Finite Group Databasebeta

← C139×#10394 #48004990

Subgroups — C139×#10394 #48004990

Order 35584.

772 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2617×C139C211yesmaximal, characteristic
2#1874×C139C211yesmaximal, characteristic, complemented
3#1852×C139C211yesmaximal, characteristic, complemented
4C2×#327×C139C211yesmaximal, characteristic, complemented
5C2×#323×C139C211yesmaximal, characteristic, complemented
6#1439×C139C211yesmaximal, characteristic, complemented
7#1294×C139C211yesmaximal, characteristic, complemented
8C2×#121×C139C2211yescharacteristic
9C2×#120×C139—21no—
10C22×C4⋊C4×C139C2211yescharacteristic
11C22×C22⋊C4×C139—21no—
12C22×C22⋊C4×C139C2211yescharacteristic
13C2×#107×C139—21no—
14C2×#102×C139—21no—
15C2×C22⋊C8×C139C2211yescharacteristic
16C2×C22⋊C8×C139C2211yescharacteristic
17#397×C139—21no—
18#394×C139—21no—
19#394×C139—21no—
20#392×C139—21no—
21#386×C139—21no—
22#380×C139C2211yescharacteristic
23C2×#95×C139—21no—
24C2×#95×C139C2211yescharacteristic
25#340×C139—21no—
26#340×C139—21no—
27#327×C139—22no—
28#323×C139—22no—
29C25×C139D411yescharacteristic
30C22×D4×C139—21no—
31C22×D4×C139—21no—
32C22×D4×C139—21no—
33C22×D4×C139D411yescharacteristic
34C23×C4×C139—21no—
35C23×C4×C139—21no—
36C23×C4×C139D411yescharacteristic
37C23×C4×C139C2311yescharacteristic
38C22×C8×C139—21no—
39C22×C8×C139—21no—
40#121×C139—21no—
41#121×C139—21no—
42#121×C139—21no—
43#121×C139—21no—
44#120×C139—42no—
45#120×C139—42no—
46C2×C4⋊C4×C139—21no—
47C2×C4⋊C4×C139—21no—
48C2×C4⋊C4×C139—42no—
49C2×C4⋊C4×C139D411yescharacteristic
50C2×C4⋊C4×C139D411yescharacteristic
51C2×C4⋊C4×C139D411yescharacteristic
52C2×C22⋊C4×C139—21no—
53C2×C22⋊C4×C139—21no—
54C2×C22⋊C4×C139—21no—
55C2×C22⋊C4×C139—21no—
56C2×C22⋊C4×C139—21no—
57C2×C22⋊C4×C139—21no—
58C2×C22⋊C4×C139—21no—
59C2×C22⋊C4×C139—21no—
60C2×C22⋊C4×C139—21no—
61C2×C22⋊C4×C139—21no—
62C2×C22⋊C4×C139—21no—
63C2×C22⋊C4×C139—21no—
64C2×C22⋊C4×C139—42no—
65C2×C22⋊C4×C139—42no—
66C2×C22⋊C4×C139—42no—
67#107×C139—42no—
68#102×C139—42no—
69C22⋊C8×C139—21no—
70C22⋊C8×C139—21no—
71C22⋊C8×C139—21no—
72C22⋊C8×C139D412yescomplemented
73#95×C139—21no—
74#95×C139—21no—
75#95×C139—21no—
76#95×C139—21no—
77#95×C139—21no—
78#95×C139—42no—
79C24×C139—21no—
80C24×C139—21no—
81C24×C139—21no—
82C24×C139—21no—
83C24×C139—21no—
84C24×C139—21no—
85C24×C139—21no—
86C24×C139—41no—
87C24×C139—41no—
88C24×C139—41no—
89C24×C139—41no—
90C24×C139D812yes—
91C24×C139C2×D411yescharacteristic
92C2×D4×C139—21no—
93C2×D4×C139—21no—
94C2×D4×C139—41no—
95C2×D4×C139—41no—
96C2×D4×C139—42no—
97C2×D4×C139—42no—
98C2×D4×C139—41no—
99C2×D4×C139—41no—
100C2×D4×C139—41no—
101C2×D4×C139—41no—
102C2×D4×C139—41no—
103C2×D4×C139—41no—
104C2×D4×C139—81no—
105C2×D4×C139—81no—
106C2×D4×C139—81no—
107C2×D4×C139—81no—
108C22×C4×C139—22no—
109C22×C4×C139—22no—
110C22×C4×C139—21no—
111C22×C4×C139—21no—
112C22×C4×C139—21no—
113C22×C4×C139—21no—
114C22×C4×C139—21no—
115C22×C4×C139—21no—
116C22×C4×C139—41no—
117C22×C4×C139—41no—
118C22×C4×C139—41no—
119C22×C4×C139—41no—
120C22×C4×C139—41no—
121C22×C4×C139—41no—
122C22×C4×C139—41no—
123C22×C4×C139—41no—
124C22×C4×C139—41no—
125C22×C4×C139—41no—
126C22×C4×C139—41no—
127C22×C4×C139—41no—
128C22×C4×C139—41no—
129C22×C4×C139—41no—
130C22×C4×C139—41no—
131C22×C4×C139—41no—
132C22×C4×C139C2×D411yescharacteristic
133C22×C4×C139C2×D411yescharacteristic
134C22×C4×C139C2×D411yescharacteristic
135C22×C4×C139#4111yescharacteristic
136C22×C4×C139#4111yescharacteristic
137C22×C4×C139#4111yescharacteristic
138C2×C8×C139—22no—
139C2×C8×C139—41no—
140C2×C8×C139—41no—
141C2×C8×C139—41no—
142C2×C8×C139—41no—
143C2×C8×C139—41no—
144C4⋊C4×C139—22no—
145C4⋊C4×C139—22no—
146C4⋊C4×C139—21no—
147C4⋊C4×C139—21no—
148C4⋊C4×C139—41no—
149C4⋊C4×C139—41no—
150C4⋊C4×C139—41no—
151C4⋊C4×C139—41no—
152C22⋊C4×C139—42no—
153C22⋊C4×C139—42no—
154C22⋊C4×C139—48no—
155C22⋊C4×C139—41no—
156C22⋊C4×C139—41no—
157C22⋊C4×C139—41no—
158C22⋊C4×C139—41no—
159C22⋊C4×C139—41no—
160C22⋊C4×C139—41no—
161C22⋊C4×C139—41no—
162C22⋊C4×C139—41no—
163C22⋊C4×C139—81no—
164C22⋊C4×C139—81no—
165C23×C139—21no—
166C23×C139—21no—
167C23×C139—21no—
168C23×C139—21no—
169C23×C139—22no—
170C23×C139—22no—
171C23×C139—22no—
172C23×C139—42no—
173C23×C139—42no—
174C23×C139—42no—
175C23×C139—42no—
176C23×C139—42no—
177C23×C139—42no—
178C23×C139—41no—
179C23×C139—41no—
180C23×C139—41no—
181C23×C139—41no—
182C23×C139—41no—
183C23×C139—41no—
184C23×C139—41no—
185C23×C139—41no—
186C23×C139—41no—
187C23×C139—41no—
188C23×C139—41no—
189C23×C139—41no—
190C23×C139—41no—
191C23×C139—41no—
192C23×C139—41no—
193C23×C139—81no—
194C23×C139—81no—
195C23×C139—81no—
196C23×C139—81no—
197C23×C139—81no—
198C23×C139—81no—
199C23×C139#12011yescharacteristic
200C23×C139#12111yescharacteristic
201C23×C139#12311yescharacteristic
202C23×C139C2×D811yescharacteristic
203C23×C139#13511yescharacteristic
204C23×C139AGL(1,ℤ/8)11yescharacteristic
205C23×C139#13711yescharacteristic
206D4×C139—42no—
207D4×C139—81no—
208D4×C139—84no—
209D4×C139—84no—
210D4×C139—81no—
211D4×C139—81no—
212D4×C139—81no—
213D4×C139—81no—
214C2×C4×C139—21no—
215C2×C4×C139—21no—
216C2×C4×C139—21no—
217C2×C4×C139—21no—
218C2×C4×C139—41no—
219C2×C4×C139—41no—
220C2×C4×C139—41no—
221C2×C4×C139—41no—
222C2×C4×C139—42no—
223C2×C4×C139—42no—
224C2×C4×C139—42no—
225C2×C4×C139—42no—
226C2×C4×C139—42no—
227C2×C4×C139—42no—
228C2×C4×C139—41no—
229C2×C4×C139—41no—
230C2×C4×C139—41no—
231C2×C4×C139—41no—
232C2×C4×C139—41no—
233C2×C4×C139—41no—
234C2×C4×C139—41no—
235C2×C4×C139—41no—
236C2×C4×C139—41no—
237C2×C4×C139—41no—
238C2×C4×C139—42no—
239C2×C4×C139—41no—
240C2×C4×C139—41no—
241C2×C4×C139—81no—
242C2×C4×C139—81no—
243C2×C4×C139—81no—
244C2×C4×C139—81no—
245C2×C4×C139—81no—
246C2×C4×C139—81no—
247C2×C4×C139—81no—
248C2×C4×C139—81no—
249C2×C4×C139—81no—
250C2×C4×C139#12111yescharacteristic
251C2×C4×C139#12111yescharacteristic
252C2×C4×C139#12311yescharacteristic
253C2×C4×C139#12411yescharacteristic
254C8×C139—42no—
255C8×C139—81no—
256C22×C139—21no—
257C22×C139—21no—
258C22×C139—21no—
259C22×C139—21no—
260C22×C139—21no—
261C22×C139—21no—
262C22×C139—21no—
263C22×C139—21no—
264C22×C139—21no—
265C22×C139—21no—
266C22×C139—21no—
267C22×C139—21no—
268C22×C139—44no—
269C22×C139—42no—
270C22×C139—42no—
271C22×C139—42no—
272C22×C139—82no—
273C22×C139—82no—
274C22×C139—82no—
275C22×C139—81no—
276C22×C139—81no—
277C22×C139—81no—
278C22×C139—81no—
279C22×C139—81no—
280C22×C139—81no—
281C22×C139—81no—
282C22×C139—81no—
283C22×C139—81no—
284C22×C139—81no—
285C22×C139—81no—
286C22×C139#39411yescharacteristic
287C22×C139#44711yescharacteristic
288C22×C139#45211yescharacteristic
289C22×C139#45311yescharacteristic
290C22×C139#45511yescharacteristic
291C22×C139B(4,𝔽2)11yescharacteristic
292C22×C139#45811yescharacteristic
293C22×C139#46611yescharacteristic
294C22×C139#46811yescharacteristic
295C22×C139#48011yescharacteristic
296C22×C139#48211yescharacteristic
297C4×C139—21no—
298C4×C139—21no—
299C4×C139—21no—
300C4×C139—21no—
301C4×C139—82no—
302C4×C139—82no—
303C4×C139—81no—
304C4×C139—81no—
305C4×C139—81no—
306C4×C139—81no—
307C2×C139—21no—
308C2×C139—21no—
309C2×C139—21no—
310C2×C139—21no—
311C2×C139—82no—
312C2×C139—161no—
313C2×C139#159511yescharacteristic
314C2×C139#160611yescharacteristic
315C2×C139#160711yescharacteristic
316C2×C139#161811yescharacteristic
317C2×C139#203311yescharacteristic
318C2×C139#203711yescharacteristic
319C2×C139#204411yescharacteristic
320#10394C13911yesmaximal, characteristic, direct product factor, Sylow
321C139#1039411yescharacteristic, direct product factor, Sylow
322#2617C2×C13911yescharacteristic
323#1874C2×C13911yescharacteristic, complemented
324#1852C2×C13911yescharacteristic, complemented
325C2×#327C2×C13911yescharacteristic, complemented
326C2×#323C2×C13911yescharacteristic, complemented
327#1439C2×C13911yescharacteristic, complemented
328#1294C2×C13911yescharacteristic, complemented
329C2×#121C22×C13911yescharacteristic
330C2×#120—21no—
331C22×C4⋊C4C22×C13911yescharacteristic
332C22×C22⋊C4—21no—
333C22×C22⋊C4C22×C13911yescharacteristic
334C2×#107—21no—
335C2×#102—21no—
336C2×C22⋊C8C22×C13911yescharacteristic
337C2×C22⋊C8C22×C13911yescharacteristic
338#397—21no—
339#394—21no—
340#394—21no—
341#392—21no—
342#386—21no—
343#380C22×C13911yescharacteristic
344C2×#95—21no—
345C2×#95C22×C13911yescharacteristic
346#340—21no—
347#340—21no—
348#327—22no—
349#323—22no—
350C25D4×C13911yescharacteristic
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4D4×C13911yescharacteristic
355C23×C4—21no—
356C23×C4—21no—
357C23×C4D4×C13911yescharacteristic
358C23×C4C23×C13911yescharacteristic
359C22×C8—21no—
360C22×C8—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#120—42no—
366#120—42no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4D4×C13911yescharacteristic
371C2×C4⋊C4D4×C13911yescharacteristic
372C2×C4⋊C4D4×C13911yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388#107—42no—
389#102—42no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8D4×C13912yescomplemented
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—42no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24D8×C13912yes—
412C24C2×D4×C13911yescharacteristic
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C2×D4—81no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C13911yescharacteristic
454C22×C4C2×D4×C13911yescharacteristic
455C22×C4C2×D4×C13911yescharacteristic
456C22×C4#41×C13911yescharacteristic
457C22×C4#41×C13911yescharacteristic
458C22×C4#41×C13911yescharacteristic
459C2×C8—22no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—48no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—81no—
515C23—81no—
516C23—81no—
517C23—81no—
518C23—81no—
519C23—81no—
520C23#120×C13911yescharacteristic
521C23#121×C13911yescharacteristic
522C23#123×C13911yescharacteristic
523C23C2×D8×C13911yescharacteristic
524C23#135×C13911yescharacteristic
525C23AGL(1,ℤ/8)×C13911yescharacteristic
526C23#137×C13911yescharacteristic
527D4—42no—
528D4—81no—
529D4—84no—
530D4—84no—
531D4—81no—
532D4—81no—
533D4—81no—
534D4—81no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4#121×C13911yescharacteristic
572C2×C4#121×C13911yescharacteristic
573C2×C4#123×C13911yescharacteristic
574C2×C4#124×C13911yescharacteristic
575C8—42no—
576C8—81no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#394×C13911yescharacteristic
608C22#447×C13911yescharacteristic
609C22#452×C13911yescharacteristic
610C22#453×C13911yescharacteristic
611C22#455×C13911yescharacteristic
612C22B(4,𝔽2)×C13911yescharacteristic
613C22#458×C13911yescharacteristic
614C22#466×C13911yescharacteristic
615C22#468×C13911yescharacteristic
616C22#480×C13911yescharacteristic
617C22#482×C13911yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—82no—
623C4—81no—
624C4—81no—
625C4—82no—
626C4—81no—
627C4—81no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—161no—
634C2#1595×C13911yescharacteristic
635C2#1606×C13911yescharacteristic
636C2#1607×C13911yescharacteristic
637C2#1618×C13911yescharacteristic
638C2#2033×C13911yescharacteristic
639C2#2037×C13911yescharacteristic
640C2#2044×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#120
commutator, Frattini, cosocleC23×C4C23×C139
prime radical#2617×C139C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1874×C139C2semidirect
3. #1852×C139C2semidirect
4. C2×#327×C139C2semidirect
5. C2×#323×C139C2semidirect
6. #1439×C139C2semidirect
7. #1294×C139C2semidirect
72. C22⋊C8×C139D4semidirect
320. #10394C139direct (N × H)
321. C139#10394direct (N × H)
323. #1874C2×C139semidirect
324. #1852C2×C139semidirect
325. C2×#327C2×C139semidirect
326. C2×#323C2×C139semidirect
327. #1439C2×C139semidirect
328. #1294C2×C139semidirect
393. C22⋊C8D4×C139semidirect

Maximal subgroups

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

subgroupindex
#2617×C1392
#1874×C1392
#1852×C1392
C2×#327×C1392
C2×#323×C1392
#1439×C1392
#1294×C1392
#10394139