Finite Group Databasebeta

← C139×#13348 #48007944

Subgroups — C139×#13348 #48007944

Order 35584.

900 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×B(4,𝔽2)×C139C211yesmaximal, characteristic
2C2×#455×C139C211yesmaximal, characteristic, complemented
3#2684×C139C211yesmaximal, characteristic, complemented
4C2×#354×C139C211yesmaximal, characteristic, complemented
5C2×AΣL(1,𝔽16)×C139C211yesmaximal, characteristic, complemented
6#1790×C139C211yesmaximal, characteristic, complemented
7#1390×C139C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C139C2211yescharacteristic
9C2×#137×C139—21no—
10C2×#124×C139C2211yescharacteristic
11C2×#120×C139—21no—
12C2×#120×C139C2211yescharacteristic
13B(4,𝔽2)×C139—22no—
14B(4,𝔽2)×C139—22no—
15#455×C139—22no—
16#455×C139—22no—
17C2×#104×C139—21no—
18C2×#100×C139C2211yescharacteristic
19C2×#99×C139—21no—
20C2×#99×C139—21no—
21C2×#99×C139C2211yescharacteristic
22C2×#99×C139C2211yescharacteristic
23#397×C139—21no—
24#394×C139—21no—
25#393×C139—21no—
26#388×C139—21no—
27#386×C139—21no—
28#386×C139—21no—
29#386×C139C2211yescharacteristic
30#379×C139—21no—
31#354×C139—22no—
32AΣL(1,𝔽16)×C139—22no—
33C25×C139D411yescharacteristic
34H(5,𝔽2)×C139—21no—
35H(5,𝔽2)×C139—21no—
36H(5,𝔽2)×C139—21no—
37H(5,𝔽2)×C139—42no—
38H(5,𝔽2)×C139D412yes—
39C2×#41×C139—21no—
40C2×#41×C139—41no—
41C22×Q8×C139D411yescharacteristic, complemented
42C22×D4×C139—21no—
43C22×D4×C139—21no—
44C22×D4×C139—21no—
45C22×D4×C139—41no—
46C22×D4×C139—41no—
47C22×D4×C139C2311yescharacteristic
48C23×C4×C139D411yescharacteristic, complemented
49#137×C139—24no—
50#137×C139—42no—
51C2×Q16×C139—41no—
52C2×SD16×C139—41no—
53C2×M16×C139—21no—
54#124×C139—21no—
55#124×C139—21no—
56#124×C139—21no—
57#124×C139—21no—
58#120×C139—24no—
59#120×C139—21no—
60#120×C139—21no—
61#120×C139—21no—
62#120×C139—21no—
63#120×C139—42no—
64C2×C4⋊C4×C139—21no—
65C2×C22⋊C4×C139—21no—
66C2×C22⋊C4×C139—21no—
67C2×C22⋊C4×C139—21no—
68C2×C22⋊C4×C139—21no—
69C2×C22⋊C4×C139—21no—
70C2×C22⋊C4×C139—21no—
71C2×C22⋊C4×C139—21no—
72C2×C22⋊C4×C139—21no—
73C2×C22⋊C4×C139—21no—
74C2×C22⋊C4×C139—21no—
75C2×C22⋊C4×C139—41no—
76C2×C22⋊C4×C139—41no—
77C2×C22⋊C4×C139D411yescharacteristic
78C2×C22⋊C4×C139D411yescharacteristic, complemented
79C2×C42×C139D411yescharacteristic, complemented
80#104×C139—24no—
81#100×C139—21no—
82#100×C139D412yescomplemented
83#99×C139—24no—
84#99×C139—21no—
85#99×C139—21no—
86#99×C139—21no—
87#99×C139—42no—
88#99×C139D412yes—
89#95×C139—21no—
90#95×C139—21no—
91#95×C139—21no—
92#95×C139—21no—
93#95×C139—41no—
94C24×C139—21no—
95C24×C139—21no—
96C24×C139—21no—
97C24×C139—21no—
98C24×C139—21no—
99C24×C139—41no—
100C24×C139—41no—
101C24×C139—42no—
102C24×C139—81no—
103C24×C139C2×D411yescharacteristic
104C24×C139C2×D411yescharacteristic
105#41×C139—22no—
106#41×C139—22no—
107#41×C139—42no—
108#41×C139—41no—
109#41×C139—42no—
110#41×C139—42no—
111#41×C139—42no—
112#41×C139—41no—
113C2×Q8×C139—21no—
114C2×Q8×C139—21no—
115C2×Q8×C139—21no—
116C2×Q8×C139—41no—
117C2×Q8×C139—41no—
118C2×D4×C139—21no—
119C2×D4×C139—22no—
120C2×D4×C139—22no—
121C2×D4×C139—22no—
122C2×D4×C139—22no—
123C2×D4×C139—41no—
124C2×D4×C139—41no—
125C2×D4×C139—42no—
126C2×D4×C139—42no—
127C2×D4×C139—41no—
128C2×D4×C139—41no—
129C2×D4×C139—41no—
130C2×D4×C139—41no—
131C2×D4×C139—42no—
132C2×D4×C139—42no—
133C2×D4×C139—41no—
134C2×D4×C139—41no—
135C2×D4×C139—41no—
136C2×D4×C139—44no—
137C2×D4×C139—42no—
138C2×D4×C139—41no—
139C2×D4×C139—41no—
140C2×D4×C139—81no—
141C2×D4×C139—82no—
142C2×D4×C139—82no—
143C2×D4×C139C2×D411yescharacteristic
144C2×D4×C139C2×D411yescharacteristic
145C2×D4×C139C2×D411yescharacteristic
146C2×D4×C139#4111yescharacteristic
147C22×C4×C139—21no—
148C22×C4×C139—21no—
149C22×C4×C139—21no—
150C22×C4×C139—21no—
151C22×C4×C139—21no—
152C22×C4×C139—21no—
153C22×C4×C139—21no—
154C22×C4×C139—41no—
155C22×C4×C139—41no—
156C22×C4×C139—41no—
157C22×C4×C139—41no—
158C22×C4×C139—81no—
159C22×C4×C139C2×D411yescharacteristic
160Q16×C139—44no—
161SD16×C139—44no—
162M16×C139—22no—
163M16×C139—41no—
164C2×C8×C139—41no—
165C4⋊C4×C139—81no—
166C22⋊C4×C139—21no—
167C22⋊C4×C139—22no—
168C22⋊C4×C139—21no—
169C22⋊C4×C139—44no—
170C22⋊C4×C139—42no—
171C22⋊C4×C139—41no—
172C22⋊C4×C139—41no—
173C22⋊C4×C139—41no—
174C22⋊C4×C139—41no—
175C22⋊C4×C139—41no—
176C22⋊C4×C139—41no—
177C22⋊C4×C139—41no—
178C22⋊C4×C139—41no—
179C22⋊C4×C139—41no—
180C22⋊C4×C139—41no—
181C22⋊C4×C139—81no—
182C22⋊C4×C139—81no—
183C22⋊C4×C139—81no—
184C22⋊C4×C139—81no—
185C22⋊C4×C139—82no—
186C42×C139—21no—
187C42×C139—21no—
188C23×C139—21no—
189C23×C139—21no—
190C23×C139—21no—
191C23×C139—21no—
192C23×C139—22no—
193C23×C139—22no—
194C23×C139—22no—
195C23×C139—41no—
196C23×C139—41no—
197C23×C139—41no—
198C23×C139—41no—
199C23×C139—42no—
200C23×C139—41no—
201C23×C139—41no—
202C23×C139—41no—
203C23×C139—41no—
204C23×C139—41no—
205C23×C139—42no—
206C23×C139—42no—
207C23×C139—41no—
208C23×C139—41no—
209C23×C139—41no—
210C23×C139—41no—
211C23×C139—81no—
212C23×C139—82no—
213C23×C139—81no—
214C23×C139—82no—
215C23×C139—84no—
216C23×C139—81no—
217C23×C139—81no—
218C23×C139—81no—
219C23×C139—81no—
220C23×C139—81no—
221C23×C139#12011yescharacteristic
222C23×C139#12011yescharacteristic
223C23×C139#12111yescharacteristic
224C23×C139#12111yescharacteristic
225C23×C139#12711yescharacteristic
226Q8×C139—22no—
227Q8×C139—41no—
228Q8×C139—42no—
229Q8×C139—81no—
230D4×C139—22no—
231D4×C139—41no—
232D4×C139—41no—
233D4×C139—41no—
234D4×C139—41no—
235D4×C139—41no—
236D4×C139—42no—
237D4×C139—42no—
238D4×C139—42no—
239D4×C139—42no—
240D4×C139—42no—
241D4×C139—42no—
242D4×C139—82no—
243D4×C139—82no—
244D4×C139—88no—
245C2×C4×C139—21no—
246C2×C4×C139—21no—
247C2×C4×C139—22no—
248C2×C4×C139—22no—
249C2×C4×C139—42no—
250C2×C4×C139—42no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—42no—
255C2×C4×C139—41no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—41no—
260C2×C4×C139—41no—
261C2×C4×C139—41no—
262C2×C4×C139—41no—
263C2×C4×C139—42no—
264C2×C4×C139—41no—
265C2×C4×C139—41no—
266C2×C4×C139—41no—
267C2×C4×C139—41no—
268C2×C4×C139—41no—
269C2×C4×C139—41no—
270C2×C4×C139—41no—
271C2×C4×C139—81no—
272C2×C4×C139—81no—
273C2×C4×C139—81no—
274C2×C4×C139—81no—
275C2×C4×C139—81no—
276C2×C4×C139—81no—
277C2×C4×C139#12011yescharacteristic
278C2×C4×C139#12111yescharacteristic
279C8×C139—42no—
280C22×C139—21no—
281C22×C139—21no—
282C22×C139—21no—
283C22×C139—21no—
284C22×C139—21no—
285C22×C139—21no—
286C22×C139—41no—
287C22×C139—41no—
288C22×C139—41no—
289C22×C139—41no—
290C22×C139—42no—
291C22×C139—42no—
292C22×C139—41no—
293C22×C139—41no—
294C22×C139—41no—
295C22×C139—41no—
296C22×C139—44no—
297C22×C139—42no—
298C22×C139—42no—
299C22×C139—81no—
300C22×C139—81no—
301C22×C139—81no—
302C22×C139—81no—
303C22×C139—82no—
304C22×C139—82no—
305C22×C139—82no—
306C22×C139—82no—
307C22×C139—82no—
308C22×C139—81no—
309C22×C139—81no—
310C22×C139—81no—
311C22×C139—81no—
312C22×C139—161no—
313C22×C139—161no—
314C22×C139#39211yescharacteristic
315C22×C139B(4,𝔽2)11yescharacteristic
316C22×C139B(4,𝔽2)11yescharacteristic
317C4×C139—21no—
318C4×C139—21no—
319C4×C139—42no—
320C4×C139—81no—
321C4×C139—81no—
322C4×C139—81no—
323C4×C139—82no—
324C4×C139—81no—
325C4×C139—81no—
326C4×C139—161no—
327C2×C139—21no—
328C2×C139—21no—
329C2×C139—41no—
330C2×C139—41no—
331C2×C139—41no—
332C2×C139—41no—
333C2×C139—82no—
334C2×C139—82no—
335C2×C139#202111yescharacteristic
336C2×C139#219711yescharacteristic
337C2×C139#219911yescharacteristic
338#13348C13911yesmaximal, characteristic, direct product factor, Sylow
339C139#1334811yescharacteristic, direct product factor, Sylow
340C2×B(4,𝔽2)C2×C13911yescharacteristic
341C2×#455C2×C13911yescharacteristic, complemented
342#2684C2×C13911yescharacteristic, complemented
343C2×#354C2×C13911yescharacteristic, complemented
344C2×AΣL(1,𝔽16)C2×C13911yescharacteristic, complemented
345#1790C2×C13911yescharacteristic, complemented
346#1390C2×C13911yescharacteristic, complemented
347C2×H(5,𝔽2)C22×C13911yescharacteristic
348C2×#137—21no—
349C2×#124C22×C13911yescharacteristic
350C2×#120—21no—
351C2×#120C22×C13911yescharacteristic
352B(4,𝔽2)—22no—
353B(4,𝔽2)—22no—
354#455—22no—
355#455—22no—
356C2×#104—21no—
357C2×#100C22×C13911yescharacteristic
358C2×#99—21no—
359C2×#99—21no—
360C2×#99C22×C13911yescharacteristic
361C2×#99C22×C13911yescharacteristic
362#397—21no—
363#394—21no—
364#393—21no—
365#388—21no—
366#386—21no—
367#386—21no—
368#386C22×C13911yescharacteristic
369#379—21no—
370#354—22no—
371AΣL(1,𝔽16)—22no—
372C25D4×C13911yescharacteristic
373H(5,𝔽2)—21no—
374H(5,𝔽2)—21no—
375H(5,𝔽2)—21no—
376H(5,𝔽2)—42no—
377H(5,𝔽2)D4×C13912yes—
378C2×#41—21no—
379C2×#41—41no—
380C22×Q8D4×C13911yescharacteristic, complemented
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—21no—
384C22×D4—41no—
385C22×D4—41no—
386C22×D4C23×C13911yescharacteristic
387C23×C4D4×C13911yescharacteristic, complemented
388#137—24no—
389#137—42no—
390C2×Q16—41no—
391C2×SD16—41no—
392C2×M16—21no—
393#124—21no—
394#124—21no—
395#124—21no—
396#124—21no—
397#120—24no—
398#120—21no—
399#120—21no—
400#120—21no—
401#120—21no—
402#120—42no—
403C2×C4⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—41no—
415C2×C22⋊C4—41no—
416C2×C22⋊C4D4×C13911yescharacteristic
417C2×C22⋊C4D4×C13911yescharacteristic, complemented
418C2×C42D4×C13911yescharacteristic, complemented
419#104—24no—
420#100—21no—
421#100D4×C13912yescomplemented
422#99—24no—
423#99—21no—
424#99—21no—
425#99—21no—
426#99—42no—
427#99D4×C13912yes—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—41no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—41no—
439C24—41no—
440C24—42no—
441C24—81no—
442C24C2×D4×C13911yescharacteristic
443C24C2×D4×C13911yescharacteristic
444#41—22no—
445#41—22no—
446#41—42no—
447#41—41no—
448#41—42no—
449#41—42no—
450#41—42no—
451#41—41no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—44no—
476C2×D4—42no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—81no—
480C2×D4—82no—
481C2×D4—82no—
482C2×D4C2×D4×C13911yescharacteristic
483C2×D4C2×D4×C13911yescharacteristic
484C2×D4C2×D4×C13911yescharacteristic
485C2×D4#41×C13911yescharacteristic
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—81no—
498C22×C4C2×D4×C13911yescharacteristic
499Q16—44no—
500SD16—44no—
501M16—22no—
502M16—41no—
503C2×C8—41no—
504C4⋊C4—81no—
505C22⋊C4—21no—
506C22⋊C4—22no—
507C22⋊C4—21no—
508C22⋊C4—44no—
509C22⋊C4—42no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—81no—
521C22⋊C4—81no—
522C22⋊C4—81no—
523C22⋊C4—81no—
524C22⋊C4—82no—
525C42—21no—
526C42—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—42no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—81no—
551C23—82no—
552C23—81no—
553C23—82no—
554C23—84no—
555C23—81no—
556C23—81no—
557C23—81no—
558C23—81no—
559C23—81no—
560C23#120×C13911yescharacteristic
561C23#120×C13911yescharacteristic
562C23#121×C13911yescharacteristic
563C23#121×C13911yescharacteristic
564C23#127×C13911yescharacteristic
565Q8—22no—
566Q8—41no—
567Q8—42no—
568Q8—81no—
569D4—22no—
570D4—41no—
571D4—41no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—42no—
576D4—42no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—42no—
581D4—82no—
582D4—82no—
583D4—88no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—81no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4#120×C13911yescharacteristic
617C2×C4#121×C13911yescharacteristic
618C8—42no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—42no—
630C22—42no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—44no—
636C22—42no—
637C22—42no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—82no—
643C22—82no—
644C22—82no—
645C22—82no—
646C22—82no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—161no—
652C22—161no—
653C22#392×C13911yescharacteristic
654C22B(4,𝔽2)×C13911yescharacteristic
655C22B(4,𝔽2)×C13911yescharacteristic
656C4—21no—
657C4—21no—
658C4—42no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—82no—
663C4—81no—
664C4—81no—
665C4—161no—
666C2—21no—
667C2—21no—
668C2—41no—
669C2—41no—
670C2—41no—
671C2—41no—
672C2—82no—
673C2—82no—
674C2#2021×C13911yescharacteristic
675C2#2197×C13911yescharacteristic
676C2#2199×C13911yescharacteristic
subgroupG/H
center, socleC22×C139B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C139
prime radicalC2×B(4,𝔽2)×C139C2
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C139 ◁ C22×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#455×C139C2semidirect
3. #2684×C139C2semidirect
4. C2×#354×C139C2semidirect
5. C2×AΣL(1,𝔽16)×C139C2semidirect
6. #1790×C139C2semidirect
7. #1390×C139C2semidirect
41. C22×Q8×C139D4semidirect
48. C23×C4×C139D4semidirect
78. C2×C22⋊C4×C139D4semidirect
79. C2×C42×C139D4semidirect
82. #100×C139D4semidirect
338. #13348C139direct (N × H)
339. C139#13348direct (N × H)
341. C2×#455C2×C139semidirect
342. #2684C2×C139semidirect
343. C2×#354C2×C139semidirect
344. C2×AΣL(1,𝔽16)C2×C139semidirect
345. #1790C2×C139semidirect
346. #1390C2×C139semidirect
380. C22×Q8D4×C139semidirect
387. C23×C4D4×C139semidirect
417. C2×C22⋊C4D4×C139semidirect
418. C2×C42D4×C139semidirect
421. #100D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×B(4,𝔽2)×C1392
C2×#455×C1392
#2684×C1392
C2×#354×C1392
C2×AΣL(1,𝔽16)×C1392
#1790×C1392
#1390×C1392
#13348139