Finite Group Databasebeta

← C139×#10991 #48005587

Subgroups — C139×#10991 #48005587

Order 35584.

3122 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C139C211yesmaximal, characteristic
2C22×#99×C139C211yesmaximal, characteristic, complemented
3#2308×C139C211yesmaximal, characteristic, complemented
4C2×#379×C139C212yesmaximal, complemented
5C2×#342×C139C212yesmaximal, complemented
6C26×C139C2211yescharacteristic
7C23×D4×C139—21no—
8C23×D4×C139C2211yescharacteristic
9C2×#120×C139—24no—
10C2×#120×C139—22no—
11C2×#120×C139—24no—
12C2×#120×C139C414yescomplemented
13C22×C22⋊C4×C139—21no—
14C22×C22⋊C4×C139—24no—
15C22×C22⋊C4×C139C2212yes—
16C22×C22⋊C4×C139C2212yes—
17C22×C22⋊C4×C139C2211yescharacteristic
18C2×#99×C139—22no—
19C2×#99×C139—24no—
20#386×C139—24no—
21#381×C139—21no—
22#379×C139—24no—
23#379×C139—21no—
24#379×C139—24no—
25#342×C139—24no—
26C25×C139—22no—
27C25×C139—21no—
28C25×C139—21no—
29C25×C139—22no—
30C25×C139—22no—
31C25×C139—22no—
32C25×C139—22no—
33C25×C139—48no—
34C25×C139C2×C412yes—
35C25×C139D414yes—
36C25×C139D411yescharacteristic
37C25×C139C2311yescharacteristic
38C22×D4×C139—28no—
39C22×D4×C139—24no—
40C22×D4×C139—22no—
41C22×D4×C139—22no—
42C22×D4×C139—22no—
43C22×D4×C139—22no—
44C22×D4×C139—22no—
45C22×D4×C139—22no—
46C22×D4×C139—48no—
47C22×D4×C139C2×C412yes—
48C22×D4×C139D412yes—
49C23×C4×C139—21no—
50C23×C4×C139—22no—
51C23×C4×C139D411yescharacteristic
52C23×C4×C139D414yescomplemented
53#120×C139—216no—
54#120×C139—28no—
55#120×C139—28no—
56C2×C22⋊C4×C139—28no—
57C2×C22⋊C4×C139—22no—
58C2×C22⋊C4×C139—21no—
59C2×C22⋊C4×C139—24no—
60C2×C22⋊C4×C139—22no—
61C2×C22⋊C4×C139—22no—
62C2×C22⋊C4×C139—22no—
63C2×C22⋊C4×C139—22no—
64C2×C22⋊C4×C139—216no—
65C2×C22⋊C4×C139—22no—
66C2×C22⋊C4×C139—22no—
67C2×C22⋊C4×C139—22no—
68C2×C22⋊C4×C139—22no—
69C2×C22⋊C4×C139—22no—
70C2×C22⋊C4×C139—22no—
71C2×C22⋊C4×C139—22no—
72C2×C22⋊C4×C139—24no—
73C2×C22⋊C4×C139—416no—
74C2×C22⋊C4×C139C2×C412yes—
75C2×C22⋊C4×C139D414yes—
76C2×C22⋊C4×C139D414yescomplemented
77#99×C139—28no—
78#95×C139—24no—
79C24×C139—216no—
80C24×C139—28no—
81C24×C139—22no—
82C24×C139—24no—
83C24×C139—24no—
84C24×C139—24no—
85C24×C139—24no—
86C24×C139—22no—
87C24×C139—24no—
88C24×C139—24no—
89C24×C139—22no—
90C24×C139—21no—
91C24×C139—24no—
92C24×C139—24no—
93C24×C139—22no—
94C24×C139—21no—
95C24×C139—48no—
96C24×C139—416no—
97C24×C139—44no—
98C24×C139—48no—
99C24×C139—44no—
100C24×C139—416no—
101C24×C139—48no—
102C24×C139—416no—
103C24×C139—416no—
104C24×C139—416no—
105C24×C139—44no—
106C24×C139—41no—
107C24×C139—41no—
108C24×C139—42no—
109C24×C139—42no—
110C24×C139—42no—
111C24×C139—42no—
112C24×C139—41no—
113C24×C139—41no—
114C24×C139—42no—
115C24×C139—42no—
116C24×C139C22⋊C414yescomplemented
117C24×C139C22⋊C412yescomplemented
118C24×C139C22×C411yescharacteristic
119C24×C139C2×D411yescharacteristic
120C24×C139C2×D412yes—
121C24×C139C2×D412yes—
122C24×C139C2×D411yescharacteristic
123C24×C139C2×D412yes—
124C24×C139C2×D412yes—
125C24×C139#4112yes—
126C24×C139#4112yes—
127C2×D4×C139—216no—
128C2×D4×C139—22no—
129C2×D4×C139—22no—
130C2×D4×C139—24no—
131C2×D4×C139—24no—
132C2×D4×C139—22no—
133C2×D4×C139—24no—
134C2×D4×C139—24no—
135C2×D4×C139—22no—
136C2×D4×C139—416no—
137C2×D4×C139—432no—
138C2×D4×C139—42no—
139C2×D4×C139—42no—
140C2×D4×C139—42no—
141C2×D4×C139—42no—
142C2×D4×C139—42no—
143C2×D4×C139—42no—
144C2×D4×C139—42no—
145C2×D4×C139—42no—
146C22×C4×C139—22no—
147C22×C4×C139—22no—
148C22×C4×C139—24no—
149C22×C4×C139—21no—
150C22×C4×C139—22no—
151C22×C4×C139—21no—
152C22×C4×C139—24no—
153C22×C4×C139—24no—
154C22×C4×C139—24no—
155C22×C4×C139—24no—
156C22×C4×C139—44no—
157C22×C4×C139—48no—
158C22×C4×C139—48no—
159C22×C4×C139—42no—
160C22×C4×C139—42no—
161C22×C4×C139C22⋊C412yescomplemented
162C22⋊C4×C139—216no—
163C22⋊C4×C139—22no—
164C22⋊C4×C139—24no—
165C22⋊C4×C139—24no—
166C22⋊C4×C139—24no—
167C22⋊C4×C139—432no—
168C22⋊C4×C139—42no—
169C22⋊C4×C139—42no—
170C22⋊C4×C139—42no—
171C22⋊C4×C139—42no—
172C22⋊C4×C139—42no—
173C22⋊C4×C139—42no—
174C22⋊C4×C139—84no—
175C22⋊C4×C139C22⋊C414yescomplemented
176C23×C139—28no—
177C23×C139—24no—
178C23×C139—216no—
179C23×C139—28no—
180C23×C139—216no—
181C23×C139—216no—
182C23×C139—216no—
183C23×C139—24no—
184C23×C139—28no—
185C23×C139—22no—
186C23×C139—22no—
187C23×C139—22no—
188C23×C139—48no—
189C23×C139—42no—
190C23×C139—42no—
191C23×C139—44no—
192C23×C139—44no—
193C23×C139—44no—
194C23×C139—44no—
195C23×C139—44no—
196C23×C139—44no—
197C23×C139—416no—
198C23×C139—48no—
199C23×C139—48no—
200C23×C139—48no—
201C23×C139—48no—
202C23×C139—416no—
203C23×C139—416no—
204C23×C139—48no—
205C23×C139—416no—
206C23×C139—48no—
207C23×C139—416no—
208C23×C139—416no—
209C23×C139—416no—
210C23×C139—416no—
211C23×C139—44no—
212C23×C139—48no—
213C23×C139—48no—
214C23×C139—416no—
215C23×C139—48no—
216C23×C139—416no—
217C23×C139—42no—
218C23×C139—42no—
219C23×C139—44no—
220C23×C139—44no—
221C23×C139—44no—
222C23×C139—44no—
223C23×C139—44no—
224C23×C139—48no—
225C23×C139—42no—
226C23×C139—42no—
227C23×C139—44no—
228C23×C139—82no—
229C23×C139—84no—
230C23×C139C2×C22⋊C411yescharacteristic
231C23×C139C2×C22⋊C411yescharacteristic
232C23×C139C2×C22⋊C411yescharacteristic
233C23×C139C4×D412yes—
234C23×C139C4×D412yes—
235C23×C139#12012yes—
236C23×C139#12012yes—
237C23×C139#12012yes—
238C23×C139#12011yescharacteristic
239C23×C139#12011yescharacteristic
240C23×C139#12112yes—
241C23×C139#12112yes—
242C23×C139#12112yes—
243C23×C139#12112yes—
244C23×C139#12112yes—
245C23×C139#12112yes—
246C23×C139#12311yescharacteristic
247C23×C139#12311yescharacteristic
248C23×C139#12312yes—
249C23×C139#12412yes—
250C23×C139#12712yes—
251D4×C139—432no—
252D4×C139—44no—
253D4×C139—44no—
254D4×C139—44no—
255D4×C139—44no—
256C2×C4×C139—22no—
257C2×C4×C139—24no—
258C2×C4×C139—22no—
259C2×C4×C139—22no—
260C2×C4×C139—44no—
261C2×C4×C139—48no—
262C2×C4×C139—42no—
263C2×C4×C139—42no—
264C2×C4×C139—48no—
265C2×C4×C139—48no—
266C2×C4×C139—44no—
267C2×C4×C139—44no—
268C2×C4×C139—48no—
269C2×C4×C139—84no—
270C2×C4×C139—84no—
271C2×C4×C139—84no—
272C22×C139—22no—
273C22×C139—24no—
274C22×C139—24no—
275C22×C139—22no—
276C22×C139—24no—
277C22×C139—24no—
278C22×C139—24no—
279C22×C139—24no—
280C22×C139—24no—
281C22×C139—24no—
282C22×C139—28no—
283C22×C139—216no—
284C22×C139—41no—
285C22×C139—41no—
286C22×C139—42no—
287C22×C139—42no—
288C22×C139—41no—
289C22×C139—42no—
290C22×C139—42no—
291C22×C139—42no—
292C22×C139—41no—
293C22×C139—42no—
294C22×C139—44no—
295C22×C139—416no—
296C22×C139—48no—
297C22×C139—48no—
298C22×C139—416no—
299C22×C139—416no—
300C22×C139—416no—
301C22×C139—44no—
302C22×C139—48no—
303C22×C139—44no—
304C22×C139—416no—
305C22×C139—44no—
306C22×C139—42no—
307C22×C139—82no—
308C22×C139—84no—
309C22×C139—84no—
310C22×C139#37911yescharacteristic
311C22×C139#38611yescharacteristic
312C22×C139#38612yes—
313C22×C139#38611yescharacteristic
314C22×C139#39012yes—
315C22×C139#39212yes—
316C22×C139#39212yes—
317C22×C139#39412yes—
318C22×C139#39412yes—
319C22×C139B(4,𝔽2)14yes—
320C4×C139—44no—
321C4×C139—42no—
322C4×C139—84no—
323C4×C139—84no—
324C2×C139—21no—
325C2×C139—22no—
326C2×C139—22no—
327C2×C139—21no—
328C2×C139—22no—
329C2×C139—22no—
330C2×C139—22no—
331C2×C139—48no—
332C2×C139—82no—
333C2×C139#143811yescharacteristic
334C2×C139#188912yes—
335C2×C139#202114yes—
336#10991C13911yesmaximal, characteristic, direct product factor, Sylow
337C139#1099111yescharacteristic, direct product factor, Sylow
338C22×#120C2×C13911yescharacteristic
339C22×#99C2×C13911yescharacteristic, complemented
340#2308C2×C13911yescharacteristic, complemented
341C2×#379C2×C13912yescomplemented
342C2×#342C2×C13912yescomplemented
343C26C22×C13911yescharacteristic
344C23×D4—21no—
345C23×D4C22×C13911yescharacteristic
346C2×#120—24no—
347C2×#120—22no—
348C2×#120—24no—
349C2×#120C4×C13914yescomplemented
350C22×C22⋊C4—21no—
351C22×C22⋊C4—24no—
352C22×C22⋊C4C22×C13912yes—
353C22×C22⋊C4C22×C13912yes—
354C22×C22⋊C4C22×C13911yescharacteristic
355C2×#99—22no—
356C2×#99—24no—
357#386—24no—
358#381—21no—
359#379—21no—
360#379—24no—
361#379—24no—
362#342—24no—
363C25—22no—
364C25—21no—
365C25—21no—
366C25—22no—
367C25—22no—
368C25—22no—
369C25—22no—
370C25—48no—
371C25C2×C4×C13912yes—
372C25D4×C13914yes—
373C25D4×C13911yescharacteristic
374C25C23×C13911yescharacteristic
375C22×D4—28no—
376C22×D4—24no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—22no—
382C22×D4—22no—
383C22×D4—48no—
384C22×D4C2×C4×C13912yes—
385C22×D4D4×C13912yes—
386C23×C4—21no—
387C23×C4—22no—
388C23×C4D4×C13911yescharacteristic
389C23×C4D4×C13914yescomplemented
390#120—216no—
391#120—28no—
392#120—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—216no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—416no—
411C2×C22⋊C4C2×C4×C13912yes—
412C2×C22⋊C4D4×C13914yes—
413C2×C22⋊C4D4×C13914yescomplemented
414#99—28no—
415#95—24no—
416C24—216no—
417C24—28no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—24no—
425C24—21no—
426C24—24no—
427C24—22no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—21no—
432C24—48no—
433C24—416no—
434C24—44no—
435C24—48no—
436C24—44no—
437C24—416no—
438C24—416no—
439C24—48no—
440C24—416no—
441C24—416no—
442C24—44no—
443C24—41no—
444C24—41no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—41no—
450C24—41no—
451C24—42no—
452C24—42no—
453C24C22⋊C4×C13914yescomplemented
454C24C22⋊C4×C13912yescomplemented
455C24C22×C4×C13911yescharacteristic
456C24C2×D4×C13911yescharacteristic
457C24C2×D4×C13912yes—
458C24C2×D4×C13912yes—
459C24C2×D4×C13911yescharacteristic
460C24C2×D4×C13912yes—
461C24C2×D4×C13912yes—
462C24#41×C13912yes—
463C24#41×C13912yes—
464C2×D4—216no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—22no—
473C2×D4—416no—
474C2×D4—432no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—44no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4C22⋊C4×C13912yescomplemented
499C22⋊C4—216no—
500C22⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—432no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—84no—
512C22⋊C4C22⋊C4×C13914yescomplemented
513C23—28no—
514C23—24no—
515C23—216no—
516C23—216no—
517C23—28no—
518C23—216no—
519C23—216no—
520C23—24no—
521C23—28no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—48no—
526C23—42no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—42no—
531C23—44no—
532C23—44no—
533C23—48no—
534C23—48no—
535C23—416no—
536C23—416no—
537C23—48no—
538C23—416no—
539C23—44no—
540C23—416no—
541C23—48no—
542C23—48no—
543C23—48no—
544C23—416no—
545C23—416no—
546C23—416no—
547C23—416no—
548C23—44no—
549C23—48no—
550C23—48no—
551C23—416no—
552C23—48no—
553C23—416no—
554C23—48no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23—44no—
561C23—44no—
562C23—44no—
563C23—42no—
564C23—42no—
565C23—82no—
566C23—84no—
567C23C2×C22⋊C4×C13911yescharacteristic
568C23C2×C22⋊C4×C13911yescharacteristic
569C23C2×C22⋊C4×C13911yescharacteristic
570C23C4×D4×C13912yes—
571C23C4×D4×C13912yes—
572C23#120×C13912yes—
573C23#120×C13912yes—
574C23#120×C13912yes—
575C23#120×C13911yescharacteristic
576C23#120×C13911yescharacteristic
577C23#121×C13912yes—
578C23#121×C13912yes—
579C23#121×C13912yes—
580C23#121×C13912yes—
581C23#121×C13912yes—
582C23#121×C13912yes—
583C23#123×C13911yescharacteristic
584C23#123×C13911yescharacteristic
585C23#123×C13912yes—
586C23#124×C13912yes—
587C23#127×C13912yes—
588D4—432no—
589D4—44no—
590D4—44no—
591D4—44no—
592D4—44no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—48no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—48no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—84no—
607C2×C4—84no—
608C2×C4—84no—
609C22—24no—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—24no—
614C22—24no—
615C22—22no—
616C22—24no—
617C22—24no—
618C22—22no—
619C22—28no—
620C22—216no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—42no—
625C22—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—41no—
630C22—42no—
631C22—44no—
632C22—416no—
633C22—48no—
634C22—48no—
635C22—416no—
636C22—416no—
637C22—416no—
638C22—44no—
639C22—416no—
640C22—48no—
641C22—44no—
642C22—44no—
643C22—42no—
644C22—82no—
645C22—84no—
646C22—84no—
647C22#379×C13911yescharacteristic
648C22#386×C13911yescharacteristic
649C22#386×C13912yes—
650C22#386×C13911yescharacteristic
651C22#390×C13912yes—
652C22#392×C13912yes—
653C22#392×C13912yes—
654C22#394×C13912yes—
655C22#394×C13912yes—
656C22B(4,𝔽2)×C13914yes—
657C4—44no—
658C4—42no—
659C4—84no—
660C4—84no—
661C2—21no—
662C2—22no—
663C2—22no—
664C2—21no—
665C2—22no—
666C2—22no—
667C2—22no—
668C2—48no—
669C2—82no—
670C2#1438×C13911yescharacteristic
671C2#1889×C13912yes—
672C2#2021×C13914yes—
subgroupG/H
center, socleC23×C139#120
commutatorC24C22×C4×C139
Frattini, cosocleC25C23×C139
prime radicalC22×#120×C139C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C25×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C139C2semidirect
3. #2308×C139C2semidirect
4. C2×#379×C139C2semidirect
5. C2×#342×C139C2semidirect
12. C2×#120×C139C4semidirect
52. C23×C4×C139D4semidirect
76. C2×C22⋊C4×C139D4semidirect
116. C24×C139C22⋊C4semidirect
117. C24×C139C22⋊C4semidirect
161. C22×C4×C139C22⋊C4semidirect
175. C22⋊C4×C139C22⋊C4semidirect
336. #10991C139direct (N × H)
337. C139#10991direct (N × H)
339. C22×#99C2×C139semidirect
340. #2308C2×C139semidirect
341. C2×#379C2×C139semidirect
342. C2×#342C2×C139semidirect
349. C2×#120C4×C139semidirect
389. C23×C4D4×C139semidirect
413. C2×C22⋊C4D4×C139semidirect
453. C24C22⋊C4×C139semidirect
454. C24C22⋊C4×C139semidirect
498. C22×C4C22⋊C4×C139semidirect
512. C22⋊C4C22⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1392
C22×#99×C1392
#2308×C1392
C2×#379×C1392
C2×#342×C1392
#10991139