Finite Group Databasebeta

← C139×#25140 #48019736

Subgroups — C139×#25140 #48019736

Order 35584.

1140 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C139C211yesmaximal, characteristic, complemented
2#3055×C139C211yesmaximal, characteristic, complemented
3#3003×C139C211yesmaximal, characteristic, complemented
4C2×#447×C139C211yesmaximal, characteristic, complemented
5#2933×C139C211yesmaximal, characteristic, complemented
6C22×#100×C139C211yesmaximal, characteristic, complemented
7#2063×C139C211yesmaximal, characteristic, complemented
8#2051×C139C211yesmaximal, characteristic, complemented
9#2045×C139C211yesmaximal, characteristic, complemented
10#2018×C139C211yesmaximal, characteristic, complemented
11#1978×C139C211yesmaximal, characteristic, complemented
12#1931×C139C211yesmaximal, characteristic, complemented
13#1907×C139C211yesmaximal, characteristic, complemented
14#1900×C139C211yesmaximal, characteristic, complemented
15#1855×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
20C22×D8×C139C2211yescharacteristic
21C22×D8×C139C2211yescharacteristic
22C2×#131×C139C2211yescharacteristic, complemented
23C22×M16×C139C2211yescharacteristic
24C22×M16×C139C2211yescharacteristic
25#525×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27#472×C139—24no—
28#469×C139—21no—
29#468×C139—21no—
30#466×C139—21no—
31#465×C139—21no—
32#450×C139—21no—
33#450×C139—21no—
34#447×C139—21no—
35#447×C139—21no—
36#447×C139—21no—
37#447×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#418×C139C2211yescharacteristic
49#418×C139C2211yescharacteristic
50#418×C139C2211yescharacteristic, complemented
51#417×C139C2211yescharacteristic, complemented
52C2×#102×C139C2211yescharacteristic
53C2×#102×C139C2211yescharacteristic
54C2×#100×C139—24no—
55C2×#100×C139C2211yescharacteristic
56C2×#100×C139C2211yescharacteristic
57C2×#100×C139C2211yescharacteristic
58C2×#100×C139C2211yescharacteristic
59C2×#100×C139C2211yescharacteristic, complemented
60C2×#100×C139C2211yescharacteristic, complemented
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×D4×C139—22no—
72C22×D4×C139—22no—
73C22×D4×C139—21no—
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
83C22×D4×C139C2311yescharacteristic
84C23×C4×C139C2311yescharacteristic
85AGL(1,ℤ/8)×C139—22no—
86AGL(1,ℤ/8)×C139—22no—
87AGL(1,ℤ/8)×C139—22no—
88AGL(1,ℤ/8)×C139—41no—
89AGL(1,ℤ/8)×C139—41no—
90AGL(1,ℤ/8)×C139—41no—
91C2×SD16×C139—21no—
92C2×SD16×C139—21no—
93C2×SD16×C139—21no—
94C2×D8×C139—21no—
95C2×D8×C139—21no—
96C2×D8×C139—21no—
97C2×D8×C139—22no—
98C2×D8×C139—22no—
99C2×D8×C139—21no—
100C2×D8×C139—21no—
101C2×D8×C139—21no—
102C2×D8×C139—21no—
103C2×D8×C139—41no—
104C2×D8×C139—41no—
105#131×C139—22no—
106#131×C139—41no—
107C2×M16×C139—21no—
108C2×M16×C139—21no—
109C2×M16×C139—21no—
110C2×M16×C139—22no—
111C2×M16×C139—22no—
112C2×M16×C139—41no—
113C2×M16×C139—41no—
114C2×M16×C139C2311yescharacteristic
115C2×M16×C139C2311yescharacteristic
116C2×M16×C139C2311yescharacteristic
117C2×M16×C139C2311yescharacteristic
118C2×M16×C139C2311yescharacteristic
119C2×M16×C139C2311yescharacteristic
120C22×C8×C139—21no—
121C22×C8×C139—21no—
122C22×C8×C139—21no—
123C22×C8×C139C2311yescharacteristic
124C22×C8×C139C2311yescharacteristic
125#123×C139—21no—
126C22⋊Q8×C139D411yescharacteristic
127C22⋊Q8×C139D411yescharacteristic
128#121×C139—21no—
129#121×C139—21no—
130#121×C139—21no—
131#121×C139—21no—
132#121×C139D411yescharacteristic
133#121×C139D411yescharacteristic
134#120×C139—21no—
135C4×D4×C139—21no—
136C4×D4×C139—21no—
137#117×C139C2311yescharacteristic
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#102×C139—21no—
148#102×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#100×C139—22no—
159#100×C139—22no—
160#100×C139—22no—
161#100×C139—22no—
162#100×C139—41no—
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—21no—
178C24×C139—42no—
179C24×C139—41no—
180C24×C139—41no—
181C24×C139—82no—
182C24×C139—82no—
183C24×C139#4111yescharacteristic
184#41×C139—21no—
185#41×C139—21no—
186#41×C139—21no—
187#41×C139—21no—
188C2×Q8×C139C2×D411yescharacteristic
189C2×D4×C139—24no—
190C2×D4×C139—21no—
191C2×D4×C139—21no—
192C2×D4×C139—21no—
193C2×D4×C139—21no—
194C2×D4×C139—21no—
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—21no—
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—42no—
218C2×D4×C139—41no—
219C2×D4×C139—41no—
220C2×D4×C139—41no—
221C2×D4×C139—41no—
222C2×D4×C139—82no—
223C2×D4×C139C2×D412yes—
224C2×D4×C139C2×D411yescharacteristic
225C2×D4×C139#4112yes—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
229C22×C4×C139—21no—
230C22×C4×C139—21no—
231C22×C4×C139—21no—
232C22×C4×C139C2×D411yescharacteristic
233C22×C4×C139C2×D411yescharacteristic
234C22×C4×C139C2×D411yescharacteristic
235C22×C4×C139C2×D411yescharacteristic
236C22×C4×C139#4111yescharacteristic
237C22×C4×C139C2411yescharacteristic
238SD16×C139—42no—
239SD16×C139—42no—
240SD16×C139—42no—
241D8×C139—42no—
242D8×C139—42no—
243D8×C139—42no—
244D8×C139—42no—
245D8×C139—42no—
246D8×C139—42no—
247D8×C139—42no—
248M16×C139—21no—
249M16×C139—21no—
250M16×C139—21no—
251M16×C139—21no—
252M16×C139—21no—
253M16×C139—21no—
254M16×C139—21no—
255M16×C139—21no—
256M16×C139—21no—
257M16×C139—21no—
258M16×C139—42no—
259M16×C139—42no—
260M16×C139—42no—
261M16×C139C2×D412yes—
262M16×C139C2×D412yes—
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—21no—
271C2×C8×C139—21no—
272C2×C8×C139—21no—
273C2×C8×C139—42no—
274C2×C8×C139—42no—
275C2×C8×C139—42no—
276C2×C8×C139C2×D411yescharacteristic
277C2×C8×C139C2×D411yescharacteristic
278C2×C8×C139C2×D411yescharacteristic
279C2×C8×C139C2×D411yescharacteristic
280C4⋊C4×C139—21no—
281C4⋊C4×C139—21no—
282C4⋊C4×C139—21no—
283C4⋊C4×C139—21no—
284C4⋊C4×C139C2×D411yescharacteristic
285C4⋊C4×C139C2×D411yescharacteristic
286C22⋊C4×C139—21no—
287C22⋊C4×C139—21no—
288C22⋊C4×C139—21no—
289C22⋊C4×C139—21no—
290C22⋊C4×C139—21no—
291C22⋊C4×C139—41no—
292C22⋊C4×C139—41no—
293C42×C139—21no—
294C23×C139—21no—
295C23×C139—21no—
296C23×C139—22no—
297C23×C139—21no—
298C23×C139—22no—
299C23×C139—22no—
300C23×C139—41no—
301C23×C139—44no—
302C23×C139—44no—
303C23×C139—41no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—41no—
307C23×C139—41no—
308C23×C139—41no—
309C23×C139—41no—
310C23×C139—81no—
311C23×C139—81no—
312C23×C139—81no—
313C23×C139—81no—
314C23×C139—82no—
315C23×C139—82no—
316C23×C139—82no—
317C23×C139—81no—
318C23×C139—81no—
319C23×C139—88no—
320C23×C139—88no—
321C23×C139—82no—
322C23×C139#12111yescharacteristic
323C23×C139#12111yescharacteristic
324C23×C139C2×#4111yescharacteristic
325Q8×C139—21no—
326Q8×C139—21no—
327D4×C139—21no—
328D4×C139—22no—
329D4×C139—22no—
330D4×C139—22no—
331D4×C139—21no—
332D4×C139—22no—
333D4×C139—44no—
334D4×C139—44no—
335D4×C139—41no—
336D4×C139—41no—
337D4×C139—42no—
338D4×C139—41no—
339D4×C139—41no—
340D4×C139—41no—
341D4×C139—41no—
342D4×C139—41no—
343D4×C139—41no—
344D4×C139—41no—
345D4×C139—41no—
346D4×C139—81no—
347D4×C139—82no—
348D4×C139—82no—
349C2×C4×C139—21no—
350C2×C4×C139—21no—
351C2×C4×C139—21no—
352C2×C4×C139—21no—
353C2×C4×C139—21no—
354C2×C4×C139—21no—
355C2×C4×C139—21no—
356C2×C4×C139—21no—
357C2×C4×C139—21no—
358C2×C4×C139—21no—
359C2×C4×C139—21no—
360C2×C4×C139—21no—
361C2×C4×C139—21no—
362C2×C4×C139—41no—
363C2×C4×C139—41no—
364C2×C4×C139—41no—
365C2×C4×C139—81no—
366C2×C4×C139#12111yescharacteristic
367C2×C4×C139#12111yescharacteristic
368C2×C4×C139C22×D411yescharacteristic
369C2×C4×C139C22×D411yescharacteristic
370C2×C4×C139C22×D411yescharacteristic
371C2×C4×C139C2×#4111yescharacteristic
372C2×C4×C139H(5,𝔽2)11yescharacteristic
373C2×C4×C139H(5,𝔽2)11yescharacteristic
374C8×C139—21no—
375C8×C139—21no—
376C8×C139—22no—
377C8×C139—22no—
378C8×C139—21no—
379C8×C139—21no—
380C8×C139—41no—
381C8×C139—41no—
382C8×C139—41no—
383C8×C139—41no—
384C22×C139—21no—
385C22×C139—21no—
386C22×C139—21no—
387C22×C139—21no—
388C22×C139—21no—
389C22×C139—21no—
390C22×C139—21no—
391C22×C139—42no—
392C22×C139—42no—
393C22×C139—41no—
394C22×C139—42no—
395C22×C139—42no—
396C22×C139—41no—
397C22×C139—41no—
398C22×C139—82no—
399C22×C139—82no—
400C22×C139—88no—
401C22×C139—82no—
402C22×C139—82no—
403C22×C139—88no—
404C22×C139—81no—
405C22×C139—81no—
406C22×C139—81no—
407C22×C139—81no—
408C22×C139—81no—
409C22×C139—81no—
410C22×C139—81no—
411C22×C139—161no—
412C22×C139—161no—
413C22×C139#47212yescomplemented
414C22×C139C2×#12111yescharacteristic
415C22×C139#52511yescharacteristic
416C22×C139#53811yescharacteristic
417C4×C139—21no—
418C4×C139—21no—
419C4×C139—41no—
420C4×C139—41no—
421C4×C139—41no—
422C4×C139—81no—
423C4×C139D4211yescharacteristic
424C4×C139D4211yescharacteristic
425C4×C139#54611yescharacteristic
426C4×C139#54611yescharacteristic
427C2×C139—21no—
428C2×C139—21no—
429C2×C139—22no—
430C2×C139—41no—
431C2×C139—81no—
432C2×C139—82no—
433C2×C139—82no—
434C2×C139—161no—
435C2×C139#242411yescharacteristic
436C2×C139C2×#47211yescharacteristic
437C2×C139#306811yescharacteristic
438#25140C13911yesmaximal, characteristic, direct product factor, Sylow
439C139#2514011yescharacteristic, direct product factor, Sylow
440C2×#472C2×C13911yescharacteristic, complemented
441#3055C2×C13911yescharacteristic, complemented
442#3003C2×C13911yescharacteristic, complemented
443C2×#447C2×C13911yescharacteristic, complemented
444#2933C2×C13911yescharacteristic, complemented
445C22×#100C2×C13911yescharacteristic, complemented
446#2063C2×C13911yescharacteristic, complemented
447#2051C2×C13911yescharacteristic, complemented
448#2045C2×C13911yescharacteristic, complemented
449#2018C2×C13911yescharacteristic, complemented
450#1978C2×C13911yescharacteristic, complemented
451#1931C2×C13911yescharacteristic, complemented
452#1907C2×C13911yescharacteristic, complemented
453#1900C2×C13911yescharacteristic, complemented
454#1855C2×C13911yescharacteristic, complemented
455C23×D4C22×C13911yescharacteristic
456C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
457C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
458C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
459C22×D8C22×C13911yescharacteristic
460C22×D8C22×C13911yescharacteristic
461C2×#131C22×C13911yescharacteristic, complemented
462C22×M16C22×C13911yescharacteristic
463C22×M16C22×C13911yescharacteristic
464#525C22×C13911yescharacteristic
465C2×#121C22×C13911yescharacteristic
466#472—24no—
467#469—21no—
468#468—21no—
469#466—21no—
470#465—21no—
471#450—21no—
472#450—21no—
473#447—21no—
474#447—21no—
475#447—21no—
476#447—21no—
477#447—21no—
478#447—21no—
479#436—21no—
480#435—21no—
481#435—21no—
482C8×D4—21no—
483C2×#108C22×C13911yescharacteristic, complemented
484C2×#108C22×C13911yescharacteristic, complemented
485#428C22×C13911yescharacteristic, complemented
486#424C22×C13911yescharacteristic, complemented
487#418C22×C13911yescharacteristic
488#418C22×C13911yescharacteristic
489#418C22×C13911yescharacteristic, complemented
490#417C22×C13911yescharacteristic, complemented
491C2×#102C22×C13911yescharacteristic
492C2×#102C22×C13911yescharacteristic
493C2×#100—24no—
494C2×#100C22×C13911yescharacteristic
495C2×#100C22×C13911yescharacteristic
496C2×#100C22×C13911yescharacteristic
497C2×#100C22×C13911yescharacteristic
498C2×#100C22×C13911yescharacteristic, complemented
499C2×#100C22×C13911yescharacteristic, complemented
500#408C22×C13911yescharacteristic, complemented
501#407C22×C13911yescharacteristic
502C2×C22⋊C8C22×C13911yescharacteristic
503#405C22×C13911yescharacteristic, complemented
504#343C22×C13911yescharacteristic, complemented
505#343C22×C13911yescharacteristic, complemented
506#341C22×C13911yescharacteristic, complemented
507#341C22×C13911yescharacteristic, complemented
508C25—21no—
509C2×#41C23×C13911yescharacteristic
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C23×C13911yescharacteristic
521C22×D4C23×C13911yescharacteristic
522C22×D4C23×C13911yescharacteristic
523C23×C4C23×C13911yescharacteristic
524AGL(1,ℤ/8)—22no—
525AGL(1,ℤ/8)—22no—
526AGL(1,ℤ/8)—22no—
527AGL(1,ℤ/8)—41no—
528AGL(1,ℤ/8)—41no—
529AGL(1,ℤ/8)—41no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×SD16—21no—
533C2×D8—22no—
534C2×D8—21no—
535C2×D8—21no—
536C2×D8—21no—
537C2×D8—22no—
538C2×D8—21no—
539C2×D8—21no—
540C2×D8—21no—
541C2×D8—21no—
542C2×D8—41no—
543C2×D8—41no—
544#131—22no—
545#131—41no—
546C2×M16—21no—
547C2×M16—21no—
548C2×M16—21no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16C23×C13911yescharacteristic
554C2×M16C23×C13911yescharacteristic
555C2×M16C23×C13911yescharacteristic
556C2×M16C23×C13911yescharacteristic
557C2×M16C23×C13911yescharacteristic
558C2×M16C23×C13911yescharacteristic
559C22×C8—21no—
560C22×C8—21no—
561C22×C8—21no—
562C22×C8C23×C13911yescharacteristic
563C22×C8C23×C13911yescharacteristic
564#123—21no—
565C22⋊Q8D4×C13911yescharacteristic
566C22⋊Q8D4×C13911yescharacteristic
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121D4×C13911yescharacteristic
572#121D4×C13911yescharacteristic
573#120—21no—
574C4×D4—21no—
575C4×D4—21no—
576#117C23×C13911yescharacteristic
577C2×C4⋊C4C23×C13911yescharacteristic
578C2×C22⋊C4—21no—
579#108—22no—
580#108—41no—
581#107—21no—
582#106—21no—
583C4⋊C8—21no—
584C4⋊C8—21no—
585#103—21no—
586#102—21no—
587#102—21no—
588#102—21no—
589#102—21no—
590#102—21no—
591#102—21no—
592#102—21no—
593#102—21no—
594#102—21no—
595#102—21no—
596#102—21no—
597#100—22no—
598#100—22no—
599#100—22no—
600#100—22no—
601#100—41no—
602#100D4×C13914yescomplemented
603C22⋊C8—21no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607C22⋊C8D4×C13911yescharacteristic
608C22⋊C8D4×C13911yescharacteristic
609C22⋊C8D4×C13911yescharacteristic
610C22⋊C8D4×C13911yescharacteristic
611#97—21no—
612C4×C8—21no—
613C24—24no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—42no—
618C24—41no—
619C24—41no—
620C24—82no—
621C24—82no—
622C24#41×C13911yescharacteristic
623#41—21no—
624#41—21no—
625#41—21no—
626#41—21no—
627C2×Q8C2×D4×C13911yescharacteristic
628C2×D4—24no—
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—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—41no—
658C2×D4—41no—
659C2×D4—41no—
660C2×D4—41no—
661C2×D4—82no—
662C2×D4C2×D4×C13912yes—
663C2×D4C2×D4×C13911yescharacteristic
664C2×D4#41×C13912yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4C2×D4×C13911yescharacteristic
672C22×C4C2×D4×C13911yescharacteristic
673C22×C4C2×D4×C13911yescharacteristic
674C22×C4C2×D4×C13911yescharacteristic
675C22×C4#41×C13911yescharacteristic
676C22×C4C24×C13911yescharacteristic
677SD16—42no—
678SD16—42no—
679SD16—42no—
680D8—42no—
681D8—42no—
682D8—42no—
683D8—42no—
684D8—42no—
685D8—42no—
686D8—42no—
687M16—21no—
688M16—21no—
689M16—21no—
690M16—21no—
691M16—21no—
692M16—21no—
693M16—21no—
694M16—21no—
695M16—21no—
696M16—21no—
697M16—42no—
698M16—42no—
699M16—42no—
700M16C2×D4×C13912yes—
701M16C2×D4×C13912yes—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—42no—
713C2×C8—42no—
714C2×C8—42no—
715C2×C8C2×D4×C13911yescharacteristic
716C2×C8C2×D4×C13911yescharacteristic
717C2×C8C2×D4×C13911yescharacteristic
718C2×C8C2×D4×C13911yescharacteristic
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4C2×D4×C13911yescharacteristic
724C4⋊C4C2×D4×C13911yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—41no—
731C22⋊C4—41no—
732C42—21no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—41no—
740C23—44no—
741C23—44no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—82no—
754C23—82no—
755C23—82no—
756C23—81no—
757C23—81no—
758C23—88no—
759C23—88no—
760C23—82no—
761C23#121×C13911yescharacteristic
762C23#121×C13911yescharacteristic
763C23C2×#41×C13911yescharacteristic
764Q8—21no—
765Q8—21no—
766D4—21no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—21no—
771D4—22no—
772D4—44no—
773D4—44no—
774D4—42no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—81no—
786D4—82no—
787D4—82no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—81no—
805C2×C4#121×C13911yescharacteristic
806C2×C4#121×C13911yescharacteristic
807C2×C4C22×D4×C13911yescharacteristic
808C2×C4C22×D4×C13911yescharacteristic
809C2×C4C22×D4×C13911yescharacteristic
810C2×C4C2×#41×C13911yescharacteristic
811C2×C4H(5,𝔽2)×C13911yescharacteristic
812C2×C4H(5,𝔽2)×C13911yescharacteristic
813C8—21no—
814C8—21no—
815C8—22no—
816C8—22no—
817C8—21no—
818C8—21no—
819C8—41no—
820C8—41no—
821C8—41no—
822C8—41no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—88no—
842C22—88no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—161no—
851C22—161no—
852C22#472×C13912yescomplemented
853C22C2×#121×C13911yescharacteristic
854C22#525×C13911yescharacteristic
855C22#538×C13911yescharacteristic
856C4—21no—
857C4—21no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—81no—
862C4D42×C13911yescharacteristic
863C4D42×C13911yescharacteristic
864C4#546×C13911yescharacteristic
865C4#546×C13911yescharacteristic
866C2—21no—
867C2—21no—
868C2—22no—
869C2—41no—
870C2—81no—
871C2—82no—
872C2—82no—
873C2—161no—
874C2#2424×C13911yescharacteristic
875C2C2×#472×C13911yescharacteristic
876C2#3068×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#121
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. C2×#472×C139C2semidirect
2. #3055×C139C2semidirect
3. #3003×C139C2semidirect
4. C2×#447×C139C2semidirect
5. #2933×C139C2semidirect
6. C22×#100×C139C2semidirect
7. #2063×C139C2semidirect
8. #2051×C139C2semidirect
9. #2045×C139C2semidirect
10. #2018×C139C2semidirect
11. #1978×C139C2semidirect
12. #1931×C139C2semidirect
13. #1907×C139C2semidirect
14. #1900×C139C2semidirect
15. #1855×C139C2semidirect
19. C2×AGL(1,ℤ/8)×C139C22semidirect
22. C2×#131×C139C22semidirect
44. C2×#108×C139C22semidirect
45. C2×#108×C139C22semidirect
46. #428×C139C22semidirect
47. #424×C139C22semidirect
50. #418×C139C22semidirect
51. #417×C139C22semidirect
59. C2×#100×C139C22semidirect
60. C2×#100×C139C22semidirect
61. #408×C139C22semidirect
64. #405×C139C22semidirect
65. #343×C139C22semidirect
66. #343×C139C22semidirect
67. #341×C139C22semidirect
68. #341×C139C22semidirect
163. #100×C139D4semidirect
413. C22×C139#472semidirect
438. #25140C139direct (N × H)
439. C139#25140direct (N × H)
440. C2×#472C2×C139semidirect
441. #3055C2×C139semidirect
442. #3003C2×C139semidirect
443. C2×#447C2×C139semidirect
444. #2933C2×C139semidirect
445. C22×#100C2×C139semidirect
446. #2063C2×C139semidirect
447. #2051C2×C139semidirect
448. #2045C2×C139semidirect
449. #2018C2×C139semidirect
450. #1978C2×C139semidirect
451. #1931C2×C139semidirect
452. #1907C2×C139semidirect
453. #1900C2×C139semidirect
454. #1855C2×C139semidirect
458. C2×AGL(1,ℤ/8)C22×C139semidirect
461. C2×#131C22×C139semidirect
483. C2×#108C22×C139semidirect
484. C2×#108C22×C139semidirect
485. #428C22×C139semidirect
486. #424C22×C139semidirect
489. #418C22×C139semidirect
490. #417C22×C139semidirect
498. C2×#100C22×C139semidirect
499. C2×#100C22×C139semidirect
500. #408C22×C139semidirect
503. #405C22×C139semidirect
504. #343C22×C139semidirect
505. #343C22×C139semidirect
506. #341C22×C139semidirect
507. #341C22×C139semidirect
602. #100D4×C139semidirect
852. C22#472×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#472×C1392
#3055×C1392
#3003×C1392
C2×#447×C1392
#2933×C1392
C22×#100×C1392
#2063×C1392
#2051×C1392
#2045×C1392
#2018×C1392
#1978×C1392
#1931×C1392
#1907×C1392
#1900×C1392
#1855×C1392
#25140139