Finite Group Databasebeta

← C139×#26839 #48021435

Subgroups — C139×#26839 #48021435

Order 35584.

784 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#488×C139C211yesmaximal, characteristic
2C2×#441×C139C211yesmaximal, characteristic, complemented
3#2453×C139C211yesmaximal, characteristic, complemented
4#2448×C139C211yesmaximal, characteristic
5#2065×C139C211yesmaximal, characteristic
6#2059×C139C211yesmaximal, characteristic, complemented
7#2056×C139C211yesmaximal, characteristic, complemented
8#2015×C139C211yesmaximal, characteristic
9#1973×C139C211yesmaximal, characteristic
10#1936×C139C211yesmaximal, characteristic
11#1935×C139C211yesmaximal, characteristic, complemented
12#1933×C139C211yesmaximal, characteristic, complemented
13#1880×C139C211yesmaximal, characteristic
14#1863×C139C211yesmaximal, characteristic, complemented
15#1771×C139C211yesmaximal, characteristic, complemented
16C22×Q16×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C2×#125×C139C2211yescharacteristic
19C2×#124×C139C2211yescharacteristic
20C2×C4×Q8×C139C2211yescharacteristic
21C2×C4×Q8×C139C2211yescharacteristic
22#488×C139—24no—
23#441×C139—24no—
24C2×#107×C139C2211yescharacteristic
25C2×#106×C139C2211yescharacteristic
26C2×C4⋊C8×C139C2211yescharacteristic
27C2×#103×C139C2211yescharacteristic
28C2×#103×C139C2211yescharacteristic
29C2×#103×C139C2211yescharacteristic
30C2×#103×C139C2211yescharacteristic
31C2×#103×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#97×C139C2211yescharacteristic
36C2×#97×C139C2211yescharacteristic
37C2×C4×C8×C139C2211yescharacteristic
38#400×C139—21no—
39#399×C139—21no—
40#398×C139—21no—
41#397×C139—21no—
42#391×C139C2211yescharacteristic
43#391×C139C2211yescharacteristic
44#391×C139C2211yescharacteristic
45#390×C139C2211yescharacteristic
46#390×C139C2211yescharacteristic
47#389×C139—21no—
48#389×C139C2211yescharacteristic
49#389×C139C2211yescharacteristic
50#389×C139C2211yescharacteristic
51#388×C139—21no—
52#388×C139—21no—
53#387×C139—21no—
54C4×C4⋊C4×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#336×C139C2211yescharacteristic
60#336×C139C2211yescharacteristic
61C22×Q8×C139C2311yescharacteristic
62C22×Q8×C139C2311yescharacteristic
63C22×D4×C139C2311yescharacteristic
64C2×Q16×C139—22no—
65C2×Q16×C139—22no—
66C2×Q16×C139—22no—
67C2×SD16×C139—22no—
68C2×SD16×C139—22no—
69C2×SD16×C139—41no—
70C22×C8×C139C2311yescharacteristic
71C22×C8×C139C2311yescharacteristic
72C22×C8×C139C2311yescharacteristic
73C22×C8×C139C2311yescharacteristic
74#125×C139—22no—
75#125×C139—41no—
76#124×C139—22no—
77#124×C139—41no—
78C4×Q8×C139—22no—
79C4×Q8×C139—22no—
80C4×Q8×C139—41no—
81C4×Q8×C139—41no—
82C2×C4⋊C4×C139—21no—
83C2×C4⋊C4×C139—21no—
84C2×C4⋊C4×C139—21no—
85C2×C4⋊C4×C139—21no—
86C2×C4⋊C4×C139—21no—
87C2×C4⋊C4×C139—21no—
88C2×C4⋊C4×C139—21no—
89C2×C4⋊C4×C139D411yescharacteristic
90C2×C4⋊C4×C139D411yescharacteristic
91C2×C4⋊C4×C139C2311yescharacteristic
92C2×C4⋊C4×C139C2311yescharacteristic
93C2×C4⋊C4×C139C2311yescharacteristic
94C2×C4⋊C4×C139C2311yescharacteristic
95C2×C4⋊C4×C139C2311yescharacteristic
96C2×C22⋊C4×C139—21no—
97C2×C22⋊C4×C139—21no—
98C2×C22⋊C4×C139—21no—
99C2×C22⋊C4×C139—21no—
100C2×C22⋊C4×C139—21no—
101C2×C22⋊C4×C139—21no—
102C2×C42×C139—21no—
103C2×C42×C139—21no—
104C2×C42×C139C2311yescharacteristic
105C2×C42×C139C2311yescharacteristic
106C2×C42×C139C2311yescharacteristic
107#107×C139—41no—
108#106×C139—22no—
109C4⋊C8×C139—22no—
110#103×C139—22no—
111#103×C139—22no—
112#103×C139—22no—
113#103×C139—22no—
114#103×C139D414yes—
115#102×C139—22no—
116#102×C139—22no—
117#102×C139—22no—
118#97×C139—22no—
119#97×C139—22no—
120C4×C8×C139—22no—
121#95×C139—21no—
122#95×C139—21no—
123#95×C139—21no—
124#95×C139—21no—
125#95×C139—21no—
126#95×C139—21no—
127#95×C139—21no—
128#95×C139—21no—
129#95×C139—21no—
130#95×C139D411yescharacteristic
131#95×C139D411yescharacteristic
132C24×C139—21no—
133C2×Q8×C139—21no—
134C2×Q8×C139—21no—
135C2×Q8×C139—21no—
136C2×Q8×C139—21no—
137C2×Q8×C139—21no—
138C2×Q8×C139—21no—
139C2×Q8×C139—21no—
140C2×Q8×C139—21no—
141C2×Q8×C139—21no—
142C2×Q8×C139—21no—
143C2×Q8×C139C2×D412yes—
144C2×Q8×C139#4112yes—
145C2×D4×C139—21no—
146C2×D4×C139—21no—
147C2×D4×C139—21no—
148C2×D4×C139—21no—
149C2×D4×C139—21no—
150C2×D4×C139—21no—
151C22×C4×C139—21no—
152C22×C4×C139—21no—
153C22×C4×C139—21no—
154C22×C4×C139—21no—
155C22×C4×C139—21no—
156C22×C4×C139—21no—
157C22×C4×C139—21no—
158C22×C4×C139C2×D411yescharacteristic
159C22×C4×C139C2×D411yescharacteristic
160C22×C4×C139C2×D411yescharacteristic
161C22×C4×C139C2×D411yescharacteristic
162C22×C4×C139C2×D411yescharacteristic
163C22×C4×C139C2×D411yescharacteristic
164C22×C4×C139C2411yescharacteristic
165Q16×C139—28no—
166SD16×C139—44no—
167C2×C8×C139—21no—
168C2×C8×C139—21no—
169C2×C8×C139—21no—
170C2×C8×C139—21no—
171C2×C8×C139—21no—
172C2×C8×C139—21no—
173C2×C8×C139—21no—
174C2×C8×C139—21no—
175C2×C8×C139—21no—
176C2×C8×C139C2×D412yes—
177C2×C8×C139#4112yes—
178C2×C8×C139#4112yes—
179C4⋊C4×C139—21no—
180C4⋊C4×C139—21no—
181C4⋊C4×C139—21no—
182C4⋊C4×C139—21no—
183C4⋊C4×C139—21no—
184C4⋊C4×C139—21no—
185C4⋊C4×C139—21no—
186C4⋊C4×C139—21no—
187C4⋊C4×C139—21no—
188C4⋊C4×C139—41no—
189C4⋊C4×C139—41no—
190C4⋊C4×C139—42no—
191C4⋊C4×C139—42no—
192C4⋊C4×C139—42no—
193C4⋊C4×C139—42no—
194C4⋊C4×C139—42no—
195C4⋊C4×C139—42no—
196C4⋊C4×C139—81no—
197C4⋊C4×C139C2×D412yes—
198C22⋊C4×C139—42no—
199C22⋊C4×C139—42no—
200C22⋊C4×C139—42no—
201C22⋊C4×C139—42no—
202C22⋊C4×C139—81no—
203C22⋊C4×C139—81no—
204C42×C139—21no—
205C42×C139—21no—
206C42×C139—21no—
207C42×C139—21no—
208C42×C139—21no—
209C42×C139—21no—
210C42×C139—42no—
211C42×C139—42no—
212C23×C139—41no—
213C23×C139—41no—
214C23×C139—41no—
215C23×C139—41no—
216C23×C139—41no—
217C23×C139—41no—
218C23×C139—41no—
219C23×C139C22×D411yescharacteristic
220Q8×C139—22no—
221Q8×C139—22no—
222Q8×C139—22no—
223Q8×C139—22no—
224Q8×C139—41no—
225Q8×C139—41no—
226Q8×C139—41no—
227Q8×C139—41no—
228D4×C139—41no—
229D4×C139—41no—
230D4×C139—41no—
231D4×C139—41no—
232C2×C4×C139—21no—
233C2×C4×C139—21no—
234C2×C4×C139—21no—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—21no—
238C2×C4×C139—22no—
239C2×C4×C139—22no—
240C2×C4×C139—22no—
241C2×C4×C139—21no—
242C2×C4×C139—21no—
243C2×C4×C139—21no—
244C2×C4×C139—21no—
245C2×C4×C139—21no—
246C2×C4×C139—21no—
247C2×C4×C139—21no—
248C2×C4×C139—21no—
249C2×C4×C139—21no—
250C2×C4×C139—21no—
251C2×C4×C139—21no—
252C2×C4×C139—21no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—41no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—41no—
260C2×C4×C139—41no—
261C2×C4×C139—41no—
262C2×C4×C139—41no—
263C2×C4×C139—41no—
264C2×C4×C139—41no—
265C2×C4×C139—41no—
266C2×C4×C139—41no—
267C2×C4×C139—41no—
268C2×C4×C139—41no—
269C2×C4×C139—41no—
270C2×C4×C139—41no—
271C2×C4×C139C22×D411yescharacteristic
272C2×C4×C139C2×#4111yescharacteristic
273C2×C4×C139C2×#4111yescharacteristic
274C2×C4×C139C2×#4111yescharacteristic
275C2×C4×C139H(5,𝔽2)11yescharacteristic
276C2×C4×C1392−1+411yescharacteristic
277C8×C139—22no—
278C8×C139—22no—
279C8×C139—22no—
280C8×C139—41no—
281C22×C139—81no—
282C22×C139—81no—
283C22×C139—81no—
284C22×C139—81no—
285C22×C139—81no—
286C22×C139—81no—
287C22×C139—81no—
288C22×C139#53211yescharacteristic
289C22×C139D4211yescharacteristic
290C22×C139#54811yescharacteristic
291C22×C139#57511yescharacteristic
292C22×C139#57511yescharacteristic
293C22×C139#57711yescharacteristic
294C22×C139#57811yescharacteristic
295C4×C139—41no—
296C4×C139—41no—
297C4×C139—42no—
298C4×C139—42no—
299C4×C139—41no—
300C4×C139—41no—
301C4×C139—42no—
302C4×C139—41no—
303C4×C139—41no—
304C4×C139—81no—
305C4×C139—81no—
306C4×C139—81no—
307C4×C139—81no—
308C4×C139#52511yescharacteristic
309C4×C139#54211yescharacteristic
310C4×C139#54711yescharacteristic
311C4×C139#55111yescharacteristic
312C2×C139—161no—
313C2×C139#246111yescharacteristic
314C2×C139#317811yescharacteristic
315C2×C139#318311yescharacteristic
316C2×C139#326911yescharacteristic
317C2×C139#327111yescharacteristic
318C2×C139#337111yescharacteristic
319C2×C139#337711yescharacteristic
320#26839C13911yesmaximal, characteristic, direct product factor, Sylow
321C139#2683911yescharacteristic, direct product factor, Sylow
322C2×#488C2×C13911yescharacteristic
323C2×#441C2×C13911yescharacteristic, complemented
324#2453C2×C13911yescharacteristic, complemented
325#2448C2×C13911yescharacteristic
326#2065C2×C13911yescharacteristic
327#2059C2×C13911yescharacteristic, complemented
328#2056C2×C13911yescharacteristic, complemented
329#2015C2×C13911yescharacteristic
330#1973C2×C13911yescharacteristic
331#1936C2×C13911yescharacteristic
332#1935C2×C13911yescharacteristic, complemented
333#1933C2×C13911yescharacteristic, complemented
334#1880C2×C13911yescharacteristic
335#1863C2×C13911yescharacteristic, complemented
336#1771C2×C13911yescharacteristic, complemented
337C22×Q16C22×C13911yescharacteristic
338C22×SD16C22×C13911yescharacteristic
339C2×#125C22×C13911yescharacteristic
340C2×#124C22×C13911yescharacteristic
341C2×C4×Q8C22×C13911yescharacteristic
342C2×C4×Q8C22×C13911yescharacteristic
343#488—24no—
344#441—24no—
345C2×#107C22×C13911yescharacteristic
346C2×#106C22×C13911yescharacteristic
347C2×C4⋊C8C22×C13911yescharacteristic
348C2×#103C22×C13911yescharacteristic
349C2×#103C22×C13911yescharacteristic
350C2×#103C22×C13911yescharacteristic
351C2×#103C22×C13911yescharacteristic
352C2×#103C22×C13911yescharacteristic
353C2×#102C22×C13911yescharacteristic
354C2×#102C22×C13911yescharacteristic
355C2×#102C22×C13911yescharacteristic
356C2×#97C22×C13911yescharacteristic
357C2×#97C22×C13911yescharacteristic
358C2×C4×C8C22×C13911yescharacteristic
359#400—21no—
360#399—21no—
361#398—21no—
362#397—21no—
363#391C22×C13911yescharacteristic
364#391C22×C13911yescharacteristic
365#391C22×C13911yescharacteristic
366#390C22×C13911yescharacteristic
367#390C22×C13911yescharacteristic
368#389—21no—
369#389C22×C13911yescharacteristic
370#389C22×C13911yescharacteristic
371#389C22×C13911yescharacteristic
372#388—21no—
373#388—21no—
374#387—21no—
375C4×C4⋊C4C22×C13911yescharacteristic
376#340C22×C13911yescharacteristic
377#340C22×C13911yescharacteristic
378#340C22×C13911yescharacteristic
379#340C22×C13911yescharacteristic
380#336C22×C13911yescharacteristic
381#336C22×C13911yescharacteristic
382C22×Q8C23×C13911yescharacteristic
383C22×Q8C23×C13911yescharacteristic
384C22×D4C23×C13911yescharacteristic
385C2×Q16—22no—
386C2×Q16—22no—
387C2×Q16—22no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16—41no—
391C22×C8C23×C13911yescharacteristic
392C22×C8C23×C13911yescharacteristic
393C22×C8C23×C13911yescharacteristic
394C22×C8C23×C13911yescharacteristic
395#125—22no—
396#125—41no—
397#124—22no—
398#124—41no—
399C4×Q8—22no—
400C4×Q8—22no—
401C4×Q8—41no—
402C4×Q8—41no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4D4×C13911yescharacteristic
411C2×C4⋊C4D4×C13911yescharacteristic
412C2×C4⋊C4C23×C13911yescharacteristic
413C2×C4⋊C4C23×C13911yescharacteristic
414C2×C4⋊C4C23×C13911yescharacteristic
415C2×C4⋊C4C23×C13911yescharacteristic
416C2×C4⋊C4C23×C13911yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42C23×C13911yescharacteristic
426C2×C42C23×C13911yescharacteristic
427C2×C42C23×C13911yescharacteristic
428#107—41no—
429#106—22no—
430C4⋊C8—22no—
431#103—22no—
432#103—22no—
433#103—22no—
434#103—22no—
435#103D4×C13914yes—
436#102—22no—
437#102—22no—
438#102—22no—
439#97—22no—
440#97—22no—
441C4×C8—22no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95D4×C13911yescharacteristic
452#95D4×C13911yescharacteristic
453C24—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8C2×D4×C13912yes—
465C2×Q8#41×C13912yes—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4C2×D4×C13911yescharacteristic
480C22×C4C2×D4×C13911yescharacteristic
481C22×C4C2×D4×C13911yescharacteristic
482C22×C4C2×D4×C13911yescharacteristic
483C22×C4C2×D4×C13911yescharacteristic
484C22×C4C2×D4×C13911yescharacteristic
485C22×C4C24×C13911yescharacteristic
486Q16—28no—
487SD16—44no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8C2×D4×C13912yes—
498C2×C8#41×C13912yes—
499C2×C8#41×C13912yes—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—42no—
516C4⋊C4—42no—
517C4⋊C4—81no—
518C4⋊C4C2×D4×C13912yes—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—42no—
532C42—42no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23C22×D4×C13911yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—22no—
544Q8—22no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4C22×D4×C13911yescharacteristic
593C2×C4C2×#41×C13911yescharacteristic
594C2×C4C2×#41×C13911yescharacteristic
595C2×C4C2×#41×C13911yescharacteristic
596C2×C4H(5,𝔽2)×C13911yescharacteristic
597C2×C42−1+4×C13911yescharacteristic
598C8—22no—
599C8—22no—
600C8—22no—
601C8—41no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22#532×C13911yescharacteristic
610C22D42×C13911yescharacteristic
611C22#548×C13911yescharacteristic
612C22#575×C13911yescharacteristic
613C22#575×C13911yescharacteristic
614C22#577×C13911yescharacteristic
615C22#578×C13911yescharacteristic
616C4—41no—
617C4—41no—
618C4—42no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—42no—
623C4—41no—
624C4—41no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—81no—
629C4#525×C13911yescharacteristic
630C4#542×C13911yescharacteristic
631C4#547×C13911yescharacteristic
632C4#551×C13911yescharacteristic
633C2—161no—
634C2#2461×C13911yescharacteristic
635C2#3178×C13911yescharacteristic
636C2#3183×C13911yescharacteristic
637C2#3269×C13911yescharacteristic
638C2#3271×C13911yescharacteristic
639C2#3371×C13911yescharacteristic
640C2#3377×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC22×D4×C139C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C4⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#441×C139C2semidirect
3. #2453×C139C2semidirect
6. #2059×C139C2semidirect
7. #2056×C139C2semidirect
11. #1935×C139C2semidirect
12. #1933×C139C2semidirect
14. #1863×C139C2semidirect
15. #1771×C139C2semidirect
320. #26839C139direct (N × H)
321. C139#26839direct (N × H)
323. C2×#441C2×C139semidirect
324. #2453C2×C139semidirect
327. #2059C2×C139semidirect
328. #2056C2×C139semidirect
332. #1935C2×C139semidirect
333. #1933C2×C139semidirect
335. #1863C2×C139semidirect
336. #1771C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#488×C1392
C2×#441×C1392
#2453×C1392
#2448×C1392
#2065×C1392
#2059×C1392
#2056×C1392
#2015×C1392
#1973×C1392
#1936×C1392
#1935×C1392
#1933×C1392
#1880×C1392
#1863×C1392
#1771×C1392
#26839139