Finite Group Databasebeta

← C139×#29029 #48023625

Subgroups — C139×#29029 #48023625

Order 35584.

668 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2507×C139C211yesmaximal, characteristic, complemented
2#2448×C139C211yesmaximal, characteristic
3#2099×C139C211yesmaximal, characteristic, complemented
4#2067×C139C211yesmaximal, characteristic
5#2066×C139C211yesmaximal, characteristic, complemented
6#2042×C139C211yesmaximal, characteristic
7#1959×C139C211yesmaximal, characteristic
8#1944×C139C211yesmaximal, characteristic, complemented
9#1936×C139C211yesmaximal, characteristic
10#1935×C139C211yesmaximal, characteristic, complemented
11#1934×C139C211yesmaximal, characteristic
12#1926×C139C211yesmaximal, characteristic
13#1863×C139C211yesmaximal, characteristic, complemented
14#1771×C139C211yesmaximal, characteristic, complemented
15C4×#103×C139C211yesmaximal, characteristic, complemented
16C2×#124×C139C2211yescharacteristic
17C2×C4×Q8×C139C2211yescharacteristic
18C2×#107×C139C2211yescharacteristic
19C2×#106×C139C2211yescharacteristic
20C2×C4⋊C8×C139C2211yescharacteristic
21C2×#103×C139C2211yescharacteristic
22C2×#103×C139C2211yescharacteristic
23C2×#103×C139C2211yescharacteristic
24C2×#103×C139C2211yescharacteristic
25C2×#102×C139C2211yescharacteristic
26C2×#102×C139C2211yescharacteristic
27C2×#102×C139C2211yescharacteristic
28C2×#102×C139C2211yescharacteristic
29C2×#97×C139C2211yescharacteristic
30C2×#97×C139C2211yescharacteristic
31C2×C4×C8×C139C2211yescharacteristic
32#399×C139—21no—
33#398×C139—21no—
34#398×C139—21no—
35#397×C139—21no—
36#391×C139C2211yescharacteristic
37#390×C139C2211yescharacteristic
38#390×C139C2211yescharacteristic
39#389×C139—21no—
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#124×C139—22no—
66#124×C139—41no—
67C4×Q8×C139—22no—
68C4×Q8×C139—41no—
69C2×C4⋊C4×C139—21no—
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×C139D411yescharacteristic
78C2×C4⋊C4×C139D411yescharacteristic
79C2×C4⋊C4×C139C2311yescharacteristic
80C2×C4⋊C4×C139C2311yescharacteristic
81C2×C4⋊C4×C139C2311yescharacteristic
82C2×C4⋊C4×C139C2311yescharacteristic
83C2×C4⋊C4×C139C2311yescharacteristic
84C2×C4⋊C4×C139C2311yescharacteristic
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×C139—21no—
91C2×C42×C139—21no—
92C2×C42×C139—21no—
93C2×C42×C139C2311yescharacteristic
94C2×C42×C139C2311yescharacteristic
95C2×C42×C139C2311yescharacteristic
96#107×C139—41no—
97#106×C139—22no—
98C4⋊C8×C139—22no—
99#103×C139—22no—
100#103×C139—22no—
101#103×C139—22no—
102#103×C139—22no—
103#102×C139—22no—
104#102×C139—22no—
105#102×C139—22no—
106#102×C139—41no—
107#97×C139—22no—
108#97×C139—41no—
109C4×C8×C139—41no—
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—
121C2×Q8×C139—21no—
122C2×Q8×C139—21no—
123C2×Q8×C139—21no—
124C2×Q8×C139—21no—
125C2×Q8×C139—21no—
126C2×Q8×C139#4112yes—
127C2×D4×C139—21no—
128C2×D4×C139—21no—
129C2×D4×C139—21no—
130C2×D4×C139—21no—
131C2×D4×C139—21no—
132C2×D4×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×C139C2×D411yescharacteristic
141C22×C4×C139C2×D411yescharacteristic
142C22×C4×C139C2×D411yescharacteristic
143C22×C4×C139C2×D411yescharacteristic
144C22×C4×C139C2×D411yescharacteristic
145C22×C4×C139C2×D411yescharacteristic
146C22×C4×C139C2411yescharacteristic
147C2×C8×C139—21no—
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#4112yes—
158C2×C8×C139#4112yes—
159C4⋊C4×C139—22no—
160C4⋊C4×C139—21no—
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—41no—
172C4⋊C4×C139—42no—
173C4⋊C4×C139—42no—
174C4⋊C4×C139—81no—
175C4⋊C4×C139—81no—
176C4⋊C4×C139—81no—
177C4⋊C4×C139—81no—
178C4⋊C4×C139—81no—
179C4⋊C4×C139—81no—
180C4⋊C4×C139#4112yes—
181C22⋊C4×C139—42no—
182C22⋊C4×C139—42no—
183C22⋊C4×C139—42no—
184C22⋊C4×C139—42no—
185C22⋊C4×C139—81no—
186C22⋊C4×C139—81no—
187C42×C139—21no—
188C42×C139—21no—
189C42×C139—21no—
190C42×C139—21no—
191C42×C139—21no—
192C42×C139—21no—
193C42×C139—42no—
194C42×C139—81no—
195C23×C139—41no—
196C23×C139—41no—
197C23×C139—41no—
198C23×C139—41no—
199C23×C139—41no—
200C23×C139—41no—
201C23×C139—41no—
202C23×C139C22×D411yescharacteristic
203Q8×C139—22no—
204Q8×C139—22no—
205Q8×C139—41no—
206Q8×C139—41no—
207D4×C139—41no—
208D4×C139—41no—
209D4×C139—41no—
210D4×C139—41no—
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—22no—
219C2×C4×C139—22no—
220C2×C4×C139—21no—
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—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#13712yes—
250C2×C4×C139C2×#4111yescharacteristic
251C2×C4×C139C2×#4111yescharacteristic
252C2×C4×C139C2×#4111yescharacteristic
253C2×C4×C139C2×#4111yescharacteristic
254C2×C4×C139H(5,𝔽2)11yescharacteristic
255C2×C4×C1392−1+411yescharacteristic
256C8×C139—22no—
257C8×C139—22no—
258C8×C139—41no—
259C8×C139—41no—
260C22×C139—81no—
261C22×C139—81no—
262C22×C139—81no—
263C22×C139—81no—
264C22×C139—81no—
265C22×C139—81no—
266C22×C139—81no—
267C22×C139#53211yescharacteristic
268C22×C139#54611yescharacteristic
269C22×C139#54811yescharacteristic
270C22×C139C2×#13711yescharacteristic
271C22×C139#57511yescharacteristic
272C22×C139#57611yescharacteristic
273C22×C139#57711yescharacteristic
274C4×C139—22no—
275C4×C139—42no—
276C4×C139—41no—
277C4×C139—41no—
278C4×C139—41no—
279C4×C139—41no—
280C4×C139—41no—
281C4×C139—42no—
282C4×C139—81no—
283C4×C139—81no—
284C4×C139—81no—
285C4×C139—81no—
286C4×C139—81no—
287C4×C139#52911yescharacteristic
288C4×C139#53911yescharacteristic
289C4×C139#55211yescharacteristic
290C4×C139#55311yescharacteristic
291C2×C139—161no—
292C2×C139#255811yescharacteristic
293C2×C139#317211yescharacteristic
294C2×C139#317911yescharacteristic
295C2×C139#330911yescharacteristic
296C2×C139#331611yescharacteristic
297C2×C139#337511yescharacteristic
298C2×C139#337611yescharacteristic
299#29029C13911yesmaximal, characteristic, direct product factor, Sylow
300C139#2902911yescharacteristic, direct product factor, Sylow
301#2507C2×C13911yescharacteristic, complemented
302#2448C2×C13911yescharacteristic
303#2099C2×C13911yescharacteristic, complemented
304#2067C2×C13911yescharacteristic
305#2066C2×C13911yescharacteristic, complemented
306#2042C2×C13911yescharacteristic
307#1959C2×C13911yescharacteristic
308#1944C2×C13911yescharacteristic, complemented
309#1936C2×C13911yescharacteristic
310#1935C2×C13911yescharacteristic, complemented
311#1934C2×C13911yescharacteristic
312#1926C2×C13911yescharacteristic
313#1863C2×C13911yescharacteristic, complemented
314#1771C2×C13911yescharacteristic, complemented
315C4×#103C2×C13911yescharacteristic, complemented
316C2×#124C22×C13911yescharacteristic
317C2×C4×Q8C22×C13911yescharacteristic
318C2×#107C22×C13911yescharacteristic
319C2×#106C22×C13911yescharacteristic
320C2×C4⋊C8C22×C13911yescharacteristic
321C2×#103C22×C13911yescharacteristic
322C2×#103C22×C13911yescharacteristic
323C2×#103C22×C13911yescharacteristic
324C2×#103C22×C13911yescharacteristic
325C2×#102C22×C13911yescharacteristic
326C2×#102C22×C13911yescharacteristic
327C2×#102C22×C13911yescharacteristic
328C2×#102C22×C13911yescharacteristic
329C2×#97C22×C13911yescharacteristic
330C2×#97C22×C13911yescharacteristic
331C2×C4×C8C22×C13911yescharacteristic
332#399—21no—
333#398—21no—
334#398—21no—
335#397—21no—
336#391C22×C13911yescharacteristic
337#390C22×C13911yescharacteristic
338#390C22×C13911yescharacteristic
339#389—21no—
340#389C22×C13911yescharacteristic
341#389C22×C13911yescharacteristic
342#389C22×C13911yescharacteristic
343#389C22×C13911yescharacteristic
344#389C22×C13911yescharacteristic
345#388—21no—
346#388—21no—
347#387—21no—
348#384C22×C13911yescharacteristic
349C4×C4⋊C4C22×C13911yescharacteristic
350C4×C4⋊C4C22×C13911yescharacteristic
351#340C22×C13911yescharacteristic
352#340C22×C13911yescharacteristic
353#340C22×C13911yescharacteristic
354#340C22×C13911yescharacteristic
355#340C22×C13911yescharacteristic
356#340C22×C13911yescharacteristic
357#336C22×C13911yescharacteristic
358#336C22×C13911yescharacteristic
359C22×Q8C23×C13911yescharacteristic
360C22×D4C23×C13911yescharacteristic
361C22×C8C23×C13911yescharacteristic
362C22×C8C23×C13911yescharacteristic
363C22×C8C23×C13911yescharacteristic
364C22×C8C23×C13911yescharacteristic
365#124—22no—
366#124—41no—
367C4×Q8—22no—
368C4×Q8—41no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
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⋊C4D4×C13911yescharacteristic
378C2×C4⋊C4D4×C13911yescharacteristic
379C2×C4⋊C4C23×C13911yescharacteristic
380C2×C4⋊C4C23×C13911yescharacteristic
381C2×C4⋊C4C23×C13911yescharacteristic
382C2×C4⋊C4C23×C13911yescharacteristic
383C2×C4⋊C4C23×C13911yescharacteristic
384C2×C4⋊C4C23×C13911yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C13911yescharacteristic
394C2×C42C23×C13911yescharacteristic
395C2×C42C23×C13911yescharacteristic
396#107—41no—
397#106—22no—
398C4⋊C8—22no—
399#103—22no—
400#103—22no—
401#103—22no—
402#103—22no—
403#102—22no—
404#102—22no—
405#102—22no—
406#102—41no—
407#97—22no—
408#97—41no—
409C4×C8—41no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95D4×C13911yescharacteristic
419#95D4×C13911yescharacteristic
420C24—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#41×C13912yes—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4C2×D4×C13911yescharacteristic
441C22×C4C2×D4×C13911yescharacteristic
442C22×C4C2×D4×C13911yescharacteristic
443C22×C4C2×D4×C13911yescharacteristic
444C22×C4C2×D4×C13911yescharacteristic
445C22×C4C2×D4×C13911yescharacteristic
446C22×C4C24×C13911yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
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#41×C13912yes—
458C2×C8#41×C13912yes—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
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—41no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4#41×C13912yes—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—81no—
486C22⋊C4—81no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—81no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23C22×D4×C13911yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
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—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#137×C13912yes—
550C2×C4C2×#41×C13911yescharacteristic
551C2×C4C2×#41×C13911yescharacteristic
552C2×C4C2×#41×C13911yescharacteristic
553C2×C4C2×#41×C13911yescharacteristic
554C2×C4H(5,𝔽2)×C13911yescharacteristic
555C2×C42−1+4×C13911yescharacteristic
556C8—22no—
557C8—22no—
558C8—41no—
559C8—41no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22#532×C13911yescharacteristic
568C22#546×C13911yescharacteristic
569C22#548×C13911yescharacteristic
570C22C2×#137×C13911yescharacteristic
571C22#575×C13911yescharacteristic
572C22#576×C13911yescharacteristic
573C22#577×C13911yescharacteristic
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—42no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4#529×C13911yescharacteristic
588C4#539×C13911yescharacteristic
589C4#552×C13911yescharacteristic
590C4#553×C13911yescharacteristic
591C2—161no—
592C2#2558×C13911yescharacteristic
593C2#3172×C13911yescharacteristic
594C2#3179×C13911yescharacteristic
595C2#3309×C13911yescharacteristic
596C2#3316×C13911yescharacteristic
597C2#3375×C13911yescharacteristic
598C2#3376×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. #2507×C139C2semidirect
3. #2099×C139C2semidirect
5. #2066×C139C2semidirect
8. #1944×C139C2semidirect
10. #1935×C139C2semidirect
13. #1863×C139C2semidirect
14. #1771×C139C2semidirect
15. C4×#103×C139C2semidirect
299. #29029C139direct (N × H)
300. C139#29029direct (N × H)
301. #2507C2×C139semidirect
303. #2099C2×C139semidirect
305. #2066C2×C139semidirect
308. #1944C2×C139semidirect
310. #1935C2×C139semidirect
313. #1863C2×C139semidirect
314. #1771C2×C139semidirect
315. C4×#103C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2507×C1392
#2448×C1392
#2099×C1392
#2067×C1392
#2066×C1392
#2042×C1392
#1959×C1392
#1944×C1392
#1936×C1392
#1935×C1392
#1934×C1392
#1926×C1392
#1863×C1392
#1771×C1392
C4×#103×C1392
#29029139