Finite Group Databasebeta

← C139×#27129 #48021725

Subgroups — C139×#27129 #48021725

Order 35584.

686 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2513×C139C211yesmaximal, characteristic
2#2365×C139C211yesmaximal, characteristic, complemented
3#2101×C139C211yesmaximal, characteristic, complemented
4#2065×C139C211yesmaximal, characteristic
5#2058×C139C211yesmaximal, characteristic, complemented
6#2023×C139C211yesmaximal, characteristic
7#1949×C139C211yesmaximal, characteristic, complemented
8#1934×C139C211yesmaximal, characteristic
9#1926×C139C211yesmaximal, characteristic
10#1926×C139C211yesmaximal, characteristic
11#1925×C139C211yesmaximal, characteristic
12#1921×C139C211yesmaximal, characteristic, complemented
13#1919×C139C211yesmaximal, characteristic, complemented
14#1916×C139C211yesmaximal, characteristic, complemented
15C4×#106×C139C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C139C2211yescharacteristic
17C2×C4×Q8×C139—21no—
18C2×#107×C139C2211yescharacteristic
19C2×#106×C139C2211yescharacteristic
20C2×#106×C139C2211yescharacteristic
21C2×#106×C139C2211yescharacteristic
22C2×C4⋊C8×C139C2211yescharacteristic
23C2×#102×C139C2211yescharacteristic
24C2×#102×C139C2211yescharacteristic
25C2×#102×C139C2211yescharacteristic
26C2×#102×C139C2211yescharacteristic
27C2×C4×C8×C139C2211yescharacteristic
28#397×C139—21no—
29#397×C139—21no—
30#391×C139—21no—
31#390×C139C2211yescharacteristic
32#390×C139C2211yescharacteristic
33#390×C139C2211yescharacteristic
34#389×C139C2211yescharacteristic
35#389×C139C2211yescharacteristic
36#389×C139C2211yescharacteristic
37#388×C139—21no—
38#388×C139—21no—
39#387×C139—21no—
40#387×C139—21no—
41#382×C139C2211yescharacteristic
42C4×C4⋊C4×C139C2211yescharacteristic
43C4×C4⋊C4×C139C2211yescharacteristic
44C4×C4⋊C4×C139C2211yescharacteristic
45C4×C4⋊C4×C139C2211yescharacteristic
46C4×C4⋊C4×C139C2211yescharacteristic
47#340×C139C2211yescharacteristic
48#340×C139C2211yescharacteristic
49#340×C139C2211yescharacteristic
50#340×C139C2211yescharacteristic
51#340×C139C2211yescharacteristic
52#340×C139C2211yescharacteristic
53#340×C139C2211yescharacteristic
54#340×C139C2211yescharacteristic
55#336×C139C2211yescharacteristic
56#336×C139C2211yescharacteristic
57#336×C139C2211yescharacteristic
58#336×C139C2211yescharacteristic
59C22×Q8×C139—21no—
60C22×D4×C139C2311yescharacteristic
61C22×C8×C139C2311yescharacteristic
62C22×C8×C139C2311yescharacteristic
63C22×C8×C139C2311yescharacteristic
64C22×C8×C139C2311yescharacteristic
65C4⋊Q8×C139—22no—
66C4⋊Q8×C139—22no—
67C4×Q8×C139—44no—
68C2×C4⋊C4×C139—21no—
69C2×C4⋊C4×C139—21no—
70C2×C4⋊C4×C139—21no—
71C2×C4⋊C4×C139—21no—
72C2×C4⋊C4×C139D411yescharacteristic
73C2×C4⋊C4×C139D411yescharacteristic
74C2×C4⋊C4×C139C2311yescharacteristic
75C2×C4⋊C4×C139C2311yescharacteristic
76C2×C4⋊C4×C139C2311yescharacteristic
77C2×C4⋊C4×C139C2311yescharacteristic
78C2×C4⋊C4×C139C2311yescharacteristic
79C2×C4⋊C4×C139C2311yescharacteristic
80C2×C4⋊C4×C139C2311yescharacteristic
81C2×C22⋊C4×C139—21no—
82C2×C22⋊C4×C139—21no—
83C2×C22⋊C4×C139—21no—
84C2×C22⋊C4×C139—21no—
85C2×C22⋊C4×C139—21no—
86C2×C22⋊C4×C139—21no—
87C2×C42×C139—21no—
88C2×C42×C139—21no—
89C2×C42×C139—21no—
90C2×C42×C139—21no—
91C2×C42×C139C2311yescharacteristic
92C2×C42×C139C2311yescharacteristic
93C2×C42×C139C2311yescharacteristic
94#107×C139—22no—
95#106×C139—22no—
96#106×C139—22no—
97#106×C139—22no—
98C4⋊C8×C139—22no—
99#102×C139—22no—
100#102×C139—22no—
101#102×C139—22no—
102#102×C139—22no—
103C4×C8×C139—22no—
104#95×C139—21no—
105#95×C139—21no—
106#95×C139—21no—
107#95×C139—21no—
108#95×C139—21no—
109#95×C139—21no—
110#95×C139—21no—
111#95×C139—21no—
112#95×C139—21no—
113#95×C139D411yescharacteristic
114#95×C139D411yescharacteristic
115C24×C139—21no—
116C2×Q8×C139—24no—
117C2×Q8×C139—42no—
118C2×Q8×C139—42no—
119C2×D4×C139—21no—
120C2×D4×C139—21no—
121C2×D4×C139—21no—
122C2×D4×C139—21no—
123C2×D4×C139—21no—
124C2×D4×C139—21no—
125C22×C4×C139—21no—
126C22×C4×C139—21no—
127C22×C4×C139—21no—
128C22×C4×C139—21no—
129C22×C4×C139—21no—
130C22×C4×C139—21no—
131C22×C4×C139—21no—
132C22×C4×C139C2×D411yescharacteristic
133C22×C4×C139C2×D411yescharacteristic
134C22×C4×C139C2×D411yescharacteristic
135C22×C4×C139C2×D411yescharacteristic
136C22×C4×C139C2×D411yescharacteristic
137C22×C4×C139C2×D411yescharacteristic
138C22×C4×C139C2411yescharacteristic
139C2×C8×C139—21no—
140C2×C8×C139—21no—
141C2×C8×C139—21no—
142C2×C8×C139—21no—
143C2×C8×C139—21no—
144C2×C8×C139—21no—
145C2×C8×C139—21no—
146C2×C8×C139—21no—
147C2×C8×C139—21no—
148C2×C8×C139—21no—
149C2×C8×C139—21no—
150C2×C8×C139#4112yes—
151C4⋊C4×C139—24no—
152C4⋊C4×C139—22no—
153C4⋊C4×C139—22no—
154C4⋊C4×C139—21no—
155C4⋊C4×C139—21no—
156C4⋊C4×C139—21no—
157C4⋊C4×C139—21no—
158C4⋊C4×C139—21no—
159C4⋊C4×C139—21no—
160C4⋊C4×C139—21no—
161C4⋊C4×C139—21no—
162C4⋊C4×C139—21no—
163C4⋊C4×C139—21no—
164C4⋊C4×C139—21no—
165C4⋊C4×C139—42no—
166C4⋊C4×C139—42no—
167C4⋊C4×C139—81no—
168C4⋊C4×C139#4112yes—
169C4⋊C4×C139#4112yes—
170C4⋊C4×C139#4112yes—
171C22⋊C4×C139—42no—
172C22⋊C4×C139—42no—
173C22⋊C4×C139—81no—
174C22⋊C4×C139—81no—
175C22⋊C4×C139—81no—
176C22⋊C4×C139—81no—
177C42×C139—21no—
178C42×C139—21no—
179C42×C139—21no—
180C42×C139—21no—
181C42×C139—21no—
182C42×C139—21no—
183C42×C139—42no—
184C42×C139—42no—
185C42×C139—42no—
186C42×C139—81no—
187C23×C139—41no—
188C23×C139—41no—
189C23×C139—41no—
190C23×C139—41no—
191C23×C139—41no—
192C23×C139—41no—
193C23×C139—41no—
194C23×C139C22×D411yescharacteristic
195Q8×C139—48no—
196D4×C139—41no—
197D4×C139—41no—
198D4×C139—41no—
199D4×C139—41no—
200C2×C4×C139—21no—
201C2×C4×C139—21no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—21no—
205C2×C4×C139—22no—
206C2×C4×C139—22no—
207C2×C4×C139—21no—
208C2×C4×C139—21no—
209C2×C4×C139—21no—
210C2×C4×C139—22no—
211C2×C4×C139—21no—
212C2×C4×C139—21no—
213C2×C4×C139—21no—
214C2×C4×C139—21no—
215C2×C4×C139—21no—
216C2×C4×C139—21no—
217C2×C4×C139—21no—
218C2×C4×C139—21no—
219C2×C4×C139—41no—
220C2×C4×C139—41no—
221C2×C4×C139—41no—
222C2×C4×C139—41no—
223C2×C4×C139—41no—
224C2×C4×C139—41no—
225C2×C4×C139—41no—
226C2×C4×C139—41no—
227C2×C4×C139—41no—
228C2×C4×C139—41no—
229C2×C4×C139—41no—
230C2×C4×C139—41no—
231C2×C4×C139—41no—
232C2×C4×C139—41no—
233C2×C4×C139—41no—
234C2×C4×C139—41no—
235C2×C4×C139—41no—
236C2×C4×C139—41no—
237C2×C4×C139#13512yes—
238C2×C4×C139AGL(1,ℤ/8)12yes—
239C2×C4×C139C2×#4111yescharacteristic
240C2×C4×C139C2×#4111yescharacteristic
241C2×C4×C139C2×#4111yescharacteristic
242C2×C4×C139C2×#4111yescharacteristic
243C2×C4×C1392−1+411yescharacteristic
244C2×C4×C1392−1+411yescharacteristic
245C8×C139—22no—
246C8×C139—41no—
247C8×C139—41no—
248C8×C139—41no—
249C22×C139—81no—
250C22×C139—81no—
251C22×C139—81no—
252C22×C139—81no—
253C22×C139—81no—
254C22×C139—81no—
255C22×C139—81no—
256C22×C139#52511yescharacteristic
257C22×C139#54711yescharacteristic
258C22×C139#54811yescharacteristic
259C22×C139C2×#13511yescharacteristic
260C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C139#57711yescharacteristic
262C22×C139#57711yescharacteristic
263C4×C139—22no—
264C4×C139—22no—
265C4×C139—41no—
266C4×C139—41no—
267C4×C139—41no—
268C4×C139—42no—
269C4×C139—42no—
270C4×C139—42no—
271C4×C139—41no—
272C4×C139—81no—
273C4×C139—81no—
274C4×C139—81no—
275C4×C139—81no—
276C4×C139#52911yescharacteristic
277C4×C139#54111yescharacteristic
278C4×C139#55611yescharacteristic
279C4×C139#55611yescharacteristic
280C2×C139—161no—
281C2×C139#246911yescharacteristic
282C2×C139#310511yescharacteristic
283C2×C139#312611yescharacteristic
284C2×C139#334011yescharacteristic
285C2×C139#334511yescharacteristic
286C2×C139#336511yescharacteristic
287C2×C139#337311yescharacteristic
288#27129C13911yesmaximal, characteristic, direct product factor, Sylow
289C139#2712911yescharacteristic, direct product factor, Sylow
290#2513C2×C13911yescharacteristic
291#2365C2×C13911yescharacteristic, complemented
292#2101C2×C13911yescharacteristic, complemented
293#2065C2×C13911yescharacteristic
294#2058C2×C13911yescharacteristic, complemented
295#2023C2×C13911yescharacteristic
296#1949C2×C13911yescharacteristic, complemented
297#1934C2×C13911yescharacteristic
298#1926C2×C13911yescharacteristic
299#1926C2×C13911yescharacteristic
300#1925C2×C13911yescharacteristic
301#1921C2×C13911yescharacteristic, complemented
302#1919C2×C13911yescharacteristic, complemented
303#1916C2×C13911yescharacteristic, complemented
304C4×#106C2×C13911yescharacteristic, complemented
305C2×C4⋊Q8C22×C13911yescharacteristic
306C2×C4×Q8—21no—
307C2×#107C22×C13911yescharacteristic
308C2×#106C22×C13911yescharacteristic
309C2×#106C22×C13911yescharacteristic
310C2×#106C22×C13911yescharacteristic
311C2×C4⋊C8C22×C13911yescharacteristic
312C2×#102C22×C13911yescharacteristic
313C2×#102C22×C13911yescharacteristic
314C2×#102C22×C13911yescharacteristic
315C2×#102C22×C13911yescharacteristic
316C2×C4×C8C22×C13911yescharacteristic
317#397—21no—
318#397—21no—
319#391—21no—
320#390C22×C13911yescharacteristic
321#390C22×C13911yescharacteristic
322#390C22×C13911yescharacteristic
323#389C22×C13911yescharacteristic
324#389C22×C13911yescharacteristic
325#389C22×C13911yescharacteristic
326#388—21no—
327#388—21no—
328#387—21no—
329#387—21no—
330#382C22×C13911yescharacteristic
331C4×C4⋊C4C22×C13911yescharacteristic
332C4×C4⋊C4C22×C13911yescharacteristic
333C4×C4⋊C4C22×C13911yescharacteristic
334C4×C4⋊C4C22×C13911yescharacteristic
335C4×C4⋊C4C22×C13911yescharacteristic
336#340C22×C13911yescharacteristic
337#340C22×C13911yescharacteristic
338#340C22×C13911yescharacteristic
339#340C22×C13911yescharacteristic
340#340C22×C13911yescharacteristic
341#340C22×C13911yescharacteristic
342#340C22×C13911yescharacteristic
343#340C22×C13911yescharacteristic
344#336C22×C13911yescharacteristic
345#336C22×C13911yescharacteristic
346#336C22×C13911yescharacteristic
347#336C22×C13911yescharacteristic
348C22×Q8—21no—
349C22×D4C23×C13911yescharacteristic
350C22×C8C23×C13911yescharacteristic
351C22×C8C23×C13911yescharacteristic
352C22×C8C23×C13911yescharacteristic
353C22×C8C23×C13911yescharacteristic
354C4⋊Q8—22no—
355C4⋊Q8—22no—
356C4×Q8—44no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4D4×C13911yescharacteristic
362C2×C4⋊C4D4×C13911yescharacteristic
363C2×C4⋊C4C23×C13911yescharacteristic
364C2×C4⋊C4C23×C13911yescharacteristic
365C2×C4⋊C4C23×C13911yescharacteristic
366C2×C4⋊C4C23×C13911yescharacteristic
367C2×C4⋊C4C23×C13911yescharacteristic
368C2×C4⋊C4C23×C13911yescharacteristic
369C2×C4⋊C4C23×C13911yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42C23×C13911yescharacteristic
381C2×C42C23×C13911yescharacteristic
382C2×C42C23×C13911yescharacteristic
383#107—22no—
384#106—22no—
385#106—22no—
386#106—22no—
387C4⋊C8—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391#102—22no—
392C4×C8—22no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95D4×C13911yescharacteristic
403#95D4×C13911yescharacteristic
404C24—21no—
405C2×Q8—24no—
406C2×Q8—42no—
407C2×Q8—42no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4C2×D4×C13911yescharacteristic
422C22×C4C2×D4×C13911yescharacteristic
423C22×C4C2×D4×C13911yescharacteristic
424C22×C4C2×D4×C13911yescharacteristic
425C22×C4C2×D4×C13911yescharacteristic
426C22×C4C2×D4×C13911yescharacteristic
427C22×C4C24×C13911yescharacteristic
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8#41×C13912yes—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4#41×C13912yes—
458C4⋊C4#41×C13912yes—
459C4⋊C4#41×C13912yes—
460C22⋊C4—42no—
461C22⋊C4—42no—
462C22⋊C4—81no—
463C22⋊C4—81no—
464C22⋊C4—81no—
465C22⋊C4—81no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—42no—
473C42—42no—
474C42—42no—
475C42—81no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23C22×D4×C13911yescharacteristic
484Q8—48no—
485D4—41no—
486D4—41no—
487D4—41no—
488D4—41no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4#135×C13912yes—
527C2×C4AGL(1,ℤ/8)×C13912yes—
528C2×C4C2×#41×C13911yescharacteristic
529C2×C4C2×#41×C13911yescharacteristic
530C2×C4C2×#41×C13911yescharacteristic
531C2×C4C2×#41×C13911yescharacteristic
532C2×C42−1+4×C13911yescharacteristic
533C2×C42−1+4×C13911yescharacteristic
534C8—22no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22#525×C13911yescharacteristic
546C22#547×C13911yescharacteristic
547C22#548×C13911yescharacteristic
548C22C2×#135×C13911yescharacteristic
549C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
550C22#577×C13911yescharacteristic
551C22#577×C13911yescharacteristic
552C4—22no—
553C4—22no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4#529×C13911yescharacteristic
566C4#541×C13911yescharacteristic
567C4#556×C13911yescharacteristic
568C4#556×C13911yescharacteristic
569C2—161no—
570C2#2469×C13911yescharacteristic
571C2#3105×C13911yescharacteristic
572C2#3126×C13911yescharacteristic
573C2#3340×C13911yescharacteristic
574C2#3345×C13911yescharacteristic
575C2#3365×C13911yescharacteristic
576C2#3373×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. #2365×C139C2semidirect
3. #2101×C139C2semidirect
5. #2058×C139C2semidirect
7. #1949×C139C2semidirect
12. #1921×C139C2semidirect
13. #1919×C139C2semidirect
14. #1916×C139C2semidirect
15. C4×#106×C139C2semidirect
288. #27129C139direct (N × H)
289. C139#27129direct (N × H)
291. #2365C2×C139semidirect
292. #2101C2×C139semidirect
294. #2058C2×C139semidirect
296. #1949C2×C139semidirect
301. #1921C2×C139semidirect
302. #1919C2×C139semidirect
303. #1916C2×C139semidirect
304. C4×#106C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2513×C1392
#2365×C1392
#2101×C1392
#2065×C1392
#2058×C1392
#2023×C1392
#1949×C1392
#1934×C1392
#1926×C1392
#1925×C1392
#1921×C1392
#1919×C1392
#1916×C1392
C4×#106×C1392
#27129139