Finite Group Databasebeta

← C139×#25563 #48020159

Subgroups — C139×#25563 #48020159

Order 35584.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3490×C139C211yesmaximal, characteristic, complemented
2#2410×C139C212yesmaximal, complemented
3#2405×C139C211yesmaximal, characteristic, complemented
4#2062×C139C211yesmaximal, characteristic, complemented
5#2044×C139C211yesmaximal, characteristic, complemented
6#2029×C139C211yesmaximal, characteristic, complemented
7#2021×C139C211yesmaximal, characteristic, complemented
8#1898×C139C212yesmaximal, complemented
9#1889×C139C212yesmaximal, complemented
10#1867×C139C212yesmaximal, complemented
11C2×#342×C139C211yesmaximal, characteristic, complemented
12C23×D4×C139C2211yescharacteristic
13#551×C139—22no—
14#551×C139—22no—
15#546×C139—22no—
16#546×C139—22no—
17#543×C139C2211yescharacteristic
18#538×C139—21no—
19#538×C139—21no—
20#534×C139C2211yescharacteristic
21#525×C139—21no—
22#525×C139—21no—
23C2×#123×C139—21no—
24C2×#121×C139—22no—
25C2×#120×C139C2212yes—
26C2×#120×C139C2212yes—
27#518×C139C2212yes—
28C22×C22⋊C4×C139C2211yescharacteristic
29C22×C22⋊C4×C139C2212yes—
30C2×#99×C139C2212yes—
31C2×#99×C139C2212yes—
32#394×C139—21no—
33#394×C139—21no—
34#394×C139—22no—
35#392×C139—22no—
36#386×C139—21no—
37#386×C139—22no—
38#386×C139C2212yes—
39#385×C139C2211yescharacteristic
40#385×C139C2212yes—
41#385×C139C2211yescharacteristic
42#379×C139C2211yescharacteristic
43#379×C139C2212yes—
44#379×C139C2211yescharacteristic
45#379×C139C2211yescharacteristic
46#342×C139C2211yescharacteristic
47#342×C139C2211yescharacteristic
48#342×C139C2212yes—
49#342×C139C2212yes—
50#342×C139C2212yes—
51C25×C139C2311yescharacteristic
52C25×C139C2311yescharacteristic
53C2×#41×C139—21no—
54C2×#41×C139—21no—
55C22×D4×C139—22no—
56C22×D4×C139—21no—
57C22×D4×C139—22no—
58C22×D4×C139—21no—
59C22×D4×C139—22no—
60C22×D4×C139—44no—
61C22×D4×C139D412yescomplemented
62C22×D4×C139D412yescomplemented
63C22×D4×C139C2312yes—
64C23×C4×C139—22no—
65C23×C4×C139D411yescharacteristic, complemented
66C23×C4×C139D411yescharacteristic, complemented
67C23×C4×C139C2311yescharacteristic
68#126×C139—22no—
69#126×C139—22no—
70#124×C139—22no—
71#124×C139—22no—
72#123×C139—22no—
73#123×C139—22no—
74#123×C139—22no—
75#123×C139—22no—
76#123×C139—22no—
77#123×C139—44no—
78C22⋊Q8×C139—21no—
79C22⋊Q8×C139—21no—
80C22⋊Q8×C139—21no—
81C22⋊Q8×C139—21no—
82C22⋊Q8×C139—22no—
83C22⋊Q8×C139—22no—
84#121×C139—21no—
85#121×C139—21no—
86#121×C139—22no—
87#121×C139—22no—
88#121×C139—21no—
89#121×C139—21no—
90#121×C139—48no—
91#120×C139—22no—
92#120×C139—22no—
93#120×C139—22no—
94#120×C139—22no—
95#120×C139—22no—
96#120×C139—24no—
97#120×C139—42no—
98C4×D4×C139—22no—
99C4×D4×C139—22no—
100C4×D4×C139—22no—
101C4×D4×C139—22no—
102C4×D4×C139—22no—
103C4×D4×C139—22no—
104#117×C139—21no—
105#117×C139—21no—
106#117×C139—22no—
107C2×C4⋊C4×C139—22no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C22⋊C4×C139—22no—
111C2×C22⋊C4×C139—22no—
112C2×C22⋊C4×C139—22no—
113C2×C22⋊C4×C139—24no—
114C2×C22⋊C4×C139—22no—
115C2×C22⋊C4×C139—22no—
116C2×C22⋊C4×C139—21no—
117C2×C22⋊C4×C139—22no—
118C2×C22⋊C4×C139—22no—
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—22no—
123C2×C22⋊C4×C139—21no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—42no—
126C2×C22⋊C4×C139D411yescharacteristic, complemented
127C2×C22⋊C4×C139D411yescharacteristic, complemented
128C2×C22⋊C4×C139D412yescomplemented
129C2×C22⋊C4×C139D412yescomplemented
130C2×C22⋊C4×C139C2311yescharacteristic
131C2×C22⋊C4×C139C2311yescharacteristic
132C2×C22⋊C4×C139C2312yes—
133C2×C22⋊C4×C139C2311yescharacteristic
134C2×C22⋊C4×C139C2311yescharacteristic
135C2×C22⋊C4×C139C2312yes—
136C2×C22⋊C4×C139C2312yes—
137#99×C139—24no—
138#99×C139—42no—
139#95×C139—22no—
140#95×C139—21no—
141#95×C139—21no—
142#95×C139—22no—
143C24×C139—22no—
144C24×C139—21no—
145C24×C139—21no—
146C24×C139—21no—
147C24×C139—22no—
148C24×C139—22no—
149C24×C139—21no—
150C24×C139—21no—
151C24×C139—42no—
152C24×C139—42no—
153C24×C139—81no—
154C24×C139—81no—
155C24×C139C2×D412yes—
156C24×C139C2×D411yescharacteristic
157C24×C139C2×D412yes—
158C24×C139C2×D412yes—
159C24×C139C2×D411yescharacteristic
160C24×C139C2411yescharacteristic
161#41×C139—82no—
162#41×C139—82no—
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×D4×C139—28no—
166C2×D4×C139—24no—
167C2×D4×C139—22no—
168C2×D4×C139—22no—
169C2×D4×C139—22no—
170C2×D4×C139—22no—
171C2×D4×C139—22no—
172C2×D4×C139—22no—
173C2×D4×C139—22no—
174C2×D4×C139—22no—
175C2×D4×C139—21no—
176C2×D4×C139—21no—
177C2×D4×C139—22no—
178C2×D4×C139—22no—
179C2×D4×C139—44no—
180C2×D4×C139—42no—
181C2×D4×C139—44no—
182C2×D4×C139—42no—
183C2×D4×C139—44no—
184C2×D4×C139—42no—
185C2×D4×C139—44no—
186C2×D4×C139—42no—
187C2×D4×C139—41no—
188C2×D4×C139—41no—
189C2×D4×C139—44no—
190C2×D4×C139—44no—
191C2×D4×C139—82no—
192C2×D4×C139—82no—
193C22×C4×C139—21no—
194C22×C4×C139—21no—
195C22×C4×C139—22no—
196C22×C4×C139—21no—
197C22×C4×C139—22no—
198C22×C4×C139—22no—
199C22×C4×C139—22no—
200C22×C4×C139—21no—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—22no—
205C22×C4×C139—42no—
206C22×C4×C139—44no—
207C22×C4×C139—42no—
208C22×C4×C139—44no—
209C22×C4×C139—81no—
210C22×C4×C139—82no—
211C22×C4×C139C2×D412yes—
212C22×C4×C139C2×D411yescharacteristic
213C22×C4×C139C2×D412yes—
214C22×C4×C139C2×D411yescharacteristic
215C22×C4×C139C2×D411yescharacteristic
216C22×C4×C139C2×D412yes—
217C22×C4×C139C2×D411yescharacteristic
218C4⋊C4×C139—22no—
219C4⋊C4×C139—22no—
220C4⋊C4×C139—21no—
221C4⋊C4×C139—21no—
222C4⋊C4×C139—21no—
223C4⋊C4×C139—21no—
224C4⋊C4×C139—22no—
225C4⋊C4×C139—22no—
226C4⋊C4×C139—44no—
227C4⋊C4×C139—42no—
228C4⋊C4×C139—42no—
229C22⋊C4×C139—22no—
230C22⋊C4×C139—22no—
231C22⋊C4×C139—22no—
232C22⋊C4×C139—22no—
233C22⋊C4×C139—22no—
234C22⋊C4×C139—22no—
235C22⋊C4×C139—22no—
236C22⋊C4×C139—22no—
237C22⋊C4×C139—22no—
238C22⋊C4×C139—22no—
239C22⋊C4×C139—22no—
240C22⋊C4×C139—22no—
241C22⋊C4×C139—22no—
242C22⋊C4×C139—22no—
243C22⋊C4×C139—22no—
244C22⋊C4×C139—22no—
245C22⋊C4×C139—22no—
246C22⋊C4×C139—21no—
247C22⋊C4×C139—22no—
248C22⋊C4×C139—21no—
249C22⋊C4×C139—44no—
250C22⋊C4×C139—44no—
251C22⋊C4×C139—44no—
252C22⋊C4×C139—44no—
253C22⋊C4×C139—42no—
254C22⋊C4×C139—42no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—81no—
257C22⋊C4×C139—81no—
258C22⋊C4×C139—82no—
259C22⋊C4×C139—81no—
260C22⋊C4×C139#4114yescomplemented
261C42×C139—22no—
262C42×C139—22no—
263C23×C139—21no—
264C23×C139—21no—
265C23×C139—22no—
266C23×C139—22no—
267C23×C139—22no—
268C23×C139—24no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—22no—
272C23×C139—22no—
273C23×C139—22no—
274C23×C139—24no—
275C23×C139—22no—
276C23×C139—22no—
277C23×C139—22no—
278C23×C139—41no—
279C23×C139—41no—
280C23×C139—42no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—42no—
285C23×C139—42no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139—42no—
289C23×C139—41no—
290C23×C139—42no—
291C23×C139—42no—
292C23×C139—42no—
293C23×C139—42no—
294C23×C139—41no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—42no—
298C23×C139—42no—
299C23×C139—84no—
300C23×C139—84no—
301C23×C139—82no—
302C23×C139—82no—
303C23×C139—82no—
304C23×C139—82no—
305C23×C139#12012yes—
306C23×C139#12011yescharacteristic
307C23×C139#12011yescharacteristic
308C23×C139C22×D411yescharacteristic
309C23×C139C22×D412yes—
310C23×C139C2×#4112yes—
311C23×C139H(5,𝔽2)11yescharacteristic
312C23×C1392−1+411yescharacteristic
313Q8×C139—81no—
314Q8×C139—81no—
315D4×C139—44no—
316D4×C139—48no—
317D4×C139—44no—
318D4×C139—42no—
319D4×C139—42no—
320D4×C139—42no—
321D4×C139—42no—
322D4×C139—44no—
323D4×C139—44no—
324D4×C139—82no—
325D4×C139—82no—
326D4×C139—81no—
327D4×C139—81no—
328D4×C139—88no—
329C2×C4×C139—24no—
330C2×C4×C139—22no—
331C2×C4×C139—22no—
332C2×C4×C139—21no—
333C2×C4×C139—21no—
334C2×C4×C139—22no—
335C2×C4×C139—22no—
336C2×C4×C139—21no—
337C2×C4×C139—21no—
338C2×C4×C139—24no—
339C2×C4×C139—22no—
340C2×C4×C139—22no—
341C2×C4×C139—42no—
342C2×C4×C139—41no—
343C2×C4×C139—42no—
344C2×C4×C139—42no—
345C2×C4×C139—42no—
346C2×C4×C139—41no—
347C2×C4×C139—42no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—42no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
353C2×C4×C139—42no—
354C2×C4×C139—41no—
355C2×C4×C139—41no—
356C2×C4×C139—42no—
357C2×C4×C139—41no—
358C2×C4×C139—41no—
359C2×C4×C139—42no—
360C2×C4×C139—41no—
361C2×C4×C139—41no—
362C2×C4×C139—42no—
363C2×C4×C139—81no—
364C2×C4×C139—81no—
365C2×C4×C139—82no—
366C2×C4×C139—82no—
367C2×C4×C139—88no—
368C22×C139—21no—
369C22×C139—21no—
370C22×C139—22no—
371C22×C139—21no—
372C22×C139—22no—
373C22×C139—21no—
374C22×C139—21no—
375C22×C139—22no—
376C22×C139—21no—
377C22×C139—22no—
378C22×C139—21no—
379C22×C139—22no—
380C22×C139—42no—
381C22×C139—41no—
382C22×C139—41no—
383C22×C139—44no—
384C22×C139—42no—
385C22×C139—42no—
386C22×C139—44no—
387C22×C139—44no—
388C22×C139—42no—
389C22×C139—42no—
390C22×C139—44no—
391C22×C139—42no—
392C22×C139—42no—
393C22×C139—42no—
394C22×C139—42no—
395C22×C139—82no—
396C22×C139—81no—
397C22×C139—81no—
398C22×C139—82no—
399C22×C139—82no—
400C22×C139—82no—
401C22×C139—82no—
402C22×C139—81no—
403C22×C139—81no—
404C22×C139—82no—
405C22×C139—81no—
406C22×C139—81no—
407C22×C139B(4,𝔽2)12yes—
408C22×C139C2×#12011yescharacteristic
409C22×C139#53211yescharacteristic
410C22×C139#53711yescharacteristic
411C22×C139#54612yes—
412C22×C139#54712yes—
413C4×C139—44no—
414C4×C139—42no—
415C4×C139—42no—
416C4×C139—41no—
417C4×C139—41no—
418C4×C139—42no—
419C4×C139—41no—
420C4×C139—41no—
421C4×C139—42no—
422C4×C139—81no—
423C4×C139—81no—
424C4×C139—82no—
425C2×C139—22no—
426C2×C139—21no—
427C2×C139—21no—
428C2×C139—22no—
429C2×C139—22no—
430C2×C139—41no—
431C2×C139—42no—
432C2×C139—82no—
433C2×C139—82no—
434C2×C139#243011yescharacteristic
435C2×C139C2×B(4,𝔽2)11yescharacteristic
436C2×C139#302611yescharacteristic
437#25563C13911yesmaximal, characteristic, direct product factor, Sylow
438C139#2556311yescharacteristic, direct product factor, Sylow
439#3490C2×C13911yescharacteristic, complemented
440#2410C2×C13912yescomplemented
441#2405C2×C13911yescharacteristic, complemented
442#2062C2×C13911yescharacteristic, complemented
443#2044C2×C13911yescharacteristic, complemented
444#2029C2×C13911yescharacteristic, complemented
445#2021C2×C13911yescharacteristic, complemented
446#1898C2×C13912yescomplemented
447#1889C2×C13912yescomplemented
448#1867C2×C13912yescomplemented
449C2×#342C2×C13911yescharacteristic, complemented
450C23×D4C22×C13911yescharacteristic
451#551—22no—
452#551—22no—
453#546—22no—
454#546—22no—
455#543C22×C13911yescharacteristic
456#538—21no—
457#538—21no—
458#534C22×C13911yescharacteristic
459#525—21no—
460#525—21no—
461C2×#123—21no—
462C2×#121—22no—
463C2×#120C22×C13912yes—
464C2×#120C22×C13912yes—
465#518C22×C13912yes—
466C22×C22⋊C4C22×C13911yescharacteristic
467C22×C22⋊C4C22×C13912yes—
468C2×#99C22×C13912yes—
469C2×#99C22×C13912yes—
470#394—21no—
471#394—21no—
472#394—22no—
473#392—22no—
474#386—21no—
475#386—22no—
476#386C22×C13912yes—
477#385C22×C13912yes—
478#385C22×C13911yescharacteristic
479#385C22×C13911yescharacteristic
480#379C22×C13911yescharacteristic
481#379C22×C13912yes—
482#379C22×C13911yescharacteristic
483#379C22×C13911yescharacteristic
484#342C22×C13912yes—
485#342C22×C13911yescharacteristic
486#342C22×C13912yes—
487#342C22×C13912yes—
488#342C22×C13911yescharacteristic
489C25C23×C13911yescharacteristic
490C25C23×C13911yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C13912yescomplemented
500C22×D4D4×C13912yescomplemented
501C22×D4C23×C13912yes—
502C23×C4—22no—
503C23×C4D4×C13911yescharacteristic, complemented
504C23×C4D4×C13911yescharacteristic, complemented
505C23×C4C23×C13911yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C13911yescharacteristic, complemented
565C2×C22⋊C4D4×C13911yescharacteristic, complemented
566C2×C22⋊C4D4×C13912yescomplemented
567C2×C22⋊C4D4×C13912yescomplemented
568C2×C22⋊C4C23×C13912yes—
569C2×C22⋊C4C23×C13911yescharacteristic
570C2×C22⋊C4C23×C13911yescharacteristic
571C2×C22⋊C4C23×C13911yescharacteristic
572C2×C22⋊C4C23×C13911yescharacteristic
573C2×C22⋊C4C23×C13912yes—
574C2×C22⋊C4C23×C13912yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C13912yes—
594C24C2×D4×C13911yescharacteristic
595C24C2×D4×C13912yes—
596C24C2×D4×C13912yes—
597C24C2×D4×C13911yescharacteristic
598C24C24×C13911yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C13912yes—
650C22×C4C2×D4×C13911yescharacteristic
651C22×C4C2×D4×C13912yes—
652C22×C4C2×D4×C13911yescharacteristic
653C22×C4C2×D4×C13911yescharacteristic
654C22×C4C2×D4×C13912yes—
655C22×C4C2×D4×C13911yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C13914yescomplemented
699C42—22no—
700C42—22no—
701C23—22no—
702C23—24no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C13912yes—
744C23#120×C13911yescharacteristic
745C23#120×C13911yescharacteristic
746C23C22×D4×C13911yescharacteristic
747C23C22×D4×C13912yes—
748C23C2×#41×C13912yes—
749C23H(5,𝔽2)×C13911yescharacteristic
750C232−1+4×C13911yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—22no—
808C22—21no—
809C22—22no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22B(4,𝔽2)×C13912yes—
846C22C2×#120×C13911yescharacteristic
847C22#532×C13911yescharacteristic
848C22#537×C13911yescharacteristic
849C22#546×C13912yes—
850C22#547×C13912yes—
851C4—44no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—41no—
858C4—42no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2#2430×C13911yescharacteristic
873C2C2×B(4,𝔽2)×C13911yescharacteristic
874C2#3026×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC24C24×C139
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C25×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3490×C139C2semidirect
2. #2410×C139C2semidirect
3. #2405×C139C2semidirect
4. #2062×C139C2semidirect
5. #2044×C139C2semidirect
6. #2029×C139C2semidirect
7. #2021×C139C2semidirect
8. #1898×C139C2semidirect
9. #1889×C139C2semidirect
10. #1867×C139C2semidirect
11. C2×#342×C139C2semidirect
61. C22×D4×C139D4semidirect
62. C22×D4×C139D4semidirect
65. C23×C4×C139D4semidirect
66. C23×C4×C139D4semidirect
126. C2×C22⋊C4×C139D4semidirect
127. C2×C22⋊C4×C139D4semidirect
128. C2×C22⋊C4×C139D4semidirect
129. C2×C22⋊C4×C139D4semidirect
260. C22⋊C4×C139#41semidirect
437. #25563C139direct (N × H)
438. C139#25563direct (N × H)
439. #3490C2×C139semidirect
440. #2410C2×C139semidirect
441. #2405C2×C139semidirect
442. #2062C2×C139semidirect
443. #2044C2×C139semidirect
444. #2029C2×C139semidirect
445. #2021C2×C139semidirect
446. #1898C2×C139semidirect
447. #1889C2×C139semidirect
448. #1867C2×C139semidirect
449. C2×#342C2×C139semidirect
499. C22×D4D4×C139semidirect
500. C22×D4D4×C139semidirect
503. C23×C4D4×C139semidirect
504. C23×C4D4×C139semidirect
564. C2×C22⋊C4D4×C139semidirect
565. C2×C22⋊C4D4×C139semidirect
566. C2×C22⋊C4D4×C139semidirect
567. C2×C22⋊C4D4×C139semidirect
698. C22⋊C4#41×C139semidirect

Maximal subgroups

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

subgroupindex
#3490×C1392
#2410×C1392
#2405×C1392
#2062×C1392
#2044×C1392
#2029×C1392
#2021×C1392
#1898×C1392
#1889×C1392
#1867×C1392
C2×#342×C1392
#25563139