Finite Group Databasebeta

← C139×#25172 #48019768

Subgroups — C139×#25172 #48019768

Order 35584.

1310 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C139C211yesmaximal, characteristic, complemented
2C2×#450×C139C211yesmaximal, characteristic, complemented
3C2×#447×C139C211yesmaximal, characteristic
4C2×#442×C139C211yesmaximal, characteristic, complemented
5#2427×C139C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C139C211yesmaximal, characteristic, complemented
7#2065×C139C211yesmaximal, characteristic, complemented
8#2035×C139C211yesmaximal, characteristic, complemented
9#2033×C139C211yesmaximal, characteristic, complemented
10#2012×C139C211yesmaximal, characteristic, complemented
11#1973×C139C211yesmaximal, characteristic, complemented
12#1924×C139C211yesmaximal, characteristic, complemented
13#1879×C139C211yesmaximal, characteristic, complemented
14#1877×C139C211yesmaximal, characteristic, complemented
15#1862×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic
20C22×D8×C139C2211yescharacteristic
21C2×#124×C139C2211yescharacteristic, complemented
22C2×C22⋊Q8×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×C4×D4×C139C2211yescharacteristic
25C2×C4×D4×C139C2211yescharacteristic
26C2×C4×D4×C139C2211yescharacteristic, complemented
27C22×C22⋊C4×C139—21no—
28#463×C139—24no—
29#450×C139—24no—
30#447×C139—24no—
31#442×C139—24no—
32C2×#107×C139C2211yescharacteristic, complemented
33C2×#106×C139C2211yescharacteristic, complemented
34C2×C4⋊C8×C139C2211yescharacteristic, complemented
35C2×#103×C139C2211yescharacteristic, complemented
36C2×#103×C139C2211yescharacteristic, complemented
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic, complemented
42C2×#102×C139C2211yescharacteristic, complemented
43C2×C22⋊C8×C139C2211yescharacteristic
44C2×C22⋊C8×C139C2211yescharacteristic
45C2×#97×C139C2211yescharacteristic, complemented
46#397×C139—21no—
47#394×C139—21no—
48#391×C139C2211yescharacteristic, complemented
49#390×C139C2211yescharacteristic
50#390×C139C2211yescharacteristic
51#389×C139C2211yescharacteristic, complemented
52#386×C139—21no—
53#386×C139—21no—
54#386×C139—21no—
55#380×C139—21no—
56#380×C139C2211yescharacteristic
57#379×C139—21no—
58C4×C22⋊C4×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#336×C139C2211yescharacteristic, complemented
62#336×C139C2211yescharacteristic, complemented
63C25×C139—21no—
64C22×Q8×C139C2311yescharacteristic
65C22×D4×C139—22no—
66C22×D4×C139—22no—
67C22×D4×C139—22no—
68C22×D4×C139—22no—
69C22×D4×C139—21no—
70C22×D4×C139—21no—
71C22×D4×C139—41no—
72C22×D4×C139—41no—
73C22×D4×C139C2311yescharacteristic
74C22×D4×C139C2311yescharacteristic
75C22×D4×C139C2311yescharacteristic
76C23×C4×C139—21no—
77C23×C4×C139—21no—
78C23×C4×C139—21no—
79C23×C4×C139C2311yescharacteristic
80C2×SD16×C139—22no—
81C2×SD16×C139—22no—
82C2×SD16×C139—22no—
83C2×SD16×C139—22no—
84C2×SD16×C139—22no—
85C2×SD16×C139—41no—
86C2×D8×C139—22no—
87C2×D8×C139—22no—
88C2×D8×C139—22no—
89C2×D8×C139—22no—
90C2×D8×C139—41no—
91C2×D8×C139D414yes—
92C22×C8×C139C2311yescharacteristic
93C22×C8×C139C2311yescharacteristic
94C22×C8×C139C2311yescharacteristic
95C22×C8×C139C2311yescharacteristic
96#124×C139—22no—
97#124×C139—41no—
98C22⋊Q8×C139—22no—
99C22⋊Q8×C139—41no—
100#121×C139—22no—
101#121×C139—41no—
102C4×D4×C139—22no—
103C4×D4×C139—22no—
104C4×D4×C139—22no—
105C4×D4×C139—41no—
106C4×D4×C139—41no—
107C4×D4×C139—41no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139C2311yescharacteristic
111C2×C4⋊C4×C139C2311yescharacteristic
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C22⋊C4×C139—21no—
115C2×C22⋊C4×C139—21no—
116C2×C22⋊C4×C139—21no—
117C2×C22⋊C4×C139—21no—
118C2×C22⋊C4×C139—21no—
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—21no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—44no—
127C2×C22⋊C4×C139D411yescharacteristic
128C2×C22⋊C4×C139D411yescharacteristic
129C2×C42×C139C2311yescharacteristic
130C2×C42×C139C2311yescharacteristic
131#107×C139—41no—
132#106×C139—22no—
133C4⋊C8×C139—22no—
134#103×C139—22no—
135#103×C139—41no—
136#102×C139—22no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139D414yescomplemented
142C22⋊C8×C139—22no—
143C22⋊C8×C139—22no—
144#97×C139—22no—
145#95×C139—21no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139—21no—
149#95×C139D411yescharacteristic
150#95×C139D411yescharacteristic
151C24×C139—21no—
152C24×C139—24no—
153C24×C139—21no—
154C24×C139—21no—
155C24×C139—42no—
156C24×C139—42no—
157C24×C139—42no—
158C24×C139—42no—
159C24×C139—81no—
160C24×C139—81no—
161C24×C139C2×D411yescharacteristic
162C2×Q8×C139—21no—
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×Q8×C139—21no—
166C2×Q8×C139—21no—
167C2×Q8×C139—21no—
168C2×D4×C139—24no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139—21no—
176C2×D4×C139—21no—
177C2×D4×C139—21no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—42no—
183C2×D4×C139—42no—
184C2×D4×C139—44no—
185C2×D4×C139—44no—
186C2×D4×C139—44no—
187C2×D4×C139—44no—
188C2×D4×C139—42no—
189C2×D4×C139—42no—
190C2×D4×C139—81no—
191C2×D4×C139C2×D412yes—
192C2×D4×C139C2×D412yes—
193C2×D4×C139C2×D412yes—
194C2×D4×C139#4112yes—
195C2×D4×C139#4112yes—
196C22×C4×C139—21no—
197C22×C4×C139—21no—
198C22×C4×C139—21no—
199C22×C4×C139—21no—
200C22×C4×C139—21no—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—21no—
205C22×C4×C139—21no—
206C22×C4×C139—21no—
207C22×C4×C139—42no—
208C22×C4×C139—42no—
209C22×C4×C139—42no—
210C22×C4×C139—42no—
211C22×C4×C139—42no—
212C22×C4×C139—42no—
213C22×C4×C139—81no—
214C22×C4×C139—81no—
215C22×C4×C139—81no—
216C22×C4×C139C2×D411yescharacteristic
217C22×C4×C139C2×D411yescharacteristic
218C22×C4×C139C2×D411yescharacteristic
219C22×C4×C139C2×D411yescharacteristic
220C22×C4×C139C2×D411yescharacteristic
221C22×C4×C139C2411yescharacteristic
222SD16×C139—44no—
223SD16×C139—44no—
224D8×C139—28no—
225D8×C139—44no—
226C2×C8×C139—21no—
227C2×C8×C139—21no—
228C2×C8×C139—21no—
229C2×C8×C139—21no—
230C2×C8×C139—21no—
231C2×C8×C139—21no—
232C2×C8×C139—21no—
233C2×C8×C139—21no—
234C2×C8×C139—21no—
235C2×C8×C139—21no—
236C2×C8×C139C2×D412yes—
237C2×C8×C139C2×D412yes—
238C4⋊C4×C139—21no—
239C4⋊C4×C139—21no—
240C4⋊C4×C139—21no—
241C4⋊C4×C139—21no—
242C4⋊C4×C139—21no—
243C4⋊C4×C139—21no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139—42no—
246C4⋊C4×C139—81no—
247C4⋊C4×C139C2×D412yes—
248C22⋊C4×C139—22no—
249C22⋊C4×C139—41no—
250C22⋊C4×C139—42no—
251C22⋊C4×C139—42no—
252C22⋊C4×C139—42no—
253C22⋊C4×C139—42no—
254C22⋊C4×C139—42no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—42no—
257C22⋊C4×C139—42no—
258C22⋊C4×C139—42no—
259C22⋊C4×C139—42no—
260C22⋊C4×C139—81no—
261C22⋊C4×C139—81no—
262C42×C139—21no—
263C42×C139—21no—
264C42×C139—21no—
265C42×C139—21no—
266C23×C139—21no—
267C23×C139—22no—
268C23×C139—21no—
269C23×C139—22no—
270C23×C139—22no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—21no—
275C23×C139—22no—
276C23×C139—22no—
277C23×C139—48no—
278C23×C139—48no—
279C23×C139—41no—
280C23×C139—41no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—41no—
285C23×C139—41no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139—41no—
289C23×C139—41no—
290C23×C139—41no—
291C23×C139—41no—
292C23×C139—41no—
293C23×C139—41no—
294C23×C139—41no—
295C23×C139—84no—
296C23×C139—84no—
297C23×C139—84no—
298C23×C139—84no—
299C23×C139—84no—
300C23×C139AGL(1,ℤ/8)12yes—
301C23×C139C22×D411yescharacteristic
302Q8×C139—41no—
303Q8×C139—41no—
304Q8×C139—41no—
305Q8×C139—41no—
306D4×C139—22no—
307D4×C139—22no—
308D4×C139—22no—
309D4×C139—22no—
310D4×C139—22no—
311D4×C139—22no—
312D4×C139—22no—
313D4×C139—48no—
314D4×C139—41no—
315D4×C139—41no—
316D4×C139—41no—
317D4×C139—41no—
318D4×C139—84no—
319D4×C139#12114yes—
320C2×C4×C139—21no—
321C2×C4×C139—21no—
322C2×C4×C139—21no—
323C2×C4×C139—21no—
324C2×C4×C139—21no—
325C2×C4×C139—22no—
326C2×C4×C139—21no—
327C2×C4×C139—21no—
328C2×C4×C139—21no—
329C2×C4×C139—21no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—21no—
333C2×C4×C139—21no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—41no—
337C2×C4×C139—41no—
338C2×C4×C139—41no—
339C2×C4×C139—41no—
340C2×C4×C139—41no—
341C2×C4×C139—41no—
342C2×C4×C139—41no—
343C2×C4×C139—41no—
344C2×C4×C139—41no—
345C2×C4×C139—41no—
346C2×C4×C139—41no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—41no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
353C2×C4×C139—41no—
354C2×C4×C139—84no—
355C2×C4×C139—84no—
356C2×C4×C139—84no—
357C2×C4×C139C22×D411yescharacteristic
358C2×C4×C139C22×D411yescharacteristic
359C2×C4×C139C2×#4111yescharacteristic
360C2×C4×C139C2×#4111yescharacteristic
361C2×C4×C139H(5,𝔽2)11yescharacteristic
362C2×C4×C139H(5,𝔽2)11yescharacteristic
363C8×C139—22no—
364C8×C139—22no—
365C8×C139—41no—
366C8×C139—41no—
367C22×C139—22no—
368C22×C139—24no—
369C22×C139—22no—
370C22×C139—22no—
371C22×C139—42no—
372C22×C139—41no—
373C22×C139—42no—
374C22×C139—41no—
375C22×C139—42no—
376C22×C139—42no—
377C22×C139—41no—
378C22×C139—42no—
379C22×C139—41no—
380C22×C139—42no—
381C22×C139—42no—
382C22×C139—42no—
383C22×C139—42no—
384C22×C139—42no—
385C22×C139—42no—
386C22×C139—42no—
387C22×C139—816no—
388C22×C139—81no—
389C22×C139—81no—
390C22×C139—81no—
391C22×C139—81no—
392C22×C139—81no—
393C22×C139—81no—
394C22×C139—81no—
395C22×C139—81no—
396C22×C139#52511yescharacteristic
397C22×C139D4211yescharacteristic
398C22×C139D4211yescharacteristic
399C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C139#57511yescharacteristic
401C22×C139#57611yescharacteristic
402C22×C139#57711yescharacteristic
403C4×C139—41no—
404C4×C139—41no—
405C4×C139—41no—
406C4×C139—41no—
407C4×C139—41no—
408C4×C139—42no—
409C4×C139—81no—
410C4×C139—81no—
411C4×C139—81no—
412C4×C139—81no—
413C4×C139C2×#12111yescharacteristic
414C4×C139#53811yescharacteristic
415C4×C139#54611yescharacteristic
416C4×C139#54611yescharacteristic
417C2×C139—42no—
418C2×C139—44no—
419C2×C139—82no—
420C2×C139—82no—
421C2×C139#242411yescharacteristic
422C2×C139#311411yescharacteristic
423C2×C139#311811yescharacteristic
424C2×C139#326411yescharacteristic
425C2×C139#326511yescharacteristic
426C2×C139#326711yescharacteristic
427C2×C139#327311yescharacteristic
428#25172C13911yesmaximal, characteristic, direct product factor, Sylow
429C139#2517211yescharacteristic, direct product factor, Sylow
430C2×#463C2×C13911yescharacteristic, complemented
431C2×#450C2×C13911yescharacteristic, complemented
432C2×#447C2×C13911yescharacteristic
433C2×#442C2×C13911yescharacteristic, complemented
434#2427C2×C13911yescharacteristic, complemented
435D4×C22⋊C4C2×C13911yescharacteristic, complemented
436#2065C2×C13911yescharacteristic, complemented
437#2035C2×C13911yescharacteristic, complemented
438#2033C2×C13911yescharacteristic, complemented
439#2012C2×C13911yescharacteristic, complemented
440#1973C2×C13911yescharacteristic, complemented
441#1924C2×C13911yescharacteristic, complemented
442#1879C2×C13911yescharacteristic, complemented
443#1877C2×C13911yescharacteristic, complemented
444#1862C2×C13911yescharacteristic, complemented
445C23×D4C22×C13911yescharacteristic
446C22×SD16C22×C13911yescharacteristic
447C22×SD16C22×C13911yescharacteristic
448C22×D8C22×C13911yescharacteristic
449C22×D8C22×C13911yescharacteristic
450C2×#124C22×C13911yescharacteristic, complemented
451C2×C22⋊Q8C22×C13911yescharacteristic
452C2×#121C22×C13911yescharacteristic
453C2×C4×D4C22×C13911yescharacteristic
454C2×C4×D4C22×C13911yescharacteristic
455C2×C4×D4C22×C13911yescharacteristic, complemented
456C22×C22⋊C4—21no—
457#463—24no—
458#450—24no—
459#447—24no—
460#442—24no—
461C2×#107C22×C13911yescharacteristic, complemented
462C2×#106C22×C13911yescharacteristic, complemented
463C2×C4⋊C8C22×C13911yescharacteristic, complemented
464C2×#103C22×C13911yescharacteristic, complemented
465C2×#103C22×C13911yescharacteristic, complemented
466C2×#102C22×C13911yescharacteristic
467C2×#102C22×C13911yescharacteristic
468C2×#102C22×C13911yescharacteristic
469C2×#102C22×C13911yescharacteristic
470C2×#102C22×C13911yescharacteristic, complemented
471C2×#102C22×C13911yescharacteristic, complemented
472C2×C22⋊C8C22×C13911yescharacteristic
473C2×C22⋊C8C22×C13911yescharacteristic
474C2×#97C22×C13911yescharacteristic, complemented
475#397—21no—
476#394—21no—
477#391C22×C13911yescharacteristic, complemented
478#390C22×C13911yescharacteristic
479#390C22×C13911yescharacteristic
480#389C22×C13911yescharacteristic, complemented
481#386—21no—
482#386—21no—
483#386—21no—
484#380—21no—
485#380C22×C13911yescharacteristic
486#379—21no—
487C4×C22⋊C4C22×C13911yescharacteristic
488#340C22×C13911yescharacteristic, complemented
489#340C22×C13911yescharacteristic, complemented
490#336C22×C13911yescharacteristic, complemented
491#336C22×C13911yescharacteristic, complemented
492C25—21no—
493C22×Q8C23×C13911yescharacteristic
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C23×C13911yescharacteristic
503C22×D4C23×C13911yescharacteristic
504C22×D4C23×C13911yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C23×C13911yescharacteristic
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—41no—
520C2×D8D4×C13914yes—
521C22×C8C23×C13911yescharacteristic
522C22×C8C23×C13911yescharacteristic
523C22×C8C23×C13911yescharacteristic
524C22×C8C23×C13911yescharacteristic
525#124—22no—
526#124—41no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529#121—22no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4C23×C13911yescharacteristic
540C2×C4⋊C4C23×C13911yescharacteristic
541C2×C4⋊C4C23×C13911yescharacteristic
542C2×C4⋊C4C23×C13911yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C13911yescharacteristic
557C2×C22⋊C4D4×C13911yescharacteristic
558C2×C42C23×C13911yescharacteristic
559C2×C42C23×C13911yescharacteristic
560#107—41no—
561#106—22no—
562C4⋊C8—22no—
563#103—22no—
564#103—41no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102D4×C13914yescomplemented
571C22⋊C8—22no—
572C22⋊C8—22no—
573#97—22no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95D4×C13911yescharacteristic
579#95D4×C13911yescharacteristic
580C24—21no—
581C24—24no—
582C24—21no—
583C24—21no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C13911yescharacteristic
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C13912yes—
621C2×D4C2×D4×C13912yes—
622C2×D4C2×D4×C13912yes—
623C2×D4#41×C13912yes—
624C2×D4#41×C13912yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4C2×D4×C13911yescharacteristic
646C22×C4C2×D4×C13911yescharacteristic
647C22×C4C2×D4×C13911yescharacteristic
648C22×C4C2×D4×C13911yescharacteristic
649C22×C4C2×D4×C13911yescharacteristic
650C22×C4C24×C13911yescharacteristic
651SD16—44no—
652SD16—44no—
653D8—28no—
654D8—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8C2×D4×C13912yes—
666C2×C8C2×D4×C13912yes—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—42no—
675C4⋊C4—81no—
676C4⋊C4C2×D4×C13912yes—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—81no—
690C22⋊C4—81no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—48no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23AGL(1,ℤ/8)×C13912yes—
730C23C22×D4×C13911yescharacteristic
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—48no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4#121×C13914yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4C22×D4×C13911yescharacteristic
787C2×C4C22×D4×C13911yescharacteristic
788C2×C4C2×#41×C13911yescharacteristic
789C2×C4C2×#41×C13911yescharacteristic
790C2×C4H(5,𝔽2)×C13911yescharacteristic
791C2×C4H(5,𝔽2)×C13911yescharacteristic
792C8—22no—
793C8—22no—
794C8—41no—
795C8—41no—
796C22—22no—
797C22—24no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—816no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22#525×C13911yescharacteristic
826C22D42×C13911yescharacteristic
827C22D42×C13911yescharacteristic
828C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
829C22#575×C13911yescharacteristic
830C22#576×C13911yescharacteristic
831C22#577×C13911yescharacteristic
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—42no—
838C4—81no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4C2×#121×C13911yescharacteristic
843C4#538×C13911yescharacteristic
844C4#546×C13911yescharacteristic
845C4#546×C13911yescharacteristic
846C2—42no—
847C2—44no—
848C2—82no—
849C2—82no—
850C2#2424×C13911yescharacteristic
851C2#3114×C13911yescharacteristic
852C2#3118×C13911yescharacteristic
853C2#3264×C13911yescharacteristic
854C2#3265×C13911yescharacteristic
855C2#3267×C13911yescharacteristic
856C2#3273×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#447×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#463×C139C2semidirect
2. C2×#450×C139C2semidirect
4. C2×#442×C139C2semidirect
5. #2427×C139C2semidirect
6. D4×C22⋊C4×C139C2semidirect
7. #2065×C139C2semidirect
8. #2035×C139C2semidirect
9. #2033×C139C2semidirect
10. #2012×C139C2semidirect
11. #1973×C139C2semidirect
12. #1924×C139C2semidirect
13. #1879×C139C2semidirect
14. #1877×C139C2semidirect
15. #1862×C139C2semidirect
21. C2×#124×C139C22semidirect
26. C2×C4×D4×C139C22semidirect
32. C2×#107×C139C22semidirect
33. C2×#106×C139C22semidirect
34. C2×C4⋊C8×C139C22semidirect
35. C2×#103×C139C22semidirect
36. C2×#103×C139C22semidirect
41. C2×#102×C139C22semidirect
42. C2×#102×C139C22semidirect
45. C2×#97×C139C22semidirect
48. #391×C139C22semidirect
51. #389×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #336×C139C22semidirect
62. #336×C139C22semidirect
141. #102×C139D4semidirect
428. #25172C139direct (N × H)
429. C139#25172direct (N × H)
430. C2×#463C2×C139semidirect
431. C2×#450C2×C139semidirect
433. C2×#442C2×C139semidirect
434. #2427C2×C139semidirect
435. D4×C22⋊C4C2×C139semidirect
436. #2065C2×C139semidirect
437. #2035C2×C139semidirect
438. #2033C2×C139semidirect
439. #2012C2×C139semidirect
440. #1973C2×C139semidirect
441. #1924C2×C139semidirect
442. #1879C2×C139semidirect
443. #1877C2×C139semidirect
444. #1862C2×C139semidirect
450. C2×#124C22×C139semidirect
455. C2×C4×D4C22×C139semidirect
461. C2×#107C22×C139semidirect
462. C2×#106C22×C139semidirect
463. C2×C4⋊C8C22×C139semidirect
464. C2×#103C22×C139semidirect
465. C2×#103C22×C139semidirect
470. C2×#102C22×C139semidirect
471. C2×#102C22×C139semidirect
474. C2×#97C22×C139semidirect
477. #391C22×C139semidirect
480. #389C22×C139semidirect
488. #340C22×C139semidirect
489. #340C22×C139semidirect
490. #336C22×C139semidirect
491. #336C22×C139semidirect
570. #102D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1392
C2×#450×C1392
C2×#447×C1392
C2×#442×C1392
#2427×C1392
D4×C22⋊C4×C1392
#2065×C1392
#2035×C1392
#2033×C1392
#2012×C1392
#1973×C1392
#1924×C1392
#1879×C1392
#1877×C1392
#1862×C1392
#25172139