Finite Group Databasebeta

← C139×#23876 #48018472

Subgroups — C139×#23876 #48018472

Order 35584.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C139C211yesmaximal, characteristic, complemented
2#3488×C139C211yesmaximal, characteristic, complemented
3C2×#453×C139C212yesmaximal, complemented
4#3003×C139C211yesmaximal, characteristic, complemented
5#2433×C139C211yesmaximal, characteristic, complemented
6#2006×C139C212yesmaximal, complemented
7#2002×C139C212yesmaximal, complemented
8#1900×C139C211yesmaximal, characteristic, complemented
9#1883×C139C212yesmaximal, complemented
10#1871×C139C211yesmaximal, characteristic, complemented
11#1789×C139C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C139C2211yescharacteristic, complemented
13C22×#41×C139C2211yescharacteristic
14C23×D4×C139C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C139—21no—
16C2×AGL(1,ℤ/8)×C139—21no—
17C2×AGL(1,ℤ/8)×C139—28no—
18C2×AGL(1,ℤ/8)×C139C2212yes—
19C2×AGL(1,ℤ/8)×C139C2212yescomplemented
20C2×AGL(1,ℤ/8)×C139C2212yescomplemented
21C22×SD16×C139—21no—
22C22×D8×C139—21no—
23C22×M16×C139C2211yescharacteristic, complemented
24#550×C139—21no—
25#548×C139—21no—
26#546×C139—21no—
27#546×C139—22no—
28D42×C139—22no—
29D42×C139—21no—
30#537×C139—21no—
31#537×C139C2211yescharacteristic, complemented
32#535×C139—21no—
33#535×C139C2211yescharacteristic, complemented
34C2×#127×C139C2212yescomplemented
35#525×C139—21no—
36#525×C139C2211yescharacteristic
37C2×#121×C139—21no—
38C2×#121×C139C2211yescharacteristic
39C2×#120×C139—22no—
40#520×C139C2211yescharacteristic, complemented
41#453×C139—28no—
42#450×C139—21no—
43#450×C139—21no—
44#447×C139—21no—
45#447×C139—21no—
46C2×#104×C139C2212yescomplemented
47C2×#104×C139C2212yescomplemented
48C2×#104×C139C2212yescomplemented
49#418×C139C2212yescomplemented
50C2×#100×C139C2212yescomplemented
51#407×C139C2211yescharacteristic, complemented
52#392×C139—22no—
53#390×C139C2212yescomplemented
54C4×C22⋊C4×C139C2211yescharacteristic, complemented
55#343×C139C2212yescomplemented
56#339×C139C2212yescomplemented
57C25×C139—21no—
58H(5,𝔽2)×C139—24no—
59H(5,𝔽2)×C139—42no—
60C2×#41×C139—21no—
61C2×#41×C139—21no—
62C2×#41×C139—21no—
63C2×#41×C139—21no—
64C2×#41×C139—24no—
65C2×#41×C139—42no—
66C2×#41×C139D411yescharacteristic, complemented
67C2×#41×C139D411yescharacteristic, complemented
68C2×#41×C139C2311yescharacteristic
69C2×#41×C139C2311yescharacteristic
70C2×#41×C139C2311yescharacteristic
71C22×Q8×C139D411yescharacteristic, complemented
72C22×D4×C139—24no—
73C22×D4×C139—21no—
74C22×D4×C139—22no—
75C22×D4×C139—22no—
76C22×D4×C139—21no—
77C22×D4×C139—21no—
78C22×D4×C139—24no—
79C22×D4×C139—21no—
80C22×D4×C139—21no—
81C22×D4×C139—21no—
82C22×D4×C139—21no—
83C22×D4×C139—21no—
84C22×D4×C139—42no—
85C22×D4×C139D412yes—
86C22×D4×C139D411yescharacteristic, complemented
87C22×D4×C139C2311yescharacteristic
88C22×D4×C139C2312yes—
89C23×C4×C139—21no—
90C23×C4×C139C2311yescharacteristic
91AGL(1,ℤ/8)×C139—28no—
92AGL(1,ℤ/8)×C139—28no—
93AGL(1,ℤ/8)×C139—24no—
94AGL(1,ℤ/8)×C139—24no—
95AGL(1,ℤ/8)×C139—24no—
96AGL(1,ℤ/8)×C139—24no—
97AGL(1,ℤ/8)×C139—42no—
98AGL(1,ℤ/8)×C139D418yescomplemented
99C2×SD16×C139—28no—
100C2×SD16×C139—22no—
101C2×SD16×C139—22no—
102C2×SD16×C139—22no—
103C2×D8×C139—28no—
104C2×D8×C139—22no—
105C2×D8×C139—22no—
106C2×D8×C139—22no—
107C2×M16×C139—21no—
108C2×M16×C139—24no—
109C2×M16×C139C2312yes—
110C2×M16×C139C2312yes—
111C22×C8×C139—21no—
112#127×C139—22no—
113#127×C139—21no—
114#127×C139—24no—
115#127×C139—42no—
116#124×C139—22no—
117#124×C139—21no—
118#123×C139—22no—
119#123×C139—21no—
120C22⋊Q8×C139—22no—
121C22⋊Q8×C139—21no—
122C22⋊Q8×C139—21no—
123C22⋊Q8×C139D411yescharacteristic, complemented
124C22⋊Q8×C139D411yescharacteristic, complemented
125#121×C139—22no—
126#121×C139—22no—
127#121×C139—22no—
128#121×C139—22no—
129#121×C139—22no—
130#121×C139—21no—
131#121×C139—21no—
132#121×C139—21no—
133#121×C139—21no—
134#121×C139—21no—
135#121×C139—21no—
136#121×C139—22no—
137#121×C139—21no—
138#121×C139—21no—
139#121×C139D411yescharacteristic, complemented
140#121×C139D411yescharacteristic, complemented
141#120×C139—22no—
142#120×C139—22no—
143#120×C139—22no—
144#120×C139—21no—
145#120×C139—22no—
146#120×C139—48no—
147C4×Q8×C139—21no—
148C4×D4×C139—22no—
149C4×D4×C139—22no—
150C4×D4×C139—21no—
151C4×D4×C139—22no—
152C4×D4×C139—21no—
153C4×D4×C139—21no—
154#117×C139—21no—
155#117×C139C2311yescharacteristic
156C2×C4⋊C4×C139—21no—
157C2×C4⋊C4×C139C2311yescharacteristic
158C2×C22⋊C4×C139—22no—
159C2×C22⋊C4×C139—21no—
160C2×C22⋊C4×C139—24no—
161C2×C22⋊C4×C139D412yes—
162C2×C42×C139C2312yes—
163#104×C139—24no—
164#104×C139—24no—
165#104×C139—42no—
166#102×C139—22no—
167#102×C139—22no—
168#100×C139—24no—
169C22⋊C8×C139—21no—
170C22⋊C8×C139—21no—
171#95×C139—21no—
172C24×C139—22no—
173C24×C139—22no—
174C24×C139—21no—
175C24×C139—44no—
176C24×C139—44no—
177C24×C139—41no—
178C24×C139—41no—
179C24×C139—82no—
180C24×C139C2×D411yescharacteristic
181C24×C139C2×D412yes—
182#41×C139—22no—
183#41×C139—22no—
184#41×C139—22no—
185#41×C139—22no—
186#41×C139—22no—
187#41×C139—22no—
188#41×C139—22no—
189#41×C139—44no—
190#41×C139—41no—
191#41×C139—41no—
192#41×C139—44no—
193#41×C139—44no—
194#41×C139—42no—
195#41×C139—42no—
196#41×C139C2×D414yes—
197C2×Q8×C139—21no—
198C2×Q8×C139—22no—
199C2×Q8×C139—41no—
200C2×Q8×C139C2×D411yescharacteristic
201C2×Q8×C139C2×D411yescharacteristic
202C2×Q8×C139C2×D411yescharacteristic
203C2×D4×C139—21no—
204C2×D4×C139—24no—
205C2×D4×C139—24no—
206C2×D4×C139—22no—
207C2×D4×C139—22no—
208C2×D4×C139—22no—
209C2×D4×C139—22no—
210C2×D4×C139—21no—
211C2×D4×C139—21no—
212C2×D4×C139—21no—
213C2×D4×C139—21no—
214C2×D4×C139—21no—
215C2×D4×C139—22no—
216C2×D4×C139—22no—
217C2×D4×C139—22no—
218C2×D4×C139—21no—
219C2×D4×C139—22no—
220C2×D4×C139—21no—
221C2×D4×C139—22no—
222C2×D4×C139—22no—
223C2×D4×C139—22no—
224C2×D4×C139—22no—
225C2×D4×C139—21no—
226C2×D4×C139—21no—
227C2×D4×C139—22no—
228C2×D4×C139—22no—
229C2×D4×C139—22no—
230C2×D4×C139—41no—
231C2×D4×C139—44no—
232C2×D4×C139—44no—
233C2×D4×C139—44no—
234C2×D4×C139—44no—
235C2×D4×C139—42no—
236C2×D4×C139—42no—
237C2×D4×C139—48no—
238C2×D4×C139—44no—
239C2×D4×C139—48no—
240C2×D4×C139—42no—
241C2×D4×C139—42no—
242C2×D4×C139—44no—
243C2×D4×C139—48no—
244C2×D4×C139—41no—
245C2×D4×C139—41no—
246C2×D4×C139—84no—
247C2×D4×C139—84no—
248C2×D4×C139C2×D411yescharacteristic
249C2×D4×C139C2×D411yescharacteristic
250C2×D4×C139C2×D411yescharacteristic
251C2×D4×C139C2×D414yescomplemented
252C22×C4×C139—21no—
253C22×C4×C139—22no—
254C22×C4×C139—22no—
255C22×C4×C139—22no—
256C22×C4×C139—21no—
257C22×C4×C139—22no—
258C22×C4×C139—22no—
259C22×C4×C139—21no—
260C22×C4×C139—21no—
261C22×C4×C139—21no—
262C22×C4×C139—21no—
263C22×C4×C139—44no—
264C22×C4×C139C2×D411yescharacteristic
265C22×C4×C139C2×D411yescharacteristic
266C22×C4×C139C2×D411yescharacteristic
267C22×C4×C139C2×D411yescharacteristic
268C22×C4×C139C2×D411yescharacteristic
269C22×C4×C139C2×D412yes—
270C22×C4×C139C2411yescharacteristic
271SD16×C139—28no—
272SD16×C139—28no—
273SD16×C139—44no—
274D8×C139—28no—
275D8×C139—28no—
276D8×C139—44no—
277M16×C139—24no—
278M16×C139—22no—
279M16×C139—22no—
280M16×C139—22no—
281M16×C139C2×D414yescomplemented
282C2×C8×C139—24no—
283C2×C8×C139—22no—
284C2×C8×C139—22no—
285C4⋊C4×C139—22no—
286C4⋊C4×C139—22no—
287C4⋊C4×C139—21no—
288C4⋊C4×C139—21no—
289C4⋊C4×C139—21no—
290C4⋊C4×C139—21no—
291C4⋊C4×C139C2×D411yescharacteristic
292C4⋊C4×C139C2×D411yescharacteristic
293C22⋊C4×C139—22no—
294C22⋊C4×C139—22no—
295C22⋊C4×C139—24no—
296C22⋊C4×C139—22no—
297C22⋊C4×C139—22no—
298C22⋊C4×C139—22no—
299C22⋊C4×C139—21no—
300C22⋊C4×C139—21no—
301C22⋊C4×C139—21no—
302C22⋊C4×C139—21no—
303C22⋊C4×C139—22no—
304C22⋊C4×C139—22no—
305C22⋊C4×C139—21no—
306C22⋊C4×C139—48no—
307C42×C139—22no—
308C42×C139—21no—
309C42×C139—22no—
310C42×C139—22no—
311C23×C139—21no—
312C23×C139—22no—
313C23×C139—22no—
314C23×C139—22no—
315C23×C139—21no—
316C23×C139—21no—
317C23×C139—24no—
318C23×C139—24no—
319C23×C139—41no—
320C23×C139—42no—
321C23×C139—44no—
322C23×C139—44no—
323C23×C139—44no—
324C23×C139—44no—
325C23×C139—44no—
326C23×C139—42no—
327C23×C139—42no—
328C23×C139—42no—
329C23×C139—42no—
330C23×C139—42no—
331C23×C139—81no—
332C23×C139—82no—
333C23×C139—82no—
334C23×C139—82no—
335C23×C139—82no—
336C23×C139—82no—
337C23×C139—816no—
338C23×C139—82no—
339C23×C139#12011yescharacteristic
340C23×C139#12011yescharacteristic
341C23×C139C22×D411yescharacteristic
342Q8×C139—21no—
343Q8×C139—21no—
344Q8×C139—21no—
345Q8×C139—22no—
346Q8×C139—42no—
347Q8×C139#12012yescomplemented
348D4×C139—24no—
349D4×C139—21no—
350D4×C139—24no—
351D4×C139—21no—
352D4×C139—21no—
353D4×C139—22no—
354D4×C139—24no—
355D4×C139—42no—
356D4×C139—42no—
357D4×C139—44no—
358D4×C139—44no—
359D4×C139—44no—
360D4×C139—42no—
361D4×C139—44no—
362D4×C139—42no—
363D4×C139—42no—
364D4×C139—44no—
365D4×C139—42no—
366D4×C139—41no—
367D4×C139—42no—
368D4×C139—41no—
369D4×C139—42no—
370D4×C139—42no—
371D4×C139—81no—
372D4×C139—82no—
373D4×C139—82no—
374D4×C139—82no—
375D4×C139—82no—
376D4×C139—816no—
377D4×C139#12012yescomplemented
378C2×C4×C139—21no—
379C2×C4×C139—22no—
380C2×C4×C139—21no—
381C2×C4×C139—21no—
382C2×C4×C139—21no—
383C2×C4×C139—21no—
384C2×C4×C139—22no—
385C2×C4×C139—22no—
386C2×C4×C139—24no—
387C2×C4×C139—24no—
388C2×C4×C139—21no—
389C2×C4×C139—22no—
390C2×C4×C139—21no—
391C2×C4×C139—21no—
392C2×C4×C139—21no—
393C2×C4×C139—42no—
394C2×C4×C139—42no—
395C2×C4×C139—42no—
396C2×C4×C139—44no—
397C2×C4×C139—42no—
398C2×C4×C139—42no—
399C2×C4×C139—41no—
400C2×C4×C139—41no—
401C2×C4×C139—42no—
402C2×C4×C139—42no—
403C2×C4×C139—82no—
404C2×C4×C139#12011yescharacteristic
405C2×C4×C139#12011yescharacteristic
406C2×C4×C139C22×D411yescharacteristic
407C2×C4×C139C22×D412yes—
408C2×C4×C139C22×D411yescharacteristic
409C2×C4×C139H(5,𝔽2)12yes—
410C8×C139—24no—
411C8×C139—42no—
412C22×C139—21no—
413C22×C139—21no—
414C22×C139—21no—
415C22×C139—21no—
416C22×C139—21no—
417C22×C139—22no—
418C22×C139—21no—
419C22×C139—21no—
420C22×C139—44no—
421C22×C139—48no—
422C22×C139—41no—
423C22×C139—41no—
424C22×C139—41no—
425C22×C139—41no—
426C22×C139—42no—
427C22×C139—44no—
428C22×C139—42no—
429C22×C139—41no—
430C22×C139—41no—
431C22×C139—41no—
432C22×C139—42no—
433C22×C139—41no—
434C22×C139—84no—
435C22×C139—84no—
436C22×C139—84no—
437C22×C139—88no—
438C22×C139—88no—
439C22×C139—82no—
440C22×C139—82no—
441C22×C139—164no—
442C22×C139#45312yescomplemented
443C22×C139C2×#12011yescharacteristic
444C22×C139D4212yes—
445C4×C139—21no—
446C4×C139—21no—
447C4×C139—22no—
448C4×C139—44no—
449C4×C139—41no—
450C4×C139—41no—
451C4×C139—42no—
452C4×C139—41no—
453C4×C139—41no—
454C4×C139C2×#12011yescharacteristic
455C4×C139#53411yescharacteristic
456C4×C139D4212yes—
457C2×C139—22no—
458C2×C139—22no—
459C2×C139—41no—
460C2×C139—42no—
461C2×C139—81no—
462C2×C139—84no—
463C2×C139—82no—
464C2×C139—81no—
465C2×C139#240311yescharacteristic
466C2×C139C2×#45311yescharacteristic
467C2×C139#302111yescharacteristic
468#23876C13911yesmaximal, characteristic, direct product factor, Sylow
469C139#2387611yescharacteristic, direct product factor, Sylow
470C22×AGL(1,ℤ/8)C2×C13911yescharacteristic, complemented
471#3488C2×C13911yescharacteristic, complemented
472C2×#453C2×C13912yescomplemented
473#3003C2×C13911yescharacteristic, complemented
474#2433C2×C13911yescharacteristic, complemented
475#2006C2×C13912yescomplemented
476#2002C2×C13912yescomplemented
477#1900C2×C13911yescharacteristic, complemented
478#1883C2×C13912yescomplemented
479#1871C2×C13911yescharacteristic, complemented
480#1789C2×C13911yescharacteristic, complemented
481C2×H(5,𝔽2)C22×C13911yescharacteristic, complemented
482C22×#41C22×C13911yescharacteristic
483C23×D4C22×C13911yescharacteristic, complemented
484C2×AGL(1,ℤ/8)—21no—
485C2×AGL(1,ℤ/8)—21no—
486C2×AGL(1,ℤ/8)—28no—
487C2×AGL(1,ℤ/8)C22×C13912yes—
488C2×AGL(1,ℤ/8)C22×C13912yescomplemented
489C2×AGL(1,ℤ/8)C22×C13912yescomplemented
490C22×SD16—21no—
491C22×D8—21no—
492C22×M16C22×C13911yescharacteristic, complemented
493#550—21no—
494#548—21no—
495#546—21no—
496#546—22no—
497D42—22no—
498D42—21no—
499#537—21no—
500#537C22×C13911yescharacteristic, complemented
501#535—21no—
502#535C22×C13911yescharacteristic, complemented
503C2×#127C22×C13912yescomplemented
504#525—21no—
505#525C22×C13911yescharacteristic
506C2×#121—21no—
507C2×#121C22×C13911yescharacteristic
508C2×#120—22no—
509#520C22×C13911yescharacteristic, complemented
510#453—28no—
511#450—21no—
512#450—21no—
513#447—21no—
514#447—21no—
515C2×#104C22×C13912yescomplemented
516C2×#104C22×C13912yescomplemented
517C2×#104C22×C13912yescomplemented
518#418C22×C13912yescomplemented
519C2×#100C22×C13912yescomplemented
520#407C22×C13911yescharacteristic, complemented
521#392—22no—
522#390C22×C13912yescomplemented
523C4×C22⋊C4C22×C13911yescharacteristic, complemented
524#343C22×C13912yescomplemented
525#339C22×C13912yescomplemented
526C25—21no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41D4×C13911yescharacteristic, complemented
536C2×#41D4×C13911yescharacteristic, complemented
537C2×#41C23×C13911yescharacteristic
538C2×#41C23×C13911yescharacteristic
539C2×#41C23×C13911yescharacteristic
540C22×Q8D4×C13911yescharacteristic, complemented
541C22×D4—24no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—24no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—42no—
554C22×D4D4×C13912yes—
555C22×D4D4×C13911yescharacteristic, complemented
556C22×D4C23×C13911yescharacteristic
557C22×D4C23×C13912yes—
558C23×C4—21no—
559C23×C4C23×C13911yescharacteristic
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—28no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—42no—
567AGL(1,ℤ/8)D4×C13918yescomplemented
568C2×SD16—28no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—28no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×M16—21no—
577C2×M16—24no—
578C2×M16C23×C13912yes—
579C2×M16C23×C13912yes—
580C22×C8—21no—
581#127—22no—
582#127—21no—
583#127—24no—
584#127—42no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C13911yescharacteristic, complemented
593C22⋊Q8D4×C13911yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121D4×C13911yescharacteristic, complemented
609#121D4×C13911yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—48no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C23×C13911yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C13911yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C13912yes—
631C2×C42C23×C13912yes—
632#104—24no—
633#104—24no—
634#104—42no—
635#102—22no—
636#102—22no—
637#100—24no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640#95—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C13911yescharacteristic
650C24C2×D4×C13912yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C13914yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C13911yescharacteristic
670C2×Q8C2×D4×C13911yescharacteristic
671C2×Q8C2×D4×C13911yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C13911yescharacteristic
718C2×D4C2×D4×C13911yescharacteristic
719C2×D4C2×D4×C13911yescharacteristic
720C2×D4C2×D4×C13914yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C13911yescharacteristic
734C22×C4C2×D4×C13911yescharacteristic
735C22×C4C2×D4×C13911yescharacteristic
736C22×C4C2×D4×C13911yescharacteristic
737C22×C4C2×D4×C13911yescharacteristic
738C22×C4C2×D4×C13912yes—
739C22×C4C24×C13911yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C13914yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C13911yescharacteristic
761C4⋊C4C2×D4×C13911yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23#120×C13911yescharacteristic
809C23#120×C13911yescharacteristic
810C23C22×D4×C13911yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#120×C13912yescomplemented
817D4—24no—
818D4—21no—
819D4—24no—
820D4—21no—
821D4—21no—
822D4—22no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—44no—
832D4—42no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—42no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—82no—
841D4—81no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4#120×C13912yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4#120×C13911yescharacteristic
874C2×C4#120×C13911yescharacteristic
875C2×C4C22×D4×C13911yescharacteristic
876C2×C4C22×D4×C13912yes—
877C2×C4C22×D4×C13911yescharacteristic
878C2×C4H(5,𝔽2)×C13912yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—21no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22#453×C13912yescomplemented
912C22C2×#120×C13911yescharacteristic
913C22D42×C13912yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—41no—
923C4C2×#120×C13911yescharacteristic
924C4#534×C13911yescharacteristic
925C4D42×C13912yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2#2403×C13911yescharacteristic
935C2C2×#453×C13911yescharacteristic
936C2#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. C22×AGL(1,ℤ/8)×C139C2semidirect
2. #3488×C139C2semidirect
3. C2×#453×C139C2semidirect
4. #3003×C139C2semidirect
5. #2433×C139C2semidirect
6. #2006×C139C2semidirect
7. #2002×C139C2semidirect
8. #1900×C139C2semidirect
9. #1883×C139C2semidirect
10. #1871×C139C2semidirect
11. #1789×C139C2semidirect
12. C2×H(5,𝔽2)×C139C22semidirect
14. C23×D4×C139C22semidirect
19. C2×AGL(1,ℤ/8)×C139C22semidirect
20. C2×AGL(1,ℤ/8)×C139C22semidirect
23. C22×M16×C139C22semidirect
31. #537×C139C22semidirect
33. #535×C139C22semidirect
34. C2×#127×C139C22semidirect
40. #520×C139C22semidirect
46. C2×#104×C139C22semidirect
47. C2×#104×C139C22semidirect
48. C2×#104×C139C22semidirect
49. #418×C139C22semidirect
50. C2×#100×C139C22semidirect
51. #407×C139C22semidirect
53. #390×C139C22semidirect
54. C4×C22⋊C4×C139C22semidirect
55. #343×C139C22semidirect
56. #339×C139C22semidirect
66. C2×#41×C139D4semidirect
67. C2×#41×C139D4semidirect
71. C22×Q8×C139D4semidirect
86. C22×D4×C139D4semidirect
98. AGL(1,ℤ/8)×C139D4semidirect
123. C22⋊Q8×C139D4semidirect
124. C22⋊Q8×C139D4semidirect
139. #121×C139D4semidirect
140. #121×C139D4semidirect
251. C2×D4×C139C2×D4semidirect
281. M16×C139C2×D4semidirect
347. Q8×C139#120semidirect
377. D4×C139#120semidirect
442. C22×C139#453semidirect
468. #23876C139direct (N × H)
469. C139#23876direct (N × H)
470. C22×AGL(1,ℤ/8)C2×C139semidirect
471. #3488C2×C139semidirect
472. C2×#453C2×C139semidirect
473. #3003C2×C139semidirect
474. #2433C2×C139semidirect
475. #2006C2×C139semidirect
476. #2002C2×C139semidirect
477. #1900C2×C139semidirect
478. #1883C2×C139semidirect
479. #1871C2×C139semidirect
480. #1789C2×C139semidirect
481. C2×H(5,𝔽2)C22×C139semidirect
483. C23×D4C22×C139semidirect
488. C2×AGL(1,ℤ/8)C22×C139semidirect
489. C2×AGL(1,ℤ/8)C22×C139semidirect
492. C22×M16C22×C139semidirect
500. #537C22×C139semidirect
502. #535C22×C139semidirect
503. C2×#127C22×C139semidirect
509. #520C22×C139semidirect
515. C2×#104C22×C139semidirect
516. C2×#104C22×C139semidirect
517. C2×#104C22×C139semidirect
518. #418C22×C139semidirect
519. C2×#100C22×C139semidirect
520. #407C22×C139semidirect
522. #390C22×C139semidirect
523. C4×C22⋊C4C22×C139semidirect
524. #343C22×C139semidirect
525. #339C22×C139semidirect
535. C2×#41D4×C139semidirect
536. C2×#41D4×C139semidirect
540. C22×Q8D4×C139semidirect
555. C22×D4D4×C139semidirect
567. AGL(1,ℤ/8)D4×C139semidirect
592. C22⋊Q8D4×C139semidirect
593. C22⋊Q8D4×C139semidirect
608. #121D4×C139semidirect
609. #121D4×C139semidirect
720. C2×D4C2×D4×C139semidirect
750. M16C2×D4×C139semidirect
816. Q8#120×C139semidirect
846. D4#120×C139semidirect
911. C22#453×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
#3488×C1392
C2×#453×C1392
#3003×C1392
#2433×C1392
#2006×C1392
#2002×C1392
#1900×C1392
#1883×C1392
#1871×C1392
#1789×C1392
#23876139