Finite Group Databasebeta

← C139×#10972 #48005568

Subgroups — C139×#10972 #48005568

Order 35584.

1634 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C139C211yesmaximal, characteristic
2C22×#99×C139C212yesmaximal, complemented
3C22×#99×C139C211yesmaximal, characteristic, complemented
4#2308×C139C211yesmaximal, characteristic, complemented
5C2×#342×C139C212yesmaximal, complemented
6C23×D4×C139C2211yescharacteristic
7C23×D4×C139C2211yescharacteristic
8#534×C139—24no—
9#534×C139—24no—
10C2×#123×C139—21no—
11C2×#123×C139C412yescomplemented
12C2×#121×C139—22no—
13C2×#120×C139—21no—
14C2×#120×C139C412yescomplemented
15C22×C22⋊C4×C139C2212yes—
16C22×C22⋊C4×C139C2212yes—
17C22×C22⋊C4×C139C2211yescharacteristic
18C2×#99×C139—22no—
19C2×#99×C139—24no—
20C2×#99×C139—24no—
21C2×#99×C139—24no—
22C2×#99×C139—24no—
23#386×C139—24no—
24#381×C139—21no—
25#379×C139—21no—
26#342×C139—24no—
27C25×C139C2×C411yescharacteristic
28C25×C139D411yescharacteristic
29C25×C139C2311yescharacteristic
30C22×D4×C139—22no—
31C22×D4×C139—22no—
32C22×D4×C139—22no—
33C22×D4×C139—21no—
34C22×D4×C139—21no—
35C22×D4×C139—22no—
36C22×D4×C139—22no—
37C22×D4×C139—22no—
38C22×D4×C139—22no—
39C22×D4×C139—22no—
40C22×D4×C139—22no—
41C22×D4×C139—22no—
42C22×D4×C139—22no—
43C22×D4×C139—22no—
44C22×D4×C139C2×C412yes—
45C22×D4×C139D412yes—
46C22×D4×C139D414yes—
47C23×C4×C139—21no—
48C23×C4×C139—22no—
49C23×C4×C139—22no—
50C23×C4×C139C2×C411yescharacteristic
51C23×C4×C139D411yescharacteristic
52#123×C139—28no—
53#123×C139—24no—
54#123×C139—24no—
55#121×C139—216no—
56#120×C139—28no—
57#120×C139—24no—
58#120×C139—24no—
59C2×C4⋊C4×C139—22no—
60C2×C22⋊C4×C139—22no—
61C2×C22⋊C4×C139—21no—
62C2×C22⋊C4×C139—22no—
63C2×C22⋊C4×C139—22no—
64C2×C22⋊C4×C139—22no—
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—22no—
73C2×C22⋊C4×C139—22no—
74C2×C22⋊C4×C139—24no—
75C2×C22⋊C4×C139C2×C412yes—
76C2×C22⋊C4×C139D414yes—
77C2×C22⋊C4×C139D414yescomplemented
78C2×C22⋊C4×C139D414yescomplemented
79#99×C139—28no—
80#99×C139—216no—
81#95×C139—24no—
82C24×C139—21no—
83C24×C139—21no—
84C24×C139—21no—
85C24×C139—22no—
86C24×C139—22no—
87C24×C139—22no—
88C24×C139—22no—
89C24×C139—21no—
90C24×C139—82no—
91C24×C139—82no—
92C24×C139—82no—
93C24×C139C22⋊C412yes—
94C24×C139C22⋊C412yescomplemented
95C24×C139C22×C411yescharacteristic
96C24×C139C2×D411yescharacteristic
97C24×C139C2×D411yescharacteristic
98C24×C139C2×D412yes—
99C24×C139C2×D412yes—
100C24×C139C2×D412yes—
101C24×C139C2×D412yes—
102C24×C139#4112yes—
103C24×C139#4112yes—
104C2×D4×C139—22no—
105C2×D4×C139—22no—
106C2×D4×C139—24no—
107C2×D4×C139—24no—
108C2×D4×C139—22no—
109C2×D4×C139—24no—
110C2×D4×C139—24no—
111C2×D4×C139—24no—
112C2×D4×C139—24no—
113C2×D4×C139—24no—
114C2×D4×C139—24no—
115C2×D4×C139—24no—
116C2×D4×C139—22no—
117C2×D4×C139—24no—
118C2×D4×C139—28no—
119C2×D4×C139—41no—
120C2×D4×C139—41no—
121C2×D4×C139—42no—
122C2×D4×C139—42no—
123C2×D4×C139—42no—
124C2×D4×C139—42no—
125C2×D4×C139—42no—
126C2×D4×C139—42no—
127C2×D4×C139—42no—
128C2×D4×C139—42no—
129C2×D4×C139—42no—
130C2×D4×C139—41no—
131C2×D4×C139—41no—
132C2×D4×C139—42no—
133C2×D4×C139—42no—
134C2×D4×C139—42no—
135C2×D4×C139—42no—
136C2×D4×C139—42no—
137C2×D4×C139—84no—
138C22×C4×C139—22no—
139C22×C4×C139—21no—
140C22×C4×C139—21no—
141C22×C4×C139—22no—
142C22×C4×C139—22no—
143C22×C4×C139—21no—
144C22×C4×C139—22no—
145C22×C4×C139—22no—
146C22×C4×C139—21no—
147C22×C4×C139—24no—
148C22×C4×C139—24no—
149C22×C4×C139—24no—
150C22×C4×C139—42no—
151C22×C4×C139—42no—
152C22×C4×C139—42no—
153C22×C4×C139—42no—
154C22×C4×C139—82no—
155C22×C4×C139—84no—
156C22×C4×C139—84no—
157C22×C4×C139C22⋊C412yes—
158C22×C4×C139C22⋊C412yescomplemented
159C4⋊C4×C139—28no—
160C22⋊C4×C139—28no—
161C22⋊C4×C139—28no—
162C22⋊C4×C139—22no—
163C22⋊C4×C139—24no—
164C22⋊C4×C139—24no—
165C22⋊C4×C139—24no—
166C22⋊C4×C139—24no—
167C22⋊C4×C139—24no—
168C22⋊C4×C139—42no—
169C22⋊C4×C139—42no—
170C22⋊C4×C139—42no—
171C22⋊C4×C139—42no—
172C22⋊C4×C139—84no—
173C22⋊C4×C139C22⋊C414yescomplemented
174C23×C139—22no—
175C23×C139—22no—
176C23×C139—22no—
177C23×C139—22no—
178C23×C139—24no—
179C23×C139—44no—
180C23×C139—42no—
181C23×C139—44no—
182C23×C139—42no—
183C23×C139—42no—
184C23×C139—44no—
185C23×C139—44no—
186C23×C139—44no—
187C23×C139—41no—
188C23×C139—41no—
189C23×C139—42no—
190C23×C139—42no—
191C23×C139—42no—
192C23×C139—82no—
193C23×C139—84no—
194C23×C139—82no—
195C23×C139—82no—
196C23×C139—82no—
197C23×C139—82no—
198C23×C139—82no—
199C23×C139—82no—
200C23×C139—84no—
201C23×C139—84no—
202C23×C139—84no—
203C23×C139C2×C22⋊C411yescharacteristic
204C23×C139C2×C22⋊C411yescharacteristic
205C23×C139C2×C22⋊C411yescharacteristic
206C23×C139C4×D412yes—
207C23×C139C4×D412yes—
208C23×C139#12011yescharacteristic
209C23×C139#12012yes—
210C23×C139#12012yes—
211C23×C139#12011yescharacteristic
212C23×C139#12012yes—
213C23×C139#12112yes—
214C23×C139#12112yes—
215C23×C139#12112yes—
216C23×C139#12112yes—
217C23×C139#12112yes—
218C23×C139#12112yes—
219C23×C139#12311yescharacteristic
220C23×C139#12311yescharacteristic
221C23×C139#12312yes—
222C23×C139#12412yes—
223C23×C139#12712yes—
224D4×C139—44no—
225D4×C139—44no—
226D4×C139—44no—
227D4×C139—44no—
228D4×C139—44no—
229D4×C139—44no—
230D4×C139—44no—
231D4×C139—44no—
232D4×C139—88no—
233C2×C4×C139—24no—
234C2×C4×C139—22no—
235C2×C4×C139—22no—
236C2×C4×C139—22no—
237C2×C4×C139—24no—
238C2×C4×C139—22no—
239C2×C4×C139—44no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—42no—
243C2×C4×C139—42no—
244C2×C4×C139—42no—
245C2×C4×C139—48no—
246C2×C4×C139—44no—
247C2×C4×C139—44no—
248C2×C4×C139—84no—
249C2×C4×C139—84no—
250C2×C4×C139—84no—
251C2×C4×C139—84no—
252C2×C4×C139—84no—
253C2×C4×C139—84no—
254C22×C139—22no—
255C22×C139—22no—
256C22×C139—24no—
257C22×C139—24no—
258C22×C139—22no—
259C22×C139—42no—
260C22×C139—42no—
261C22×C139—42no—
262C22×C139—42no—
263C22×C139—42no—
264C22×C139—41no—
265C22×C139—41no—
266C22×C139—42no—
267C22×C139—42no—
268C22×C139—42no—
269C22×C139—42no—
270C22×C139—41no—
271C22×C139—42no—
272C22×C139—41no—
273C22×C139—42no—
274C22×C139—42no—
275C22×C139—44no—
276C22×C139—44no—
277C22×C139—44no—
278C22×C139—42no—
279C22×C139—42no—
280C22×C139—82no—
281C22×C139—84no—
282C22×C139—84no—
283C22×C139—82no—
284C22×C139—84no—
285C22×C139—84no—
286C22×C139—82no—
287C22×C139#37911yescharacteristic
288C22×C139#38611yescharacteristic
289C22×C139#38612yes—
290C22×C139#38611yescharacteristic
291C22×C139#39012yes—
292C22×C139#39212yes—
293C22×C139#39212yes—
294C22×C139#39412yes—
295C22×C139#39412yes—
296C4×C139—44no—
297C4×C139—42no—
298C4×C139—42no—
299C4×C139—84no—
300C4×C139—84no—
301C2×C139—21no—
302C2×C139—22no—
303C2×C139—22no—
304C2×C139—21no—
305C2×C139—22no—
306C2×C139—22no—
307C2×C139—22no—
308C2×C139—22no—
309C2×C139—82no—
310C2×C139—82no—
311C2×C139#143811yescharacteristic
312C2×C139#191312yes—
313#10972C13911yesmaximal, characteristic, direct product factor, Sylow
314C139#1097211yescharacteristic, direct product factor, Sylow
315C2×#534C2×C13911yescharacteristic
316C22×#99C2×C13912yescomplemented
317C22×#99C2×C13911yescharacteristic, complemented
318#2308C2×C13911yescharacteristic, complemented
319C2×#342C2×C13912yescomplemented
320C23×D4C22×C13911yescharacteristic
321C23×D4C22×C13911yescharacteristic
322#534—24no—
323#534—24no—
324C2×#123—21no—
325C2×#123C4×C13912yescomplemented
326C2×#121—22no—
327C2×#120—21no—
328C2×#120C4×C13912yescomplemented
329C22×C22⋊C4C22×C13912yes—
330C22×C22⋊C4C22×C13912yes—
331C22×C22⋊C4C22×C13911yescharacteristic
332C2×#99—22no—
333C2×#99—24no—
334C2×#99—24no—
335C2×#99—24no—
336C2×#99—24no—
337#386—24no—
338#381—21no—
339#379—21no—
340#342—24no—
341C25C2×C4×C13911yescharacteristic
342C25D4×C13911yescharacteristic
343C25C23×C13911yescharacteristic
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4C2×C4×C13912yes—
359C22×D4D4×C13912yes—
360C22×D4D4×C13914yes—
361C23×C4—21no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4C2×C4×C13911yescharacteristic
365C23×C4D4×C13911yescharacteristic
366#123—28no—
367#123—24no—
368#123—24no—
369#121—216no—
370#120—28no—
371#120—24no—
372#120—24no—
373C2×C4⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4C2×C4×C13912yes—
390C2×C22⋊C4D4×C13914yes—
391C2×C22⋊C4D4×C13914yescomplemented
392C2×C22⋊C4D4×C13914yescomplemented
393#99—216no—
394#99—28no—
395#95—24no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—82no—
405C24—82no—
406C24—82no—
407C24C22⋊C4×C13912yes—
408C24C22⋊C4×C13912yescomplemented
409C24C22×C4×C13911yescharacteristic
410C24C2×D4×C13911yescharacteristic
411C24C2×D4×C13911yescharacteristic
412C24C2×D4×C13912yes—
413C24C2×D4×C13912yes—
414C24C2×D4×C13912yes—
415C24C2×D4×C13912yes—
416C24#41×C13912yes—
417C24#41×C13912yes—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—22no—
431C2×D4—24no—
432C2×D4—28no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—84no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—82no—
469C22×C4—84no—
470C22×C4—84no—
471C22×C4C22⋊C4×C13912yes—
472C22×C4C22⋊C4×C13912yescomplemented
473C4⋊C4—28no—
474C22⋊C4—28no—
475C22⋊C4—28no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—84no—
487C22⋊C4C22⋊C4×C13914yescomplemented
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—44no—
494C23—42no—
495C23—44no—
496C23—42no—
497C23—42no—
498C23—44no—
499C23—44no—
500C23—44no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—82no—
507C23—84no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23—82no—
512C23—82no—
513C23—82no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23C2×C22⋊C4×C13911yescharacteristic
518C23C2×C22⋊C4×C13911yescharacteristic
519C23C2×C22⋊C4×C13911yescharacteristic
520C23C4×D4×C13912yes—
521C23C4×D4×C13912yes—
522C23#120×C13911yescharacteristic
523C23#120×C13912yes—
524C23#120×C13912yes—
525C23#120×C13911yescharacteristic
526C23#120×C13912yes—
527C23#121×C13912yes—
528C23#121×C13912yes—
529C23#121×C13912yes—
530C23#121×C13912yes—
531C23#121×C13912yes—
532C23#121×C13912yes—
533C23#123×C13911yescharacteristic
534C23#123×C13911yescharacteristic
535C23#123×C13912yes—
536C23#124×C13912yes—
537C23#127×C13912yes—
538D4—44no—
539D4—44no—
540D4—44no—
541D4—44no—
542D4—44no—
543D4—44no—
544D4—44no—
545D4—44no—
546D4—88no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—44no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—84no—
563C2×C4—84no—
564C2×C4—84no—
565C2×C4—84no—
566C2×C4—84no—
567C2×C4—84no—
568C22—22no—
569C22—22no—
570C22—24no—
571C22—24no—
572C22—22no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22—42no—
586C22—41no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—82no—
595C22—84no—
596C22—84no—
597C22—82no—
598C22—84no—
599C22—84no—
600C22—82no—
601C22#379×C13911yescharacteristic
602C22#386×C13911yescharacteristic
603C22#386×C13912yes—
604C22#386×C13911yescharacteristic
605C22#390×C13912yes—
606C22#392×C13912yes—
607C22#392×C13912yes—
608C22#394×C13912yes—
609C22#394×C13912yes—
610C4—44no—
611C4—42no—
612C4—42no—
613C4—84no—
614C4—84no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—21no—
619C2—22no—
620C2—22no—
621C2—22no—
622C2—22no—
623C2—82no—
624C2—82no—
625C2#1438×C13911yescharacteristic
626C2#1913×C13912yes—
subgroupG/H
center, socleC22×C139#386
commutatorC24C22×C4×C139
Frattini, cosocleC25C23×C139
prime radicalC2×#534×C139C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C25×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C139C2semidirect
3. C22×#99×C139C2semidirect
4. #2308×C139C2semidirect
5. C2×#342×C139C2semidirect
11. C2×#123×C139C4semidirect
14. C2×#120×C139C4semidirect
77. C2×C22⋊C4×C139D4semidirect
78. C2×C22⋊C4×C139D4semidirect
94. C24×C139C22⋊C4semidirect
158. C22×C4×C139C22⋊C4semidirect
173. C22⋊C4×C139C22⋊C4semidirect
313. #10972C139direct (N × H)
314. C139#10972direct (N × H)
316. C22×#99C2×C139semidirect
317. C22×#99C2×C139semidirect
318. #2308C2×C139semidirect
319. C2×#342C2×C139semidirect
325. C2×#123C4×C139semidirect
328. C2×#120C4×C139semidirect
391. C2×C22⋊C4D4×C139semidirect
392. C2×C22⋊C4D4×C139semidirect
408. C24C22⋊C4×C139semidirect
472. C22×C4C22⋊C4×C139semidirect
487. C22⋊C4C22⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#534×C1392
C22×#99×C1392
#2308×C1392
C2×#342×C1392
#10972139