Finite Group Databasebeta

← C139×#23903 #48018499

Subgroups — C139×#23903 #48018499

Order 35584.

2096 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C139C211yesmaximal, characteristic, complemented
2C2×#534×C139C211yesmaximal, characteristic, complemented
3C2×#458×C139C211yesmaximal, characteristic, complemented
4C2×B(4,𝔽2)×C139C211yesmaximal, characteristic, complemented
5#2613×C139C212yesmaximal, complemented
6#2022×C139C212yesmaximal, complemented
7#2021×C139C212yesmaximal, complemented
8#1898×C139C212yesmaximal, complemented
9#1890×C139C211yesmaximal, characteristic, complemented
10#1889×C139C211yesmaximal, characteristic, complemented
11#1781×C139C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C139C2211yescharacteristic
13C23×D4×C139C2211yescharacteristic
14C23×D4×C139C2211yescharacteristic, complemented
15#546×C139—24no—
16D42×C139—24no—
17#535×C139—21no—
18#534×C139—21no—
19#534×C139—24no—
20#534×C139—24no—
21#534×C139C2212yes—
22#525×C139—21no—
23C2×#123×C139—21no—
24C2×#123×C139C2211yescharacteristic
25C2×#123×C139C2211yescharacteristic, complemented
26C2×#123×C139C2212yescomplemented
27C2×#121×C139—21no—
28C2×#121×C139—21no—
29C2×#120×C139—21no—
30C2×#120×C139—21no—
31C2×#120×C139C2211yescharacteristic
32C2×#120×C139C2212yes—
33C2×#120×C139C2211yescharacteristic, complemented
34C2×#120×C139C2212yescomplemented
35#518×C139C2211yescharacteristic
36C22×C22⋊C4×C139C2211yescharacteristic, complemented
37#458×C139—24no—
38B(4,𝔽2)×C139—24no—
39C2×#99×C139C2211yescharacteristic
40C2×#99×C139C2211yescharacteristic
41C2×#99×C139C2212yescomplemented
42C2×#99×C139C2212yescomplemented
43C2×#99×C139C2212yescomplemented
44#394×C139—24no—
45#392×C139—24no—
46#381×C139C2212yescomplemented
47#379×C139C2212yescomplemented
48#379×C139C2212yescomplemented
49#342×C139C2212yescomplemented
50#342×C139C2212yescomplemented
51C25×C139D411yescharacteristic, complemented
52C25×C139C2311yescharacteristic
53C25×C139C2311yescharacteristic
54H(5,𝔽2)×C139—22no—
55H(5,𝔽2)×C139—22no—
56H(5,𝔽2)×C139—42no—
57C2×#41×C139—21no—
58C2×#41×C139—22no—
59C22×D4×C139—21no—
60C22×D4×C139—21no—
61C22×D4×C139—21no—
62C22×D4×C139—22no—
63C22×D4×C139—24no—
64C22×D4×C139—22no—
65C22×D4×C139—22no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139—22no—
69C22×D4×C139—22no—
70C22×D4×C139—24no—
71C22×D4×C139—22no—
72C22×D4×C139—22no—
73C22×D4×C139—42no—
74C22×D4×C139—42no—
75C22×D4×C139D411yescharacteristic, complemented
76C22×D4×C139D411yescharacteristic, complemented
77C22×D4×C139D414yescomplemented
78C22×D4×C139C2312yes—
79C22×D4×C139C2311yescharacteristic
80C22×D4×C139C2311yescharacteristic
81C23×C4×C139—21no—
82C23×C4×C139D411yescharacteristic, complemented
83C23×C4×C139C2311yescharacteristic
84#127×C139—22no—
85#124×C139—22no—
86#123×C139—28no—
87#123×C139—22no—
88#123×C139—22no—
89#123×C139—22no—
90#123×C139—22no—
91#123×C139—22no—
92#123×C139—22no—
93#123×C139—24no—
94#123×C139—42no—
95#123×C139D414yescomplemented
96C22⋊Q8×C139—22no—
97#121×C139—28no—
98#121×C139—28no—
99#121×C139—22no—
100#121×C139—24no—
101#121×C139—24no—
102#121×C139—24no—
103#120×C139—28no—
104#120×C139—24no—
105#120×C139—22no—
106#120×C139—22no—
107#120×C139—22no—
108#120×C139—22no—
109#120×C139—24no—
110#120×C139—22no—
111#120×C139—22no—
112#120×C139—22no—
113#120×C139—22no—
114#120×C139—24no—
115#120×C139—42no—
116#120×C139D414yescomplemented
117C4×D4×C139—24no—
118C4×D4×C139—24no—
119#117×C139—21no—
120C2×C4⋊C4×C139—21no—
121C2×C4⋊C4×C139—21no—
122C2×C4⋊C4×C139—22no—
123C2×C22⋊C4×C139—22no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—21no—
129C2×C22⋊C4×C139—21no—
130C2×C22⋊C4×C139—22no—
131C2×C22⋊C4×C139—22no—
132C2×C22⋊C4×C139—22no—
133C2×C22⋊C4×C139—22no—
134C2×C22⋊C4×C139—24no—
135C2×C22⋊C4×C139—24no—
136C2×C22⋊C4×C139D414yescomplemented
137C2×C22⋊C4×C139C2312yes—
138C2×C22⋊C4×C139C2312yes—
139C2×C22⋊C4×C139C2312yes—
140C2×C22⋊C4×C139C2311yescharacteristic
141C2×C22⋊C4×C139C2311yescharacteristic
142#99×C139—22no—
143#99×C139—22no—
144#99×C139—24no—
145#99×C139—24no—
146#99×C139—42no—
147#95×C139—24no—
148C24×C139—21no—
149C24×C139—21no—
150C24×C139—22no—
151C24×C139—21no—
152C24×C139—22no—
153C24×C139—21no—
154C24×C139—22no—
155C24×C139—22no—
156C24×C139—21no—
157C24×C139—22no—
158C24×C139—41no—
159C24×C139—82no—
160C24×C139—82no—
161C24×C139—82no—
162C24×C139C2×D411yescharacteristic
163C24×C139C2×D412yes—
164C24×C139C2×D411yescharacteristic
165C24×C139C2×D414yes—
166C24×C139C2×D411yescharacteristic
167C24×C139C2×D411yescharacteristic
168C24×C139C2×D412yescomplemented
169C24×C139C2411yescharacteristic
170#41×C139—44no—
171#41×C139—44no—
172#41×C139—42no—
173#41×C139—42no—
174C2×Q8×C139—21no—
175C2×D4×C139—22no—
176C2×D4×C139—22no—
177C2×D4×C139—22no—
178C2×D4×C139—24no—
179C2×D4×C139—24no—
180C2×D4×C139—21no—
181C2×D4×C139—24no—
182C2×D4×C139—22no—
183C2×D4×C139—22no—
184C2×D4×C139—22no—
185C2×D4×C139—22no—
186C2×D4×C139—22no—
187C2×D4×C139—22no—
188C2×D4×C139—22no—
189C2×D4×C139—21no—
190C2×D4×C139—21no—
191C2×D4×C139—22no—
192C2×D4×C139—22no—
193C2×D4×C139—22no—
194C2×D4×C139—22no—
195C2×D4×C139—24no—
196C2×D4×C139—24no—
197C2×D4×C139—24no—
198C2×D4×C139—24no—
199C2×D4×C139—22no—
200C2×D4×C139—41no—
201C2×D4×C139—41no—
202C2×D4×C139—48no—
203C2×D4×C139—48no—
204C2×D4×C139—48no—
205C2×D4×C139—44no—
206C2×D4×C139—44no—
207C2×D4×C139—48no—
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—44no—
215C2×D4×C139—84no—
216C2×D4×C139—82no—
217C2×D4×C139—82no—
218C2×D4×C139—84no—
219C2×D4×C139—84no—
220C2×D4×C139C2×D412yes—
221C2×D4×C139C2×D412yes—
222C22×C4×C139—21no—
223C22×C4×C139—22no—
224C22×C4×C139—22no—
225C22×C4×C139—22no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
229C22×C4×C139—21no—
230C22×C4×C139—22no—
231C22×C4×C139—22no—
232C22×C4×C139—24no—
233C22×C4×C139—22no—
234C22×C4×C139—22no—
235C22×C4×C139—22no—
236C22×C4×C139—41no—
237C22×C4×C139—82no—
238C22×C4×C139C2×D412yes—
239C22×C4×C139C2×D411yescharacteristic
240C22×C4×C139C2×D411yescharacteristic
241C22×C4×C139C2×D414yes—
242C22×C4×C139C2×D412yescomplemented
243C4⋊C4×C139—24no—
244C4⋊C4×C139—22no—
245C4⋊C4×C139—24no—
246C4⋊C4×C139—24no—
247C4⋊C4×C139—44no—
248C22⋊C4×C139—24no—
249C22⋊C4×C139—22no—
250C22⋊C4×C139—24no—
251C22⋊C4×C139—24no—
252C22⋊C4×C139—24no—
253C22⋊C4×C139—24no—
254C22⋊C4×C139—24no—
255C22⋊C4×C139—24no—
256C22⋊C4×C139—24no—
257C22⋊C4×C139—21no—
258C22⋊C4×C139—21no—
259C22⋊C4×C139—22no—
260C22⋊C4×C139—22no—
261C22⋊C4×C139—24no—
262C22⋊C4×C139—22no—
263C22⋊C4×C139—22no—
264C22⋊C4×C139—22no—
265C22⋊C4×C139—22no—
266C22⋊C4×C139—44no—
267C22⋊C4×C139—44no—
268C22⋊C4×C139—84no—
269C22⋊C4×C139—84no—
270C22⋊C4×C139C2×D412yescomplemented
271C22⋊C4×C139C2×D412yescomplemented
272C42×C139—22no—
273C23×C139—21no—
274C23×C139—21no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—21no—
279C23×C139—24no—
280C23×C139—24no—
281C23×C139—21no—
282C23×C139—22no—
283C23×C139—21no—
284C23×C139—22no—
285C23×C139—24no—
286C23×C139—21no—
287C23×C139—22no—
288C23×C139—22no—
289C23×C139—42no—
290C23×C139—42no—
291C23×C139—42no—
292C23×C139—44no—
293C23×C139—44no—
294C23×C139—44no—
295C23×C139—42no—
296C23×C139—42no—
297C23×C139—44no—
298C23×C139—44no—
299C23×C139—42no—
300C23×C139—42no—
301C23×C139—44no—
302C23×C139—42no—
303C23×C139—44no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—42no—
307C23×C139—82no—
308C23×C139—82no—
309C23×C139—82no—
310C23×C139—82no—
311C23×C139—82no—
312C23×C139—84no—
313C23×C139—84no—
314C23×C139—84no—
315C23×C139—82no—
316C23×C139—84no—
317C23×C139#12012yes—
318C23×C139#12012yes—
319C23×C139#12012yes—
320C23×C139C22×D411yescharacteristic
321C23×C139C22×D412yes—
322C23×C139C22×D411yescharacteristic
323C23×C139C22×D411yescharacteristic
324C23×C139H(5,𝔽2)12yes—
325Q8×C139—42no—
326D4×C139—24no—
327D4×C139—24no—
328D4×C139—44no—
329D4×C139—42no—
330D4×C139—44no—
331D4×C139—48no—
332D4×C139—48no—
333D4×C139—44no—
334D4×C139—48no—
335D4×C139—42no—
336D4×C139—42no—
337D4×C139—42no—
338D4×C139—42no—
339D4×C139—42no—
340D4×C139—42no—
341D4×C139—84no—
342D4×C139—84no—
343D4×C139—84no—
344D4×C139—84no—
345D4×C139—88no—
346C2×C4×C139—21no—
347C2×C4×C139—21no—
348C2×C4×C139—22no—
349C2×C4×C139—22no—
350C2×C4×C139—21no—
351C2×C4×C139—22no—
352C2×C4×C139—24no—
353C2×C4×C139—22no—
354C2×C4×C139—21no—
355C2×C4×C139—21no—
356C2×C4×C139—22no—
357C2×C4×C139—24no—
358C2×C4×C139—22no—
359C2×C4×C139—44no—
360C2×C4×C139—44no—
361C2×C4×C139—42no—
362C2×C4×C139—42no—
363C2×C4×C139—42no—
364C2×C4×C139—41no—
365C2×C4×C139—41no—
366C2×C4×C139—42no—
367C2×C4×C139—44no—
368C2×C4×C139—44no—
369C2×C4×C139—44no—
370C2×C4×C139—42no—
371C2×C4×C139—42no—
372C2×C4×C139—84no—
373C2×C4×C139—82no—
374C2×C4×C139#12012yes—
375C22×C139—24no—
376C22×C139—22no—
377C22×C139—22no—
378C22×C139—22no—
379C22×C139—22no—
380C22×C139—22no—
381C22×C139—24no—
382C22×C139—22no—
383C22×C139—41no—
384C22×C139—41no—
385C22×C139—42no—
386C22×C139—42no—
387C22×C139—42no—
388C22×C139—42no—
389C22×C139—42no—
390C22×C139—42no—
391C22×C139—42no—
392C22×C139—42no—
393C22×C139—42no—
394C22×C139—44no—
395C22×C139—44no—
396C22×C139—42no—
397C22×C139—42no—
398C22×C139—42no—
399C22×C139—41no—
400C22×C139—44no—
401C22×C139—42no—
402C22×C139—84no—
403C22×C139—84no—
404C22×C139—81no—
405C22×C139—82no—
406C22×C139—82no—
407C22×C139—81no—
408C22×C139—84no—
409C22×C139—82no—
410C22×C139—88no—
411C22×C139—82no—
412C22×C139—162no—
413C22×C139C2×#12011yescharacteristic
414C22×C139C2×#12011yescharacteristic
415C22×C139#53411yescharacteristic
416C22×C139D4212yes—
417C22×C139D4212yes—
418C4×C139—22no—
419C4×C139—42no—
420C4×C139—42no—
421C4×C139—41no—
422C4×C139—42no—
423C4×C139—42no—
424C4×C139—44no—
425C4×C139—82no—
426C4×C139—82no—
427C2×C139—21no—
428C2×C139—22no—
429C2×C139—22no—
430C2×C139—21no—
431C2×C139—42no—
432C2×C139—42no—
433C2×C139—42no—
434C2×C139—82no—
435C2×C139—81no—
436C2×C139—82no—
437C2×C139#240311yescharacteristic
438C2×C139#302612yes—
439#23903C13911yesmaximal, characteristic, direct product factor, Sylow
440C139#2390311yescharacteristic, direct product factor, Sylow
441#3484C2×C13911yescharacteristic, complemented
442C2×#534C2×C13911yescharacteristic, complemented
443C2×#458C2×C13911yescharacteristic, complemented
444C2×B(4,𝔽2)C2×C13911yescharacteristic, complemented
445#2613C2×C13912yescomplemented
446#2022C2×C13912yescomplemented
447#2021C2×C13912yescomplemented
448#1898C2×C13912yescomplemented
449#1890C2×C13911yescharacteristic, complemented
450#1889C2×C13911yescharacteristic, complemented
451#1781C2×C13911yescharacteristic, complemented
452C2×H(5,𝔽2)C22×C13911yescharacteristic
453C23×D4C22×C13911yescharacteristic
454C23×D4C22×C13911yescharacteristic, complemented
455#546—24no—
456D42—24no—
457#535—21no—
458#534—21no—
459#534—24no—
460#534—24no—
461#534C22×C13912yes—
462#525—21no—
463C2×#123—21no—
464C2×#123C22×C13911yescharacteristic
465C2×#123C22×C13911yescharacteristic, complemented
466C2×#123C22×C13912yescomplemented
467C2×#121—21no—
468C2×#121—21no—
469C2×#120—21no—
470C2×#120—21no—
471C2×#120C22×C13911yescharacteristic
472C2×#120C22×C13912yes—
473C2×#120C22×C13911yescharacteristic, complemented
474C2×#120C22×C13912yescomplemented
475#518C22×C13911yescharacteristic
476C22×C22⋊C4C22×C13911yescharacteristic, complemented
477#458—24no—
478B(4,𝔽2)—24no—
479C2×#99C22×C13911yescharacteristic
480C2×#99C22×C13911yescharacteristic
481C2×#99C22×C13912yescomplemented
482C2×#99C22×C13912yescomplemented
483C2×#99C22×C13912yescomplemented
484#394—24no—
485#392—24no—
486#381C22×C13912yescomplemented
487#379C22×C13912yescomplemented
488#379C22×C13912yescomplemented
489#342C22×C13912yescomplemented
490#342C22×C13912yescomplemented
491C25D4×C13911yescharacteristic, complemented
492C25C23×C13911yescharacteristic
493C25C23×C13911yescharacteristic
494H(5,𝔽2)—22no—
495H(5,𝔽2)—22no—
496H(5,𝔽2)—42no—
497C2×#41—21no—
498C2×#41—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—24no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—24no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—42no—
514C22×D4—42no—
515C22×D4D4×C13911yescharacteristic, complemented
516C22×D4D4×C13911yescharacteristic, complemented
517C22×D4D4×C13914yescomplemented
518C22×D4C23×C13912yes—
519C22×D4C23×C13911yescharacteristic
520C22×D4C23×C13911yescharacteristic
521C23×C4—21no—
522C23×C4D4×C13911yescharacteristic, complemented
523C23×C4C23×C13911yescharacteristic
524#127—22no—
525#124—22no—
526#123—28no—
527#123—22no—
528#123—22no—
529#123—22no—
530#123—22no—
531#123—22no—
532#123—22no—
533#123—24no—
534#123—42no—
535#123D4×C13914yescomplemented
536C22⋊Q8—22no—
537#121—28no—
538#121—28no—
539#121—22no—
540#121—24no—
541#121—24no—
542#121—24no—
543#120—28no—
544#120—24no—
545#120—22no—
546#120—22no—
547#120—22no—
548#120—22no—
549#120—24no—
550#120—22no—
551#120—22no—
552#120—22no—
553#120—22no—
554#120—24no—
555#120—42no—
556#120D4×C13914yescomplemented
557C4×D4—24no—
558C4×D4—24no—
559#117—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4D4×C13914yescomplemented
577C2×C22⋊C4C23×C13912yes—
578C2×C22⋊C4C23×C13912yes—
579C2×C22⋊C4C23×C13912yes—
580C2×C22⋊C4C23×C13911yescharacteristic
581C2×C22⋊C4C23×C13911yescharacteristic
582#99—22no—
583#99—22no—
584#99—24no—
585#99—24no—
586#99—42no—
587#95—24no—
588C24—21no—
589C24—21no—
590C24—22no—
591C24—21no—
592C24—22no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—21no—
597C24—22no—
598C24—41no—
599C24—82no—
600C24—82no—
601C24—82no—
602C24C2×D4×C13911yescharacteristic
603C24C2×D4×C13912yes—
604C24C2×D4×C13911yescharacteristic
605C24C2×D4×C13914yes—
606C24C2×D4×C13911yescharacteristic
607C24C2×D4×C13911yescharacteristic
608C24C2×D4×C13912yescomplemented
609C24C24×C13911yescharacteristic
610#41—44no—
611#41—44no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—24no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—22no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—48no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—44no—
655C2×D4—84no—
656C2×D4—82no—
657C2×D4—82no—
658C2×D4—84no—
659C2×D4—84no—
660C2×D4C2×D4×C13912yes—
661C2×D4C2×D4×C13912yes—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—24no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—41no—
677C22×C4—82no—
678C22×C4C2×D4×C13912yes—
679C22×C4C2×D4×C13911yescharacteristic
680C22×C4C2×D4×C13911yescharacteristic
681C22×C4C2×D4×C13914yes—
682C22×C4C2×D4×C13912yescomplemented
683C4⋊C4—24no—
684C4⋊C4—22no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—44no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—84no—
709C22⋊C4—84no—
710C22⋊C4C2×D4×C13912yescomplemented
711C22⋊C4C2×D4×C13912yescomplemented
712C42—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—24no—
720C23—24no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—21no—
727C23—22no—
728C23—22no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—42no—
736C23—42no—
737C23—44no—
738C23—44no—
739C23—42no—
740C23—42no—
741C23—44no—
742C23—42no—
743C23—44no—
744C23—41no—
745C23—41no—
746C23—42no—
747C23—82no—
748C23—82no—
749C23—82no—
750C23—82no—
751C23—82no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—82no—
756C23—84no—
757C23#120×C13912yes—
758C23#120×C13912yes—
759C23#120×C13912yes—
760C23C22×D4×C13911yescharacteristic
761C23C22×D4×C13912yes—
762C23C22×D4×C13911yescharacteristic
763C23C22×D4×C13911yescharacteristic
764C23H(5,𝔽2)×C13912yes—
765Q8—42no—
766D4—24no—
767D4—24no—
768D4—44no—
769D4—42no—
770D4—44no—
771D4—48no—
772D4—48no—
773D4—44no—
774D4—48no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—42no—
779D4—42no—
780D4—42no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785D4—88no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—84no—
813C2×C4—82no—
814C2×C4#120×C13912yes—
815C22—24no—
816C22—22no—
817C22—22no—
818C22—24no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—44no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—41no—
842C22—84no—
843C22—84no—
844C22—81no—
845C22—82no—
846C22—81no—
847C22—82no—
848C22—84no—
849C22—82no—
850C22—88no—
851C22—82no—
852C22—162no—
853C22C2×#120×C13911yescharacteristic
854C22C2×#120×C13911yescharacteristic
855C22#534×C13911yescharacteristic
856C22D42×C13912yes—
857C22D42×C13912yes—
858C4—22no—
859C4—42no—
860C4—42no—
861C4—44no—
862C4—41no—
863C4—42no—
864C4—42no—
865C4—82no—
866C4—82no—
867C2—21no—
868C2—22no—
869C2—22no—
870C2—21no—
871C2—42no—
872C2—42no—
873C2—42no—
874C2—82no—
875C2—81no—
876C2—82no—
877C2#2403×C13911yescharacteristic
878C2#3026×C13912yes—
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. #3484×C139C2semidirect
2. C2×#534×C139C2semidirect
3. C2×#458×C139C2semidirect
4. C2×B(4,𝔽2)×C139C2semidirect
5. #2613×C139C2semidirect
6. #2022×C139C2semidirect
7. #2021×C139C2semidirect
8. #1898×C139C2semidirect
9. #1890×C139C2semidirect
10. #1889×C139C2semidirect
11. #1781×C139C2semidirect
14. C23×D4×C139C22semidirect
25. C2×#123×C139C22semidirect
26. C2×#123×C139C22semidirect
33. C2×#120×C139C22semidirect
34. C2×#120×C139C22semidirect
36. C22×C22⋊C4×C139C22semidirect
41. C2×#99×C139C22semidirect
42. C2×#99×C139C22semidirect
43. C2×#99×C139C22semidirect
46. #381×C139C22semidirect
47. #379×C139C22semidirect
48. #379×C139C22semidirect
49. #342×C139C22semidirect
50. #342×C139C22semidirect
51. C25×C139D4semidirect
75. C22×D4×C139D4semidirect
76. C22×D4×C139D4semidirect
77. C22×D4×C139D4semidirect
82. C23×C4×C139D4semidirect
95. #123×C139D4semidirect
116. #120×C139D4semidirect
136. C2×C22⋊C4×C139D4semidirect
168. C24×C139C2×D4semidirect
242. C22×C4×C139C2×D4semidirect
270. C22⋊C4×C139C2×D4semidirect
271. C22⋊C4×C139C2×D4semidirect
439. #23903C139direct (N × H)
440. C139#23903direct (N × H)
441. #3484C2×C139semidirect
442. C2×#534C2×C139semidirect
443. C2×#458C2×C139semidirect
444. C2×B(4,𝔽2)C2×C139semidirect
445. #2613C2×C139semidirect
446. #2022C2×C139semidirect
447. #2021C2×C139semidirect
448. #1898C2×C139semidirect
449. #1890C2×C139semidirect
450. #1889C2×C139semidirect
451. #1781C2×C139semidirect
454. C23×D4C22×C139semidirect
465. C2×#123C22×C139semidirect
466. C2×#123C22×C139semidirect
473. C2×#120C22×C139semidirect
474. C2×#120C22×C139semidirect
476. C22×C22⋊C4C22×C139semidirect
481. C2×#99C22×C139semidirect
482. C2×#99C22×C139semidirect
483. C2×#99C22×C139semidirect
486. #381C22×C139semidirect
487. #379C22×C139semidirect
488. #379C22×C139semidirect
489. #342C22×C139semidirect
490. #342C22×C139semidirect
491. C25D4×C139semidirect
515. C22×D4D4×C139semidirect
516. C22×D4D4×C139semidirect
517. C22×D4D4×C139semidirect
522. C23×C4D4×C139semidirect
535. #123D4×C139semidirect
556. #120D4×C139semidirect
576. C2×C22⋊C4D4×C139semidirect
608. C24C2×D4×C139semidirect
682. C22×C4C2×D4×C139semidirect
710. C22⋊C4C2×D4×C139semidirect
711. C22⋊C4C2×D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3484×C1392
C2×#534×C1392
C2×#458×C1392
C2×B(4,𝔽2)×C1392
#2613×C1392
#2022×C1392
#2021×C1392
#1898×C1392
#1890×C1392
#1889×C1392
#1781×C1392
#23903139