Finite Group Databasebeta

← C139×#23860 #48018456

Subgroups — C139×#23860 #48018456

Order 35584.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C139C211yesmaximal, characteristic, complemented
2C2×D42×C139C211yesmaximal, characteristic, complemented
3C2×#449×C139C211yesmaximal, characteristic, complemented
4C2×#450×C139C211yesmaximal, characteristic, complemented
5C2×#447×C139C211yesmaximal, characteristic, complemented
6#2407×C139C211yesmaximal, characteristic, complemented
7#2014×C139C211yesmaximal, characteristic, complemented
8#2011×C139C211yesmaximal, characteristic, complemented
9#2000×C139C211yesmaximal, characteristic, complemented
10#1999×C139C211yesmaximal, characteristic, complemented
11#1895×C139C211yesmaximal, characteristic, complemented
12#1879×C139C211yesmaximal, characteristic, complemented
13#1877×C139C211yesmaximal, characteristic, complemented
14#1870×C139C211yesmaximal, characteristic, complemented
15#1786×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic, complemented
17C23×D4×C139—21no—
18C23×D4×C139C2211yescharacteristic
19C23×D4×C139C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C139—24no—
21C2×AGL(1,ℤ/8)×C139—24no—
22C2×AGL(1,ℤ/8)×C139—24no—
23C22×SD16×C139C2211yescharacteristic
24C22×SD16×C139C2211yescharacteristic, complemented
25C22×SD16×C139C2211yescharacteristic, complemented
26C22×D8×C139C2211yescharacteristic
27C22×D8×C139C2211yescharacteristic, complemented
28C22×D8×C139C2211yescharacteristic, complemented
29C22×M16×C139C2211yescharacteristic, complemented
30D42×C139—24no—
31D42×C139—24no—
32C2×#127×C139C2211yescharacteristic
33C2×C22⋊Q8×C139C2211yescharacteristic, complemented
34C2×#121×C139—21no—
35C2×#121×C139C2211yescharacteristic
36C2×#121×C139C2211yescharacteristic
37C2×#121×C139C2211yescharacteristic, complemented
38C2×#120×C139—21no—
39C2×#120×C139—21no—
40C2×C4×D4×C139C2211yescharacteristic
41C2×C4×D4×C139C2211yescharacteristic
42#450×C139—24no—
43#449×C139—24no—
44#447×C139—24no—
45C2×#103×C139C2211yescharacteristic, complemented
46C2×#102×C139C2211yescharacteristic
47C2×#102×C139C2211yescharacteristic
48C2×#102×C139C2211yescharacteristic, complemented
49C2×#102×C139C2211yescharacteristic, complemented
50C2×#102×C139C2211yescharacteristic, complemented
51C2×#102×C139C2211yescharacteristic, complemented
52C2×#102×C139C2211yescharacteristic, complemented
53C2×C22⋊C8×C139C2211yescharacteristic, complemented
54C2×C22⋊C8×C139C2211yescharacteristic, complemented
55C2×C22⋊C8×C139C2211yescharacteristic, complemented
56#394×C139—21no—
57#392×C139—21no—
58#391×C139C2211yescharacteristic, complemented
59#390×C139C2211yescharacteristic, complemented
60#386×C139—21no—
61#385×C139—21no—
62#380×C139C2211yescharacteristic, complemented
63#340×C139C2211yescharacteristic, complemented
64#340×C139C2211yescharacteristic, complemented
65#336×C139C2211yescharacteristic, complemented
66#336×C139C2211yescharacteristic, complemented
67C25×C139—21no—
68C25×C139—21no—
69C2×#41×C139—22no—
70C2×#41×C139—22no—
71C2×#41×C139—22no—
72C2×#41×C139—22no—
73C2×#41×C139—41no—
74C2×#41×C139—41no—
75C22×Q8×C139C2311yescharacteristic
76C22×D4×C139—22no—
77C22×D4×C139—22no—
78C22×D4×C139—28no—
79C22×D4×C139—21no—
80C22×D4×C139—21no—
81C22×D4×C139—22no—
82C22×D4×C139—22no—
83C22×D4×C139—22no—
84C22×D4×C139—22no—
85C22×D4×C139—21no—
86C22×D4×C139—21no—
87C22×D4×C139—21no—
88C22×D4×C139—21no—
89C22×D4×C139—21no—
90C22×D4×C139—22no—
91C22×D4×C139—21no—
92C22×D4×C139—41no—
93C22×D4×C139—41no—
94C22×D4×C139—41no—
95C22×D4×C139—41no—
96C22×D4×C139—44no—
97C22×D4×C139—44no—
98C22×D4×C139D411yescharacteristic
99C22×D4×C139D414yescomplemented
100C22×D4×C139C2311yescharacteristic
101C22×D4×C139C2311yescharacteristic
102C22×D4×C139C2311yescharacteristic
103C22×D4×C139C2311yescharacteristic
104C23×C4×C139—21no—
105C23×C4×C139—21no—
106C23×C4×C139C2311yescharacteristic
107C23×C4×C139C2311yescharacteristic
108AGL(1,ℤ/8)×C139—232no—
109C2×SD16×C139—22no—
110C2×SD16×C139—22no—
111C2×SD16×C139—22no—
112C2×SD16×C139—22no—
113C2×SD16×C139—22no—
114C2×SD16×C139—22no—
115C2×SD16×C139—22no—
116C2×SD16×C139—41no—
117C2×SD16×C139D414yescomplemented
118C2×D8×C139—22no—
119C2×D8×C139—22no—
120C2×D8×C139—22no—
121C2×D8×C139—22no—
122C2×D8×C139—22no—
123C2×D8×C139—22no—
124C2×D8×C139—22no—
125C2×D8×C139—41no—
126C2×D8×C139D414yescomplemented
127C2×M16×C139—22no—
128C2×M16×C139—22no—
129C2×M16×C139—22no—
130C22×C8×C139C2311yescharacteristic
131C22×C8×C139C2311yescharacteristic
132C22×C8×C139C2311yescharacteristic
133C22×C8×C139C2311yescharacteristic
134#127×C139—22no—
135#127×C139—22no—
136C22⋊Q8×C139—22no—
137C22⋊Q8×C139—41no—
138#121×C139—28no—
139#121×C139—22no—
140#121×C139—22no—
141#121×C139—22no—
142#121×C139—22no—
143#121×C139—41no—
144#121×C139D414yescomplemented
145#120×C139—28no—
146#120×C139—28no—
147C4×D4×C139—22no—
148C4×D4×C139—22no—
149C4×D4×C139—22no—
150C4×D4×C139—22no—
151C2×C4⋊C4×C139—21no—
152C2×C4⋊C4×C139D411yescharacteristic
153C2×C4⋊C4×C139C2311yescharacteristic
154C2×C4⋊C4×C139C2311yescharacteristic
155C2×C4⋊C4×C139C2311yescharacteristic
156C2×C22⋊C4×C139—21no—
157C2×C22⋊C4×C139—21no—
158C2×C22⋊C4×C139—21no—
159C2×C22⋊C4×C139—21no—
160C2×C22⋊C4×C139—21no—
161C2×C22⋊C4×C139—21no—
162C2×C22⋊C4×C139—21no—
163C2×C22⋊C4×C139—21no—
164C2×C22⋊C4×C139D411yescharacteristic
165C2×C22⋊C4×C139D411yescharacteristic
166C2×C42×C139C2311yescharacteristic
167#103×C139—22no—
168#102×C139—22no—
169#102×C139—22no—
170#102×C139—22no—
171#102×C139—22no—
172#102×C139—22no—
173#102×C139—41no—
174#102×C139—41no—
175C22⋊C8×C139—22no—
176C22⋊C8×C139—22no—
177C22⋊C8×C139—22no—
178#95×C139—21no—
179#95×C139—21no—
180#95×C139—21no—
181C24×C139—21no—
182C24×C139—24no—
183C24×C139—21no—
184C24×C139—21no—
185C24×C139—21no—
186C24×C139—24no—
187C24×C139—42no—
188C24×C139—42no—
189C24×C139—42no—
190C24×C139—42no—
191C24×C139—42no—
192C24×C139—42no—
193C24×C139—42no—
194C24×C139—42no—
195C24×C139—81no—
196C24×C139—81no—
197C24×C139—81no—
198C24×C139—81no—
199C24×C139C2×D411yescharacteristic
200C24×C139C2×D411yescharacteristic
201#41×C139—28no—
202#41×C139—44no—
203#41×C139—44no—
204#41×C139—44no—
205C2×Q8×C139—21no—
206C2×Q8×C139—21no—
207C2×Q8×C139—21no—
208C2×Q8×C139—21no—
209C2×Q8×C139—21no—
210C2×Q8×C139C2×D412yescomplemented
211C2×D4×C139—22no—
212C2×D4×C139—22no—
213C2×D4×C139—28no—
214C2×D4×C139—24no—
215C2×D4×C139—24no—
216C2×D4×C139—24no—
217C2×D4×C139—24no—
218C2×D4×C139—24no—
219C2×D4×C139—24no—
220C2×D4×C139—22no—
221C2×D4×C139—21no—
222C2×D4×C139—21no—
223C2×D4×C139—21no—
224C2×D4×C139—21no—
225C2×D4×C139—21no—
226C2×D4×C139—21no—
227C2×D4×C139—21no—
228C2×D4×C139—21no—
229C2×D4×C139—21no—
230C2×D4×C139—21no—
231C2×D4×C139—21no—
232C2×D4×C139—21no—
233C2×D4×C139—21no—
234C2×D4×C139—21no—
235C2×D4×C139—21no—
236C2×D4×C139—21no—
237C2×D4×C139—21no—
238C2×D4×C139—21no—
239C2×D4×C139—44no—
240C2×D4×C139—44no—
241C2×D4×C139—44no—
242C2×D4×C139—42no—
243C2×D4×C139—42no—
244C2×D4×C139—42no—
245C2×D4×C139—42no—
246C2×D4×C139—42no—
247C2×D4×C139—42no—
248C2×D4×C139—44no—
249C2×D4×C139—44no—
250C2×D4×C139—432no—
251C2×D4×C139—44no—
252C2×D4×C139—42no—
253C2×D4×C139—42no—
254C2×D4×C139—42no—
255C2×D4×C139—42no—
256C2×D4×C139—42no—
257C2×D4×C139—42no—
258C2×D4×C139—44no—
259C2×D4×C139—42no—
260C2×D4×C139—42no—
261C2×D4×C139—42no—
262C2×D4×C139—81no—
263C2×D4×C139—81no—
264C2×D4×C139—81no—
265C2×D4×C139C2×D412yes—
266C2×D4×C139C2×D412yes—
267C2×D4×C139C2×D412yes—
268C2×D4×C139C2×D412yes—
269C2×D4×C139C2×D412yes—
270C2×D4×C139C2×D412yescomplemented
271C22×C4×C139—21no—
272C22×C4×C139—21no—
273C22×C4×C139—21no—
274C22×C4×C139—21no—
275C22×C4×C139—24no—
276C22×C4×C139—21no—
277C22×C4×C139—21no—
278C22×C4×C139—21no—
279C22×C4×C139—21no—
280C22×C4×C139—21no—
281C22×C4×C139—21no—
282C22×C4×C139—21no—
283C22×C4×C139—21no—
284C22×C4×C139—21no—
285C22×C4×C139—21no—
286C22×C4×C139—42no—
287C22×C4×C139—42no—
288C22×C4×C139—42no—
289C22×C4×C139—42no—
290C22×C4×C139—42no—
291C22×C4×C139C2×D411yescharacteristic
292C22×C4×C139C2×D411yescharacteristic
293C22×C4×C139C2×D411yescharacteristic
294C22×C4×C139C2×D412yes—
295C22×C4×C139C2×D412yes—
296C22×C4×C139C2×D411yescharacteristic
297C22×C4×C139C2411yescharacteristic
298SD16×C139—28no—
299SD16×C139—28no—
300SD16×C139—44no—
301D8×C139—28no—
302D8×C139—28no—
303D8×C139—44no—
304M16×C139—28no—
305C2×C8×C139—21no—
306C2×C8×C139—21no—
307C2×C8×C139—21no—
308C2×C8×C139—21no—
309C2×C8×C139—21no—
310C2×C8×C139—21no—
311C2×C8×C139—21no—
312C2×C8×C139—21no—
313C2×C8×C139—21no—
314C2×C8×C139—21no—
315C2×C8×C139C2×D412yescomplemented
316C2×C8×C139C2×D412yescomplemented
317C4⋊C4×C139—22no—
318C4⋊C4×C139—21no—
319C4⋊C4×C139—21no—
320C4⋊C4×C139—21no—
321C4⋊C4×C139—21no—
322C4⋊C4×C139—21no—
323C4⋊C4×C139—42no—
324C4⋊C4×C139C2×D412yes—
325C22⋊C4×C139—24no—
326C22⋊C4×C139—24no—
327C22⋊C4×C139—22no—
328C22⋊C4×C139—24no—
329C22⋊C4×C139—22no—
330C22⋊C4×C139—42no—
331C22⋊C4×C139—42no—
332C22⋊C4×C139—42no—
333C22⋊C4×C139—81no—
334C22⋊C4×C139—81no—
335C42×C139—21no—
336C42×C139—21no—
337C23×C139—21no—
338C23×C139—22no—
339C23×C139—21no—
340C23×C139—21no—
341C23×C139—21no—
342C23×C139—21no—
343C23×C139—22no—
344C23×C139—22no—
345C23×C139—21no—
346C23×C139—21no—
347C23×C139—21no—
348C23×C139—21no—
349C23×C139—21no—
350C23×C139—21no—
351C23×C139—21no—
352C23×C139—22no—
353C23×C139—22no—
354C23×C139—22no—
355C23×C139—48no—
356C23×C139—48no—
357C23×C139—48no—
358C23×C139—48no—
359C23×C139—41no—
360C23×C139—41no—
361C23×C139—41no—
362C23×C139—41no—
363C23×C139—41no—
364C23×C139—41no—
365C23×C139—41no—
366C23×C139—41no—
367C23×C139—41no—
368C23×C139—41no—
369C23×C139—41no—
370C23×C139—41no—
371C23×C139—41no—
372C23×C139—41no—
373C23×C139—41no—
374C23×C139—41no—
375C23×C139—41no—
376C23×C139—41no—
377C23×C139—41no—
378C23×C139—41no—
379C23×C139—41no—
380C23×C139—41no—
381C23×C139—84no—
382C23×C139—84no—
383C23×C139—84no—
384C23×C139—84no—
385C23×C139—84no—
386C23×C139—84no—
387C23×C139—84no—
388C23×C139—84no—
389C23×C139—84no—
390C23×C139—84no—
391C23×C139#12012yes—
392C23×C139AGL(1,ℤ/8)12yescomplemented
393C23×C139C22×D411yescharacteristic
394Q8×C139—22no—
395Q8×C139—22no—
396Q8×C139—41no—
397Q8×C139—41no—
398D4×C139—28no—
399D4×C139—22no—
400D4×C139—22no—
401D4×C139—22no—
402D4×C139—22no—
403D4×C139—22no—
404D4×C139—22no—
405D4×C139—22no—
406D4×C139—22no—
407D4×C139—22no—
408D4×C139—48no—
409D4×C139—48no—
410D4×C139—48no—
411D4×C139—48no—
412D4×C139—48no—
413D4×C139—48no—
414D4×C139—41no—
415D4×C139—41no—
416D4×C139—41no—
417D4×C139—41no—
418D4×C139—41no—
419D4×C139—41no—
420D4×C139—84no—
421D4×C139—84no—
422D4×C139#12014yes—
423C2×C4×C139—21no—
424C2×C4×C139—21no—
425C2×C4×C139—21no—
426C2×C4×C139—21no—
427C2×C4×C139—22no—
428C2×C4×C139—22no—
429C2×C4×C139—22no—
430C2×C4×C139—22no—
431C2×C4×C139—21no—
432C2×C4×C139—21no—
433C2×C4×C139—22no—
434C2×C4×C139—21no—
435C2×C4×C139—22no—
436C2×C4×C139—21no—
437C2×C4×C139—21no—
438C2×C4×C139—21no—
439C2×C4×C139—48no—
440C2×C4×C139—48no—
441C2×C4×C139—41no—
442C2×C4×C139—41no—
443C2×C4×C139—41no—
444C2×C4×C139—41no—
445C2×C4×C139—41no—
446C2×C4×C139—41no—
447C2×C4×C139—41no—
448C2×C4×C139—41no—
449C2×C4×C139—41no—
450C2×C4×C139—41no—
451C2×C4×C139—41no—
452C2×C4×C139—41no—
453C2×C4×C139—41no—
454C2×C4×C139—41no—
455C2×C4×C139#12012yes—
456C2×C4×C139AGL(1,ℤ/8)12yescomplemented
457C2×C4×C139C22×D411yescharacteristic
458C2×C4×C139C22×D411yescharacteristic
459C2×C4×C139C22×D411yescharacteristic
460C2×C4×C139C22×D411yescharacteristic
461C2×C4×C139H(5,𝔽2)11yescharacteristic
462C2×C4×C139H(5,𝔽2)11yescharacteristic
463C8×C139—22no—
464C8×C139—22no—
465C8×C139—41no—
466C8×C139—41no—
467C22×C139—22no—
468C22×C139—24no—
469C22×C139—22no—
470C22×C139—22no—
471C22×C139—22no—
472C22×C139—22no—
473C22×C139—22no—
474C22×C139—41no—
475C22×C139—42no—
476C22×C139—41no—
477C22×C139—42no—
478C22×C139—41no—
479C22×C139—42no—
480C22×C139—41no—
481C22×C139—42no—
482C22×C139—41no—
483C22×C139—41no—
484C22×C139—42no—
485C22×C139—41no—
486C22×C139—41no—
487C22×C139—42no—
488C22×C139—42no—
489C22×C139—42no—
490C22×C139—42no—
491C22×C139—42no—
492C22×C139—42no—
493C22×C139—42no—
494C22×C139—42no—
495C22×C139—42no—
496C22×C139—42no—
497C22×C139—816no—
498C22×C139—816no—
499C22×C139—81no—
500C22×C139—81no—
501C22×C139—81no—
502C22×C139—81no—
503C22×C139—81no—
504C22×C139—81no—
505C22×C139—81no—
506C22×C139—81no—
507C22×C139—81no—
508C22×C139—81no—
509C22×C139—81no—
510C22×C139—81no—
511C22×C139C2×#12011yescharacteristic
512C22×C139D4211yescharacteristic
513C22×C139D4211yescharacteristic
514C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
515C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
516C22×C139#57611yescharacteristic
517C22×C139#57711yescharacteristic
518C4×C139—22no—
519C4×C139—22no—
520C4×C139—41no—
521C4×C139—42no—
522C4×C139—42no—
523C4×C139—41no—
524C4×C139—81no—
525C4×C139—81no—
526C4×C139C2×#12011yescharacteristic
527C4×C139#53411yescharacteristic
528C4×C139D4211yescharacteristic
529C4×C139D4211yescharacteristic
530C2×C139—42no—
531C2×C139—42no—
532C2×C139—44no—
533C2×C139—82no—
534C2×C139—82no—
535C2×C139—82no—
536C2×C139#240311yescharacteristic
537C2×C139#300311yescharacteristic
538C2×C139#301211yescharacteristic
539C2×C139#326411yescharacteristic
540C2×C139#326511yescharacteristic
541C2×C139#327211yescharacteristic
542C2×C139#327411yescharacteristic
543#23860C13911yesmaximal, characteristic, direct product factor, Sylow
544C139#2386011yescharacteristic, direct product factor, Sylow
545C22×AGL(1,ℤ/8)C2×C13911yescharacteristic, complemented
546C2×D42C2×C13911yescharacteristic, complemented
547C2×#449C2×C13911yescharacteristic, complemented
548C2×#450C2×C13911yescharacteristic, complemented
549C2×#447C2×C13911yescharacteristic, complemented
550#2407C2×C13911yescharacteristic, complemented
551#2014C2×C13911yescharacteristic, complemented
552#2011C2×C13911yescharacteristic, complemented
553#2000C2×C13911yescharacteristic, complemented
554#1999C2×C13911yescharacteristic, complemented
555#1895C2×C13911yescharacteristic, complemented
556#1879C2×C13911yescharacteristic, complemented
557#1877C2×C13911yescharacteristic, complemented
558#1870C2×C13911yescharacteristic, complemented
559#1786C2×C13911yescharacteristic, complemented
560C22×#41C22×C13911yescharacteristic, complemented
561C23×D4—21no—
562C23×D4C22×C13911yescharacteristic
563C23×D4C22×C13911yescharacteristic
564C2×AGL(1,ℤ/8)—24no—
565C2×AGL(1,ℤ/8)—24no—
566C2×AGL(1,ℤ/8)—24no—
567C22×SD16C22×C13911yescharacteristic
568C22×SD16C22×C13911yescharacteristic, complemented
569C22×SD16C22×C13911yescharacteristic, complemented
570C22×D8C22×C13911yescharacteristic
571C22×D8C22×C13911yescharacteristic, complemented
572C22×D8C22×C13911yescharacteristic, complemented
573C22×M16C22×C13911yescharacteristic, complemented
574D42—24no—
575D42—24no—
576C2×#127C22×C13911yescharacteristic
577C2×C22⋊Q8C22×C13911yescharacteristic, complemented
578C2×#121—21no—
579C2×#121C22×C13911yescharacteristic
580C2×#121C22×C13911yescharacteristic
581C2×#121C22×C13911yescharacteristic, complemented
582C2×#120—21no—
583C2×#120—21no—
584C2×C4×D4C22×C13911yescharacteristic
585C2×C4×D4C22×C13911yescharacteristic
586#450—24no—
587#449—24no—
588#447—24no—
589C2×#103C22×C13911yescharacteristic, complemented
590C2×#102C22×C13911yescharacteristic
591C2×#102C22×C13911yescharacteristic
592C2×#102C22×C13911yescharacteristic, complemented
593C2×#102C22×C13911yescharacteristic, complemented
594C2×#102C22×C13911yescharacteristic, complemented
595C2×#102C22×C13911yescharacteristic, complemented
596C2×#102C22×C13911yescharacteristic, complemented
597C2×C22⋊C8C22×C13911yescharacteristic, complemented
598C2×C22⋊C8C22×C13911yescharacteristic, complemented
599C2×C22⋊C8C22×C13911yescharacteristic, complemented
600#394—21no—
601#392—21no—
602#391C22×C13911yescharacteristic, complemented
603#390C22×C13911yescharacteristic, complemented
604#386—21no—
605#385—21no—
606#380C22×C13911yescharacteristic, complemented
607#340C22×C13911yescharacteristic, complemented
608#340C22×C13911yescharacteristic, complemented
609#336C22×C13911yescharacteristic, complemented
610#336C22×C13911yescharacteristic, complemented
611C25—21no—
612C25—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C22×Q8C23×C13911yescharacteristic
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—28no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—21no—
634C22×D4—22no—
635C22×D4—21no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4—44no—
641C22×D4—44no—
642C22×D4D4×C13911yescharacteristic
643C22×D4D4×C13914yescomplemented
644C22×D4C23×C13911yescharacteristic
645C22×D4C23×C13911yescharacteristic
646C22×D4C23×C13911yescharacteristic
647C22×D4C23×C13911yescharacteristic
648C23×C4—21no—
649C23×C4—21no—
650C23×C4C23×C13911yescharacteristic
651C23×C4C23×C13911yescharacteristic
652AGL(1,ℤ/8)—232no—
653C2×SD16—22no—
654C2×SD16—22no—
655C2×SD16—22no—
656C2×SD16—22no—
657C2×SD16—22no—
658C2×SD16—22no—
659C2×SD16—22no—
660C2×SD16—41no—
661C2×SD16D4×C13914yescomplemented
662C2×D8—22no—
663C2×D8—22no—
664C2×D8—22no—
665C2×D8—22no—
666C2×D8—22no—
667C2×D8—22no—
668C2×D8—22no—
669C2×D8—41no—
670C2×D8D4×C13914yescomplemented
671C2×M16—22no—
672C2×M16—22no—
673C2×M16—22no—
674C22×C8C23×C13911yescharacteristic
675C22×C8C23×C13911yescharacteristic
676C22×C8C23×C13911yescharacteristic
677C22×C8C23×C13911yescharacteristic
678#127—22no—
679#127—22no—
680C22⋊Q8—22no—
681C22⋊Q8—41no—
682#121—28no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—41no—
688#121D4×C13914yescomplemented
689#120—28no—
690#120—28no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4D4×C13911yescharacteristic
697C2×C4⋊C4C23×C13911yescharacteristic
698C2×C4⋊C4C23×C13911yescharacteristic
699C2×C4⋊C4C23×C13911yescharacteristic
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4D4×C13911yescharacteristic
709C2×C22⋊C4D4×C13911yescharacteristic
710C2×C42C23×C13911yescharacteristic
711#103—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—41no—
718#102—41no—
719C22⋊C8—22no—
720C22⋊C8—22no—
721C22⋊C8—22no—
722#95—21no—
723#95—21no—
724#95—21no—
725C24—21no—
726C24—24no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—24no—
731C24—42no—
732C24—42no—
733C24—42no—
734C24—42no—
735C24—42no—
736C24—42no—
737C24—42no—
738C24—42no—
739C24—81no—
740C24—81no—
741C24—81no—
742C24—81no—
743C24C2×D4×C13911yescharacteristic
744C24C2×D4×C13911yescharacteristic
745#41—28no—
746#41—44no—
747#41—44no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8C2×D4×C13912yescomplemented
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—28no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—432no—
795C2×D4—44no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—44no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4C2×D4×C13912yes—
810C2×D4C2×D4×C13912yes—
811C2×D4C2×D4×C13912yes—
812C2×D4C2×D4×C13912yes—
813C2×D4C2×D4×C13912yes—
814C2×D4C2×D4×C13912yescomplemented
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4C2×D4×C13911yescharacteristic
836C22×C4C2×D4×C13911yescharacteristic
837C22×C4C2×D4×C13911yescharacteristic
838C22×C4C2×D4×C13912yes—
839C22×C4C2×D4×C13912yes—
840C22×C4C2×D4×C13911yescharacteristic
841C22×C4C24×C13911yescharacteristic
842SD16—28no—
843SD16—28no—
844SD16—44no—
845D8—28no—
846D8—28no—
847D8—44no—
848M16—28no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C13912yescomplemented
860C2×C8C2×D4×C13912yescomplemented
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4C2×D4×C13912yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—22no—
872C22⋊C4—24no—
873C22⋊C4—22no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C42—21no—
880C42—21no—
881C23—21no—
882C23—22no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—22no—
888C23—22no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—48no—
900C23—48no—
901C23—48no—
902C23—48no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—84no—
926C23—84no—
927C23—84no—
928C23—84no—
929C23—84no—
930C23—84no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23#120×C13912yes—
936C23AGL(1,ℤ/8)×C13912yescomplemented
937C23C22×D4×C13911yescharacteristic
938Q8—22no—
939Q8—22no—
940Q8—41no—
941Q8—41no—
942D4—28no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—22no—
949D4—22no—
950D4—22no—
951D4—22no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—48no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—84no—
965D4—84no—
966D4#120×C13914yes—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4#120×C13912yes—
1000C2×C4AGL(1,ℤ/8)×C13912yescomplemented
1001C2×C4C22×D4×C13911yescharacteristic
1002C2×C4C22×D4×C13911yescharacteristic
1003C2×C4C22×D4×C13911yescharacteristic
1004C2×C4C22×D4×C13911yescharacteristic
1005C2×C4H(5,𝔽2)×C13911yescharacteristic
1006C2×C4H(5,𝔽2)×C13911yescharacteristic
1007C8—22no—
1008C8—22no—
1009C8—41no—
1010C8—41no—
1011C22—22no—
1012C22—24no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—42no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—41no—
1028C22—42no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—816no—
1042C22—816no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22C2×#120×C13911yescharacteristic
1056C22D42×C13911yescharacteristic
1057C22D42×C13911yescharacteristic
1058C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
1059C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
1060C22#576×C13911yescharacteristic
1061C22#577×C13911yescharacteristic
1062C4—22no—
1063C4—22no—
1064C4—41no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—81no—
1069C4—81no—
1070C4C2×#120×C13911yescharacteristic
1071C4#534×C13911yescharacteristic
1072C4D42×C13911yescharacteristic
1073C4D42×C13911yescharacteristic
1074C2—42no—
1075C2—42no—
1076C2—44no—
1077C2—82no—
1078C2—82no—
1079C2—82no—
1080C2#2403×C13911yescharacteristic
1081C2#3003×C13911yescharacteristic
1082C2#3012×C13911yescharacteristic
1083C2#3264×C13911yescharacteristic
1084C2#3265×C13911yescharacteristic
1085C2#3272×C13911yescharacteristic
1086C2#3274×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C139C2semidirect
2. C2×D42×C139C2semidirect
3. C2×#449×C139C2semidirect
4. C2×#450×C139C2semidirect
5. C2×#447×C139C2semidirect
6. #2407×C139C2semidirect
7. #2014×C139C2semidirect
8. #2011×C139C2semidirect
9. #2000×C139C2semidirect
10. #1999×C139C2semidirect
11. #1895×C139C2semidirect
12. #1879×C139C2semidirect
13. #1877×C139C2semidirect
14. #1870×C139C2semidirect
15. #1786×C139C2semidirect
16. C22×#41×C139C22semidirect
24. C22×SD16×C139C22semidirect
25. C22×SD16×C139C22semidirect
27. C22×D8×C139C22semidirect
28. C22×D8×C139C22semidirect
29. C22×M16×C139C22semidirect
33. C2×C22⋊Q8×C139C22semidirect
37. C2×#121×C139C22semidirect
45. C2×#103×C139C22semidirect
48. C2×#102×C139C22semidirect
49. C2×#102×C139C22semidirect
50. C2×#102×C139C22semidirect
51. C2×#102×C139C22semidirect
52. C2×#102×C139C22semidirect
53. C2×C22⋊C8×C139C22semidirect
54. C2×C22⋊C8×C139C22semidirect
55. C2×C22⋊C8×C139C22semidirect
58. #391×C139C22semidirect
59. #390×C139C22semidirect
62. #380×C139C22semidirect
63. #340×C139C22semidirect
64. #340×C139C22semidirect
65. #336×C139C22semidirect
66. #336×C139C22semidirect
99. C22×D4×C139D4semidirect
117. C2×SD16×C139D4semidirect
126. C2×D8×C139D4semidirect
144. #121×C139D4semidirect
210. C2×Q8×C139C2×D4semidirect
270. C2×D4×C139C2×D4semidirect
315. C2×C8×C139C2×D4semidirect
316. C2×C8×C139C2×D4semidirect
392. C23×C139AGL(1,ℤ/8)semidirect
456. C2×C4×C139AGL(1,ℤ/8)semidirect
543. #23860C139direct (N × H)
544. C139#23860direct (N × H)
545. C22×AGL(1,ℤ/8)C2×C139semidirect
546. C2×D42C2×C139semidirect
547. C2×#449C2×C139semidirect
548. C2×#450C2×C139semidirect
549. C2×#447C2×C139semidirect
550. #2407C2×C139semidirect
551. #2014C2×C139semidirect
552. #2011C2×C139semidirect
553. #2000C2×C139semidirect
554. #1999C2×C139semidirect
555. #1895C2×C139semidirect
556. #1879C2×C139semidirect
557. #1877C2×C139semidirect
558. #1870C2×C139semidirect
559. #1786C2×C139semidirect
560. C22×#41C22×C139semidirect
568. C22×SD16C22×C139semidirect
569. C22×SD16C22×C139semidirect
571. C22×D8C22×C139semidirect
572. C22×D8C22×C139semidirect
573. C22×M16C22×C139semidirect
577. C2×C22⋊Q8C22×C139semidirect
581. C2×#121C22×C139semidirect
589. C2×#103C22×C139semidirect
592. C2×#102C22×C139semidirect
593. C2×#102C22×C139semidirect
594. C2×#102C22×C139semidirect
595. C2×#102C22×C139semidirect
596. C2×#102C22×C139semidirect
597. C2×C22⋊C8C22×C139semidirect
598. C2×C22⋊C8C22×C139semidirect
599. C2×C22⋊C8C22×C139semidirect
602. #391C22×C139semidirect
603. #390C22×C139semidirect
606. #380C22×C139semidirect
607. #340C22×C139semidirect
608. #340C22×C139semidirect
609. #336C22×C139semidirect
610. #336C22×C139semidirect
643. C22×D4D4×C139semidirect
661. C2×SD16D4×C139semidirect
670. C2×D8D4×C139semidirect
688. #121D4×C139semidirect
754. C2×Q8C2×D4×C139semidirect
814. C2×D4C2×D4×C139semidirect
859. C2×C8C2×D4×C139semidirect
860. C2×C8C2×D4×C139semidirect
936. C23AGL(1,ℤ/8)×C139semidirect
1000. C2×C4AGL(1,ℤ/8)×C139semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1392
C2×D42×C1392
C2×#449×C1392
C2×#450×C1392
C2×#447×C1392
#2407×C1392
#2014×C1392
#2011×C1392
#2000×C1392
#1999×C1392
#1895×C1392
#1879×C1392
#1877×C1392
#1870×C1392
#1786×C1392
#23860139