Finite Group Databasebeta

← C139×#27036 #48021632

Subgroups — C139×#27036 #48021632

Order 35584.

708 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2497×C139C211yesmaximal, characteristic
2#2360×C139C211yesmaximal, characteristic
3#2072×C139C211yesmaximal, characteristic, complemented
4#2068×C139C211yesmaximal, characteristic, complemented
5#2036×C139C211yesmaximal, characteristic
6#2036×C139C211yesmaximal, characteristic
7#1947×C139C211yesmaximal, characteristic, complemented
8#1942×C139C211yesmaximal, characteristic, complemented
9#1923×C139C211yesmaximal, characteristic
10#1921×C139C211yesmaximal, characteristic, complemented
11#1921×C139C211yesmaximal, characteristic, complemented
12#1863×C139C211yesmaximal, characteristic, complemented
13#1852×C139C211yesmaximal, characteristic
14#1824×C139C211yesmaximal, characteristic
15C4×#103×C139C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×C139C2211yescharacteristic
17C2×C4×Q8×C139C2211yescharacteristic
18C22×C4⋊C4×C139C2211yescharacteristic
19C2×#107×C139C2211yescharacteristic
20C2×#107×C139C2211yescharacteristic
21C2×#107×C139C2211yescharacteristic
22C2×#107×C139C2211yescharacteristic
23C2×C4⋊C8×C139C2211yescharacteristic
24C2×#103×C139C2211yescharacteristic
25C2×#103×C139C2211yescharacteristic
26C2×#103×C139C2211yescharacteristic
27C2×#103×C139C2211yescharacteristic
28C2×C22⋊C8×C139C2211yescharacteristic
29C2×C22⋊C8×C139C2211yescharacteristic
30C2×C4×C8×C139C2211yescharacteristic
31#400×C139—21no—
32#396×C139—21no—
33#391×C139C2211yescharacteristic
34#389×C139—21no—
35#389×C139C2211yescharacteristic
36#389×C139C2211yescharacteristic
37#389×C139C2211yescharacteristic
38#388×C139—21no—
39#387×C139—21no—
40#387×C139—21no—
41#385×C139—21no—
42#384×C139C2211yescharacteristic
43#380×C139C2211yescharacteristic
44#380×C139C2211yescharacteristic
45C4×C4⋊C4×C139C2211yescharacteristic
46C4×C4⋊C4×C139C2211yescharacteristic
47C4×C22⋊C4×C139—21no—
48C4×C22⋊C4×C139C2211yescharacteristic
49#340×C139C2211yescharacteristic
50#340×C139C2211yescharacteristic
51#340×C139C2211yescharacteristic
52#340×C139C2211yescharacteristic
53#340×C139C2211yescharacteristic
54#340×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#336×C139C2211yescharacteristic
58#336×C139C2211yescharacteristic
59C22×Q8×C139C2311yescharacteristic
60C23×C4×C139—21no—
61C23×C4×C139C2311yescharacteristic
62C22×C8×C139C2311yescharacteristic
63C22×C8×C139C2311yescharacteristic
64C22×C8×C139C2311yescharacteristic
65C22×C8×C139C2311yescharacteristic
66C22⋊Q8×C139—22no—
67C22⋊Q8×C139—22no—
68C4×Q8×C139—22no—
69C4×Q8×C139—41no—
70C2×C4⋊C4×C139—21no—
71C2×C4⋊C4×C139—22no—
72C2×C4⋊C4×C139—21no—
73C2×C4⋊C4×C139—21no—
74C2×C4⋊C4×C139—21no—
75C2×C4⋊C4×C139—21no—
76C2×C4⋊C4×C139—21no—
77C2×C4⋊C4×C139—21no—
78C2×C4⋊C4×C139—21no—
79C2×C4⋊C4×C139—41no—
80C2×C4⋊C4×C139C2311yescharacteristic
81C2×C4⋊C4×C139C2311yescharacteristic
82C2×C4⋊C4×C139C2311yescharacteristic
83C2×C4⋊C4×C139C2311yescharacteristic
84C2×C4⋊C4×C139C2311yescharacteristic
85C2×C4⋊C4×C139C2311yescharacteristic
86C2×C4⋊C4×C139C2311yescharacteristic
87C2×C22⋊C4×C139—21no—
88C2×C22⋊C4×C139—21no—
89C2×C22⋊C4×C139—21no—
90C2×C22⋊C4×C139D411yescharacteristic
91C2×C22⋊C4×C139D411yescharacteristic
92C2×C42×C139—21no—
93C2×C42×C139—21no—
94C2×C42×C139—21no—
95C2×C42×C139C2311yescharacteristic
96C2×C42×C139C2311yescharacteristic
97#107×C139—22no—
98#107×C139—22no—
99#107×C139—22no—
100#107×C139—41no—
101C4⋊C8×C139—22no—
102#103×C139—22no—
103#103×C139—22no—
104#103×C139—22no—
105#103×C139—41no—
106C22⋊C8×C139—22no—
107C22⋊C8×C139—41no—
108C4×C8×C139—41no—
109#95×C139—21no—
110#95×C139—21no—
111#95×C139—21no—
112#95×C139—21no—
113#95×C139—21no—
114#95×C139—21no—
115#95×C139—21no—
116#95×C139—21no—
117#95×C139—21no—
118#95×C139D411yescharacteristic
119#95×C139D411yescharacteristic
120C24×C139C2×D411yescharacteristic
121C2×Q8×C139—21no—
122C2×Q8×C139—21no—
123C2×Q8×C139—21no—
124C2×Q8×C139—21no—
125C2×Q8×C139—21no—
126C2×Q8×C139#4112yes—
127C22×C4×C139—21no—
128C22×C4×C139—21no—
129C22×C4×C139—21no—
130C22×C4×C139—21no—
131C22×C4×C139—21no—
132C22×C4×C139—21no—
133C22×C4×C139—21no—
134C22×C4×C139—21no—
135C22×C4×C139—21no—
136C22×C4×C139—21no—
137C22×C4×C139—21no—
138C22×C4×C139—21no—
139C22×C4×C139—21no—
140C22×C4×C139—21no—
141C22×C4×C139—42no—
142C22×C4×C139—42no—
143C22×C4×C139—81no—
144C22×C4×C139C2×D411yescharacteristic
145C22×C4×C139C2×D411yescharacteristic
146C22×C4×C139C2×D411yescharacteristic
147C22×C4×C139C2×D411yescharacteristic
148C22×C4×C139C2×D411yescharacteristic
149C22×C4×C139C2411yescharacteristic
150C2×C8×C139—21no—
151C2×C8×C139—21no—
152C2×C8×C139—21no—
153C2×C8×C139—21no—
154C2×C8×C139—21no—
155C2×C8×C139—21no—
156C2×C8×C139—21no—
157C2×C8×C139—21no—
158C2×C8×C139—21no—
159C2×C8×C139—21no—
160C2×C8×C139—21no—
161C2×C8×C139#4112yes—
162C4⋊C4×C139—24no—
163C4⋊C4×C139—21no—
164C4⋊C4×C139—21no—
165C4⋊C4×C139—21no—
166C4⋊C4×C139—21no—
167C4⋊C4×C139—21no—
168C4⋊C4×C139—21no—
169C4⋊C4×C139—21no—
170C4⋊C4×C139—21no—
171C4⋊C4×C139—21no—
172C4⋊C4×C139—21no—
173C4⋊C4×C139—21no—
174C4⋊C4×C139—21no—
175C4⋊C4×C139—42no—
176C4⋊C4×C139—42no—
177C4⋊C4×C139—42no—
178C4⋊C4×C139—81no—
179C4⋊C4×C139—81no—
180C4⋊C4×C139—81no—
181C4⋊C4×C139—81no—
182C4⋊C4×C139#4112yes—
183C4⋊C4×C139#4112yes—
184C22⋊C4×C139—24no—
185C22⋊C4×C139—41no—
186C22⋊C4×C139—81no—
187C22⋊C4×C139—81no—
188C22⋊C4×C139Q1614yes—
189C42×C139—21no—
190C42×C139—21no—
191C42×C139—21no—
192C42×C139—21no—
193C42×C139—42no—
194C42×C139—81no—
195C42×C139—81no—
196C23×C139—21no—
197C23×C139—21no—
198C23×C139—21no—
199C23×C139—21no—
200C23×C139—21no—
201C23×C139—21no—
202C23×C139C2×Q1612yes—
203C23×C139C22×D411yescharacteristic
204Q8×C139—22no—
205Q8×C139—22no—
206Q8×C139—41no—
207Q8×C139—41no—
208C2×C4×C139—21no—
209C2×C4×C139—21no—
210C2×C4×C139—21no—
211C2×C4×C139—21no—
212C2×C4×C139—22no—
213C2×C4×C139—22no—
214C2×C4×C139—21no—
215C2×C4×C139—21no—
216C2×C4×C139—22no—
217C2×C4×C139—21no—
218C2×C4×C139—21no—
219C2×C4×C139—21no—
220C2×C4×C139—21no—
221C2×C4×C139—21no—
222C2×C4×C139—21no—
223C2×C4×C139—21no—
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—41no—
238C2×C4×C139—41no—
239C2×C4×C139—41no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—41no—
243C2×C4×C139—41no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
246C2×C4×C139—41no—
247C2×C4×C139—41no—
248C2×C4×C139—41no—
249C2×C4×C139—84no—
250C2×C4×C139C2×Q1612yes—
251C2×C4×C139C2×Q1612yes—
252C2×C4×C139C2×#4111yescharacteristic
253C2×C4×C139C2×#4111yescharacteristic
254C2×C4×C139C2×#4111yescharacteristic
255C2×C4×C139C2×#4111yescharacteristic
256C2×C4×C139H(5,𝔽2)11yescharacteristic
257C2×C4×C1392−1+411yescharacteristic
258C8×C139—22no—
259C8×C139—41no—
260C8×C139—41no—
261C8×C139—41no—
262C22×C139—22no—
263C22×C139—22no—
264C22×C139—22no—
265C22×C139—41no—
266C22×C139—41no—
267C22×C139—41no—
268C22×C139—41no—
269C22×C139#52511yescharacteristic
270C22×C139#54611yescharacteristic
271C22×C139#54711yescharacteristic
272C22×C139C22×Q1611yescharacteristic
273C22×C139#57511yescharacteristic
274C22×C139#57611yescharacteristic
275C22×C139#57711yescharacteristic
276C4×C139—22no—
277C4×C139—22no—
278C4×C139—41no—
279C4×C139—42no—
280C4×C139—41no—
281C4×C139—42no—
282C4×C139—41no—
283C4×C139—42no—
284C4×C139—81no—
285C4×C139—81no—
286C4×C139—81no—
287C4×C139—81no—
288C4×C139—81no—
289C4×C139#52911yescharacteristic
290C4×C139#53911yescharacteristic
291C4×C139#55311yescharacteristic
292C4×C139#55611yescharacteristic
293C2×C139—42no—
294C2×C139#246611yescharacteristic
295C2×C139#310411yescharacteristic
296C2×C139#311911yescharacteristic
297C2×C139#329911yescharacteristic
298C2×C139#331911yescharacteristic
299C2×C139#333811yescharacteristic
300C2×C139#335111yescharacteristic
301#27036C13911yesmaximal, characteristic, direct product factor, Sylow
302C139#2703611yescharacteristic, direct product factor, Sylow
303#2497C2×C13911yescharacteristic
304#2360C2×C13911yescharacteristic
305#2072C2×C13911yescharacteristic, complemented
306#2068C2×C13911yescharacteristic, complemented
307#2036C2×C13911yescharacteristic
308#2036C2×C13911yescharacteristic
309#1947C2×C13911yescharacteristic, complemented
310#1942C2×C13911yescharacteristic, complemented
311#1923C2×C13911yescharacteristic
312#1921C2×C13911yescharacteristic, complemented
313#1921C2×C13911yescharacteristic, complemented
314#1863C2×C13911yescharacteristic, complemented
315#1852C2×C13911yescharacteristic
316#1824C2×C13911yescharacteristic
317C4×#103C2×C13911yescharacteristic, complemented
318C2×C22⋊Q8C22×C13911yescharacteristic
319C2×C4×Q8C22×C13911yescharacteristic
320C22×C4⋊C4C22×C13911yescharacteristic
321C2×#107C22×C13911yescharacteristic
322C2×#107C22×C13911yescharacteristic
323C2×#107C22×C13911yescharacteristic
324C2×#107C22×C13911yescharacteristic
325C2×C4⋊C8C22×C13911yescharacteristic
326C2×#103C22×C13911yescharacteristic
327C2×#103C22×C13911yescharacteristic
328C2×#103C22×C13911yescharacteristic
329C2×#103C22×C13911yescharacteristic
330C2×C22⋊C8C22×C13911yescharacteristic
331C2×C22⋊C8C22×C13911yescharacteristic
332C2×C4×C8C22×C13911yescharacteristic
333#400—21no—
334#396—21no—
335#391C22×C13911yescharacteristic
336#389—21no—
337#389C22×C13911yescharacteristic
338#389C22×C13911yescharacteristic
339#389C22×C13911yescharacteristic
340#388—21no—
341#387—21no—
342#387—21no—
343#385—21no—
344#384C22×C13911yescharacteristic
345#380C22×C13911yescharacteristic
346#380C22×C13911yescharacteristic
347C4×C4⋊C4C22×C13911yescharacteristic
348C4×C4⋊C4C22×C13911yescharacteristic
349C4×C22⋊C4—21no—
350C4×C22⋊C4C22×C13911yescharacteristic
351#340C22×C13911yescharacteristic
352#340C22×C13911yescharacteristic
353#340C22×C13911yescharacteristic
354#340C22×C13911yescharacteristic
355#340C22×C13911yescharacteristic
356#340C22×C13911yescharacteristic
357#340C22×C13911yescharacteristic
358#340C22×C13911yescharacteristic
359#336C22×C13911yescharacteristic
360#336C22×C13911yescharacteristic
361C22×Q8C23×C13911yescharacteristic
362C23×C4—21no—
363C23×C4C23×C13911yescharacteristic
364C22×C8C23×C13911yescharacteristic
365C22×C8C23×C13911yescharacteristic
366C22×C8C23×C13911yescharacteristic
367C22×C8C23×C13911yescharacteristic
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C4×Q8—22no—
371C4×Q8—41no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4C23×C13911yescharacteristic
383C2×C4⋊C4C23×C13911yescharacteristic
384C2×C4⋊C4C23×C13911yescharacteristic
385C2×C4⋊C4C23×C13911yescharacteristic
386C2×C4⋊C4C23×C13911yescharacteristic
387C2×C4⋊C4C23×C13911yescharacteristic
388C2×C4⋊C4C23×C13911yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4D4×C13911yescharacteristic
393C2×C22⋊C4D4×C13911yescharacteristic
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C23×C13911yescharacteristic
398C2×C42C23×C13911yescharacteristic
399#107—22no—
400#107—22no—
401#107—22no—
402#107—41no—
403C4⋊C8—22no—
404#103—22no—
405#103—22no—
406#103—22no—
407#103—41no—
408C22⋊C8—22no—
409C22⋊C8—41no—
410C4×C8—41no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95D4×C13911yescharacteristic
421#95D4×C13911yescharacteristic
422C24C2×D4×C13911yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8#41×C13912yes—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—81no—
446C22×C4C2×D4×C13911yescharacteristic
447C22×C4C2×D4×C13911yescharacteristic
448C22×C4C2×D4×C13911yescharacteristic
449C22×C4C2×D4×C13911yescharacteristic
450C22×C4C2×D4×C13911yescharacteristic
451C22×C4C24×C13911yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8#41×C13912yes—
464C4⋊C4—24no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4#41×C13912yes—
485C4⋊C4#41×C13912yes—
486C22⋊C4—24no—
487C22⋊C4—41no—
488C22⋊C4—81no—
489C22⋊C4—81no—
490C22⋊C4Q16×C13914yes—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—42no—
496C42—81no—
497C42—81no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23C2×Q16×C13912yes—
505C23C22×D4×C13911yescharacteristic
506Q8—22no—
507Q8—22no—
508Q8—41no—
509Q8—41no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—84no—
552C2×C4C2×Q16×C13912yes—
553C2×C4C2×Q16×C13912yes—
554C2×C4C2×#41×C13911yescharacteristic
555C2×C4C2×#41×C13911yescharacteristic
556C2×C4C2×#41×C13911yescharacteristic
557C2×C4C2×#41×C13911yescharacteristic
558C2×C4H(5,𝔽2)×C13911yescharacteristic
559C2×C42−1+4×C13911yescharacteristic
560C8—22no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22#525×C13911yescharacteristic
572C22#546×C13911yescharacteristic
573C22#547×C13911yescharacteristic
574C22C22×Q16×C13911yescharacteristic
575C22#575×C13911yescharacteristic
576C22#576×C13911yescharacteristic
577C22#577×C13911yescharacteristic
578C4—22no—
579C4—22no—
580C4—41no—
581C4—42no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4#529×C13911yescharacteristic
592C4#539×C13911yescharacteristic
593C4#553×C13911yescharacteristic
594C4#556×C13911yescharacteristic
595C2—42no—
596C2#2466×C13911yescharacteristic
597C2#3104×C13911yescharacteristic
598C2#3119×C13911yescharacteristic
599C2#3299×C13911yescharacteristic
600C2#3319×C13911yescharacteristic
601C2#3338×C13911yescharacteristic
602C2#3351×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC24×C139C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2072×C139C2semidirect
4. #2068×C139C2semidirect
7. #1947×C139C2semidirect
8. #1942×C139C2semidirect
10. #1921×C139C2semidirect
11. #1921×C139C2semidirect
12. #1863×C139C2semidirect
15. C4×#103×C139C2semidirect
301. #27036C139direct (N × H)
302. C139#27036direct (N × H)
305. #2072C2×C139semidirect
306. #2068C2×C139semidirect
309. #1947C2×C139semidirect
310. #1942C2×C139semidirect
312. #1921C2×C139semidirect
313. #1921C2×C139semidirect
314. #1863C2×C139semidirect
317. C4×#103C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2497×C1392
#2360×C1392
#2072×C1392
#2068×C1392
#2036×C1392
#1947×C1392
#1942×C1392
#1923×C1392
#1921×C1392
#1863×C1392
#1852×C1392
#1824×C1392
C4×#103×C1392
#27036139