Finite Group Databasebeta

← C139×#15622 #48010218

Subgroups — C139×#15622 #48010218

Order 35584.

1722 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#395×C139C212yesmaximal, complemented
2C2×#393×C139C211yesmaximal, characteristic
3C2×#385×C139C211yesmaximal, characteristic
4C2×#385×C139C212yesmaximal
5#1442×C139C212yesmaximal, complemented
6#1441×C139C212yesmaximal, complemented
7#1439×C139C212yesmaximal
8#1437×C139C211yesmaximal, characteristic
9C4⋊#95×C139C212yesmaximal, complemented
10C23×Q8×C139C2211yescharacteristic
11C24×C4×C139C2211yescharacteristic
12C22×C4⋊C4×C139C2212yes—
13C22×C4⋊C4×C139C2212yes—
14C22×C4⋊C4×C139C2212yes—
15C22×C4⋊C4×C139C2212yes—
16C22×C22⋊C4×C139C2211yescharacteristic
17C22×C22⋊C4×C139C2212yes—
18C22×C22⋊C4×C139C2212yes—
19C22×C22⋊C4×C139C2211yescharacteristic
20C22×C42×C139C2211yescharacteristic
21#395×C139—28no—
22#393×C139—24no—
23#385×C139—28no—
24#385×C139—24no—
25C2×#95×C139C2212yes—
26C2×#95×C139C2212yes—
27C2×#95×C139C2212yes—
28C2×#95×C139C2212yes—
29C2×#95×C139C2211yescharacteristic
30C2×#95×C139C2212yes—
31C2×#95×C139C2212yes—
32C2×#95×C139C2212yes—
33C2×#95×C139C2212yes—
34C2×#95×C139C2211yescharacteristic
35C25×C139C2311yescharacteristic
36C22×Q8×C139—24no—
37C22×Q8×C139—22no—
38C22×Q8×C139—41no—
39C22×Q8×C139—42no—
40C22×Q8×C139—41no—
41C23×C4×C139—22no—
42C23×C4×C139—24no—
43C23×C4×C139—41no—
44C23×C4×C139—42no—
45C23×C4×C139—41no—
46C23×C4×C139C2312yes—
47C23×C4×C139C2311yescharacteristic
48C23×C4×C139C2312yes—
49C23×C4×C139C2311yescharacteristic
50C23×C4×C139C2312yes—
51C23×C4×C139C2312yes—
52C23×C4×C139C2312yes—
53C23×C4×C139C2312yes—
54C2×C4⋊C4×C139—24no—
55C2×C4⋊C4×C139—24no—
56C2×C4⋊C4×C139—24no—
57C2×C4⋊C4×C139—24no—
58C2×C4⋊C4×C139—24no—
59C2×C4⋊C4×C139—24no—
60C2×C4⋊C4×C139—42no—
61C2×C4⋊C4×C139—42no—
62C2×C4⋊C4×C139—42no—
63C2×C4⋊C4×C139—42no—
64C2×C4⋊C4×C139—42no—
65C2×C4⋊C4×C139D418yes—
66C2×C22⋊C4×C139—22no—
67C2×C22⋊C4×C139—24no—
68C2×C22⋊C4×C139—24no—
69C2×C22⋊C4×C139—24no—
70C2×C22⋊C4×C139—24no—
71C2×C22⋊C4×C139—24no—
72C2×C22⋊C4×C139—41no—
73C2×C22⋊C4×C139—41no—
74C2×C22⋊C4×C139—42no—
75C2×C22⋊C4×C139D414yes—
76C2×C22⋊C4×C139Q818yescomplemented
77C2×C42×C139—24no—
78C2×C42×C139—41no—
79#95×C139—24no—
80#95×C139—24no—
81#95×C139—24no—
82#95×C139—24no—
83#95×C139—24no—
84#95×C139—24no—
85#95×C139—24no—
86#95×C139—22no—
87#95×C139—24no—
88#95×C139—41no—
89C24×C139—22no—
90C24×C139—22no—
91C24×C139—22no—
92C24×C139—21no—
93C24×C139—21no—
94C24×C139—22no—
95C24×C139—22no—
96C24×C139C2×D412yes—
97C24×C139C2×Q814yes—
98C24×C139C2411yescharacteristic
99C2×Q8×C139—48no—
100C2×Q8×C139—44no—
101C2×Q8×C139—44no—
102C2×Q8×C139—48no—
103C2×Q8×C139—44no—
104C22×C4×C139—22no—
105C22×C4×C139—22no—
106C22×C4×C139—22no—
107C22×C4×C139—22no—
108C22×C4×C139—22no—
109C22×C4×C139—22no—
110C22×C4×C139—22no—
111C22×C4×C139—22no—
112C22×C4×C139—22no—
113C22×C4×C139—22no—
114C22×C4×C139—22no—
115C22×C4×C139—22no—
116C22×C4×C139—22no—
117C22×C4×C139—22no—
118C22×C4×C139—22no—
119C22×C4×C139—22no—
120C22×C4×C139—22no—
121C22×C4×C139—22no—
122C22×C4×C139—21no—
123C22×C4×C139—22no—
124C22×C4×C139—21no—
125C22×C4×C139—21no—
126C22×C4×C139—21no—
127C22×C4×C139—22no—
128C22×C4×C139—22no—
129C22×C4×C139—22no—
130C22×C4×C139—22no—
131C22×C4×C139—22no—
132C22×C4×C139—22no—
133C22×C4×C139—22no—
134C22×C4×C139—22no—
135C22×C4×C139—22no—
136C22×C4×C139—22no—
137C22×C4×C139—22no—
138C22×C4×C139—22no—
139C22×C4×C139—22no—
140C22×C4×C139—22no—
141C22×C4×C139—22no—
142C22×C4×C139—22no—
143C22×C4×C139—22no—
144C22×C4×C139—22no—
145C22×C4×C139—22no—
146C22×C4×C139—22no—
147C22×C4×C139—44no—
148C22×C4×C139—48no—
149C22×C4×C139—48no—
150C22×C4×C139—44no—
151C22×C4×C139—44no—
152C22×C4×C139C2×D412yes—
153C22×C4×C139C2×D414yes—
154C22×C4×C139C2×D412yes—
155C22×C4×C139C2×D414yes—
156C22×C4×C139C2×D414yes—
157C22×C4×C139C2×Q814yes—
158C22×C4×C139C2×Q814yes—
159C22×C4×C139#4114yes—
160C22×C4×C139#4114yes—
161C4⋊C4×C139—48no—
162C4⋊C4×C139—48no—
163C4⋊C4×C139—48no—
164C4⋊C4×C139—48no—
165C22⋊C4×C139—28no—
166C22⋊C4×C139—216no—
167C22⋊C4×C139—44no—
168C22⋊C4×C139—48no—
169C42×C139—44no—
170C23×C139—24no—
171C23×C139—22no—
172C23×C139—22no—
173C23×C139—24no—
174C23×C139—24no—
175C23×C139—24no—
176C23×C139—24no—
177C23×C139—24no—
178C23×C139—24no—
179C23×C139—24no—
180C23×C139—42no—
181C23×C139—42no—
182C23×C139—42no—
183C23×C139—42no—
184C23×C139—41no—
185C23×C139—42no—
186C23×C139—41no—
187C23×C139—42no—
188C23×C139—41no—
189C23×C139—41no—
190C23×C139C4⋊Q814yes—
191C23×C139C22×D412yes—
192C23×C139C22×D411yescharacteristic
193C23×C139C22×Q812yes—
194C23×C139C2×#4112yes—
195C23×C139C2×#4112yes—
196C23×C139H(5,𝔽2)11yescharacteristic
197C23×C139H(5,𝔽2)11yescharacteristic
198C23×C139H(5,𝔽2)12yes—
199C23×C1392−1+412yes—
200Q8×C139—416no—
201C2×C4×C139—24no—
202C2×C4×C139—24no—
203C2×C4×C139—24no—
204C2×C4×C139—24no—
205C2×C4×C139—24no—
206C2×C4×C139—24no—
207C2×C4×C139—24no—
208C2×C4×C139—24no—
209C2×C4×C139—22no—
210C2×C4×C139—22no—
211C2×C4×C139—24no—
212C2×C4×C139—24no—
213C2×C4×C139—24no—
214C2×C4×C139—24no—
215C2×C4×C139—24no—
216C2×C4×C139—24no—
217C2×C4×C139—24no—
218C2×C4×C139—24no—
219C2×C4×C139—24no—
220C2×C4×C139—24no—
221C2×C4×C139—24no—
222C2×C4×C139—24no—
223C2×C4×C139—416no—
224C2×C4×C139—42no—
225C2×C4×C139—42no—
226C2×C4×C139—42no—
227C2×C4×C139—42no—
228C2×C4×C139—42no—
229C2×C4×C139—42no—
230C2×C4×C139—42no—
231C2×C4×C139—42no—
232C2×C4×C139—42no—
233C2×C4×C139—42no—
234C2×C4×C139—42no—
235C2×C4×C139—42no—
236C2×C4×C139—42no—
237C2×C4×C139—42no—
238C2×C4×C139—41no—
239C2×C4×C139—42no—
240C2×C4×C139—42no—
241C2×C4×C139—41no—
242C2×C4×C139—42no—
243C2×C4×C139—41no—
244C2×C4×C139—42no—
245C2×C4×C139—41no—
246C2×C4×C139—42no—
247C2×C4×C139—42no—
248C2×C4×C139—42no—
249C2×C4×C139—42no—
250C2×C4×C139—42no—
251C2×C4×C139—42no—
252C2×C4×C139—42no—
253C2×C4×C139C22⋊Q818yes—
254C22×C139—24no—
255C22×C139—28no—
256C22×C139—44no—
257C22×C139—42no—
258C22×C139—44no—
259C22×C139—44no—
260C22×C139—42no—
261C22×C139—44no—
262C22×C139—44no—
263C22×C139C2×C22⋊Q812yes—
264C22×C139#52511yescharacteristic
265C22×C139C2×C4⋊Q811yescharacteristic
266C22×C139#53212yes—
267C22×C139#53412yes—
268C22×C139#53411yescharacteristic
269C22×C139#54212yes—
270C22×C139#54212yes—
271C22×C139#54412yes—
272C22×C139D4212yes—
273C22×C139D4211yescharacteristic
274C22×C139#54712yes—
275C22×C139#54812yes—
276C22×C139D4×Q812yes—
277C22×C139#55111yescharacteristic
278C22×C139#55112yes—
279C22×C139#55412yes—
280C22×C139#55412yes—
281C22×C139#55412yes—
282C22×C139H(3,𝔽4)11yescharacteristic
283C22×C139#56311yescharacteristic
284C4×C139—28no—
285C4×C139—44no—
286C4×C139—42no—
287C4×C139—44no—
288C4×C139—44no—
289C4×C139—44no—
290C4×C139—42no—
291C4×C139—82no—
292C2×C139—44no—
293C2×C139#244012yes—
294C2×C139#245212yes—
295C2×C139#246112yes—
296C2×C139#256412yes—
297C2×C139#258311yescharacteristic
298C2×C139#267911yescharacteristic
299C2×C139#271711yescharacteristic
300C2×C139#272912yes—
301C2×C139#276312yes—
302#15622C13911yesmaximal, characteristic, direct product factor, Sylow
303C139#1562211yescharacteristic, direct product factor, Sylow
304C2×#395C2×C13912yescomplemented
305C2×#393C2×C13911yescharacteristic
306C2×#385C2×C13911yescharacteristic
307C2×#385C2×C13912yes—
308#1442C2×C13912yescomplemented
309#1441C2×C13912yescomplemented
310#1439C2×C13912yes—
311#1437C2×C13911yescharacteristic
312C4⋊#95C2×C13912yescomplemented
313C23×Q8C22×C13911yescharacteristic
314C24×C4C22×C13911yescharacteristic
315C22×C4⋊C4C22×C13912yes—
316C22×C4⋊C4C22×C13912yes—
317C22×C4⋊C4C22×C13912yes—
318C22×C4⋊C4C22×C13912yes—
319C22×C22⋊C4C22×C13911yescharacteristic
320C22×C22⋊C4C22×C13912yes—
321C22×C22⋊C4C22×C13912yes—
322C22×C22⋊C4C22×C13911yescharacteristic
323C22×C42C22×C13911yescharacteristic
324#395—28no—
325#393—24no—
326#385—28no—
327#385—24no—
328C2×#95C22×C13912yes—
329C2×#95C22×C13911yescharacteristic
330C2×#95C22×C13912yes—
331C2×#95C22×C13912yes—
332C2×#95C22×C13912yes—
333C2×#95C22×C13912yes—
334C2×#95C22×C13912yes—
335C2×#95C22×C13912yes—
336C2×#95C22×C13912yes—
337C2×#95C22×C13911yescharacteristic
338C25C23×C13911yescharacteristic
339C22×Q8—22no—
340C22×Q8—24no—
341C22×Q8—41no—
342C22×Q8—42no—
343C22×Q8—41no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—41no—
347C23×C4—42no—
348C23×C4—41no—
349C23×C4C23×C13912yes—
350C23×C4C23×C13912yes—
351C23×C4C23×C13911yescharacteristic
352C23×C4C23×C13911yescharacteristic
353C23×C4C23×C13912yes—
354C23×C4C23×C13912yes—
355C23×C4C23×C13912yes—
356C23×C4C23×C13912yes—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4D4×C13918yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4D4×C13914yes—
379C2×C22⋊C4Q8×C13918yescomplemented
380C2×C42—24no—
381C2×C42—41no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—22no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—41no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—21no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24C2×D4×C13912yes—
400C24C2×Q8×C13914yes—
401C24C24×C13911yescharacteristic
402C2×Q8—48no—
403C2×Q8—44no—
404C2×Q8—44no—
405C2×Q8—48no—
406C2×Q8—44no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—44no—
451C22×C4—48no—
452C22×C4—48no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4C2×D4×C13912yes—
456C22×C4C2×D4×C13914yes—
457C22×C4C2×D4×C13912yes—
458C22×C4C2×D4×C13914yes—
459C22×C4C2×D4×C13914yes—
460C22×C4C2×Q8×C13914yes—
461C22×C4C2×Q8×C13914yes—
462C22×C4#41×C13914yes—
463C22×C4#41×C13914yes—
464C4⋊C4—48no—
465C4⋊C4—48no—
466C4⋊C4—48no—
467C4⋊C4—48no—
468C22⋊C4—28no—
469C22⋊C4—216no—
470C22⋊C4—44no—
471C22⋊C4—48no—
472C42—44no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—41no—
488C23—42no—
489C23—41no—
490C23—42no—
491C23—41no—
492C23—41no—
493C23C4⋊Q8×C13914yes—
494C23C22×D4×C13912yes—
495C23C22×D4×C13911yescharacteristic
496C23C22×Q8×C13912yes—
497C23C2×#41×C13912yes—
498C23C2×#41×C13912yes—
499C23H(5,𝔽2)×C13911yescharacteristic
500C23H(5,𝔽2)×C13911yescharacteristic
501C23H(5,𝔽2)×C13912yes—
502C232−1+4×C13912yes—
503Q8—416no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—416no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4C22⋊Q8×C13918yes—
557C22—24no—
558C22—28no—
559C22—44no—
560C22—42no—
561C22—44no—
562C22—44no—
563C22—42no—
564C22—44no—
565C22—44no—
566C22C2×C22⋊Q8×C13912yes—
567C22#525×C13911yescharacteristic
568C22C2×C4⋊Q8×C13911yescharacteristic
569C22#532×C13912yes—
570C22#534×C13912yes—
571C22#534×C13911yescharacteristic
572C22#542×C13912yes—
573C22#542×C13912yes—
574C22#544×C13912yes—
575C22D42×C13912yes—
576C22D42×C13911yescharacteristic
577C22#547×C13912yes—
578C22#548×C13912yes—
579C22D4×Q8×C13912yes—
580C22#551×C13911yescharacteristic
581C22#551×C13912yes—
582C22#554×C13912yes—
583C22#554×C13912yes—
584C22#554×C13912yes—
585C22H(3,𝔽4)×C13911yescharacteristic
586C22#563×C13911yescharacteristic
587C4—28no—
588C4—44no—
589C4—42no—
590C4—44no—
591C4—44no—
592C4—44no—
593C4—42no—
594C4—82no—
595C2—44no—
596C2#2440×C13912yes—
597C2#2452×C13912yes—
598C2#2461×C13912yes—
599C2#2564×C13912yes—
600C2#2583×C13911yescharacteristic
601C2#2679×C13911yescharacteristic
602C2#2717×C13911yescharacteristic
603C2#2729×C13912yes—
604C2#2763×C13912yes—
subgroupG/H
center, socleC24×C139C24
commutator, Frattini, cosocleC24C24×C139
prime radicalC25×C139C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#395×C139C2semidirect
5. #1442×C139C2semidirect
6. #1441×C139C2semidirect
9. C4⋊#95×C139C2semidirect
76. C2×C22⋊C4×C139Q8semidirect
302. #15622C139direct (N × H)
303. C139#15622direct (N × H)
304. C2×#395C2×C139semidirect
308. #1442C2×C139semidirect
309. #1441C2×C139semidirect
312. C4⋊#95C2×C139semidirect
379. C2×C22⋊C4Q8×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#395×C1392
C2×#393×C1392
C2×#385×C1392
#1442×C1392
#1441×C1392
#1439×C1392
#1437×C1392
C4⋊#95×C1392
#15622139