Finite Group Databasebeta

← C139×#24468 #48019064

Subgroups — C139×#24468 #48019064

Order 35584.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C139C211yesmaximal, characteristic, complemented
2#3055×C139C211yesmaximal, characteristic, complemented
3C2×#453×C139C211yesmaximal, characteristic, complemented
4#3006×C139C211yesmaximal, characteristic, complemented
5C2×#421×C139C211yesmaximal, characteristic, complemented
6#2619×C139C211yesmaximal, characteristic, complemented
7#2040×C139C211yesmaximal, characteristic, complemented
8#2037×C139C211yesmaximal, characteristic, complemented
9#2006×C139C211yesmaximal, characteristic, complemented
10#2002×C139C211yesmaximal, characteristic, complemented
11#1900×C139C211yesmaximal, characteristic, complemented
12#1897×C139C211yesmaximal, characteristic, complemented
13#1883×C139C211yesmaximal, characteristic, complemented
14#1860×C139C211yesmaximal, characteristic, complemented
15#1792×C139C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
21C22×M16×C139C2211yescharacteristic, complemented
22#550×C139—21no—
23#548×C139—21no—
24#546×C139—21no—
25#546×C139—22no—
26D42×C139—22no—
27D42×C139—21no—
28#537×C139—21no—
29#537×C139C2211yescharacteristic
30#535×C139—21no—
31#535×C139C2211yescharacteristic
32C2×#127×C139C2211yescharacteristic, complemented
33#525×C139—21no—
34#525×C139C2211yescharacteristic
35C2×#121×C139—21no—
36C2×#121×C139C2211yescharacteristic
37C2×#121×C139C2211yescharacteristic, complemented
38#520×C139C2211yescharacteristic
39C2×#117×C139C2211yescharacteristic, complemented
40#469×C139—21no—
41#468×C139—21no—
42#466×C139—21no—
43#465×C139—21no—
44#453×C139—24no—
45#449×C139—21no—
46#449×C139—21no—
47#448×C139—21no—
48#447×C139—21no—
49#428×C139C2211yescharacteristic, complemented
50#421×C139—24no—
51C2×#104×C139C2211yescharacteristic
52C2×#104×C139C2211yescharacteristic
53C2×#104×C139C2211yescharacteristic, complemented
54C2×#104×C139C2211yescharacteristic, complemented
55C2×#104×C139C2211yescharacteristic, complemented
56C2×#104×C139C2211yescharacteristic, complemented
57#418×C139C2211yescharacteristic, complemented
58#417×C139C2211yescharacteristic
59#417×C139C2211yescharacteristic, complemented
60#417×C139C2211yescharacteristic, complemented
61C2×#100×C139C2211yescharacteristic, complemented
62C2×#100×C139C2211yescharacteristic, complemented
63#407×C139C2211yescharacteristic, complemented
64#394×C139—22no—
65#392×C139—22no—
66#390×C139C2211yescharacteristic, complemented
67#390×C139C2211yescharacteristic, complemented
68#382×C139C2211yescharacteristic, complemented
69#343×C139C2211yescharacteristic, complemented
70#343×C139C2211yescharacteristic, complemented
71#339×C139C2211yescharacteristic, complemented
72#339×C139C2211yescharacteristic, complemented
73H(5,𝔽2)×C139—22no—
74H(5,𝔽2)×C139—22no—
75H(5,𝔽2)×C139—41no—
76H(5,𝔽2)×C139—41no—
77C2×#41×C139—21no—
78C2×#41×C139—21no—
79C2×#41×C139—21no—
80C2×#41×C139—21no—
81C2×#41×C139—22no—
82C2×#41×C139—22no—
83C2×#41×C139—41no—
84C2×#41×C139—41no—
85C2×#41×C139D411yescharacteristic, complemented
86C2×#41×C139D411yescharacteristic, complemented
87C2×#41×C139C2311yescharacteristic
88C2×#41×C139C2311yescharacteristic
89C2×#41×C139C2311yescharacteristic
90C22×Q8×C139D411yescharacteristic, complemented
91C22×D4×C139—21no—
92C22×D4×C139—22no—
93C22×D4×C139—22no—
94C22×D4×C139—21no—
95C22×D4×C139—21no—
96C22×D4×C139—21no—
97C22×D4×C139—22no—
98C22×D4×C139D412yes—
99C22×D4×C139D411yescharacteristic, complemented
100C22×D4×C139C2311yescharacteristic
101C22×D4×C139C2311yescharacteristic
102C23×C4×C139—21no—
103C23×C4×C139C2311yescharacteristic
104AGL(1,ℤ/8)×C139—22no—
105AGL(1,ℤ/8)×C139—22no—
106AGL(1,ℤ/8)×C139—22no—
107AGL(1,ℤ/8)×C139—41no—
108AGL(1,ℤ/8)×C139—41no—
109AGL(1,ℤ/8)×C139—41no—
110C2×SD16×C139—21no—
111C2×SD16×C139—21no—
112C2×SD16×C139—21no—
113C2×D8×C139—21no—
114C2×D8×C139—21no—
115C2×D8×C139—21no—
116C2×M16×C139—21no—
117C2×M16×C139—22no—
118C2×M16×C139—41no—
119C2×M16×C139C2311yescharacteristic
120C2×M16×C139C2311yescharacteristic
121C2×M16×C139C2311yescharacteristic
122C2×M16×C139C2311yescharacteristic
123C22×C8×C139—21no—
124#127×C139—22no—
125#127×C139—21no—
126#127×C139—22no—
127#127×C139—41no—
128#124×C139—22no—
129#124×C139—21no—
130#123×C139—22no—
131#123×C139—21no—
132C22⋊Q8×C139—22no—
133C22⋊Q8×C139—21no—
134C22⋊Q8×C139—21no—
135C22⋊Q8×C139D411yescharacteristic, complemented
136C22⋊Q8×C139D411yescharacteristic, complemented
137#121×C139—22no—
138#121×C139—22no—
139#121×C139—22no—
140#121×C139—22no—
141#121×C139—22no—
142#121×C139—21no—
143#121×C139—21no—
144#121×C139—21no—
145#121×C139—21no—
146#121×C139—21no—
147#121×C139—21no—
148#121×C139—22no—
149#121×C139—21no—
150#121×C139—21no—
151#121×C139—21no—
152#121×C139—21no—
153#121×C139—21no—
154#121×C139—21no—
155#121×C139D411yescharacteristic, complemented
156#121×C139D411yescharacteristic, complemented
157#120×C139—22no—
158#120×C139—22no—
159#120×C139—22no—
160#120×C139—21no—
161#120×C139—22no—
162C4×Q8×C139—21no—
163C4×D4×C139—22no—
164C4×D4×C139—22no—
165C4×D4×C139—21no—
166C4×D4×C139—22no—
167C4×D4×C139—21no—
168C4×D4×C139—21no—
169#117×C139—21no—
170#117×C139—22no—
171#117×C139—41no—
172#117×C139C2311yescharacteristic
173C2×C4⋊C4×C139—21no—
174C2×C4⋊C4×C139—21no—
175C2×C4⋊C4×C139C2311yescharacteristic
176C2×C4⋊C4×C139C2311yescharacteristic
177C2×C22⋊C4×C139—22no—
178C2×C22⋊C4×C139—21no—
179C2×C22⋊C4×C139—21no—
180C2×C22⋊C4×C139—22no—
181C2×C22⋊C4×C139—22no—
182C2×C22⋊C4×C139D412yes—
183C2×C42×C139C2311yescharacteristic
184C2×C42×C139C2311yescharacteristic
185#107×C139—21no—
186#106×C139—21no—
187#104×C139—22no—
188#104×C139—22no—
189#104×C139—22no—
190#104×C139—22no—
191#104×C139—41no—
192#104×C139D414yescomplemented
193#103×C139—21no—
194#103×C139—21no—
195#103×C139—21no—
196#102×C139—21no—
197#102×C139—21no—
198#102×C139—21no—
199#102×C139—21no—
200#102×C139—21no—
201#100×C139—22no—
202#100×C139—41no—
203C22⋊C8×C139—21no—
204C22⋊C8×C139—21no—
205#95×C139—22no—
206C24×C139—22no—
207C24×C139—21no—
208C24×C139—21no—
209C24×C139C2×D412yes—
210C24×C139C2×D411yescharacteristic
211#41×C139—21no—
212#41×C139—21no—
213#41×C139—22no—
214#41×C139—22no—
215#41×C139—21no—
216#41×C139—21no—
217#41×C139—21no—
218#41×C139—21no—
219#41×C139—21no—
220#41×C139—21no—
221#41×C139—21no—
222#41×C139—21no—
223#41×C139—42no—
224#41×C139—42no—
225#41×C139—41no—
226#41×C139—41no—
227#41×C139—42no—
228#41×C139—42no—
229#41×C139—42no—
230#41×C139—42no—
231#41×C139—42no—
232#41×C139—42no—
233#41×C139C2×D412yes—
234#41×C139#4112yes—
235C2×Q8×C139—21no—
236C2×Q8×C139—22no—
237C2×Q8×C139—41no—
238C2×Q8×C139C2×D411yescharacteristic
239C2×Q8×C139C2×D411yescharacteristic
240C2×Q8×C139C2×D411yescharacteristic
241C2×D4×C139—21no—
242C2×D4×C139—22no—
243C2×D4×C139—22no—
244C2×D4×C139—22no—
245C2×D4×C139—22no—
246C2×D4×C139—21no—
247C2×D4×C139—21no—
248C2×D4×C139—21no—
249C2×D4×C139—21no—
250C2×D4×C139—21no—
251C2×D4×C139—22no—
252C2×D4×C139—22no—
253C2×D4×C139—22no—
254C2×D4×C139—21no—
255C2×D4×C139—22no—
256C2×D4×C139—21no—
257C2×D4×C139—21no—
258C2×D4×C139—21no—
259C2×D4×C139—21no—
260C2×D4×C139—21no—
261C2×D4×C139—21no—
262C2×D4×C139—21no—
263C2×D4×C139—21no—
264C2×D4×C139—21no—
265C2×D4×C139—21no—
266C2×D4×C139—21no—
267C2×D4×C139—21no—
268C2×D4×C139—21no—
269C2×D4×C139—41no—
270C2×D4×C139—42no—
271C2×D4×C139—42no—
272C2×D4×C139—44no—
273C2×D4×C139—42no—
274C2×D4×C139—42no—
275C2×D4×C139—44no—
276C2×D4×C139—44no—
277C2×D4×C139—42no—
278C2×D4×C139—42no—
279C2×D4×C139—41no—
280C2×D4×C139—41no—
281C2×D4×C139—82no—
282C2×D4×C139—82no—
283C2×D4×C139—82no—
284C2×D4×C139—82no—
285C2×D4×C139—84no—
286C2×D4×C139C2×D411yescharacteristic
287C2×D4×C139C2×D411yescharacteristic
288C2×D4×C139C2×D411yescharacteristic
289C22×C4×C139—21no—
290C22×C4×C139—21no—
291C22×C4×C139—21no—
292C22×C4×C139—21no—
293C22×C4×C139—21no—
294C22×C4×C139—22no—
295C22×C4×C139—21no—
296C22×C4×C139—21no—
297C22×C4×C139—22no—
298C22×C4×C139—21no—
299C22×C4×C139—21no—
300C22×C4×C139—21no—
301C22×C4×C139—21no—
302C22×C4×C139—21no—
303C22×C4×C139—21no—
304C22×C4×C139—42no—
305C22×C4×C139—42no—
306C22×C4×C139C2×D411yescharacteristic
307C22×C4×C139C2×D411yescharacteristic
308C22×C4×C139C2×D411yescharacteristic
309C22×C4×C139C2×D411yescharacteristic
310C22×C4×C139C2×D411yescharacteristic
311C22×C4×C139C2×D412yes—
312C22×C4×C139C2411yescharacteristic
313SD16×C139—42no—
314SD16×C139—42no—
315SD16×C139—42no—
316D8×C139—42no—
317D8×C139—42no—
318D8×C139—42no—
319M16×C139—21no—
320M16×C139—21no—
321M16×C139—21no—
322M16×C139—21no—
323M16×C139—21no—
324M16×C139—21no—
325M16×C139—21no—
326M16×C139—42no—
327M16×C139C2×D412yescomplemented
328C2×C8×C139—21no—
329C2×C8×C139—21no—
330C2×C8×C139—21no—
331C2×C8×C139—21no—
332C2×C8×C139—42no—
333C4⋊C4×C139—22no—
334C4⋊C4×C139—22no—
335C4⋊C4×C139—21no—
336C4⋊C4×C139—21no—
337C4⋊C4×C139—21no—
338C4⋊C4×C139—21no—
339C4⋊C4×C139—21no—
340C4⋊C4×C139—21no—
341C4⋊C4×C139—42no—
342C4⋊C4×C139C2×D411yescharacteristic
343C4⋊C4×C139C2×D411yescharacteristic
344C22⋊C4×C139—22no—
345C22⋊C4×C139—22no—
346C22⋊C4×C139—22no—
347C22⋊C4×C139—22no—
348C22⋊C4×C139—22no—
349C22⋊C4×C139—21no—
350C22⋊C4×C139—21no—
351C22⋊C4×C139—21no—
352C22⋊C4×C139—21no—
353C22⋊C4×C139—22no—
354C22⋊C4×C139—22no—
355C22⋊C4×C139—21no—
356C22⋊C4×C139—42no—
357C22⋊C4×C139—41no—
358C22⋊C4×C139—41no—
359C22⋊C4×C139—82no—
360C22⋊C4×C139—82no—
361C42×C139—22no—
362C42×C139—21no—
363C42×C139—21no—
364C42×C139—21no—
365C42×C139—21no—
366C42×C139C2×D412yescomplemented
367C23×C139—21no—
368C23×C139—21no—
369C23×C139—21no—
370C23×C139—22no—
371C23×C139—21no—
372C23×C139—21no—
373C23×C139—22no—
374C23×C139—22no—
375C23×C139—41no—
376C23×C139—41no—
377C23×C139—42no—
378C23×C139—42no—
379C23×C139—44no—
380C23×C139—42no—
381C23×C139—42no—
382C23×C139—42no—
383C23×C139—42no—
384C23×C139—41no—
385C23×C139—41no—
386C23×C139—41no—
387C23×C139—81no—
388C23×C139—82no—
389C23×C139—82no—
390C23×C139#12011yescharacteristic
391C23×C139#12011yescharacteristic
392C23×C139C22×D411yescharacteristic
393Q8×C139—21no—
394Q8×C139—21no—
395Q8×C139—21no—
396Q8×C139—21no—
397Q8×C139—21no—
398Q8×C139—42no—
399Q8×C139#12112yes—
400D4×C139—22no—
401D4×C139—22no—
402D4×C139—21no—
403D4×C139—21no—
404D4×C139—21no—
405D4×C139—21no—
406D4×C139—21no—
407D4×C139—42no—
408D4×C139—42no—
409D4×C139—44no—
410D4×C139—42no—
411D4×C139—44no—
412D4×C139—44no—
413D4×C139—42no—
414D4×C139—41no—
415D4×C139—41no—
416D4×C139—41no—
417D4×C139—41no—
418D4×C139—41no—
419D4×C139—41no—
420D4×C139—41no—
421D4×C139—41no—
422D4×C139—41no—
423D4×C139—41no—
424D4×C139—41no—
425D4×C139—41no—
426D4×C139—81no—
427D4×C139—82no—
428D4×C139—82no—
429D4×C139—82no—
430D4×C139—82no—
431D4×C139—88no—
432D4×C139—82no—
433D4×C139—82no—
434D4×C139#12112yes—
435C2×C4×C139—21no—
436C2×C4×C139—21no—
437C2×C4×C139—21no—
438C2×C4×C139—21no—
439C2×C4×C139—21no—
440C2×C4×C139—21no—
441C2×C4×C139—21no—
442C2×C4×C139—21no—
443C2×C4×C139—21no—
444C2×C4×C139—22no—
445C2×C4×C139—21no—
446C2×C4×C139—21no—
447C2×C4×C139—22no—
448C2×C4×C139—21no—
449C2×C4×C139—22no—
450C2×C4×C139—21no—
451C2×C4×C139—21no—
452C2×C4×C139—21no—
453C2×C4×C139—22no—
454C2×C4×C139—42no—
455C2×C4×C139—42no—
456C2×C4×C139—42no—
457C2×C4×C139—44no—
458C2×C4×C139—41no—
459C2×C4×C139—41no—
460C2×C4×C139—41no—
461C2×C4×C139—41no—
462C2×C4×C139—41no—
463C2×C4×C139—41no—
464C2×C4×C139—42no—
465C2×C4×C139—41no—
466C2×C4×C139—41no—
467C2×C4×C139—42no—
468C2×C4×C139—41no—
469C2×C4×C139—41no—
470C2×C4×C139—82no—
471C2×C4×C139#12011yescharacteristic
472C2×C4×C139#12011yescharacteristic
473C2×C4×C139C22×D411yescharacteristic
474C2×C4×C139C22×D411yescharacteristic
475C2×C4×C139C22×D411yescharacteristic
476C2×C4×C139C2×#4111yescharacteristic
477C2×C4×C139H(5,𝔽2)11yescharacteristic
478C2×C4×C139H(5,𝔽2)11yescharacteristic
479C8×C139—22no—
480C8×C139—41no—
481C8×C139—41no—
482C8×C139—41no—
483C22×C139—21no—
484C22×C139—21no—
485C22×C139—21no—
486C22×C139—21no—
487C22×C139—22no—
488C22×C139—21no—
489C22×C139—21no—
490C22×C139—21no—
491C22×C139—21no—
492C22×C139—41no—
493C22×C139—41no—
494C22×C139—41no—
495C22×C139—41no—
496C22×C139—42no—
497C22×C139—42no—
498C22×C139—41no—
499C22×C139—41no—
500C22×C139—41no—
501C22×C139—42no—
502C22×C139—41no—
503C22×C139—81no—
504C22×C139—81no—
505C22×C139—82no—
506C22×C139—82no—
507C22×C139—82no—
508C22×C139—82no—
509C22×C139—84no—
510C22×C139—81no—
511C22×C139—81no—
512C22×C139—81no—
513C22×C139—164no—
514C22×C139C2×#12011yescharacteristic
515C22×C139D4211yescharacteristic
516C22×C139#54611yescharacteristic
517C4×C139—21no—
518C4×C139—21no—
519C4×C139—22no—
520C4×C139—42no—
521C4×C139—41no—
522C4×C139—41no—
523C4×C139—42no—
524C4×C139—41no—
525C4×C139—41no—
526C4×C139—81no—
527C4×C139—81no—
528C4×C139C2×#12111yescharacteristic
529C4×C139#53411yescharacteristic
530C4×C139D4211yescharacteristic
531C4×C139#54611yescharacteristic
532C2×C139—21no—
533C2×C139—21no—
534C2×C139—41no—
535C2×C139—41no—
536C2×C139—42no—
537C2×C139—81no—
538C2×C139—82no—
539C2×C139—81no—
540C2×C139—161no—
541C2×C139#241011yescharacteristic
542C2×C139#301911yescharacteristic
543C2×C139#302111yescharacteristic
544#24468C13911yesmaximal, characteristic, direct product factor, Sylow
545C139#2446811yescharacteristic, direct product factor, Sylow
546#3488C2×C13911yescharacteristic, complemented
547#3055C2×C13911yescharacteristic, complemented
548C2×#453C2×C13911yescharacteristic, complemented
549#3006C2×C13911yescharacteristic, complemented
550C2×#421C2×C13911yescharacteristic, complemented
551#2619C2×C13911yescharacteristic, complemented
552#2040C2×C13911yescharacteristic, complemented
553#2037C2×C13911yescharacteristic, complemented
554#2006C2×C13911yescharacteristic, complemented
555#2002C2×C13911yescharacteristic, complemented
556#1900C2×C13911yescharacteristic, complemented
557#1897C2×C13911yescharacteristic, complemented
558#1883C2×C13911yescharacteristic, complemented
559#1860C2×C13911yescharacteristic, complemented
560#1792C2×C13911yescharacteristic, complemented
561C2×H(5,𝔽2)C22×C13911yescharacteristic
562C22×#41C22×C13911yescharacteristic
563C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
564C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
565C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
566C22×M16C22×C13911yescharacteristic, complemented
567#550—21no—
568#548—21no—
569#546—21no—
570#546—22no—
571D42—22no—
572D42—21no—
573#537—21no—
574#537C22×C13911yescharacteristic
575#535—21no—
576#535C22×C13911yescharacteristic
577C2×#127C22×C13911yescharacteristic, complemented
578#525—21no—
579#525C22×C13911yescharacteristic
580C2×#121—21no—
581C2×#121C22×C13911yescharacteristic
582C2×#121C22×C13911yescharacteristic, complemented
583#520C22×C13911yescharacteristic
584C2×#117C22×C13911yescharacteristic, complemented
585#469—21no—
586#468—21no—
587#466—21no—
588#465—21no—
589#453—24no—
590#449—21no—
591#449—21no—
592#448—21no—
593#447—21no—
594#428C22×C13911yescharacteristic, complemented
595#421—24no—
596C2×#104C22×C13911yescharacteristic
597C2×#104C22×C13911yescharacteristic
598C2×#104C22×C13911yescharacteristic, complemented
599C2×#104C22×C13911yescharacteristic, complemented
600C2×#104C22×C13911yescharacteristic, complemented
601C2×#104C22×C13911yescharacteristic, complemented
602#418C22×C13911yescharacteristic, complemented
603#417C22×C13911yescharacteristic
604#417C22×C13911yescharacteristic, complemented
605#417C22×C13911yescharacteristic, complemented
606C2×#100C22×C13911yescharacteristic, complemented
607C2×#100C22×C13911yescharacteristic, complemented
608#407C22×C13911yescharacteristic, complemented
609#394—22no—
610#392—22no—
611#390C22×C13911yescharacteristic, complemented
612#390C22×C13911yescharacteristic, complemented
613#382C22×C13911yescharacteristic, complemented
614#343C22×C13911yescharacteristic, complemented
615#343C22×C13911yescharacteristic, complemented
616#339C22×C13911yescharacteristic, complemented
617#339C22×C13911yescharacteristic, complemented
618H(5,𝔽2)—22no—
619H(5,𝔽2)—22no—
620H(5,𝔽2)—41no—
621H(5,𝔽2)—41no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—22no—
627C2×#41—22no—
628C2×#41—41no—
629C2×#41—41no—
630C2×#41D4×C13911yescharacteristic, complemented
631C2×#41D4×C13911yescharacteristic, complemented
632C2×#41C23×C13911yescharacteristic
633C2×#41C23×C13911yescharacteristic
634C2×#41C23×C13911yescharacteristic
635C22×Q8D4×C13911yescharacteristic, complemented
636C22×D4—21no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—21no—
640C22×D4—21no—
641C22×D4—21no—
642C22×D4—22no—
643C22×D4D4×C13912yes—
644C22×D4D4×C13911yescharacteristic, complemented
645C22×D4C23×C13911yescharacteristic
646C22×D4C23×C13911yescharacteristic
647C23×C4—21no—
648C23×C4C23×C13911yescharacteristic
649AGL(1,ℤ/8)—22no—
650AGL(1,ℤ/8)—22no—
651AGL(1,ℤ/8)—22no—
652AGL(1,ℤ/8)—41no—
653AGL(1,ℤ/8)—41no—
654AGL(1,ℤ/8)—41no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16—21no—
658C2×D8—21no—
659C2×D8—21no—
660C2×D8—21no—
661C2×M16—21no—
662C2×M16—22no—
663C2×M16—41no—
664C2×M16C23×C13911yescharacteristic
665C2×M16C23×C13911yescharacteristic
666C2×M16C23×C13911yescharacteristic
667C2×M16C23×C13911yescharacteristic
668C22×C8—21no—
669#127—22no—
670#127—21no—
671#127—22no—
672#127—41no—
673#124—22no—
674#124—21no—
675#123—22no—
676#123—21no—
677C22⋊Q8—22no—
678C22⋊Q8—21no—
679C22⋊Q8—21no—
680C22⋊Q8D4×C13911yescharacteristic, complemented
681C22⋊Q8D4×C13911yescharacteristic, complemented
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—22no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—21no—
700#121D4×C13911yescharacteristic, complemented
701#121D4×C13911yescharacteristic, complemented
702#120—22no—
703#120—22no—
704#120—22no—
705#120—21no—
706#120—22no—
707C4×Q8—21no—
708C4×D4—22no—
709C4×D4—22no—
710C4×D4—21no—
711C4×D4—22no—
712C4×D4—21no—
713C4×D4—21no—
714#117—21no—
715#117—22no—
716#117—41no—
717#117C23×C13911yescharacteristic
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4C23×C13911yescharacteristic
721C2×C4⋊C4C23×C13911yescharacteristic
722C2×C22⋊C4—22no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4D4×C13912yes—
728C2×C42C23×C13911yescharacteristic
729C2×C42C23×C13911yescharacteristic
730#107—21no—
731#106—21no—
732#104—22no—
733#104—22no—
734#104—22no—
735#104—22no—
736#104—41no—
737#104D4×C13914yescomplemented
738#103—21no—
739#103—21no—
740#103—21no—
741#102—21no—
742#102—21no—
743#102—21no—
744#102—21no—
745#102—21no—
746#100—22no—
747#100—41no—
748C22⋊C8—21no—
749C22⋊C8—21no—
750#95—22no—
751C24—22no—
752C24—21no—
753C24—21no—
754C24C2×D4×C13912yes—
755C24C2×D4×C13911yescharacteristic
756#41—21no—
757#41—21no—
758#41—22no—
759#41—22no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—42no—
769#41—42no—
770#41—41no—
771#41—41no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41—42no—
778#41C2×D4×C13912yes—
779#41#41×C13912yes—
780C2×Q8—21no—
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8C2×D4×C13911yescharacteristic
784C2×Q8C2×D4×C13911yescharacteristic
785C2×Q8C2×D4×C13911yescharacteristic
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—84no—
831C2×D4C2×D4×C13911yescharacteristic
832C2×D4C2×D4×C13911yescharacteristic
833C2×D4C2×D4×C13911yescharacteristic
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C2×D4×C13911yescharacteristic
852C22×C4C2×D4×C13911yescharacteristic
853C22×C4C2×D4×C13911yescharacteristic
854C22×C4C2×D4×C13911yescharacteristic
855C22×C4C2×D4×C13911yescharacteristic
856C22×C4C2×D4×C13912yes—
857C22×C4C24×C13911yescharacteristic
858SD16—42no—
859SD16—42no—
860SD16—42no—
861D8—42no—
862D8—42no—
863D8—42no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—21no—
871M16—42no—
872M16C2×D4×C13912yescomplemented
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—42no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—42no—
887C4⋊C4C2×D4×C13911yescharacteristic
888C4⋊C4C2×D4×C13911yescharacteristic
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—21no—
901C22⋊C4—42no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—82no—
905C22⋊C4—82no—
906C42—22no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42C2×D4×C13912yescomplemented
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23#120×C13911yescharacteristic
936C23#120×C13911yescharacteristic
937C23C22×D4×C13911yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8#121×C13912yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—82no—
972D4—81no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4#121×C13912yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4#120×C13911yescharacteristic
1017C2×C4#120×C13911yescharacteristic
1018C2×C4C22×D4×C13911yescharacteristic
1019C2×C4C22×D4×C13911yescharacteristic
1020C2×C4C22×D4×C13911yescharacteristic
1021C2×C4C2×#41×C13911yescharacteristic
1022C2×C4H(5,𝔽2)×C13911yescharacteristic
1023C2×C4H(5,𝔽2)×C13911yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—22no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—42no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—42no—
1047C22—41no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×#120×C13911yescharacteristic
1060C22D42×C13911yescharacteristic
1061C22#546×C13911yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—42no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×#121×C13911yescharacteristic
1074C4#534×C13911yescharacteristic
1075C4D42×C13911yescharacteristic
1076C4#546×C13911yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2#2410×C13911yescharacteristic
1087C2#3019×C13911yescharacteristic
1088C2#3021×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3488×C139C2semidirect
2. #3055×C139C2semidirect
3. C2×#453×C139C2semidirect
4. #3006×C139C2semidirect
5. C2×#421×C139C2semidirect
6. #2619×C139C2semidirect
7. #2040×C139C2semidirect
8. #2037×C139C2semidirect
9. #2006×C139C2semidirect
10. #2002×C139C2semidirect
11. #1900×C139C2semidirect
12. #1897×C139C2semidirect
13. #1883×C139C2semidirect
14. #1860×C139C2semidirect
15. #1792×C139C2semidirect
19. C2×AGL(1,ℤ/8)×C139C22semidirect
20. C2×AGL(1,ℤ/8)×C139C22semidirect
21. C22×M16×C139C22semidirect
32. C2×#127×C139C22semidirect
37. C2×#121×C139C22semidirect
39. C2×#117×C139C22semidirect
49. #428×C139C22semidirect
53. C2×#104×C139C22semidirect
54. C2×#104×C139C22semidirect
55. C2×#104×C139C22semidirect
56. C2×#104×C139C22semidirect
57. #418×C139C22semidirect
59. #417×C139C22semidirect
60. #417×C139C22semidirect
61. C2×#100×C139C22semidirect
62. C2×#100×C139C22semidirect
63. #407×C139C22semidirect
66. #390×C139C22semidirect
67. #390×C139C22semidirect
68. #382×C139C22semidirect
69. #343×C139C22semidirect
70. #343×C139C22semidirect
71. #339×C139C22semidirect
72. #339×C139C22semidirect
85. C2×#41×C139D4semidirect
86. C2×#41×C139D4semidirect
90. C22×Q8×C139D4semidirect
99. C22×D4×C139D4semidirect
135. C22⋊Q8×C139D4semidirect
136. C22⋊Q8×C139D4semidirect
155. #121×C139D4semidirect
156. #121×C139D4semidirect
192. #104×C139D4semidirect
327. M16×C139C2×D4semidirect
366. C42×C139C2×D4semidirect
544. #24468C139direct (N × H)
545. C139#24468direct (N × H)
546. #3488C2×C139semidirect
547. #3055C2×C139semidirect
548. C2×#453C2×C139semidirect
549. #3006C2×C139semidirect
550. C2×#421C2×C139semidirect
551. #2619C2×C139semidirect
552. #2040C2×C139semidirect
553. #2037C2×C139semidirect
554. #2006C2×C139semidirect
555. #2002C2×C139semidirect
556. #1900C2×C139semidirect
557. #1897C2×C139semidirect
558. #1883C2×C139semidirect
559. #1860C2×C139semidirect
560. #1792C2×C139semidirect
564. C2×AGL(1,ℤ/8)C22×C139semidirect
565. C2×AGL(1,ℤ/8)C22×C139semidirect
566. C22×M16C22×C139semidirect
577. C2×#127C22×C139semidirect
582. C2×#121C22×C139semidirect
584. C2×#117C22×C139semidirect
594. #428C22×C139semidirect
598. C2×#104C22×C139semidirect
599. C2×#104C22×C139semidirect
600. C2×#104C22×C139semidirect
601. C2×#104C22×C139semidirect
602. #418C22×C139semidirect
604. #417C22×C139semidirect
605. #417C22×C139semidirect
606. C2×#100C22×C139semidirect
607. C2×#100C22×C139semidirect
608. #407C22×C139semidirect
611. #390C22×C139semidirect
612. #390C22×C139semidirect
613. #382C22×C139semidirect
614. #343C22×C139semidirect
615. #343C22×C139semidirect
616. #339C22×C139semidirect
617. #339C22×C139semidirect
630. C2×#41D4×C139semidirect
631. C2×#41D4×C139semidirect
635. C22×Q8D4×C139semidirect
644. C22×D4D4×C139semidirect
680. C22⋊Q8D4×C139semidirect
681. C22⋊Q8D4×C139semidirect
700. #121D4×C139semidirect
701. #121D4×C139semidirect
737. #104D4×C139semidirect
872. M16C2×D4×C139semidirect
911. C42C2×D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3488×C1392
#3055×C1392
C2×#453×C1392
#3006×C1392
C2×#421×C1392
#2619×C1392
#2040×C1392
#2037×C1392
#2006×C1392
#2002×C1392
#1900×C1392
#1897×C1392
#1883×C1392
#1860×C1392
#1792×C1392
#24468139