Finite Group Databasebeta

← C139×#35918 #48030514

Subgroups — C139×#35918 #48030514

Order 35584.

2224 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2648×C139C213yesmaximal, complemented
2#2587×C139C213yesmaximal, complemented
3#2559×C139C213yesmaximal, complemented
4#2476×C139C213yesmaximal, complemented
5#2428×C139C213yesmaximal, complemented
6#2424×C139C213yesmaximal, complemented
7#2424×C139C213yesmaximal, complemented
8#2392×C139C213yesmaximal, complemented
9#2364×C139C213yesmaximal, complemented
10#2363×C139C213yesmaximal, complemented
11#2273×C139C211yesmaximal, characteristic, complemented
12C2×#127×C139C2211yescharacteristic, complemented
13C2×#126×C139C2211yescharacteristic, complemented
14C2×#121×C139C2213yes—
15C2×#121×C139C2213yes—
16C2×#121×C139C2213yes—
17C2×#121×C139C2213yes—
18C2×#120×C139C2213yes—
19C2×#120×C139C2211yescharacteristic
20C2×C4×D4×C139C2213yes—
21C2×C4×D4×C139C2213yes—
22C2×C4×D4×C139C2213yescomplemented
23C2×#117×C139C2213yescomplemented
24C22×C22⋊C4×C139C2213yes—
25#400×C139C2213yescomplemented
26#398×C139C2213yescomplemented
27#397×C139C2213yescomplemented
28#396×C139C2213yes—
29#396×C139C2213yes—
30#396×C139C2211yescharacteristic, complemented
31#394×C139C2213yes—
32#394×C139C2213yes—
33#394×C139C2213yes—
34#394×C139C2213yes—
35#394×C139C2213yescomplemented
36#394×C139C2213yescomplemented
37#392×C139C2213yes—
38#392×C139C2213yes—
39#390×C139C2213yes—
40#390×C139C2213yes—
41#390×C139C2213yescomplemented
42#389×C139C2213yescomplemented
43#389×C139C2213yescomplemented
44#388×C139C2213yes—
45#388×C139C2213yes—
46#388×C139C2213yescomplemented
47#388×C139C2213yescomplemented
48#388×C139C2213yescomplemented
49#387×C139C2213yescomplemented
50#387×C139C2213yescomplemented
51#386×C139C2213yes—
52#386×C139C2213yes—
53#386×C139C2213yes—
54#386×C139C2213yes—
55#386×C139C2213yescomplemented
56#386×C139C2213yescomplemented
57#385×C139C2213yes—
58#385×C139C2213yes—
59C4×C4⋊C4×C139C2213yescomplemented
60C4×C22⋊C4×C139C2213yes—
61C4×C22⋊C4×C139C2213yes—
62C4×C22⋊C4×C139C2213yes—
63C4×C22⋊C4×C139C2213yes—
64C4×C22⋊C4×C139C2213yescomplemented
65C4×C22⋊C4×C139C2213yescomplemented
66C2×#95×C139C2211yescharacteristic, complemented
67C25×C139C2311yescharacteristic
68C22×D4×C139C2313yes—
69C22×D4×C139C2313yes—
70C22×D4×C139C2313yes—
71C22×D4×C139C2313yes—
72C22×D4×C139C2313yes—
73C22×D4×C139C2313yes—
74C23×C4×C139C2313yes—
75C23×C4×C139C2313yes—
76C23×C4×C139C2313yes—
77C23×C4×C139C2313yes—
78#127×C139—42no—
79#126×C139—42no—
80#121×C139—212no—
81#121×C139—212no—
82#121×C139—46no—
83#121×C139—46no—
84#120×C139—46no—
85#120×C139—42no—
86C4×D4×C139—46no—
87C4×D4×C139—46no—
88C4×D4×C139—46no—
89#117×C139—46no—
90C2×C4⋊C4×C139C2313yes—
91C2×C4⋊C4×C139C2313yes—
92C2×C4⋊C4×C139C2313yes—
93C2×C4⋊C4×C139C2313yes—
94C2×C4⋊C4×C139C2313yes—
95C2×C4⋊C4×C139C2313yes—
96C2×C4⋊C4×C139C2313yes—
97C2×C4⋊C4×C139C2313yes—
98C2×C22⋊C4×C139—212no—
99C2×C22⋊C4×C139C2313yes—
100C2×C22⋊C4×C139C2313yes—
101C2×C22⋊C4×C139C2313yes—
102C2×C22⋊C4×C139C2313yes—
103C2×C22⋊C4×C139C2313yes—
104C2×C22⋊C4×C139C2313yes—
105C2×C22⋊C4×C139C2313yes—
106C2×C22⋊C4×C139C2313yes—
107C2×C22⋊C4×C139C2313yes—
108C2×C22⋊C4×C139C2313yes—
109C2×C22⋊C4×C139C2313yes—
110C2×C22⋊C4×C139C2313yes—
111C2×C22⋊C4×C139C2313yes—
112C2×C22⋊C4×C139C2313yes—
113C2×C22⋊C4×C139C2313yes—
114C2×C22⋊C4×C139C2313yes—
115C2×C22⋊C4×C139C2313yes—
116C2×C22⋊C4×C139C2313yes—
117C2×C42×C139C2313yes—
118C2×C42×C139C2313yes—
119C2×C42×C139C2313yes—
120C2×C42×C139C2313yes—
121C2×C42×C139C2311yescharacteristic
122C2×C42×C139C2311yescharacteristic
123#95×C139C2313yes—
124#95×C139C2313yes—
125#95×C139C2311yescharacteristic
126#95×C139C2313yes—
127#95×C139C2313yes—
128#95×C139C2313yes—
129#95×C139C2313yes—
130#95×C139C2313yes—
131#95×C139C2311yescharacteristic
132#95×C139C2313yes—
133#95×C139C2313yes—
134#95×C139C2313yes—
135C24×C139—26no—
136C24×C139—43no—
137C24×C139—41no—
138C24×C139C2413yes—
139C24×C139C2413yes—
140C24×C139C2411yescharacteristic
141C2×D4×C139—26no—
142C2×D4×C139—26no—
143C2×D4×C139—26no—
144C2×D4×C139—26no—
145C2×D4×C139—26no—
146C2×D4×C139—26no—
147C2×D4×C139—26no—
148C2×D4×C139—26no—
149C2×D4×C139—26no—
150C2×D4×C139—43no—
151C2×D4×C139—43no—
152C2×D4×C139—43no—
153C2×D4×C139—43no—
154C2×D4×C139—43no—
155C2×D4×C139—43no—
156C2×D4×C139—43no—
157C2×D4×C139—43no—
158C2×D4×C139—43no—
159C22×C4×C139—26no—
160C22×C4×C139—26no—
161C22×C4×C139—26no—
162C22×C4×C139—26no—
163C22×C4×C139—26no—
164C22×C4×C139—43no—
165C22×C4×C139—43no—
166C22×C4×C139—43no—
167C22×C4×C139—43no—
168C22×C4×C139—43no—
169C22×C4×C139—43no—
170C22×C4×C139—43no—
171C22×C4×C139C2413yes—
172C22×C4×C139C2413yes—
173C22×C4×C139C2413yes—
174C22×C4×C139C2413yes—
175C22×C4×C139C2413yes—
176C22×C4×C139C2413yes—
177C22×C4×C139C2413yes—
178C22×C4×C139C2413yes—
179C4⋊C4×C139—26no—
180C4⋊C4×C139—26no—
181C4⋊C4×C139—26no—
182C4⋊C4×C139—26no—
183C4⋊C4×C139—43no—
184C4⋊C4×C139—43no—
185C4⋊C4×C139—43no—
186C4⋊C4×C139—43no—
187C22⋊C4×C139—26no—
188C22⋊C4×C139—26no—
189C22⋊C4×C139—26no—
190C22⋊C4×C139—26no—
191C22⋊C4×C139—26no—
192C22⋊C4×C139—26no—
193C22⋊C4×C139—26no—
194C22⋊C4×C139—26no—
195C22⋊C4×C139—26no—
196C22⋊C4×C139—26no—
197C22⋊C4×C139—43no—
198C22⋊C4×C139—43no—
199C22⋊C4×C139—43no—
200C22⋊C4×C139—43no—
201C22⋊C4×C139—43no—
202C22⋊C4×C139—43no—
203C22⋊C4×C139—43no—
204C22⋊C4×C139#41112yes—
205C42×C139—26no—
206C42×C139—43no—
207C42×C139—43no—
208C42×C139—43no—
209C42×C139—41no—
210C42×C139—41no—
211C23×C139—28no—
212C23×C139—23no—
213C23×C139—23no—
214C23×C139—23no—
215C23×C139—23no—
216C23×C139—23no—
217C23×C139—23no—
218C23×C139—23no—
219C23×C139—23no—
220C23×C139—23no—
221C23×C139—23no—
222C23×C139—23no—
223C23×C139—23no—
224C23×C139—23no—
225C23×C139—23no—
226C23×C139—23no—
227C23×C139—86no—
228C23×C139—86no—
229C23×C139C2×#4116yes—
230C23×C139H(5,𝔽2)12yes—
231C23×C139C2511yescharacteristic
232D4×C139—412no—
233D4×C139—412no—
234D4×C139—412no—
235D4×C139—86no—
236D4×C139—86no—
237D4×C139—86no—
238C2×C4×C139—23no—
239C2×C4×C139—23no—
240C2×C4×C139—23no—
241C2×C4×C139—23no—
242C2×C4×C139—23no—
243C2×C4×C139—23no—
244C2×C4×C139—23no—
245C2×C4×C139—23no—
246C2×C4×C139—23no—
247C2×C4×C139—23no—
248C2×C4×C139—23no—
249C2×C4×C139—23no—
250C2×C4×C139—23no—
251C2×C4×C139—23no—
252C2×C4×C139—23no—
253C2×C4×C139—23no—
254C2×C4×C139—23no—
255C2×C4×C139—23no—
256C2×C4×C139—23no—
257C2×C4×C139—23no—
258C2×C4×C139—23no—
259C2×C4×C139—412no—
260C2×C4×C139—86no—
261C2×C4×C139—86no—
262C2×C4×C139—86no—
263C2×C4×C139C2×#4116yes—
264C2×C4×C139C2×#4116yes—
265C2×C4×C139H(5,𝔽2)16yes—
266C22×C139—26no—
267C22×C139—26no—
268C22×C139—26no—
269C22×C139—26no—
270C22×C139—41no—
271C22×C139—43no—
272C22×C139—43no—
273C22×C139—43no—
274C22×C139—43no—
275C22×C139—43no—
276C22×C139—43no—
277C22×C139—43no—
278C22×C139—43no—
279C22×C139—43no—
280C22×C139—43no—
281C22×C139—43no—
282C22×C139—43no—
283C22×C139—88no—
284C22×C139C22×#4113yes—
285C22×C139C2×H(5,𝔽2)11yescharacteristic
286C22×C139C2×H(5,𝔽2)13yes—
287C4×C139—26no—
288C4×C139—26no—
289C4×C139—26no—
290C4×C139—43no—
291C4×C139—43no—
292C4×C139—43no—
293C4×C139—43no—
294C4×C139—43no—
295C2×C139—42no—
296C2×C139—46no—
297C2×C139—83no—
298C2×C139#344411yescharacteristic
299C2×C139#351913yes—
300C2×C139#351913yes—
301#35918C13911yesmaximal, characteristic, direct product factor, Sylow
302C139#3591811yescharacteristic, direct product factor, Sylow
303#2648C2×C13913yescomplemented
304#2587C2×C13913yescomplemented
305#2559C2×C13913yescomplemented
306#2476C2×C13913yescomplemented
307#2428C2×C13913yescomplemented
308#2424C2×C13913yescomplemented
309#2424C2×C13913yescomplemented
310#2392C2×C13913yescomplemented
311#2364C2×C13913yescomplemented
312#2363C2×C13913yescomplemented
313#2273C2×C13911yescharacteristic, complemented
314C2×#127C22×C13911yescharacteristic, complemented
315C2×#126C22×C13911yescharacteristic, complemented
316C2×#121C22×C13913yes—
317C2×#121C22×C13913yes—
318C2×#121C22×C13913yes—
319C2×#121C22×C13913yes—
320C2×#120C22×C13913yes—
321C2×#120C22×C13911yescharacteristic
322C2×C4×D4C22×C13913yes—
323C2×C4×D4C22×C13913yes—
324C2×C4×D4C22×C13913yescomplemented
325C2×#117C22×C13913yescomplemented
326C22×C22⋊C4C22×C13913yes—
327#400C22×C13913yescomplemented
328#398C22×C13913yescomplemented
329#397C22×C13913yescomplemented
330#396C22×C13913yes—
331#396C22×C13913yes—
332#396C22×C13911yescharacteristic, complemented
333#394C22×C13913yes—
334#394C22×C13913yes—
335#394C22×C13913yes—
336#394C22×C13913yes—
337#394C22×C13913yescomplemented
338#394C22×C13913yescomplemented
339#392C22×C13913yes—
340#392C22×C13913yes—
341#390C22×C13913yes—
342#390C22×C13913yes—
343#390C22×C13913yescomplemented
344#389C22×C13913yescomplemented
345#389C22×C13913yescomplemented
346#388C22×C13913yes—
347#388C22×C13913yes—
348#388C22×C13913yescomplemented
349#388C22×C13913yescomplemented
350#388C22×C13913yescomplemented
351#387C22×C13913yescomplemented
352#387C22×C13913yescomplemented
353#386C22×C13913yes—
354#386C22×C13913yes—
355#386C22×C13913yes—
356#386C22×C13913yes—
357#386C22×C13913yescomplemented
358#386C22×C13913yescomplemented
359#385C22×C13913yes—
360#385C22×C13913yes—
361C4×C4⋊C4C22×C13913yescomplemented
362C4×C22⋊C4C22×C13913yes—
363C4×C22⋊C4C22×C13913yes—
364C4×C22⋊C4C22×C13913yes—
365C4×C22⋊C4C22×C13913yes—
366C4×C22⋊C4C22×C13913yescomplemented
367C4×C22⋊C4C22×C13913yescomplemented
368C2×#95C22×C13911yescharacteristic, complemented
369C25C23×C13911yescharacteristic
370C22×D4C23×C13913yes—
371C22×D4C23×C13913yes—
372C22×D4C23×C13913yes—
373C22×D4C23×C13913yes—
374C22×D4C23×C13913yes—
375C22×D4C23×C13913yes—
376C23×C4C23×C13913yes—
377C23×C4C23×C13913yes—
378C23×C4C23×C13913yes—
379C23×C4C23×C13913yes—
380#127—42no—
381#126—42no—
382#121—212no—
383#121—212no—
384#121—46no—
385#121—46no—
386#120—46no—
387#120—42no—
388C4×D4—46no—
389C4×D4—46no—
390C4×D4—46no—
391#117—46no—
392C2×C4⋊C4C23×C13913yes—
393C2×C4⋊C4C23×C13913yes—
394C2×C4⋊C4C23×C13913yes—
395C2×C4⋊C4C23×C13913yes—
396C2×C4⋊C4C23×C13913yes—
397C2×C4⋊C4C23×C13913yes—
398C2×C4⋊C4C23×C13913yes—
399C2×C4⋊C4C23×C13913yes—
400C2×C22⋊C4—212no—
401C2×C22⋊C4C23×C13913yes—
402C2×C22⋊C4C23×C13913yes—
403C2×C22⋊C4C23×C13913yes—
404C2×C22⋊C4C23×C13913yes—
405C2×C22⋊C4C23×C13913yes—
406C2×C22⋊C4C23×C13913yes—
407C2×C22⋊C4C23×C13913yes—
408C2×C22⋊C4C23×C13913yes—
409C2×C22⋊C4C23×C13913yes—
410C2×C22⋊C4C23×C13913yes—
411C2×C22⋊C4C23×C13913yes—
412C2×C22⋊C4C23×C13913yes—
413C2×C22⋊C4C23×C13913yes—
414C2×C22⋊C4C23×C13913yes—
415C2×C22⋊C4C23×C13913yes—
416C2×C22⋊C4C23×C13913yes—
417C2×C22⋊C4C23×C13913yes—
418C2×C22⋊C4C23×C13913yes—
419C2×C42C23×C13913yes—
420C2×C42C23×C13913yes—
421C2×C42C23×C13913yes—
422C2×C42C23×C13913yes—
423C2×C42C23×C13911yescharacteristic
424C2×C42C23×C13911yescharacteristic
425#95C23×C13911yescharacteristic
426#95C23×C13913yes—
427#95C23×C13913yes—
428#95C23×C13913yes—
429#95C23×C13911yescharacteristic
430#95C23×C13913yes—
431#95C23×C13913yes—
432#95C23×C13913yes—
433#95C23×C13913yes—
434#95C23×C13913yes—
435#95C23×C13913yes—
436#95C23×C13913yes—
437C24—26no—
438C24—43no—
439C24—41no—
440C24C24×C13913yes—
441C24C24×C13913yes—
442C24C24×C13911yescharacteristic
443C2×D4—26no—
444C2×D4—26no—
445C2×D4—26no—
446C2×D4—26no—
447C2×D4—26no—
448C2×D4—26no—
449C2×D4—26no—
450C2×D4—26no—
451C2×D4—26no—
452C2×D4—43no—
453C2×D4—43no—
454C2×D4—43no—
455C2×D4—43no—
456C2×D4—43no—
457C2×D4—43no—
458C2×D4—43no—
459C2×D4—43no—
460C2×D4—43no—
461C22×C4—26no—
462C22×C4—26no—
463C22×C4—26no—
464C22×C4—26no—
465C22×C4—26no—
466C22×C4—43no—
467C22×C4—43no—
468C22×C4—43no—
469C22×C4—43no—
470C22×C4—43no—
471C22×C4—43no—
472C22×C4—43no—
473C22×C4C24×C13913yes—
474C22×C4C24×C13913yes—
475C22×C4C24×C13913yes—
476C22×C4C24×C13913yes—
477C22×C4C24×C13913yes—
478C22×C4C24×C13913yes—
479C22×C4C24×C13913yes—
480C22×C4C24×C13913yes—
481C4⋊C4—26no—
482C4⋊C4—26no—
483C4⋊C4—26no—
484C4⋊C4—26no—
485C4⋊C4—43no—
486C4⋊C4—43no—
487C4⋊C4—43no—
488C4⋊C4—43no—
489C22⋊C4—26no—
490C22⋊C4—26no—
491C22⋊C4—26no—
492C22⋊C4—26no—
493C22⋊C4—26no—
494C22⋊C4—26no—
495C22⋊C4—26no—
496C22⋊C4—26no—
497C22⋊C4—26no—
498C22⋊C4—26no—
499C22⋊C4—43no—
500C22⋊C4—43no—
501C22⋊C4—43no—
502C22⋊C4—43no—
503C22⋊C4—43no—
504C22⋊C4—43no—
505C22⋊C4—43no—
506C22⋊C4#41×C139112yes—
507C42—26no—
508C42—43no—
509C42—43no—
510C42—43no—
511C42—41no—
512C42—41no—
513C23—28no—
514C23—23no—
515C23—23no—
516C23—23no—
517C23—23no—
518C23—23no—
519C23—23no—
520C23—23no—
521C23—23no—
522C23—23no—
523C23—23no—
524C23—23no—
525C23—23no—
526C23—23no—
527C23—23no—
528C23—23no—
529C23—86no—
530C23—86no—
531C23C2×#41×C13916yes—
532C23H(5,𝔽2)×C13912yes—
533C23C25×C13911yescharacteristic
534D4—412no—
535D4—412no—
536D4—412no—
537D4—86no—
538D4—86no—
539D4—86no—
540C2×C4—23no—
541C2×C4—23no—
542C2×C4—23no—
543C2×C4—23no—
544C2×C4—23no—
545C2×C4—23no—
546C2×C4—23no—
547C2×C4—23no—
548C2×C4—23no—
549C2×C4—23no—
550C2×C4—23no—
551C2×C4—23no—
552C2×C4—23no—
553C2×C4—23no—
554C2×C4—23no—
555C2×C4—23no—
556C2×C4—23no—
557C2×C4—23no—
558C2×C4—23no—
559C2×C4—23no—
560C2×C4—23no—
561C2×C4—412no—
562C2×C4—86no—
563C2×C4—86no—
564C2×C4—86no—
565C2×C4C2×#41×C13916yes—
566C2×C4C2×#41×C13916yes—
567C2×C4H(5,𝔽2)×C13916yes—
568C22—26no—
569C22—26no—
570C22—26no—
571C22—26no—
572C22—41no—
573C22—43no—
574C22—43no—
575C22—43no—
576C22—43no—
577C22—43no—
578C22—43no—
579C22—43no—
580C22—43no—
581C22—43no—
582C22—43no—
583C22—43no—
584C22—43no—
585C22—88no—
586C22C22×#41×C13913yes—
587C22C2×H(5,𝔽2)×C13911yescharacteristic
588C22C2×H(5,𝔽2)×C13913yes—
589C4—26no—
590C4—26no—
591C4—26no—
592C4—43no—
593C4—43no—
594C4—43no—
595C4—43no—
596C4—43no—
597C2—46no—
598C2—42no—
599C2—83no—
600C2#3444×C13911yescharacteristic
601C2#3519×C13913yes—
602C2#3519×C13913yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #2648×C139C2semidirect
2. #2587×C139C2semidirect
3. #2559×C139C2semidirect
4. #2476×C139C2semidirect
5. #2428×C139C2semidirect
6. #2424×C139C2semidirect
7. #2424×C139C2semidirect
8. #2392×C139C2semidirect
9. #2364×C139C2semidirect
10. #2363×C139C2semidirect
11. #2273×C139C2semidirect
12. C2×#127×C139C22semidirect
13. C2×#126×C139C22semidirect
22. C2×C4×D4×C139C22semidirect
23. C2×#117×C139C22semidirect
25. #400×C139C22semidirect
26. #398×C139C22semidirect
27. #397×C139C22semidirect
30. #396×C139C22semidirect
35. #394×C139C22semidirect
36. #394×C139C22semidirect
41. #390×C139C22semidirect
42. #389×C139C22semidirect
43. #389×C139C22semidirect
46. #388×C139C22semidirect
47. #388×C139C22semidirect
48. #388×C139C22semidirect
49. #387×C139C22semidirect
50. #387×C139C22semidirect
55. #386×C139C22semidirect
56. #386×C139C22semidirect
59. C4×C4⋊C4×C139C22semidirect
64. C4×C22⋊C4×C139C22semidirect
65. C4×C22⋊C4×C139C22semidirect
66. C2×#95×C139C22semidirect
301. #35918C139direct (N × H)
302. C139#35918direct (N × H)
303. #2648C2×C139semidirect
304. #2587C2×C139semidirect
305. #2559C2×C139semidirect
306. #2476C2×C139semidirect
307. #2428C2×C139semidirect
308. #2424C2×C139semidirect
309. #2424C2×C139semidirect
310. #2392C2×C139semidirect
311. #2364C2×C139semidirect
312. #2363C2×C139semidirect
313. #2273C2×C139semidirect
314. C2×#127C22×C139semidirect
315. C2×#126C22×C139semidirect
324. C2×C4×D4C22×C139semidirect
325. C2×#117C22×C139semidirect
327. #400C22×C139semidirect
328. #398C22×C139semidirect
329. #397C22×C139semidirect
332. #396C22×C139semidirect
337. #394C22×C139semidirect
338. #394C22×C139semidirect
343. #390C22×C139semidirect
344. #389C22×C139semidirect
345. #389C22×C139semidirect
348. #388C22×C139semidirect
349. #388C22×C139semidirect
350. #388C22×C139semidirect
351. #387C22×C139semidirect
352. #387C22×C139semidirect
357. #386C22×C139semidirect
358. #386C22×C139semidirect
361. C4×C4⋊C4C22×C139semidirect
366. C4×C22⋊C4C22×C139semidirect
367. C4×C22⋊C4C22×C139semidirect
368. C2×#95C22×C139semidirect

Maximal subgroups

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

subgroupindex
#2648×C1392
#2587×C1392
#2559×C1392
#2476×C1392
#2428×C1392
#2424×C1392
#2392×C1392
#2364×C1392
#2363×C1392
#2273×C1392
#35918139