Finite Group Databasebeta

← C139×#25144 #48019740

Subgroups — C139×#25144 #48019740

Order 35584.

1114 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×#471×C139C211yesmaximal, characteristic, complemented
2#3056×C139C211yesmaximal, characteristic, complemented
3#3003×C139C211yesmaximal, characteristic
4C2×#450×C139C211yesmaximal, characteristic, complemented
5#2933×C139C211yesmaximal, characteristic, complemented
6C22×#100×C139C211yesmaximal, characteristic, complemented
7#2063×C139C211yesmaximal, characteristic, complemented
8#2051×C139C211yesmaximal, characteristic, complemented
9#2046×C139C211yesmaximal, characteristic, complemented
10#2019×C139C211yesmaximal, characteristic, complemented
11#1977×C139C211yesmaximal, characteristic, complemented
12#1931×C139C211yesmaximal, characteristic, complemented
13#1907×C139C211yesmaximal, characteristic, complemented
14#1901×C139C211yesmaximal, characteristic, complemented
15#1855×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C2×#137×C139C2211yescharacteristic, complemented
18C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
20C22×SD16×C139C2211yescharacteristic
21C22×SD16×C139C2211yescharacteristic
22C2×#131×C139C2211yescharacteristic, complemented
23C22×M16×C139C2211yescharacteristic
24C22×M16×C139C2211yescharacteristic
25#525×C139C2211yescharacteristic
26C2×C22⋊Q8×C139C2211yescharacteristic
27#471×C139—24no—
28#470×C139—21no—
29#468×C139—21no—
30#467×C139—21no—
31#465×C139—21no—
32#450×C139—21no—
33#450×C139—21no—
34#450×C139—21no—
35#450×C139—21no—
36#450×C139—21no—
37#450×C139—21no—
38#447×C139—21no—
39#447×C139—21no—
40#436×C139—21no—
41#435×C139—21no—
42#435×C139—21no—
43C8×D4×C139—21no—
44C2×#108×C139C2211yescharacteristic, complemented
45C2×#108×C139C2211yescharacteristic, complemented
46#428×C139C2211yescharacteristic, complemented
47#424×C139C2211yescharacteristic, complemented
48#419×C139C2211yescharacteristic, complemented
49#418×C139C2211yescharacteristic
50#418×C139C2211yescharacteristic
51#417×C139C2211yescharacteristic, complemented
52C2×#102×C139C2211yescharacteristic
53C2×#102×C139C2211yescharacteristic
54C2×#101×C139C2211yescharacteristic, complemented
55C2×#101×C139C2211yescharacteristic, complemented
56C2×#100×C139—24no—
57C2×#100×C139C2211yescharacteristic
58C2×#100×C139C2211yescharacteristic
59C2×#100×C139C2211yescharacteristic
60C2×#100×C139C2211yescharacteristic
61#408×C139C2211yescharacteristic, complemented
62#407×C139C2211yescharacteristic
63C2×C22⋊C8×C139C2211yescharacteristic
64#405×C139C2211yescharacteristic, complemented
65#343×C139C2211yescharacteristic, complemented
66#343×C139C2211yescharacteristic, complemented
67#341×C139C2211yescharacteristic, complemented
68#341×C139C2211yescharacteristic, complemented
69C25×C139—21no—
70C2×#41×C139C2311yescharacteristic
71C22×Q8×C139C2311yescharacteristic
72C22×D4×C139—22no—
73C22×D4×C139—22no—
74C22×D4×C139—21no—
75C22×D4×C139—21no—
76C22×D4×C139—21no—
77C22×D4×C139—21no—
78C22×D4×C139—21no—
79C22×D4×C139—41no—
80C22×D4×C139—41no—
81C22×D4×C139C2311yescharacteristic
82C22×D4×C139C2311yescharacteristic
83C23×C4×C139C2311yescharacteristic
84#137×C139—22no—
85#137×C139—41no—
86AGL(1,ℤ/8)×C139—22no—
87AGL(1,ℤ/8)×C139—22no—
88AGL(1,ℤ/8)×C139—41no—
89AGL(1,ℤ/8)×C139—41no—
90C2×Q16×C139—21no—
91C2×SD16×C139—21no—
92C2×SD16×C139—21no—
93C2×SD16×C139—21no—
94C2×SD16×C139—22no—
95C2×SD16×C139—22no—
96C2×SD16×C139—21no—
97C2×SD16×C139—21no—
98C2×SD16×C139—21no—
99C2×SD16×C139—21no—
100C2×SD16×C139—41no—
101C2×SD16×C139—41no—
102C2×D8×C139—21no—
103C2×D8×C139—21no—
104#131×C139—22no—
105#131×C139—41no—
106C2×M16×C139—21no—
107C2×M16×C139—21no—
108C2×M16×C139—21no—
109C2×M16×C139—22no—
110C2×M16×C139—22no—
111C2×M16×C139—41no—
112C2×M16×C139—41no—
113C2×M16×C139C2311yescharacteristic
114C2×M16×C139C2311yescharacteristic
115C2×M16×C139C2311yescharacteristic
116C2×M16×C139C2311yescharacteristic
117C2×M16×C139C2311yescharacteristic
118C2×M16×C139C2311yescharacteristic
119C22×C8×C139—21no—
120C22×C8×C139—21no—
121C22×C8×C139—21no—
122C22×C8×C139C2311yescharacteristic
123C22×C8×C139C2311yescharacteristic
124#123×C139—21no—
125C22⋊Q8×C139—21no—
126C22⋊Q8×C139—21no—
127C22⋊Q8×C139—21no—
128C22⋊Q8×C139—21no—
129C22⋊Q8×C139D411yescharacteristic
130C22⋊Q8×C139D411yescharacteristic
131#121×C139D411yescharacteristic
132#121×C139D411yescharacteristic
133#120×C139—21no—
134C4×D4×C139—21no—
135C4×D4×C139—21no—
136#117×C139C2311yescharacteristic
137C2×C4⋊C4×C139—21no—
138C2×C4⋊C4×C139C2311yescharacteristic
139C2×C22⋊C4×C139—21no—
140#108×C139—22no—
141#108×C139—41no—
142#107×C139—21no—
143#106×C139—21no—
144C4⋊C8×C139—21no—
145C4⋊C8×C139—21no—
146#103×C139—21no—
147#103×C139—21no—
148#103×C139—21no—
149#102×C139—21no—
150#102×C139—21no—
151#102×C139—21no—
152#102×C139—21no—
153#102×C139—21no—
154#102×C139—21no—
155#102×C139—21no—
156#102×C139—21no—
157#102×C139—21no—
158#101×C139—22no—
159#101×C139—41no—
160#100×C139—22no—
161#100×C139—22no—
162#100×C139—22no—
163#100×C139D414yescomplemented
164C22⋊C8×C139—21no—
165C22⋊C8×C139—21no—
166C22⋊C8×C139—21no—
167C22⋊C8×C139—21no—
168C22⋊C8×C139D411yescharacteristic
169C22⋊C8×C139D411yescharacteristic
170C22⋊C8×C139D411yescharacteristic
171C22⋊C8×C139D411yescharacteristic
172#97×C139—21no—
173C4×C8×C139—21no—
174C24×C139—24no—
175C24×C139—21no—
176C24×C139—21no—
177C24×C139—42no—
178C24×C139—41no—
179C24×C139—41no—
180C24×C139—82no—
181C24×C139—82no—
182C24×C139#4111yescharacteristic
183#41×C139—21no—
184#41×C139—21no—
185#41×C139—21no—
186#41×C139—21no—
187C2×Q8×C139—21no—
188C2×Q8×C139—21no—
189C2×Q8×C139—21no—
190C2×Q8×C139—21no—
191C2×Q8×C139—21no—
192C2×Q8×C139—21no—
193C2×Q8×C139C2×D411yescharacteristic
194C2×D4×C139—24no—
195C2×D4×C139—21no—
196C2×D4×C139—21no—
197C2×D4×C139—21no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—21no—
208C2×D4×C139—42no—
209C2×D4×C139—42no—
210C2×D4×C139—42no—
211C2×D4×C139—42no—
212C2×D4×C139—42no—
213C2×D4×C139—42no—
214C2×D4×C139—42no—
215C2×D4×C139—42no—
216C2×D4×C139—42no—
217C2×D4×C139—41no—
218C2×D4×C139—41no—
219C2×D4×C139C2×D412yes—
220C2×D4×C139C2×D411yescharacteristic
221C2×D4×C139#4112yes—
222C22×C4×C139—21no—
223C22×C4×C139—21no—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
229C22×C4×C139C2×D411yescharacteristic
230C22×C4×C139C2×D411yescharacteristic
231C22×C4×C139C2×D411yescharacteristic
232C22×C4×C139C2×D411yescharacteristic
233C22×C4×C139#4111yescharacteristic
234C22×C4×C139C2411yescharacteristic
235Q16×C139—42no—
236SD16×C139—42no—
237SD16×C139—42no—
238SD16×C139—42no—
239SD16×C139—42no—
240SD16×C139—42no—
241SD16×C139—42no—
242SD16×C139—42no—
243D8×C139—42no—
244D8×C139—42no—
245M16×C139—21no—
246M16×C139—21no—
247M16×C139—21no—
248M16×C139—21no—
249M16×C139—21no—
250M16×C139—21no—
251M16×C139—21no—
252M16×C139—21no—
253M16×C139—21no—
254M16×C139—21no—
255M16×C139—42no—
256M16×C139—42no—
257M16×C139—42no—
258M16×C139C2×D412yes—
259M16×C139C2×D412yes—
260C2×C8×C139—21no—
261C2×C8×C139—21no—
262C2×C8×C139—21no—
263C2×C8×C139—21no—
264C2×C8×C139—21no—
265C2×C8×C139—21no—
266C2×C8×C139—21no—
267C2×C8×C139—21no—
268C2×C8×C139—21no—
269C2×C8×C139—21no—
270C2×C8×C139—42no—
271C2×C8×C139—42no—
272C2×C8×C139—42no—
273C2×C8×C139C2×D411yescharacteristic
274C2×C8×C139C2×D411yescharacteristic
275C2×C8×C139C2×D411yescharacteristic
276C2×C8×C139C2×D411yescharacteristic
277C4⋊C4×C139—21no—
278C4⋊C4×C139—21no—
279C4⋊C4×C139—21no—
280C4⋊C4×C139—21no—
281C4⋊C4×C139—41no—
282C4⋊C4×C139—41no—
283C4⋊C4×C139C2×D411yescharacteristic
284C4⋊C4×C139C2×D411yescharacteristic
285C22⋊C4×C139—21no—
286C22⋊C4×C139—21no—
287C22⋊C4×C139—21no—
288C22⋊C4×C139—21no—
289C22⋊C4×C139—21no—
290C22⋊C4×C139—41no—
291C22⋊C4×C139—41no—
292C42×C139—21no—
293C23×C139—21no—
294C23×C139—21no—
295C23×C139—22no—
296C23×C139—21no—
297C23×C139—22no—
298C23×C139—22no—
299C23×C139—41no—
300C23×C139—44no—
301C23×C139—44no—
302C23×C139—41no—
303C23×C139—41no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—81no—
307C23×C139—81no—
308C23×C139—81no—
309C23×C139—81no—
310C23×C139—82no—
311C23×C139—82no—
312C23×C139—82no—
313C23×C139—88no—
314C23×C139—88no—
315C23×C139—82no—
316C23×C139#12111yescharacteristic
317C23×C139#12111yescharacteristic
318C23×C139C2×#4111yescharacteristic
319Q8×C139—21no—
320Q8×C139—21no—
321Q8×C139—41no—
322Q8×C139—41no—
323Q8×C139—41no—
324Q8×C139—41no—
325D4×C139—21no—
326D4×C139—22no—
327D4×C139—22no—
328D4×C139—21no—
329D4×C139—22no—
330D4×C139—22no—
331D4×C139—44no—
332D4×C139—44no—
333D4×C139—41no—
334D4×C139—41no—
335D4×C139—42no—
336D4×C139—41no—
337D4×C139—41no—
338D4×C139—41no—
339D4×C139—41no—
340D4×C139—81no—
341C2×C4×C139—21no—
342C2×C4×C139—21no—
343C2×C4×C139—21no—
344C2×C4×C139—21no—
345C2×C4×C139—21no—
346C2×C4×C139—21no—
347C2×C4×C139—21no—
348C2×C4×C139—21no—
349C2×C4×C139—21no—
350C2×C4×C139—21no—
351C2×C4×C139—21no—
352C2×C4×C139—21no—
353C2×C4×C139—21no—
354C2×C4×C139—41no—
355C2×C4×C139—41no—
356C2×C4×C139—41no—
357C2×C4×C139—41no—
358C2×C4×C139—41no—
359C2×C4×C139—41no—
360C2×C4×C139—81no—
361C2×C4×C139#12111yescharacteristic
362C2×C4×C139#12111yescharacteristic
363C2×C4×C139C22×D411yescharacteristic
364C2×C4×C139C22×D411yescharacteristic
365C2×C4×C139C22×D411yescharacteristic
366C2×C4×C139C2×#4111yescharacteristic
367C2×C4×C139H(5,𝔽2)11yescharacteristic
368C2×C4×C139H(5,𝔽2)11yescharacteristic
369C8×C139—21no—
370C8×C139—21no—
371C8×C139—22no—
372C8×C139—22no—
373C8×C139—21no—
374C8×C139—21no—
375C8×C139—41no—
376C8×C139—41no—
377C8×C139—41no—
378C8×C139—41no—
379C22×C139—21no—
380C22×C139—21no—
381C22×C139—21no—
382C22×C139—21no—
383C22×C139—21no—
384C22×C139—21no—
385C22×C139—21no—
386C22×C139—42no—
387C22×C139—42no—
388C22×C139—41no—
389C22×C139—42no—
390C22×C139—42no—
391C22×C139—41no—
392C22×C139—41no—
393C22×C139—82no—
394C22×C139—82no—
395C22×C139—88no—
396C22×C139—82no—
397C22×C139—82no—
398C22×C139—88no—
399C22×C139—81no—
400C22×C139—81no—
401C22×C139—81no—
402C22×C139—81no—
403C22×C139#47112yescomplemented
404C22×C139C2×#12111yescharacteristic
405C22×C139#52511yescharacteristic
406C22×C139#53811yescharacteristic
407C4×C139—21no—
408C4×C139—21no—
409C4×C139—41no—
410C4×C139—41no—
411C4×C139—41no—
412C4×C139—81no—
413C4×C139—81no—
414C4×C139D4211yescharacteristic
415C4×C139D4211yescharacteristic
416C4×C139#54611yescharacteristic
417C4×C139#54611yescharacteristic
418C2×C139—21no—
419C2×C139—21no—
420C2×C139—22no—
421C2×C139—41no—
422C2×C139—81no—
423C2×C139—82no—
424C2×C139—82no—
425C2×C139#242411yescharacteristic
426C2×C139C2×#47111yescharacteristic
427C2×C139#306811yescharacteristic
428#25144C13911yesmaximal, characteristic, direct product factor, Sylow
429C139#2514411yescharacteristic, direct product factor, Sylow
430C2×#471C2×C13911yescharacteristic, complemented
431#3056C2×C13911yescharacteristic, complemented
432#3003C2×C13911yescharacteristic
433C2×#450C2×C13911yescharacteristic, complemented
434#2933C2×C13911yescharacteristic, complemented
435C22×#100C2×C13911yescharacteristic, complemented
436#2063C2×C13911yescharacteristic, complemented
437#2051C2×C13911yescharacteristic, complemented
438#2046C2×C13911yescharacteristic, complemented
439#2019C2×C13911yescharacteristic, complemented
440#1977C2×C13911yescharacteristic, complemented
441#1931C2×C13911yescharacteristic, complemented
442#1907C2×C13911yescharacteristic, complemented
443#1901C2×C13911yescharacteristic, complemented
444#1855C2×C13911yescharacteristic, complemented
445C23×D4C22×C13911yescharacteristic
446C2×#137C22×C13911yescharacteristic, complemented
447C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
448C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
449C22×SD16C22×C13911yescharacteristic
450C22×SD16C22×C13911yescharacteristic
451C2×#131C22×C13911yescharacteristic, complemented
452C22×M16C22×C13911yescharacteristic
453C22×M16C22×C13911yescharacteristic
454#525C22×C13911yescharacteristic
455C2×C22⋊Q8C22×C13911yescharacteristic
456#471—24no—
457#470—21no—
458#468—21no—
459#467—21no—
460#465—21no—
461#450—21no—
462#450—21no—
463#450—21no—
464#450—21no—
465#450—21no—
466#450—21no—
467#447—21no—
468#447—21no—
469#436—21no—
470#435—21no—
471#435—21no—
472C8×D4—21no—
473C2×#108C22×C13911yescharacteristic, complemented
474C2×#108C22×C13911yescharacteristic, complemented
475#428C22×C13911yescharacteristic, complemented
476#424C22×C13911yescharacteristic, complemented
477#419C22×C13911yescharacteristic, complemented
478#418C22×C13911yescharacteristic
479#418C22×C13911yescharacteristic
480#417C22×C13911yescharacteristic, complemented
481C2×#102C22×C13911yescharacteristic
482C2×#102C22×C13911yescharacteristic
483C2×#101C22×C13911yescharacteristic, complemented
484C2×#101C22×C13911yescharacteristic, complemented
485C2×#100—24no—
486C2×#100C22×C13911yescharacteristic
487C2×#100C22×C13911yescharacteristic
488C2×#100C22×C13911yescharacteristic
489C2×#100C22×C13911yescharacteristic
490#408C22×C13911yescharacteristic, complemented
491#407C22×C13911yescharacteristic
492C2×C22⋊C8C22×C13911yescharacteristic
493#405C22×C13911yescharacteristic, complemented
494#343C22×C13911yescharacteristic, complemented
495#343C22×C13911yescharacteristic, complemented
496#341C22×C13911yescharacteristic, complemented
497#341C22×C13911yescharacteristic, complemented
498C25—21no—
499C2×#41C23×C13911yescharacteristic
500C22×Q8C23×C13911yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C23×C13911yescharacteristic
511C22×D4C23×C13911yescharacteristic
512C23×C4C23×C13911yescharacteristic
513#137—22no—
514#137—41no—
515AGL(1,ℤ/8)—22no—
516AGL(1,ℤ/8)—22no—
517AGL(1,ℤ/8)—41no—
518AGL(1,ℤ/8)—41no—
519C2×Q16—21no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—22no—
523C2×SD16—21no—
524C2×SD16—22no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×D8—21no—
532C2×D8—21no—
533#131—22no—
534#131—41no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16C23×C13911yescharacteristic
543C2×M16C23×C13911yescharacteristic
544C2×M16C23×C13911yescharacteristic
545C2×M16C23×C13911yescharacteristic
546C2×M16C23×C13911yescharacteristic
547C2×M16C23×C13911yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8C23×C13911yescharacteristic
552C22×C8C23×C13911yescharacteristic
553#123—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8D4×C13911yescharacteristic
559C22⋊Q8D4×C13911yescharacteristic
560#121D4×C13911yescharacteristic
561#121D4×C13911yescharacteristic
562#120—21no—
563C4×D4—21no—
564C4×D4—21no—
565#117C23×C13911yescharacteristic
566C2×C4⋊C4—21no—
567C2×C4⋊C4C23×C13911yescharacteristic
568C2×C22⋊C4—21no—
569#108—22no—
570#108—41no—
571#107—21no—
572#106—21no—
573C4⋊C8—21no—
574C4⋊C8—21no—
575#103—21no—
576#103—21no—
577#103—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102—21no—
583#102—21no—
584#102—21no—
585#102—21no—
586#102—21no—
587#101—22no—
588#101—41no—
589#100—22no—
590#100—22no—
591#100—22no—
592#100D4×C13914yescomplemented
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8—21no—
597C22⋊C8D4×C13911yescharacteristic
598C22⋊C8D4×C13911yescharacteristic
599C22⋊C8D4×C13911yescharacteristic
600C22⋊C8D4×C13911yescharacteristic
601#97—21no—
602C4×C8—21no—
603C24—24no—
604C24—21no—
605C24—21no—
606C24—42no—
607C24—41no—
608C24—41no—
609C24—82no—
610C24—82no—
611C24#41×C13911yescharacteristic
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8C2×D4×C13911yescharacteristic
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4C2×D4×C13912yes—
649C2×D4C2×D4×C13911yescharacteristic
650C2×D4#41×C13912yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4C2×D4×C13911yescharacteristic
659C22×C4C2×D4×C13911yescharacteristic
660C22×C4C2×D4×C13911yescharacteristic
661C22×C4C2×D4×C13911yescharacteristic
662C22×C4#41×C13911yescharacteristic
663C22×C4C24×C13911yescharacteristic
664Q16—42no—
665SD16—42no—
666SD16—42no—
667SD16—42no—
668SD16—42no—
669SD16—42no—
670SD16—42no—
671SD16—42no—
672D8—42no—
673D8—42no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C13912yes—
688M16C2×D4×C13912yes—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—42no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8C2×D4×C13911yescharacteristic
703C2×C8C2×D4×C13911yescharacteristic
704C2×C8C2×D4×C13911yescharacteristic
705C2×C8C2×D4×C13911yescharacteristic
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—41no—
711C4⋊C4—41no—
712C4⋊C4C2×D4×C13911yescharacteristic
713C4⋊C4C2×D4×C13911yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C42—21no—
722C23—22no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—41no—
729C23—44no—
730C23—44no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—88no—
743C23—88no—
744C23—82no—
745C23#121×C13911yescharacteristic
746C23#121×C13911yescharacteristic
747C23C2×#41×C13911yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754D4—21no—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—44no—
762D4—42no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—81no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—81no—
790C2×C4#121×C13911yescharacteristic
791C2×C4#121×C13911yescharacteristic
792C2×C4C22×D4×C13911yescharacteristic
793C2×C4C22×D4×C13911yescharacteristic
794C2×C4C22×D4×C13911yescharacteristic
795C2×C4C2×#41×C13911yescharacteristic
796C2×C4H(5,𝔽2)×C13911yescharacteristic
797C2×C4H(5,𝔽2)×C13911yescharacteristic
798C8—21no—
799C8—21no—
800C8—22no—
801C8—22no—
802C8—21no—
803C8—21no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—41no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—88no—
827C22—88no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22#471×C13912yescomplemented
833C22C2×#121×C13911yescharacteristic
834C22#525×C13911yescharacteristic
835C22#538×C13911yescharacteristic
836C4—21no—
837C4—21no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—81no—
842C4—81no—
843C4D42×C13911yescharacteristic
844C4D42×C13911yescharacteristic
845C4#546×C13911yescharacteristic
846C4#546×C13911yescharacteristic
847C2—22no—
848C2—21no—
849C2—21no—
850C2—41no—
851C2—81no—
852C2—82no—
853C2—82no—
854C2#2424×C13911yescharacteristic
855C2C2×#471×C13911yescharacteristic
856C2#3068×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#121
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#3003×C139C2
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. C2×#471×C139C2semidirect
2. #3056×C139C2semidirect
4. C2×#450×C139C2semidirect
5. #2933×C139C2semidirect
6. C22×#100×C139C2semidirect
7. #2063×C139C2semidirect
8. #2051×C139C2semidirect
9. #2046×C139C2semidirect
10. #2019×C139C2semidirect
11. #1977×C139C2semidirect
12. #1931×C139C2semidirect
13. #1907×C139C2semidirect
14. #1901×C139C2semidirect
15. #1855×C139C2semidirect
17. C2×#137×C139C22semidirect
22. C2×#131×C139C22semidirect
44. C2×#108×C139C22semidirect
45. C2×#108×C139C22semidirect
46. #428×C139C22semidirect
47. #424×C139C22semidirect
48. #419×C139C22semidirect
51. #417×C139C22semidirect
54. C2×#101×C139C22semidirect
55. C2×#101×C139C22semidirect
61. #408×C139C22semidirect
64. #405×C139C22semidirect
65. #343×C139C22semidirect
66. #343×C139C22semidirect
67. #341×C139C22semidirect
68. #341×C139C22semidirect
163. #100×C139D4semidirect
403. C22×C139#471semidirect
428. #25144C139direct (N × H)
429. C139#25144direct (N × H)
430. C2×#471C2×C139semidirect
431. #3056C2×C139semidirect
433. C2×#450C2×C139semidirect
434. #2933C2×C139semidirect
435. C22×#100C2×C139semidirect
436. #2063C2×C139semidirect
437. #2051C2×C139semidirect
438. #2046C2×C139semidirect
439. #2019C2×C139semidirect
440. #1977C2×C139semidirect
441. #1931C2×C139semidirect
442. #1907C2×C139semidirect
443. #1901C2×C139semidirect
444. #1855C2×C139semidirect
446. C2×#137C22×C139semidirect
451. C2×#131C22×C139semidirect
473. C2×#108C22×C139semidirect
474. C2×#108C22×C139semidirect
475. #428C22×C139semidirect
476. #424C22×C139semidirect
477. #419C22×C139semidirect
480. #417C22×C139semidirect
483. C2×#101C22×C139semidirect
484. C2×#101C22×C139semidirect
490. #408C22×C139semidirect
493. #405C22×C139semidirect
494. #343C22×C139semidirect
495. #343C22×C139semidirect
496. #341C22×C139semidirect
497. #341C22×C139semidirect
592. #100D4×C139semidirect
832. C22#471×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#471×C1392
#3056×C1392
#3003×C1392
C2×#450×C1392
#2933×C1392
C22×#100×C1392
#2063×C1392
#2051×C1392
#2046×C1392
#2019×C1392
#1977×C1392
#1931×C1392
#1907×C1392
#1901×C1392
#1855×C1392
#25144139