Finite Group Databasebeta

← C139×#27136 #48021732

Subgroups — C139×#27136 #48021732

Order 35584.

642 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2513×C139C211yesmaximal, characteristic
2#2370×C139C211yesmaximal, characteristic, complemented
3#2101×C139C211yesmaximal, characteristic, complemented
4#2065×C139C211yesmaximal, characteristic
5#2059×C139C211yesmaximal, characteristic, complemented
6#2025×C139C211yesmaximal, characteristic
7#1949×C139C211yesmaximal, characteristic, complemented
8#1934×C139C211yesmaximal, characteristic
9#1926×C139C211yesmaximal, characteristic
10#1925×C139C211yesmaximal, characteristic
11#1925×C139C211yesmaximal, characteristic
12#1921×C139C211yesmaximal, characteristic, complemented
13#1918×C139C211yesmaximal, characteristic, complemented
14#1916×C139C211yesmaximal, characteristic, complemented
15C4×#106×C139C211yesmaximal, characteristic, complemented
16C2×#125×C139C2211yescharacteristic
17C2×#107×C139C2211yescharacteristic
18C2×#107×C139C2211yescharacteristic
19C2×#106×C139C2211yescharacteristic
20C2×#106×C139C2211yescharacteristic
21C2×C4⋊C8×C139C2211yescharacteristic
22C2×#102×C139C2211yescharacteristic
23C2×#102×C139C2211yescharacteristic
24C2×#102×C139C2211yescharacteristic
25C2×#102×C139C2211yescharacteristic
26C2×C4×C8×C139C2211yescharacteristic
27#397×C139—21no—
28#397×C139—21no—
29#390×C139C2211yescharacteristic
30#390×C139C2211yescharacteristic
31#390×C139C2211yescharacteristic
32#389×C139—21no—
33#389×C139C2211yescharacteristic
34#389×C139C2211yescharacteristic
35#389×C139C2211yescharacteristic
36#388×C139—21no—
37#388×C139—21no—
38#387×C139—21no—
39#387×C139—21no—
40#382×C139C2211yescharacteristic
41C4×C4⋊C4×C139—21no—
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×D4×C139C2311yescharacteristic
60C22×C8×C139C2311yescharacteristic
61C22×C8×C139C2311yescharacteristic
62C22×C8×C139C2311yescharacteristic
63C22×C8×C139C2311yescharacteristic
64#125×C139—22no—
65#125×C139—22no—
66C2×C4⋊C4×C139—21no—
67C2×C4⋊C4×C139—21no—
68C2×C4⋊C4×C139—21no—
69C2×C4⋊C4×C139—21no—
70C2×C4⋊C4×C139—21no—
71C2×C4⋊C4×C139D411yescharacteristic
72C2×C4⋊C4×C139D411yescharacteristic
73C2×C4⋊C4×C139C2311yescharacteristic
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×C22⋊C4×C139—21no—
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×C42×C139—21no—
87C2×C42×C139—21no—
88C2×C42×C139—21no—
89C2×C42×C139—21no—
90C2×C42×C139C2311yescharacteristic
91C2×C42×C139C2311yescharacteristic
92C2×C42×C139C2311yescharacteristic
93#107×C139—22no—
94#107×C139—22no—
95#106×C139—22no—
96#106×C139—22no—
97C4⋊C8×C139—22no—
98#102×C139—22no—
99#102×C139—22no—
100#102×C139—22no—
101#102×C139—22no—
102C4×C8×C139—22no—
103#95×C139—21no—
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×C139D411yescharacteristic
113#95×C139D411yescharacteristic
114C24×C139—21no—
115C2×D4×C139—21no—
116C2×D4×C139—21no—
117C2×D4×C139—21no—
118C2×D4×C139—21no—
119C2×D4×C139—21no—
120C2×D4×C139—21no—
121C22×C4×C139—21no—
122C22×C4×C139—21no—
123C22×C4×C139—21no—
124C22×C4×C139—21no—
125C22×C4×C139—21no—
126C22×C4×C139—21no—
127C22×C4×C139—21no—
128C22×C4×C139C2×D411yescharacteristic
129C22×C4×C139C2×D411yescharacteristic
130C22×C4×C139C2×D411yescharacteristic
131C22×C4×C139C2×D411yescharacteristic
132C22×C4×C139C2×D411yescharacteristic
133C22×C4×C139C2×D411yescharacteristic
134C22×C4×C139C2411yescharacteristic
135C2×C8×C139—21no—
136C2×C8×C139—21no—
137C2×C8×C139—21no—
138C2×C8×C139—21no—
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#4112yes—
147C4⋊C4×C139—24no—
148C4⋊C4×C139—24no—
149C4⋊C4×C139—22no—
150C4⋊C4×C139—21no—
151C4⋊C4×C139—21no—
152C4⋊C4×C139—21no—
153C4⋊C4×C139—21no—
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—41no—
162C4⋊C4×C139—42no—
163C4⋊C4×C139—81no—
164C4⋊C4×C139—81no—
165C4⋊C4×C139#4112yes—
166C4⋊C4×C139#4112yes—
167C4⋊C4×C139#4112yes—
168C22⋊C4×C139—42no—
169C22⋊C4×C139—42no—
170C22⋊C4×C139—81no—
171C22⋊C4×C139—81no—
172C22⋊C4×C139—81no—
173C22⋊C4×C139—81no—
174C42×C139—21no—
175C42×C139—21no—
176C42×C139—21no—
177C42×C139—21no—
178C42×C139—21no—
179C42×C139—21no—
180C42×C139—42no—
181C42×C139—81no—
182C42×C139—81no—
183C42×C139—81no—
184C23×C139—41no—
185C23×C139—41no—
186C23×C139—41no—
187C23×C139—41no—
188C23×C139—41no—
189C23×C139—41no—
190C23×C139—41no—
191C23×C139C22×D411yescharacteristic
192D4×C139—41no—
193D4×C139—41no—
194D4×C139—41no—
195D4×C139—41no—
196C2×C4×C139—21no—
197C2×C4×C139—21no—
198C2×C4×C139—21no—
199C2×C4×C139—21no—
200C2×C4×C139—22no—
201C2×C4×C139—22no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—21no—
205C2×C4×C139—22no—
206C2×C4×C139—21no—
207C2×C4×C139—21no—
208C2×C4×C139—21no—
209C2×C4×C139—21no—
210C2×C4×C139—21no—
211C2×C4×C139—21no—
212C2×C4×C139—21no—
213C2×C4×C139—21no—
214C2×C4×C139—21no—
215C2×C4×C139—21no—
216C2×C4×C139—41no—
217C2×C4×C139—41no—
218C2×C4×C139—41no—
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#13512yes—
235C2×C4×C139C2×#4111yescharacteristic
236C2×C4×C139C2×#4111yescharacteristic
237C2×C4×C139C2×#4111yescharacteristic
238C2×C4×C139C2×#4111yescharacteristic
239C2×C4×C1392−1+411yescharacteristic
240C2×C4×C1392−1+411yescharacteristic
241C8×C139—22no—
242C8×C139—41no—
243C8×C139—41no—
244C8×C139—41no—
245C22×C139—81no—
246C22×C139—81no—
247C22×C139—81no—
248C22×C139—81no—
249C22×C139—81no—
250C22×C139—81no—
251C22×C139—81no—
252C22×C139#52511yescharacteristic
253C22×C139#54711yescharacteristic
254C22×C139#54811yescharacteristic
255C22×C139C2×#13511yescharacteristic
256C22×C139#57511yescharacteristic
257C22×C139#57611yescharacteristic
258C22×C139#57711yescharacteristic
259C4×C139—22no—
260C4×C139—41no—
261C4×C139—41no—
262C4×C139—41no—
263C4×C139—41no—
264C4×C139—42no—
265C4×C139—42no—
266C4×C139—41no—
267C4×C139—42no—
268C4×C139—81no—
269C4×C139—81no—
270C4×C139—81no—
271C4×C139—81no—
272C4×C139#52911yescharacteristic
273C4×C139#54111yescharacteristic
274C4×C139#55611yescharacteristic
275C4×C139#55611yescharacteristic
276C2×C139—161no—
277C2×C139#246911yescharacteristic
278C2×C139#310211yescharacteristic
279C2×C139#311911yescharacteristic
280C2×C139#333711yescharacteristic
281C2×C139#334711yescharacteristic
282C2×C139#336111yescharacteristic
283C2×C139#337111yescharacteristic
284#27136C13911yesmaximal, characteristic, direct product factor, Sylow
285C139#2713611yescharacteristic, direct product factor, Sylow
286#2513C2×C13911yescharacteristic
287#2370C2×C13911yescharacteristic, complemented
288#2101C2×C13911yescharacteristic, complemented
289#2065C2×C13911yescharacteristic
290#2059C2×C13911yescharacteristic, complemented
291#2025C2×C13911yescharacteristic
292#1949C2×C13911yescharacteristic, complemented
293#1934C2×C13911yescharacteristic
294#1926C2×C13911yescharacteristic
295#1925C2×C13911yescharacteristic
296#1925C2×C13911yescharacteristic
297#1921C2×C13911yescharacteristic, complemented
298#1918C2×C13911yescharacteristic, complemented
299#1916C2×C13911yescharacteristic, complemented
300C4×#106C2×C13911yescharacteristic, complemented
301C2×#125C22×C13911yescharacteristic
302C2×#107C22×C13911yescharacteristic
303C2×#107C22×C13911yescharacteristic
304C2×#106C22×C13911yescharacteristic
305C2×#106C22×C13911yescharacteristic
306C2×C4⋊C8C22×C13911yescharacteristic
307C2×#102C22×C13911yescharacteristic
308C2×#102C22×C13911yescharacteristic
309C2×#102C22×C13911yescharacteristic
310C2×#102C22×C13911yescharacteristic
311C2×C4×C8C22×C13911yescharacteristic
312#397—21no—
313#397—21no—
314#390C22×C13911yescharacteristic
315#390C22×C13911yescharacteristic
316#390C22×C13911yescharacteristic
317#389—21no—
318#389C22×C13911yescharacteristic
319#389C22×C13911yescharacteristic
320#389C22×C13911yescharacteristic
321#388—21no—
322#388—21no—
323#387—21no—
324#387—21no—
325#382C22×C13911yescharacteristic
326C4×C4⋊C4—21no—
327C4×C4⋊C4C22×C13911yescharacteristic
328C4×C4⋊C4C22×C13911yescharacteristic
329C4×C4⋊C4C22×C13911yescharacteristic
330C4×C4⋊C4C22×C13911yescharacteristic
331C4×C4⋊C4C22×C13911yescharacteristic
332#340C22×C13911yescharacteristic
333#340C22×C13911yescharacteristic
334#340C22×C13911yescharacteristic
335#340C22×C13911yescharacteristic
336#340C22×C13911yescharacteristic
337#340C22×C13911yescharacteristic
338#340C22×C13911yescharacteristic
339#340C22×C13911yescharacteristic
340#336C22×C13911yescharacteristic
341#336C22×C13911yescharacteristic
342#336C22×C13911yescharacteristic
343#336C22×C13911yescharacteristic
344C22×D4C23×C13911yescharacteristic
345C22×C8C23×C13911yescharacteristic
346C22×C8C23×C13911yescharacteristic
347C22×C8C23×C13911yescharacteristic
348C22×C8C23×C13911yescharacteristic
349#125—22no—
350#125—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4D4×C13911yescharacteristic
357C2×C4⋊C4D4×C13911yescharacteristic
358C2×C4⋊C4C23×C13911yescharacteristic
359C2×C4⋊C4C23×C13911yescharacteristic
360C2×C4⋊C4C23×C13911yescharacteristic
361C2×C4⋊C4C23×C13911yescharacteristic
362C2×C4⋊C4C23×C13911yescharacteristic
363C2×C4⋊C4C23×C13911yescharacteristic
364C2×C4⋊C4C23×C13911yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42C23×C13911yescharacteristic
376C2×C42C23×C13911yescharacteristic
377C2×C42C23×C13911yescharacteristic
378#107—22no—
379#107—22no—
380#106—22no—
381#106—22no—
382C4⋊C8—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386#102—22no—
387C4×C8—22no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95D4×C13911yescharacteristic
398#95D4×C13911yescharacteristic
399C24—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4C2×D4×C13911yescharacteristic
414C22×C4C2×D4×C13911yescharacteristic
415C22×C4C2×D4×C13911yescharacteristic
416C22×C4C2×D4×C13911yescharacteristic
417C22×C4C2×D4×C13911yescharacteristic
418C22×C4C2×D4×C13911yescharacteristic
419C22×C4C24×C13911yescharacteristic
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8#41×C13912yes—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—41no—
447C4⋊C4—42no—
448C4⋊C4—81no—
449C4⋊C4—81no—
450C4⋊C4#41×C13912yes—
451C4⋊C4#41×C13912yes—
452C4⋊C4#41×C13912yes—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—81no—
456C22⋊C4—81no—
457C22⋊C4—81no—
458C22⋊C4—81no—
459C42—21no—
460C42—21no—
461C42—21no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—42no—
466C42—81no—
467C42—81no—
468C42—81no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23C22×D4×C13911yescharacteristic
477D4—41no—
478D4—41no—
479D4—41no—
480D4—41no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
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#135×C13912yes—
520C2×C4C2×#41×C13911yescharacteristic
521C2×C4C2×#41×C13911yescharacteristic
522C2×C4C2×#41×C13911yescharacteristic
523C2×C4C2×#41×C13911yescharacteristic
524C2×C42−1+4×C13911yescharacteristic
525C2×C42−1+4×C13911yescharacteristic
526C8—22no—
527C8—41no—
528C8—41no—
529C8—41no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22#525×C13911yescharacteristic
538C22#547×C13911yescharacteristic
539C22#548×C13911yescharacteristic
540C22C2×#135×C13911yescharacteristic
541C22#575×C13911yescharacteristic
542C22#576×C13911yescharacteristic
543C22#577×C13911yescharacteristic
544C4—22no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—42no—
551C4—41no—
552C4—42no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4#529×C13911yescharacteristic
558C4#541×C13911yescharacteristic
559C4#556×C13911yescharacteristic
560C4#556×C13911yescharacteristic
561C2—161no—
562C2#2469×C13911yescharacteristic
563C2#3102×C13911yescharacteristic
564C2#3119×C13911yescharacteristic
565C2#3337×C13911yescharacteristic
566C2#3347×C13911yescharacteristic
567C2#3361×C13911yescharacteristic
568C2#3371×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. #2370×C139C2semidirect
3. #2101×C139C2semidirect
5. #2059×C139C2semidirect
7. #1949×C139C2semidirect
12. #1921×C139C2semidirect
13. #1918×C139C2semidirect
14. #1916×C139C2semidirect
15. C4×#106×C139C2semidirect
284. #27136C139direct (N × H)
285. C139#27136direct (N × H)
287. #2370C2×C139semidirect
288. #2101C2×C139semidirect
290. #2059C2×C139semidirect
292. #1949C2×C139semidirect
297. #1921C2×C139semidirect
298. #1918C2×C139semidirect
299. #1916C2×C139semidirect
300. 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
#2370×C1392
#2101×C1392
#2065×C1392
#2059×C1392
#2025×C1392
#1949×C1392
#1934×C1392
#1926×C1392
#1925×C1392
#1921×C1392
#1918×C1392
#1916×C1392
C4×#106×C1392
#27136139