Finite Group Databasebeta

← C139×#29035 #48023631

Subgroups — C139×#29035 #48023631

Order 35584.

674 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2509×C139C211yesmaximal, characteristic, complemented
2#2447×C139C211yesmaximal, characteristic
3#2101×C139C211yesmaximal, characteristic, complemented
4#2066×C139C211yesmaximal, characteristic, complemented
5#2065×C139C211yesmaximal, characteristic
6#2042×C139C211yesmaximal, characteristic
7#1958×C139C211yesmaximal, characteristic
8#1941×C139C211yesmaximal, characteristic, complemented
9#1936×C139C211yesmaximal, characteristic
10#1935×C139C211yesmaximal, characteristic, complemented
11#1935×C139C211yesmaximal, characteristic, complemented
12#1927×C139C211yesmaximal, characteristic, complemented
13#1864×C139C211yesmaximal, characteristic
14#1771×C139C211yesmaximal, characteristic, complemented
15#1762×C139C211yesmaximal, characteristic
16C2×#124×C139C2211yescharacteristic
17C2×C4×D4×C139C2211yescharacteristic
18C2×#106×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#400×C139—21no—
33#400×C139—21no—
34#397×C139—21no—
35#397×C139—21no—
36#391×C139C2211yescharacteristic
37#391×C139C2211yescharacteristic
38#390×C139C2211yescharacteristic
39#389×C139—21no—
40#389×C139C2211yescharacteristic
41#389×C139C2211yescharacteristic
42#389×C139C2211yescharacteristic
43#389×C139C2211yescharacteristic
44#389×C139C2211yescharacteristic
45#387×C139—21no—
46#385×C139—21no—
47#382×C139C2211yescharacteristic
48#381×C139—21no—
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
61C23×C4×C139—21no—
62C22×C8×C139C2311yescharacteristic
63C22×C8×C139C2311yescharacteristic
64C22×C8×C139C2311yescharacteristic
65C22×C8×C139C2311yescharacteristic
66#124×C139—22no—
67#124×C139—41no—
68C4×D4×C139—22no—
69C4×D4×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×C139D411yescharacteristic
76C2×C4⋊C4×C139D411yescharacteristic
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×C42×C139—21no—
89C2×C42×C139C2311yescharacteristic
90C2×C42×C139C2311yescharacteristic
91C2×C42×C139C2311yescharacteristic
92#106×C139—22no—
93#106×C139—41no—
94C4⋊C8×C139—22no—
95#103×C139—22no—
96#103×C139—22no—
97#103×C139—22no—
98#103×C139—41no—
99#102×C139—22no—
100#102×C139—22no—
101#102×C139—22no—
102#102×C139—22no—
103#97×C139—22no—
104#97×C139—41no—
105C4×C8×C139—41no—
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×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—21no—
127C2×D4×C139—21no—
128C2×D4×C139—21no—
129C2×D4×C139—21no—
130C2×D4×C139—21no—
131C2×D4×C139—21no—
132C2×D4×C139#4112yes—
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—42no—
141C22×C4×C139—42no—
142C22×C4×C139—81no—
143C22×C4×C139C2×D411yescharacteristic
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#4112yes—
161C2×C8×C139#4112yes—
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—21no—
173C4⋊C4×C139—41no—
174C4⋊C4×C139—41no—
175C4⋊C4×C139—42no—
176C4⋊C4×C139—42no—
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—
186C42×C139—21no—
187C42×C139—21no—
188C42×C139—21no—
189C42×C139—21no—
190C42×C139—21no—
191C42×C139—21no—
192C42×C139—81no—
193C23×C139—22no—
194C23×C139—41no—
195C23×C139—41no—
196C23×C139—41no—
197C23×C139—41no—
198C23×C139—41no—
199C23×C139—41no—
200C23×C139C22×D411yescharacteristic
201Q8×C139—41no—
202Q8×C139—41no—
203Q8×C139—41no—
204Q8×C139—41no—
205D4×C139—22no—
206D4×C139—22no—
207D4×C139—41no—
208D4×C139—41no—
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—22no—
216C2×C4×C139—21no—
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—21no—
225C2×C4×C139—21no—
226C2×C4×C139—21no—
227C2×C4×C139—21no—
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—84no—
249C2×C4×C139C2×#4111yescharacteristic
250C2×C4×C139C2×#4111yescharacteristic
251C2×C4×C139C2×#4111yescharacteristic
252C2×C4×C139C2×#4111yescharacteristic
253C2×C4×C139H(5,𝔽2)11yescharacteristic
254C2×C4×C1392−1+411yescharacteristic
255C8×C139—22no—
256C8×C139—22no—
257C8×C139—41no—
258C8×C139—41no—
259C22×C139—42no—
260C22×C139—42no—
261C22×C139—42no—
262C22×C139—81no—
263C22×C139—81no—
264C22×C139—81no—
265C22×C139—81no—
266C22×C139#53211yescharacteristic
267C22×C139#54611yescharacteristic
268C22×C139#54811yescharacteristic
269C22×C139#57511yescharacteristic
270C22×C139#57511yescharacteristic
271C22×C139#57711yescharacteristic
272C22×C139#57711yescharacteristic
273C4×C139—42no—
274C4×C139—41no—
275C4×C139—41no—
276C4×C139—41no—
277C4×C139—41no—
278C4×C139—41no—
279C4×C139—41no—
280C4×C139—81no—
281C4×C139—81no—
282C4×C139—81no—
283C4×C139—81no—
284C4×C139—81no—
285C4×C139—81no—
286C4×C139#52911yescharacteristic
287C4×C139#53911yescharacteristic
288C4×C139#55211yescharacteristic
289C4×C139#55311yescharacteristic
290C2×C139—82no—
291C2×C139#255811yescharacteristic
292C2×C139#317311yescharacteristic
293C2×C139#318311yescharacteristic
294C2×C139#330711yescharacteristic
295C2×C139#331111yescharacteristic
296C2×C139#337111yescharacteristic
297C2×C139#337611yescharacteristic
298#29035C13911yesmaximal, characteristic, direct product factor, Sylow
299C139#2903511yescharacteristic, direct product factor, Sylow
300#2509C2×C13911yescharacteristic, complemented
301#2447C2×C13911yescharacteristic
302#2101C2×C13911yescharacteristic, complemented
303#2066C2×C13911yescharacteristic, complemented
304#2065C2×C13911yescharacteristic
305#2042C2×C13911yescharacteristic
306#1958C2×C13911yescharacteristic
307#1941C2×C13911yescharacteristic, complemented
308#1936C2×C13911yescharacteristic
309#1935C2×C13911yescharacteristic, complemented
310#1935C2×C13911yescharacteristic, complemented
311#1927C2×C13911yescharacteristic, complemented
312#1864C2×C13911yescharacteristic
313#1771C2×C13911yescharacteristic, complemented
314#1762C2×C13911yescharacteristic
315C2×#124C22×C13911yescharacteristic
316C2×C4×D4C22×C13911yescharacteristic
317C2×#106C22×C13911yescharacteristic
318C2×#106C22×C13911yescharacteristic
319C2×C4⋊C8C22×C13911yescharacteristic
320C2×#103C22×C13911yescharacteristic
321C2×#103C22×C13911yescharacteristic
322C2×#103C22×C13911yescharacteristic
323C2×#103C22×C13911yescharacteristic
324C2×#102C22×C13911yescharacteristic
325C2×#102C22×C13911yescharacteristic
326C2×#102C22×C13911yescharacteristic
327C2×#102C22×C13911yescharacteristic
328C2×#97C22×C13911yescharacteristic
329C2×#97C22×C13911yescharacteristic
330C2×C4×C8C22×C13911yescharacteristic
331#400—21no—
332#400—21no—
333#397—21no—
334#397—21no—
335#391C22×C13911yescharacteristic
336#391C22×C13911yescharacteristic
337#390C22×C13911yescharacteristic
338#389—21no—
339#389C22×C13911yescharacteristic
340#389C22×C13911yescharacteristic
341#389C22×C13911yescharacteristic
342#389C22×C13911yescharacteristic
343#389C22×C13911yescharacteristic
344#387—21no—
345#385—21no—
346#382C22×C13911yescharacteristic
347#381—21no—
348C4×C4⋊C4C22×C13911yescharacteristic
349C4×C4⋊C4C22×C13911yescharacteristic
350#340C22×C13911yescharacteristic
351#340C22×C13911yescharacteristic
352#340C22×C13911yescharacteristic
353#340C22×C13911yescharacteristic
354#340C22×C13911yescharacteristic
355#340C22×C13911yescharacteristic
356#336C22×C13911yescharacteristic
357#336C22×C13911yescharacteristic
358C22×Q8C23×C13911yescharacteristic
359C22×D4C23×C13911yescharacteristic
360C23×C4—21no—
361C22×C8C23×C13911yescharacteristic
362C22×C8C23×C13911yescharacteristic
363C22×C8C23×C13911yescharacteristic
364C22×C8C23×C13911yescharacteristic
365#124—22no—
366#124—41no—
367C4×D4—22no—
368C4×D4—41no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C13911yescharacteristic
375C2×C4⋊C4D4×C13911yescharacteristic
376C2×C4⋊C4C23×C13911yescharacteristic
377C2×C4⋊C4C23×C13911yescharacteristic
378C2×C4⋊C4C23×C13911yescharacteristic
379C2×C4⋊C4C23×C13911yescharacteristic
380C2×C4⋊C4C23×C13911yescharacteristic
381C2×C4⋊C4C23×C13911yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—21no—
388C2×C42C23×C13911yescharacteristic
389C2×C42C23×C13911yescharacteristic
390C2×C42C23×C13911yescharacteristic
391#106—22no—
392#106—41no—
393C4⋊C8—22no—
394#103—22no—
395#103—22no—
396#103—22no—
397#103—41no—
398#102—22no—
399#102—22no—
400#102—22no—
401#102—22no—
402#97—22no—
403#97—41no—
404C4×C8—41no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95D4×C13911yescharacteristic
418#95D4×C13911yescharacteristic
419C24—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4#41×C13912yes—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—81no—
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—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—21no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4#41×C13912yes—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—81no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—81no—
492C23—22no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23C22×D4×C13911yescharacteristic
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504D4—22no—
505D4—22no—
506D4—41no—
507D4—41no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
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—84no—
548C2×C4C2×#41×C13911yescharacteristic
549C2×C4C2×#41×C13911yescharacteristic
550C2×C4C2×#41×C13911yescharacteristic
551C2×C4C2×#41×C13911yescharacteristic
552C2×C4H(5,𝔽2)×C13911yescharacteristic
553C2×C42−1+4×C13911yescharacteristic
554C8—22no—
555C8—22no—
556C8—41no—
557C8—41no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22#532×C13911yescharacteristic
566C22#546×C13911yescharacteristic
567C22#548×C13911yescharacteristic
568C22#575×C13911yescharacteristic
569C22#575×C13911yescharacteristic
570C22#577×C13911yescharacteristic
571C22#577×C13911yescharacteristic
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4#529×C13911yescharacteristic
586C4#539×C13911yescharacteristic
587C4#552×C13911yescharacteristic
588C4#553×C13911yescharacteristic
589C2—82no—
590C2#2558×C13911yescharacteristic
591C2#3173×C13911yescharacteristic
592C2#3183×C13911yescharacteristic
593C2#3307×C13911yescharacteristic
594C2#3311×C13911yescharacteristic
595C2#3371×C13911yescharacteristic
596C2#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. #2509×C139C2semidirect
3. #2101×C139C2semidirect
4. #2066×C139C2semidirect
8. #1941×C139C2semidirect
10. #1935×C139C2semidirect
11. #1935×C139C2semidirect
12. #1927×C139C2semidirect
14. #1771×C139C2semidirect
298. #29035C139direct (N × H)
299. C139#29035direct (N × H)
300. #2509C2×C139semidirect
302. #2101C2×C139semidirect
303. #2066C2×C139semidirect
307. #1941C2×C139semidirect
309. #1935C2×C139semidirect
310. #1935C2×C139semidirect
311. #1927C2×C139semidirect
313. #1771C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2509×C1392
#2447×C1392
#2101×C1392
#2066×C1392
#2065×C1392
#2042×C1392
#1958×C1392
#1941×C1392
#1936×C1392
#1935×C1392
#1927×C1392
#1864×C1392
#1771×C1392
#1762×C1392
#29035139