Finite Group Databasebeta

← C139×#27040 #48021636

Subgroups — C139×#27040 #48021636

Order 35584.

734 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2494×C139C211yesmaximal, characteristic, complemented
2#2363×C139C211yesmaximal, characteristic
3#2073×C139C211yesmaximal, characteristic, complemented
4#2065×C139C211yesmaximal, characteristic, complemented
5#2034×C139C211yesmaximal, characteristic
6#2033×C139C211yesmaximal, characteristic
7#1949×C139C211yesmaximal, characteristic, complemented
8#1941×C139C211yesmaximal, characteristic, complemented
9#1923×C139C211yesmaximal, characteristic, complemented
10#1921×C139C211yesmaximal, characteristic, complemented
11#1918×C139C211yesmaximal, characteristic, complemented
12#1862×C139C211yesmaximal, characteristic, complemented
13#1854×C139C211yesmaximal, characteristic, complemented
14#1825×C139C211yesmaximal, characteristic, complemented
15C4×#102×C139C211yesmaximal, characteristic, complemented
16C2×#121×C139C2211yescharacteristic
17C2×C4×D4×C139C2211yescharacteristic
18C2×#117×C139C2211yescharacteristic
19C2×#107×C139C2211yescharacteristic
20C2×#107×C139C2211yescharacteristic
21C2×#106×C139C2211yescharacteristic
22C2×#106×C139C2211yescharacteristic
23C2×C4⋊C8×C139C2211yescharacteristic
24C2×#102×C139C2211yescharacteristic
25C2×#102×C139C2211yescharacteristic
26C2×#102×C139C2211yescharacteristic
27C2×#102×C139C2211yescharacteristic
28C2×C22⋊C8×C139C2211yescharacteristic
29C2×C22⋊C8×C139C2211yescharacteristic
30C2×C4×C8×C139C2211yescharacteristic
31#401×C139—21no—
32#397×C139—21no—
33#390×C139—21no—
34#390×C139C2211yescharacteristic
35#389×C139C2211yescharacteristic
36#389×C139C2211yescharacteristic
37#389×C139C2211yescharacteristic
38#388×C139—21no—
39#388×C139—21no—
40#387×C139—21no—
41#386×C139—21no—
42#382×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×D4×C139—21no—
60C22×D4×C139C2311yescharacteristic
61C23×C4×C139—21no—
62C23×C4×C139C2311yescharacteristic
63C22×C8×C139C2311yescharacteristic
64C22×C8×C139C2311yescharacteristic
65C22×C8×C139C2311yescharacteristic
66C22×C8×C139C2311yescharacteristic
67#121×C139—22no—
68#121×C139—22no—
69C4×D4×C139—22no—
70C4×D4×C139—41no—
71#117×C139—22no—
72#117×C139—41no—
73C2×C4⋊C4×C139—21no—
74C2×C4⋊C4×C139—21no—
75C2×C4⋊C4×C139—21no—
76C2×C4⋊C4×C139C2311yescharacteristic
77C2×C4⋊C4×C139C2311yescharacteristic
78C2×C4⋊C4×C139C2311yescharacteristic
79C2×C4⋊C4×C139C2311yescharacteristic
80C2×C4⋊C4×C139C2311yescharacteristic
81C2×C4⋊C4×C139C2311yescharacteristic
82C2×C4⋊C4×C139C2311yescharacteristic
83C2×C22⋊C4×C139—21no—
84C2×C22⋊C4×C139—21no—
85C2×C22⋊C4×C139—21no—
86C2×C22⋊C4×C139—21no—
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#106×C139—22no—
100#106×C139—41no—
101C4⋊C8×C139—22no—
102#102×C139—22no—
103#102×C139—22no—
104#102×C139—22no—
105#102×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×C139—21no—
121C24×C139C2×D411yescharacteristic
122C2×D4×C139—24no—
123C2×D4×C139—21no—
124C2×D4×C139—21no—
125C2×D4×C139—21no—
126C2×D4×C139—21no—
127C2×D4×C139—21no—
128C2×D4×C139—81no—
129C2×D4×C139—81no—
130C2×D4×C139#4112yes—
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—21no—
142C22×C4×C139—21no—
143C22×C4×C139—21no—
144C22×C4×C139—42no—
145C22×C4×C139—42no—
146C22×C4×C139—81no—
147C22×C4×C139C2×D411yescharacteristic
148C22×C4×C139C2×D411yescharacteristic
149C22×C4×C139C2×D411yescharacteristic
150C22×C4×C139C2×D411yescharacteristic
151C22×C4×C139C2×D411yescharacteristic
152C22×C4×C139C2411yescharacteristic
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—21no—
162C2×C8×C139—21no—
163C2×C8×C139—21no—
164C2×C8×C139#4112yes—
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—21no—
176C4⋊C4×C139—21no—
177C4⋊C4×C139—42no—
178C4⋊C4×C139—81no—
179C4⋊C4×C139—81no—
180C4⋊C4×C139#4112yes—
181C4⋊C4×C139#4112yes—
182C22⋊C4×C139—24no—
183C22⋊C4×C139—22no—
184C22⋊C4×C139—41no—
185C22⋊C4×C139—42no—
186C22⋊C4×C139—42no—
187C22⋊C4×C139—42no—
188C22⋊C4×C139—42no—
189C22⋊C4×C139—81no—
190C22⋊C4×C139—81no—
191C42×C139—21no—
192C42×C139—21no—
193C42×C139—21no—
194C42×C139—21no—
195C42×C139—42no—
196C42×C139—81no—
197C42×C139—81no—
198C23×C139—22no—
199C23×C139—21no—
200C23×C139—21no—
201C23×C139—21no—
202C23×C139—21no—
203C23×C139—21no—
204C23×C139—21no—
205C23×C139—21no—
206C23×C139—41no—
207C23×C139—41no—
208C23×C139—41no—
209C23×C139—41no—
210C23×C139—41no—
211C23×C139—41no—
212C23×C139C22×D411yescharacteristic
213D4×C139—22no—
214D4×C139—22no—
215D4×C139—41no—
216D4×C139—41no—
217D4×C139—84no—
218C2×C4×C139—21no—
219C2×C4×C139—21no—
220C2×C4×C139—21no—
221C2×C4×C139—22no—
222C2×C4×C139—21no—
223C2×C4×C139—21no—
224C2×C4×C139—22no—
225C2×C4×C139—21no—
226C2×C4×C139—21no—
227C2×C4×C139—21no—
228C2×C4×C139—21no—
229C2×C4×C139—21no—
230C2×C4×C139—21no—
231C2×C4×C139—21no—
232C2×C4×C139—21no—
233C2×C4×C139—21no—
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—41no—
250C2×C4×C139—41no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—41no—
256C2×C4×C139—41no—
257C2×C4×C139—84no—
258C2×C4×C139#13512yes—
259C2×C4×C139C2×#4111yescharacteristic
260C2×C4×C139C2×#4111yescharacteristic
261C2×C4×C139C2×#4111yescharacteristic
262C2×C4×C139C2×#4111yescharacteristic
263C2×C4×C139H(5,𝔽2)11yescharacteristic
264C2×C4×C1392−1+411yescharacteristic
265C8×C139—22no—
266C8×C139—41no—
267C8×C139—41no—
268C8×C139—41no—
269C22×C139—41no—
270C22×C139—41no—
271C22×C139—41no—
272C22×C139—42no—
273C22×C139—41no—
274C22×C139—42no—
275C22×C139—41no—
276C22×C139—42no—
277C22×C139—41no—
278C22×C139—41no—
279C22×C139—81no—
280C22×C139—81no—
281C22×C139—81no—
282C22×C139—81no—
283C22×C139#52511yescharacteristic
284C22×C139#54611yescharacteristic
285C22×C139#54711yescharacteristic
286C22×C139C2×#13511yescharacteristic
287C22×C139#57511yescharacteristic
288C22×C139#57611yescharacteristic
289C22×C139#57711yescharacteristic
290C4×C139—22no—
291C4×C139—41no—
292C4×C139—41no—
293C4×C139—42no—
294C4×C139—41no—
295C4×C139—42no—
296C4×C139—41no—
297C4×C139—81no—
298C4×C139—81no—
299C4×C139—81no—
300C4×C139—81no—
301C4×C139—81no—
302C4×C139#52911yescharacteristic
303C4×C139#53911yescharacteristic
304C4×C139#55311yescharacteristic
305C4×C139#55611yescharacteristic
306C2×C139—81no—
307C2×C139—82no—
308C2×C139#246611yescharacteristic
309C2×C139#310211yescharacteristic
310C2×C139#311811yescharacteristic
311C2×C139#329711yescharacteristic
312C2×C139#331711yescharacteristic
313C2×C139#334011yescharacteristic
314C2×C139#335511yescharacteristic
315#27040C13911yesmaximal, characteristic, direct product factor, Sylow
316C139#2704011yescharacteristic, direct product factor, Sylow
317#2494C2×C13911yescharacteristic, complemented
318#2363C2×C13911yescharacteristic
319#2073C2×C13911yescharacteristic, complemented
320#2065C2×C13911yescharacteristic, complemented
321#2034C2×C13911yescharacteristic
322#2033C2×C13911yescharacteristic
323#1949C2×C13911yescharacteristic, complemented
324#1941C2×C13911yescharacteristic, complemented
325#1923C2×C13911yescharacteristic, complemented
326#1921C2×C13911yescharacteristic, complemented
327#1918C2×C13911yescharacteristic, complemented
328#1862C2×C13911yescharacteristic, complemented
329#1854C2×C13911yescharacteristic, complemented
330#1825C2×C13911yescharacteristic, complemented
331C4×#102C2×C13911yescharacteristic, complemented
332C2×#121C22×C13911yescharacteristic
333C2×C4×D4C22×C13911yescharacteristic
334C2×#117C22×C13911yescharacteristic
335C2×#107C22×C13911yescharacteristic
336C2×#107C22×C13911yescharacteristic
337C2×#106C22×C13911yescharacteristic
338C2×#106C22×C13911yescharacteristic
339C2×C4⋊C8C22×C13911yescharacteristic
340C2×#102C22×C13911yescharacteristic
341C2×#102C22×C13911yescharacteristic
342C2×#102C22×C13911yescharacteristic
343C2×#102C22×C13911yescharacteristic
344C2×C22⋊C8C22×C13911yescharacteristic
345C2×C22⋊C8C22×C13911yescharacteristic
346C2×C4×C8C22×C13911yescharacteristic
347#401—21no—
348#397—21no—
349#390—21no—
350#390C22×C13911yescharacteristic
351#389C22×C13911yescharacteristic
352#389C22×C13911yescharacteristic
353#389C22×C13911yescharacteristic
354#388—21no—
355#388—21no—
356#387—21no—
357#386—21no—
358#382C22×C13911yescharacteristic
359#380C22×C13911yescharacteristic
360#380C22×C13911yescharacteristic
361C4×C4⋊C4C22×C13911yescharacteristic
362C4×C4⋊C4C22×C13911yescharacteristic
363C4×C22⋊C4—21no—
364C4×C22⋊C4C22×C13911yescharacteristic
365#340C22×C13911yescharacteristic
366#340C22×C13911yescharacteristic
367#340C22×C13911yescharacteristic
368#340C22×C13911yescharacteristic
369#340C22×C13911yescharacteristic
370#340C22×C13911yescharacteristic
371#340C22×C13911yescharacteristic
372#340C22×C13911yescharacteristic
373#336C22×C13911yescharacteristic
374#336C22×C13911yescharacteristic
375C22×D4—21no—
376C22×D4C23×C13911yescharacteristic
377C23×C4—21no—
378C23×C4C23×C13911yescharacteristic
379C22×C8C23×C13911yescharacteristic
380C22×C8C23×C13911yescharacteristic
381C22×C8C23×C13911yescharacteristic
382C22×C8C23×C13911yescharacteristic
383#121—22no—
384#121—22no—
385C4×D4—22no—
386C4×D4—41no—
387#117—22no—
388#117—41no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C23×C13911yescharacteristic
393C2×C4⋊C4C23×C13911yescharacteristic
394C2×C4⋊C4C23×C13911yescharacteristic
395C2×C4⋊C4C23×C13911yescharacteristic
396C2×C4⋊C4C23×C13911yescharacteristic
397C2×C4⋊C4C23×C13911yescharacteristic
398C2×C4⋊C4C23×C13911yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4D4×C13911yescharacteristic
407C2×C22⋊C4D4×C13911yescharacteristic
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C23×C13911yescharacteristic
412C2×C42C23×C13911yescharacteristic
413#107—22no—
414#107—22no—
415#106—22no—
416#106—41no—
417C4⋊C8—22no—
418#102—22no—
419#102—22no—
420#102—22no—
421#102—41no—
422C22⋊C8—22no—
423C22⋊C8—41no—
424C4×C8—41no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95D4×C13911yescharacteristic
435#95D4×C13911yescharacteristic
436C24—21no—
437C24C2×D4×C13911yescharacteristic
438C2×D4—24no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—81no—
445C2×D4—81no—
446C2×D4#41×C13912yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—81no—
463C22×C4C2×D4×C13911yescharacteristic
464C22×C4C2×D4×C13911yescharacteristic
465C22×C4C2×D4×C13911yescharacteristic
466C22×C4C2×D4×C13911yescharacteristic
467C22×C4C2×D4×C13911yescharacteristic
468C22×C4C24×C13911yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8#41×C13912yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4#41×C13912yes—
497C4⋊C4#41×C13912yes—
498C22⋊C4—24no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—81no—
513C42—81no—
514C23—22no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C22×D4×C13911yescharacteristic
529D4—22no—
530D4—22no—
531D4—41no—
532D4—41no—
533D4—84no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—84no—
574C2×C4#135×C13912yes—
575C2×C4C2×#41×C13911yescharacteristic
576C2×C4C2×#41×C13911yescharacteristic
577C2×C4C2×#41×C13911yescharacteristic
578C2×C4C2×#41×C13911yescharacteristic
579C2×C4H(5,𝔽2)×C13911yescharacteristic
580C2×C42−1+4×C13911yescharacteristic
581C8—22no—
582C8—41no—
583C8—41no—
584C8—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22#525×C13911yescharacteristic
600C22#546×C13911yescharacteristic
601C22#547×C13911yescharacteristic
602C22C2×#135×C13911yescharacteristic
603C22#575×C13911yescharacteristic
604C22#576×C13911yescharacteristic
605C22#577×C13911yescharacteristic
606C4—22no—
607C4—42no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4#529×C13911yescharacteristic
619C4#539×C13911yescharacteristic
620C4#553×C13911yescharacteristic
621C4#556×C13911yescharacteristic
622C2—81no—
623C2—82no—
624C2#2466×C13911yescharacteristic
625C2#3102×C13911yescharacteristic
626C2#3118×C13911yescharacteristic
627C2#3297×C13911yescharacteristic
628C2#3317×C13911yescharacteristic
629C2#3340×C13911yescharacteristic
630C2#3355×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#121×C139C22
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
1. #2494×C139C2semidirect
3. #2073×C139C2semidirect
4. #2065×C139C2semidirect
7. #1949×C139C2semidirect
8. #1941×C139C2semidirect
9. #1923×C139C2semidirect
10. #1921×C139C2semidirect
11. #1918×C139C2semidirect
12. #1862×C139C2semidirect
13. #1854×C139C2semidirect
14. #1825×C139C2semidirect
15. C4×#102×C139C2semidirect
315. #27040C139direct (N × H)
316. C139#27040direct (N × H)
317. #2494C2×C139semidirect
319. #2073C2×C139semidirect
320. #2065C2×C139semidirect
323. #1949C2×C139semidirect
324. #1941C2×C139semidirect
325. #1923C2×C139semidirect
326. #1921C2×C139semidirect
327. #1918C2×C139semidirect
328. #1862C2×C139semidirect
329. #1854C2×C139semidirect
330. #1825C2×C139semidirect
331. C4×#102C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2494×C1392
#2363×C1392
#2073×C1392
#2065×C1392
#2034×C1392
#2033×C1392
#1949×C1392
#1941×C1392
#1923×C1392
#1921×C1392
#1918×C1392
#1862×C1392
#1854×C1392
#1825×C1392
C4×#102×C1392
#27040139