Finite Group Databasebeta

← C2×#1390×C139 #48007168

Subgroups — C2×#1390×C139 #48007168

Order 35584.

1202 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C139C211yesmaximal, characteristic
2C22×#99×C139C211yesmaximal, characteristic
3C2×#386×C139C211yesmaximal, characteristic
4#1390×C139C214yesmaximal, direct product factor
5C23×D4×C139C2211yescharacteristic
6C24×C4×C139C411yescharacteristic, complemented
7C22×M16×C139—21no—
8C22×C22⋊C4×C139—21no—
9C22×C22⋊C4×C139—21no—
10C22×C22⋊C4×C139C411yescharacteristic, complemented
11C2×#100×C139—21no—
12C2×#100×C139—22no—
13C2×#100×C139C414yescomplemented
14C2×#100×C139C2212yes—
15C2×#99×C139—21no—
16C2×#99×C139—22no—
17C2×#99×C139C414yescomplemented
18C2×#99×C139C2212yes—
19#386×C139—21no—
20#386×C139—21no—
21#386×C139C412yescomplemented
22#386×C139C2212yes—
23C2×#95×C139—21no—
24C25×C139C2×C411yescharacteristic
25C25×C139D411yescharacteristic
26C22×D4×C139—42no—
27C22×D4×C139—41no—
28C22×D4×C139—41no—
29C22×D4×C139C2×C411yescharacteristic
30C22×D4×C139C2×C412yes—
31C22×D4×C139C2×C412yes—
32C22×D4×C139D411yescharacteristic
33C22×D4×C139D412yes—
34C22×D4×C139D411yescharacteristic
35C22×D4×C139Q812yes—
36C22×D4×C139C2311yescharacteristic
37C23×C4×C139—21no—
38C23×C4×C139—21no—
39C23×C4×C139—21no—
40C23×C4×C139—44no—
41C23×C4×C139—41no—
42C23×C4×C139—41no—
43C23×C4×C139—41no—
44C23×C4×C139C2×C412yescomplemented
45C23×C4×C139D411yescharacteristic
46C2×M16×C139—24no—
47C2×M16×C139—22no—
48C2×M16×C139—42no—
49C2×M16×C139—41no—
50C22×C8×C139—41no—
51C2×C22⋊C4×C139—24no—
52C2×C22⋊C4×C139—22no—
53C2×C22⋊C4×C139—22no—
54C2×C22⋊C4×C139—21no—
55C2×C22⋊C4×C139—22no—
56C2×C22⋊C4×C139—44no—
57C2×C22⋊C4×C139—41no—
58C2×C22⋊C4×C139—42no—
59C2×C22⋊C4×C139—42no—
60C2×C22⋊C4×C139C2×C412yescomplemented
61#100×C139—24no—
62#100×C139—22no—
63#100×C139C2×C414yescomplemented
64#99×C139—24no—
65#99×C139—22no—
66#99×C139C2×C414yescomplemented
67#95×C139—22no—
68#95×C139—22no—
69C24×C139—22no—
70C24×C139—21no—
71C24×C139—21no—
72C24×C139—21no—
73C24×C139—22no—
74C24×C139—21no—
75C24×C139—42no—
76C24×C139—42no—
77C24×C139—42no—
78C24×C139—42no—
79C24×C139C4212yes—
80C24×C139C22⋊C412yes—
81C24×C139C22⋊C411yescharacteristic
82C24×C139C22⋊C411yescharacteristic
83C24×C139C22⋊C411yescharacteristic
84C24×C139C4⋊C412yes—
85C24×C139C4⋊C412yes—
86C24×C139C22×C411yescharacteristic
87C24×C139C2×D411yescharacteristic
88C2×D4×C139—42no—
89C2×D4×C139—42no—
90C2×D4×C139—42no—
91C2×D4×C139—42no—
92C2×D4×C139—41no—
93C2×D4×C139—41no—
94C2×D4×C139—42no—
95C2×D4×C139—42no—
96C2×D4×C139—41no—
97C2×D4×C139—41no—
98C2×D4×C139—41no—
99C2×D4×C139—41no—
100C2×D4×C139—42no—
101C2×D4×C139—42no—
102C2×D4×C139—41no—
103C2×D4×C139—41no—
104C2×D4×C139C4212yes—
105C2×D4×C139C22⋊C412yes—
106C2×D4×C139C22⋊C412yes—
107C2×D4×C139C4⋊C412yes—
108C2×D4×C139C4⋊C412yes—
109C2×D4×C139C4⋊C412yes—
110C2×D4×C139C22×C411yescharacteristic
111C2×D4×C139C22×C411yescharacteristic
112C2×D4×C139C2×D411yescharacteristic
113C2×D4×C139C2×Q811yescharacteristic
114C22×C4×C139—22no—
115C22×C4×C139—21no—
116C22×C4×C139—21no—
117C22×C4×C139—24no—
118C22×C4×C139—22no—
119C22×C4×C139—22no—
120C22×C4×C139—44no—
121C22×C4×C139—44no—
122C22×C4×C139—42no—
123C22×C4×C139—42no—
124C22×C4×C139—48no—
125C22×C4×C139—44no—
126C22×C4×C139—41no—
127C22×C4×C139—41no—
128C22×C4×C139—42no—
129C22×C4×C139—44no—
130C22×C4×C139—44no—
131C22×C4×C139—42no—
132C22×C4×C139—42no—
133C22×C4×C139—42no—
134C22×C4×C139—42no—
135C22×C4×C139—82no—
136C22×C4×C139—82no—
137C22×C4×C139C22⋊C411yescharacteristic
138C22×C4×C139C22⋊C412yes—
139C22×C4×C139C4⋊C412yes—
140C22×C4×C139C2×D411yescharacteristic
141M16×C139—24no—
142M16×C139—44no—
143M16×C139—42no—
144C2×C8×C139—44no—
145C2×C8×C139—42no—
146C22⋊C4×C139—24no—
147C22⋊C4×C139—44no—
148C22⋊C4×C139—44no—
149C22⋊C4×C139—44no—
150C22⋊C4×C139—42no—
151C22⋊C4×C139—42no—
152C22⋊C4×C139—42no—
153C23×C139—22no—
154C23×C139—22no—
155C23×C139—22no—
156C23×C139—22no—
157C23×C139—22no—
158C23×C139—22no—
159C23×C139—22no—
160C23×C139—22no—
161C23×C139—21no—
162C23×C139—21no—
163C23×C139—21no—
164C23×C139—21no—
165C23×C139—21no—
166C23×C139—21no—
167C23×C139—22no—
168C23×C139—22no—
169C23×C139—21no—
170C23×C139—21no—
171C23×C139—41no—
172C23×C139—41no—
173C23×C139—44no—
174C23×C139—41no—
175C23×C139—44no—
176C23×C139—41no—
177C23×C139—42no—
178C23×C139—42no—
179C23×C139—48no—
180C23×C139—41no—
181C23×C139—41no—
182C23×C139—41no—
183C23×C139—44no—
184C23×C139—44no—
185C23×C139—41no—
186C23×C139—42no—
187C23×C139—42no—
188C23×C139—42no—
189C23×C139—42no—
190C23×C139—81no—
191C23×C139—81no—
192C23×C139—84no—
193C23×C139#9512yes—
194C23×C139#9512yes—
195C23×C139#9512yes—
196C23×C139#9911yescharacteristic
197C23×C139#9912yes—
198C23×C139#9911yescharacteristic
199C23×C139C2×C4211yescharacteristic
200C23×C139C2×C22⋊C411yescharacteristic
201C23×C139C2×C22⋊C411yescharacteristic
202C23×C139C2×C4⋊C411yescharacteristic
203C23×C139C2×C4⋊C411yescharacteristic
204D4×C139—42no—
205D4×C139—42no—
206D4×C139—42no—
207D4×C139—42no—
208D4×C139—42no—
209D4×C139—42no—
210D4×C139—41no—
211D4×C139—41no—
212D4×C139—41no—
213D4×C139—41no—
214C2×C4×C139—22no—
215C2×C4×C139—22no—
216C2×C4×C139—22no—
217C2×C4×C139—22no—
218C2×C4×C139—21no—
219C2×C4×C139—21no—
220C2×C4×C139—21no—
221C2×C4×C139—21no—
222C2×C4×C139—24no—
223C2×C4×C139—42no—
224C2×C4×C139—44no—
225C2×C4×C139—48no—
226C2×C4×C139—44no—
227C2×C4×C139—44no—
228C2×C4×C139—42no—
229C2×C4×C139—44no—
230C2×C4×C139—44no—
231C2×C4×C139—42no—
232C2×C4×C139—42no—
233C2×C4×C139—42no—
234C2×C4×C139—84no—
235C2×C4×C139—82no—
236C2×C4×C139—82no—
237C2×C4×C139—88no—
238C2×C4×C139#9512yes—
239C2×C4×C139C2×C22⋊C411yescharacteristic
240C2×C4×C139C2×C4⋊C411yescharacteristic
241C8×C139—44no—
242C22×C139—21no—
243C22×C139—21no—
244C22×C139—21no—
245C22×C139—21no—
246C22×C139—24no—
247C22×C139—24no—
248C22×C139—21no—
249C22×C139—22no—
250C22×C139—22no—
251C22×C139—21no—
252C22×C139—21no—
253C22×C139—21no—
254C22×C139—42no—
255C22×C139—42no—
256C22×C139—41no—
257C22×C139—41no—
258C22×C139—41no—
259C22×C139—41no—
260C22×C139—42no—
261C22×C139—42no—
262C22×C139—44no—
263C22×C139—44no—
264C22×C139—41no—
265C22×C139—41no—
266C22×C139—41no—
267C22×C139—41no—
268C22×C139—41no—
269C22×C139—41no—
270C22×C139—41no—
271C22×C139—41no—
272C22×C139—44no—
273C22×C139—44no—
274C22×C139—44no—
275C22×C139—44no—
276C22×C139—81no—
277C22×C139—81no—
278C22×C139—82no—
279C22×C139—82no—
280C22×C139#34212yes—
281C22×C139#34212yes—
282C22×C139AΣL(1,𝔽16)12yes—
283C22×C139#35212yes—
284C22×C139C2×#9511yescharacteristic
285C22×C139C2×#9911yescharacteristic
286C22×C139C2×#9911yescharacteristic
287C4×C139—21no—
288C4×C139—22no—
289C4×C139—21no—
290C4×C139—44no—
291C4×C139—82no—
292C4×C139—84no—
293C2×C139—21no—
294C2×C139—21no—
295C2×C139—22no—
296C2×C139—41no—
297C2×C139—42no—
298C2×C139—41no—
299C2×C139—41no—
300C2×C139—42no—
301C2×C139—41no—
302C2×C139#139014yesdirect product factor
303C2×C139C2×#34211yescharacteristic
304C2×C139C2×AΣL(1,𝔽16)11yescharacteristic
305C2×C139C2×#35211yescharacteristic
306C2×#1390C13911yesmaximal, characteristic, direct product factor, Sylow
307C139C2×#139011yescharacteristic, direct product factor, Sylow
308C22×#100C2×C13911yescharacteristic
309C22×#99C2×C13911yescharacteristic
310C2×#386C2×C13911yescharacteristic
311#1390C2×C13914yesdirect product factor
312C23×D4C22×C13911yescharacteristic
313C24×C4C4×C13911yescharacteristic, complemented
314C22×M16—21no—
315C22×C22⋊C4—21no—
316C22×C22⋊C4—21no—
317C22×C22⋊C4C4×C13911yescharacteristic, complemented
318C2×#100—21no—
319C2×#100—22no—
320C2×#100C4×C13914yescomplemented
321C2×#100C22×C13912yes—
322C2×#99—21no—
323C2×#99—22no—
324C2×#99C4×C13914yescomplemented
325C2×#99C22×C13912yes—
326#386—21no—
327#386—21no—
328#386C4×C13912yescomplemented
329#386C22×C13912yes—
330C2×#95—21no—
331C25C2×C4×C13911yescharacteristic
332C25D4×C13911yescharacteristic
333C22×D4—41no—
334C22×D4—42no—
335C22×D4—41no—
336C22×D4C2×C4×C13911yescharacteristic
337C22×D4C2×C4×C13912yes—
338C22×D4C2×C4×C13912yes—
339C22×D4D4×C13911yescharacteristic
340C22×D4D4×C13912yes—
341C22×D4D4×C13911yescharacteristic
342C22×D4Q8×C13912yes—
343C22×D4C23×C13911yescharacteristic
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—44no—
348C23×C4—41no—
349C23×C4—41no—
350C23×C4—41no—
351C23×C4C2×C4×C13912yescomplemented
352C23×C4D4×C13911yescharacteristic
353C2×M16—24no—
354C2×M16—22no—
355C2×M16—41no—
356C2×M16—42no—
357C22×C8—41no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4C2×C4×C13912yescomplemented
368#100—24no—
369#100—22no—
370#100C2×C4×C13914yescomplemented
371#99—24no—
372#99—22no—
373#99C2×C4×C13914yescomplemented
374#95—22no—
375#95—22no—
376C24—22no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—22no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24C42×C13912yes—
387C24C22⋊C4×C13911yescharacteristic
388C24C22⋊C4×C13911yescharacteristic
389C24C22⋊C4×C13912yes—
390C24C22⋊C4×C13911yescharacteristic
391C24C4⋊C4×C13912yes—
392C24C4⋊C4×C13912yes—
393C24C22×C4×C13911yescharacteristic
394C24C2×D4×C13911yescharacteristic
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4C42×C13912yes—
412C2×D4C22⋊C4×C13912yes—
413C2×D4C22⋊C4×C13912yes—
414C2×D4C4⋊C4×C13912yes—
415C2×D4C4⋊C4×C13912yes—
416C2×D4C4⋊C4×C13912yes—
417C2×D4C22×C4×C13911yescharacteristic
418C2×D4C22×C4×C13911yescharacteristic
419C2×D4C2×D4×C13911yescharacteristic
420C2×D4C2×Q8×C13911yescharacteristic
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—48no—
432C22×C4—44no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—42no—
436C22×C4—44no—
437C22×C4—42no—
438C22×C4—44no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—82no—
443C22×C4—82no—
444C22×C4C22⋊C4×C13911yescharacteristic
445C22×C4C22⋊C4×C13912yes—
446C22×C4C4⋊C4×C13912yes—
447C22×C4C2×D4×C13911yescharacteristic
448M16—24no—
449M16—42no—
450M16—44no—
451C2×C8—42no—
452C2×C8—44no—
453C22⋊C4—24no—
454C22⋊C4—44no—
455C22⋊C4—44no—
456C22⋊C4—42no—
457C22⋊C4—44no—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C23—22no—
461C23—22no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—21no—
475C23—21no—
476C23—22no—
477C23—22no—
478C23—41no—
479C23—41no—
480C23—44no—
481C23—41no—
482C23—44no—
483C23—41no—
484C23—42no—
485C23—42no—
486C23—48no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—44no—
491C23—44no—
492C23—41no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—81no—
498C23—81no—
499C23—84no—
500C23#95×C13912yes—
501C23#95×C13912yes—
502C23#95×C13912yes—
503C23#99×C13911yescharacteristic
504C23#99×C13912yes—
505C23#99×C13911yescharacteristic
506C23C2×C42×C13911yescharacteristic
507C23C2×C22⋊C4×C13911yescharacteristic
508C23C2×C22⋊C4×C13911yescharacteristic
509C23C2×C4⋊C4×C13911yescharacteristic
510C23C2×C4⋊C4×C13911yescharacteristic
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—48no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—88no—
545C2×C4#95×C13912yes—
546C2×C4C2×C22⋊C4×C13911yescharacteristic
547C2×C4C2×C4⋊C4×C13911yescharacteristic
548C8—44no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—24no—
554C22—24no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—42no—
562C22—42no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—42no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—81no—
584C22—81no—
585C22—82no—
586C22—82no—
587C22#342×C13912yes—
588C22#342×C13912yes—
589C22AΣL(1,𝔽16)×C13912yes—
590C22#352×C13912yes—
591C22C2×#95×C13911yescharacteristic
592C22C2×#99×C13911yescharacteristic
593C22C2×#99×C13911yescharacteristic
594C4—21no—
595C4—22no—
596C4—21no—
597C4—44no—
598C4—82no—
599C4—84no—
600C2—21no—
601C2—21no—
602C2—22no—
603C2—41no—
604C2—42no—
605C2—41no—
606C2—41no—
607C2—42no—
608C2—41no—
609C2#1390×C13914yesdirect product factor
610C2C2×#342×C13911yescharacteristic
611C2C2×AΣL(1,𝔽16)×C13911yescharacteristic
612C2C2×#352×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#99
commutatorC23C2×C42×C139
Frattini, cosocleC22×D4C23×C139
prime radicalC23×D4×C139C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C24×C139 ◁ C23×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1390×C139C2direct (N × H)
6. C24×C4×C139C4semidirect
10. C22×C22⋊C4×C139C4semidirect
13. C2×#100×C139C4semidirect
17. C2×#99×C139C4semidirect
21. #386×C139C4semidirect
44. C23×C4×C139C2×C4semidirect
60. C2×C22⋊C4×C139C2×C4semidirect
63. #100×C139C2×C4semidirect
66. #99×C139C2×C4semidirect
302. C2×C139#1390direct (N × H)
306. C2×#1390C139direct (N × H)
307. C139C2×#1390direct (N × H)
311. #1390C2×C139direct (N × H)
313. C24×C4C4×C139semidirect
317. C22×C22⋊C4C4×C139semidirect
320. C2×#100C4×C139semidirect
324. C2×#99C4×C139semidirect
328. #386C4×C139semidirect
351. C23×C4C2×C4×C139semidirect
367. C2×C22⋊C4C2×C4×C139semidirect
370. #100C2×C4×C139semidirect
373. #99C2×C4×C139semidirect
609. C2#1390×C139direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#100×C1392
C22×#99×C1392
C2×#386×C1392
#1390×C1392
C2×#1390139