Finite Group Databasebeta

← C139×#29025 #48023621

Subgroups — C139×#29025 #48023621

Order 35584.

688 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2506×C139C211yesmaximal, characteristic, complemented
2#2448×C139C211yesmaximal, characteristic
3#2100×C139C211yesmaximal, characteristic, complemented
4#2068×C139C211yesmaximal, characteristic, complemented
5#2065×C139C211yesmaximal, characteristic
6#2042×C139C211yesmaximal, characteristic
7#1959×C139C211yesmaximal, characteristic
8#1943×C139C211yesmaximal, characteristic, complemented
9#1936×C139C211yesmaximal, characteristic
10#1935×C139C211yesmaximal, characteristic, complemented
11#1934×C139C211yesmaximal, characteristic
12#1925×C139C211yesmaximal, characteristic
13#1865×C139C211yesmaximal, characteristic, complemented
14#1771×C139C211yesmaximal, characteristic, complemented
15C4×#103×C139C211yesmaximal, characteristic, complemented
16C2×#125×C139—21no—
17C2×#124×C139C2211yescharacteristic
18C2×C4×Q8×C139C2211yescharacteristic
19C2×#107×C139C2211yescharacteristic
20C2×#106×C139C2211yescharacteristic
21C2×C4⋊C8×C139C2211yescharacteristic
22C2×#103×C139C2211yescharacteristic
23C2×#103×C139C2211yescharacteristic
24C2×#103×C139C2211yescharacteristic
25C2×#103×C139C2211yescharacteristic
26C2×#102×C139C2211yescharacteristic
27C2×#102×C139C2211yescharacteristic
28C2×#102×C139C2211yescharacteristic
29C2×#102×C139C2211yescharacteristic
30C2×#97×C139C2211yescharacteristic
31C2×#97×C139C2211yescharacteristic
32C2×C4×C8×C139C2211yescharacteristic
33#400×C139—21no—
34#399×C139—21no—
35#398×C139—21no—
36#397×C139—21no—
37#391×C139C2211yescharacteristic
38#390×C139C2211yescharacteristic
39#390×C139C2211yescharacteristic
40#389×C139C2211yescharacteristic
41#389×C139C2211yescharacteristic
42#389×C139C2211yescharacteristic
43#389×C139C2211yescharacteristic
44#389×C139C2211yescharacteristic
45#388×C139—21no—
46#388×C139—21no—
47#387×C139—21no—
48#384×C139C2211yescharacteristic
49C4×C4⋊C4×C139C2211yescharacteristic
50C4×C4⋊C4×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
60C22×D4×C139C2311yescharacteristic
61C22×C8×C139C2311yescharacteristic
62C22×C8×C139C2311yescharacteristic
63C22×C8×C139C2311yescharacteristic
64C22×C8×C139C2311yescharacteristic
65#125×C139—44no—
66#124×C139—22no—
67#124×C139—41no—
68C4×Q8×C139—22no—
69C4×Q8×C139—41no—
70C2×C4⋊C4×C139—21no—
71C2×C4⋊C4×C139—21no—
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×C139D411yescharacteristic
79C2×C4⋊C4×C139D411yescharacteristic
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×C22⋊C4×C139—21no—
87C2×C22⋊C4×C139—21no—
88C2×C22⋊C4×C139—21no—
89C2×C22⋊C4×C139—21no—
90C2×C22⋊C4×C139—21no—
91C2×C22⋊C4×C139—21no—
92C2×C42×C139—21no—
93C2×C42×C139—21no—
94C2×C42×C139C2311yescharacteristic
95C2×C42×C139C2311yescharacteristic
96C2×C42×C139C2311yescharacteristic
97#107×C139—22no—
98#106×C139—41no—
99C4⋊C8×C139—22no—
100#103×C139—22no—
101#103×C139—22no—
102#103×C139—22no—
103#103×C139—22no—
104#102×C139—22no—
105#102×C139—22no—
106#102×C139—22no—
107#102×C139—41no—
108#97×C139—22no—
109#97×C139—41no—
110C4×C8×C139—41no—
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×C139—21no—
119#95×C139D411yescharacteristic
120#95×C139D411yescharacteristic
121C24×C139—21no—
122C2×Q8×C139—21no—
123C2×Q8×C139—21no—
124C2×Q8×C139—21no—
125C2×Q8×C139—21no—
126C2×Q8×C139—21no—
127C2×Q8×C139#4112yes—
128C2×D4×C139—21no—
129C2×D4×C139—21no—
130C2×D4×C139—21no—
131C2×D4×C139—21no—
132C2×D4×C139—21no—
133C2×D4×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×C139C2×D411yescharacteristic
142C22×C4×C139C2×D411yescharacteristic
143C22×C4×C139C2×D411yescharacteristic
144C22×C4×C139C2×D411yescharacteristic
145C22×C4×C139C2×D411yescharacteristic
146C22×C4×C139C2×D411yescharacteristic
147C22×C4×C139C2411yescharacteristic
148C2×C8×C139—21no—
149C2×C8×C139—21no—
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#4112yes—
159C2×C8×C139#4112yes—
160C4⋊C4×C139—22no—
161C4⋊C4×C139—21no—
162C4⋊C4×C139—21no—
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—41no—
173C4⋊C4×C139—42no—
174C4⋊C4×C139—42no—
175C4⋊C4×C139—42no—
176C4⋊C4×C139—42no—
177C4⋊C4×C139—42no—
178C4⋊C4×C139—42no—
179C4⋊C4×C139—42no—
180C4⋊C4×C139—81no—
181C4⋊C4×C139#4112yes—
182C22⋊C4×C139—42no—
183C22⋊C4×C139—42no—
184C22⋊C4×C139—42no—
185C22⋊C4×C139—42no—
186C22⋊C4×C139—81no—
187C22⋊C4×C139—81no—
188C42×C139—21no—
189C42×C139—21no—
190C42×C139—21no—
191C42×C139—21no—
192C42×C139—21no—
193C42×C139—21no—
194C42×C139—42no—
195C42×C139—42no—
196C23×C139—41no—
197C23×C139—41no—
198C23×C139—41no—
199C23×C139—41no—
200C23×C139—41no—
201C23×C139—41no—
202C23×C139—41no—
203C23×C139C22×D411yescharacteristic
204Q8×C139—22no—
205Q8×C139—22no—
206Q8×C139—41no—
207Q8×C139—41no—
208D4×C139—41no—
209D4×C139—41no—
210D4×C139—41no—
211D4×C139—41no—
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—22no—
220C2×C4×C139—22no—
221C2×C4×C139—21no—
222C2×C4×C139—21no—
223C2×C4×C139—21no—
224C2×C4×C139—21no—
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—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—41no—
250C2×C4×C139AGL(1,ℤ/8)12yes—
251C2×C4×C139C2×#4111yescharacteristic
252C2×C4×C139C2×#4111yescharacteristic
253C2×C4×C139C2×#4111yescharacteristic
254C2×C4×C139C2×#4111yescharacteristic
255C2×C4×C139H(5,𝔽2)11yescharacteristic
256C2×C4×C1392−1+411yescharacteristic
257C8×C139—22no—
258C8×C139—22no—
259C8×C139—41no—
260C8×C139—41no—
261C22×C139—81no—
262C22×C139—81no—
263C22×C139—81no—
264C22×C139—81no—
265C22×C139—81no—
266C22×C139—81no—
267C22×C139—81no—
268C22×C139#53211yescharacteristic
269C22×C139#54611yescharacteristic
270C22×C139#54811yescharacteristic
271C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C139#57511yescharacteristic
273C22×C139#57711yescharacteristic
274C22×C139#57811yescharacteristic
275C4×C139—22no—
276C4×C139—42no—
277C4×C139—41no—
278C4×C139—41no—
279C4×C139—41no—
280C4×C139—41no—
281C4×C139—41no—
282C4×C139—42no—
283C4×C139—81no—
284C4×C139—81no—
285C4×C139—81no—
286C4×C139—81no—
287C4×C139—81no—
288C4×C139#52911yescharacteristic
289C4×C139#53911yescharacteristic
290C4×C139#55211yescharacteristic
291C4×C139#55311yescharacteristic
292C2×C139—161no—
293C2×C139#255811yescharacteristic
294C2×C139#317111yescharacteristic
295C2×C139#317811yescharacteristic
296C2×C139#330811yescharacteristic
297C2×C139#331711yescharacteristic
298C2×C139#337311yescharacteristic
299C2×C139#337711yescharacteristic
300#29025C13911yesmaximal, characteristic, direct product factor, Sylow
301C139#2902511yescharacteristic, direct product factor, Sylow
302#2506C2×C13911yescharacteristic, complemented
303#2448C2×C13911yescharacteristic
304#2100C2×C13911yescharacteristic, complemented
305#2068C2×C13911yescharacteristic, complemented
306#2065C2×C13911yescharacteristic
307#2042C2×C13911yescharacteristic
308#1959C2×C13911yescharacteristic
309#1943C2×C13911yescharacteristic, complemented
310#1936C2×C13911yescharacteristic
311#1935C2×C13911yescharacteristic, complemented
312#1934C2×C13911yescharacteristic
313#1925C2×C13911yescharacteristic
314#1865C2×C13911yescharacteristic, complemented
315#1771C2×C13911yescharacteristic, complemented
316C4×#103C2×C13911yescharacteristic, complemented
317C2×#125—21no—
318C2×#124C22×C13911yescharacteristic
319C2×C4×Q8C22×C13911yescharacteristic
320C2×#107C22×C13911yescharacteristic
321C2×#106C22×C13911yescharacteristic
322C2×C4⋊C8C22×C13911yescharacteristic
323C2×#103C22×C13911yescharacteristic
324C2×#103C22×C13911yescharacteristic
325C2×#103C22×C13911yescharacteristic
326C2×#103C22×C13911yescharacteristic
327C2×#102C22×C13911yescharacteristic
328C2×#102C22×C13911yescharacteristic
329C2×#102C22×C13911yescharacteristic
330C2×#102C22×C13911yescharacteristic
331C2×#97C22×C13911yescharacteristic
332C2×#97C22×C13911yescharacteristic
333C2×C4×C8C22×C13911yescharacteristic
334#400—21no—
335#399—21no—
336#398—21no—
337#397—21no—
338#391C22×C13911yescharacteristic
339#390C22×C13911yescharacteristic
340#390C22×C13911yescharacteristic
341#389C22×C13911yescharacteristic
342#389C22×C13911yescharacteristic
343#389C22×C13911yescharacteristic
344#389C22×C13911yescharacteristic
345#389C22×C13911yescharacteristic
346#388—21no—
347#388—21no—
348#387—21no—
349#384C22×C13911yescharacteristic
350C4×C4⋊C4C22×C13911yescharacteristic
351C4×C4⋊C4C22×C13911yescharacteristic
352#340C22×C13911yescharacteristic
353#340C22×C13911yescharacteristic
354#340C22×C13911yescharacteristic
355#340C22×C13911yescharacteristic
356#340C22×C13911yescharacteristic
357#340C22×C13911yescharacteristic
358#336C22×C13911yescharacteristic
359#336C22×C13911yescharacteristic
360C22×Q8C23×C13911yescharacteristic
361C22×D4C23×C13911yescharacteristic
362C22×C8C23×C13911yescharacteristic
363C22×C8C23×C13911yescharacteristic
364C22×C8C23×C13911yescharacteristic
365C22×C8C23×C13911yescharacteristic
366#125—44no—
367#124—22no—
368#124—41no—
369C4×Q8—22no—
370C4×Q8—41no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C13911yescharacteristic
380C2×C4⋊C4D4×C13911yescharacteristic
381C2×C4⋊C4C23×C13911yescharacteristic
382C2×C4⋊C4C23×C13911yescharacteristic
383C2×C4⋊C4C23×C13911yescharacteristic
384C2×C4⋊C4C23×C13911yescharacteristic
385C2×C4⋊C4C23×C13911yescharacteristic
386C2×C4⋊C4C23×C13911yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42C23×C13911yescharacteristic
396C2×C42C23×C13911yescharacteristic
397C2×C42C23×C13911yescharacteristic
398#107—22no—
399#106—41no—
400C4⋊C8—22no—
401#103—22no—
402#103—22no—
403#103—22no—
404#103—22no—
405#102—22no—
406#102—22no—
407#102—22no—
408#102—41no—
409#97—22no—
410#97—41no—
411C4×C8—41no—
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
422C24—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8#41×C13912yes—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4C2×D4×C13911yescharacteristic
443C22×C4C2×D4×C13911yescharacteristic
444C22×C4C2×D4×C13911yescharacteristic
445C22×C4C2×D4×C13911yescharacteristic
446C22×C4C2×D4×C13911yescharacteristic
447C22×C4C2×D4×C13911yescharacteristic
448C22×C4C24×C13911yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8#41×C13912yes—
460C2×C8#41×C13912yes—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
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—41no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4#41×C13912yes—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—42no—
496C42—42no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23C22×D4×C13911yescharacteristic
505Q8—22no—
506Q8—22no—
507Q8—41no—
508Q8—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
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×C4AGL(1,ℤ/8)×C13912yes—
552C2×C4C2×#41×C13911yescharacteristic
553C2×C4C2×#41×C13911yescharacteristic
554C2×C4C2×#41×C13911yescharacteristic
555C2×C4C2×#41×C13911yescharacteristic
556C2×C4H(5,𝔽2)×C13911yescharacteristic
557C2×C42−1+4×C13911yescharacteristic
558C8—22no—
559C8—22no—
560C8—41no—
561C8—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#532×C13911yescharacteristic
570C22#546×C13911yescharacteristic
571C22#548×C13911yescharacteristic
572C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
573C22#575×C13911yescharacteristic
574C22#577×C13911yescharacteristic
575C22#578×C13911yescharacteristic
576C4—22no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—42no—
581C4—42no—
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4#529×C13911yescharacteristic
590C4#539×C13911yescharacteristic
591C4#552×C13911yescharacteristic
592C4#553×C13911yescharacteristic
593C2—161no—
594C2#2558×C13911yescharacteristic
595C2#3171×C13911yescharacteristic
596C2#3178×C13911yescharacteristic
597C2#3308×C13911yescharacteristic
598C2#3317×C13911yescharacteristic
599C2#3373×C13911yescharacteristic
600C2#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
1. #2506×C139C2semidirect
3. #2100×C139C2semidirect
4. #2068×C139C2semidirect
8. #1943×C139C2semidirect
10. #1935×C139C2semidirect
13. #1865×C139C2semidirect
14. #1771×C139C2semidirect
15. C4×#103×C139C2semidirect
300. #29025C139direct (N × H)
301. C139#29025direct (N × H)
302. #2506C2×C139semidirect
304. #2100C2×C139semidirect
305. #2068C2×C139semidirect
309. #1943C2×C139semidirect
311. #1935C2×C139semidirect
314. #1865C2×C139semidirect
315. #1771C2×C139semidirect
316. C4×#103C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2506×C1392
#2448×C1392
#2100×C1392
#2068×C1392
#2065×C1392
#2042×C1392
#1959×C1392
#1943×C1392
#1936×C1392
#1935×C1392
#1934×C1392
#1925×C1392
#1865×C1392
#1771×C1392
C4×#103×C1392
#29025139