Finite Group Databasebeta

← C139×#24404 #48019000

Subgroups — C139×#24404 #48019000

Order 35584.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C139C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C139C211yesmaximal, characteristic, complemented
3C22×#99×C139C211yesmaximal, characteristic, complemented
4#2410×C139C212yesmaximal, complemented
5#2403×C139C211yesmaximal, characteristic, complemented
6#2044×C139C212yesmaximal, complemented
7#2021×C139C212yesmaximal, complemented
8#1898×C139C212yesmaximal, complemented
9#1889×C139C211yesmaximal, characteristic, complemented
10#1867×C139C211yesmaximal, characteristic, complemented
11#1790×C139C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C139C2211yescharacteristic
13C23×D4×C139C2211yescharacteristic
14C23×D4×C139C2211yescharacteristic, complemented
15#546×C139—22no—
16#546×C139—22no—
17D42×C139—22no—
18D42×C139—22no—
19#535×C139—21no—
20#534×C139—21no—
21#534×C139C2212yes—
22#525×C139—21no—
23C2×#121×C139—22no—
24C2×#120×C139—21no—
25C2×#120×C139—21no—
26C2×#120×C139C2211yescharacteristic
27C2×#120×C139C2212yes—
28C2×#120×C139C2212yescomplemented
29C2×#120×C139C2211yescharacteristic, complemented
30#518×C139C2211yescharacteristic
31C22×C22⋊C4×C139C2212yescomplemented
32B(4,𝔽2)×C139—24no—
33C2×#99×C139—24no—
34C2×#99×C139C2211yescharacteristic
35C2×#99×C139C2211yescharacteristic
36C2×#99×C139C2212yescomplemented
37C2×#99×C139C2212yescomplemented
38C2×#99×C139C2212yescomplemented
39#394×C139—22no—
40#392×C139—21no—
41#392×C139—21no—
42#392×C139—22no—
43#386×C139—21no—
44#386×C139—22no—
45#386×C139C2211yescharacteristic
46#386×C139C2211yescharacteristic, complemented
47#386×C139C2212yescomplemented
48#385×C139C2212yescomplemented
49#379×C139C2212yescomplemented
50#379×C139C2211yescharacteristic, complemented
51#342×C139C2212yescomplemented
52#342×C139C2212yescomplemented
53C25×C139D411yescharacteristic, complemented
54C25×C139C2311yescharacteristic
55C25×C139C2311yescharacteristic
56H(5,𝔽2)×C139—22no—
57H(5,𝔽2)×C139—22no—
58H(5,𝔽2)×C139—42no—
59C2×#41×C139—21no—
60C2×#41×C139—22no—
61C22×D4×C139—21no—
62C22×D4×C139—21no—
63C22×D4×C139—22no—
64C22×D4×C139—22no—
65C22×D4×C139—22no—
66C22×D4×C139—22no—
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—22no—
70C22×D4×C139—22no—
71C22×D4×C139—21no—
72C22×D4×C139—22no—
73C22×D4×C139—21no—
74C22×D4×C139—21no—
75C22×D4×C139—22no—
76C22×D4×C139—44no—
77C22×D4×C139—42no—
78C22×D4×C139D411yescharacteristic, complemented
79C22×D4×C139D411yescharacteristic, complemented
80C22×D4×C139D412yescomplemented
81C22×D4×C139D412yescomplemented
82C22×D4×C139C2312yes—
83C22×D4×C139C2311yescharacteristic
84C22×D4×C139C2311yescharacteristic
85C23×C4×C139—22no—
86C23×C4×C139D411yescharacteristic, complemented
87C23×C4×C139C2311yescharacteristic
88#127×C139—22no—
89#124×C139—22no—
90#123×C139—22no—
91#123×C139—22no—
92#123×C139—22no—
93C22⋊Q8×C139—21no—
94C22⋊Q8×C139—21no—
95#121×C139—21no—
96#121×C139—21no—
97#121×C139—22no—
98#121×C139—22no—
99#121×C139—22no—
100#121×C139—22no—
101#121×C139—22no—
102#121×C139—22no—
103#121×C139—48no—
104#120×C139—22no—
105#120×C139—22no—
106#120×C139—22no—
107#120×C139—22no—
108#120×C139—22no—
109#120×C139—22no—
110#120×C139—22no—
111#120×C139—22no—
112#120×C139—22no—
113#120×C139—22no—
114#120×C139—22no—
115#120×C139—24no—
116#120×C139—42no—
117#120×C139—42no—
118#120×C139—44no—
119C4×D4×C139—22no—
120C4×D4×C139—22no—
121C4×D4×C139—22no—
122C4×D4×C139—22no—
123#117×C139—21no—
124C2×C4⋊C4×C139—22no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—24no—
129C2×C22⋊C4×C139—22no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—22no—
134C2×C22⋊C4×C139—21no—
135C2×C22⋊C4×C139—21no—
136C2×C22⋊C4×C139—22no—
137C2×C22⋊C4×C139—22no—
138C2×C22⋊C4×C139—21no—
139C2×C22⋊C4×C139—22no—
140C2×C22⋊C4×C139—42no—
141C2×C22⋊C4×C139D412yescomplemented
142C2×C22⋊C4×C139D412yescomplemented
143C2×C22⋊C4×C139C2312yes—
144C2×C22⋊C4×C139C2311yescharacteristic
145C2×C22⋊C4×C139C2311yescharacteristic
146C2×C22⋊C4×C139C2312yes—
147C2×C22⋊C4×C139C2312yes—
148#99×C139—22no—
149#99×C139—24no—
150#99×C139—24no—
151#99×C139—42no—
152#99×C139D414yescomplemented
153#95×C139—22no—
154#95×C139—21no—
155#95×C139—21no—
156#95×C139—22no—
157C24×C139—21no—
158C24×C139—21no—
159C24×C139—22no—
160C24×C139—21no—
161C24×C139—22no—
162C24×C139—21no—
163C24×C139—21no—
164C24×C139—21no—
165C24×C139—22no—
166C24×C139—21no—
167C24×C139—21no—
168C24×C139—22no—
169C24×C139—41no—
170C24×C139—42no—
171C24×C139—42no—
172C24×C139—42no—
173C24×C139—81no—
174C24×C139—81no—
175C24×C139—81no—
176C24×C139C2×D411yescharacteristic
177C24×C139C2×D412yes—
178C24×C139C2×D411yescharacteristic
179C24×C139C2×D412yes—
180C24×C139C2×D412yes—
181C24×C139C2×D411yescharacteristic
182C24×C139C2×D411yescharacteristic
183C24×C139C2411yescharacteristic
184#41×C139—44no—
185#41×C139—44no—
186#41×C139—42no—
187#41×C139—42no—
188C2×Q8×C139—21no—
189C2×D4×C139—22no—
190C2×D4×C139—22no—
191C2×D4×C139—22no—
192C2×D4×C139—24no—
193C2×D4×C139—21no—
194C2×D4×C139—28no—
195C2×D4×C139—22no—
196C2×D4×C139—22no—
197C2×D4×C139—22no—
198C2×D4×C139—22no—
199C2×D4×C139—22no—
200C2×D4×C139—21no—
201C2×D4×C139—22no—
202C2×D4×C139—22no—
203C2×D4×C139—22no—
204C2×D4×C139—22no—
205C2×D4×C139—21no—
206C2×D4×C139—22no—
207C2×D4×C139—22no—
208C2×D4×C139—22no—
209C2×D4×C139—22no—
210C2×D4×C139—22no—
211C2×D4×C139—22no—
212C2×D4×C139—22no—
213C2×D4×C139—22no—
214C2×D4×C139—22no—
215C2×D4×C139—41no—
216C2×D4×C139—41no—
217C2×D4×C139—42no—
218C2×D4×C139—44no—
219C2×D4×C139—44no—
220C2×D4×C139—44no—
221C2×D4×C139—44no—
222C2×D4×C139—44no—
223C2×D4×C139—44no—
224C2×D4×C139—44no—
225C2×D4×C139—44no—
226C2×D4×C139—44no—
227C2×D4×C139—42no—
228C2×D4×C139—42no—
229C2×D4×C139—44no—
230C2×D4×C139—42no—
231C2×D4×C139—41no—
232C2×D4×C139—42no—
233C2×D4×C139—41no—
234C2×D4×C139—42no—
235C2×D4×C139—44no—
236C2×D4×C139—42no—
237C2×D4×C139—42no—
238C2×D4×C139—42no—
239C2×D4×C139—44no—
240C2×D4×C139—42no—
241C2×D4×C139—82no—
242C2×D4×C139—82no—
243C2×D4×C139—81no—
244C2×D4×C139—81no—
245C2×D4×C139—82no—
246C2×D4×C139—82no—
247C2×D4×C139C2×D412yes—
248C2×D4×C139#4112yes—
249C22×C4×C139—21no—
250C22×C4×C139—22no—
251C22×C4×C139—21no—
252C22×C4×C139—21no—
253C22×C4×C139—21no—
254C22×C4×C139—22no—
255C22×C4×C139—22no—
256C22×C4×C139—21no—
257C22×C4×C139—21no—
258C22×C4×C139—22no—
259C22×C4×C139—22no—
260C22×C4×C139—21no—
261C22×C4×C139—21no—
262C22×C4×C139—42no—
263C22×C4×C139—41no—
264C22×C4×C139—44no—
265C22×C4×C139—44no—
266C22×C4×C139—82no—
267C22×C4×C139C2×D412yes—
268C22×C4×C139C2×D411yescharacteristic
269C22×C4×C139C2×D411yescharacteristic
270C22×C4×C139C2×D412yes—
271C22×C4×C139C2×D412yes—
272C4⋊C4×C139—21no—
273C4⋊C4×C139—21no—
274C4⋊C4×C139—22no—
275C4⋊C4×C139—22no—
276C4⋊C4×C139—44no—
277C22⋊C4×C139—22no—
278C22⋊C4×C139—22no—
279C22⋊C4×C139—22no—
280C22⋊C4×C139—22no—
281C22⋊C4×C139—22no—
282C22⋊C4×C139—22no—
283C22⋊C4×C139—22no—
284C22⋊C4×C139—22no—
285C22⋊C4×C139—22no—
286C22⋊C4×C139—22no—
287C22⋊C4×C139—22no—
288C22⋊C4×C139—22no—
289C22⋊C4×C139—22no—
290C22⋊C4×C139—21no—
291C22⋊C4×C139—21no—
292C22⋊C4×C139—22no—
293C22⋊C4×C139—22no—
294C22⋊C4×C139—44no—
295C22⋊C4×C139—44no—
296C22⋊C4×C139—42no—
297C22⋊C4×C139—42no—
298C22⋊C4×C139—42no—
299C22⋊C4×C139—44no—
300C22⋊C4×C139—42no—
301C22⋊C4×C139—44no—
302C22⋊C4×C139—42no—
303C22⋊C4×C139—82no—
304C22⋊C4×C139—81no—
305C22⋊C4×C139C2×D414yescomplemented
306C42×C139—22no—
307C23×C139—21no—
308C23×C139—21no—
309C23×C139—21no—
310C23×C139—22no—
311C23×C139—22no—
312C23×C139—22no—
313C23×C139—24no—
314C23×C139—21no—
315C23×C139—21no—
316C23×C139—21no—
317C23×C139—22no—
318C23×C139—22no—
319C23×C139—24no—
320C23×C139—22no—
321C23×C139—21no—
322C23×C139—22no—
323C23×C139—21no—
324C23×C139—21no—
325C23×C139—22no—
326C23×C139—22no—
327C23×C139—41no—
328C23×C139—42no—
329C23×C139—41no—
330C23×C139—41no—
331C23×C139—41no—
332C23×C139—42no—
333C23×C139—41no—
334C23×C139—42no—
335C23×C139—42no—
336C23×C139—42no—
337C23×C139—41no—
338C23×C139—41no—
339C23×C139—41no—
340C23×C139—41no—
341C23×C139—42no—
342C23×C139—42no—
343C23×C139—41no—
344C23×C139—42no—
345C23×C139—41no—
346C23×C139—41no—
347C23×C139—42no—
348C23×C139—42no—
349C23×C139—42no—
350C23×C139—42no—
351C23×C139—41no—
352C23×C139—41no—
353C23×C139—41no—
354C23×C139—42no—
355C23×C139—42no—
356C23×C139—42no—
357C23×C139—81no—
358C23×C139—81no—
359C23×C139—82no—
360C23×C139—82no—
361C23×C139—82no—
362C23×C139—82no—
363C23×C139—84no—
364C23×C139—84no—
365C23×C139—81no—
366C23×C139—81no—
367C23×C139—84no—
368C23×C139—84no—
369C23×C139#12011yescharacteristic
370C23×C139#12012yes—
371C23×C139#12011yescharacteristic
372C23×C139#12112yescomplemented
373C23×C139C22×D411yescharacteristic
374C23×C139C22×D412yes—
375C23×C139C22×D411yescharacteristic
376C23×C139C2×#4111yescharacteristic
377C23×C139H(5,𝔽2)12yes—
378Q8×C139—42no—
379D4×C139—24no—
380D4×C139—24no—
381D4×C139—44no—
382D4×C139—42no—
383D4×C139—44no—
384D4×C139—48no—
385D4×C139—44no—
386D4×C139—44no—
387D4×C139—44no—
388D4×C139—42no—
389D4×C139—42no—
390D4×C139—42no—
391D4×C139—42no—
392D4×C139—42no—
393D4×C139—42no—
394D4×C139—44no—
395D4×C139—44no—
396D4×C139—82no—
397D4×C139—82no—
398D4×C139—82no—
399D4×C139—82no—
400D4×C139—88no—
401D4×C139—84no—
402D4×C139—84no—
403C2×C4×C139—21no—
404C2×C4×C139—21no—
405C2×C4×C139—22no—
406C2×C4×C139—24no—
407C2×C4×C139—22no—
408C2×C4×C139—22no—
409C2×C4×C139—22no—
410C2×C4×C139—21no—
411C2×C4×C139—21no—
412C2×C4×C139—21no—
413C2×C4×C139—24no—
414C2×C4×C139—22no—
415C2×C4×C139—22no—
416C2×C4×C139—42no—
417C2×C4×C139—42no—
418C2×C4×C139—44no—
419C2×C4×C139—42no—
420C2×C4×C139—42no—
421C2×C4×C139—41no—
422C2×C4×C139—42no—
423C2×C4×C139—42no—
424C2×C4×C139—41no—
425C2×C4×C139—42no—
426C2×C4×C139—42no—
427C2×C4×C139—42no—
428C2×C4×C139—41no—
429C2×C4×C139—41no—
430C2×C4×C139—42no—
431C2×C4×C139—41no—
432C2×C4×C139—41no—
433C2×C4×C139—41no—
434C2×C4×C139—41no—
435C2×C4×C139—42no—
436C2×C4×C139—81no—
437C2×C4×C139—81no—
438C2×C4×C139—88no—
439C2×C4×C139#12112yescomplemented
440C22×C139—21no—
441C22×C139—22no—
442C22×C139—21no—
443C22×C139—22no—
444C22×C139—21no—
445C22×C139—21no—
446C22×C139—21no—
447C22×C139—22no—
448C22×C139—22no—
449C22×C139—22no—
450C22×C139—21no—
451C22×C139—21no—
452C22×C139—22no—
453C22×C139—41no—
454C22×C139—41no—
455C22×C139—42no—
456C22×C139—44no—
457C22×C139—44no—
458C22×C139—42no—
459C22×C139—42no—
460C22×C139—42no—
461C22×C139—44no—
462C22×C139—42no—
463C22×C139—42no—
464C22×C139—42no—
465C22×C139—44no—
466C22×C139—41no—
467C22×C139—41no—
468C22×C139—42no—
469C22×C139—41no—
470C22×C139—42no—
471C22×C139—42no—
472C22×C139—41no—
473C22×C139—42no—
474C22×C139—41no—
475C22×C139—82no—
476C22×C139—81no—
477C22×C139—81no—
478C22×C139—81no—
479C22×C139—82no—
480C22×C139—84no—
481C22×C139—82no—
482C22×C139—82no—
483C22×C139—81no—
484C22×C139—82no—
485C22×C139—81no—
486C22×C139—81no—
487C22×C139—82no—
488C22×C139—84no—
489C22×C139—81no—
490C22×C139—81no—
491C22×C139—162no—
492C22×C139B(4,𝔽2)12yescomplemented
493C22×C139C2×#12011yescharacteristic
494C22×C139C2×#12111yescharacteristic
495C22×C139#53411yescharacteristic
496C22×C139D4212yes—
497C22×C139#54612yes—
498C4×C139—22no—
499C4×C139—44no—
500C4×C139—41no—
501C4×C139—42no—
502C4×C139—42no—
503C4×C139—42no—
504C4×C139—42no—
505C4×C139—82no—
506C4×C139—81no—
507C4×C139—81no—
508C2×C139—22no—
509C2×C139—21no—
510C2×C139—21no—
511C2×C139—22no—
512C2×C139—22no—
513C2×C139—42no—
514C2×C139—41no—
515C2×C139—42no—
516C2×C139—82no—
517C2×C139—81no—
518C2×C139—82no—
519C2×C139#241011yescharacteristic
520C2×C139C2×B(4,𝔽2)11yescharacteristic
521C2×C139#302611yescharacteristic
522#24404C13911yesmaximal, characteristic, direct product factor, Sylow
523C139#2440411yescharacteristic, direct product factor, Sylow
524#3484C2×C13911yescharacteristic, complemented
525C2×B(4,𝔽2)C2×C13911yescharacteristic, complemented
526C22×#99C2×C13911yescharacteristic, complemented
527#2410C2×C13912yescomplemented
528#2403C2×C13911yescharacteristic, complemented
529#2044C2×C13912yescomplemented
530#2021C2×C13912yescomplemented
531#1898C2×C13912yescomplemented
532#1889C2×C13911yescharacteristic, complemented
533#1867C2×C13911yescharacteristic, complemented
534#1790C2×C13911yescharacteristic, complemented
535C2×H(5,𝔽2)C22×C13911yescharacteristic
536C23×D4C22×C13911yescharacteristic
537C23×D4C22×C13911yescharacteristic, complemented
538#546—22no—
539#546—22no—
540D42—22no—
541D42—22no—
542#535—21no—
543#534—21no—
544#534C22×C13912yes—
545#525—21no—
546C2×#121—22no—
547C2×#120—21no—
548C2×#120—21no—
549C2×#120C22×C13911yescharacteristic
550C2×#120C22×C13912yes—
551C2×#120C22×C13912yescomplemented
552C2×#120C22×C13911yescharacteristic, complemented
553#518C22×C13911yescharacteristic
554C22×C22⋊C4C22×C13912yescomplemented
555B(4,𝔽2)—24no—
556C2×#99—24no—
557C2×#99C22×C13911yescharacteristic
558C2×#99C22×C13911yescharacteristic
559C2×#99C22×C13912yescomplemented
560C2×#99C22×C13912yescomplemented
561C2×#99C22×C13912yescomplemented
562#394—22no—
563#392—21no—
564#392—21no—
565#392—22no—
566#386—21no—
567#386—22no—
568#386C22×C13911yescharacteristic
569#386C22×C13911yescharacteristic, complemented
570#386C22×C13912yescomplemented
571#385C22×C13912yescomplemented
572#379C22×C13912yescomplemented
573#379C22×C13911yescharacteristic, complemented
574#342C22×C13912yescomplemented
575#342C22×C13912yescomplemented
576C25D4×C13911yescharacteristic, complemented
577C25C23×C13911yescharacteristic
578C25C23×C13911yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C13911yescharacteristic, complemented
602C22×D4D4×C13911yescharacteristic, complemented
603C22×D4D4×C13912yescomplemented
604C22×D4D4×C13912yescomplemented
605C22×D4C23×C13912yes—
606C22×D4C23×C13911yescharacteristic
607C22×D4C23×C13911yescharacteristic
608C23×C4—22no—
609C23×C4D4×C13911yescharacteristic, complemented
610C23×C4C23×C13911yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C13912yescomplemented
665C2×C22⋊C4D4×C13912yescomplemented
666C2×C22⋊C4C23×C13912yes—
667C2×C22⋊C4C23×C13911yescharacteristic
668C2×C22⋊C4C23×C13911yescharacteristic
669C2×C22⋊C4C23×C13912yes—
670C2×C22⋊C4C23×C13912yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C13914yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C13911yescharacteristic
700C24C2×D4×C13912yes—
701C24C2×D4×C13911yescharacteristic
702C24C2×D4×C13912yes—
703C24C2×D4×C13912yes—
704C24C2×D4×C13911yescharacteristic
705C24C2×D4×C13911yescharacteristic
706C24C24×C13911yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C13912yes—
771C2×D4#41×C13912yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C13912yes—
791C22×C4C2×D4×C13911yescharacteristic
792C22×C4C2×D4×C13911yescharacteristic
793C22×C4C2×D4×C13912yes—
794C22×C4C2×D4×C13912yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C13914yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C13911yescharacteristic
893C23#120×C13912yes—
894C23#120×C13911yescharacteristic
895C23#121×C13912yescomplemented
896C23C22×D4×C13911yescharacteristic
897C23C22×D4×C13912yes—
898C23C22×D4×C13911yescharacteristic
899C23C2×#41×C13911yescharacteristic
900C23H(5,𝔽2)×C13912yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C13912yescomplemented
963C22—22no—
964C22—21no—
965C22—22no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—21no—
971C22—21no—
972C22—22no—
973C22—21no—
974C22—22no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—42no—
993C22—41no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22B(4,𝔽2)×C13912yescomplemented
1016C22C2×#120×C13911yescharacteristic
1017C22C2×#121×C13911yescharacteristic
1018C22#534×C13911yescharacteristic
1019C22D42×C13912yes—
1020C22#546×C13912yes—
1021C4—22no—
1022C4—44no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—41no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2#2410×C13911yescharacteristic
1043C2C2×B(4,𝔽2)×C13911yescharacteristic
1044C2#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. #3484×C139C2semidirect
2. C2×B(4,𝔽2)×C139C2semidirect
3. C22×#99×C139C2semidirect
4. #2410×C139C2semidirect
5. #2403×C139C2semidirect
6. #2044×C139C2semidirect
7. #2021×C139C2semidirect
8. #1898×C139C2semidirect
9. #1889×C139C2semidirect
10. #1867×C139C2semidirect
11. #1790×C139C2semidirect
14. C23×D4×C139C22semidirect
28. C2×#120×C139C22semidirect
29. C2×#120×C139C22semidirect
31. C22×C22⋊C4×C139C22semidirect
36. C2×#99×C139C22semidirect
37. C2×#99×C139C22semidirect
38. C2×#99×C139C22semidirect
46. #386×C139C22semidirect
47. #386×C139C22semidirect
48. #385×C139C22semidirect
49. #379×C139C22semidirect
50. #379×C139C22semidirect
51. #342×C139C22semidirect
52. #342×C139C22semidirect
53. C25×C139D4semidirect
78. C22×D4×C139D4semidirect
79. C22×D4×C139D4semidirect
80. C22×D4×C139D4semidirect
81. C22×D4×C139D4semidirect
86. C23×C4×C139D4semidirect
141. C2×C22⋊C4×C139D4semidirect
142. C2×C22⋊C4×C139D4semidirect
152. #99×C139D4semidirect
305. C22⋊C4×C139C2×D4semidirect
372. C23×C139#121semidirect
439. C2×C4×C139#121semidirect
492. C22×C139B(4,𝔽2)semidirect
522. #24404C139direct (N × H)
523. C139#24404direct (N × H)
524. #3484C2×C139semidirect
525. C2×B(4,𝔽2)C2×C139semidirect
526. C22×#99C2×C139semidirect
527. #2410C2×C139semidirect
528. #2403C2×C139semidirect
529. #2044C2×C139semidirect
530. #2021C2×C139semidirect
531. #1898C2×C139semidirect
532. #1889C2×C139semidirect
533. #1867C2×C139semidirect
534. #1790C2×C139semidirect
537. C23×D4C22×C139semidirect
551. C2×#120C22×C139semidirect
552. C2×#120C22×C139semidirect
554. C22×C22⋊C4C22×C139semidirect
559. C2×#99C22×C139semidirect
560. C2×#99C22×C139semidirect
561. C2×#99C22×C139semidirect
569. #386C22×C139semidirect
570. #386C22×C139semidirect
571. #385C22×C139semidirect
572. #379C22×C139semidirect
573. #379C22×C139semidirect
574. #342C22×C139semidirect
575. #342C22×C139semidirect
576. C25D4×C139semidirect
601. C22×D4D4×C139semidirect
602. C22×D4D4×C139semidirect
603. C22×D4D4×C139semidirect
604. C22×D4D4×C139semidirect
609. C23×C4D4×C139semidirect
664. C2×C22⋊C4D4×C139semidirect
665. C2×C22⋊C4D4×C139semidirect
675. #99D4×C139semidirect
828. C22⋊C4C2×D4×C139semidirect
895. C23#121×C139semidirect
962. C2×C4#121×C139semidirect
1015. C22B(4,𝔽2)×C139semidirect

Maximal subgroups

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

subgroupindex
#3484×C1392
C2×B(4,𝔽2)×C1392
C22×#99×C1392
#2410×C1392
#2403×C1392
#2044×C1392
#2021×C1392
#1898×C1392
#1889×C1392
#1867×C1392
#1790×C1392
#24404139