13912yes—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4C2×D4×C13912yes—
425C2×D4C2×D4×C13912yes—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4C2×D4×C13911yescharacteristic
431C22×C4C2×D4×C13911yescharacteristic
432C22×C4C2×D4×C13911yescharacteristic
433Q16—82no—
434SD16—82no—
435M16—81no—
436M16—81no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—42no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4C2×D4×C13912yes—
459C4⋊C4C2×D4×C13912yes—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—41no—
468C42—22no—
469C42—41no—
470C42C2×D4×C13911yescharacteristic
471C42C2×D4×C13911yescharacteristic
472C42C2×D4×C13911yescharacteristic
473C42C24×C13911yescharacteristic
474C23—22no—
475C23—22no—
476C23#120×C13911yescharacteristic
477Q8—22no—
478Q8—22no—
479Q8—42no—
480Q8—42no—
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—81no—
486D4—22no—
487D4—22no—
488D4—42no—
489D4—42no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—81no—
495D4—82no—
496D4—82no—
497D4—84no—
498D4—84no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—44no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—84no—
514C2×C4—84no—
515C2×C4#120×C13911yescharacteristic
516C2×C4#120×C13911yescharacteristic
517C2×C4#120×C13911yescharacteristic
518C2×C4C22×D4×C13911yescharacteristic
519C2×C4C22×D4×C13911yescharacteristic
520C2×C4C22×D4×C13911yescharacteristic
521C8—41no—
522C8—41no—
523C8—42no—
524C8—42no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22C2×#120×C13911yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—42no—
539C4—42no—
540C4—42no—
541C4—42no—
542C4—81no—
543C4—81no—
544C4#455×C13912yes—
545C4#576×C13911yescharacteristic
546C4#577×C13911yescharacteristic
547C4#577×C13911yescharacteristic
548C4#578×C13911yescharacteristic
549C2—41no—
550C2—82no—
551C2—82no—
552C2#3012×C13911yescharacteristic
553C2#3013×C13911yescharacteristic
554C2C2×#455×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC42C24×C139
prime radical#3548×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. #3255×C139C2semidirect
3. #3254×C139C2semidirect
4. #3131×C139C2semidirect
5. #1644×C139C2semidirect
6. #1643×C139C2semidirect
7. #1642×C139C2semidirect
8. #1641×C139C2semidirect
9. #1560×C139C2semidirect
10. #1493×C139C2semidirect
11. #1492×C139C2semidirect
277. #18692C139direct (N × H)
278. C139#18692direct (N × H)
280. #3255C2×C139semidirect
281. #3254C2×C139semidirect
282. #3131C2×C139semidirect
283. #1644C2×C139semidirect
284. #1643C2×C139semidirect
285. #1642C2×C139semidirect
286. #1641C2×C139semidirect
287. #1560C2×C139semidirect
288. #1493C2×C139semidirect
289. #1492C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3548×C1392
#3255×C1392
#3254×C1392
#3131×C1392
#1644×C1392
#1643×C1392
#1642×C1392
#1641×C1392
#1560×C1392
#1493×C1392
#1492×C1392
#18692139